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Vibrations of ice I and some clathrate-hydrates below 200°K Hardin, Arvid Holger 1970-12-31

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THE VIBRATIONS OF ICE I AND SOME CLATHRATE-HYDRATES BELOW  200°K  fey A r v i d Holger Hardin B.Sc.(Hons.), The U n i v e r s i t y o f B r i t i s h Columbia, 1 9 6 3  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Chemistry  We accept t h i s t h e s i s as conforming t o the required, standard  THE UNIVERSITY OF BRITISH COLUMBIA July, 1970  In p r e s e n t i n g t h i s  thesis  an advanced degree at  the U n i v e r s i t y  the L i b r a r y s h a l l make i t I  in p a r t i a l  f u l f i l m e n t of of B r i t i s h  freely available  for  the requirements  Columbia,  I agree  for  that  r e f e r e n c e and Study.  f u r t h e r agree that p e r m i s s i o n f o r e x t e n s i v e copying of t h i s  thesis  f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s of  this  representatives.  It  thes,is f o r f i n a n c i a l  is understood that copying or p u b l i c a t i o n gain s h a l l  written permission.  The U n i v e r s i t y of B r i t i s h Vancouver. 8, Canada  Date  Columbia  not be allowed without my  ABSTRACT  The v i b r a t i o n s of H2O, HDO and D 0 molecules p a r t i c i p a t i n g i n the 2  hydrogen bonding of v i t r e o u s and c r y s t a l l i n e s o l i d s , and some a l k y l h a l i d e s and halogens encaged i n these s o l i d s , were studied by i n f r a r e d between h.2 and 200°K over the iiOOO t o of 0 - H *  , , -  0  l60  cm"" frequency range. -  1  spectroscopy Four kinds  hydrogen bonding l a t t i c e s were i n v e s t i g a t e d , v i t r e o u s and  annealed (cubic) i c e I and v i t r e o u s and annealed clathrate-hydrate mixtures. In v i t r e o u s i c e I the e f f e c t s on the molecular and l a t t i c e v i b r a t i o n s were observed i n d e t a i l f o r H 2 O between  77  and l 8 0 ° K during the phase  transformation t o cubic i c e I , and the r e s u l t s of the transformation f o r HDO and D2O were recorded.  As w e l l , the e f f e c t s on the molecular and :  l a t t i c e v i b r a t i o n s of H 0 , D 0 , H 0 ( 5 - 9 W HDO), and D 0 (h.00% HDO) cubic 2  2  2  2  ices I were studied during warming from h.2 t o 200°K. S i m i l a r studies were made f o r the v i b r a t i o n s of H 0 , HDO, D 0 and 2  2  guest molecules, during the v i t r e o u s - c r y s t a l l i n e phase transformation of seven clathrate-hydrate mixtures and during warming of the r e s u l t i n g \ annealed mixtures. For i c e I the method involved condensation  of the vapour at 77°K,  observation of the spectra during warming i n stages t o 1 8 5 1 5°K, c o o l i n g to k.2°K, and observation of the cubic sample spectra during warming t o 200°K.  The r e s u l t s were p l o t t e d as a function of temperature and were  correlated to calculated  distances and RMS amplitudes of t r a n s l a t i o n .  As w e l l four models f o r molecular l i b r a t i o n were i n v e s t i g a t e d . Three approaches were taken t o the clathrate-hydrate problem. In p a r a l l e l t o the i c e I method gaseous s t o i c h i o m e t r i c mixtures were con-  densed, observed during transformation, cooled t o h.2°K and observed warm-up.  during  Other gaseous c l a t h r a t e mixtures were condensed i n an i s o l a t e d  sample chamber, t o prevent sample f r a c t i o n a t i o n , and t r e a t e d as before. F i n a l l y , low temperature mulls of s o l i d clathrate-hydrate mixtures were prepared and observed at 83 - 3°K. The r e s u l t s show that on warming the i c e I phase transformation occurred between 120 ± 5 and 135 - 5°K and required, l e s s than 1 8 minutes at 135 i 3°K. Weak peaks due t o oligomeric H2O and D2O u n i t s disappeared during annealing, while a l l hydrogen bonded H2O molecular modes s h i f t e d t o lower frequency and a l l l a t t i c e modes s h i f t e d t o higher frequency. h a l f - h e i g h t widths of the composite  H2O  band  (v2/2vp)  The  appeared t o increase  upon annealing and t o decrease upon warming while the ( V R , V R + vp) and ( l , V 3 , v i + vrp) bands had the opposite behaviour. v  This was interpreted,  as i n d i c a t i n g a weak 2v^ band underlying the stronger \>£ absorption near 1600  cm . -1  The frequency-temperature  dependences of a l l cubic i c e I bands were  i n t e r p r e t e d on a b i l i n e a r , high and low temperature b a s i s (the l a t t i c e modes s h i f t e d t o lower frequency and the molecular modes t o higher  frequency  with i n c r e a s i n g temperature).  1  cm /°K, Av -1  For HDO above  86°K  Av  / A T  was 0.200  0.005  /AT was 0.123 + 0.005 cm /°K, the frequencies were " f r o z e n - i n " -1  at 8 0 ± 5°K and 6 5 ± 5°K and had i r r e g u l a r behaviours between 50 and 70°K. The low temperature dependences were 0.0^7 ± 0.005 cm "V°K i n both modes. An explanation i s given f o r the apparent displacement of the HDO s t r e t c h i n g frequencies from the H2O and D2O frequencies. The HDO r e s u l t s also permitted the accurate determination of Av  /AR(O  -1 0) as 1921 cm /A and Av 0  -1 / A R as 128l cm /A above 150°K and 0  iv -1  as  8202  cm  °  -1 °  /A and 6 6 2 9 cm  /A below 100°K.  As w e l l , the HDO s t r e t c h i n g  frequencies gave an anharmonicity which increased from h.2 t o 80°K and then decreased between 8 0 and 200°K.  1  The clathrate-hydrate mixtures transformed on warming i n the temperature range 1 2 5 - 5 t o 1 U 5 + 5°K and required l e s s than l 8 minutes at 135°K as f o r i c e I . S i m i l a r l y , the weak oligomeric and guest absorptions disappeared upon annealing.  From the comparison of the three sets of " c l a t h r a t e "  r e s u l t s and the behaviour o f annealed sample peaks we concluded that cubic i c e I and not clathrate-hydrate was probably formed.  TABLE OF CONTENTS PAGE Abstract  i i  Table of Contents  v  L i s t of Tables  ix  L i s t of Figures  xi  Acknowledgements  xiv  INTRODUCTION  1  Hydrogen Bonding  1  A.  Theories of Hydrogen Bonding  2  B.  Spectroscopic Manifestations of Hydrogen Bonding . . .  6  Clathrate-Hydrates A. B. C. D. E.  12  The Clathrate-Hydrate Problem The Structures of the Clathrate-Hydrates Formation of Clathrate-Hydrates Previous Investigations of the Clathrate-Hydrates. . . The Present Approach t o the Clathrate-Hydrate  12 12 17 18  Problem  19  Ice  •  A. B. C. D. CHAPTER ONE:  The Ice Problem Non-Spectroscopic I n v e s t i g a t i o n s of Ice Spectroscopic Investigations of Ice The Present Approach t o the Ice Problem APPARATUS  20 20 20 27 37 38  1.1  The Perkin-Elmer 112-G Spectrophotometer  38  1.2  The Perkin-Elmer 1+21 Spectrophotometer  1+0  1.3  The Perkin-Elmer 301 Spectrophotometer  . 1+2  1.1+  The Hornig-Wagner L i q u i d Nitrogen C e l l  1+2  1.5  The Duerig-Mador L i q u i d Helium C e l l  1+5  1.6  The Metal L i q u i d Nitrogen C e l l  *+5  vi PAGE CHAPTER TWO:  hi  METHODS AND MATERIALS  2.1  Water Samples and C l a t h r a t i o n M a t e r i a l s  ^7  2.2  Infrared Windows.and Sample Mounts  U8  2.3  Preparation of Clathrate-hydrates  h9  A.  Preparation of S o l i d Samples  ^9  B.  Preparation of Stoichiometric Gaseous Mixtures . . .  50  2. h  Preparation of I n f r a r e d Specimens  52  A. B.  Low Temperature M u l l i n g I s o l a t e d Chamber Condensation  52 53  C.  Open Chamber Condensation  5*+  2.5  Devitrification  55  2.6  Temperature V a r i a t i o n Methods  56  CHAPTER THREE: 3.1  3.2  3.3  3. U  ICE I : EXPERIMENTAL AND RESULTS  58  The Vitreous-Cubic Ice Phase Transformation  58  A.  Experimental  58  B.  Results of D e v i t r i f i c a t i o n  59  Temperature Dependence of Cubic Ice I Absorptions. . . . .  69  A.  Temperature Dependence of HDO Absorptions  69  B.  Temperature Dependence of H 0 and D 0 Absorptions. 2  The H 0 , D 0 2  2  and HDO  2  Ice I Absorptions at 83°K  .. 7 9 95  A.  Experimental  95  B.  Results at 83°K  95  Summary of Ice I Results  101  A. Vitreous-Cubic Ice I Transformation B. . HDO i n Cubic Ice I . . C. H 0 and D 0 i n Cubic Ice I  101 102 102  2  2  vii PAGE 103  CHAPTER FOUR: DISCUSSION OF ICE I  k.l  The Ice I Vitreous-Cubic Phase Transformation A. B. C. D. . E.  h.2  it. 3  it.U  General Discussion 10k Fundamental L a t t i c e Mode Transformations 107 Fundamental Molecular Mode Transformations I l l Combination and Overtone Mode Transformation . . . . 117 Confidence i n the Cubic Ice I Samples 118  Temperature Dependence of Cubic Ice I Absorptions. . . . 1 2 0 A.  Dependence of HDO Bands on Temperature  B.  Dependence of H 2 O and D 0 Bands on Temperature . . . 2  Assignments of the Cubic Ice I Absorption Bands  5.3  159 175  The Fundamental L a t t i c e Modes The Fundamental Molecular Modes  175 177  C.  The Overtone and Combination Modes  186  The L'ibration of HDO, H 0 and D 0 2  2  5.2  121  A. B.  2  A. The Moments-of-Intertia Models B. The H 0 Model of Ice ; C. A Summary of H 2 O , HDO and D 2 O L i b r a t i o n s CHAPTER FIVE: CLATHRATE-HYDRATE EXPERIMENTAL DETAILS AND RESULTS 5.1  103  3  187 187 198  211 2lh  The V i t r e o u s - C r y s t a l l i n e Clathrate-Mixture Phase Transformation  2lh  A.  Experimental  2lh  B.  Results of D e v i t r i f i c a t i o n  C l a t h r a t e M i x t u r e Guest Absorptions, A. Condensation i n an Open Chamber B. Condensation i n an I s o l a t e d Chamber C. Low Temperature Mulls Temperature Dependence of the C r y s t a l l i n e Clathrate Mixture Absorptions A. B.  2l6 228 229 233 233 23^  Temperature Dependence of the EDO Absorptions. . . . 23** Temperature Dependence of the H 2 O and D 2 O Absorptions 239  viii PAGE  CHAPTER SIX: 6:1  The Clathrate Mixture V i t r e o u s - C r y s t a l l i n e Phase Transformation A. B. C. D.  6.2  6.3  DISCUSSION OF THE CLATHRATE MIXTURES  General Discussion Annealing C 1 ' 7 . 6 7 H 0 on C s l Oligomeric H 0 Absorptions Unannealed Sample Guest Absorptions 2  2  2  2^7 21*8  251 251 255  A. B. C.  256 257 258  I s o l a t e d Chamber Condensation Low Temperature Mulls Summary  The Temperature Dependences of C r y s t a l l i n e Clathrate Mixture Absorptions HDO i n Clathrate Mixtures H 0 and D 0 i n Clathrate Mixtures 2  2  259 259 2 6 l  26k  CHAPTER SEVEN: SUMMARY  7.2  2*+7  Guest Species Absorptions  A. B.  7.1  2*+7  Suggestions f o r Further Work  26k  A. B.  Clathrate Mixtures Ice Systems  2.6k 265  C.  Other Chemical Systems  267  Conclusions  268  A. Annealing Ice I B. HDO Studies C. The H 0 and D 0 Studies D. Clathrate Mixture Annealing REFERENCES . . . . . T  2  2  268 268 270 272 273  LIST OF TABLES TABLE  PAGE  0.1  T y p i c a l clathrate-hydrates and t h e i r p r o p e r t i e s  lU  0.2  Clathrate-hydrate u n i t c e l l dimensions, guest s i z e s and f i l l e d cavities  l 6  0.3  Stable temperature ranges of v i t r e o u s , cubic and hexagonal ice I  23  O.k  Some p h y s i c a l properties of the ices  25  0.5  H 0 vapour, l i q u i d and i c e I frequencies and assignments .  29  III.I  Cubic and v i t r e o u s i c e I frequencies at 82°K  III.II  Vitreous i c e I oligomeric absorptions  65  III.Ill  H 0 composite band h a l f - h e i g h t widths  68  III.IV  The behaviour of HDO s t r e t c h i n g modes i n cubic i c e I . . .  72  III.V  The behaviour of HDO l i b r a t i o n a l modes i n cubic i c e I . . .  7*+  III.VI  HDO s t r e t c h i n g modes h a l f - h e i g h t widths  76  III.VII  HDO s t r e t c h i n g modes peak heights  77  III.VIII  Ice I sample h i s t o r i e s  80  III.IX  Cubic i c e I H 0 and D 0 absorptions  83  III.X  Cubic i c e I v ( H 0 ) absorptions  91  III.XI  (a) Fresent and previous H 0 assignments f o r cubic i c e I .  96  2  2  2  2  T  2  2  (b) Present and previous frequencies f o r  v  T  ( H 2 0 )  62  97  III.XII  Present and previous HDO frequencies f o r cubic i c e I . . .  98  I I I . XIII  Present and previous D 0 assignments f o r cubic i c e I . . .  99  IV. I  Calculated and observed RMS amplitudes of t r a n s l a t i o n  2  for  H 0 2  and  1^9  D 2 O  IV.II  H 0 , HDO and D 0 moments-of-inertia  IV.Ill  Symmetric G-matrix elements f o r  2  2  H 2 O 3  190 2 0 1  X  TABLE  PAGE  IV. IV  HgCg and D 0  V. I  The clathrate-mixture sample h i s t o r i e s  V.II  RV,0 frequencies i n unannealed and annealed CH-^Cl• 7• 6 7 H 0 . 221  V.III  Oligomeric frequencies at 83°K i n unannealed mixtures  V.IV.  2  3  force constants f o r i c e 1  208 215 2  clathrate223  Temperature dependences of oligomeric frequencies i n unannealed  22k  c l a t h r a t e mixtures  V.V  The stable temperature ranges of the oligomer peaks.  V.VI  The a l k y l h a l i d e guest absorptions i n unannealed c l a t h r a t e mixtures at 83°K The temperature dependence of the guest frequencies  230  during annealing  231  V.VII  . . . 225  V.VIII  The stable temperature ranges f o r the guest absorptions. . 232  V.IX  The behaviour of HDO s t r e t c h i n g modes f o r annealed c l a t h r a t e mixtures  237  V.X  HDO l i b r a t i o n s f o r three annealed c l a t h r a t e mixtures . . . 2^1  V.XI  Average H 0 and D 0 frequency-temperature data f o r annealed c l a t h r a t e mixtures 2kk Data f o r C l 2 ' 7 . 6 7 H 0 and B r - 8 . 6 H 2 0 on C s l and AgCl. . . . 2^5 H 0 frequencies f o r hydrated a l k a l a i h a l i d e s a l t s 250  V. XII VI. I VI.II VI.Ill  2  2  2  2  2  Oligomeric H 0 and D 0 peaks i n c l a t h r a t e mixtures and rare gas matrices |  252  A l k y l halide frequencies i n pure s o l i d s and c l a t h r a t e mixtures  25^  2  2  LIST OF FIGURES  FIGURE  PAGE  1.1  The s t a i n l e s s s t e e l deposition tube  kk  1.2  The i s o l a t e d sample chamber  k6  3.1  Representative spectra of v i t r e o u s and cubic i c e s  60  3.2  Frequency s h i f t s during phase transformation . . .  61  3.3  Oligomeric H 0 and D 0 absorptions i n v i t r e o u s i c e I . . . .  6k  3.k  Half-height width s h i f t s f o r ( v , v  2  2  R  (v  l 5  v ,v 3  1  + v ) and  R  T  +v )  66  T  3.5  Half-height width s h i f t s f o r ( v , 2 v )  67  3.6  HDO s t r e t c h i n g frequency s h i f t s f o r cubic i c e 1  71  3.7  HDO l i b r a t i o n a l frequency s h i f t s f o r cubic i c e I  73  3.8  HDO s t r e t c h i n g mode h a l f - h e i g h t width s h i f t s f o r cubic ice 1  2  R  75  3.9  HDO s t r e t c h i n g mode peak height s h i f t s f o r cubic i c e I . . .  78  3.10  The s h i f t s of cubic i c e I v  82  3.11  The s h i f t s of cubic i c e I vj_  3.12  3  85  . The s h i f t s of cubic i c e I v  2  • 86  3.13  The s h i f t s of cubic i c e I v  R  88  3.1k  The cubic i c e I v ( H 0 ) band at 83°K  3.15  The shifts- of cubic i c e I v  3.16  The s h i f t s of cubic i c e I ( v i + v ) . .  3.17  The s h i f t s of cubic i c e I 3 v  3.18  The s h i f t s of cubic i c e I ( v + v )  T  89  2  .  T  T  .  92 93  R  R  90  T  9k  xii FIGURE  P  h.l  The c a l c u l a t e d l i n e a r thermal expansion c o e f f i c i e n t of cubic i c e I  it. 2  The c a l c u l a t e d cubic i c e I l a t t i c e parameter as a function of temperature  U.3  A  G  E  128  129  The c a l c u l a t e d 0-••-0 distance f o r cubic i c e I as a function of temperature  131  k.h  Cubic i c e I HDO s t r e t c h i n g frequencies as a function of R(0 0)  132  U.5  Comparison of observed and predicted v dependence  13T  k.6  (HDO) - R(0-*--0)  The c a l c u l a t e d cubic i c e I harmonic HDO frequency as a function of temperature  1^3  it. 7  The c a l c u l a t e d HDO anharmonicity  ihk  It.8  A p l o t of HDO anharmonicity against R(O----O)  1^5  k.9  Calculated RMS amplitudes of t r a n s l a t i o n f C A r ^ >  150  it. 10 it. 11  A p l o t o f < A r ^ > against R(0 0) A p l o t of v^CHDO) and v^(HDO) a g a i n s t < A r > 2  2  Un  151 152  OD  it.12  The cubic i c e I  dependences on RCO'^'O)  4.13  The c a l c u l a t e d hexagonal i c e I V 3 dependence on R(0  it.lU  The c a l c u l a t e d hexagonal i c e I v (HD0) and v (HDO) QH  dependences on R ( 0  , , , ,  165 0) . . 1 6 6  or)  0)  l6T  it. 15  H 2 O , HDO and D 0 vapour and cubic i c e I phase frequencies . . 1 8 0  it. 1 6  The e f f e c t s of uncoupling on the HDO s t r e t c h i n g  2  frequencies  •  l8U  it. IT  The p r i n c i p a l axes of H 0, HDO and D 0  it. 1 8  The H 0  it. 19  The i n t e r n a l coordinates of  H 2 O 3 .  it.20  The symmetry coordinates of  H 2 O 3  2  2  3  2  model of H 0 i n i c e  189 199  2  . .-  202 203  xiii FIGURE  PAGE  5.1  Clathrate-mixture  5.2  T y p i c a l annealing spectra f o r clathrate-mixtures  5.3  5.U  frequency s h i f t s during transformation  Typical annealing spectra f o r clathrate-mixtures  . 217  CH^Br and CH^I  C H 3 C I ,  218 C H C I 3  and C H5Br 2  219  T y p i c a l annealing spectra f o r B r and C l mixtures 2  2  clathrate220  5.5  Consecutive spectra for annealing C1 *7.67H 0 on C s l . . . 227  5.6  Frequency s h i f t s f o r v (k.00% HDO)  (HDO) of annealed CH^Br•7.67D 0  Frequency s h i f t s f o r v ( 5 . 9 W HDO)  (HDO) of annealed  5.7  5.8  5.9  2  2  2  235 CH Br•7.67H 0 3  2  236  The half-height width s h i f t s f o r clathrate-mixtures  and v  of several 238  The s h i f t of (HD0) i n annealed CH^Br•7.67D 0 v  R  2  (k.00% HDO)  2i+0  5.10  Shifts of v ( D 2 0 )  5.11  Shifts of .v (D 0) f o r annealed CH Br• 7.67D 0  1  3  2  f o r annealed CH^Br•7.67D2O 3  2  2^2 2^3  ACKNOWLEDGEMENTS  To Professor K.B. Harvey who has the assured f a i t h i n graduate students t o allow them t o choose and pursue a range of i n t e r e s t s i n v i b r a t i o n a l spectroscopy, and who i n s t i l l s a b e n e f i c i a l but often f r u s t r a t i n g independence of thought and a c t i o n . To Professors R.F. Snider and A. Bree who as members o f my committee were also w i l l i n g t o discuss problems r e l a t e d to t h i s work. To the members of the mechanical, glass blowing and e l e c t r o n i c s workshops f o r t h e i r e x c e l l e n t craftsmanship  and c h e e r f u l  aid. To Raymond Green and other students and f a c u l t y f o r the many opportunities t o discuss diverse problems and f o r the ready mutual exchange of ideas. And t o my wife and family f o r t h e i r s p e c i a l help and the j o y they provide.  DEDICATION:  To my parents K a r l Johan F r i t h i o f Hardin and Beatrice Mary (.Trojanoski) Hardin  INTRODUCTION The phenomenon of hydrogen bonding has played an i n c r e a s i n g l y import a n t r o l e i n the t h e o r i e s of c e r t a i n chemical and bio-chemical systems f o r more than three decades.  Several models, depending on the p h y s i c a l proper-  t y i n v e s t i g a t e d , have been proposed t o e x p l a i n the experimental r e s u l t s . However, f o r c r y s t a l s a u n i f i e d hydrogen bond model has "not y e t developed which i s c o n s i s t e n t w i t h a l l the chemical and p h y s i c a l p r o p e r t i e s of the s o l i d state. The present work i s a spectroscopic i n v e s t i g a t i o n of s o l i d s t a t e hydrogen bonding i n v i t r e o u s and cubic i c e I and i n v i t r e o u s and c r y s t a l l i n e c l a t h r a t e - h y d r a t e mixtures; the nature of the c l a t h r a t e - h y d r a t e s o l i d s formed by vapour condensation i s u n c e r t a i n . A d e t a i l e d study of the large changes ( r e l a t i v e t o non-hydrcgen-bonded s o l i d s ) i n the infrared, ( i r ) absort i o n s as a f u n c t i o n of temperature provides information on changes i n hydrogen bonding as a f u n c t i o n of the oxygen-oxygen nearest-neighbour distance (R(0''-'0)) both f o r i n d i v i d u a l molecules and f o r the c o l l e c t i v e s o l i d arrays. These data help t o describe p r e c i s e l y changes i n one s o l i d ' s molecular  p o t e n t i a l and should a i d i n the development of a u n i f i e d hydrogen  bond model. Hydrogen Bonding The main e f f e c t s manifested by the hydrogen bond (A-X-H••••Y-B) on the i r spectra are: l ) large frequency s h i f t s , 2) a l t e r a t i o n s i n i n t e n s i t y , 3) increased band w i d t h , and k) the appearance of new bands a s s o c i a t e d with the deformation o f the hydrogen bond.  The general phenomenon of hydrogen  bonding has been reviewed by Pimentel and M c C l e l l a n ( l ) , Sokolov and  Tschulanovski ( 2 ) , and by Hadzi and Thompson ( 3 ) . Recently Hamilton and Ibers (h)  discussed the r o l e s of hydrogen bonding i n chemical s t r u c t u r e s .  The s p e c i f i c e f f e c t s of hydrogen bonds on the chemical and p h y s i c a l propert i e s of i c e are t r e a t e d i n books by Eizenberg and Kaufmann (5) and by R i e h l , Bullemer and Engelhardt ( 6 ) . A.  Theories of Hydrogen Bonding  Hydrogen bonding t h e o r i e s f a l l i n t o two c l a s s e s — c l a s s i c a l and quantum mechanical; the l a t t e r includes three separate approaches—valence bond (VB), charge t r a n s f e r (CT) and molecular o r b i t a l (MO) representations.  The  conclusions drawn from a l l the t h e o r i e s are that both e l e c t r o s t a t i c , charge m i g r a t i o n and short range r e p u l s i o n give concerted e f f e c t s and both are concurrently important ( 7 ) . ( i ) C l a s s i c a l Theories The c l a s s i c a l e l e c t r o s t a t i c t h e o r i e s are based on Pauling's (8) desc r i p t i o n which assumed the H atom could form a s i n g l e covalent "bond only. . (a)- P o i n t charge models.  In the e a r l y work (1933-1957) the charge  d i s t r i b u t i o n was approximated "by a set of point charges (9-12).  For the  i c e and c l a t h r a t e - h y d r a t e systems w i t h 0-H««--0 "bonds, h electrons (2 i n the 0-H bond and  2 i n the 0 lone p a i r ) were considered and the remaining  e l e c t r o n s and protons were assumed t o form the molecular core.  The charges  were l o c a t e d so t h a t the correct 0-H and lone p a i r d i p o l e moments were obtained.  The i n t e r a c t i o n energy of the hydrogen bond, c a l c u l a t e d by  assuming a simple Coulomb p o t e n t i a l , was then 6 kcal/mole. The t h e o r i e s have s u c c e s s f u l l y explained the lengthening of the X-H bond (r(Xr--H)) and the X-H s t r e t c h i n g frequency ( v ) red s h i f t .  3 Two conclusions have been drawn from the simple e l e c t r o s t a t i c model. F i r s t , e l e c t r o s t a t i c energy i s important i n hydrogen bonding as i s i n d i c a t e d by the decreasing bond strength w i t h decreasing e l e c t r o n e g a t i v i t y of the proton acceptor and proton donor. l e a s t part of  A R ( X *  ,  -  ,  Y )  Secondly, e l e c t r o s t a t i c energy causes at  and Av . vrr  An  (b) Continuous charge d i s t r i b u t i o n model.  This model was presented  i n 1 9 6 4 by Bader (13) f o r the 0-H-••-0 system t y p i c a l of i c e and c l a t h r a t e hydrates.  He considered a l l the e l e c t r o n s , by methods developed f o r hydrides  and binary hydrides (lU,15), i n s p h e r i c a l charge d i s t r i b u t i o n s and c a l c u l a t e d the e l e c t r o s t a t i c force by c l a s s i c a l e l e c t r o s t a t i c methods.  The conclusions  and i n t e r p r e t a t i o n of Bader's model are the same as f o r the point charge model. (c) Summary of the c l a s s i c a l t h e o r i e s . The e l e c t r o s t a t i c t h e o r i e s ignore four important f a c t s about hydrogen bonding.  For example, hydrogen  bonds may not be completely i o n i c since there i s no c o r r e l a t i o n between d i pole moments and hydrogen bond strengths i n the hydroxides.  As w e l l , both  the point and continuous charge d i s t r i b u t i o n models assume the e l e c t r o n i c charge d i s t r i b u t i o n s are undistorted by the formation of a hydrogen bond. Another point t o consider i s that the X the covalent  - . . . Y  distances are much l e s s than  van der Waal's r a d i i suggesting that forces other than.re-  pulsion are important.  F i n a l l y , the e l e c t r o s t a t i c t h e o r i e s cannot e x p l a i n  the increase of i n t e n s i t y of the X-H s t r e t c h i n g mode. ( i i ) Quantum Mechanical Theories The f i r s t quantum mechanical theory of the hydrogen bond was published in  1952  by Sokolov  recently.  .(l6),  although such methods have become p r a c t i c a l only  Since the r e s u l t s of t h i s t h e s i s are not i n t e r p r e t e d i n d e t a i l  by the quantum t h e o r i e s , they w i l l only be o u t l i n e d and t h e i r r e s u l t s w i l l be stated.  k  (a) Valence bond t h e o r i e s .  The VB c a l c u l a t i o n s (16,17) d i d not give  exact p h y s i c a l s o l u t i o n s since the method has a l a r g e l y e m p i r i c a l o r i g i n . As i n the elementary e l e c t r o s t a t i c models only four electrons were considered. Later Tsubomura ( l 8 ) showed that four e f f e c t s contribute t o the hydrogen bond, and t h a t the agreement of the e l e c t r o s t a t i c model with experiment may be f o r t u i t o u s since the three n o n - e l e c t r o s t a t i c e f f e c t s may cancel each other. The four energies c o n t r i b u t i n g t o the hydrogen bond energy are:  l ) the  e l e c t r o s t a t i c energy, 2) the short-range r e p u l s i o n energy, 3) the d i s p e r s i o n energy, and k) the d e r e a l i z a t i o n energy due t o CT. e f f e c t s 2, 3 and k e x p l i c i t l y .  Tsubomura c h a r a c t e r i z e d  He assumed there were 5 c o n t r i b u t i n g  resonant s t r u c t u r e s : *1 *2 Y  3  Xr- -|H  Y  covalent  Y  pure i o n i c pure i o n i c  X  -  H  X  +  H~  Y  H|  «Y  X"  V  +  +  H~  X-H  covalent  H-Y CT  covalent  X-Y CT  Tsubomura's c a l c u l a t i o n showed that the d e l o c a l i z a t i o n energy amounts t o 8.1 kcal/mole—about 1.5 times l a r g e r than the e l e c t r o s t a t i c energy.  The  r e p u l s i o n energy and d i s p e r s i o n energy are of opposite sign t o the d e l o c a l i z a t i o n energy and appear t o cancel i t . The VB method has received more recent treatments (19,20). Daiyasu and Yomosa (20)reported gen bond p o t e n t i a l energy. t u r e s and constructed  a four e l e c t r o n VB c a l c u l a t i o n of the hydro-  They used Tsubomura's ( l 8 ) 5 resonant s t r u c -  the c o n t r i b u t i n g ^-functions from t r i g o n a l or t e t r a -  h e d r a l p l a t e r atomic o r b i t a l s . f u n c t i o n of R(0  Hasegawa,  The proton p o t e n t i a l was c a l c u l a t e d as a  0) and r(O-H).  As w e l l , the s h i f t s i n r(0-H) and v  5 upon hydrogen bonding were studied. The c a l c u l a t i o n s of Hasegawa et a l . ignored the c o n t r i b u t i o n s of the CT s t r u c t u r e s , potential.  1^  and IJJ^-, and r e s u l t e d i n an . asymmetric,.single minimum  They deduced that to account f o r Ar(O-H) and Av_„  t i o n of the surroundings must be considered, i_.e_. ip^ and  the p o l a r i z a -  must be  included.  When that was done a double minimum p o t e n t i a l r e s u l t e d . t One  can summarize the VB t h e o r i e s by s t a t i n g the f o l l o w i n g conclusions  l ) i n a d d i t i o n to e l e c t r o s t a t i c forces other forces are  important—dispersion  exchange r e p u l s i o n and d e l o c a l i z a t i o n , 2) CT from Y to X i s not n e g l i g i b l e f o r short bonds but may be f o r long bonds, 3) the amount of CT changes very r a p i d l y as a f u n c t i o n of r(X-H) and r(X-Y)(the c o n t r i b u t i o n of ^ f a s t e r (10 times) than the c o n t r i b u t i o n s of ipg, ^ (b) Charge t r a n s f e r t h e o r i e s .  r i s e s much  and ^ ^ ) .  Since a w e l l developed theory f o r CT  e x i s t s , s e v e r a l workers a p p l i e d these techniques to the hydrogen bond (21, 22,23).  Bratoz (22) a p p l i e d the CT theory to 0-H  0 with four electrons  i n three o r b i t a l s , the OH bonding and antibonding o r b i t a l s and the 0 lone pair.orbital The conclusions Bratoz  (7) reached from these CT t h e o r i e s are:  l ) the VB p i c t u r e of the hydrogen bond i s v a l i d , 2) since the H atom'is s m a l l , the short range r e p u l s i v e forces are small and the H atom has  a  s p e c i a l r o l e f o r t h i s k i n d of intermolecular i n t e r a c t i o n , 3) a f r a c t i o n of an e l e c t r o n e x i s t s i n the OH antibonding and allowing longer r(X-Y) and weaker X-H  o r b i t a l , reducing the bond strength force constants, k\  CT t h e o r i e s  p r e d i c t an increased p o l a r i t y i n the O-H-'-'O complex and therefore an i n creased i n f r a r e d v  n w  intensity.  '(c) Molecular o r b i t a l t h e o r i e s .  The FHF anion has been examined i n  d e t a i l since i t i s r e l a t i v e l y small with respect t o p h y s i c a l s i z e , bond length and number of e l e c t r o n s .  Larger systems such as (H^O),.,, (HF),_>, and  (HgS)^ cannot be t r e a t e d e x a c t l y since d r a s t i c approximations must be made. For O-H'-'-O Weissmann and Cohen (2k) found a very asymmetric s i n g l e minimum p o t e n t i a l , i n contrast t o the e m p i r i c a l double minimum r e s u l t of L i p p i n c o t t and Schroeder ( 2 5 ) .  Weissmann's r e s u l t s p r e d i c t e d an H^O dipole  moment of 2.k0 D i n i c e , i n good agreement with the experimental value of Eisenberg  ( 5 ) , 2.U0-2.87  D, however., the method was l e s s s u c c e s s f u l i n pre-  d i c t i n g the r(X-H) and r(X-Y) distances.  More r e c e n t l y , Rein, Clarke and  H a r r i s ( 2 6 ) studied the hydrogen bond of water by MO methods.  The important  point o f t h i s work i s that the atomic charges and overlap populations  indi-  cate a s u b s t a n t i a l CT across the hydrogen bond. . .  Molecular o r b i t a l t h e o r i e s so f a r i n d i c a t e 2 properties of hydrogen  bonds:  l ) formation  of a hydrogen bond induces e l e c t r o n charge migration  from t h e molecular core t o the e x t e r n a l region and 2 ) the H 2p^  atomic  o r b i t a l c o n t r i b u t i o n t o the ground state i s not n e g l i g i b l e — t h e r e i s a small amount o f TT character i n the hydrogen bond.  B.  Spectroscopic  Manifestations  of Hydrogen  Bonding As e a r l y as 1933 Bernal and Fowler (9) recognized s h i f t i n v..,, ( A v ^ = v (vapour) - v Un  bonding.  Un  OTJ Un  Un  rtTI  i n H^O the large  (hydrogen bonded)) caused by hydrogen  I n f r a r e d techniques s t i l l remain the most v e r s a t i l e t o o l t o i n -  v e s t i g a t e the hydrogen bonds i n vapours, l i q u i d s and s o l i d s . r e l a t i v e l y large e l e c t r o n migrations  However, the  induced by hydrogen bonds give  large  7 changes i n nuclear s h i e l d i n g and s h i f t s i n the nmr t r a n s i t i o n s .  The present  work i s concerned only w i t h the i r manifestations of hydrogen bonding i n the 0-H "0 system i c e I and i n c l a t h r a t e - h y d r a t e s . -,,  ( i ) The' General E f f e c t s of Hydrogen Bonding The four main spectroscopic e f f e c t s i n hydrogen bonded s o l i d s are often l a r g e i n contrast t o t h e small e f f e c t s found between the vapour and s o l i d phases of molecules incapable of hydrogen bonding.  The f i r s t  correla-  t i o n made from t h e experimental data was the r e l a t i o n s h i p between R(X***-Y) and the v^. s h i f t s from the monomer frequency i n the bonded complex. An TT  a l l y i t i s found that the s h i f t , breadth and i n t e n s i t y of v  VXJ  Gener-  depends on  An  the  strength of the hydrogen bond. Those  p r o p e r t i e s are l a r g e s t f o r the strong hydrogen bonding system  FHF , but are much smaller i n the weak UK* * • 'II systems since the II van der -  Waal's r a d i i are l a r g e r . (a) are  The four e f f e c t s w i l l now be considered i n d e t a i l .  Frequency s h i f t s .  Wot a l l of the molecular v i b r a t i o n frequencies  s t r o n g l y a f f e c t e d by hydrogen bonding.  The X-H s t r e t c h i n g frequency i s  s h i f t e d t o lower frequency by 10-50% of the vapour phase frequency and the R-X-H bending v i b r a t i o n experiences a r e l a t i v e l y smaller s h i f t t o higher frequency.  The n o v e l t y of the l a r g e s t r e t c h i n g mode s h i f t s can be grasped  by comparing non-hydrogen bonding and hydrogen bonding molecules. (b) Solid AV Vapour (a) (b)  no hydrogen bonding  CO CHT  1285 cm 291k cm" 1  1285 c m 2906 cm" -1  hydrogen bonding i ) FHF VHF Av R(F-••-F)  HF vapour klhO cm-1  (a) Nakamoto et a l . , Ref. 27- 0>). C 0  2  (HF)  1  Cal KHF,  Ca)  3UU0 cm -700 cm" 2.55 X  bonding mode.  1  -1 0 cm 8 cm"  1  1  -1 1U50 cm -2690 c m 2.26 £  _1  .8  Tables and p l o t s of v„  TT  as a f u n c t i o n of R(X....Y) were compiled by  Art  Nakamoto, Margoshes and Rundle (27) f o r the FHF, OHO, 0HC1  and NHC1  NHF,  f a m i l i e s of hydrogen bonding compounds.  OHN,  NHO,  NHN,  For small R(X....Y)  the v vs. R r e l a t i o n s h i p s are l i n e a r as Pimentel and Sederholm (28) proposed. For l a r g e R(X....Y) the v vs. R r e l a t i o n s h i p i s non-linear:  the behaviour o  over a l l R(X....Y) suggested an asymptotic r e l a t i o n s h i p . (b) found f o r v  An  Band broadening.  An incresed h a l f - h e i g h t width (Av ) i s 2  and i t s overtones i n hydrogen bonded systems (29).  the e f f e c t i s much smaller on the width of the R-X-H  In contrast  bending modes.  In the e a r l y work the explanation f o r braodening was the form of the intermolecular p o t e n t i a l p e r t u r b a t i o n .  thought to l i e i n  Such an explanation  i s s u f f i c i e n t only f o r weak or moderate strength hydrogen bonds, but not f o r strong hydrogen bonds.  Strong hydrogen bonds give broad bands i n the vapour  phase as w e l l as i n the l i q u i d and s o l i d phases.  Hence the breadth i s inde-  pendent of the non-hydrogen bond intermolecular forces to the f i r s t order. Bratoz and Hadzi (30) and Reid (31) suggested that the breadth a r i s e s from the anharmonicity anharmonicity  perturbations and changes or d i f f e r e n c e s i n the  over many molecules.  G e n e r a l i z i n g the discussions of i c e  they suggested that i n a l l X-H....Y systems the breadth of the v  absorption An  a r i s e s from a group of c l o s e l y spaced bands. (c)  Band i n t e n s i t y .  The integrated i n t e n s i t y c o e f f i c i e n t s o f t e n  increase many-fold upon hydrogen bond formation. A l s o the overtones of h v decrease i n i n t e n s i t y . The apparent r e l a t i o n s h i p s among Av, Av and An  i n t e n s i t y (large s h i f t , broad band, l a r g e i n t e n s i t y ) do not n e c e s s a r i l y h o l d f o r a l l types of hydrogen bonding complexes.  There i s l i t t l e r e l i a b l e data on i n t e g r a t e d i n t e n s i t i e s due t o e x p e r i mental d i f f i c u l t i e s , however, e a r l y work by Huggins and Pimentel (29) e s t a b l i s h e d that hydrogen bonded complexes which show no increase i n the i n t e n s i t y of v appeared t o have non-linear hydrogen bonds. XH VTJ  The increased i n t e n s i t y of v  X H  and the unaffected i n t e n s i t y of v  R  cannot be explained by e l e c t r o s t a t i c t h e o r i e s of the hydrogen bond: E l e c t r o s t a t i c s r e q u i r e s that both v  and  increase i n i n t e n s i t y .  However,  An n increases i n i n t e n s i t y .  CT t h e o r i e s p r e d i c t that only (d) New absorptions.  v t r  For X-H *Y systems new bands appear i n the ,-,  spectra associated w i t h the deformation  of the hydrogen bond.  hydrogen bond s t r e t c h and hydrogen bond bend correspond  In i c e the  t o molecular t r a n s -  l a t i o n (v„) and molecular l i b r a t i o n (v_) modes, the s o - c a l l e d l a t t i c e modes, i  n  ( i i ) The 0-H  0 Hydrogen Bond E f f e c t s  The d i s c u s s i o n s here have so f a r been concerned w i t h c o r r e l a t i o n s among d i f f e r e n t hydrogen bonding f a m i l i e s .  However, there i s a very b i g  problem i n v o l v e d i n such comparisons, the d i f f e r e n t X-H *Y systems have ,,,  d i f f e r e n c e s i n molecular p o l a r i z a b i l i t y , van der Waal's r a d i i , s i z e s of o r b i t a l s , dispersion forces, etc.  Therefore one must expect d i f f e r e n t r e l a -  ys t i o n s h i p s among A v ,  i n t e n s i t y and R(X**''Y).  v u  An  These parameters i n  An  cubic i c e I and the c l a t h r a t e - h y d r a t e s can best be compared t o other 0-H'-'*0 systems and p r e f e r a b l y t o other H^O a l l o t r o p e s , i_.e_. , the high  pressure  ices. In order t o study v  VTJ  An  as a f u n c t i o n of R ( 0  - - ,  * 0 ) , Nakamoto et a l . (27)  compiled Av and R(0'*'"0) data f o r 26 compounds. As w e l l , they c o r r e l a t e d On R ( 0 * * 0 ) t o r(O-H) from neutron d i f f r a c t i o n data. The r e s u l t s i n d i c a t e OTJ  ,,  10 that as R ( 0 * * 0 ) decreases then r(O-H) increases l i n e a r l y f o r long hydrogen --  bonds and e x p o n e n t i a l l y f o r strong (short) hydrogen bonds.  They f e l t that  i n c l u s i o n of covalency i n the hydrogen bond was important, as i n Tsubomura's ( 1 8 ) work. In order t o understand the p o t e n t i a l energy of the proton as a funct i o n of R ( 0 * * * 0 ) , L i p p i n c o t t and Schroeder (25) constructed a one dimen-  s i o n a l model of the hydrogen bond.  By applying the conditions of e q u i l i b r i u m ,  they obtained r e l a t i o n s f o r Av ^, r(O-H) , hydrogen bond energy and f o r c e constants as a f u n c t i o n of R ( 0  , , - -  0).  Their r e s u l t s agree w e l l with e x p e r i o  ment:  v  f o r i c e , where R ( 0 - 0 ) = 2 . 7 6 * 0.1 A, >  and R(0'* 0) i s l i n e a r . -  t h e i r r e l a t i o n s h i p between  ,,  Unfortunately t h e i r formulas are not good f o r  p r e d i c t i n g the v,-„ of i c e over a small range of R(0-«--0) since there i s some a r b i t r a r i n e s s i n d e f i n i n g the hydrogen bond d i s s o c i a t i o n energy. Reid (31) constructed the p o t e n t i a l surface f o r simultaneous H and 0 motion i n 0-H **0 hydrogen bonds over a wide range of R ( 0 -,  r(O-H).  - - , -  0 ) and  He modified the Lippincott-Schroeder p o t e n t i a l by changing the  hydrogen bond d i s s o c i a t i o n energy from molecule t o molecule, i^.e_. , with changing R ( 0  - , -  *0).  Reid used h i s p o t e n t i a l functions t o i n t e r p r e t the  changes i n i r r e s u l t s with changes i n c r y s t a l l i n e l a t t i c e dimensions. He proposed that the breadth of v was due t o i t s strong dependence OH on R ( 0 - - 0 ) . ,,  many  v  During any v^ v i b r a t i o n many R ( 0 * * 0 ) distances occur and --  observed. Recently Bellamy and Pace (32) reviewed the r e l a t i o n s among Av„  QJJ'  s  a r e  TT  An  and R(X-•••Y).  They deduced that X and Y can approach only t o the. combined  van der Waal's r a d i i , f u r t h e r approach of X and Y i s permitted only i f  11 hydrogen bonding occurs.  For example i n the  0-H'*'*0  system the van  der  o  Waal's r a d i i give an  0----0  c l o s e s t approach distance of o  hydrogen bond has an R(O----O) of  A,  3.36  upon formation of the hydrogen bond.  therefore  The weakest  3 . 6 A.  \  R(0----0)  contracts  Extrapolations of the X-Y p l o t s of  Wakamoto et_ al_. i n d i c a t e d that the l i m i t i n g R(X-• •-Y) i s the sum of X and Y van der Waal's r a d i i but not i n c l u d i n g H: FHF"  o  o  i n t e r c e p t 2.7 A ( c a l c . 2.7 A ) o  OH  o  0 i n t e r c e p t 2.8*1 A ( c a l c . 2.8 A )  This suggested that i n hydrogen bonds the H o r b i t a l disappears or i s comp l e t e l y overlapped  and that there i s no r e p u l s i o n due to i t .  Bellamy and Owen ( 3 3 ) extended t h i s idea and proposed that the rate of increase of r e p u l s i o n i s p r o p o r t i o n a l to the r a t e of increase i n lone p a i r - lone p a i r r e p u l s i o n s .  They adopted the 6-12 p o t e n t i a l t o describe  the r e p u l s i v e terms from lone p a i r s i n X and Y and f i n a l l y obtained an expression r e l a t i n g A v ^  and R ( X -  , - ,  Y).  An  12  3.35 A V  OH  =•  5 0  For  [ ( i r  }  0-H----0 6  3.35  - <  R  t h i s has the form  >  I-  This r e l a t i o n s h i p give's good agreement with the work of Nakamoto et_ a l . However by i n s p e c t i o n of Nakamoto's work one sees that no unique v  On  - R(0* ""0) 4  variables.  r e l a t i o n e x i s t s f o r the 0-H*••*0 f a m i l y .  I t seems more reasonable t o study one molecular  i n a v a r i e t y of c r y s t a l habits and to attempt to vary only way.  There are too many system l i k e H 2 O R(0-  - , ,  0)  i n some  For example, a study of H 2 O i n a l l 9 i c e phases and i n c l a t h r a t e -  hydrates as a function of temperature may provide u s e f u l r e s u l t s .  12  Clathrate-Hydrates A.-  The Clathrate-Hydrate Problem  Quantized r o t a t i o n or l i b r a t i o n of trapped (guest) molecules i n the (host) l a t t i c e c a v i t i e s has been suggested by previous i r (36,37)  studies.  (3^,35)  and nmr  Now d e t a i l e d i r assignments of the guest r o t a t i o n s and  t h e i r behaviour i n the host c a v i t y are required t o determine the form of the p o t e n t i a l w e l l surrounding the guest molecules.  In order t o determine the  changes i n the i n t e r a c t i o n s of the guest molecules with the host l a t t i c e and the height of the b a r r i e r t o guest r o t a t i o n s , i t i s necessary t o know prec i s e l y how the guest molecule absorptions and host l a t t i c e absorptions vary as a function of temperature.  B.  The Structures of the Clathrate-Hydrates  Clathrates are a type of i n c l u s i o n compound i n which one stable molecule forms a union with 2 or more other stable molecules, atoms or molecular elements without the existence of chemical bonds between the components. (The enclosing l a t t i c e which contains the c a v i t i e s i s c a l l e d the host and the enclosed molecule i s c a l l e d the guest.)  A common property of some im-  portant c l a t h r a t e compounds i s hydrogen bonding.  Some examples of c l a t h -  rates are: 1) g-quinol c l a t h r a t e s , 0 .Jk Kr-3 CgH^(.0H)  2  2)  gas hydrates,  Ar*7.67  H^O  3) tetraalkylammonium c l a t h r a t e s , s a l t hydrates [(n - C^H ) N] 9  U  C H C0 -39.5 6  U) Ni(CN) NH -C Hg . 2  3  6  5  2  H^O  13 A clathrate-hydrate i s a c l a t h r a t e compound formed with an H^O host l a t t i c e i n which a v a r i e t y of small atoms and covalent molecules are trapped. The clathrate-hydrates can be separated i n t o two c l a s s e s :  The gas hydrates  are c l a t h r a t e s formed between H^O (host) and s m a l l , covalent gases (guests, G) and l i q u i d hydrates are c l a t h r a t e s formed between H^O (host) and molecules of v o l a t i l e l i q u i d s (guests, G). Three c r y s t a l s t r u c t u r e s have been found f o r the clathrate-hydrates. The s o - c a l l e d gas hydrate c l a t h r a t e s , Type I , are cubic and have maximum i d e a l s t o i c h i o m e t r i e s of SG'^HgO or 6G-U6H 0. 2  The s o - c a l l e d l i q u i d c l a t h r a t e -  hydrates, Type I I , are a l s o cubic and have maximum i d e a l s t o i c h i o m e t r i e s of 8G-136H 0 or l 6 G ' - 8 G - 1 3 6 H 0 . 2  2  Bromine l i q u i d c l a t h r a t e - h y d r a t e , Type I I I , i s  t e t r a g o n a l and has a maximum i d e a l stoichiometry of 20G*172H 0. 2  (i)  Type I  Clathrate-Hydrates  These compounds form a cubic c r y s t a l of Pm3n symmetry (38,39) with a o 12.A u n i t c e l l edge and U6 HgO molecules i n a u n i t c e l l .  Two pentagonal  dodecahedrons are formed by 20 HgO molecules each. Those two c a v i t i e s are l i n k e d by t h e remaining 6 H^O molecules t o form 6 tetrakaidecahedra, g i v i n g a t o t a l of 8 c a v i t i e s per u n i t c e l l . In Type I clathrate-hydrates o hedra have f r e e diameters of ,3.95 A o f r e e diameters of 5-8 A ( f o r a 12.0  the nearly s p h e r i c a l pentagonal dodecaand the spheroidal tetrakaidecahedra have o A u n i t c e l l ) . Molecules and atoms whose o  maximum dimensions are l e s s than 5.1 A can f i l l a l l 8 c a v i t i e s and would have an i d e a l c l a t h r a t e stoichiometry of SG'^H^O (i..e_. G = A r , CH^, H ^ S ) . Molecules and atoms whose maximum dimensions are l e s s than 5.8 A but are l a r g e r than 5.1 A w i l l f i l l only the 6 tetrakaidecahedra and would have  Table 0 . 1 Some t y p i c a l c l a t h r a t e s and t h e i r p r o p e r t i e s , P,. gives the c l a t h r a t e decomposition pressure at 0°C, diss ' T gives the maximum stable temperature of the c l a t h r a l Tiq gives b o i l i n g temperature of pure guest.*  Type  Clathrate  d i s s at 0°C  G  o A  8G'U6H 0 2  Ar  95.5 atm  Kr  lh.5  83 121  Xe  11.97  HS  12.00  6 9 8 Torr  29.5  213  12.03  252  28.7  239  CH C1 3  12.00  311  2.1  2U9  CH^Br  12.09  187  1U.5  277  S0„  11.9^  297  12.1  263  U.3  316  1.6  33U  2  (cubic)  max  1.15  166  6G-1*6H 0 2  CI  2  8G-136H O 2  n.ik  CH I 3  CHC1 II  [cubic]  17-30  50  C H Br  17.26  155  CH C1  17.31  116  2  3  5  2  2  17.ho  3 8 C H C1  C  H  2  17.30  5  {l.lh  311 atm)  (tetrag)  a o c Q  Reference kO  5.69  228 286  It.8  2  Br„  315  201  20G-1T2H 0 III  1.7  23.8 12.2  332  U3.90 5.81  x  6G'U6H 0 2  stoichiometry ( C l ^ , SO^, C^H^-).  5  Some p r o p e r t i e s of the c l a t h r a t e s  formed i n these two r a t i o s are given i n Table 0.1. One may a l s o form a mixed hydrate of the form 2G-6G'-U6H_0, i . e . 2H„S• 6C^H.• 1+6R.0. 2 2 2 6 2 I n the p r a c t i c a l s i t u a t i o n the u n i t c e l l dimension v a r i e s according t o the s i z e of the guest s p e c i e s , Table 0.2. (ii)  Type I I Clathrate-Hydrates o These compounds form a cubic c r y s t a l o f Fd3m ( 3 8 ) symmetry with a IT A  u n i t c e l l edge and 136 H^O molecules i n a u n i t c e l l (i_>e_- G = CH^I, CHCl^, C^H^Br).  There are 16 pentagonal dodecahedral c a v i t i e s and 8 hexakaidecao h e d r a l c a v i t i e s i n one u n i t c e l l . The f r e e diameters are 5.0 and 6.T A o r e s p e c t i v e l y ( f o r a 17.h A u n i t c e l l ) . o Molecules which have a maximum dimension greater than 5>8 A and l e s s o than 6.7 A cannot form Type I c l a t h r a t e s , but do form Type I I c l a t h r a t e s . That i m p l i e s they occupy only the hexakaidecahedr.a metry o f 8 G ' 1 3 6 H £ 0 .  w i t h an i d e a l s t o i c h i o -  Some Type I I c l a t h r a t e s , the guest s i z e s , and the u n i t  c e l l dimensions are given i n Tables 0.1 and 0.2. ( i i i ) Type I I I Clathrate-Hydrates The c l a t h r a t e - h y d r a t e of B r ^ was o r i g i n a l l y thought t o be o f Type I I . However, work by A l l e n and J e f f r e y (1*1) has shown that i t forms a t e t r a g o n a l o c r y s t a l o f symmetry k/xamm w i t h a = 2 3 . 8 and c = 1 2 . 2 A u n i t c e l l edges and 172 HgO molecules i n a u n i t c e l l .  They reported 20 polyhedral c a v i t i e s l a r g e  enough t o accomodate Br^ molecules, 10 small pentagonal dodecahedra, 1 6 tetrakaidecahedral then 2 0 B r -1T2H 0.  and k pentakaidecahedral.  The i d e a l stoichiometry i s  Some data are given i n Tables 0.1 and 0.2.  Table 0.2  The types of c a v i t i e s , the maximum allowed occupancy, guest s i z e s and u n i t c e l l dimensions o f t y p i c a l clathrate-hydrates. f  Type  Clathrate  a  c  0  8G'ii6H 0  Q  2  6G-U6H O CI CH3CI CH Br 2  k.ko k.ho  12.03  5.17 5.06 5.33 5.00  0(2) 0 0 0  5.TO  0(16) 0 0  12.00 12.09 11.9h  3  S0  11.97 12.00  2(2)* 2 2 2 •  k.ok  a  2  8G-I36H O 2  CH3I  II  17.30  17.26 17 • 31 17.^0 • 17.30 ,  C H Sr CH2C1 C3H8 2  (cubic)  YJ.lh  CHCI3 5  2  C2H5CI  20G-1T2H 0 2  III (tetrag) V^ *  2  Br  2  a c  0 0  23.8 12.2  pentagonaldodecahedron, V.^ ^. ^  occupancy of c a v i t i e s . 16  15  Ik  0  3.76  Ar Kr Xe HS  (cubic)  V  Allowed  A  A  2  I  Guest size  o o  6.kh 6 M  6.08 6.28 6.20  6(6) 6 6 6 6 6 6 . 6 8(8) 8 8  •8  0 0 0  5-68  0(10)  . 16(16)  .  8  8  k(k)  - t e t r a k a i , pentakai, hexakaidodecahedrons.  - numbers i n brackets show maximum number o f c a v i t i e s per u n i t c e l l . 1  H  17  Since the present experiments attempt t o a c c u r a t e l y c o r r e l a t e R(0  and OH 0) f o r seven Type I , II., and I I I c l a t h r a t e - h y d r a t e s , the R(O----O) v  distances are required. However, the structures were determined by assuming o  constant R(O--'-O) throughout the u n i t c e l l , e_.g_. 2.8l A f o r a Type I o  o  o  c l a t h r a t e (12.0 A u n i t c e l l ) and 2.78 A f o r a Type I I c l a t h r a t e (17-3 A u n i t cell).  In order to accomodate the pentagonal dodecahedra and other polyhedra  i n the u n i t c e l l , the 0-0-0  angles were d i s t o r t e d from t e t r a h e d r a l .  Stackelberg (38) reported angles from 100.0° to 12k.6°. i n r e a l i t y the 0  - - , -  Von  I t seems l i k e l y that  0 distances are a l s o i r r e g u l a r and a range of R(0--«0)  e x i s t f o r each clathrate-hydrate.  That w i l l u n f o r t u n a t e l y broaden the i r  r e s u l t s even more than i n i c e I . Indeed f o r Type I clathrate-hydrates ( c u b i c , Pm3n) the H^O  oxygen atoms  l i e on 3 u n i t c e l l s i t e s (k, i , and c ) . - Consequently, there are it- types of hydrogen bonds; k-k, k - i , k-c, i - i .  I t seems reasonable that these may;not  be i d e n t i c a l i n the r e a l c r y s t a l . C.  Formation of Clathrate-Hydrates  A general phase diagram was proposed by Roozeboom and i s shown i n von Stackelberg's work (38).  At constant temperature there are 2 boundary con-  d i t i o n s t o permit formation of c l a t h r a t e - h y d r a t e s , r a i s i n g the pressure of G to form e i t h e r guest G(gas) or G ( l i q u i d ) plus hydrate.  I f the p a r t i a l pressure  of guest applied to the sample i s l e s s than the e q u i l i b r i u m d i s s o c i a t i o n part i a l pressure then the c l a t h r a t e d i s s o c i a t e s . In a recent review Byk and Fomina (it2) discussed the conditions f o r formation and the thermodynamics of formation.  As w e l l , Barrer and Ruzicka  (it3) studied the k i n e t i c s of rare gas c l a t h r a t e formation at low temperatures.  18  S p e c i f i c a l l y , they i n v e s t i g a t e d the formation of clathrate-hydrate from i c e and Ar, Kr and Xe gases at  90°K  and  195°K.  Their technique involved depositing a t h i n l a y e r of H^O bulb at TT°K.  The sample was warmed to  Torr) was admitted.  i n a glass  and e i t h e r Ar, Kr or Xe  195°K  (190  The gas uptake as a f u n c t i o n of time was measured.  They found that Kr and Xe, but not Ar, reacted with i c e at found to react slowly at  90°K  at  Torr.  190  Ar  195°K.  was  Their r e s u l t s suggested the  ready formation of clathrate-hydrates at low temperatures with a c r i t i c a l formation pressure of l e s s than 1 9 0 Torr. D.  Previous I n v e s t i g a t i o n s of the  Clathrate-Hydrates  Contemporary i n t e r e s t i n c l a t h r a t e s has been centered on the motion of the guest molecules i n the host l a t t i c e s . relaxation (38),  (1+1+-1+6),  x-ray d i f f r a c t i o n  and i r spectroscopy  (52-57,  (38,1+7),  Thus the methods of d i e l e c t r i c nmr  (1+8-51),  thermodynamics  have been applied to q u i n o l c l a t h r a t e s  3l+)  and clathrate-hydrates to discover whether guest r o t a t i o n s are free ,or r e s t r i c t e d , how f a s t they r o t a t e , and what are the b a r r i e r s to free r o t a t i o n . S i m i l a r l y , deductions with respect to hindered t r a n s l a t i o n s ( r a t t l i n g ) of the  guest  have been made  (1+8-51).  The f i r s t work on clathrate-hydrates i n the i r was reported by McCourt (56). SO2. 21+25  He studied the three Type I clathrate-hydrates of Ar,; Kr., and  The main points of h i s t h e s i s were: cm  i n a d d i t i o n to the w e l l known i c e absorptions,  s h i f t e d - 5 0 cm the host were at  2^+55  l ) there was an E^O host band at  cm  from i c e I , 3 ) the 1 6 0 0 cm ^ and 2 2 1 0 cm v  and  (HOH bending) and v 3570  0  2)  the v  absorptions  .+ . v,, r e s p e c t i v e l y , h) S 0  cm ^ (a weak shoulder on v  band was  R  o  of  absorbed  and v_, the symmetric and  19  assymetric  stretches,, of H^O) i n the c l a t h r a t e - h y d r a t e .  S h u r v e l l (57) followed up the above work by observing SO^, H^S, and Kr Type I c l a t h r a t e hydrates (SG-UeH^).  For S0 '7-67H 0 S h u r v e l l reported: 2  2  l ) t h a t v_, (H 0) was ho cm"'" l e s s than that o f i c e , 2) that the 1600 cm "*" -  O  band o f i c e was a t 1.6k0 cm "*" i n the clathra.te and was therefore  rather  than 2v , 3) that the 2230 cm"" was v_ •+• . v , and k) that H O i n c l a t h r a t e s -  1  T3  had. a new feature at 2^10 cm "*" i n a d d i t i o n t o the i c e bands.  As w e l l , he  found that the v^SO^) had a c e n t r a l peak and 2 wings, 1336, 13^2 and 13U8 cm"*". There was no s p l i t t i n g o f v^tso,.,) as i n the pure SO^ s o l i d and the -  c l a t h r a t e d SO^ bands were broadened by " r a t t l i n g " and r o t a t i o n a l f i n e s t r u c ture.  The wings were thought t o be due t o combinations w i t h l i b r a t i o n s  (hindered r o t a t i o n s ) and t r a n s l a t i o n s . Both McCourt (56) and S h u r v e l l (57) formed the clathrate-hydrates by condensation of s t o i c h i o m e t r i c gas mixtures on C s l windows at 77°K. r e p o r t e d h i s samples were annealed t o d e v i t r i f y the condensed phase.  Shurvell The  r e s u l t s o f these p r e l i m i n a r y i n v e s t i g a t i o n s on Type I clathrate-hydrates were summarized by Harvey, McCourt and S h u r v e l l '• E.  (3k).  The Present Approach t o the Clathrate-Hydrate Problem  Three f a c e t s o f the clathrate-hydrate i r absorptions were s t u d i e d i n t h i s work.  F i r s t , i n order t o analyze previous work (.56,57), the forms of  the c l a t h r a t e - h y d r a t e absorptions were determined from low temperature mulls of s o l i d c l a t h r a t e samples.  Secondly, the v i t r e o u s - c r y s t a l l i n e phase t r a n s -  formation was observed by i r spectroscopy  as a f u n c t i o n of temperature f o r  c l a t h r a t e - h y d r a t e s (types I , I I and I I I ) condensed from gaseous s t o i c h i o m e t r i c  20  mixtures.  T h i r d l y , the temperature dependences were determined f o r the i r  absorption of d e v i t r i f i e d " c l a t h r a t e " samples.  Ice  A.  The Ice Problem  Many t h e o r i e s have been proposed t o e x p l a i n the o r i g i n s of the f r e quency s h i f t s , t h e large band widths and the large i n t e n s i t i e s i n i c e .  Now  data are required which w i l l e i t h e r support an e x i s t i n g theory or which w i l l suggest some m o d i f i c a t i o n s t o the theory. S p e c i f i c a l l y , the c o r r e l a t i o n s of absorption band frequencies, widths and heights t o AR(O-'-'O) are required for i c e I . B.  Non-Spectroscopic I n v e s t i g a t i o n s of Ice  ( i ) S t r u c t u r a l Studies Ice  e x i s t s i n at l e a s t twelve s t r u c t u r a l a l l o t r o p e s above TT°K and at  pressures of up t o are  25,000  atmospheres.  The i c e phases stable at  1  atmosphere  a l l c a l l e d i c e I . In f a c t , there are three a l l o t r o p e s of i c e I , the  v i t r e o u s or amorphous, the cubic and the hexagonal phases ( i v , Ic and I h ) . The i c e I s t r u c t u r a l r e s u l t s up t o 1 9 5 8 were summarized by Lonsdale ( 5 8 ) and Owston ( 5 9 ) . the  R e c e n t l y , B r i l l e and Tippe ( 6 0 ) measured by x-ray d i f f r a c t i o n  i c e I h l a t t i c e parameters between  15°  and  200°K.  As w e l l , A r n o l d , F i n c h ,  Rabideau and Wenzel ( 6 l ) reported a neutron d i f f r a c t i o n study of i c e I c . (a) Hexagonal i c e I . The ordinary phase of i c e at S.T.P. i s hexagonal i c e I ( i h ) i n which the oxygen atoms form a P62/mmc u n i t c e l l w i t h h molecules. *  Assuming s o l i d polywater i s a unique s o l i d of H2O.  21  The u n i t c e l l dimensions are ( 6 2 ) ; a  o  H 0  (l63°K)  k.H93  D 0  (ll+3°K)  1+.1+95  2  2  c  A  o  7.337  A  7.335  o The oxygen-oxygen nearest-neighbour distances at l 6 3 ° K .  (R(0••••0))  i n H^O are 2 . 7 6 A  The molecules are hydrogen bonded t o 1+ nearest-neighbours i n l a y e r s  of hexagonal, puckered r i n g s . perpendicular t o the c  Q  The open s t r u c t u r e has channels p a r a l l e l and  axis.  There i s s t i l l some u n c e r t a i n t y about the u n i t c e l l dimensions of i c e Ih.  The disagreement between Lonsdale's ( 5 8 ) expansion c o e f f i c i e n t s and the  d i r e c t d i l a t o m e t r i c measurements seems t o a r i s e from d i f f e r e n c e s i n c r y s t a l l i n i t y among the worker's samples.  The x-ray d i f f r a c t i o n work of La Placa and  Post ( 6 3 ) agrees w e l l w i t h Dantl's (6I4) d i r e c t thermal expansion measurements: La P l a c a and Post's ( 6 3 ) work was confirmed by B r i l l e and Tippe ( 6 0 ) . l a t t e r found that the c/a r a t i o 1.633  The  i s temperature independent, not reaching  even a t 15°K; they found c/a =  1.6280  ±  0.0002.  (b) Amorphous i c e I . This phase i s formed by the slow condensation of vapour onto a c o l d surface.  Beaumount, Chihara and Morrison ( 6 5 ) found that  amorphous i c e I was formed when the d e p o s i t i o n rate at 135°K was l e s s than 0.0U the  g/cm^/hour.  The x-ray and e l e c t r o n d i f f r a c t i o n patterns are d i f f u s e and  samples are c l e a r , transparent f i l m s .  The samples have consequently been  v a r i o u s l y described as v i t r e o u s , amorphous or microcry'stalline.  Virtually  nothing i s known about the s t r u c t u r e o f amorphous i c e I . (c) Cubic i c e I . I c e I c can be formed by the i r r e v e r s i b l e t r a n s f o r mation o f amorphous i c e I or from the high pressure i c e s .  The vftreous-cubic  ice I transformation has been reported t o s t a r t as low as 110°K and as high  22 . i  as 153°K by various authors, Table 0.3. The high pressure i c e - c u b i c i c e transformations have been studied by B e r t i e , Calvert and Whalley ( 6 6 ) at T7°K by release of pressure.  Cubic i c e I can a l s o be formed by vapour con-  densation between 133° and 153°K. transforms i r r e v e r s i b l y  When warmed above  cubic i c e I  210°K  t o hexagonal i c e I with a small enthalpy change,  iLe_. <1.5 cal/gm (65). The c r y s t a l s t r u c t u r e of the oxygen atoms i n cubic i c e I i s the "diamond" s t r u c t u r e , Fd3m w i t h 8 molecules per u n i t c e l l .  The oxygens are  arranged i n a s i m i l a r fashion t o that of hexagonal i c e i n l a y e r s o f puckered hexagonal r i n g s .  However, the s i x 0 atoms a d j o i n i n g 2 nearest-neighbours are  e c l i p s e d i n cubic i c e I and staggered i n hexagonal i c e I . The l a t t i c e o o parameters ( 6 2 ) a t li+3°K are a ( H 0 ) = 6 . 3 5 0 A and a ( D 0 ) = 6 . 3 5 1 A. o  2  o  2  (d) Disorder i n Ice I . The neutron d i f f r a c t i o n work of Peterson and Levy (quoted i n Lonsdale ( 5 8 ) ) showed that each oxygen was surrounded by four o 1/2 hydrogens a t 1.01 A. They asserted that the DOD angle t h e r e f o r e , that the hydrogen bonds are l i n e a r .  =  000 angle and,  Their r e s u l t s were the same  at 123° and 223°K, i n d i c a t i n g no ordering o f the l a t t i c e down t o 123°K. Pauling predicted a r e s i d u a l entropy at 0°K o f R l n 3/2 or  0.805  e.u. However  Onsager and Dupuis ( 6 7 ) showed that Pauling's r e s u l t i s only the lower bound to the true c a l c u l a t e d value. the t h e o r e t i c a l value i s  O.81U5  Nagle ( 6 8 ) found by l a t t i c e s t a t i s t i c s that  t  0.0002 e.u., compared t o an experimental  value o f 0.82 i 0.15 e.u. Disorder i n cubic i c e I was confirmed by e l e c t r o n :  diffraction(69).  P i t z e r and P o l i s s a r ( 7 0 ) discussed the order-disorder problem i n i c e I and concluded that the ordered s t r u c t u r e i s more s t a b l e at low temperatures However, they estimated that the transformation time may exceed a day.  They  Table 0 . 3  Temperature ranges of s t a b i l i t y at 1 atmosphere of v i t r e o u s , cubic and hexagonal i c e I by several experimental methods.  heat capacity  77  elect.diffrac.  TT -  calorimetry  TT  elect.diffrac.  crystalline  - Ikk amorphous  10T  10T  -(150  amorphous TT -  t  10)  -  -  Workers  2T3  ihh  190  190  crystalline 151  151  Hexagonal Phase Range °K  Cubic Phase Range °K  Low Temperature Phase and Range °K  Technique  150  -  273  (a)  Hon jo et_ a l .  (b)  de Wordwall et a l . ( c )  2T3  173  Pryde et_ a l .  173  -  2T3  Blackman et a l . (d)  amorphous x-ray d i f f r a c . d i f f . t h e r m , anal.  113 - 1U3  lh3  -  2T3  Dowell et a l .  TT -  lk9  -  186  -  2T3  McMillan et a l . ( f )  glass  lk9  x-ray d i f f r a c .  TT -(1U8  thermal a n a l y s i s  TT - 15U  calorimetry  TT -  (a) Ref.  71,  amorphous  +  8)  (1U8  +  186  8)  -  (220120)  220±20  -  Beaumont et_ a l . (g)  2T3  -  208  208  -  2T3  Ghormley  135 -  160  160  -  2T3  Sugisaki et_ a l . ( i )  15U  (h)  amorphous 135  amorphous  (b) Ref.  (e)  HO amorphous  TT -  69,  (c) Ref.  (h) Ref. 7 6 , ( i ) page 3 2 9 , Ref. 6.  72,  (d) Ref.  73,  (e) Ref.  7^,  ( f ) Ref.  75,  (g) Ref.  65,  24  also estimated the Curie p o i n t to be near 60°K. (e)  High pressure i c e s .  may not c o n s i t u t e a l l p o s s i b i l i t i e s . and a t higher pressures.  The a l i o t r o p e s of i c e s I I through IX More a l l o t r o p e s may e x i s t below 77°K  Some of the c r y s t a l l o g r a p h i c p r o p e r t i e s and s t r u c -  t u r a l parameters of the i c e a l l o t r o p e s are given i n Table 0.4.  Phases I I ,  V I I I and IX a r e ordered and a l l others are disordered w i t h respect to proton position.  The higher d e n s i t i e s of the high pressure i c e s d e r i v e not from  shorter R(0....)) but from d i s t o r t e d hydrogen bonds.  The d i s t o r t i o n s r e s u l t  o  o  i n much c l o s e r (3.2 A) next-nearest-neighbours compared to i c e Ih(4.5 A ) . There i s considerable d i s t o r t i o n of the HOH angles:  I c e I I has 18 HOH angles  between 80° and 128°. (ii)  E l e c t r i c a l P r o p e r t i e s of I c e Recently d i e l e c t r i c constant work was reported by Wilson et a l . (77)  and by Whalley and Heath (78).  I n general, they found that i c e I has a  l a r g e r e c i p r o c a l d i e l e c t r i c r e l a x a t i o n constant (about 10"* r e o r i e n t a t i o n s per T - l i second), and that the disordered high pressure i c e s have even l a r g e r The T  ^  ^'s of ordered i c e s , however, a r e small (no r e o r i e n t a t i o n s ) .  ^  s.  The  o f i c e I increases very r a p i d l y w i t h decreasing temperature due to the  i n c r e a s i n g e l e c t r i c f i e l d of the approaching neighbouring molecules:  T ^^  i s 2000 times l a r g e r a t 208°K than at 273°K. An accepted mechanism of r e o r i e n t a t i o n invokes the m i g r a t i o n of Bjerrum (79) D- and L- d e f e c t s . (iii)  Thermodynamic P r o p e r t i e s of I c e There i s support f o r some ordering i n i c e I h from heat c a p a c i t y (Cp)  and e l e c t r i c i t y measurements.  Helmreich and R i e h l (80) deduced from e l e c -  t r i c i t y measurements that the proton d i s o r d e r i s p a r t i a l l y removed as  \ Table O.U  P h y s i c a l p r o p e r t i e s of the i c e s .  Ih  Ic  C r y s t a l System  Hexag  Cub.  Space Group  P63/mmc  ICE  Fd3m  Ill  II  Density g/cm^ No.n-neighbours  R3  pit ? 2 A2/a  R n-neighbours  12  8  0.9k  —  1.17  k  k  k  2.15  2.76  .  2.1k  2.15  k.k9  U.50  0  A R n.n-neighbours  r  1  k  k  -2.8U 3.2U  28  1.1k  %  109.5  109.5  deg k positions  *  disord. disord.  Table from r e f . ( 5 ) .  VI  -2.80 3.U7-.  A2/a  pl*2/  28  m m c  0  1.23  1.31  k  k  2.76  ••  VII  VIII  IX  Cub.  Cub.  Tetrag.  Im3n  Im3m  2  2  Vk.2 2 1 1 12  1.50 8  k  8  2.81  2.86  2.86  3.51  2.86  2.86  -2.87 3.28 3.1*6  •  0  A  V  Rhomb. Tetrag. Monocl. Monocl. Tetrag. r  Z  . IV  80 -128  87  8U  -li+1  -135  ord.  disord.  ord.  .  76  .  100.5  109.5  -128  disord.. d i s o r d .  disord.  ord.  -  ord.  26  temperature decreases.  The e f f e c t s found were small and they therefore  deduced a small f r a c t i o n of the sample was ordered: ordered domains i n a disordered continuum.  A f i n i t e number of  P i c k ( 8 l ) also suggested that  regions of short-range ordering are formed as the temperature of i c e I i s lowered.  However, he pointed out that the D- and L- defects responsible  f o r r e o r i e n t a t i o n (ordering) decrease i n number exponentially w i t h temperature.  decreasing  Hence .the time f o r e s t a b l i s h i n g an ordered c r y s t a l increases  exponentially as temperature decreases. The heat capacity of i c e Ih above 15°K was f i r s t i n v e s t i g a t e d by Giauque and Stout ( 8 2 ) .  They found that the samples a t t a i n e d thermodynamic  e q u i l i b r i u m i n the range 8 5 ° to 115°K only slowly.  The reason i s not under-  stood. Recently Flubacher et_ a l . ( 8 3 ) studied the i c e Ih Cp below 15°K. They found Cp extrapolates to zero at 0°K and i s consistent with a continuous decrease.  As w e l l they pointed out that the t r a n s l a t i o n a l , l i b r a t i . o n a l  and i n t e r n a l energies are separable and that the l i b r a t i o n a l c o n t r i b u t i o n to Cp i s explained w e l l by an average frequency f o r H^O Leadbetter  of 6 2 0 cm'  ( 8 U ) , i n a comprehensive i n t e r p r e t a t i o n of the i c e I ,  thermodynamics, explained Cp i n terms of the e x c i t a t i o n of t r a n s l a t i o n a l (v^) and l i b r a t i o n a l ( ) V  R  v i b r a t i o n s . Below 80°K, Cp was derived e n t i r e l y  from e x c i t a t i o n s of v , while above 150°K v~ gave a s i g n i f i c a n t c o n t r i b u t i o n . m  He also predicted that between 8 + 2 $ and that v  R  0°  and 273°K the  s h i f t s by 6 ± 2% f o r H 0 g  frequency shifts...by  (for D 0 g  ±0 ± 2% and 8. + 2%  respectively). Blue's ( 8 5 ) elementary treatment of Cp gave a s u r p r i s i n g l y good;value f o r the l i b r a t i o n a l average frequency, 6 6 0 cm ^.  He also gave a convenient  formula f o r deducing the set of i r l i b r a t i o n a l frequencies:  27  :1  [1]  2TTCI.  n  where I  n  i s the moment of i n e r t i a about a x i s n i n gm/cm ,  k. i s the force constant r e s t r a i n i n g atom i from r o t a t i o n about axi in n i n dynes/cm,  •'  - r . i s the normal distance of atom i to a x i s n i n in  cm,  6 i s the v e l o c i t y of l i g h t cm/sec.  C. The  Spectroscopic I n v e s t i g a t i o n s  of Ice  e f f e c t s of hydrogen bonding have been observed i n 3 f i e l d s of  spectroscopy; e l e c t r o n i c , nmr  and v i b r a t i o n a l .  For example, both red  and  blue s h i f t s (from the non-hydrogen bonded frequency) are observed dependin on whether the hydrogen bond i s stronger i n the ground e l e c t r o n i c state or i n the e x c i t e d s t a t e .  In nmr  spectra the proton s i g n a l s of (H atoms in)  hydrogen bonded molecules are s h i f t e d to a lower f i e l d than f o r the hydrogen bonded molecule.  In i c e , nmr  non-  has been used t o f i n d proton separa  t i o n s and t o determine charge r e d i s t r i b u t i o n s . V i b r a t i o n a l studies of i c e have been made by neutron i n e l a s t i c s c a t t e r i n g , Raman, and i n f r a r e d spectroscopy. considered i n two  The previous work w i l l  s e c t i o n s , modes occurring below and above 1000  fundamental l a t t i c e and molecular mode regions ).  The  cm  be (the  r e s u l t s of previous  works are tabulated i n Chapter 3 f o r comparison to the r e s u l t s of the present work. The H^O  molecule has 3 molecular v i b r a t i o n s ; a symmetric and  •asymetric s t r e t c h and a symmetric HOH respectively).  bend (v ( a ^ ) , v„(b  an  ) and. y~(a-j_)  In cubic i c e I (Fd3m) w i t h 2 molecules per p r i m i t i v e unit  c e l l (Z = 2) there are (3n)Z  (where n i s the number of atoms/molecule) c.v  28  18 c r y s t a l v i b r a t i o n s .  Of those, (3n-6)Z or 6 of these are molecular v i b r a -  t i o n s , 3Z or 6 are r o t a t o r y i n nature, 3(Z-1) or 3 are t r a n s l a t o r y v i b r a t i o n s and 3 are simple t r a n s l a t i o n s of the complete u n i t c e l l .  Hence i n a mole  (N)  of u n i t c e l l s there are 6N molecular v i b r a t i o n s , 6N r o t a t o r y v i b r a t i o n s , 3N o p t i c a l t r a n s l a t i o n s and 3N  acoustical translations.  Ice spectra are characterized below 1000  cm ^ i n the ^ 0  centred near 230 cm  ices.  by 5 very broad bands.  Two  bands occur  A band with at l e a s t 6 features  and  i s a t t r i b u t e d to hydrogen bond s t r e t c h i n g modes, the  l a t t i c e t r a n s l a t i o n a l modes v^,.  A band w i t h from 3 to 16 features and  cen-  tered near 830 cm ^ i s a t t r i b u t e d to hydrogen bond bending modes, the l a t t i c e hindered r o t a t i o n a l modes, v . w  Between 1000  and 4000 cm ^ 3 bands are observed.  cm ^ has been a t t r i b u t e d to Iv*.,  v  0  or to overlapping 2 v / v .  near 2200 cm ^ has been assigned to v ^  3200 cm (105),  D  0  /,  + v  n  K  or 3V,,. K  2)  v  r  \>y  v  3  + v  T  (108), and  3)  0  1)  2^2*  a l l as v ( H 0 ) (95). Q H  2  1630  The band  The features of  band have been assigned by various authors to:  vapour, l i q u i d and i c e I frequencies, i n Table  The band near  v  the  3'  v  l  The  with the various assignments are given  0.5.  The a n a l y s i s of the v i b r a t i o n s of c r y s t a l l i n e m a t e r i a l s  usually  begins w i t h a f a c t o r group a n a l y s i s based on the known d i f f r a c t i o n symmetry, jL.ji. based on oxygen atoms and -|H atoms.  Now  the disordered H p o s i t i o n s  are averaged i n the time of a d i f f r a c t i o n experiment, w h i l e i n v i b r a t i o n spectroscopy the instantaneous symmetry of the u n i t c e l l i s important, (i)  The L a t t i c e Modes (a)  Translations.  For i c e s Ih and  Ic the f a c t o r group a n a l y s i s ,  based on symmetric -^H p o s i t i o n s and the above d i f f r a c t i o n symmetries, pre-  Table 0.5  H^O vapour, l i q u i d and i c e I h i n f r a r e d absorption frequencies, h a l f - h e i g h t widths and i n t e n s i t i e s and the divergent assignments made t o the bands of i c e .  (a) Vapour  H0 2  -1  cm  (D 0) 9  (D) Liquid  -1  cm  (1178)  3657 (2671) 3756 (2788)  (d) Ice Av^  160 (170)  (218)  650  800  1957  (e) Hornig  (f) Pimentel  1958  1959  200  strong  1961+  med.  R  .(590) 161+0  250  (1210)  (150)  2130  2225  200  (1620)  (1620)  (180)  3219 ( - )  (231+7)  weak  V  V  2  311+2  +  v  300  3252  (2440) 3352  (g) Whalley  weak  1570,16U5  31+1+5  (c) Ockman  cm  (1160,1210)  (2500)  (d) Ice Peak Heii  -1  -1  cm 232  (500) 1595  (c) Ice I  verystrong  V  2  3v R  R  R V  2  3v  V T  3  2v,  l  V  V  2  + V  • R  v (H 0) O H  2  v (H 0) Q H  (250)  v  .  V  2  3  + v  2  T  (2514)  HDO  weak  810* (6oo)<* 3707 (2727)  31+05  3275  (2520)  (21+16)  80 •  (2)  (a) Ref. 1 1 6 , (b) Ref. 9 8 , (c) Ref.  108,  very strong  V  R v OH  V  "0D  V  V  (d) Ref. 1 0 6 , (e) Ref. 1 0 5 , ( f ) Ref. 9 7 , (g) Ref.  V  R R 0H 0D  95-  ro  30 d i e t s 9 o p t i c a l modes f o r I h (Ajg, B ,  E  l g  o p t i c a l modes f o r I c ( F i g ) .  , ^2g' ^ 2 u ^ a n  l g  E  a n < i  The normal k_ = 0 s e l e c t i o n r u l e s predict  that  a l l these modes are i r i n a c t i v e and that a l l g modes are Raman a c t i v e . However, i r t r a n s l a t i o n a l absorption (v^) _is_ observed ( 8 6 ) f o r both I h and Ic i c e s .  I n f a c t t h e absorptions are n e a r l y i d e n t i c a l .  The f a c t o r group  a n a l y s i s f a i l s f o r Vfj of hexagonal and cubic i c e s , as w e l l as f o r the other disordered i c e s , V and VI ( 8 6 ) . In c o n t r a s t , the f a c t o r group a n a l y s i s works w e l l f o r  of i c e s I I  and V I I I , the ordered H atom ices ( 8 6 ) . The H atoms i n i c e Ic are not symmetrically placed along R(O----O) i n the u n i t c e l l .  Even i f the H atoms were p e r f e c t l y ordered, w i t h 2 near and 2  away from each 0 atom, the c r y s t a l symmetry of i c e Ic could not be Fd3m since the  symmetry would be destroyed.  One'might expect i c e Ic t o order i t s e l f  i n a sub-group of Fd3m or s i m i l a r t o one of the structures or IX (R3, Im3n or P, „ - ) . ^l2i2  i n ices I I , VIII  Then the v modes may not be a l l i n a c t i v e i n T m  the i r . I f short range ordering i s present (as suggested before) then the e f f e c t i v e c r y s t a l symmetry may be a.subgroup of Sg, 0^ or Dli, since the nearest molecules determine the e f f e c t i v e p o t e n t i a l at the c e n t r a l molecule. (h) Disorder theory.  Whalley and B e r t i e ( 8 7 ) proposed a theory t o  e x p l a i n the a c t i v i t y of l a t t i c e modes i n o r i e n t a t i o n a l l y disordered c r y s tals.  They considered i c e I c t o have (near) p o s i t i o n a l symmetry (order) of  the 0 atoms but o r i e n t a t i o n a l disorder of the H atoms.  They suggested that  the r e s u l t i s a small e f f e c t on the mechanical form of the t r a n s l a t i o n a l v i b r a t i o n s , t h e r e f o r e the t r a n s l a t i o n a l modes are mechanically However, since i n the course of a v i b r a t i o n  regular.  Ay_ v a r i e s according t o the  l o c a l molecular o r i e n t a t i o n s , then the. c r y s t a l t r a n s l a t i o n a l v i b r a t i o n s are electrically irregular.  31 Whalley and B e r t i e ( 8 7 ) assumed that the dipole d e r i v a t i v e could be s p l i t i n t o a symmetric p a r t , M', (corresponding t o d i f f r a c t i o n symmetry part) and an asymmetric, i r r e g u l a r p a r t , M'', due t o the H atom disorder. Then they showed that the molecular i n t e n s i t y of absorption has a part f o r zero wave vector (k_ = 0 ) t r a n s i t i o n s , which are the normal symmetry allowed t r a n s i t i o n s , and a f i n i t e i n t e n s i t y f o r a l l k  0 t r a n s i t i o n s due t o M' . 1  Therefore they deduced that a l l t r a n s l a t i o n a l v i b r a t i o n s are i r a c t i v e . In a subsequent paper B e r t i e and Whalley ( 8 8 ) used the above theory to describe the density of states i n 229.2  of i c e s I h and I c .  cm"*" peak t o degenerate l o n g i t u d i n a l and transverse o p t i c a l modes at -  the zone center, the l 6 0 cm"" peak t o the l o n g i t u d i n a l -  1  zone boundary, and the 1 9 0 cm the same zone boundary. and  They assigned the  a c o u s t i c a l mode of a  shoulder t o the l o n g i t u d i n a l o p t i c a l mode at  They showed a density of states curve f o r i c e s I h  Ic. As w e l l , B e r t i e and Whalley ( 8 8 ) . found that v^RgO) s h i f t e d by 7 c m  t o lower frequency upon r a i s i n g the temperature from 100° t o l 6 8 ° K .  They  a t t r i b u t e d the red s h i f t t o e x c i t a t i o n of hot bands. The r e s u l t s of v^H^O) f o r v i t r e o u s i c e I are c o n f l i c t i n g  (88,89).  Giguere and Arraudeau ( 8 9 ) i n d i c a t e d considerable band structure." (c) Raman spectra.  S c a t t e r i n g from v^H^O) was reported by Val'kov  and Maslenkova ( 9 0 ) with a medium i n t e n s i t y peak at 230 cm "*" and weak features at 291 and 310 cm  As w e l l , Taylor and Whalley (91) reported  the Raman spectra of ices I h , I c , I I , I I I and I I .  They reported a peak a t  -1 ' -1 2 2 5 cm i n i c e s I c and I h and at 151 cm i n ice I I . Cd.) Neutron i n e l a s t i c s c a t t e r i n g .  Spectra were reported by Prask  and B o u t i n ( 9 2 ) f o r i c e I h and Trevino ( 9 3 ) and Renker and Blanckenhagen  -1  32 (9*0 c a l c u l a t e d the v  spectra of i c e I .  The frequency d i s t r i b u t i o n s c a l -  culated and observed i n neutron work agree quite w e l l w i t h B e r t i e and Whalley's ( 8 8 ) p r e d i c t i o n s from the i r . (e) L i b r a t i o n .  Hydrogen bonding also gives r i s e to hindered r o t a t i o n a l  t r a n s i t i o n s i n the i c e s . and f o r D 0 from 7 5 0 cm d  o  For H^O t h i s absorption i s seen from 1 0 0 0 - hOO cm  -1  t o 3 5 0 cm  -1  . The r a t i o of v  0  f o r H-0 and D 0 a  d  d o  1  would  i d e a l l y be 1.1*1 f o r purely r o t a t i o n a l motion and 1 . 0 5 f o r purely t r a n s l a t i o n a l motion:  The observed values l i e c l o s e r to 1 . 3 5 • Blue's ( 8 5 ) treatment of H^O l i b r a t i o n was based on the assumption of  three  uncoupled, degenerate l i b r a t o r s .  The hydrogen bond bending: force  constant was assumed to be symmetric about the  0-H-"-*0  axis and only  nearest-neighbour i n t e r a c t i o n s were considered. In such an approximation the l i b r a t i o n about the  2v  axis i s i r i n a c t i v e .  B e r t i e and Whalley ( 9 5 ) , i n contrast, pointed out that the very existence of the v  bands i s due t o the strong coupling of the 3N l i b r a t i o n s  of N molecules i n a mole of u n i t c e l l s .  The c r y s t a l f i e l d and hydrogen-bond  coupling y i e l d a broad band of c r y s t a l frequencies.  Since i c e Ic i s d i s :  ordered and has only symmetry E, a l l the c r y s t a l frequencies are i r a c t i v e . However, the d i s t r i b u t i o n of i r i n t e n s i t i e s across the band of c r y s t a l f r e quencies i s unknown, and the shape of the i r absorption band i s not n e c e s s a r i l y the shape of the c r y s t a l l i n e v i b r a t i o n band. B e r t i e and Whalley ( 9 5 ) reported that the v and Ih are i d e n t i c a l .  For HO  absorptions of i c e s Ic  they observed 5 features on v  d  555 cm  f o r D^O  n  between 9 0 0 and  R  they observed 3 features between 6 7 5 and 1+25 cm \,  the m u l l i n g agent used obscured the r e s u l t s i n some areas.) were observed i n the high pressure ices ( 9 6 ) .  (However,  S i m i l a r bands  33  The ordered i c e I I appears t o obey the f a c t o r group s p l i t t i n g pred i c t i o n s w i t h respect t o v_.  B e r t i e C86) suggested 12 v  In f a c t , 16(9] features were observed between kJ5 center at 800 (593) cm . D  +• v  and 1066 cm"" w i t h a band -  1  As w e l l , B e r t i e and Whalley (96) suggested that a  -1  mode v  i r a c t i v e modes.  may be a c t i v e i n i c e I I . -  The l i b r a t i o n a l absorptions of v i t r e o u s , hexagonal and cubic i c e I were reported a l s o by Giguere and Arraiideau (89).  For v i t r e o u s i c e they r e -  ported features at 8 0 0 ( 6 0 0 ) , 8^0(635) and 900 (675) cm . -1  . In cubic and  hexagonal i c e I they observed only two f e a t u r e s , 835(625) and 890(673) cm . 1  The two c r y s t a l l i n e modes were assigned t o they suggested the C field.  and  + v^.  For v i t r e o u s i c e  l i b r a t i o n was a c t i v e due t o the asymmetric e l e c t r i c  The observed frequency of 800(600) cm  1  i s i n good agreement w i t h  the p r e d i c t i o n s of Blue's equation, 802(6oU) cm Zimmermann and Pimentel (97) studied the temperature dependence of and  between 93° and 273°K.  From a normal coordinate a n a l y s i s based on  an H^O^ model they deduced that the hydrogen bond bending force constant v a r i e s from 0.095 t o 0 . 0 8 5 x 1 0 ^ dynes/cm between 93° and 273°K.  This agrees  w i t h the concept of a weakening hydrogen bond as R(0* •••()) increases. ( i i ) Modes Above 1200  cm"  1  (a) Temperature dependences of the modes.  Temperature dependences of  the i c e absorptions have been observed p r e v i o u s l y by at l e a s t 5 groups. Giguere and Harvey (98) reported frequencies f o r v^, v and v_ at 1 0 3 ° , 217° n d 3 0  and 268°K f o r H^O and D^O.  They observed s o l i d s formed by condensing the  l i q u i d or vapour phase. Ice I h (H^O'^nd D^O)  s i n g l e c r y s t a l Raman spectra were reported by  Val'kov and Maslenkova (99) f o r s e v e r a l temperatures above 77°K.  On the  I  3 k  basis of intense a^ Raman s c a t t e r i n g and the s i m i l a r i t y t o vapour phase s c a t t e r i n g , they assigned i n d i v i d u a l  and  i c e frequencies. That i s i n  d i r e c t contrast to more recent work ( 9 5 ) which strongly coupled i n t o two separate but e q u a l l y mixed bands. that the r a t i o  ^  ^  o r  vapour, as w e l l as f o r D^O.  n  ^  e  so  and  Val'kov and Maslenkova  suggested  -^ - should be the same as f o r the a  They also observed other l i n e s i n the s t r e t c h i n g  region which may have a r i s e n from combinations with l a t t i c e modes. Zimmermann and Pimentel ( 9 7 ) also reported the temperature dependences of  and 3v  273°K  they found that v  Thus the  R  l600  above 93°K. As the temperature was increased from 9 3 ° ; t o and 3v^ decreased and v  cm ^ i c e band could not be  2v . n  increased i n frequency.  As w e l l , they found that at  n  93°K v ( s o l i d ) < v (vapour). 2  2  The most accurate study of temperature dependences i n i c e was r e c e n t l y reported by Ford and Falk (100) f o r the v (HDO) and v (HDO) modes.? By preQH  or)  paring a d i l u t e concentration of HDO i n HgO or DgO one maintains a constant c r y s t a l f i e l d , but removes the dynamical intermolecular coupling of one.HDO mode to the surrounding l a t t i c e (101, 102).  Consequently, Ford and F a l k  observed r e l a t i v e l y sharp HDO bands, the h a l f - h e i g h t width (Av 18 cm  h Av  f o r v (KD0) at 97°K.  -1  OTJ  i = 5 cm  ) was about  That i s s t i l l much wider than f o r ice, II:,  On  , where the H atoms are ordered.  , •  The widths of HDO bands i n i c e I I are due to hot bands, overtones, and sum and d i f f e r e n c e bands.  (Hot and d i f f e r e n c e bands should be removed near  10°K.) The widths of the HDO bands i n i c e Ih are due t o the above e f f e c t s plus H atom disorder ( i r r e g u l a r Hydrogen bond p o t e n t i a l s ) . The problem of forming hydrated s a l t windows and not i c e I was  dis-  covered by Mutter, Mecke and Lutke (103) and was c l a r i f i e d by S c h i f f e r - ( 1 0 4 ) . Hydrated s a l t window absorptions are r e a d i l y d i s t i n g u i s h e d from those of i c e .  35  (b) I n f r a r e d absorption' spectra. The' spectra of H^O,  HDO  and  D^O  were studied i n d e t a i l by Hornig, White and Reding (105), Table 0.5. fundamentals  and  The  were assumed t o have reversed order i n energy from  the vapour phase-order because of the s t r e t c h - s t r e t c h i n t e r a c t i o n constant. They a l s o estimated that the b a r r i e r t o proton jumping was 27 kcal/mole. U n f o r t u n a t e l y , i t now appears t h e i r samples were of amorphous and not crystalline ice.  (Many of t h e i r conclusions are s t i l l v a l i d however.)  Zinnnermann and Pimentel (97) pointed out the need t o anneal s o l i d samples formed by vapour condensation.  They demonstrated the i r e f f e c t s of annealin  amorphous i c e , but d i d not study the phase transformation i n d e t a i l . Ice Ih s p e c t r a of H^O, (106) at 83°K.  D^O  and HDO were obtained by Haas and Hornig  They observed 2v (HD0) and suggested that the b a r r i e r to OTI  On  proton t r a n s f e r exceeded 23 kcal/mole.  However, they suggested that proton  t u n n e l i n g may occur, l e a d i n g t o broad HDO bands. used very h i g h concentrations (8-10%) of HDO  On the other hand, they  i n H^O  and D^O.  The r e s u l t i n g  HDO-HDO coupling (neighbours) gave wider bands as w e l l as a p a i r of shoulder one on e i t h e r side of the main HDO  s t r e t c h i n g band.  Their r e s u l t s showed that the width of hydrogen bonded 0-JI s t r e t c h i n g bands was not a c h a r a c t e r i s t i c of the 0-H-'•-0 bond but arose from extensive molecule-molecule coupling of 0-H  motions.  The work of B e r t i e and Whalley (95) i s the most comprehensive study of cubic and hexagonal (HO,  HDO  and D 0) 2  ice I.  Their r e s u l t s were  obtained at 110°K by the low temperature m u l l i n g techniques developed by them (107).  The cubic or hexagonal c r y s t a l l i n i t i e s of t h e i r samples were  confirmed by x - r a y diffraction.---  36  B e r t i e and Whalley reported that the i r spectra of i c e Ih and I c -were i d e n t i c a l .  As -well, they obtained much sharper spectra than the  previous workers ( 9 7 , 1 0 5 , 1 0 6 , 1 0 8 ) due t o the absence of amorphous i c e . They r e j e c t e d the i n t e r p r e t a t i o n of the bands i n terms of v^, v^, on the basis of strong intermolecular coupling. c r y s t a l s the neighbouring  R  For example, i n i c e  v i b r a t i o n s were -assumed t o couple with ,each  other t o form one broad, symmetric band formed.  and v  band:  S i m i l a r l y a broad symmetric  F i n a l l y they suggested the  coupled-band could i n t e r a c t  with the p h y s i c a l l y and e n e r g e t i c a l l y adjacent  coupled-band t o give two  broad bands which were equal admixtures of v_ and v^; two h y b r i d v^-v^ bands. L  B e r t i e and Whalley suggested that d i f f e r e n t portions of these coupled, broad bands were i r and Raman a c t i v e , accounting f o r the d i f f e r e n c e s between the i r and Raman r e s u l t s . With respect t o the widths of the i c e I absorptions, they suggested that H atom disorder leads t o l o c a l v a r i a t i o n s i n 0 atom p o s i t i o n s and v a r i ations i n the l o c a l p o t e n t i a l , as e a r l i e r suggested by Reid ( 3 l ) . other causes of the broad bands were a l s o reviewed ( 9 6 ) .  Three  These were:  1 ) the occurrence of sum, d i f f e r e n c e and hot bands with l a t t i c e modes, 2 ) the occurrence of proton t u n n e l l i n g and the r e s u l t i n g increase i n the width of the energy l e v e l by a decreased l i f e t i m e , and 3 ) Fermi resonance between the fundamental modes and overtones or combinations. B e r t i e and Whalley ( 9 5 ) discussed the 1 6 5 0 cm ^ absorption as a r i s i n g from combined 2 v „ and v_ v i b r a t i o n s , but they pointed out that d i s c u s s i o n i n terms of a unimolecular Nv„ modes/mole of c r y s t a l .  mode i s not meaningful.  One must consider the  37 D.  The Present Approach, t o the Ice Problem  Three facets of the i c e problem were.studied i n t h i s work.  F i r s t , to  help c l a r i f y the discrepancies among i r and Raman r e s u l t s f o r i c e I samples •condensed from the vapour or c r y s t a l l i z e d from the l i q u i d , the temperature dependences of v i t r e o u s i c e absorptions were observed and the v i t r e o u s - c u b i c phase transformation was characterized.  Secondly, the temperature dependences  of cubic i c e I absorptions were observed i n order t o make s p e c i f i c c o r r e l a t i o n s of v  to  R(0* •••()) and t o discover the contributions of.hot  olK bands t o the band widths.  T h i r d l y , data from the two above methods were  used t o confirm previous i c e I band assignments-.  ;  CHAPTER ONE APPARATUS  1.1  The Perkin-Elmer 112-G Spectrophotometer  The Perkin-Elmer 112-G instrument i s a high r e s o l u t i o n s i n g l e "beam spectrophotometer  based on a double pass (model 9 9 ) g r a t i n g monochromator.  The monochromator employs a 7 5 lines/mm r e p l i c a echelette g r a t i n g which i s blazed t o r e f l e c t maximum i n t e n s i t y at 1 2 u i n the f i r s t d i f f r a c t i o n order and has a grating-ghost between 1 0 0 0 and 1 0 7 0 cm \  Unwanted orders are  eliminated by a fore-prism monochromator s i t u a t e d between a glober source and the g r a t i n g monochromator.  The fore-prism f i l t e r monochromator c o n s i s t s  of a 6 0 ° KBr prism mounted i n L i t t r o w c o n f i g u r a t i o n .  This monochromator  arrangement gives an instrument r e s o l v i n g power of 0.5 cm Spectral s l i t widths [ c a l c u l a t e d by S i e g l e r ' s method  or b e t t e r .  (109)],  are i n d i c a t e d  on the appropriate spectra. Thermal r a d i a t i o n i s detected by a thermocouple or PbS sensor. However, only 2 n d pass r a d i a t i o n i s chopped at 13 cps and amplified..in a standard model 1 0 7 a m p l i f i e r .  The 13 cps e l e c t r i c a l s i g n a l i s mechanically  r e c t i f i e d synchronously with the o p t i c a l chopper.  This d.c. s i g n a l i s  applied.to a conventional 1 0 mv Speedomax-G recorder. In the experiments t o be described, the P.E. 112-G was used from 5000  to  550  cm"'' with thermocouple detection i n a l l regions. -  was c a l i b r a t e d at each use with atmospheric H 0 and CO 9  The instrument  or with NH ( g ) .  39  Low temperature experiments on i c e are hampered i n the P.E. the small sampling area and severe atmospheric absorption.  The  112-G  by  spectro-  photometer was modified considerably to eliminate or reduce these and other difficulties.  At the PbS detector mount a simple e l l i p s o i d a l - p l a n e m i r r o r  system i s placed which produces a monochromatic source image i n free' space 50.5 cm from the e x i t s l i t s .  A second detection u n i t (thermocouple,'  focussing o p t i c s and p r e - a m p l i f i e r ) i s mounted i n s e r i e s with the added, o p t i c a l system. P.E.  112-G  These modifications o f f e r s e v e r a l advantages over standard  sampling f a c i l i t i e s .  For example, beam v i g n e t t i n g losses may  reduced and smaller samples may be used by p l a c i n g the sample at the image i n the new sample area.  be  source  A l s o , concurrent c a l i b r a t i o n and sample  observation i s p o s s i b l e when a c a l i b r a t i o n gas i s placed at the  standard  sample mount and the sample i s placed at the new sampling area.  In .addi-  t i o n , there i s 15 cm of o p t i c a l path length and ample surrounding f r e e space for mounting bulky accessories, i_.e_.  low temperature c e l l s .  A more impor-  tant advantage i s the decreased range of thermal r a d i a t i o n striking,samples mounted i n the monochromatorexit beam.  Tests i n d i c a t e a 5% energy l o s s  between the standard and modified detector c o n f i g u r a t i o n s . The complete instrument, excluding the new thermocouple detector u n i t , i s placed i n a m e t a l - p l e x i g l a s s drybox to reduce background atmospheric attenuation from H^O  and CO^.  The new detector u n i t has i t s own chamber,  and sampling accessories are used to couple the two chambers.  Spectrophoto-  meter c o n t r o l s are e a s i l y operated outside the drybox by simple mechanical extensions.  However, the g r a t i n g d r i v e and transmission are now l o c a t e d  at the f r o n t of the instrument outside the drybox.  A standard drybox a i r  lock and rubber gloves permit the i n t r o d u c t i o n and manipulation of convent i o n a l i r accessories i n the primary sample mount.  The N (g) 2  drybox  1+0  atmosphere i s c i r c u l a t e d through one of two p a r a l l e l molecular sieve columns (Linde 13X l / l 6 i n . p e l l e t s ) t o remove r e s i d u a l H^O and CO^.  When the c i r -  c u l a t i n g system i s i n use one column i s on-line while the other i s regenerated by combined evacuation and heating.  This system e l i m i n a t e s absorption from  atmospheric H^O but i s l e s s e f f e c t i v e i n reducing atmospheric CO^ absorption. To achieve maximum performance f o r fore-prism/grating monochromator assemblies of the P.E. 112-G type the two monochromators must transmit the i d e n t i c a l frequencies. Normally, the fore-prism monochromator s l i t s are set at the maximum widths which j u s t separate the various g r a t i n g orders. 'This allows the grating monochromator t o be scanned w i t h reasonable  performance  over v a r y i n g , l i m i t e d frequency ranges which depend on the region of the spectrum.  A mechanical servo system was designed t o l i n k the two mono-  chromators p e r m i t t i n g them t o be scanned i n near resonance.  Lengths of  c e r t a i n scans (at acceptable energy l e v e l s ) can be doubled by t h i s arrangement.  The design uses a v a r i a b l e r a t i o , b a l l and d i s c gearbox, reduction  gears, and l i n k i n g d r i v e s h a f t s .  A more powerful motor replaces the.-  standard g r a t i n g drive motor t o compensate f o r the added load.  Despite  the d i f f i c u l t y i n maintaining exact fore-prism/grating monochromator resonance, because of non-linear prism d i s p e r s i o n , the modification: improves the scanning c h a r a c t e r i s t i c s .  1.2  The Perkin-Elmer 1+21 Spectrophotometer  The Perkin-Elmer 1+21 instrument i s a moderate r e s o l u t i o n ( l cm  ,  double beam, n u l l recording g r a t i n g spectrophotometer of conventional design.. A Nernst glower source and thermocouple detector are used I n conjunction with i n t e r f e r e n c e . f i l t e r s (which e l i m i n a t e unwanted orders) and a  Hi  s i n g l e pass g r a t i n g monochromator.  Two removable, s e l f - c o n t a i n e d mono-  ehromators are r e a d i l y interchanged, p e r m i t t i n g r a p i d conversion o f the scanned frequency range.  Each interchange comprises the appropriate i n t e r -  ference f i l t e r s and- a p a i r of gratings mounted back-to-back on a cosecant drive:  One interchange i s used from H000 - 530 cm  1  2000 - 220 cm . 1  and the other from  G r a t i n g and f i l t e r operations are automated by pre-programed  mechanical and' e l e c t r i c a l servo systems.  S p e c t r a l s l i t widths [ c a l c u l a t e d  by the method o f Roche ( l l O ) ] are i n d i c a t e d on the appropriate spectra. Some minor up-dating m o d i f i c a t i o n s have been made, i_.e_. i n s t a l l a t i o n of a l a r g e r ( 0 . 8 amp) Nernst glower and a l t e r a t i o n o f the g r a t i n g switching mechanism t o prevent a r c i n g .  A l o c a l m o d i f i c a t i o n i s the p r o v i s i o n o f i n l e t  and exhaust p o r t s , i n the monochromator and source housings r e s p e c t i v e l y , p e r m i t t i n g the use o f a c i r c u l a t i n g dryer (manufactured by P.E. Bodenseewerk for the P.E. 2 2 5 spectrophotometer).  This drying u n i t i s remarkably e f f e c -  t i v e i n reducing atmospheric H^O absorptions but i s l e s s e f f e c t i v e w i t h respect t o CO,-,. The P.E. k21 was operated under the normal, recommended c o n d i t i o n s . S p e c i f i c conditions of operation are l i s t e d w i t h the r e s u l t s .  General con-  d i t i o n s o f operation are l i s t e d below. The automatic s l i t program was set a t 2 x 10.00 which gave s p e c t r a l —1  s l i t widths o f 3.86 and 2 . 2 2 cm  —1  at 3300 and 8 0 0 cm  respectively.  Spectra  were recorded on U.B.C. Chemistry Department c h a r t s , which were p r i n t e d on Rolland C o l o n i a l Bond rag content paper.  The charts have an inaccurate  frequency scale but frequency markers were applied w i t h the absorbance scale expansion switch t o c o i n c i d e w i t h the frequency readout drum. The drum was read t o ± 0.05 cm  1  and the marker was applied t o w i t h i n + 0 . 1 cm -1  but could be read from the charts t o ± 1 . 0 cm  -1  1  f o r 100 cm / i n . r e c o r d i n g .  U2  1.3  The Perkin-Elmer 301 Spectrophotometer  The Perkin-Elmer 301 g r a t i n g instrument i s a f a r - i n f r a r e d , double beam, recording spectrophotometer of the Halford-Savitsky type.  Two compli-  mentary, rea.dily exchangeable sources (a globar and a high pressure mercury lamp) are used t o cover the instrument range from 6 5 0 cm "*" t o lh cm"'". -  Combinations of i n t e r f e r e n c e f i l t e r s , s c a t t e r p l a t e s and c r y s t a l choppers (Csl  or BaF2) are used t o reduce scattered r a d i a t i o n and to' eliminate the  energy of unwanted d i f f r a c t i o n orders.  A standard, s i n g l e pass model 210  g r a t i n g monochromator i s used w i t h 3 p a i r s of complementary, r e a d i l y exchangeable gratings which are mounted back-to-back on kinematic mounts.  The  P.E. 301 o p t i c a l design produces a large image at the detector and n e c e s s i t a t e s a defector w i t h a l a r g e t a r g e t .  A golay sensor i s s u i t a b l e and i s  used over the f u l l instrument range.  S i g n a l t o noise r a t i o s may be doubled  i f the instrument i s operated i n the s i n g l e beam mode by r e p l a c i n g a s p l i t aperature ( l / 2 image) I-Io m i r r o r w i t h a f u l l apperature I or Io m i r r o r . An advantage of the P.E. 301 i s the chopping of source r a d i a t i o n before i t enters t h e sample chamber.  Therefore r a d i a t i o n o r i g i n a t i n g at the sample  i s not a m p l i f i e d . The P.E. 301 was modified by i n s t a l l i n g i n l e t and exhaust ports for t h e P.E. Bodenseewerk". dryer.  Severe background atmospheric water  problems can be almost completely eliminated by using t h i s dryer.  l.k  The Hornig-Wagner L i q u i d Nitrogen C e l l  The low temperature c e l l which proved most u s e f u l f o r obtaining spectra above 80°K was constructed from a design o r i g i n a l l y given by Wagner and Hornig ( i l l ) .  Our c e l l , which has been described p r e v i o u s l y  h3  (112, 57) has a glass body and r e s e r v o i r , a brass sample b l o c k , and C s l or AgCl windows.  Thermal contact between the sample window and sample block  was improved w i t h l a y e r s of s i l v e r conductive paint on contact surfaces. Temperature was measured w i t h a fused Cu-constantan thermocouple soldered "to the brass sample holder base.  Thermocouple wires and c e l l windows were  sealed t o the c e l l w i t h Cenco s o f t - s e a l Tackiwax.  This wax is- s l i g h t l y  p l a s t i c at room temperature, flows w e l l and i s i d e a l f o r vacuum s e a l i n g when extremely low pressure i s not r e q u i r e d . Although l i q u i d nitrogen coolant comes i n t o d i r e c t contact w i t h the brass sample b l o c k , the spectrophotometer "block temperature t o 83 t 3°K.  source beam r a d i a t i o n r a i s e d the  Because of non-ideal thermal contact and  low sample window thermal c o n d u c t i v i t y , sample temperature was considerably above t h a t of the block.  From melting point observations the sample window  temperature was estimated t o be 10°K higher than that of the sample block. Unless otherwise s t a t e d , a l l temperatures quoted i n t h i s work are not c o r r e c t e d f o r source heating. Two  sample d e p o s i t i o n tubes were used w i t h t h i s c e l l , one of a l l -  g l a s s and the other of metal c o n s t r u c t i o n . Both were mounted w i t h t h e i r t i p s 7mm  from the sample window surface.  At such a distance there are  l a r g e heat l o s s e s (from the sample tube t i p t o the window and c o o l i n g block) p e r m i t t i n g sample condensation at the c o l d t i p s .  Dangers of s e l e c t i v e IL^O  condensation or f r a c t i o n a t i o n of c l a t h r a t e mixtures at the tube t i p s were avoided by using e x t e r n a l heating on the s t a i n l e s s s t e e l tube, F i g . 1.1.  B  F i g . 1 . 1 The s t a i n l e s s steel- sample deposition tube: A - pyrotenax heater, B - Cu-Constantan thermocouple, C - deposition tube t i p , D - B - 1 9 c o n i c a l glass j o i n t , a Kovar metal glass j o i n t , and a brass cap, E - needle valve and "swage-lok" f i t t i n g s . a  I  1.5  1+5  The Duerig-Mador L i q u i d Helium C e l l  Spectra of samples below 83°K were observed through a l i q u i d helium c e l l which i s described elsewhere of Duerig and Mador (113).  (112, 57) and i s s i m i l a r i n design to that  A p r i n c i p a l m o d i f i c a t i o n incorporated i n our  c e l l i s the use of a vacuum seal/bearing which permits the helium container and sample holder t o be r o t a t e d through 9 0 ° f o r sample d e p o s i t i o n . Thermal contact between sample windows ( C s l or polyethylene) and the Cu sample b l o c k was improved by p a i n t i n g the contact surfaces w i t h s i l v e r conductive p a i n t . Sample block temperature was measured w i t h a Au-Co/Ag-Au thermocouple. . The thermocouple was c a l i b r a t e d at h.2°K from 77° to 273°K.  and w i t h  9  b o i l i n g l i q u i d s or slushes  A c t u a l sample window temperature was estimated t o be  10°K higher than the temperature  1.6  i n d i c a t e d with the  thermocouple.  The Metal L i q u i d Nitrogen C e l l  To prepare clathrate-hydrates by deposition from the gas phase one must f i r s t ensure that the guest and host components condense i n the proper stoichiometries.  In an attempt t o achieve the i d e a l c l a t h r a t e condensation  a l i q u i d nitrogen c e l l was constructed containing an evacuable sample chamber, F i g . 1.2. To help prevent f r a c t i o n a t i o n i n the sample chamber, one window-is embedded i n the cold block and the other i s thermally i n s u l a t e d from the f i r s t by a s t a i n l e s s s t e e l spacer r i n g (which provided the chamber body) and two t e f l o n gaskets.  Only one window i s cooled t o r e f r i g e r a n t tempera-  ture during the c e l l operation.  The sample chamber body and sample; tube  were heated by a Pyrotenax wire heater.  Sample block temperatures were  monitored with a fused Cu-Constantan thermocouple soldered to the s;ample block.  The i s o l a t e d sample chamber: A - Cu c o o l i n g block and "cold window, B - Cu-Constantan thermocouple, C r- pyrotenax heater D - coolant r e s e r v o i r , E - deposition and evacuation tube, F - pyrotenax heater, G - pressure, p l a t e and s t a i n l e s s s t e e l screws, H - sample window and holder, I - sample chamber, sample port and t e f l o n gaskets.  1  CHAPTER TWO METHODS AND MATERIALS  2.1  Water Samples and C l a t h r a t i o n M a t e r i a l s  Clathrate-hydrate guest molecules were e i t h e r Matheson compressed gases, Fisher  c e r t i f i e d reagents, or B r i t i s h Drug House  Bromomethane difluoromethane  (99.5%  (99.0%),  analar reagents.  pure), trichlorofluoromethane (99%), d i c h l o r o -  chlorotrifluoromethane  (99.0%)  and c h l o r i n e  (99«9%)  were used d i r e c t l y from t h e i r l e c t u r e b o t t l e s .  (99.5%)  was supplied i n a No. h c y l i n d e r and was used without p u r i f i c a t i o n .  Trichloromethane  ( C e r t i f i e d Reagent,  and broriioethane (C.R.  99-9%)  Chloromethane  p u r i t y ) , iodomethane (C.R.  99.9%  99-9%),  were p a r t i a l l y r e p u r i f i e d before each use by  f r e e z i n g and pumping o f f non-condensible i m p u r i t i e s . .Bromine l i q u i d (Analar Reagent,  99.0%)  was a l s o p a r t i a l l y p u r i f i e d by f r e e z i n g and pumping.  Guest  compound, p u r i t y was checked by i r vapour phase absorption spectra. Clathrate-hydrate host and i c e I compounds used were H^O, D^O, H0 2  ( 5 . 9 % HDO),  and D 0 {k.0% EDO). Before use the HgO water was d i s t i l l e d , 2  de-ionized and f i n a l l y degassed by s e v e r a l cycles o f f r e e z i n g and pumping. D^O was supplied by Merck, Sharpe and Dohme i n 1 0 0 g l o t s and had a stated p u r i t y o f 9 9 - 7 % ; D^O was degassed i n the usual way.  Mixtures o f D^O or  H 0 w i t h HDO were made by mixing 1*9.0 ml D 0 w i t h 1.0 ml HgO and 1*9.0 ml 2  g  HgO w i t h 1 . 5 ml DgO.  I n both cases the i s o t o p i c impurity was almost a l l  present as HDO a t e q u i l i b r i u m . Residual H 0 (or D 0 ) was s p e c t r o s c o p i c a l l y 2  undetected. taken.  2  No q u a n t i t a t i v e analyses o f the i s o t o p i c mixtures were under-  1+8  2.2  I n f r a r e d Windows and Sample Mounts  Choice of window m a t e r i a l i s tempered by the necessary a p p l i c a t i o n of thermal s t r e s s and e s s e n t i a l n o n - r e a c t i v i t y w i t h a p p l i e d samples.  The  latter  property i s important i n studies of water containing compounds s i n c e , as Mecke (103) found and S c h i f f e r (104) proved, t h i n hydrated l a y e r s may on a l k a l i h a l i d e c r y s t a l s .  form  C s l i s s u i t a b l e f o r a l l c r y o s t a t s used here since  i t i s r e l a t i v e l y s o f t and d u c t i l e and accepts the considerable thermal shock.  Only C l ^ * T^THgO samples reacted detectably with C s l windows.  experiment was repeated using an AgCl sample mount.  That  S i l v e r c h l o r i d e does  not transmit as widely as cesium i o d i d e over our range of i n t e r e s t , however AgCl i s s o f t and e a s i l y withstands thermal shocks.  A l s o , i t i s apparently  non-reactive t o c h l o r i n e and bromine. C e l l windows and a sample support used i n the P.E.  301 v^, experiment  were cut d i r e c t l y from commercial high density polyethylene (A powdered polyethylene was a l s o available).. to 160 cm  The windows were only used from 650  and through the temperature range 5°K t o 200°K.  cm  The polyethylene  was apparently non-reactive t o the clathrate-hydrate mixtures i n v e s t i g a t e d . Polyethylene i s not an e n t i r e l y s a t i s f a c t o r y sample support' since i t s thermal c o n d u c t i v i t y i s low and source heating may be high.  To counteract  source h e a t i n g , sample supports were pressed from powdered polyethylene embedded w i t h a brass or copper g r i d .  The method consisted of p l a c i n g a  wire g r i d between two l i g h t l y pressed (7000 p s i , unheated) 0.20  g discs,  heating t o the polyethylene flow temperature (130 t 5°K) under l i g h t pressure (1000 p s i ) and pressing t o 15,000 p s i while c o o l i n g t o l e s s than 35°C. The r e s u l t was a low s c a t t e r i n g p e l l e t w i t h 58% transmission at 3 6 l cm  h9  and 1 7 1 cm \  Energy transmission could "be improved by reducing the e f f e c -  t i v e r e f l e c t i n g surface area of the metal with f i n e r gauge wire. 2.3 A.  Preparation of Clathrate-hydrates Preparation of S o l i d Samples  Clathrate-hydrates with stoichiometries 1M'17 H^O,  and whose guest  molecules formed l i q u i d s at room temperature, were prepared by  repeated  cycles of cooling and warming s t o i c h i o m e t r i c l i q u i d mixtures between 77°K and 265°K.  To 3g HO  (0.17  moles) i n a 10 cm by  0.01 moles of l i q u i d guest compound.  1.2  The mixture was a g i t a t e d and  i v e l y immersed f o r about 30 sec i n an ice-water-sodium °K) and 30 sec i n a l i q u i d nitrogen bath. viscous s t a t e .  cm t e s t tube was added success-  c h l o r i d e bath ( 2 6 5  The sample was then warmed t o a  The procedure was repeated u n t i l a uniform, white s o l i d  formed—about 5 r e p e t i t i o n s f o r each sample.  Samples were stored over dry  ice f o r a short time before use. Clathrate-hydrate samples were prepared by two other methods, but such samples were not i n v e s t i g a t e d s p e c t r o s c o p i c a l l y . For c l a t h r a t e s i whose guest molecules are o r d i n a r i l y gases, the method of A l l e n ( l l 4 ) used with some m o d i f i c a t i o n : constructed.  was  a preparation c e l l s i m i l a r t o A l l e n ' s was  For c l a t h r a t e s whose guest molecules are o r d i n a r i l y l i q u i d s ,  the basic method of A l l e n (114) was used but with major m o d i f i c a t i o n s . ; A preparation c e l l of s i m i l a r dimensions to the one above, but with p r o v i s i o n for mechanical s t i r r i n g and l i q u i d guest a d d i t i o n , was constructed. prepared by these two methods were a l s o stored over dry i c e and were analyzed with a gas burette.  .•  Samples  50  B.  Preparation o f Stoichiometric Gaseous Mixtures  There are a number o f c r i t e r i a which must be s a t i s f i e d i n forming a s t a b l e s u i t a b l e sample.  For example, the clathrate-hydrate or i c e phase  must form a stable thermodynamic system i n the region k.2° t o 200°K.  Also,  the method must maintain the c l a t h r a t e stoichiometry, avoiding guest molecule l o s s by d i f f u s i o n and d i s s o c i a t i o n — t h e e q u i l i b r i u m d i s s o c i a t i o n . pressure of guest molecules must remain n e g l i g i b l e . As w e l l , since i c e has very large 0-H e x t i n c t i o n c o e f f i c i e n t s (VL^O) the samples must be t h i n — 3 microns or l e s s . Deposition of water vapour or a gaseous s t o i c h i o m e t r i c c l a t h r a t e mixture on a c o l d sample mount gives samples which s a t i s f y some of these criteria  (^3).  The quantity of a s t o i c h i o m e t r i c gas mixture which can be prepared i n a vacuum system i s c l e a r l y l i m i t e d by the s a t u r a t i o n vapour pressure of H^O at the given temperature and the mixing bulb volume.  The c a l i b r a t e d  mixing bulb ( i n c l u d i n g a side bulb) had a volume of 3 . 8 5 3  1  2.76  m i l l i m o l e s of HgO at 293°K and 1 7 - 5 3 Torr H 0 . 2  and contained  I f uniformly  deposited  on a t y p i c a l window w i t h a surface area of 7 cm , 2 . 7 6 m moles of H^O would 2  form a l a y e r approximately  70y  thick.  A  3.853  1  mixing bulb obviously.-  supplies enough sample f o r several deposits. o The molar r a t i o s f o r the 1 2 A cubic structure are  I 1  guest:  and 1 guest: 7 - 6 7 H 0, while the corresponding r a t i o s f o r the o 2  are very small. gas i n  3.853  1  H^O  tetragonal  and 1 7 A,cubic structures are 1 guest*8.6 HgO and 1 guest*17 H^O. the numbers of guest  5..75.  Clearly  mmoles required t o combine with 2 . 7 6 m moles of H 0  Measurement of at best o n e - f i f t h of 2 . 7 6  2  (0.U8)  mmoles of  at 20°C i s i m p r a c t i c a l due t o the large error i n measuring  51  small pressure d i f f e r e n c e s .  Gaseous guest a l i q u o t s were f i r s t i s o l a t e d i n  a 0.1039 l i t e r bulb and then expanded i n t o the  3.853  l i t e r mixing bulb.  The numbers of guest mmoles and t h e i r pressures i n the 2 bulbs are shown below f o r four c l a t h r a t e s t r u c t u r e s . Clathrate  mmole X 2.76mm H 0 2  P a r t i a l Pressure of Guest X 3.853 1 bulb 0.1039 1 bulb  1 X • 5-75 H"0  0.48  3.05 Torr  1  0.36  2.28  87.5I+  1 X • 8.60 H 0  0.32  2.01+  78.32  1 X  0.16  1.03  39.55  2  X  " 7.67 H~0 2  2  -17.0  H0 2  :  117.10 Torr  A f t e r the guest sample was expanded i n t o the mixing bulb at 20°C, the chamber was saturated with E^0 vapour from l i q u i d p r e v i o u s l y i s o l a t e d and degassed i n a side bulb. ten  The system was e q u i l i b r a t e d i n that s t a t e f o r  minutes before the l i q u i d H 0 was again i s o l a t e d from the mixing chamber. 2  Since the d e n s i t i e s -of the gases i n the bulb v a r i e d over the range from 17.3 for  x 10 g/cm f o r H"0 to 13.3 x 10 g/cm f o r B r 3  2  2  and 6.30 x 10 g/cm  3  CH^Cl, the mixing was forced by heating the lower hemisphere of ;the  chamber with an e l e c t r i c heating tape.  Such convection mixing was' main-  t a i n e d f o r a minimum of 30 minutes before sample d e p o s i t i o n . S u i t a b l y  ;  mixed gases were used e i t h e r d i r e c t l y from the mixing chamber, f o r deposit i o n i n the i s o l a t e d chamber of the metal l i q u i d n i t r o g e n c r y o s t a t , or were t r a n s f e r r e d to a portable 3.0 l i t e r bulb and attached t o a Duerig-Mador or Hornig-Wagner c r y o s t a t .  52  2.h  Preparation of I n f r a r e d Specimens A.  Low Temperature M u l l i n g  Clathrate-hydrates decompose i f mounted at 293°K by the usual spectroscopic means, but they are metastable  at 7T°K.  Low temperature mulls  of the clathrate-hydrates were prepared by an adaptation of the method B e r t i e and Whalley ( 1 0 7 ) used f o r the high pressure i c e s . Preparation of a s u i t a b l e spectroscopic sample required 0.5h.  approximately  A few grams of s o l i d c l a t h r a t e were placed in. l i q u i d nitrogen i n a ;  mortar at 77°K and ground manually f o r  10  minutes.  A small p o r t i o n of the  sample was placed i n the center of a mounted window and enough condensed l i q u i d mulling agent was dropped on the sample t o prepare a uniform suspension.  A second window was placed over the sample and secured i n place by  a retaining ring.  The window assembly was placed i n the sample block of a  standard Wagner-Hornig nitrogen c r y o s t a t . immediately  The assembled cryostat was  evacuated.  ,  Contamination of the sample by condensed atmospheric CO2 and H2O i s most l i k e l y t o occur during cryostat assembly.  Blank runs, and runs; with  mulling agent only, made i t c l e a r that l i t t l e impurity absorption was found even f o r the most intense H^O s t r e t c h i n g band [see a l s o Whalley  (107)].  R e c a l l i n g that the transmission spectrum of a mulled sample can be :  d i s t o r t e d from the i d e a l i z e d absorption spectrum, one can have confidence i n the low temperature m u l l spectra only i f d i s t o r t i o n i s minimized,by • a t t e n t i o n t o the p a r t i c l e s i z e of the sample and the r e f r a c t i v e index of the mulling agent.  Whalley ( 1 0 7 ) found that even f o r the most intense R^O  s t r e t c h i n g frequencies, where r e f l e c t i v i t y i s g r e a t e s t , the spectra; o f mulls were i n good agreement with those of t h i n f i l m s .  5  53  B.  I s o l a t e d Chamber Condensation  The sample chamber designed f o r approximate comparison of absorpt i o n i n t e n s i t i e s o f clathrate-hydrates was described i n d e t a i l i n s e c t i o n 1.6  ( page 4 5 ) .  A t y p i c a l run with t h i s i s o l a t e d sample chamber involved  degassing the metal surfaces, depositing the sample, annealing, and observing the absorption.  Those metal surfaces exposed t o the sample were degassed  by heating t o 393°K while evacuating t o  2.0  x  10 ^ -  Torr f o r two hours..  Sample block temperatures from 300°K t o a maximum of 393°K could be maintained with the coolant r e s e r v o i r empty.  Several blank spectroscopic runs were  made t o ensure that no i m p u r i t i e s were being deposited.  The sample tube  heater was l e f t on but the sample c o o l i n g block heater was shut o f f , while l i q u i d nitrogen coolant was added t o the r e s e r v o i r .  Twenty minutes a f t e r  the c o l l e c t o r p l a t e window had recooled t o 83°K, the background spectra were recorded from 5 5 0 cm  t o 4000 cm \  No impurity absorptions were observed.  For deposition the gaseous sample was expended i n short bursts ;down the heated sample tube i n t o the sample chamber which was held at 83°K . a f t e r the method of Barrer and Ruzicka ( 4 3 ) . 3^3 K 0  With the sample tube at . ;  and the sample tube heaters on, some heating of the s t a i n l e s s s t e e l  spacer occurred which aided the thermal i n s u l a t i o n of the second, "hot" window.  The C s l sample mounts are poor thermal conductors and too -;rapid  a.sample condensation may produce s u f f i c i e n t l o c a l i z e d heating t o permit s e l f - d e v i t r i f i c a t i o n — d i f f u s i o n of the guest molecules i n t o c l u s t e r s or d i f f u s i o n out of the l a t t i c e  completely.  Subsequently, samples were annealed t o temperatures between 1 6 0 l80°K  for  5  to  10  minutes.  The sample chamber was not subject t o pumping  5H  and the sample tube was warmed to 3H3°K p r i o r t o annealing. The sample block heater was used only i n the i n i t i a l stages of annealing, ji.e_. up t o 100°K.  The warming was completed by passing a stream of dry, room tempera-  ture Ng gas through the coolant r e s e r v o i r . cooling are described i n s e c t i o n 2.5.  The rates of warming and r e -  A f t e r r e c o o l i n g the sample block to  83°K, the sample tube heaters were shut o f f and the spectra were observed i n the desired range. the  The s p e c i f i c instrument conditions are l i s t e d w i t h  results.  •: C.  Open Chamber Condensation  Deposition of gaseous samples on a cold s u b s t r a t e , which was-., exposed to the cryostat c e l l body,. was used f o r both the Wagner-Hornig cryostat and the Duerig-Mador  cryostat f o r observation on e i t h e r the P.E. h21 or  P.E. 301 spectrophotometers.  Gases used were e i t h e r vapours evaporated  d i r e c t l y from l i q u i d H^O,  or H^O/D^O mixtures or were water/guest mix-  D^O  tures prepared as described i n s e c t i o n 2 . 3 .  Cryostats were degassed by  evacuation f o r a minimum of 10 hours before c o o l i n g w i t h l i q u i d nitrogen to 83°K.  To ensure a minimum c o l l e c t o r p l a t e temperature, the source beam  was blocked and the cryostat was allowed to e q u i l i b r a t e f o r 15 to 20 minutes. T y p i c a l l y , samples were deposited as f o l l o w s . (at  Ten ml of sample  a pressure at 8.7 T o r r ) , were i s o l a t e d i n the sample deposition tube.  Several of these a l i q u o t s were passed i n bursts onto the c o l l e c t o r p l a t e at 83°K.  The cryostat vacuum jacket was i s o l a t e d from the pumping s t a t i o n  during sample deposition to minimize d i s t o r t i o n of the sample gas stream. The HO  v  s t r e t c h i n g region was monitored b r i e f l y a f t e r each burst ..to  55  determine the i n t e n s i t y of absorption.  We estimated that the sample  thicknesses ranged from 0 . 6 u f o r very t h i n samples t o s e v e r a l microns f o r t h i c k samples.  The rates of deposition were estimated as 0.04 g/cm -h.  Such deposits were subsequently annealed by the standard procedure. 2.5  Devitrification  As was discussed i n the i n t r o d u c t i o n , deposition of water vapour on. a l k a l i h a l i d e substrates held near 80°K has l e d t o doubts of sample c r y s t a l l i n i t y and confusion i n the i n t e r p r e t a t i o n of the various i r r e s u l t s .  The  s i t u a t i o n was c l a r i f i e d by Beaumont, Chihara and Morrison ( 6 5 ) through corr e l a t e d heat capacity/x-ray d i f f r a c t i o n studies.  Their work  accentuated  the d i f f e r e n c e s i n sample c r y s t a l l i n i t y among the i r i c e spectra of various authors ( 1 0 5 , 1 0 6 , 9 5 , 9 7 ) and c l e a r l y demonstrated the processes of d e v i t r i f i c a t i o n and t r a n s i t i o n l i n k i n g the i c e I a l l o t r o p e s .  ;  In order t o make comparative i r studies of i c e I and clathrate-.; hydrates as a f u n c t i o n of temperature i n t h i s work, one had t o reproducibly form the i c e I a l l o t r o p e s . However, no attempt was made t o r e s t r i c t s e l f annealing by l i m i t i n g deposition rates t o that recommended by Beaumont et al. —  0.04 g/h-cm^.  That the samples d i d not undergo a high degree of  self-annealing was demonstrated by the broad, f e a t u r e l e s s i r absorption bands observed immediately a f t e r deposition. A t t e n t i o n was i n i t i a l l y d i r e c t e d t o annealing condensed, v i t r e o u s samples t o the common i c e phase, hexagonal i c e I , whose transition-temperature from cubic i c e I l i e s between  200  and 250°K.  The v i t r e o u s sample was  warmed t o the hexagonal t r a n s i t i o n at 5-0 t o 1 2 . 5 deg/min from 83°K t o 205 - 5°K (with the sample source beam o f f and no pumping i n the sample chamber).  I t was recooled t o 83°K at  50  deg/min a f t e r being held f o r  56  2 to 3 min at the maximum annealing temperature.  Unfortunately, the samples  were unstable above 195°K with respect t o t h i s procedure. In view of the great d i f f i c u l t y with sample s t a b i l i t y and the low rate of t r a n s i t i o n from cubic t o hexagonal i c e , f u r t h e r attempts t o d e v i t r i f y at 2 0 5 ± 5°K were abandoned. Further extensive t e s t s showed that t h i n f i l m s of H^O  could be  annealed under vacuum t o 1 8 5 + 5°K from 8 3 t 5°K (at between 5 and 1 2 . 5 deg/min with no pumping and the source beam o f f ) , and maintained l85°K  f o r up to  5  minutes.  s t a b l e at  The samples were s u c c e s s f u l l y recooled at 5.0°K/min  with l i t t l e l o s s of sample as detected by s l i g h t l y diminished absorption. According t o the data of Beaumont e_t_al_. ( 6 5 ) t h i s should give a w e l l developed p o l y c r y s t a l l i n e cubic i c e sample, since the t r a n s i t i o n temperature was w e l l exceeded and the r a t e of t r a n s i t i o n i s f a s t , :L_.e_. a few minutes.  Samples  observed spent a minimum of 9 minutes '-at (or above) the transition;; temperat u r e , 150°K.  Before spectroscopic i n v e s t i g a t i o n s began, the t h i n f i l m s were  thermally e q u i l i b r a t e d f o r 2 0 minutes with the sample source beam on. Discussion of the nature of samples formed,, by condensing and  anneal-  ing s t o i c h i o m e t r i c gaseous mixtures i s l e f t u n t i l Chapter 6. : 2.6  Temperature V a r i a t i o n Methods  The purposes of t h i s work are t o study the v a r i a t i o n s of i c e and c l a t h r a t e spectra as a f u n c t i o n of temperature and to show that gas condensation and d e v i t r i f i c a t i o n gives l e g i t i m a t e c r y s t a l l i n e samples. same sample heating and i r observation techniques were used f o r both vitreous and c r y s t a l l i n e sample s t u d i e s .  :  The  57  A l l the samples studied.as a f u n c t i o n of temperature were formed i n e i t h e r the glass l i q u i d nitrogen c e l l or the l i q u i d helium c e l l by the methods of s e c t i o n 2 . 4 ( c ) .  The nitrogen c e l l was mounted only i n the P.E.  421 and was used f o r p r e l i m i n a r y observations between 8 3 ° and 200°K.  The  helium c e l l was mounted e i t h e r i n the P.E. 301 or i n the P.E. 4 2 1 spectrophotometer, and was used f o r the d e t a i l e d studies between 4 . 2 ° and 200°K. Two methods of warming these c r y o s t a t s were used:  l ) natural,  unforced warming due t o r a d i a t i v e and conductive heating, and 2 ) warming with a stream of N (g). 83°K  The helium c e l l was allowed t o warm from 4 ? t o  by the n a t u r a l heat i n f l u x a f t e r evaporation of the l i q u i d helium.'  Above 83°K the helium c e l l was warmed with N,-,(g) (293°K) passing slowly through the r e s e r v o i r . The nitrogen c e l l was held at 4 t o 8 constant temperatures  (± 3°K) f o r d e v i t r i f i c a t i o n  studies (at 83°K N g ( l i q ) was used and  at higher temperatures 1-2 ml of N ( l ) were added t o the empty r e s e r v o i r 2  at appropriate i n t e r v a l s ) . Sets o f spectra were obtained by continuously r e c y c l i n g the spectrometers over the s p e c t r a l range desired as the c e l l warmed continuously, or spectra were recorded at c e r t a i n successively higher constant ( t 3°K) temperatures.  Some sets of spectra were a l s o recorded at s u c c e s s i v e l y cooler  constant temperatures  (t  3°K) from  190  -  10°K  t o 83°K a f t e r  as a check on the r e v e r s i b i l i t y of absorption maxima s h i f t s .  devitrification  CHAPTER THREE ICE I : EXPERIMENTAL AND RESULTS  This chapter i s comprised of four main s e c t i o n s .  The f i r s t s e c t i o n  contains the r e s u l t s from temperature v a r i a t i o n studies of v i t r e o u s i c e I — observations of the v i t r e o u s - c u b i c phase transformation.  The second section  contains the r e s u l t s from temperature v a r i a t i o n studies of cubic i c e I — observations of Av/AR f o r c r y s t a l l i n e i c e .  The t h i r d s e c t i o n uses the  r e s u l t s of sections one and two as an a i d i n assigning the> i c e absorptions. The fourth section i s a b r i e f summary of the r e s u l t s . 3.1  The Vitreous-Cubic Ice Phase.Transformation  The spectra recorded during v i t r e o u s - c u b i c phase transformations: exhibited diminishing oligomeric peak heights (I) and i r r e v e r s i b l e peak frequency and h a l f - h e i g h t width A.  shifts. Experimental  Two v i t r e o u s i c e I (HgO) samples were prepared (by the method of section 2 . U ( c ) ) and observed i n the glass l i q u i d nitrogen c e l l ( s e c t i o n Sample A was deposited on C s l at  82  -  3°K, warmed from  82°  to  l69°K  l.h)  i n five  stages over 1 0 5 min and was annealed t o a maximum temperature of 1 8 5 t 3°K. Sample B was deposited on C s l at  8 l ±  3°K, warmed from  8l°  to  l6l°K  i n four  stages over 1 2 0 min and was annealed t o a maximum temperature of 1 8 2 i 3°K. Seven spectra were recorded f o r each of samples A and B during d e v i t r i f i cation.  59  The basic spectrophotometer conditions were described p r e v i o u s l y ( s e c t i o n 1.2). For these samples (A and B) P.E. 421 spectra were recorded at 100  cm "Vin. No.reference c e l l compensation was used, but the i n s t r u -  ment was purged w i t h dry N^(g).  The l i q u i d nitrogen c e l l and the spectro-  photometer sample compartment were masked so that the sample compartment was a l s o purged. B.  Results of D e v i t r i f i c a t i o n  I n f r a r e d absorption spectra representative of samples A and B are shown i n F i g . 3.1 ( t o p ) .  Frequency and h a l f - h e i g h t width (Av ) data were  derived independently, but by the same methods, f o r the two sets of spectra. Peak absorptions were determined (to w i t h i n i l O cm "*") at the i n t e r s e c t i o n of l i n e s along the band s i d e s , while shoulders were determined ( t o w i t h i n i l 4 cm  at the point of minimum slope.  Band heights were measured on  the absorbance scale ( i ) from the b a s e l i n e and Av^ was measured at (1/2). ( i ) The E f f e c t of D e v i t r i f i c a t i o n on the Peak Maxima The v i t r e o u s H^O i c e I absorption maxima are p l o t t e d i n F i g . 3.2 as a f u n c t i o n of i n c r e a s i n g temperatures.  Important parameters derived from  these graphs are given i n Table I I I . I .  Although d e v i t r i f i c a t i o n s of D^O  i c e and HDO bearing i c e were not observed i n d e t a i l , data from such samples, immediately before and a f t e r d e v i t r i f i c a t i o n , are included i n Table I I I . I f o r comparison t o H^O data. ranges are i n d i c a t e d f o r v^,  I n F i g . 3.2, the transformation temperature and  + v^,.  Transformation  was assumed  t o have begun at the onset of peak s h i f t and was assumed t o have f i n i s h e d upon r e v e r s a l of peak s h i f t d i r e c t i o n .  4000  3000  i  2000  Frequency c m  1000  - 1  F i g . 3 . 1 Representative spectra of v i t r e o u s and cubic ices at various temperatures. Top:.. . A....-, ..cryostat.. background at 83°K.. (compensated),. B - H 0 i c e I at 8 3 ° , C - sample B annealed t o l 8 5 ° K and recooled t o 83°K (cubic i c e ) , D - sample ' G at T°K, -and E -- cubic ice' C H 0 ( 5 . 9 W HDO)) at 83°K; - Bottom: A - cryostat background, B - D 0 ( U . 0 % HDQ) v i t r e o u s i c e at 83°K, C - sample B annealed to 185°K, cubic i c e at 83°K. 2  2  2  y  I80-  140-  IOO2220  0  rr  D H '< tK l±J  2230  3370  33 30  3350  1570  32IO  3230  3250  840  3145  3165  3185  180'  140-  IOO OA  UJ  1590  16IO  1630  1650  180-  140  IOO 800  820  F R E Q U E N C Y C M -I Fig. 3.2  S h i f t s of H^O frequencies during the vitreous-cubic i c e phase transformation and. subsequent behaviour of cubic i c e . The f u l l c i r c l e s and t r i a n g l e s are from spectra recorded during warm-up from 83°K to l85°K. The open c i r c l e s . and -triangles give the behaviour a f t e r annealing.  OA H  62  Table I I I . I  H0 2  (D 0) 2  The frequencies of cubic and v i t r e o u s i c e I at 82°K, t h e i r d i f f e r e n c e s , the transformation range and the cubic i c e absorptions temperature dependences.  Ice Iv  Ice Ic  82°K  82°K  -1 cm V  1 T + V  V  3  3v  3367 ± 7  3253 ± 5 (2436)  (21*13)  ±  7  2220 + 5 (1617) 1660  v  2  V  V  3217 ± 311*9  (2321)  ±  5  l60l+  5  + 5°K  5  c  Av/AT cm /°K -1  0.26 + 0.05 (0.16)  -36 (-23)  125 - ll*5  0.20 (0.13)  -1+2  120 - ll*5  0.25  (0.18)  +15  115 - 130  -56  -0.11 (-0.11)  (+18) + 5  Ice I  130 - 11*5  -27  (-3U)  (-51)  115 - 130  0.36  1570  81*6 1 7 -- )  881  +  7  :(66l)  802 ± 5  5  (627)  675 ± 7 535 ± 7 212.8 + 1  .  :  +35  115 - 130  +31 (+27)  +  7  690  ±  7  +15  570  ±  7  +35  .227.8  + 5  +15  1  -38  -0.19 (-0.16)  (--)  833 ±  (600)  (0,11*)  (-18)  (1191*)  .780  Vip  7  ± 7  .2235 ± ;  Transformation Temperature Range  -1 cm  .(1635)  1570 (1212) (  R  331*0 + (21*65)  (2372) R  -1 cm  (2k99)  3191  l  v  Av Ic-Iv 82°K  115  - 130  -0.18 (-0.12)  HDO v  OH  3301* + 1 (21*37)  : 3266 +  (2kh2)  (21*16)  0.20 ± 0.005 (0.123 ± 0.005)  (-21)  (2392) •• 85!+ ± 1 . 5 792  ±1  819  +0.5  — +27  -O.I5I+ t 0.022  -0.11*7 ± 0.012  63  There are f i v e important e f f e c t s t o n o t i c e :  l ) between  115°  and l 4 5 ° K  the molecular modes s h i f t towards lower frequencies while the l a t t i c e modes s h i f t towards higher frequencies, 2 ) the r e v e r s a l of peak s h i f t d i r e c t i o n , 3) the i r r e v e r s i b i l i t y of the d e v i t r i f i c a t i o n t r a n s i t i o n s , 4 ) the large f r e quency displacements between the same bands i n cubic and v i t r e o u s i c e I at' 82°K,  and 5) the r e v e r s i b i l i t y of peak s h i f t s i n cubic i c e I . These e f f e c t s can be seen i n F i g .  3.2  f o r the v^(E^O)  data.  The f r e -  quency was constant up t o 1 2 5 i 5°K, and s h i f t e d i r r e v e r s i b l y by 3 6 * 2 c m to lower frequency between 1 2 5 t 5 and 142 t 5°K.  -1  The frequency a t t a i n e d a  p o s i t i v e , r e v e r s i b l e temperature dependence of +0.23 cm~V°K above l 4 2 ° K . Subsequent warming and c o o l i n g cycles revealed a sample with an approximately l i n e a r frequency-temperature  dependence between 82°K and l 8 0 ° K . The'remain-  ing absorptions of i c e I behaved s i m i l a r l y during d e v i t r i f i c a t i o n .  However,  a l l i n t e r n a l modes e x h i b i t e d p o s i t i v e , and a l l l i b r a t i o n a l modes e x h i b i t e d negative temperature dependences a f t e r d e v i t r i f i c a t i o n . (ii)  Oligomeric H 2 O Absorptions In a d d i t i o n t o a l l the expected v i t r e o u s i c e I absorptions, weak ab-  sorptions were observed near the frequencies p r e v i o u s l y reported ( 1 1 5 ) f o r oligomeric HgO and cm  -1  i n H 0 and 2  Weak peaks  D2O.  2720  cm  -1  (0.01  abs u n i t s ) were found near  i n D 0 and HgO shoulders near 2  3647  cm  -1  3690  (Fig.  3.3).  They p e r s i s t e d only up t o 1 2 5 1 5°K and d i d not reappear upon r e c o o l i n g the sample.  Half-height widths were between 1 5 and 2 0 cm  No d e t a i l e d study  was made f o r oligomers, but data from s e v e r a l samples are compiled i n Table III.II.  FREQUENCY 3900  CM"  1  3700  3500  o.o-  0.40.52900  2800  2700  FREQUENCY  2600  CM"  2500 1  F i g . 3 . 3 Oligomeric HgO and D 2 O absorptions i n v i t r e o u s i c e I at 83°K: l ) v i t r e o u s H 2 O i c e , 2 ) cubic H 2 O i c e , 3) v i t r e o u s D 2 O i c e , h) cubic D 2 O i c e . The features were more or l e s s accentuated depending on the d e p o s i t i o n r a t e .  65  Table I I I . I I  Oligomeric HvpOCDgO) and V 3 i r absorptions seen f o r v i t r e o u s i c e I samples before and during warm-up. The V3(H"20) absorptions were weak peaks and the v;j_(H20) and V 3 ( D 2 0 ) absorptions were weak shoulders. One V 3 ( D 2 0 ) absorption i s given i n brackets. Temperatur e of Observation,  H 0 2  (D 0) 2  82  -1  -1  cm V  3  V 1  110  94  85  cm  cm  -1  3692  3687(2724)  3689  3677  3658  3674  3637  3650  —  —  °K  cm  140  125  -1  cm  3690  -1  -1  cm  3690  3647  —  —  —  •  3640  —  ( i i i ) The E f f e c t of D e v i t r i f i c a t i o n on H 2 O Half-height Widths A comparison of H 2 O spectra B and C i n F i g . 3 . 1 (top) shows that the composite bands  v  3>  +  V  T^' ^ 2 ' ^ F J V  an<  V  ^ ^ R' R V  V  +  V  T^  a  r  e  s n a r  P  e r  i n cubic i c e I than i n v i t r e o u s i c e I . Half-height widths f o r these composite bands from the sets of H 2 O spectra (samples A and B) were measured as a f u n c t i o n of temperature, F i g s . 3 . 4 and 3 . 5 . data a r i s e s from several sources:  [The large s c a t t e r i n the  l ) the choice of baseline (± 2 cm "*"),  2 ) the error i n assessing I and TJ- I f ° intense .peaks (± 5 cm "*"), and r  3) atmospheric attenuation or d i s t o r t i o n of the V 2 band.] are compiled i n Table I I I . I I I .  The parameters  Az/  150  2  A  -  Az/  1,3,  H- T  O  LLJ  D h  A  <  A  LLJ Q_ LLJ  1 0 0 -  h  A A  O  Q  AA  70 180  2 0 0  2 2 0  270  300  •  o May A May  «4 ~i  r  I  '  1  29 3 0  1  1 400  1  350  H A L F - H E I G H T WIDTH  CM"  1  F i g . 3.H The s h i f t s of H 0 h a l f - h e i g h t widths f o r the composite H 0 bands (v , vp+vrp.) and ( v 2  VI+VT)  2  R  during the v i t r e o u s - c u b i c i c e transformation' and subsequent" to"'annealing.  c i r c l e s and t r i a n g l e s are f o r the" uhannealed sample warm-up. are f o r the annealed sample warm-up.  ls  V3.  Solid  Open 'circles and t r i a n g l e s  Az/  (z/ /2z/  2  2  )  R  A  -  50 -  ••..AO A  A  *\o '• A  -/  .•j  •"" OO A  *  /  A  May May  TO  A  -  1  280  29  •• *  30  I  "-T  A  /  /  4/ /  / /  •  O  ^  O /  /  •AAA  O  A  i  -  -  T  —  300  HALF-HEIGHT  r  1  —1  1  1  1  350  WIDTH  CM"  1  g. 3.5 The s h i f t s of h a l f - h e i g h t width f o r the composite H 0 2  ( v , 2 V R ) hand during the vitreous-cubic phase t r a n s f o r 2  mation and subsequently f o r cubic i c e I . S o l i d points were obtained during v i t r e o u s sample warm-up from 8 3 ° to l 8 5 ° K . samples.  Open points were obtained from annealed  68 Table I I I . I l l  The h a l f - h e i g h t widths of the v i t r e o u s and cubic R^O i c e composite bands at 82°K and t h e i r temperature dependences f o r cubic i c e I .  Composite Band  Vitreous A J-/2 82°K-1 cm  H 0 2  (v , v , v 1  3  + v ) T  2v )  (v ,  R' R V  V  +  Av  .  322 + 7 .350  R  2  (V  x  Cubic  10  220 + 5  L/2  82°K -1  Difference Av  Transition  L/2 Temperature Range °K  cm  82°K-1. cm  287 ± 5  -35  115 ± 5 - 130 + 5  365 ± 10  +15  115 ± 5 - 140  195+3  -25  115 ± 5 - 150 + 5  5  During warming from 82°K the h a l f - h e i g h t widths of v i t r e o u s i c e spectra s h i f t e d i r r e v e r s i b l y over the transformation temperature range.  Subsequent  warming-cooling c y c l e s showed that the cubic i c e spectra half-widths s h i f t e d r e v e r s i b l y and that the v i t r e o u s and cubic data agreed above 150°K. There are s p e c i f i c d i f f e r e n c e s among the three sets of composite bands (see F i g s . 3.4 and 3.5). These are as f o l l o w s :  l ) the s t r e t c h i n g  band Av ^ i n c r e a s e d , 2) the bending band A v ^ decreased and 3) the l i b r a t i o n a l band A v  35  appeared t o increase w i t h i n c r e a s i n g temperature.  A l s o , the  h a l f - h e i g h t width i n i t i a l l y increased during d e v i t r i f i c a t i o n , although i t was expected t o decrease. Annealing e f f e c t s on v^HgO) were not observed i n d e t a i l , but the d i f f e r e n c e s between v i t r e o u s and cubic i c e at 83°K were measured. data a r e 62.8 cm  and 23.2 cm  The  f o r v i t r e o u s and cubic i c e . A l s o , the  69  absorbance of Vp(cubic), I = 1.285, was almost e x a c t l y double that of Vrp(vit.). 212.8  The v i t r e o u s V^(H 0) absorption features were:  a peak at  2  t 0.5 cm" 'and f a i n t shoulders centered at 301 t 3 and 271 + 3 cm"'. 1  3.2 A.  1  Temperature Dependence of Cubic Ice I Absorptions Temperature Dependence of HDO Absorptions  The four observed HDO  absorptions provided the best measurements of  band parameters as a f u n c t i o n of i n c r e a s i n g temperature i n cubic i c e I . ( i ) Experimental  •  Three samples of D20(4.00% HDO)  and two samples of H 0 2  (5-9W  HDO)  were prepared ( s e c t i o n 2.4(c)) and observed i n the l i q u i d helium c e l l (section 1.5). from  85°  Samples C(l,2,3) were deposited at 8 5 1 3°K on C s l , warmed  to l87°K i n  9  minutes, annealed at 187  recooled t o 84°K i n 4 minutes.  t  3°K f o r 2 minutes and were  The r e s u l t i n g cubic C samples were then  cooled t o 4.2°K and observed f o r 3 hours before warming began: from k.2°K  t o 200°K r e q u i r e d  6-8  hours.  Warming  Samples D(l,2) (5-94$ HDO  i n H 0) 2  were deposited at 8 3 t 3°K on C s l , warmed t o 1 8 8 ± 3°K i n 8 minutes, annealed at 1 8 8 ± 3°K f o r 4 minutes and r a p i d l y recooled t o 83°K.  Samples  Dl and D2 were then t r e a t e d as i n C above. During warming sets of P.E. 421 spectra were recorded f o r each sample under i d e n t i c a l spectrophotometer c o n d i t i o n s .  The basic spectrometer con-  d i t i o n s were the same as those f o r samples A and B ( s e c t i o n 3.1 a) w i t h small v a r i a t i o n s .  For example, HDO peaks were recorded at 20 cm " V i n or  2 cm "VdiVj and a 10 cm path the  gas c e l l ( i n the reference beam) was used w i t h  Bodenseewerk u n i t f o r e f f e c t i v e instrument purging.  Among the three  TO sets of C sample spectra, frequencies were reproduced t o w i t h i n t 2 cm 1T0°K and ± 1 cm  -1  at h°K,  1  at  while among the two sets of D sample spectra f r e -  quency r e p r o d u c i b i l i t y was only ± 3 cm  1  at  or h°K.  l60°  T y p i c a l HDO  spectra were shown i n F i g . 3.1. ( i i ) Results of Warming Cubic Ice Containing  HDO  Frequencies, h a l f - h e i g h t widths and absorbances were obtained as i n section 3.1(b).  However, t o i n h i b i t personal systematic b i a s the spectra  were analyzed randomly with respect t o temperature and during a n a l y s i s no reference t o temperature was permitted.  Because of 2 cm ^ / d i v r e c o r d i n g , HDO  peak frequencies were- read t o ± 0.5 cm .  No attempt was made t o subtract  1  the 3v (HpO) weak absorption from v K  ^  VQ^(HDO)  OD  (HDO)  frequencies- are s l i g h t l y low.  absorption and  Baselines f o r absorbances and h a l f -  height widths were drawn from 339 * to 31^0 cm 1  cm"  1  to 23^0 cm (a) HDO  -1  consequently  f o r v (HD0) and from  -1  QH  2H80  f o r v (HD0). Qr)  frequencies.  The behaviour of v , (HD0) frequency w i t h i n -  creasing temperature i s shown i n F i g . 3.6.  r  TJ  The data were derived from one  set of spectra during a s i n g l e warming period.  Errors i n instrumentation  and i n the methods of data evaluation l i m i t e d the p r e c i s i o n t o t 1 cm  .  1  Pertinent parameters from F i g . 3.6 are compiled i n Table III.IV., The low temperature l i m i t i n g frequency was obtained by e x t r a p o l a t i n g the data to 0°K.  Although the data are non-linear, they can be approximated by  two s t r a i g h t l i n e s — a low and a high temperature l i n e .  The low and ..high  temperature frequency dependences were evaluated from these l i n e s and the " f r e e z e - i n " temperature was chosen as t h e i r point of i n t e r s e c t i o n .  There  i s a s l i g h t i n d i c a t i o n of i r r e g u l a r behaviour between U5° and 70°K ( F i g . 3 . 6 ) . Sample sublimation above l 8 0 ° K d i d not appear t o a f f e c t the frequency data.  z^(HOD) Frequency cm 3260  2 8 0 -  3270  3280  -1  3290  3300  6 0 -  4 0 -  >  CD  ^: CO  CD CD  2 0 -  2 0 0 -  8 0 -  6O-  C N  CD Q  CD D O  ^_ C D TEN  A C  4 0 -  2 0 -  IOO-  o this work ° Ford and .Falk  8 0 -  6O-  ^ (HOD) D  4 0 -  2 0 -  • this work • Ford and Falk  •4  O-  24IO  2420  2430  2440  2450  CHOD) Frequency cm -1 F i g . 3.6  The s h i f t s of HDO s t r e t c h i n g frequencies f o r cubic i c e I . The temperatures are not corrected f o r source beam heating, +10°K should be added. Open points represent V Q J J ( H D O ) and s o l i d points represent V O D ( H D O ) - Data of Ford and Falk (100) i s included f o r comparison.  —1  H  72 Table  The low temperature behaviour o f the HDO s t r e t c h i n g modes i n the H 0 and D 0 environments of cubic i c e I ,  I I I . I V  2  2  v  -1  Low Temperature L i m i t Ratio  v /v 0 H  cm  Q H  3263.5  1.354  Q r )  v  (HD0)  -  +  0.047 ± 0.005  Linear High Temperature Dependence  cm / K .  0.200  "Freeze-in"  _1  °K  Temperature  °K  Irregularities  Behaviour of compiled i n Table  0  VQ (HD0) D  I I I . I V .  t  0.04T-±  0.005  i s shown i n F i g .  : -  3.6  1  0.005  0 . 1 2 3 ± 0.005  80 + 5 45  +  0.001  cm / K 0  (HD0)  2412.0  1  Linear Low Temperature Dependence  _1  0 D  68  +  5  ^60  70  and some parameters are  The comments made above concerning  VQ^(HDO)  apply equally w e l l t o v^(HDO). The peak and shoulder near 8 0 0 cm [ t r a c i n g C, bottom of F i g . v (HD0) o  R  3.1]  + v ( D 0 ) respectively. m  o  1  2  i n the samples of DgO ( 4 . 0 % HDO)  were assigned t o HDO l i b r a t i o n s ,  v (HD0) R  and  (For ease of notation v_ + v_ i s designated n  1  v '.) Temperature v a r i a t i o n s of v (HDO) and V '(HDO) are shown i n F i g . 3-7 R K n and some parameters are compiled i n Table  I I I . V .  As shoulder p o s i t i o n s are  '  z/j Frequency cm  -1  180-  220 1  • •  60-  Kel ur a  •  •  •  • • •  80-  60-  Te  E  40-  20z/  -  uO i800  1 1  , 1 8IO  • •  0  •  0  • •  0 0  • • • •• • • • • •• • • • •  •  0 0  0 0 0 °0 0 0 0 0 0  •  0  •  • • •  • • •  0 00 0  ^  %gog  (H O)  T  •  z  a  1,  i/ -11  11 820  11  1 830  1 T 840  • •  ••  0  (HOD)-  R  v  • •1 1  R l  ( HOD)  1 1 850  •• 1  1  • • 1 86C  Frequency cm  -1  R  F i g . 3.7  • 0  cn Q) O CD  230 .  •  •  20-  Q) Q) ^_ 100-  CD  —  .0  •  c en  1  0  40-  >  225  „  The s h i f t s of v ( H D O ) , ' ( K D 0 ) and ( H 2 0 ) f o r cubic i c e I during, warm-up. The l i b r a t i o n a l shoulder v ' ( H D O ) i s assigned as R ( H D O ) + T(E>2 )' Temperatures are uncorrected f o r source heating. V  v  R  r  T  v  R  V  u  74  Table I I I . V  The low temperature behaviour o f the HDO l i b r a t i o n a l modes i n cubic i c e I f o r d i l u t e s o l u t i o n s of HDO i n H 2 O and D 2 O .  v (HDO)  v (HDO) + v ( D 0 )  R  Low Temperature Limit  cm  Linear Low Temperature Dependence  1  823.3  R  ± 0 . 5  cm" /°K  < -0.02  cm  -0_.l4T  T  2  ±1.5  856.2  < -0.04  Linear High Temperature Dependence  /°K  ±  0.012  "Freeze-in" Temperature  °K  55 t 5  Irregularities  °K.  105 - 1 2 0  -0.154  ±  0.022  65 ± 5 I-  d i f f i c u l t t o determine a c c u r a t e l y , v ' data have a higher e r r o r than v„—in t h i s case ± 1.5 cm  Spectra and data were obtained as i n section'3.1.  (b) HDO h a l f - h e i g h t widths.  The v^„(HD0) and v.^(HDO) h a l f - h e i g h t OH  OD  widths, F i g . 3.8, were obtained from the same sets of spectra as were the frequencies i n the preceding  section.  D e t a i l s of the p l o t s are compiled i n  Table I I I . V I . h -1 Errors i n Av.^HDO) (± 0.75 cm ) r e s u l t e d from l ) i n a c c u r a c i e s - i n OH  assigning baselines (± 0.005 absorbance), 2) errors i n estimating 1/2 I f o r I = 1.0 absorbance (± 0.01 absorbance), and 3) errors i n estimating.widths  280 60 1 40 20 > CD 2 0 0 H  en  CD  80 j 6040-  Q  CD  M [o] Sublimation  ••  20 •  D  O IOCCD Q. 8 0 E  • • Ford and Falk • o this work  60H  4020-  o-  20  i? AZ/ (HOD) 2  o0  30  * (HOD)  OH  40  Half-height width cm  50  60  -1  Fig'. 3.8 The s h i f t s of HDO stretching-modes half--height widths during warm-up of-cubic i c e I . These data were obtained from the same spectra as were the frequencies of F i g . 3 . 6 . Temperatures are uncorrected.  76  Table I I I . V I  The low temperature behaviour of the HDO s t r e t c h i n g modes h a l f - h e i g h t widths f o r HDO i n H 0 and D 0 cubic i c e I . 2  2  v (HD0)  v (HDO)  0D  OH  Low Temperature L i m i t Ratio  Av /Av Q H  Linear Low Temperature Dependence  cm /°K  Linear High Temperature Dependence  cm /°K  0.5 cm  35.5  t  23.5 ±  0.75  0.75  1.51  0 D  "Freeze-in" Temperature  (t  -1 cm  ;  _1  _1  °K  < 0.02  0.066  87 ±  ' < 0.03  '+ 0.005 5  ). Because of sample sublimation, data f o r  O.Okk  t  0.005  105 ± 5  obtained  AVQ^(HDO)  above 190°K do not extrapolate i n t o those obtained at lower temperatures. h —1 Errors i n Av (HD0) (estimated t o be ± 1.0 cm ) r e s u l t e d from QI)  l ) inaccuracies i n assigning baselines due t o an underlying 3v^(H,_,0) absorption (t 0.01: absorbance),, 2) errors i n estimating 1/2 I f o r I = 0.70 absorbance ( t 0.005 absorbance), and 3) errors i n estimating widths (±0.5 c m ) . -1  In both cases above the H D O h a l f - h e i g h t widths were quoted and p l o t t e d only t o the nearest 0.5 cm . 1  1  77 (c) HDO absorbances. Peak heights ( i ) of V-„(HDO) and v.^CHDO) were Un  UU  measured (with e r r o r s of ± 0.01 and ± 0.005 abs. u n i t s r e s p e c t i v e l y ) from c o n s i s t e n t b a s e l i n e s on the same sets of spectra as were frequency and h a l f height width.  Absorbance data ( i ) are p l o t t e d i n F i g . 3.9 and the d e t a i l s  are l i s t e d i n Table I I I . V I I .  Normalization of the two sets of i n t e n s i t i e s  was not attempted. Peak  heights  from 28° t o l'90°K.  underwent a r e l a t i v e l y smooth, continuous decrease Data obtained with the sample above l'90°K i n d i c a t e a  sharp decrease i n I as the sample sublimed.  No estimate was made of cummu-  l a t i v e sample l o s s due t o sublimation during the whole experiment. A s l i g h t , concave d i s c o n t i n u i t y centered at 125°K appears i n an otherwise convex curve for- -these data.  The data appear constant below 35°K  i n d i c a t i n g I (v^(HDO)) v a r i e d by l e s s than -0.24 x 10 Table I I I . V I I  absorbance/°K.  The low temperature behaviour of the HDO s t r e t c h i n g modes peak heights f o r cubic i c e I . .  Low Temperature L i m i t absorbance Linear Low Temperature Dependence absorbance/°K  l(v_„(HD0))  I(v--CHDO))  0.945  0.540.  -O.69 x 10'  -0.24 x 10'  -2.26 x 10  -1.07 x 10  L i n e a r High Temperature Dependence  absorbance/°K 79 ± 5  "Freeze-in" Temperature  130(?) . Irregularities  76+5  °K °K  125  200-  o LLI  [•]  [•]  150-  o o  c r  D <  100-  UJ a. LLI  50-  o  h  I  (z/  OD  (HDO ))  f.  • I (zv (HDO)) OH  O  o  '  0.2  0.4  I F i g . 3.9  0.6  0.8  ABSORBANCE  The s h i f t s of the HDO s t r e t c h i n g mode peak heights or absorbances ( i ) during warm-up of a cubic i c e I sample. The I data were obtained from the same spectra as were the frequencies and Av of F i g s . 3 . 6 and. 3 . 8 .  79 B.  Temperature Dependence of H 0 2  Eight HgO and D 0 2  and D 0 2  Absorptions  absorptions provided l e s s accurate measures of the  primary s p e c t r a l parameters than the three HDO  absorptions, but they d i d  y i e l d information on cubic i c e I . ( i ) Experimental Five sets of spectra from f i v e specimens were recorded on the 4 2 1 or P.E.  301 spectrophotometers  i n the l i q u i d helium dewar.  sample composition and preparation are given i n Table H0 2  P.E.  D e t a i l s of General  I I I . V I I I .  absorptions were: observed i n samples E and F and t h e i r r e s u l t s were  combined with those of cubic samples A and B.  General D 0 2  absorptions,  were observed i n samples H and I and t h e i r r e s u l t s were combined with those of sample C.  Samples E, F, H and I were observed on C s l i n the P.E-. 4 2 1 .  The v^HgO) absorptions were observed i n a separate sample (G) with;, polyethylene windows on the P.E. 301.  c  P.E. 421 f u n c t i o n s e t t i n g s were again i d e n t i c a l w i t h i n one set pf spectra and as consistent as p o s s i b l e between samples. were given i n s e c t i o n 3.1.  S p e c i f i c conditions  Only small a l t e r a t i o n s i n instrument purging,  reference beam attenuation and o p t i c a l wedge s e t t i n g s were made. The P.E.  301 was used i n the  mode between  I/IQ  666  with Bodenseewerk purging and no evacuated reference c e l l . scanned at 40 cm  "Vmin.  and recorded at 4.4 cm  v a r i e d but were u s u a l l y l e s s than 4 cm  "Vdiv.  cm  1  and l60, ;  :  cm  1  Spectra were  S p e c t r a l s l i t widths  \  4  Table I I I . V I I I  D e t a i l s of depositing and annealing of H 2 O , D 2 O and HDO bearing i c e I samples.  Sample  ,  ;  E  1  H0 2  Deposition Temperature Time t o warm from  (°K) to  85°K  l85°K  Maximum annealing Temperature  (min.) ••. (°K)  F H 0(D 0) 2  2  G  H  H 0  D0  2  2  I D 0(H 0) 2  2  85  85  85  85  85  12  15  17  17  15  186  183  187  185  180  2  3  2  1  2  5  4  4  5  6  18  21  18  210  123  920  348  Time maintained at maximum annealing temperature Time t o cool from  l85°K  (min.) to  85  Time t o c o o l from 85°K t o 8°K  °K (min.) (min.)  30  24  '  (25°K) .  Time maintained at 8°K (min.).  245  170  269  (25°K)  Length of warmup run  (min.)  243  166  433  Co  o  81  ( i i ) Results o f Warming H 0 and :D 0 .Cubic I c e I 2  2  :  Frequency data were obtained as i n s e c t i o n 3.IB.  The sets of spectra  were analyzed randomly w i t h respect t o temperature as i n s e c t i o n 3 . 2 A ( i i ) . Each complete s e t of spectra was analyzed one band at a time.  Because of  the breadth o f H 0 and D 0 bands, frequency data were accurate only t o t 2 . 5 2  2  -1  cm (a) Fundamental H 0 and DgO frequencies. 2  The v-j frequencies are  p l o t t e d as a f u n c t i o n o f temperature i n F i g . 3 . 1 0 and some p l o t parameters are compiled i n Table I I I . I X .  From F i g . 3 . 1 0 and Table I I I . I X i t i s apparent that  l i q u i d n i t r o g e n and l i q u i d helium c e l l data (samples A - B and E - F) do not concur.  -  ...-.=_.•.•  For v-^LVjO) no data were obtained between  51°  and 83°K since a sudden  s l i g h t r i s e i n c r y o s t a t pressure (from traces o f condensed r e s i d u a l 0  2  and  N ) caused heat l o s s e s between the n i t r o g e n s h i e l d and the helium dewar. 2  -6  Although the pressure rose only from 6.8 x 1 0  -6  Torr t o 1 5 x 1 0  Torr and  -6  dropped t o 8.2 x 1 0  i n 2 - 3 minutes, the pressure r i s e was s u f f i c i e n t t o  r a p i d l y warm the helium dewar and sample b l o c k . The 3.11 V  frequency v a r i a t i o n s during sample warming are p l o t t e d i n F i g .  and some d e t a i l s of the behaviour are given i n Table I I I . I X . For  1^2^  ^  e  n  e  H  u  m  a n <  ! nitrogen c e l l data agree reasonably w e l l .  For v ^ ( D 0 ) 2  a high s c a t t e r o f p o i n t s d i d not permit e v a l u a t i o n o f low temperature dependence.  No data was obtained between 5 1 ° and 83°K f o r the same reasons as  w i t h v^, a r a p i d pressure r i s e . Helium and nitrogen c e l l v  2  data do not agree ( F i g .  the p l o t s are given i n Table I I I . I X .  3.12).  D e t a i l s of  Data f o r three helium c e l l "samples and  two nitrogen c e l l samples are p l o t t e d ( i n c l u d i n g unannealed  sample data at  200'  82  z/ ( H O) 3  o  o  2  o  150 UJ  cr D <t IOO  or uj n UJ  h  50  3230 200  ^ (D 0) 3  0  2  150  111  or D  £ °' , 0  or UJ  o. UJ  50-  h  o24IO  2430  2420  FREQUENCY  CM- i  F i g . 3 . 1 0 The s h i f t s of cuMc i c e I during warm-up. For H 0 the open c i r c l e s represent data from experiments between 8 3 ° and l 8 0 ° K on a Hornig-Wagner a l l - g l a s s c e l l , Temperatures are uncorrected f o r source beam heating. 2  Table I I I . I X  The temperature dependences of cubic i c e I H 0 and D 0 v i b r a t i o n a l absorptions. ?  Low temperature limit H0  cm  2  V  V  +  V  T  3  V  320*1  2  3133  3R V  2  k  (3215  l  v /2v  333*+ +  R  2239 1562 (1605  v ' R  V V  R T  + +  p  Low temperature dependences  -1  High temperature dependences  cm /°K  cm /°K  1  ••  0.08  70  + 10  ±  0.08  0.03 ± 0.03  +  0.17  ±  0.05  (+  0.19  ±  0.0*0  +  0.3k  ±  0.03  65  -  0.12  ±  0.03  70  +  10  +  20  +  10  5)  3  <  -0.09  +  h  <  0.1k  + 10)  +  +  0.20  +  832  80  +  3  881  °K  1  ± 0.05  +  +  Freeze-in temperature  (0.36  ±  0.10)  7  —  -  0.19  ±  0.08  80  5  —  -  0.18  ±  0.06  75  -  0.102  2 2 9 . £! ±  0.75  ±  0.012  95  +  +  10  5  5  CO OO  Table I I I . I X  (Continued)  Low temperature limit -1  D 0  l  +  V  V  V  2  v  V V  R  T  3  l  2464 +  3  +  4  2320 +  5  2413  High temperature dependences  cm /°K  <  0.06 —  °K  cm /°K  1  —  Freeze-in temperature  1  80  ±  0.13  ± 0 . 0 4  0.19  ±  0.03  70  + 10  -0.11  ±  0.03  60  +  0.08  ±  0.05  50  + 10 + 10  0.05  100  1637  + 3  R  1189  +  2  663  +  6  —  -0.10  ±  0.05  100  630  +  4  —  -0.11  ±  0.04  65  <-0.07  0.13 ± 0.03  + 30  0.17  R  3v  V  "  cm  2  V  low temperature dependences  +  +  20  5  15  CO  Fig.  3.11  The 'shifts of cubic i c e I v during warm-up. For R^O t y p i c a l annealing run data are included f o r preand post-annealing behaviour (open c i r c l e s and squares).  0  _ |  II80  ,  II90.  ,  —  I200  ,  I2IO  FREQUENCY CM"' Fig.  3.12  The s h i f t s of i n cubic i c e I during warm-up. For comparison to the helium c e l l data, nitrogen c e l l data f o r pre and postannealing behaviour are included.' Pimentel and Zimmerman's (97) data are a l s o included f o r hexagonal i c e I . Temperatures are uncorrected.  87  83°K f o r the helium runs).  T h e - v ( D 0 ) data were not obtained from the same 2  2  set of spectra as the more intense Data r e l a t i n g the v  and  absorption data.  frequency temperature dependence are p l o t t e d  i n F i g . 3.13 and important parameters obtained from the f i g u r e are l i s t e d i n Table I I I . I X . agreement.  For v ( H 0 ) , helium and nitrogen c e l l data are i n good o  K  d.  Because the v  n  mine accurately.  band i s broad the maximum was d i f f i c u l t to deter-  Consequently, the low temperature data are poor and a,- low-  temperature/frequency dependence could not be approximated. The nature of t r a n s l a t i o n a l H 0 absorptions i s shown i n F i g . ,3.lH. 2  The peak frequency temperature dependence i s given i n F i g . 3 . 1 5 . An i r r e g u l a r s h i f t of from  155°  1.5  cm  occurs between  1  t o 200°K.  55  and 60°K and the frequency i s i n v a r i a n t  The d e t a i l s of the graph are l i s t e d i n Table I I I . I X .  Several features of  v^(E^O)  were observed.  l i n e s along peak sides was read t o * 0 . 5 0 cm estimated t o w i t h i n ± 3 cm  1  The i n t e r s e c t i o n of two  while shoulder positions, were  The peak near 1 6 5 cm  1  the r a p i d energy drop at the end of a g r a t i n g range.  i s d i s t o r t e d because of Frequencies of peaks,  minima, shoulder edges and b a s e l i n e at 25°K are l i s t e d i n Table I I I . X . ' (b) Overtone and combination frequencies. The (v p l o t t e d i n F i g . 3 . l 6 and summarized i n Table I I I . I X : helium and nitrogen c e l l data agree.  + v^) data are  One can see that the  However, the data are too poor t o  permit an approximation of a l i n e a r low temperature dependence. Both the H 0 and D 0 3v^. frequencies ( F i g . 3 . 1 7 ) decrease w i t h i n o  d  o  d  K  creasing temperature at rates i n d i c a t e d i n Table I I I . I X . and nitrogen c e l l data agree near 80°K.  Again the.helium  88 280-  60-  O  40-  . (H O)  o  20-  R  a  200-  8060-  z  4  a  " >  20-  LU  100  _l  on  80-  00 LU LU  60-  (T  40-  LU Q  20  O  A  V  o-  LU  ~I  8OO  8  W 8  20  V  V A A A A  3 0  DC °i D I— 60 l8  <  rr LU Q_  LU h-  4OH;  20 1 0 0  8060  o  40-  A  20 •  610  6 3 0  620  FREQUENCY F i g . 3.13  6 4 0  CM  -1  The s h i f t s of v f o r cubic i c e I during warm-up. For H 2 O Pimentel and Zimmerman's (97) data and l i q u i d nitrogen c e l l data are included f o r comparison. R  89  Fig.  3.14  The cubic i c e I V ^ C H ^ O ) band at 8 3 ° K and the background spectrum through the blank c e l l at 83°K. The feature near- 2 l 8 cm"! a r i s e s from a f i l t e r change.  200  z/ ( H O ) T  2  150-  100-  A  4  50  1  o-  220  -T  1  225  r  ~*  FREQUENCY CM' 3.15  A  1  1  230 1  The s h i f t s of v-d^O) f o r cubic i c e I during warm-up. The sample was mounted on a polyethylene window 0.25 cm t h i c k . The c e l l temperature d i d not reach helium temperature w i t h the source on or o f f a f t e r 3 hours of c o o l i n g . Temperature are uncorrected f o r source heating.  91  Table I I I . X  The i n t e r p r e t a t i o n o f the v^RgO) features f o r comparison to previous r e s u l t s .  T 2 Feature  Description  Frequency -1  cm  A  peak  B  minimum  C  shoulder  D  shoulder  E  peak  F  shoulder  G  <l6l 176.5  ±  edge  193  ±  3  edge  21k  ±  3  229.6  ±  edge  2U6  ±  3  shoulder  edge  272  ±  3  H  shoulder  edge  286  ±  3  I  shoulder  edge  295  ±  3  J  baseline  331+  ±  3  1  .5  The (v + v ) data are p l o t t e d i n F i g . 3 . 1 8 and summarized i n Table III.IX.  This band i s a poorly defined shoulder on the intense v_ band and r\  thus could only be estimated t o w i t h i n ± 7 cm . 1  data are not i n good agreement.  Helium and nitrogen c e l l  Low temperature dependences could not be  defined.  ,  (c) H 0 and DgO h a l f - h e i g h t widths.  Data f o r cubic i c e I ( H 0 ) were  2  2  p l o t t e d i n F i g s . 3.k and 3.5 of s e c t i o n 3 . 1 .  The h a l f - h e i g h t widths o f the  composite s t r e t c h i n g band and the composite l i b r a t i o n a l band increased with increasing temperature.  However, the composite ( v , 2 v 0  I width decreased with increasing T.  \  2  r a  )  R  band h a l f - h e i g h t  200 (zf + z / ) ( H O ) T  o  o  z  150 H  oo o  UJ  or  o  oo  IOO H  o  A  o  UJ Q_  LU  0  •  o A * A  50H  h  A  o  3320  A  A  A  3340  3360  200  o  I50H  LU  D Q:  IOO H  LU 0.  50  UJ h  2460  2470 FREQUENCY CM"  2480 1  F i g . 3 . 1 6 The s h i f t s of (v + v,p) f o r cubic i c e I during.-warm-up. | For . ., „ , Temperatures aire the nitrogen c e l l ' d"a t'a are included, uncorrected.  93 280  O  .60 4 0  3  O  20  or  v  200  80H ~Z_  6 0 4 0  \ £  CO  2 0 1 0 0  O  UJ °-1 LT 8  C9 Ld Q  UJ  6 0  4 0  2 0  *  cr  D  2210  •^r h-  2230  o  a:  L±J Q_  2220  6  V K  A  A  2250  2240  0  3v or - - (D 0) R  40  2+  20-  R  2  10080 60 4 0 20  i  o 1610  8o I—  1630  1620  FREQUENCY  o  o 1640  1650  CM  F i g 3.IT The s h i f t s of 3 v f o r cubic i c e I during -warm-up. For H 0 annealing data and data of Pimentel and Zimmerman (97) are included. Temperatures are uncorrected. R  2  200  (z/ + z/ )(H 0)  •  0  l 5  T  O •  °H  LU  oa  •  D  o  h IOO< Q: LU  n  ^> LU h  2  •  A  a  A a  °  8a  50-  o-  1  1  :  I  I  I  I  1  866  ± A £ A  i  1  T  |  i 1  876  1  1  886  200  (z/ + z/)(D 0) 2  o  I50-  LU  cr  D  h <  IOO-  LU  d  5CH LU h  A  A  A A  o-  —I 650  i  ^  A A  I  *  I 660  FREQUENCY F i g . 3.18  A A  T  T  1  r  670  CM  The s h i f t s of (v^ + v^) f o r cubic i c e I during warm-up. Nitrogen and helium c e l l data are included f o r R^O.  95  3.3  The H 0 , DgO and HDO 2  Ice I Absorptions at 83°K  In t h i s s e c t i o n are l i s t e d the d e t a i l s of the H 2 O , D 0 and HDO 2  vitreous and cubic i c e I"absorptions at 83°K f o r comparison i n Chapter h to the l i t e r a t u r e values.  A.  Experimental  T y p i c a l spectra of v i t r e o u s and cubic i c e were shown i n F i g . 3.1: v,p(H 0) was shown i n F i g . 3.1*+.  The samples, spectra and methods of t r e a t -  2  ment were described i n sections 3.1 and 3 . 2 .  B.  Results at 83°K  Vitreous and cubic i c e I have the same s k e l e t a l absorption spectra ( F i g . 3.1) but are e a s i l y d i s t i n g u i s h e d i n d e t a i l s of band s t r u c t u r e , frequency and width.  Frequencies  observed f o r the H 0 , HDO and D 0 systems 2  2  at 83°K are, compiled i n Tables I I I . X I , I I I . X I I and I I I . X I I I r e s p e c t i v e l y . Results of previous workers are included f o r comparison. ( i ) H 0 Absorptions at 83°K 2  Spectra of v i t r e o u s and cubic i c e I obtained i n t h i s work are i n sharp contrast and•exhibit features not p r e v i o u s l y observed. The s t r e t c h i n g band of cubic i c e I i s composed of one peak and two w e l l defined shoulders—33*+0 (2*+42) ( s h ) c m , 3210(2*116) c m -1  (2392)(sh)cm \  (D 0 2  data are given i n brackets.)  ice I has very weak absorptions at t i o n t o a peak at  '3253(2*+36)  cm  1  3686(2720)  cm  1  -1  and 31*+9  In contrast, vitreous and  36UO  cm  -1  i n addi-  and two poorly defined shoulders at  Table I l l . X l ( a )  The frequencies and assignments f o r cubic and.hexagonal i c e I of the present and previous workers. This  Assignment  Work  Vitreous 93°K cm v  Cubic 93°K  -1  olig  3686  vw  —  v  olig  3640  vw  —  ^3367  sh  v  l  v  3  3253  vs  v  l  ^3191  sh  2220  w  1660  m  v  +  V  T  ?  sh  -1 cm  3340 3210±5 (3217±5)* 3149  ssh  3350  vs  3220±5  ssh  3140  -1 cm  shs  (v )3360  Msh  s  (v J 3 2 1 0  vs  x  shs  (2v )3125  Msh  2  Val'kov Ockman and (e) Maslenkova(d) 77°K 100°K  2235  w  2266±20  vbw  .2225  s  1570+10 5)*  m  l650±30  vbw  1585  s  3260  2250  -1 cm  -1 cm  3321  (2)  .3340  3210  (4)  3224  3088  (10)  3140 2235 1580  R  846  ssh  881  ssh  900  sh  802  s  833  s  840  s  ^780  sh  770  sh  ^696" .  sh  660  sh  555  sh  —  ^675 R" T V  —  (1130 msh)*#  —  V  -1 cm  Giguere and Harvey(c) 100°K  (1604  1570  V  Hornig and Haas (b) 83°K  -1 cm  3  ±  Whalley and Bertie(a) 100°K  sh  535 msh  570"  msh  850  850  * data from sample A section 3 . 1 ; ** observed only i n samples annealed above 200°K. (a) Ref. 9 5 (b) Ref. 1 0 6 (c) Ref. 9 8 (d) Ref. 9 9 (e) Ref. 1 0 8 .  846  ON  Table I I I . X I ( b ) The t r a n s l a t i o n a l l a t t i c e mode features of v i t r e o u s , cubic and hexagonal i c e I .  This  v (H 0) T  Work  Giguere and Arraudeau(a)  Whalley(b)  Pimentel(c)  2  93°K  93°K  Vitreous cm ! 326  +3  173°K  Vitreous  Cubic  33U  ±  3  301  296  295  293  shoulder  271  267  259  257  212.8±0.5  ^328  (330)*  300-310 ^275  227.8±0.5  225  (ms)  223  m  229.2  change of slope  211  220  change of slope  197  200  shoulder  191  minimum  173  peak  162  * taken from F i g . 3 of Ref. ( 9 7 ) . (a) Ref,  89  (b) Ref.  -95  (c) Ref.  97-  (305) (275)  ^2k0  2U6  peak  93°K  Hexag.  -  shoulder  change of slope  100°K  Hexag.& Cub.  cm-'-  -  high frequency l i m i t  113°K  Cubic  188  190  190 180.5  15U  (m)  152  l6h  229  Table I I I . X I I  Assignment  Comparison of the present and previous HDO v i b r a t i o n frequencies near 90°K.  This  work  Vitreous  Whalley and B e r t i e (a) 1 0 0 °K  93°K  Cubic -1  -1  cm  HornijI and Haas (b)  -1  -1  cm  Hornig et a l . ( d ) 83°K  93°K  83°K -1  cm  Ford and Falk (c)  cm  cm  -1  cm  V  OH HDO i n  D 0 2  V  3304  m  (2442)  —  OD HDO i n  H 0 2  2437  3266  m  24l6 (2392)  s  3277  ±  4  2445  wsh s  2421  ±  4  2395  wsh  3275  vs  msh  2442  s  s  24l6  vs  msh  2393  s  1975  w  1490  s  s  ^ (HDO) 2  V  + V  R T HDO i n D  —  2  854  wsh  819  mw  ±  5  3300  2418  ±  3  2440  1470  0 792  R HDO i n  D 0  HDO i n  H 0  V  w  822  ±  6  m  800 620  2  "(a) Ref."  3270  515  2  '95  (b) Ref. T0'6  '(c) Ref.  100  i  10  m  (d) Ref.  105.  MO CO  Table I I I . X I I I  The frequencies and assignments of D 0 f o r the present and previous workers.  This Assignment  i c e I ( v i t r e o u s , cubic, hexagonal) near 90°K  2  work  Vitreous  . Whalley and B e r t i e (a)  93°K  Cubic  . Hornig and •Haas (b) 83°K  100°K  hex.and cub. cm olig v v  olig  —  —  21*36  s  21*13  21+25 ± 5  s  (v )  l  2372  ssh  2321  2332 ± 5  s  (v 2v )"2336 s  \  1617  w  1635  1650  ± 30  1635  s  1630  1212  m  1191*  1210  ±  1210  s  1210  ssh  661  675  sh  s  627  61*0  s  1*25  sh  v  3  2  + v  R  V  T  600  R  221*0  R ~ T V  "(a)""Ref. 9 5  cm  2720  msh  T  -1  -  21*85 ± 1 0  V  hexagonal  cm ^  -  21*65  V  V  cm !  -  Val'kov and Maslenkova (d) 100°K  hexagonal  ssh  +  V  v  cm-'-  cm  100°K  cubic  21*99  l  3  1  Giguere and Harvey (c)  '(b) Ref.  106  (c) Ref.  98  vwsh  10  (d) Ref.  (v ,2v ) 2l+95  msh  +  1  2  21*32 vs  3  lS  21*50  2  251*2  (0.5)  2l*2l*  (3)  2291  (10)  M.2l*0  630  99.  VO  100  3367(21+99) c m  -1  and 3191(2372) cm . -1  For H~ 0 cubic ice. I , the l i q u i d 2  data do not agree at 83 K  helium and l i q u i d nitrogen experimental  P  (Fig..3.10). •Two d i s t i n c t values of v^HgO) are i n d i c a t e d among l i q u i d helium /V'''  experiments and some l i q u i d nitrogen experiments. nitrogen runs gave v (83°K) at 1570 cm .  A few nitrogen runs with t h i n  -1  2  samples gave v (83°K) at l6oU cm . -1  2  A l l helium runs ,and some  Atmospheric H 0 absorptions may have 2  attenuated the weak v ( H 0 ) absorptions of t h i n samples. 2  2  Ice samples annealed with care above 200°K showed two d i s t i n c t i o n s from those annealed below 200°K. shoulder at 1130 cm  1  between the 1130 cm  1  The former gave spectra with a d i s t i n c t  (on the side of v ) .  As w e l l , a deep minimum appeared  2  shoulder and the v  R  band.  Pimentel's  (97) spectra  showed the same features although he o f f e r e d no explanations f o r them. Inspection of the cubic i c e I H 0 v 2  peaks and three shoulders. additional v  T  T  band ( F i g . 3.11+) shows, two  However, Whalley's (87) theory showed that  features y i e l d important information on the d e n s i t i e s of  phonon states. i n Table I I I . X .  Accordingly, t e n features of  v^(E^O)  In c o n t r a s t , the v i t r e o u s i c e I  quency shoulder or peak.  As w e l l the 267 c m  -1  at 93°K were reported band had no low f r e -  shoulder was p o o r l y defined.  ( i i ) D 0 Absorptions at 83°K 2  DgO i c e I has the same sets of s p e c t r a l features as H 0 i c e I . 2  Vitreous B^O i c e spectra have a weak oligomeric absorption at 2720 cm which has not been reported p r e v i o u s l y f o r i c e . are absent i n cubic D,_,0 sample spectra.  Oligomeric  1  absorptions  As i n E^O i c e I , the s t r e t c h i n g  band shoulders are.better defined i n cubic than i n v i t r e o u s i c e . The  101  problems caused by atmospheric were  H^O attenuations encountered i n H^O i c e I •  e l i m i n a t e d by more e f f i c i e n t purging.  ( i i i ) HDO Absorptions at 83°K Only three HDO absorptions were observed, the OH and 0D stretches and a n HDO l i b r a t i o n .  I n v i t r e o u s samples the three absorptions were broad,  r e l a t i v e l y weak and without shoulders.  On  h a d no shoulders, the v  OD  shoulder.  I n cubic samples the v_„ band  band had two shoulders and the v band had one n  No v^(HDO) absorption was observed near 6 0 0 cm" f o r HDO i n H^O. 1  3.h A. 1.  Summary of I c e I Results  Vitreous-Cubic I c e I Transformation  A l l HgO absorptions s h i f t i r r e v e r s i b l y  i n the temperature range  115 - l t5°K; i n t e r n a l modes s h i f t t o lower frequencies while l a t t i c e modes I  shift  to  higher frequencies.  2.  Above  150°K,  v i t r e o u s and cubic frequency data concur  and s h i f t  r e v e r s i b l y w i t h respect t o temperature.  pened  3.  Oligomeric H^O absorptions are absent above 125°K.  U.  Upon sample d e v i t r i f i c a t i o n the absorptions are s h i f t e d ,  and  5. those  of  6.  shar-  b e t t e r defined. D^O and HDO absorptions appear t o have the same behaviour as H 0. 2  Composite-band h a l f - h e i g h t widths e x h i b i t e d unusual  i n t h e case of ( v , 2 v ) . Q  p  behaviour  102 B. 1.  HDO i n Cubic Ice I  D i l u t e concentrations o f HDO i n H^O and D^O gave accurate  measures of frequency, h a l f - h e i g h t widths and absorbances as a f u n c t i o n of temperature. 2.  P l o t s of the HDO data provided low temperature l i m i t s , l i n e a r  low.and high temperature dependences and i n d i c a t i o n s of i r r e g u l a r behaviour. 3.  A new absorption was observed as a shoulder on v (HDO) and i s  designated v^HDO) + v (DJD) or v '(HDO). n  h.  K  n  m  I d  I n t e r n a l mode cubic i c e I HDO absorptions s h i f t r e v e r s i b l y t o  higher frequency and l a t t i c e mode HDO frequencies s h i f t r e v e r s i b l y t o lower frequencies as a function of increasing temperature. 5.  HDO s t r e t c h i n g mode h a l f - h e i g h t widths increased as a f u n c t i o n  of increasing temperature. 6.  HDO s t r e t c h i n g mode absorbances decreased as a f u n c t i o n of i n -  creasing temperature.  C.  H 0 and D 0 i n Cubic Ice I 2  2  These r e s u l t s provided measures of eight H^O and seven D^O absorptions that were l e s s accurate, but of the same nature, as those from HDO.  CHAPTER FOUR DISCUSSION OF ICE I  The data from cubic and v i t r e o u s i c e I i r spectra contribute t o d e t a i l e d understandings  of:  l ) the o r i g i n s of the absorptions, 2 ) the  process of the v i t r e o u s - c u b i c phase transformation, and 3) the e f f e c t s of increasing temperature, i n c r e a s i n g R(0*••-0) and decreasing hydrogen bond strength on the R 0, D 2 O , and HDO v i b r a t i o n s and p o t e n t i a l w e l l . 2  4.1  The Ice I Vitreous-Cubic Phase  Transformation  The x-ray and e l e c t r o n d i f f r a c t i o n experiments ( 5 8 ) i n d i c a t e d that the s t r u c t u r e of the s o l i d formed by condensing H 2 O vapour at low temperatures depended on the rate of deposition and the substrate temperature: Amorphous, cubic and hexagonal i c e s were observed.  The thermodynamic  studies of the i r r e v e r s i b l e phase transformations i n d i c a t e d varying t r a n s formation temperature ranges and degrees of c r y s t a l l i n i t y .  The confusion  with respect t o v i t r e o u s , cubic and hexagonal sample formation i s r e f l e c t e d i n the v a r i a t i o n s among the i r spectra of various authors B e r t i e and Whalley  (88,95)  (95, 97, 98, 105).  obtained spectra of mulled, c r y s t a l l i n e samples  (checked by x-ray d i f f r a t i o n ) and they c r i t i c i z e d the use of a " r e c i p e " such as that of Beaumont et_ a l . ( 6 5 ) . With i r observations Zimmerman and Pimentel ( 9 7 ) pointed out the need to d e v i t r i f y s o l i d s condensed from the vapour.  While they were t h e . f i r s t t o  detect the i r r e v e r s i b l e s h i f t i n the i r spectra between v i t r e o u s and cubic i c e , they d i d not study the transformation i n d e t a i l .  10k  The transformation process was observed i n t h i s work i n every  ir  absorption except v (H 0 ) , but the r e s u l t s of the transformation f o r a l l H2O, HDO  and D 0 bands were recorded.  The spectra gave four concurrent  2  measures of the transformations:  l ) the degree of increased hydrogen bonding,  2) the transformation temperature range, 3 ) the change i n v i b r a t i o n a l energy, and k) the phase transformation r a t e .  The studies showed that cubic samples  formed by transformation of the v i t r e o u s phase gave as good spectra, as. mulled, c r y s t a l l i n e samples ( 9 5 ) -  A.  General Discussion  Some general comments apply to a l l the HgO band maxima i n t h e i r behaviour before, during and a f t e r the v i t r e o u s - c u b i c phase transformation. Between 8 3 ± 3°K and-120 ± 10°K a l l H 0 band maxima had constant  frequencies  2  (Fig. 3 . 2 ) .  The absence.of frequency s h i f t s i s i n d i c a t i v e of no changes i n  the degree of hydrogen bonding.  Below 120 t 10°K the thermal k i n e t i c energy  was i n s u f f i c i e n t t o allow molecular r e o r i e n t a t i o n , softening of the g l a s s , and hydrogen bond formation. The H 0 band maxima a l l s h i f t e d i r r e v e r s i b l y during the v i t r e o u s 2  cubic transformation.  However, the data (page 6 2 ) i n d i c a t e d d i f f e r e n t ,  transformation temperature ranges f o r d i f f e r e n t bands:  Ranges from 1 1 5 i  5 ° to 130 + 5°K and 130 ± 5 ° t o I H 5 + 5°K were found f o r v  R  and v  + v.  ±  T  The differences appear to be caused by the increasing p e r i o d the sample was held at one temperature while the spectra were recorded. t  ,  For example, frequencies p l o t t e d i n F i g . 3.2 show that v up to 100°K and was completely s h i f t e d t o the cubic  R  was  constant  frequency at 125°K.  105 That i n d i c a t e s , on f i r s t i n s p e c t i o n , that the transformation f o r started at 115 1 5°K, about 10°K lower than f o r other bands.  v~(R 0) n d n  Such a con-  clusion i s incorrect. S p e c i f i c a l l y consider the p o s i t i o n s of the data i n d i c a t e d by s o l i d t r i a n g l e s ( • ) at 125°K i n F i g . 3.2 f o r a l l s i x bands.  The data were ob-  tained from one sample during one run at constant temperature. V  l  +  V  T  b a n d  -  w a s  u n s h i f t e d from the v i t r e o u s frequency, the  At 125°K the  and  bands  were only s l i g h t l y s h i f t e d , the 3 v band was s h i f t e d approximately one-half R  the t o t a l s h i f t towards 3v  c u b i c , the v band was s h i f t e d three-quarters the d  i\  t o t a l s h i f t and v was completely s h i f t e d . .The amount of s h i f t i s proporR  t i o n a l t o the time the sample was held at 125°K. scanned from 4000 t o 530 c m 3^, for  and  -1  i n 20 minutes.  I n t h i s work, s p e c t r a were,  Thus f o r  + v^, v^, v^,  the v i t r e o u s sample had been p r o g r e s s i v e l y annealed at 125°K  3.7, 4.4, 4.7, 10.2, 13.4 and 18.3 minutes r e s p e c t i v e l y . was recorded the sample had completely transformed.  By the time  I f the transforma-  t i o n r a t e i s assumed t o be l i n e a r , then a p l o t of (v^ - v^^/Cv^ - v ) c  (where t i s the time at 125°K and t =  t  _  m  i s maximum annealing s h i f t ) against -2 -1 time i n minutes gives the transformation r a t e at 125°K as 5.5 x 10 , min One concludes that the transformation temperature ranges l i s t e d ; i n Table I I I . I f o r v + v , v , v , 3 v and v were a r t i f i c i a l l y elevated,by X 1 3 1 K d 0  the recording technique.  00  0  The transformation temperature range f o r a l l bands  must be c o n s i s t e n t , 120 - 135 - 5°K (corrected f o r sample window h e a t i n g ) . During the transformation the l a t t i c e modes v n  and 3v s h i f t e d R  irre-  vers'ibly t o higher frequency while the molecular modes s h i f t e d i r r e v e r s i b l y to lower frequency due t o l a r g e a l t e r a t i o n s t o the intramolecular and i n t e r molecular potentials'which occurred.  The s h i f t s of molecular modes, are  106  consistent with the formation of more and/or stronger hydrogen bonds. During the transformation the molecules a t t a i n e d s u f f i c i e n t thermal k i n e t i c energy t o permit molecular r e o r i e n t a t i o n , the low polymers were then free t o form long chains w i t h complete hydrogen bonding, four per molecule.  The  complete sets of strong hydrogen bonds hindered l i b r a t i o n and t r a n s l a t i o n and increased the frequencies of those bands. A f t e r the i r r e v e r s i b l e s h i f t had occurred, i^.e_. above 150°K, and during a l l subsequent warming-cooling cycles the spectra had a r e v e r s i b l e temperature dependence:  the l a t t i c e modes decreased i n frequency and the  molecular modes increased i n frequency as temperature increased.  The sample  d e v i t r i f i c a t i o n was completed by warming to' 1 8 5 ± 5°K f o r 2 - 5 minutes , followed by r e c o o l i n g t o 83°K.  r  At 83°K the e f f e c t s of r e o r i e n t a t i o n and hydrogen bond formation (lengthening r(O-H) and o r b i t a l r e h y b r i d i z a t i o n ) were measured f o r H 0, 2  D 0 and HDO. 2  I f the frequency s h i f t s between cubic and v i t r e o u s i c e d i d  r i s e from hydrogen bond formation, then the r e l a t i v e e f f e c t s on H 0, D 0 2  2  and HDO frequencies should have been the same provided a l l the v i t r e o u s samples had comparable degrees of m i c r o c r y s t a l l i n i t y .  The frequency  shifts  would i d e a l l y be i n the r a t i o Av^(H 0) /Av^(D20) near 1.*+, where Av.^ 2  v^(cubic) and v  R  (vitreous) f o r the i - t h v i b r a t i o n a l mode.  Only the peaks  give reasonable agreement with the i d e a l r a t i o , i_.e_. 1.6 t 0,> 3 and  1.1 ± 0.30 r e s p e c t i v e l y . A l l the other bands were poorly defined and the r a t i o s range from 0.79 ± 0.5 t o 3.1 ± 0.5 f o r v.^ + v  T  and  respectively.  A modified product r u l e AvjAv (H 0) /Av^Avg^giO) does not improve the r a t i o . 2  2  For 4 . 0 0 % HDO i n D 0 Av (HD0) = Av (D 0) = +27 c m , Av^HgO) ./ -1  2  R  R  2  Av (HD0) = 0.94 and A v ( D 0 ) /Av--(HDO) = 1 . 1 : On 3 uu OTJ  o  ment with the i d e a l r a t i o .  o  The r a t i o f o r Av  None of these are i n agree-  (HDO) /Av  ;  (HDO) = 1 . 8 i s much  107  higher than 1.4. The observed-ratios  of the cubic i c e I fundamental  cies are near 1 . 3 5 and one deduces that Av  (HDO) i s too l a r g e , Av.^HDO) i s  On  too small (compared t o pure H2O and D 0 )  or both.  2  frequen-  OD  However, since samples  were not i d e n t i c a l l y deposited, they would have had d i f f e r e n t degrees of s e l f - a n n e a l i n g , and d i f f e r e n t frequency displacements from the cubic i c e values. Each band w i l l now be considered i n t u r n . B.  Fundamental L a t t i c e Mode Transformations  ( i ) The v^HgO) Transformation The v band had remarkable differences between the v i t r e o u s and cubic samples at 83°K:  The v i t r e o u s band was broad and f e a t u r e l e s s while the cubic  band was narrow and had nine features. d i f f e r e n t nature of the two s o l i d s .  That i s understandable from the very  For example, since the p o s i t i o n s of the  atoms i n a v i t r e o u s s o l i d are i d e a l l y completely  i r r e g u l a r , then forces  acting on the atoms are i r r e g u l a r and the normal v i b r a t i o n s of the s o l i d are also i r r e g u l a r ( 8 7 ) .  The r e s u l t i n g range of t r a n s l a t i o n a l energy l e v e l s ,  and range of t r a n s i t i o n s among the l e v e l s , i s very broad.  Combined' wi£h  the collapse of normal phonon s e l e c t i o n r u l e s ( 8 7 ) , a very broad i r . (vitreous) band i s expected and observed.  In c o n t r a s t , cubic i c e I has  r e g u l a r , long range ordering of oxygen atoms, but i r r e g u l a r , short range ordering of the protons ( o r i e n t a t i o n a l d i s o r d e r ) .  Whalley ( 8 7 ) has shown  that the o r i e n t a t i o n a l disorder does not have a s i g n i f i c a n t i r r e g u l a r e f f e c t on the mechanical v i b r a t i o n s of cubic i c e , but that i t does a f f e c t the; l o c a l electric oscillations.  Consequently, one obtains a structured  band whose features are i n d i c a t i v e of the c r y s t a l l i n e s t a t e .  (cubic) I t i s suf-  108  f i c i e n t here to compare our v i t r e o u s and cubic v^, data (83°K) to those of Whalley (88) and Giguere (89). Consider the v^, data given on pages 89, 90, and 91 of Chapter 3. v^, ( c u b i c ) , 227.8 cm \  was  7% higher than  That  (vitreous) i s understandable  simply on the b a s i s of the increased number of hydrogen bonds, the deepened hydrogen bond p o t e n t i a l and increased force constants, and the  increased  hinderance to t r a n s l a t i o n . These e f f e c t s r e s u l t e d from extension of hydrogen bonding c l o s e r to the l i m i t (4 bonds/molecule), reduction of the mean 0 d i s t a n c e , and a change i n the density i n cubic c r y s t a l s . the explanation f o r the frequency s h i f t may  However, i n r e a l i t y  not be so simple.  a w e l l defined B r i l l o u i n zone i n cubic samples may  0  Formation of  e n t a i l complex changes i n  the d e n s i t i e s of s t a t e s and s e l e c t i o n r u l e s from those of the v i t r e o u s sample. The h a l f - h e i g h t width of 'V  (vitreous) was  62.8  an \  i n sharp con-  t r a s t to that of v^, (cubic) which was very nearly one-third of that value, 2 3 . 2 cm  Increases  i n the d e n s i t i e s of states at the B r i l l o u i n zone boun-  d a r i e s probably accounts f o r t h i s dramatic change. That the peak height of ^ e x a c t l y double that of  ( c u b i c ) , 1.285  absorbance, was  almost  ( v i t r e o u s ) i s probably due to two e f f e c t s .  The  f i r s t e f f e c t i s again the increased density of states i n cubic i c e I f o r ]c_ = 0 t r a n s i t i o n s . The second e f f e c t a r i s e s from the increase i n o s c i l l a t i n g d i p o l e moments i n completely  hydrogen bonded l a t t i c e s as compared to weaker  d i p o l e s i n p a r t i a l l y hydrogen bonded glasses. The (88)  Vj, ( v i t . ) band of t h i s work compares very w e l l w i t h Whalley's  vtj, ( v i t . ) but not w i t h Giguere's (89) v  had no 162 cm  1  peak or 173 cm  1  (vit.).  The  v^, ( v i t . ) band  minimum, as Whalley (88) a l s o reported.  109  However, Whalley's 2 1 2 . 8 cm  ( v i t r e o u s ) peak was 9 cm  higher than observed here,  He d i d not l i s t the p o s i t i o n s of other v i t r e o u s band features  and i t i s hard t o determine i f the d i f f e r e n c e i s only due t o c a l i b r a t i o n errors.  [On the basis of the two sets of v  T  (cubic)  seems u n l i k e l y . ] I n contrast Giguere's ( 8 9 ) v  T  f e a t u r e s , the l a t t e r  ( v i t . ) band showed too much  structure and suggested a l a r g e l y c r y s t a l l i n e sample.  The present work  supports Whalley's observations of v^, ( v i t . ) . For \> (cubic) the r e s u l t s of t h i s work agree i n general features with both Whalley (88) and Giguere ( 8 9 ) . present work are n e a r l y 2 cm a calibration error.  However  the two peaks in:, the  lower than Whalley reported, probably due t o  1  Whalley found that a l l cubic samples, e i t h e r condensed  from the vapour or formed under pressure and mulled, gave the same tions.  Since v  absorp-  observed i n t h i s work agrees with h i s r e s u l t s , one can  conclude that the sample deposition and d e v i t r i f i c a t i o n techniques used here gave l e g i t i m a t e cubic i c e I samples with respect t o v^.  ,  ( i i ) The R Transformation v  At 83°K v i t r e o u s i c e vj^HgO) had two d i s t i n c t and two f a i n t f e a t u r e s : a d i s t i n c t peak ( 8 0 2 cm "*") and a d i s t i n c t shoulder shoulders  (846 cm  1  (535 cm "*"), and two f a i n t  and 675 cm ) . However, v i t r e o u s i c e V R ( H D O ) and 1  Vp>(Dg0) each had only a s i n g l e feature.  In c o n t r a s t , cubic i c e v ( H 0 ) had R  2  f i v e features (one peak and four shoulders) while V R ( H D O ) and v (D2.Q) had R  two features each (a peak and a high frequency  shoulder).  The HDO high  frequency shoulder, V R ( H D O ) + vij^DgO) , has not been p r e v i o u s l y reported. Changes i n frequency and h a l f - h e i g h t width between the vp> bands of v i t r e o u s and cubic H 2 O i c e samples were shown i n F i g s . 3.2 and 3 . 4 (pages 6 l and 66) and the r e s u l t s of d e v i t r i f i c a t i o n f o r v ( H 0 , D 0, HDO) were given i n R  2  2  110 Table I I I . I (page 6 2 ) . A f t e r the v i t r e o u s sample was annealed at 185 i 5°K f o r 2 - 3 and recooled t o 83°K, one found a l l the v  R  features had s h i f t e d t o higher  frequency and that three new features appeared. by +31 cm ,  v (HD0) by +27 cm  -1  v  R  -1  P r e c i s e l y , v (Hg0) s h i f t e d R  and v ( D 0 ) by + 2 7 cm . -1  R  minutes  2  As f o r v , the T  s h i f t t o higher frequency may be simply understood on the b a s i s of  R  hydrogen bonding.  Cubic i c e has more and stronger hydrogen bonds than  v i t r e o u s i c e . The r e s u l t s are a deeper hydrogen bond p o t e n t i a l , l a r g e r hydrogen bond force constants, increased.hinderance t o l i b r a t i o n and i n creased absorption frequency.  However, as f o r v^, complex changes i n the  c r y s t a l e n t a i l complex changes i n the s o l i d l i b r a t i o n s , d e n s i t i e s of states and s e l e c t i o n r u l e s .  The f i n a l explanation of v_ behaviour must combinevthe K  changes i n hydrogen bond p o t e n t i a l w i t h the l a t t i c e v i b r a t i o n theory. The p l o t of h a l f - h e i g h t widths (Av (v , v R  R  + v ) was shown i n F i g . 3.h  pressed" v  T  R  R  ) of the composite band  (page 6 6 ) .  I t a l s o i n d i c a t e d a "de-  transformation temperature range ( 1 1 5 - 130 ± 5°K).  the low range may be explained as i n s e c t i o n k.lA One a l s o sees that the behaviour of Av n 0  However,  (page I O 5 ) f o r v ^ f f r e q . ) .  above 130°K d i d not conform t o  the r e v e r s i b l e behaviour of f u l l y annealed cubic samples, i_*e_* the h a l f height width continued t o decrease.  F i n a l l y , on completing the annealing  and r e c o o l i n g of the sample t o 83°K, one found that the disorder broadening due t o i r r e g u l a r 0 p o s i t i o n s was removed but that there remained the o r i e n t a t i o n a l disorder broadening. the f o l l o w i n g  way:  The h a l f - h e i g h t widths at 83°K decreased i n  Ill H 0  HDO  2  Av ( v i t . )  220 cm  Av (cub.)  195  - 1  D 0  H 0/D 0  2  88. cm"  2  2  ^ 2 0 0 cm" 1 . 1 0  1  1  51  140  "1.30  Av^cub.) 0.89  Av^vit.)  0.58  ^0.70  1.27  The d i f f e r e n c e s may be due simply t o e r r o r s i n determining b a s e l i n e s , i n t e n s i t i e s and widths, or may a r i s e from d i f f e r e n c e s i n m i c r o c r y s t a l l i n i t y among the three v i t r e o u s samples formed.  C.  ( i ) The  v /2v 2  Fundamental Molecular Mode Transformations  Transformation  R  Absorptions between 1 0 0 0 and 1 8 0 0 cm i n H 0 i c e have been v a r i o u s l y 1  2  assigned t o  2VR  or v -  A l l previous workers  2  reported  ( 9 5 , 9 7 ,105 , 1 0 6 , 1 0 8 )  only a s i n g l e feature i n t h i s range f o r both H 0 and D 0 i c e s ( v i t r e o u s or 2  cubic).  However, Zimmermann and Pimentel's ( 9 7 ) F i g . 1 f o r cubic i c e has  shoulders at l6l5  1100  cm peak and  (83°K)  2  1  i n cubic  and  1530  H 0 2  1530  cm  - 1  and a peak at  l6l5  cm" :. They t r e a t e d the 1  cm shoulder as one band centered at 1  1580  cm"  1  ice.  Most t h i c k v i t r e o u s H 0 i c e spectra recorded i n t h i s work had two 2  f e a t u r e s , a peak at 1 6 6 0 t 1 0 cm" and a shoulder at 1 5 7 0 ± 2 0 cm" . I n 1  1  c o n t r a s t , cubic samples annealed below  190°K  cm \  had a peak at  Cubic samples annealed t o  at 1130 cm  205°K  only had a peak at 1570  t  10  1570 +  cm  -1  10  a shoulder  and a deep minimum at 1 0 5 0 c m , much l i k e Zimmermann and  Pimentel's ( 9 7 ) spectra.  -1  While the f i n a l assignments of the bands are l e f t  112  u n t i l s e c t i o n k.3 1 5 7 0 cm  (page 1 7 5 ) , i t seems l o g i c a l t o consider the v i t r e o u s  shoulder and the 1 6 6 0 cm  1  1  peak as being e i t h e r v_ or 2v . d K  Cor-  responding features were not observed i n v i t r e o u s DgO i c e I . The reasons f o r s h i f t s t o lower frequencies, Av^CH^O) = . 5 6 m  and  1  C  AV^CD^O)  =  -18  cm ^, have been explained by Zimmermann and Pimentel . ( 9 7 )  on  the b a s i s of a weakened molecular p o t e n t i a l and decreased force constants. However, the large d i f f e r e n c e s between here, i s not understood.  and D^O,  observed  In F i g . 3.5 (page 6 7 ) one saw that the v i t r e o u s  h  -1  AVg 12.5  s h i f t s f o r H^O  was constant at 3 5 0 cm -  5°K.  dence, -1.6k  Above  125°K  cm /°K. 1  Av  2  -1  up t o 1 1 5 ± 5°K and broadened t o 3 9 0 cm  at  had a negative, r e v e r s i b l e temperature depen-  A l l other v i t r e o u s H^O,  HDO and D^O  bands were  narrower a f t e r the transformation and subsequently broadened w i t h i n c r e a s i n g temperature i n the cubic phase. The anomalous behaviour of Av^ (H^O) may be explained i f the v i t r e o u s ice band i s composed of a medium absorption s l i g h t l y below 1 5 7 0 cm and a 2 v absorption s l i g h t l y above 1 6 6 0 cm \ Although v and 2V,.. both must t\ d K narrow upon d e v i t r i f i c a t i o n , t h e i r frequencies both s h i f t away from 1 5 7 0 cm 1  yielding  a net broader v / 2 v band. d  1  For t h i s explanation i t i s a l s o neces-  a  sary that the peak absorbance of 2 v  decrease i n the cubic phase.  negative temperature dependence of the  The  band r e s u l t s from the s h i f t of a  weak underlying 2 v t o lower frequency (towards 1 6 0 0 cm ) and the s h i f t 1  R  of V g to higher frequency (towards 1 6 0 0 cm ) . w i t h increasing temperature. 1  As the two absorptions f u r t h e r coalesce, the composite band becomes narrower. However, the frequency dependence of the cubic band i s determined by the more intense  absorption. The V g frequencies obtained f o r c r y s t a l l i n e i c e formed from the vapour  113 ( t h i s work, 9 7 , 1 0 5 , 1 0 6 ) do not agree with Whalley's ( 9 5 ) work. phases of i c e Whalley found  to be higher than 1 6 5 0 cm .  of t h i s work support Ockman's ( 1 0 8 ) observations liquid. cm . 1  The  -1  For a l l results  f o r samples formed from the  Ockman's ( 1 0 8 ) r e f l e c t i o n spectra i n d i c a t e d a weak maximum at 1 6 0 0  I t i s p o s s i b l e that Whalley's ( 9 5 ) m u l l i n g technique gave a d i f f e r e n t  r e f l e c t i o n spectrum than occurs f o r t h i n f i l m s and enhanced the high f r e quency p o r t i o n of h i s v^.  His r e s u l t s showed the mulling agent decreased  r e f l e c t i o n and s c a t t e r i n g compared to powder spectra.  On the other hand,  r e f l e c t i o n and s c a t t e r i n g may be severe f o r t h i n f i l m s . F i n a l l y , the weak shoulder and deep minimum ( 1 1 3 0 cm  and 1 0 5 0 cm "*")  1  may have a r i s e n from a strong Christiansen f i l t e r e f f e c t on the high, f r e quency side of v . ( i i ) The v___ Din  Transformations  In the region from 3000 to 4000 cm  1  one observes the symmetric and  asymmetric 0-H s t r e t c h i n g frequencies from H^O of polymerization and the combinational modes.  The corresponding 0-D  Data f o r  and  of H^O,  shown i n F i g s . 3.2 and 3.4  molecules i n various degrees  absorption of  with the l a t t i c e  stretches are found betweeen 2000-2800 cm  HDO  and D^O  i n the v i t r e o u s and cubic phases, were  (pages 6 l and 6 6 ) and were compiled i n Table  I I I . I (page 6 2 ) . (a) The-  . shoulder.  The low frequency shoulder  (v-^)  , w a  s very poorly  defined (at 83°K) i n v i t r e o u s i c e (3191 - 1 5 cm ) but was b e t t e r defined i n 1  cubic i c e (3149 - 1 0 cm ^ ) . In c o n t r a s t , f o r D^0 i c e the w e l l defined f o r both v i t r e o u s and cubic i c e I (2372 ± 1 0 cm  shoulder -1  was  and 2321 cm  1  )  114  Like other molecular modes,  s h i f t e d t o lower energy because of weaker  molecular bonds, a shallower p o t e n t i a l w e l l and weaker force (b) The was  3253  (AV^CD^O)  cm  1  =  peak.  The v i t r e o u s i c e s t r e t c h i n g band frequency at 83°K  while f o r cubic i c e -23  constants.  was 3 2 1 7 c m , a s h i f t of - 3 6 c m -1  cm ^~) . The explanation f o r a negative  -1  s h i f t follows from  above. (c) The HDO modes. Table I I I . I , v _ = 2 4 3 7 c m  The v i t r e o u s i c e HDO absorptions were l i s t e d i n -1  UDn  and v  The cubic i c e HDO f r e -  -1  quencies were s h i f t e d - 2 1 and - 3 8 cm values.  = 3 3 0 4 cm .  nri Un.  1  r e s p e c t i v e l y from t h e i r v i t r e o u s  Reference t o Table I I I . I shows that these s h i f t s correspond very  w e l l t o the  s h i f t s of D^O and H^O r e s p e c t i v e l y .  The v i t r e o u s - c u b i c t r a n s -  formation had the same e f f e c t on v (asymm.) or v (asymm.) of HO,-HDO and OD OH <L DgO molecules whether they were i n an H^O or D^O l a t t i c e .  There appear t o  be no d i f f e r e n c e s among the couplings of HDO, HgO and D^O molecules f o r e i t h e r v i t r e o u s or cubic i c e I . F i n a l l y , the explanation f o r the d i r e c t i o n of s h i f t follows from previous  discussion.  The HDO s t r e t c h h a l f - h e i g h t widths sharpened from 7 7 t o 23.5, c m 1 1 5 t o 35.5 cm  1  between the v i t r e o u s and cubic phases (at 83°K).  -1  and  I n vitreous  i c e both the 0 p o s i t i o n a l disorder and proton o r i e n t a t i o n a l disorder c o n t r i buted t o the widths.  In cubic i c e the 0 p o s i t i o n s were ordered, but the  proton disorder broadening remained. HDO molecules had Av solids.  For example,  Even i n the cubic phase the uncoupled  values about twice as large as expected f o r ordered Whalley ( 9 6 ) found Av  (EDO) data of 8 - 1 3 c m  -1  for  an ordered high pressure i c e . The HDO peaks were u n i n h i b i t e d by band overlap and provided ,an exc e l l e n t probe f o r making accurate transformation  rate studies of v i t r e o u s  115  ice.  The d i l u t e H / D i s o t o p i c s u b s t i t u t i o n should be employable i n r a t e  studies of other disordered systems. (d) The oligomeric modes. A l l v i t r e o u s HgO and D^O i c e samples observed i n t h i s work had very weak absorptions between i n HgO (near  2620  cm  1  in  D^O).  Typical  E^O  3600  and 3 7 0 0 cm  peaks were shown i n F i g .  (page 6k) and the frequencies were l i s t e d i n Table I I I . I I (page 6 5 ) .  1  3-3  These  absorptions occurred quite close t o the vapour phase monomeric frequencies. Shurvell ( 1 1 5 ) and Van T h i e l et_ a l . ( 1 1 7 ) studied the absorptions from d i l u t e concentrations of H^O and D^O i n various matrices.  Van T h i e l et_ a l . assigned  the (v^s v^) monomeric, dimeric and t r i m e r i c H^O ( i n an N matrix at 20°K) absorptions t o  (3725  and 3 6 2 5 c m ) , -1  (3691  and 3 5 ^ 6 c m ) , a n d ( 3 5 1 0 and-1  3355  cm ^) r e s p e c t i v e l y . For D^O S h u r v e l l reported (v^s v^) monomer and dimer absorptions f o r an respectively.  matrix at  (2765  and 2 6 5 5 cm ) and 1  and 2 6 5 0 cm ) 1  Our frequencies appear t o r i s e from dimeric systems.• We  observed h a l f - h e i g h t widths of 1 5 - 2 0 cm than i n matrix i s o l a t i o n , 2 0 - 30 cm up t o the softening temperatures 30°K.  (2725  1  which were s l i g h t l y smaller  Their oligomeric peaks were s t a b l e  of the matrix used, g e n e r a l l y l e s s than  Oligomeric absorptions observed i n t h i s work were s t a b l e up t o the  softening temperature of the H^O glassy m a t r i x , 125°K.  That corresponds t o  the temperature of onset of peak s h i f t i n other bands, i_.e_. the temperature of molecular r e o r i e n t a t i o n .  The high softening temperature i s consistent  with the increased van der Waals forces i n molecular s o l i d s compared to rare gas s o l i d s .  1  For example, S h u r v e l l ( 1 1 5 ) observed that H^O oligomers  were stable up t o 80°K i n a CCl^ matrix.  116  For t h i s work, one understands that the softening permits short-range molecular d i f f u s i o n and r e o r i e n t a t i o n r e s u l t i n g i n p r o g r e s s i v e l y higher polymerization.  The monomeric, oligomeric and medium polymers disappear as  w e l l as t h e i r absorptives. The high frequency side of the g v  greatly  T R  hand was  sharpened. One can estimate the f r a c t i o n of the sample which was i n the form of  dimers.  In t h i s work the r a t i o of  polymerized H^O  i s 1 to TO.  absorbances  f o r dimeric and f u l l y  Work by Ikawa and Maeda ( l l 8 ) on the c r y s t a l l i n e  s o l i d (complete polymer) and by F e r r i s o and Ludwig ( 1 1 9 ) on the vapour phase (monomeric H^O)  showed that the e x t i n c t i o n c o e f f i c i e n t s of monomeric  and f u l l y polymeric HgO are i n the r a t i o 1 to 30. monomeric-dimeric H^O  Thus one f i n d s 1 part of  to 2.3 parts of completely polymerized HgO.  There r e -  mains an unknown p o r t i o n of the sample i n intermediate stages of polymerization.  However, while t h i s estimate seems to be very h i g h , the point, i s -  that a considerable amount of oligomeric H^O  and DgO  sample was formed by i  our condensation technique. (e) The Av  35  of the band ( v ^ v^, v  1  + v ). T  The h a l f - h e i g h t width  h  (Av ) of the composite band (v^, v^, (v^ + v^)) sharpened from 3 2 5 i 1 0 cm  1  to  285  t  10  cm  1  (83°K)  between v i t r e o u s and cubic i c e . The band t  sharpened i r r e v e r s i b l y between 1 1 5 i 5°K and 1 2 5 ± 5°K by the s p e c i f i c l o s s of approximately 2 0 % of the high frequency absorption. a r i s e s from medium length H^O bonding.  and D^O  Such absorption  polymers with incomplete hydrogen  In a d d i t i o n , the band sharpened by the increase of 0 p o s i t i o n a l  ordering and the smaller range of molecular p o t e n t i a l energies.  117 D.  Combination and Overtone Mode Transformations  ( i ) The 3VR Transformation Absorption near  cm  2200  -1  i n HgO i c e and near  been v a r i o u s l y assigned t o 3VR a n d v had a s i n g l e f e a t u r e , a peak at  2  2220  + VR.  1600  cm  i n DgO i c e has  -1  S p e c i f i c a l l y , the H 0 absorption 2  or 2235 cm  1  i n v i t r e o u s or cubic i c e .  The s h i f t upon annealing was t o higher frequency, and was a l s o found f o r VR  and  VIJI.  The nature of the s h i f t was given i n F i g . 3.2 (page  6l)  while  data was given i n Table I I I . I (page 6 2 ) . Cubic i c e absorptions, 2 2 3 5 and  1635  cm" f o r H 0 and D 0 (at 8 3 ° K ) , 1  2  2  agreed very w e l l w i t h the s i n g l e c r y s t a l observations of Ockman III.XI.  Table  As w e l l , Haas and Hornig's ( 1 0 6 ) and Giguere and Harvey's ( 9 8 ) r e -  s u l t s were comparable. higher.  (108),  However, Whalley's  (95,96)  r e s u l t s were c o n s i s t e n t l y  As f o r v , the d i f f e r e n c e s i n Whalley's r e s u l t s may have a r i s e n from 2  changes i n the r e f l e c t i o n spectrum caused by the m u l l i n g agents. The s h i f t by + 1 5 cm  1  ( f o r H 0) t o higher frequency upon d e v i t r i f i 2  c a t i o n may provide a clue t o the o r i g i n of t h i s band. V2  +  V R then one would expect the s h i f t  Av2 + A V R = (-56 + 31) = -25 cm would expect  A(3VR)  1  A ( v + V R ) t o be p r o p o r t i o n a l t o 2  f o r H 0.  I f the band i s 3VR then one.  2  t o be p r o p o r t i o n a l t o  s h i f t t o higher frequency by + 1 5 c m  -1  I f the band i s  3(AVR)  =  +93  cm . -1  The observed  i n H 0 and + 1 8 cnT^ i n D 0 supports 2  2  the 3VR assignment. F i n a l l y , the 3VR r e s u l t s suggest that our cubic sample formation technique i s adequate since the r e s u l t s are consistent w i t h r e s u l t s from c r y s t a l l i n e samples prepared from the l i q u i d , i_.e_. (108) and Giguere ( 9 8 ) .  the r e s u l t s o f Ockman  118  ( i i ) The (v + v ) Transformation The high frequency shoulder (v + v ) was very poorly defined i n v i t r e o u s i c e , but was w e l l defined i n cubic i c e . As f o r other molecular modes, (v + v^) s h i f t e d i r r e v e r s i b l y towards lower frequency HgO and -34 cm  1  (-27 cm  1  for  f o r D^O) between 130 and 145 i 5°K. Comments made above  with respect t o the o r i g i n of the molecular mode s h i f t s and the temperatures of transformation a l s o apply t o (v + v ).  E.  Confidence i n the Cubic Ice I Samples  Does d e v i t r i f i c a t i o n provide a good cubic sample of i c e l ?  Beaumont  et a l . ( 6 5 ) found that the v i t r e o u s - c u b i c transformation took only a few minutes t o f i n i s h even at 150°K. transformed  c l e a n l y t o cubic i c e .  As w e l l they found that v i t r e o u s i c e On the other hand, Dowell and R i n f r e t (74)  estimated only a 30 per cent conversion t o cubic i c e and an average -cubic o  c r y s t a l l i t e s i z e (embedded i n the remaining 60% v i t r e o u s i c e ) of 400 A. The r e s u l t s of Dowell and R i n f r e t (74) necessitate a heat of cubic-hexagonal phase transformation of 2 4 cal/gm.  Such an e v o l u t i o n o f heat was unobserved  at higher temperatures by Beaumont et a l . of cubic-hexagonal  I n f a c t they estimated the ,heat  transformation t o be l e s s than 1.5 cal/gm.  ;  I f the samples i n the present work were only 30% cubic i c e with 60% v i t r e o u s i c e remaining, then the spectra of annealed samples should .have been c h a r a c t e r i s t i c of v i t r e o u s i c e and might have e x h i b i t e d separate maxima from cubic and v i t r e o u s i c e . Only one s t r e t c h i n g peak was observed and the bands matched very c l o s e l y the spectra of hexagonal i c e I ( 9 5 ) -  These f a c t s  support Beaumont's i n t e r p r e t a t i o n of the v i t r e o u s - c u b i c transformation.  119  . The fully  e v i d e n c e s u g g e s t s samples p r e p a r e d i n t h i s work were  to cubic  vitreous a tail  The  presence of  i c e would have broadened the  on  the  of spectra ice  ice I.  high  frequency side.  i n F i g . 3.1  I formed from the Deposition  significant  h a l f - h e i g h t w i d t h s and  favourably  rates  o f lkO  with  band  spectra of  shapes  hexagonal  i n t h e s e e x p e r i m e n t s l i e n e a r t h e maximum s e t  f o r hexagonal i c e I  microns.  The  (119) the  v o l u m e o f i c e I s a m p l e was  d e n s i t y o f 0 . 9 2 4 gm/cm^ one  had  s a m p l e s w e r e a p p l i e d i n two  b u r s t s , o f two  window i n i t i a l l y t i o n was  a t 83°K.  a t l e a s t 0.04  By  by  A s s u m i n g a v-^HgO) e x t i n c t i o n s a m p l e t h i c k n e s s was -h  1.0  giving  liquid.  Beaumont e t a l . ( 6 5 ) — 0 . 0 k gm/cm^/hour. coefficient  amounts o f r e s i d u a l  s t r e t c h i n g bands a s y m m e t r i c a l l y ,  The  compared v e r y  transformed  a t l e a s t 1.4  a minimum s a m p l e o f 1.3  x 10  x 10  seconds d u r a t i o n  a s s u m i n g a 1.0  0.5  -  At  a  3  cm  .  gms.•  Such  each, onto  crn^ i m a g e , t h e  a  r a t e of- d e p o s i -  gm/cm2/hour. -k  During (assuming the same). and  the  heats of  T h e r e was  to permit  v a p o u r r e l e a s e 0-09  cal  hexagonal i c e I are  the  r  of i n d i v i d u a l molecules.  amount o f  The  induce l o c a l i z e d extent  s e l f - a n n e a l i n g , d e p e n d e d on  the  a l s o been the  cubic  since the  experience  extensive  r a t e of; d i s s i -  c o n d i t i o n s , w e r e made t o f o r m  i c e I was  due  samples were uncovered.  of other  sharpening t o two  and  and  surface.  under v a r i o u s  sublimation  heating  of heating  However, a l l a t t e m p t s t o a n n e a l samples above 210°K l e d t o  The and  o f H^O  o f amorphous and  of heat a t t h e window-sample  instantaneous has  gms  s u f f i c i e n t heat of condensation to  Several attempts, ice.  x 10  sublimation  diffusion  d i f f u s i o n , or the pation  d e p o s i t i o n , 1.3  workers  The  almost sublimation  (120).  alteration  effects.  Such  hexagonal  of the  first  was  bands between v i t r e o u s the  diffusion  and  120  r e o r i e n t a t i o n of i n d i v i d u a l molecules i n t o l a t t i c e s i t e s i n the cubic u n i t cell.  The cubic u n i t c e l l s put a l l molecules i n the same e l e c t r i c a l en-  vironment, but where the mechanical v i b r a t i o n s were broadened by asymmetries i n proton o r i e n t a t i o n at equivalent u n i t c e l l s i t e s . The  second e f f e c t was the extension of low, medium, and high;polymer  H 2 O c l u s t e r s o f the vitreous phase i n t o f u l l y hydrogen bonded networks of the cubic phase.  During the process of c r y s t a l l i z a t i o n the c l u s t e r s amal-  gamated i n t o l a r g e r u n i t s where the deformed or absent hydrogen bonds at the contact surfaces between c l u s t e r s (or c r y s t a l l i t e s ) represented only a small f r a c t i o n of the t o t a l number of hydrogen bonds.  h.2  •  Temperature Dependence of Cubic Ice I Absorptions  1  Accurate measurements of s h i f t s i n frequencies and half-height widths in  H>>0, D 0 2  and HDO spectra between  h°K  and 2 0 0 ° K permit accurate c o r r e l a -  t i o n s of the s h i f t s t o changes i n R ( 0 * • • - 0 ) and changes i n hydrogen bond strength.  In t h i s section values of R ( 0  over the range  10° -  200°K  ,  -  ,  *0)  and p l o t t e d against  f o r cubic i c e I are c a l c u l a t e d v.  T J  (HD0)  On  and v.^(HDO') . , That OD  p l o t i s compared t o the p r e d i c t i o n s of an e m p i r i c a l equation which r e l a t e s v^(HDO) t o R ( 0  0 ) .  In a d d i t i o n , values of  Un  c a l c u l a t e d from v  (HDO) and v  <  (HD0) Un T T  and X ^  T T  (HD0)  Un  (HDO) as a function of temperature.  are  121 A.  Dependence o f HDO Bands on Temperature  A few general remarks can be made concerning the low temperature l i m i t s and temperature dependences of a l l the absorption bands.  The low  temperature l i m i t i n g frequencies were obtained by e x t r a p o l a t i o n t o Q°K simply as a matter of convenience.  The i n d i v i d u a l frequencies had v i r t u a l l y the  same values when extrapolated t o 5° or 0°K. There i s the danger that the properties of i c e are i r r e g u l a r below 5°K. However, Flubacher et_ al_. (83) proved that the thermodynamics  of i c e I are w e l l behaved down t o 2°K.  The low temperature l i m i t i n g frequencies, h a l f - h e i g h t widths and peak heights are f o r E^O molecules at the distance of minimum approach. p o t e n t i a l i s deepest and the 0-H p o t e n t i a l i s shallowest.  The' 0  - , , ,  H  The conditions at  minimum approach permit the l a r g e s t o r b i t a l overlap and degree of hydrogen bond covalency, the l a r g e s t e l e c t r o s t a t i c e f f e c t s , and the l a r g e s t c o n t r i bution of CT. As w e l l , the low temperature l i m i t i n g frequency gives the 0 -> 1 energy l e v e l spacing f o r minimum root-mean-squared of HgO t r a n s l a t i o n and 0-H v i b r a t i o n .  (RMS) amplitudes  F i n a l l y , the contours of the;bands  are l e a s t d i s t o r t e d by hot bands and v i b r a t i o n a l perturbations o f the , potential.  .< :  As the temperature was r a i s e d the i c e I sample expanded, g i v i n g ; increasing R ( 0  - , , -  0 ) and r e s u l t e d i n the weakening of the 0-*- H bonds and  a strengthening o f the 0-H bonds.  ,  Hence the l a t t i c e mode and molecular mode  force constants could be understood t o decrease and increase r e s p e c t i v e l y , i_.e_.  the frequencies r e s p e c t i v e l y decreased and increased.  While the  c r y s t a l s expanded.continuously and n o n - l i n e a r l y during warm-up, the frequencytemperature dependence was approximated by two s t r a i g h t l i n e s .  The, l i n e s  122  corresponded t o regions of slow and f a s t c r y s t a l expansions.  Below 50°K the  e f f e c t s of AR(O'--'O), changes i n RMS amplitude of t r a n s l a t i o n and hot hands (v = 1 -> 2 ) were small. F i n a l l y , some i r r e g u l a r i t i e s or d i s c o n t i n u i t i e s i n the temperature dependences i n d i c a t e p o s s i b l e changes i n the s o l i d phase or changes i n energy l e v e l populations. ( i i ) Dependence of HDO Frequencies on Temperature (a) v (HDO) and v '(HDO). n K  A f u l l d i s c u s s i o n of the o r i g i n and nature  of the l i b r a t i o n a l modes i s given i n section U . U . ature dependences were negative f o r both bands, -O.lUT cm /°K above 55°K. -1  should have been n e g l i g i b l e .  As expected, the tempercm /°K below 55°K and 1  -0.02  Below 55°K the e f f e c t s of v Above 55°K, however, v  ra  and v hot bands m  and v  hot bands, may  have contributed s i g n i f i c a n t l y t o the changes i n band frequency, width and height. For v (HDO) ( F i g . 3 . 7 ) one saw an apparent d i s c o n t i n u i t y between 1 0 5 ° n and 120°K.  The change i n slope may have a r i s e n from s i g n i f i c a n t population  of molecular mode hot bands.  The "hot" molecules would be decoupled from  the remaining l a t t i c e molecules, and would have weaker hydrogen bonds. Consequently, smaller l i b r a t i o n a l frequencies would be seen. (b) v (HD0) from h.00% HDO i n D 0 . The shallow molecular p o t e n t i a l On d i s demonstrated by the low temperature l i m i t i n g v (HDO) frequency, i . e . On rtTI  3263.5  cm  -1  at 0°K compared t o  o  3268  cm  -1  and  3288  cm  -1  at  80°  and l 8 0 ° K  respectively. The HDO frequency-temperature p l o t (.Fig. 3 . 6 ) showed unambiguously that the frequency s h i f t was continuous and non-linear i n the high and  123  low temperature approximations. least-mean-squares  Since there i s l i t t l e point i n doing a  f i t t o some a r b i t r a r y f u n c t i o n , the data were approximated  on a b i l i n e a r b a s i s .  Up t o 45 * 5°K v  (HDO) was constant w i t h i n the random On  point s c a t t e r , + 0 . T 5 cm  Within the s e n s i t i v i t y of the experimental  technique and the spectrophotometer, changes i n v  (HDO)  due t o changes i n  un R(0"*'*0)  and the e f f e c t s of v  combination bands with t r a n s l a t i o n a l hot  On  bands are i n s i g n i f i c a n t below U5°K. Linear low temperature dependence was assumed f o r v  t  (+0.0U7  creasing  cm /°K.  R(0---"0),  (HDO) below 80°K  Above lt5°K one saw a d e f i n i t e e f f e c t due.to.in-  -1  0.005)  On  the s h i f t of frequency exceeds the point s c a t t e r . .Thus  the thermal expansion data of B r i l l e and Tippe ( 6 0 ) suggest that when 0)>  AR(0  o  ±0.0001  A/°K  s i g n i f i c a n t changes i n v.^HDO) occur. On  Linear high temperature dependence was assumed f o r v 80°  and 190°K, i_.e_.  +0.200  t  0.005  cm /°K.  (HDO)  between  Data of t h i s work are i n good  -1  agreement with the data of Ford and Falk  On  (100).  Their data were shown i n  F i g . 3.6 and were obtained from the best s t r a i g h t l i n e through t h e i r F i g . 2. One sees that the s t e a d i l y i n c r e a s i n g  R(0*-  y i e l d s a s t e a d i l y increasing v  frequency.  (HDO)  - ,  0)  i n a cubic i c e l a t t i c e The s p e c i f i c dependence  On  of v  Q H  on  R(0--'-0)  i s given i n the f o l l o w i n g section•(page 1371.  ;  •  There was a s l i g h t l y i r r e g u l a r s h i f t of v (HD0) between *t5°K and OTI  On ,  70 K i n F i g . 3.6.  /'  The i r r e g u l a r i t y may Have been due t o a p a r t i a l order-  disorder phase transformation p r e d i c t e d i b be near 60°K by P i t z e r and , Polissar ( 7 0 ) .  However, they pointed out that the period of t r a n s i t i o n was  probably greater than 2h hours.  That p e i i o d i s f a r i n excess of our very  r a p i d c o o l i n g time of 15 - 2 0 minutes.  P. a order-disorder phase t r a n s f o r -  mation i s a l s o unsupported by any compara'lle s h i f t i n h a l f - h e i g h t width.  121*  A l t e r n a t e l y , the i r r e g u l a r i t y may have a r i s e n from a transformation from an as yet uncharacterized low temperature i c e phase, or from one of the d i s o r d e r e d high pressure i c e s .  A low temperature phase transformation i n i c e 1^ was not  i n d i c a t e d by heat capacity experiments ( 8 2 ) , although C„ had a s l i g h t i r r e g u l a r i t y near 80°K.  The i r i r r e g u l a r i t y represents only 1 - 2% of the  t o t a l frequency and i s probably undetectable i n Cp experiments since molecular modes c o n t r i b u t e l i t t l e t o Cp. (c) VQp(HDO) from 5-9^% HDO w i t h respect t o  VQJJ(HDO)  differences i n d e t a i l s .  apply as w e l l t o  -  The general comments made above V Q ^ H D O )  : However, there are  S p e c i f i c d i f f e r e n c e s can be seen i n F i g . 3.6 and  Table I I I . I V (pages 71 and 7 2 ) . quency was 2412.0  i n H^O.  1 cm  The low temperature l i m i t i n g v (HDO) f r e QD  The r a t i o of HDO  frequencies,  v^/v', Un  1.35^ - 0.001.  is  UD  That r a t i o i s the same as reported by Whalley (96) f o r  i c e s I , I I and I I I and i s very close t o the vapour phase r a t i o of 1.360. From the r a t i o s one can show t h a t the HDO  anharmonicity, as discussed by  Whalley ( 9 6 ) , was the same at 0°K as he found at 100°K, i_.e_.  about 100 cm  At both temperatures i t i s 23% l a r g e r than i n the vapour phase.  This does  not mean the anharmonicity i s independent of temperature as i s shown i n the next s e c t i o n .  .  The temperature dependence of v^^XHDO) i n s e v e r a l ways. Un  s c a t t e r up to 30 t  VQ^(HDO)  was d i f f e r e n t from that of  The v__(HD0) data were constant w i t h i n the p o i n t UD  5°K i n contrast t o 45 ± 5°K f o r v_„(HD0).  The low  Un  temperature dependences of v  and  were the same.. However, the high  temperature dependence of v . was (+0.123 - 0.005) cm "V°K nT  UD  (Av^/AT was Un  I.626 times h i g h e r , 0.200 cm~' "/ K). 1  0  The d i f f e r e n c e s i n the high temperature  dependences probably arose from d i f f e r e n c e s i n the p h y s i c a l p r o p e r t i e s of  125 the two mediums. The v data are from HDO i n D O while the u „ data are On d OD from HDO i n HgO. Consider the percentage s h i f t from the low temperature l i m i t i n g f r e quencies f o r the asymmetric stretches i n HDO, D^O and H^O, T _ 0 percentage s h i f t = STR STR x 100 STR T where v i s the s t r e t c h i n g frequency at temperature T, bin V  V  v  and  v^ bin mT3  i s the low temperature l i m i t i n g frequency,  One might have expected  i n H^O and D^O t o s h i f t by the same percentage of  the low temperature frequencies.  However, between  and l 6 0 ° K the  10°  —2  -2  s h i f t s of H 0 and D 0 increased from 0 . 6 x 1 0 % t o 8 2 x 1 0 % and 0 . 0 $ t o 2  G  _;2  36 x 1 0 % r e s p e c t i v e l y .  The  s t r e t c h i n g frequencies do not s h i f t propor-  tionally.  The s h i f t s of v . ^ C H D O ) and v (HDO) are not p r o p o r t i o n a l l y the un uv same, nor do they compare t o the percentage s h i f t s of i n H^O and D^O. The V Q ^ ( H D O ) s h i f t was f a s t e r than f o r v^D^O) at a l l temperatures,, w h i l e the  v  (HD0)  On O I J  s h i f t e d p r o p o r t i o n a l l y f a s t e r than  v_(H 0) 3 d O  only below  100°K.  The percentage s h i f t from the low temperature l i m i t i n g frequencies were: Temperature °K  20 1+0 60  Percentage S h i f t V  OH'  (HDO)  0 .9 2 •5 7 .0  80  ll+..1+  100 20  2 3 .6 35 . 2  1+0 60  1+6 • 9 5 9 .1+  80  73 . 2 89 . 2  200  v  Q D  (HD0)  x  102 v (H 0) 3  2  v (D ( 3  2  0 .1+  0 . .6  0  3•7 9 .1  1 , .8  1 .2  1+,. 0  1 7 .1+ 26 . 1  9..3 21. .2  3 .7 7 .0 1 1 .6  36 . 1  3 7 ..1+ 6 0 ..5  1+6 . 0 5 7 .6 7 0 .1 81+ . 2  8 1 ..7 — —  17 . 0 '25 .'2 36 . 0 55 .9 —  126  Dantl (6h)  found the thermal expansion c o e f f i c i e n t s f o r H 0 and D 0 2  l a t t i c e s were the same above 120°K.  Hence, d i f f e r e n c e s i n  an u n l i k e l y source of the d i s p e r s i o n .  AR/AT  2  seem t o be  The d i f f e r e n c e i n temperature depen-  dences may a r i s e from d i f f e r e n c e s i n HDO coupling t o H 0 and D 0 l a t t i c e s . . 2  2  I f HDO coupling t o D 0 decreases f a s t e r than t o H 0 then the OH (HDO.) hydrogen 2  2  bond t o DpO must weaken f a s t e r and the v (HDO) frequency must s h i f t f a s t e r OTI  On  than v (HDO). QD  The v  (HDO) data are not i n as good agreement with the data; of^  Ford and Falk ( 1 0 0 ) as f o r v_„(nT)0).  Again t h e i r data are from the best  Un  s t r a i g h t l i n e through t h e i r F i g . 2 . The v are displaced 2 cm  1  t o lower frequency.  ences i n instrument c a l i b r a t i o n . ( i i ) Dependence of HDO Frequencies on The r e l a t i o n s h i p between v  Un  This i s probably due t o d i f f e r -  R(0  and  slopes agree but t h e i r . d a t a  , , ,  '0)  R(0'  ,  -  ,  0)  f o r a large family of  molecules was studied by various authors (27-30) and several e m p i r i c a l r e l a t i o n s h i p s were proposed  (28,29,32)  by neglecting s p e c i f i c d i f f e r e n c e s i n  molecular p r o p e r t i e s . The e m p i r i c a l r e l a t i o n s h i p s give only an average v /R(O--'-O) behaviour. The HDO frequencies observed i n t h i s work permit Un  the v  Un  /R(0*  - -  *0)  dependence f o r one molecular system t o be accurately eva-  luated. (a) Observed HDO frequency dependence on c a l c u l a t e d  R(0«'*0).  The  observed HDO frequencies are known as a f u n c t i o n of temperature (page 7 1 ) but not d i r e c t l y as a function of  R(0*  ,  -  *0).  One requires the v a r i a t i o n  of R(O----O) i n cubic i c e I as a f u n c t i o n of temperature. A d e t a i l e d study of the temperature dependence of the l a t t i c e parameters of cubic i c e I has not been reported i n the l i t e r a t u r e .  However, the  127  cubic i c e I a (H 0)  = 6.350 ± 0.008 A and a ( D 0 ) = 6.351 - 0.008 A.  2  o  l a t t i c e parameter was given by Wyckoff (62) f o r lU3°K, o o 2  o  For hexagonal  i c e I , B r i l l e and Tippe (60) made a d e t a i l e d study of the l a t t i c e between 13° and 193°K:  a , c Q  parameters  and the l i n e a r thermal expansion c o e f f i c i e n t s  Q  were evaluated every 20° from 13° t o 193°K.  In a d d i t i o n , x-ray d i f f r a c t i o n  (58) and i r (95) studies i n d i c a t e d that the nature of the hydrogen bonding and the nearest-neighbour configurations are the same i n hexagonal and cubic i c e I . On that basis we assumed the l i n e a r thermal expansion c o e f f i c i e n t of cubic i c e I (aa,o^' ) "to be the average of the expansion c o e f f i c i e n t s o f hexa, hex hex gonal i c e I ( c t (T) + cxc ( T ) ) , _i.e. ao  a  Q  1/  cub/ x (T) =  hex, , hex 2-(cxa (T) + a c (T))  a  0  at temperature T..  0  cub Values of a (T) were determined every 10°K i n the i n t e r v a l 1 0 ° t o a Q  200°K by the f o l l o w i n g method.  B r i l l e and Tippe's (60) t e n a  and c parahex Twenty values of a a (T)  meters were p l o t t e d as a f u n c t i o n of temperature.  Q  Q  Q  hex n o and a.c (T) were determined at t e n temperatures between 20 and 200 K, two 0  values at each temperature.  The p a i r s of c o e f f i c i e n t s at each temperature  were obtained from i n t e r v a l s of 2 ° above and below that temperature, JL.e_. a  h e X  a  0  (l50°K) = I [ a ( l 4 8 ° - 1 5 0 ° ) 2 a h e X  Q  In the same way ac^ (T) was evaluated. X  CCQ (T) , t e n values of  a  h e X  a  (150°-152°)]  Q  From the t e n values of ^ao^T ) and 1  were obtained, F i g . h.l.  X  Using W y c k o f f s  +  (62) ao (H" 0) at l43°K (6.350 A) and the l i n e a r Ub  2  thermal expansion c o e f f i c i e n t s i n F i g . U . l , the cubic i c e I l a t t i c e parameter aQ (T) was c a l c u l a t e d every 2°K down from lh3°  t o 10°K and every 2°K  up from lh3°  [Since the a ^ t n ^ O )  Ub  t o 200°K, aQ (T) i s shown i n F i g . h.2. Ub  and a ^ ( D 0 ) l a t t i c e parameters were the same w i t h i n experimental e r r o r , ub  Q  6 0 -1  50  -  40  -  30  -  20  -  10 -  O O  i  1  1  1  1  50  1  1  1  1  1  100  1  1  1  1  1  T50  1  1  1 — — i  1  1  200  TEMPERATURE°K Fig." h.l—The'"'"llne"ar- thermal""expansion c o e f f i c i e n t of cubic i c e I as a function of temperature c a l c u l a t e d from the hexagonal i c e I data of B r i l l e and Tippe ( 6 0 ) .  ^ CO  2  0  0  H  129  50H Y.  o  LU  D h <  100 H  Ld CL  UJ h 50 -  O 6.345  6.350  a F i g . k.2  r  i  6.355  CUBIC  r  6.360  6.365  ICE i  !  The cuhic i c e I l a t t i c e parameter as a function of temperature. The values were c a l c u l a t e d from the experimental a at l 4 3 ° K and the c a l c u l a t e d thermal expansion c o e f f i c i e n t s . Q  130  only the a^^CHgO) parameter vas evaluated.] 0) = ( J$~ '/k)a^°{T).  the distance R(0  For the cubic i c e I u n i t c e l l  The r e s u l t i n g cubic i c e I 0  t  0  distances are p l o t t e d i n F i g . U.3 as a f u n c t i o n of temperature. HDO s t r e t c h i n g frequencies from s e c t i o n 3.2A are p l o t t e d as a f u n c t i o n of R(0**' 0) i n F i g . k.k.  Frequency and R ( 0  -  f u n c t i o n of common temperature.  , , , -  0 ) were c o r r e l a t e d as a  The frequencies were p l o t t e d as a f u n c t i o n  of the experimentally measured temperature, uncorrected f o r source beam heating  (+10°K at 83°K) since the error may not be a l i n e a r f u n c t i o n of tem-  peratures. Both the v^„(HD0) and v^(HDO) p l o t s were l i n e a r from 150° t o 200°K: Un 01) Av (HDO) — — = AR(0 0)  1.921 x 1 0 cm J  I  and A V  0D  ( H D 0 )  AR(0 However, the v  = 0)  i n Dg,0.  1.2ol x 310 -1 cm A p f l l  i n  (HDO) frequency should be p l o t t e d as a f u n c t i o n o f R(0'" "0)  f o r D 0 i c e I , since the v 2  1  -  data were obtained from a sample of k.0% HDO  There i s no experimental evidence t o suggest that the l i n e a r thermal  expansion c o e f f i c i e n t s of the HgO and D 0 i c e s are d i f f e r e n t . However, i t 2  may be i n c o r r e c t t o assume the same behaviour since the amplitudes of t r a n s l a t i o n , l i b r a t i o n and v i b r a t i o n are d i f f e r e n t . From F i g . h.k one sees that the f r e q u e n c y — R ( 0 a l s o l i n e a r between 30° and 100°K:  ,,,  * 0 ) dependence i s  250  2  0  0  H  o  •  0  •  o  UJ  ^  h <  150  o  o  •  o  w IOO  •  o  •  o C - AXIS  Q_  ©Ao  •  • A - AXIS  (-  50 H  ICE I  o  O  -T  2.745  F i g . h.3  AXIS J  ICE I h  1  r-  2.750  T  1  1 1 2.755  R (O  1  1  O) A  1  1 1 2.760  1  r  "1  1  1  2.765  "The c a l c u l a t e d 0•••-0 distance In" cubic' i c e I as" a function•of" temperature compared t o hexagonal i c e I 0*••*0 distances from experimental data.  H  132  O  CD CM ro  o 00 C\J  u  ro  y u z  UJ Z)  o UJ  or  O  LL  CM  o  ro  Q i  O O  CO  CM ro  oo  CvJ  OJ  30i oiano (o --o) d F i g . h.k  The HDO s t r e t c h i n g frequencies i n cubic i c e I as a function of R(O--'-O). 'Frequency and R(0 ••*0) were c o r r e l a t e d at common temperature. -  133  • ^ AR(0  =  8.202 x 1 0 cm" /!  =  6.629 x 10  3  1  0)  Av (HD0) 0D  AR(0  0  cm  /A  0)  Below 30°K the frequency s h i f t was n e g l i g i b l e .  Between 100° and 150°K the  frequency—R(0'*'*0) dependences were non-linear.  The points of i n t e r -  s e c t i o n of the low and high temperature l i n e a r dependences were a t 125°K o  (2.748.7A) f o r both v.„(HD0) and v.^(HDO). Un.  OD  -1  F o r 100°K Whalley (95) assumed a Av/AR dependence of 3000 cm  °  /A to  support h i s argument that the d e v i a t i o n of 0**'"0 distances a r i s i n g from o r i e n t a t i o n a l d i s o r d e r was only a few hundreths of an angstrom. The tangent to v. (HD0) v s . R ( 0 " " 0 ) at 100°K i n F i g . 4.4 has Av/A R equal Un 3 —1 ° u  to 6.750 x 10  cm  /A, showing that Whalley's estimate was low by a f a c t o r  of about two. As w e l l , Whalley (96) found that the most intense v  (HDO) bands f o r  OH  i c e s I I , I I I and V were 3323, 3318 and 3350 cm" r e s p e c t i v e l y . Using Av/AR above, then the displacements of 51, 46 and 78 cm from i c e I v (HD0) 1  1  riu  Un  (3272 cm intense v  Un  were caused by l a r g e r 0''*'0 distances. S p e c i f i c a l l y , the most (HDO) absorptions i n i c e s I I , I I I and V had R ( 0 ' " * 0 ) ' s l a r g e r o  than c u b i c i c e I (100°K) by 0.008, 0.007  and 0.012 A.  Ice I I a l s o had two  other v„ (HD0) absorptions (3357 and 3373 cm ^) which suggest two other Un u  o  sets o f 0 " " 0 d i s t a n c e s .  They are longer than R(0  0) cubic (2.748 A)  o  by 0.013 and 0.015 A r e s p e c t i v e l y . tinct O  Thus i c e I I appears to have three d i s -  0 bond lengths, 2.756, 2.761 and 2.763 A.  13h  Ice I I I had one a d d i t i o n a l peak at 100°K,  cm . 1  3326  That could be  due t o a second d i s t i n c t '0*••*0 d i s t a n c e , which i s longer than R(0  0)  o  cubic by 0.008 A .  Thus i c e I I I has two sets of 0  # , , ,  0 d i s t a n c e s , 2.755 and  2.756 A. o •  Ice V has only a s i n g l e 0"'*'0 d i s t a n c e , 2.760 A. How w e l l the Av/AR r e l a t i o n s h i p s of i c e I apply t o other i c e s i s not certain.  The estimates of RCO-'-'O) above are only approximate.  At 0°K the h a l f - h e i g h t width f o r v.^CHDO) i n D 0 cubic i c e I was o  found t o be 3 5 . 5 cm  That i n d i c a t e s that the 0'"''0 distances vary by  o  l e s s than 1  A from the average value i n cubic i c e I a t 0°K. The - l Av (HD0) rose t o U 2 . 5 cm at l 8 0 ° K . Thus the R ( 0 0 ) d e v i a t i o n must OH 0.00U  S.  OTI  o  have been l e s s than  0.022  3j  A. Since the observed  Av data were twice the  expected width f o r an ordered phase ( 9 6 ) , then the d e v i a t i o n s i n R(0-••-0) a r i s i n g from o r i e n t a t i o n a l d i s o r d e r were l e s s than 1/2 the above v a l u e s , o  ± 0.002 and ± 0 . 0 1 1 A f o r 0 ° and l 8 0 ° K r e s p e c t i v e l y . S i m i l a r l y by using Av (HD0) and. Av /AR one f i n d s d i s p e r s i o n s i n R(O--'-O) of ± 0 . 0 0 2 and 0r>  QD  o  "  '  ± 0.010 A a t 0 ° and l 8 0 ° K .  •  ..  As one would expect the d i s p e r s i o n s of R ( 0 * • • ' 0 ) i n H^O and D^O are equal but the changes i n f o r c e constants are r e l a t e d by approximately  1 y~2.  C l e a r l y one does not expect the HDO frequencies t o be a l i n e a r funct i o n o f R(0*•••()) over a l l values of RCO'-'-O).  I f the hydrogen bond i s  t r u l y p a r t i a l l y e l e c t r o s t a t i c and p a r t i a l l y covalent i n nature then the strength o f the hydrogen bond should increase as ( l / R ( 0 ' • • * 0 ) 1 ^ a s temperature i s increased.  Correspondingly the covalent nature o f the bond w i l l  135  change n o n - l i n e a r l y . are  The e f f e c t s of such changes i n hydrogen bond strength  seen i n the observed non-linear behaviour and i n the f o u r - f o l d i n -  crease i n Av/AR. (b) Comparison of observed and e m p i r i c a l Av/AR r e l a t i o n s . The d e t a i l e d study of v . (HDO) absorption as a f u n c t i o n of temperature and i t s r  tI  On  c o r r e l a t i o n to R(O----O) permitted d e t a i l e d checks of e m p i r i c a l r e l a t i o n s between s t r e t c h i n g frequencies and hydrogen bond lengths i n i c e I . Many workers  (27,28,33)  have made c o r r e l a t i o n s from data of large numbers of  compounds i n d i f f e r e n t hydrogen bonding f a m i l i e s .  The l i n e a r r e l a t i o n s h i p  of Pimentel and Sederholm ( 2 8 ) , =  k.h3  (10 ) 3  -1  ( 2 . 8 U - R ) cm'  s a t i s f i e s neither the behaviour of Av/AR i n a family of O-H'-'-O compounds as Nakamoto et a l . ( 2 7 ) found, nor the behaviour of i c e I as was shown i n Fig.  k.k.  Recently Bellamy and Owen ( 3 3 ) gave a formula r e l a t i n g the frequency s h i f t (from the monomeric frequency) t o a maximum e f f e c t i v e hydrogen bond length and the measured Av where Av  str  str  0 *'-0 ,  =  distance:  c [ ( f )  1  2  -  (|)  6  ]  s h i f t of the s t r e t c h i n g frequency from the gas phase value,  d  the sum of the c o l l i s i o n r a d i i of two oxygen atoms i n Angstroms  and  o (d = 3 . 3 5 A ) ,  R  the 0* '0 distance i n Angstroms,  C  the constant of p r o p o r t i o n a l i t y between the p o t e n t i a l  -,  and the frequency s h i f t .  136  For a family of 0 - H  -,,-  0 hydrogen bonding compounds, Bellamy and Owen (33)  suggested a constant value of C = 50 cm"".  Their predicted Av  1  ,  agreed  SX>TC  very w e l l with the observed values, p a r t i c u l a r l y at long 0'-«-0 lengths, f o r a family of 0-H-''*0 systems. By using the R(O--'-O) values determined i n section (a) above f o r 10°K and 130°K, two values of the constant C were determined f o r i c e I: cm" .9 -1 C(130°K) = 57.767 cm" C(10°K) = 58.890  1  The constants were determined by s u b s t i t u t i n g the Av  ,  values between  S X/±  of the vapour phase  VQ (HD0) H  (10°K  cm  3263.8  and 130°K  -1  c a l c u l a t e A.v . (R).  cm "*") and the cubic i c e  (3757.5 3276.8  cm ). -1  I  values  The constants were then used to  Since the thermal expansion of cubic i c e I i s only  small between 10°K and 200°K, Bellamy and Owen:.';s(33) formula could only be checked over a small range of  distances.  0*••-0  The predictions of Bellamy  and Owen's formula and the observed Av/AR r e l a t i o n are shown i n F i g . U.5. For the constant determined at 1 3 0 ° K the predicted behaviour good above 130°K but d i d not follow the observed trend below 130°K. o  the  0  range  0  Av/AR =  2,263  cm  2.7^70  _1  O  /A.  A to  2.7U80  A  2.7570  A Bellamy and Owen's formula predicted -I o  Experimentally Av/AR =  7,360  cm  /A  o  from  2.7^70  n O (10°  (130° to 2 0 0 ° K ) .  Over  o  O  to  was  to 1 1 0 ° K ) and Av/AR = 2,lhk  cm  /A from  2.7U85  A to  A  O  O  2.7570  A  Thus above 1 3 0 ° K Bellamy and Owen's formula reproduces  the i c e I experimental behaviour w e l l .  Below 130°K  (R(0'*-'6)  less than  o 2.7U85  A) t h e i r formula  fails.  Bellamy and Owen ( 3 3 ) started from the Lippincott-Schroeder p o t e n t i a l and made c e r t a i n assumptions about the intermolecular i n t e r a c t i o n .  The  Lippincott-Schroeder p o t e n t i a l ( 2 5 ) consists of four terms, one term being  137  • — 200°K 0 <  2.755-  o  6  *—*  o LU 5^  150 ° K  2.750  u* ^ 5 0  IOO°K  m  0  K  A  '-IO°K  2.7463260  70  80  FREQUENCY F i g . 4.5  90  CM  The s t r e t c h i n g frequency—R(O----O) dependence. The observed frequencies are p l o t t e d against the' R(O-'--O) distances e s t i mated f o r cubic i c e I from hexagonal i c e I l i n e a r thermal expansion c o e f f i c i e n t s and are i n d i c a t e d by s o l i d squares ( • ) . The predicted Av/AR behaviour based on Bellamy and Owen's formula are shown as c i r c l e s and t r i a n g l e s ( • , • ).  due t o van der Waals r e p u l s i v e forces.  Bellamy and Owen i n v e s t i g a t e d the  van der Waals r e p u l s i o n on the basis of a Lennard-Jones 6-12 p o t e n t i a l by assuming the i n t e r a c t i o n of non-bonding of non-polar s p h e r i c a l atoms.  f i l l e d o r b i t a l s was s i m i l a r t o that  Bellamy and Pace (32) suggested that i f the  van der Waal's r e p u l s i o n o r i g i n a t e s l a r g e l y i n the l o n e - p a i r / l o n e - p a i r repulsions of the two oxygen atoms then the 6-12 provides a good distance/ energy r e l a t i o n .  The r e l a t i o n between the p o t e n t i a l energy and the frequency  138  s h i f t was assumed t o be l i n e a r . From our r e s u l t s the assumptions of Bellamy and Pace (32) and Bellamy and Owen (33) are not c o n t r a d i c t e d between 130° and 200°K, but are c o n t r a d i c t e d below 130°K.  That suggests that the van der Waals r e p u l s i o n does not  o r i g i n a t e only i n the l o n e - p a i r / l o n e — p a i r r e p u l s i o n s below 130°K, or t h a t some complex change occurred i n the system.  The depopulation of Av . hot  bands below 130°K i s an u n l i k e l y source of the discrepancy since that would have r e s u l t e d i n a s h i f t t o higher frequency as temperature was lowered, i n o p p o s i t i o n t o the observed increase i n s h i f t t o lower frequency. I t i s p o s s i b l e that the 0-H s t r e t c h i n g amplitude a f f e c t s the s t r e n g t h of an i n d i v i d u a l hydrogen bond (and hence the frequency s h i f t ) by increased modulation of the p o t e n t i a l energy as temperature increases reaching a l i m i t i n g value at 130°K.  However, the experimental amplitudes (5) continued  t o i n c r e a s e above 130°K and d i d not reach a l i m i t i n g v a l u e , i_^e_. between 73° o and 173°K the RMS amplitude o f 0-H s t r e t c h increased by 0.0*12 A and between o 173° and 273°K i t increased by 0.028 A.  On the other hand, that does not  . mean t h a t the modulation of the p o t e n t i a l energy d i d not approach a l i m i t i n g value. The Bellamy and Owen (33) formula reproduced the Av/AR r e s u l t s f o r a large number o f molecules observed near 300°K, while our r e s u l t s were obtained below 200°K. samples above 130°K.  One i s tempted to look f o r a property common to a l l Such p r o p e r t i e s may be the population o f t r a n s l a t i o n a l  139  hot bands and large amplitudes of t r a n s l a t i o n .  Molecular t r a n s l a t i o n would  modulate the 0 - * * - 0 distance and hence the hydrogen bond energy.  Larger  amplitudes of t r a n s l a t i o n would r e s u l t i n increased modulation o f the potent i a l , weaker hydrogen bonds and smaller s h i f t s .  I f the t r a n s l a t i o n a l ampli-  tude modulation increases from 0°K t o a l i m i t i n g value at 130°K and above then the discrepancy can be understood.  At room temperature the modulation  of the hydrogen bond would be approximately the same i n a l l molecules.(c) The HDO anharmonicity (X ) and the HDO harmonic frequency (.<*>_.„) OH.  On  and t h e i r dependences on temperature and R(0*'"*0). and Pimentel ( l 2 l ) the anharmonicity X  OTI  According t o K i b l e r  of HDO i n the vapour phase, i s .  On  9 1 . 2 cm \  For cubic i c e I Haas and Hornig ( 1 0 6 ) p r e d i c t e d X  (from  On  overtone data) t o be 1 2 5 cm be 1 0 0 cm  1  while B e r t i e and Whalley ( 9 6 ) estimated i t t o  1  (by a modified product r u l e ) .  While B e r t i e and Whalley.'s ( 9 6 )  estimate was very approximate, the point i s that the anharmonicity increases only a l i t t l e from the vapour phase. Since we d i d not observe the f i r s t overtone of v-^HDO) (near  6200  Un  cm ^) the HDO anharmonicity must be estimated by the method of B e r t i e and Whalley ( 9 6 ) .  •,  A p p l i c a t i o n of free molecule theory t o s o l i d s , p a r t i c u l a r l y hydrogen bonded s o l i d s , i s suspect but the method y i e l d s u s e f u l q u a l i t a t i v e i n f o r mation.  For a f r e e , bent XY molecule one f i n d s that 2  v  l  v  v  2  3  =  u  =  l ~ u  2  -  2  X  1 1  2  X  ~  2  = o> - 2 X 3  2  3 3  X  "  12  -  X  -  X  2 1  3 1  X  13  "  x  -  X  2  3  3 2  .  ;  iko  I f X. . ( i ~f j } are assumed t o be small and are neglected then  V  l  v V  2 X  =  2  3  <°1 - 1 1 '  =  co - 2 X 2  "3  =  ~  2 X  2 2  33 -  For i s o t o p i c s u b s t i t u t i o n one can employ the T e l l e r - R e d l i c h product r u l e i p  =  a  . w  a  i i>  e  u>b  w  i  . over 1 symmetry representation e  and by analogy t o the diatomic case one a l s o knows that x A  For  1  i  1  i  lilt  1  Id  of H 0 and D^O the a p p l i c a t i o n i s s t r a i g h t f o r w a r d since v^ and v 2  are o f a^ symmetry while v^ i s o f b j symmetry (assuming the C  2 v  2  point group)  Then '  • »  ' ^-  - \ ±f  p.  and  - >  .  Hence, one can w r i t e f o r HgO  V  3  =  " and f o r DgO  v  3  =  W  3 "  2 X  33  x ^3 ~  " 2 X  33  =  2 p(  °3 ~  2  p  X  33  By assuming that p of the vapour phase (say from N i b l e r and Pimentel's harmonic data) a p p l i e s a l s o t o the s o l i d and by using the observed and D 0 frequencies, then the two equations can be solved f o r w 2  of i c e I .  ?  H0 2  and X-^  lUl  For H D O the prohlem i s more complex.  The s t r i c t product r u l e would  he V O D ^ H O D V ^ X  P  h  d  o  = • U  1  U  3  M  2 V T  \  Z  H  2 °  Even by assuming that the l i b r a t i o n a l and t r a n s l a t i o n a l force constants approach zero and the frequencies approach zero (which they obviously do n o t ) , the product r u l e i s s t i l l complex " O H W H O D W  1 3 2 W  W  As an approximation we can t r e a t the problem as a diatomic molecule H  -(0D) with the i s o t o p i c analogue W  P  =  Then the product r u l e i s  D-(OH).  0D  "OH  The expected value of p i s given by 1  W  0H  IG _ I I  "OH  -  r  M  m =  +  D  t 0 m  M  H '  1  + (m + m )  H  Q  0.T2T8  From the vapour data of N i b l e r and Pimentel  +  D  .  (121)  one finds  p=  0.'726l.  B r i e f l y the method of B e r t i e and Whalley ( 9 6 ) involved assuming such a modified product r u l e f o r H D O , where W 0 D  P and  OD X— 0H X  (ice)  cjj (ice) QH  2 =  p  u (vapour) QD  <u (vapour)  1U2  Then  v OH  where p =  O.72608  OH  - 2X. OH  and  ' v OD  of the vapour phase.  OH  -  2p X, 2  OH  The anharmonicity of the HDO  stret-  ching v i b r a t i o n s i n i c e I was then given by  (1 - p)  2p  Hence the anharmonicity can be determined as a f u n c t i o n of temperature between 1 0 ° and 200°K.  The harmonic HDO frequency and the HDO anharmonicities c a l -  culated i n t h i s way are shown i n F i g s , 4 . 6 and 4 . 7 r e s p e c t i v e l y .  While the  magnitude of the c a l c u l a t e d anharmonicity i s not accurate, the trend i n X ( T ) i n d i c a t e s some fundamental changes i n the hydrogen bonded system.  Be-  ou On  tween  10°  and 80°K X.„ underwent a regular increase of  k%  and from  80°  to  On 200°K  X_„ underwent a regular decrease of On  k%.  The low t e m p e r a t u r e ( l i m i t i n g  -1  anharmonicity was 1 0 5 . 6 cm  -2  , the low temperature dependence was 3 . 2 5 x 1 0  -1  cm  -2  -1  /°K, and the high temperature dependence was - 3 . 7 5 x 1 0  anharmonicity reached a maximum at 80°K. was 0 . 1 3 8 cm "V°K  The maximum i n the  anharmonicity i s also seen i n the harmonic frequency. R(0  ,  ,  ,  -  0),  Fig.  •  as a function of temperature were estimated from, observed v frequencies.  ;  That p l o t looks s u r p r i s -  4.8.  The harmonic HDO frequency and the anharmonicity of HDO  OD  The  The anharmonicity was  i n g l y l i k e a Lennard-Jones 6 - 1 2 p o t e n t i a l energy curve.  v_^(HD0)  /°K:.  The temperature dependence of to  i f i t was assumed to be l i n e a r .  also p l o t t e d as a function of  cm  •,  stretches  (HDO)  and  On  Hence, the v a r i a t i o n s of ui „ and X „ as a f u n c t i o n On On n  T  of temperature a r i s e from a l l sources present i n the cubic i c e I c r y s t a l s . There appear to be two major sources of changes i n the anharmonicity as a f u n c t i o n of temperature. i t contracts and  R(0 **-0) -  As the c r y s t a l i s cooled from 200°K to;5°K  decreases.  The hydrogen bond energy i n c r e a s e s ,  11+3  Oi 3475  i  i 3485 co  Fig.  h.6  1  1  \  3495  (HDO)  c m -  1  3505 1  The harmonic HDO s t r e t c h i n g frequency f o r cubic i c e I as a f u n c t i o n of temperature. The w^CHDO) was estimated from observed HDO cubic i c e I frequencies.  Ikh  . 1  Fig.  h.l  The HDO cubic i c e I anharmonicity as a function of temperature The X values were estimated from observed HDO s t r e t c h i n g frequencies and the p value of the vapour phase.  Hence one would expect a steady increase i n the c o n t r i b u t i o n of increasing hydrogen bond energy t o the t o t a l anharmonicity down t o about 80°K (the  1U6  R(O-'--O) f r e e z e - i n temperature)..  Changes i n  R(0  ,  ,  -  ,  0)  and the hydrogen bond  energy are very small below 80°K. The other source of anharmonicity i s probably due t o changes i n the amplitudes of 0-H s t r e t c h and HDO t r a n s l a t i o n .  The 0-H s t r e t c h i n g amplitude  must be discussed i n terms of the t o t a l population d i s t r i b u t i o n among a l l the energy l e v e l s .  Below 200°K v i r t u a l l y a l l of the molecules must be i n  the ground v i b r a t i o n a l s t a t e .  As was i n d i c a t e d p r e v i o u s l y , the 0-H ampli-  tudes have been measured experimentally ( r e f . 5 , page 7 8 ) and increased from o 0.150  o  A at 1°K t o  0.221  A at 200°K i n  i c e Ih.  H 0 2  o  tudes f o r D 0 were  0.129  2  Corresponding 0-D, ampli-  o  A at 1°K and  0.217  A at 223°K.  Thus the anharmon-  i c i t y experienced by the molecules can be expected t o decrease below 200°K. .As w e l l , the RMS amplitude o f t r a n s l a t i o n decreases from 200°K t o 1°K.  Since v  ,X  On  OH  , and oi  On  are a l l strongly coupled t o the instantaneous  R(O----O), then decreases i n the range of  R(0  ,  ,  -  ,  0)  through decreased ampli-  tudes of t r a n s l a t i o n w i l l give a smaller range of X_.„ and a net. smaller: Un X  0H' We suggest t h a t :  l ) below 80°K AX  nTJ  from changes i n amplitudes i s  On  greater than AX  Un  due t o changes i n hydrogen bond energy, 2 ) at 80°K the  two kinds of AX.„ are equal, and OH  3)  that above 80°K AX  On  (hydrogen bond  energy) i s greater than AX.^ (amplitude.). On  (d) C o r r e l a t i o n of the HDO s t r e t c h i n g frequencies t o the RMS.amplitudes of t r a n s l a t i o n . of  R(0'--*0)  Since the HDO s t r e t c h i n g frequencies are a f u n c t i o n  and since the rate of increase of R(O---'O) depends on<the  RMS amplitude of molecular t r a n s l a t i o n , then i t i s i n t e r e s t i n g t o consider the r e l a t i o n s h i p between  v  a n d < A r ^ > as a f u n c t i o n of temperature. 2  lVf  Decius (122).gave the mean-square displacement from the equilibrium  distance  between two atoms r e s u l t i n g from a l l modes of v i b r a t i o n as: <fir2> where o Ar^.  =  2 L k  =  2 k  <o2>  [l]  the displacement distance of i n t e r n a l coordinate t due t o a l l normal coordinates, k,  =  the element of the matrix transforming normal coordinate k i n t o i n t e r n a l coordinate t ,  and  0^.  =  "the k-th normal coordinate.  The mean-square amplitude of the k-th normal coordinate C^Q^^) was given by Morino et a l . (123) as: h <Qv >  =  where  v,  o 2 OTT^CV^  K  coth h c v±L k  r  2kT  o  l L2J  = the v i b r a t i o n a l frequency of the.k-th normal mode i n cm \ .  k  =  Boltzman's constant,  T  = the temperature  c  =  the v e l o c i t y of l i g h t , and  h  =  Planck's constant.  i n degrees K e l v i n ,  The formulas [ l ] and [2] were derived f o r t h e ' i s o l a t e d , free molecule  case.  In a rigorous treatment of i c e i t would be necessary t o consider a l l i n t e r n a l and l a t t i c e modes i n the sum over k. Cubic i c e I has two HgO molecules per p r i m i t i v e u n i t c e l l and there are three non-zero t r a n s l a t i o n a l , s i x l i b r a t i o n a l and s i x i n t e r n a l v i b r a t i o n a l modes.  I f the p a i r of HgO molecules i s considered as a weakly bonded diatomic  molecule, (HgO)••'*(H 0), then there i s one normal mode of v i b r a t i o n , the 2  IkQ  R(0-•••(}) s t r e t c h .  The mean-square amplitude of t r a n s l a t i o n between two Equations [ l ] and [ 2 ] give  molecules can then be estimated. <AR^>  = <Ar^>  h LL'T^ T  =  71 C V  and f o r the (H^cOg "diatom" DgO.  coth he 2kT  LL' = G, which i s e a s i l y evaluated f o r HgO or  The RMS amplitude of displacement i s then given by h < A r  2  >  hcvm coth i -  = UTT CV  m  2  i  .3]  2kT  T  where m^ i s the mass of H^O or D 0 , and the v a r i a t i o n of<[Ar 2)^  as a function  2  of temperature can be c a l c u l a t e d by using the observed v^CH^O) frequencies. o h  y  were c a l c u l a t e d between 1 0 ° and 200°K.  Two sets of <Ar^)  I n both  cases the v^HgO) frequencies used were from the best smooth curve through the experimental points ( F i g . 3 . 1 5 ) .  Since the v ^ H ^ O ) frequency v a r i e d by  less than 5 % between 10°K and 200°K, one set of <Ar >' was c a l c u l a t e d at 2  constant v  t  L-OL'  V  IJ  227.0  =  dominates the function.  cm  1  at 80°K.  That i s reasonable since l/T  A corresponding set of ( A r ) 2  l a t e d using the H 0 frequencies and D 0 masses. 2  2  Table IV.I and are p l o t t e d i n F i g . k.9. (Ar } " 2  3  2  5  f o r E> 0 were c a l c u 2  These data are compiled i n  For comparison, a set of HgO  were c a l c u l a t e d using the f u l l range of observed frequencies..' Those  data'are also compiled i n Table I V . I . The only s i g n i f i c a n t change was a s l i g h t decrease i n the low temperature values and a s l i g h t increase,- i n the high temperature values. P l o t s of R C 0 v  0 H  (HD0)  and  pectively.  -  VQ^HDO)  -  -  " 0 )  against ( A r ) 2  against ( A r ) 2  3 5  at equal temperatures and of  are given i n F i g s , k.10  and  U..11  res-  TABLE IV. I  The RMS amplitudes' of t r a n s l a t i o n c a l c u l a t e d from H 0 v and compared t o r e s u l t s of-thermodynamic c a l c u l a t i o n s . 2  <Ar > Temperature H0 const. Vrp 2  15  2  °K  xlO  o A  2  <Ar > D0 COnSt . Vrp 2  • v \ v tT) T  o xlO^ A  h  2  0  xlO  2  1 10  9.08  20  9.08  30  9.08  1+0  9.08  50  9.10  60  9.12  70  9.IT  80  9.25  90  9.33 •  100  9.01+  9.57  20  9-TO  30  9.81+  1+0  10.0  50  10.2  60  10.1+  TO  10.5  80  10. T  90  10.9  200  11.1  35  9  0  2  (a) Ref. 81+.  2  2  (a) _ 0  xlO^ A  xlO^ A  9.2  9.0  8.61  9.01+  8.61 8.62  9.06  8.63 8.65  9.11+  8.TO 8.TT  9.32  :  8.85  8.95  9-59  13.2  9-0T 9.20  9.96  IH.5  9.31+  9-^9 10.1+  9.65 9.82  10. T  9-99 -  10.1 11.2  10.3 10.5  18.5  223 2T3  <Ar >  8.61  9.1+1+ .  10  0  A  <Ar > H0 (a)  T  19.5  21.5  21.1+  DO 8.6  9.0  <Ar > 2  2  AxlO  2  10.5  IO.O  95  2 0 0 H  5 C H  IOO-1  50  9.0  IO.O  9.5  H O ;. U.9  W  z  f  A x IO  :  The RMS amplitudes of H 0 and DpO t r a n s l a t i o n calculated with a constant v ( H 0 ) assuming an ( H 0 ) diatomic u n i t c e l l model. 2  2  2  T  2  i— O  1  200 K 0  t O 0  <[ 2.755-1  jo I50°K X  2.750IOO°K 1  50°K loo  2.746 9.0  o  o  O  °  IO°K "i  r  9.5  IO.O  H F i g . U.10  "i  L  0<Ar ) 2  2  i  | i r I0.5  i — i  I.O  o  AxlO'  The c o r r e l a t i o n of RMS amplitude o f t r a n s l a t i o n t o the calculated 0 0 distance i n cubic i c e I . " ' R(0-• •' 0)" and ^Ar2) s were correlated as a'function of common temperature. f , , ,  i  !  H  2 0 0  0  i  K  • 3 2 9 0 -  -  2 0 0  O  I 5 0 I  K  0  A  ° K I  A  3 2 8 0 -  2 4 4 0  2 4 3 0  o  Q  0  I ••  I 5 0  Q I  I O O ° K  I  0  •  K  O  A  •  I O O ° K -  3 2 7 0 -  2 4 2 0  O A - 5 0 ° K - 4 0 ° K  >—50 O  I | 0  0  K  ° K ° K  .Z/  O D  IO°K  3 2 6 0 8.6  9.0  2  V S (Ar ) 2  —  X  2  2  H  2  O 2 4 I O  9.5  H p < A r  F i g . h.ll  (Ar ) DO  ys  IO.O  2  > "  A x  10.5  lO  II.O  2  The dependence of the observed HDO s t r e t c h i n g frequencies' on the RMS amplitudes of t r a n s l a t i o n of HgO and D 0. The frequencies continued t o decrease although the ^Ar2^ became constant at low temperatures. 3s  2  w  153  From Table TV.I one sees that the RMS amplitudes of t r a n s l a t i o n f o r HgO and D 0 agree at low temperatures, i_.e. below- 10°K, quite w e l l w i t h 2  those c a l c u l a t e d by Leadbetter ( 8 U ) from thermodynamic data. appears t o be l i n e a r i n temperature over the whole range,  1°  His data t o 273°K. .  However, the temperature dependences of our c a l c u l a t e d ( A r 2 ) ^are nonlinear  and are much smaller than h i s . -h  amplitude increased by 5-3 x 1 0 o  A/cm  _-.  °  Between  100°  and 200°K h i s RMS ,  -1  A/cm  while ours increased by 1.6 x 1 0  . For HgO i c e I at 200°K we c a l c u l a t e d RMS amplitudes of  -k  o  0.111  A while-  o  he c a l c u l a t e d 0 . 1 8 5 A.  There are probably several reasons f o r our low e s t i -  mate, among which are neglect of t r a n s l a t i o n a l hot bands above 50°K, neglect of two other t r a n s l a t i o n a l modes, and the inadequacy of the free molecule theory.  The contributions of the l a r g e r amplitudes of molecules i n e x c i t e d  t r a n s l a t i o n a l states must c e r t a i n l y increase d r a s t i c a l l y as the temperature approaches 200°K, with as much as 1 5 % of the sample i n e x c i t e d states. c o n t r i b u t i o n of the l a t t i c e fundamental at l 6 0 cm  1  The  t o the i n d i v i d u a l  molecular amplitude must be even l a r g e r than f o r the 2 2 9 cm  1  fundamental  chosen above, although the apparent density of states i s l e s s . The p l o t of < A r ) ^ against R ( 0 2  0 ) i n F i g . k.10 showed that below  50°K our c a l c u l a t e d RMS amplitude was constant although our c a l c u l a t e d 0'"''0  distance was s t i l l decreasing. As w e l l , below 50°K the frequencies  continued t o decrease. 100°K  f a c t o r s other than  These r e s u l t s also support the conclusion that below R(0  0)  a f f e c t e d the HDO s t r e t c h i n g frequencies.  15 *»• ( i i i ) HDO S t r e t c h Half -^Height Widths As can be seen from F i g . 3.8, the low temperature, l i m i t i n g h a l f height widths f o r v  ujj  pectively.  (HDO) and v ( H D 0 ) were 23.5 cm" w  \  oh.  At 100°K Av^(HDO) was 23.5 cm  i  01)  and 35.5 cm" r e s -  %  and Av^(HDO) was 35-5 cm  j  On  which compared very w e l l with the data of Ford and Falk (lOO) (23.5 cm" and 33 cm  1  r e s p e c t i v e l y ) at s i m i l a r temperatures.  1  Ford, and-Falk (100). took  great care t o ensure they had very low and w e l l known concentrations of* HDO i n D 0 and H 0. 2  For the d i l u t e samples of HDO i n HgO and D 0 used i n t h i s  2  2  work, care was taken t o prevent accumulative exchange between atmospheric H 0 and D 0 l i q u i d during handling. 2  2  In our HDO i n D 0 samples, exchange of 2  D.0 w i t h unwanted H 0 absorbed on preparative surfaces or H 0 vapour i n the 2  2  2  atmosphere enriched the concentration of HOD.  The f a c t that our Av^ (HD°) T  On  was somewhat l a r g e r than Ford and Falk's (100) i n d i c a t e d our HD0/D Q conis centration was more than the k.00% intended. Our Av (HDO) was probably 2  On  broader than F a l k ' s , due t o increased coupling.  Our widths were s t i l l much h  narrower than those observed by Whalley ( 9 6 ) , i . e . Av Av  h  -1 (HDO) = 30 cm .  — —  -1 (HDO) = 50 cm . and ;  OH  I t i s important t o recognize that the coupling-broadening does not n e c e s s a r i l y o r i g i n a t e from HDO-HDO p a i r s .  Since at l e a s t one HDO s t r e t c h i n g  frequency i s always coupled t o the host, even at low concentration, and since the  (H 0 or D 0) bands are both very broad d i s t r i b u t i o n s of frequencies, 2  2  then HDO may have a quite broad range of i n t e r a c t i o n energies w i t h H 0.and 2  D 0 neighbouring molecules.. The consequent range of perturbations i n f l i c t e d 2  on the i s o l a t e d HDO frequency also may be broad.  Hence, as the concentration  of HDO molecules increases, the group of HDO molecules w i l l be exposed t o  155  a -wider range of p e r t u r b a t i o n s g i v i n g increased AA> even i n the absence of HDO-HDO p a i r s .  C l e a r l y , the number of HDO molecules coupled to the fewer  l a t t i c e molecules with s t r e t c h i n g frequencies f a r down the sides of the band  (fewer than the number o s c i l l a t i n g at the c e n t r a l frequency) increases  as the concentration of HDO  increases.  The absorption by such molecules  increases i n importance i n the t o t a l HDO absorption. Our data f o r  VQ (HDO) D  from 5 . 9 W D 2 O i n H 2 O showed good agreement since exchange w i t h atmospheric HgO was only very slow and tended t o deplete HDO rather than increase i t . Half-height widths of s t r e t c h i n g modes i n the high pressure ices, were indicated by Whalley ices I I and I I I .  .  .  (96)  to be:  L  AvSL  =  5  \  cm  and A v ^  =  l o cm n  —1  for  There was obviously a dramatic change i n the i c e c r y s t a l  i n transforming between i c e I and ices I I or I I I .  Whalley ( 9 6 ) and others  ( 1 0 0 , 1 0 5 , 1 0 6 ) suggested a number of reasons f o r the observed i c e band widths.  The postulates can be condensed i n t o four main mechanisms.  f i r s t mechanism was f i r s t mentioned by Hornig ( 9 6 ) have described i t i n more d e t a i l .  (106),  The  but B e r t i e and Whalley  The mechanism suggested the band  width arose from c l o s e l y spaced t r a n s i t i o n s between a range of c l o s e l y spaced ground state energies and corresponding, c l o s e l y spaced f i r s t excited states found over a mole of c r y s t a l .  I t was understood that any i n d i v i d u a l  molecule had only one narrow ground state and f i r s t excited s t a t e , but that over the whole c r y s t a l the sets of equivalent molecules sat i n s i t e s of varying  0-H-*-*0  the v a r i a t i o n i n  energies. The v a r i a t i o n of 0-H*••'0 energies arose from 0----0  distances prescribed at equivalent oxygen s i t e s by  disorder allowed i n the proton o r i e n t a t i o n s .  A r e s u l t of the proton o r i e n -  t a t i o n a l disorder at.equivalent oxygen p o s i t i o n s i n the set of unit c e l l s  156  was the l o s s of s i t e symmetry.  Consequently, a l l v i b r a t i o n s became a or a'  and the s e l e c t i o n r u l e s collapsed t o one general s e l e c t i o n r u l e  allowing  t r a n s i t i o n s between a l l forms of combination and overtone l e v e l s .  The  second mechanism of s t r e t c h i n g region broadening was.through Fermi resonance of any fundamental (or the fundamental sum and d i f f e r e n c e bands with low frequency l a t t i c e modes) with other overtone and combination bands such, as 2Vg» ^ R' ^ 2 V  A N  v  +  2V  R'  Notice that because of the lack of s i t e symmetry  through proton o r i e n t a t i o n a l disorder, Fermi resonance between any two neardegenerate l e v e l s was p o s s i b l e , not j u s t between 2v^ and from c r y s t a l s i t e symmetry. certainty principle.  as was expected  The t h i r d mechanism invoked Heisenberg's un-  S p e c i f i c a l l y , the energy l e v e l u n c e r t a i n t y , AE,, was J,  increased by a shortened h a l f - l i f e , At , of the upper state by e i t h e r proton t u n n e l l i n g t o an i o n i z e d state or by resonance i n t e r a c t i o n between the ,. excited fundamental v i b r a t i o n and overtones of l a t t i c e modes g i v i n g the ground s t a t e , fundamental i n t e r n a l mode and excited l a t t i c e v i b r a t i o n s . . Both proton t u n n e l l i n g and e j e c t i o n from the excited v i b r a t i o n t o nearby upper l a t t i c e modes c o n s t i t u t e d r a d i a t i o n l e s s t r a n s i t i o n s .  The f o u r t h  mechanism of broadening was through the occurrence about the fundamental of sum and difference bands of the fundamental with low frequency t r a n s l a t i o n a l l a t t i c e modes and the occurrence of nearby hot l a t t i c e modes. The fact that neither A.vJl(HDO) nor Av^(HDO) 'underwent a smooth, OD  On.  continuous decrease at temperatures below 100°K shows that the mechanisms of hot bands and d i f f e r e n c e bands as sources of broadening are not s i g n i f i cant.  I f the observed s t r e t c h i n g modes were broadened by d i f f e r e n c e and hot  bands i n v o l v i n g l a t t i c e modes, then the s t r e t c h i n g modes should have,; undergone s i g n i f i c a n t sharpening once the higher l a t t i c e energy l e v e l s were  157  depopulated at low temperatures:  The.stretching modes were not s i g n i f i -  cantly sharpened as f a r down as 10°K. A simple c a l c u l a t i o n of the r a t i o s of numbers of molecules i n the ground, 1 s t , 2 n d and 3 r d excited states f o r —1  v ( = 2 2 9 cm T  —1  ) and v  R  C = 8 3 2 cm  were e f f e c t i v e l y depopulated.  ] showed that at 10°K a l l upper l e v e l s  These observations removed mechanism four from  consideration as a source of broadening. The observed " f r e e z e - i n " of h a l f - h e i g h t width supported mechanism one, the proton o r i e n t a t i o n a l disorder mechanism.  For that mechanism, as the  sample was cooled and the l a t t i c e contracted, the mean d e v i a t i o n from the i d e a l symmetry s i t e o f the oxygen atoms decreased.  Since the mean d e v i a t i o n  of O-'-'O distances was also a measure of the range of hydrogen bond energies and the range of s t r e t c h i n g frequencies, then as R ( 0 ^Ar ) 2  3 5  -  -  decreased so should the s t r e t c h i n g band width.  -  ,  0)  decreased and  Once the 0 ' * ' * 0 d i s -  tances were i n v a r i a n t , so was the h a l f - h e i g h t width. A further m o d i f i c a t i o n t o the s t r e t c h i n g mode of d i l u t e HDO molecules i n a parent l a t t i c e was i n l a t t i c e coupling.  I d e a l l y one wanted to.compare  the uncoupled OH s t r e t c h t o the coupled OH s t r e t c h i n i d e n t i c a l c r y s t a l f i e l d s or l a t t i c e environments.  At best one compared uncoupled, but per-  turbed OH s t r e t c h t o coupled OH s t r e t c h i n i d e n t i c a l e l e c t r o n d i s t r i b u t i o n s . However, the p e r i o d i c modulation of the electrons by l a t t i c e modes was, d i f f e r e n t f o r the two cases.  The conclusion i s that i f the stretching.modes  were broadened by l a t t i c e modes then the e f f e c t of broadening of OH(HDO) s t r e t c h by the D^O l a t t i c e was d i f f e r e n t than the broadening of OHvHgO) s t r e t c h by the HgO l a t t i c e since H 2 O and DgO have d i f f e r e n t l a t t i c e , fundamental frequencies and amplitudes.  i  158  The h a l f - h e i g h t widths had a n e a r - l i n e a r temperature dependence of 13.5 x l ( f  2  cm /°K f o r v„„(HDO) and 7.0 x 1 0 ~ cm /°K f o r v._(HD0) i n the -1  2  _1  Un  UD  high temperature range from 100° to 190°K.  Those data compare w e l l w i t h  our i n t e r p r e t a t i o n of the data of Ford and F a l k (100) i n the temperature i- 2 - 1 range 100° to 200°K,Av^HDO) changed by 4.5 x 10 cm /°K. I n the temperature range from 100° to 273°K we deduced from F a l k ' s data that the slope ofAvJf(HDC)) = 16.2 x 1 0 Un.  _ 2  c m " / ^ and o£Wn(HD0)« 10.7 ( 1 0 ) cm /°K. 1  _ 2  _1  UlJ  Our experimental data l i e w i t h i n t h e i r r e s u l t s , and our s c a t t e r of data i s s i g n i f i c a n t l y lower than t h e i r s . (iv)  Dependence of HDO Peak Heights on Temperature The HDO s t r e t c h i n g mode peak heights (I) and h a l f - h e i g h t widths were used  to approximate  the area of v  (HDO) as a f u n c t i o n of temperature.  Simple  Un  t r i a n g l e s were constructed which had heights equal to the peak height on a l i n e a r absorbance s c a l e and a base a t 1/2 of %(A.v ) . The area of two such 2  t r i a n g l e s , extended to the b a s e l i n e , was assumed to represent the i n t e g r a t e d i n t e n s i t y (A) approximately. Temperature ° K  T y p i c a l r e s u l t s are given below: Av  I  A  absorbance  cm  -1 cm  2  10  35.5  0.94  133.5  50  35.5  0.92  130.6  100  36.5  0.85  124.1  150  39.7  0.72  114.5  180  42.5  0.60  103.2  158a  The slow, smooth decrease i n v  (HDO) peak height seems to predominate i n Un  the decreased band area and i s consistent w i t h the concept of a weakening hydrogen bond and a decrease i n molecular d i p o l e with i n c r e a s i n g R(0....)) as temperature increases. Above 190°K the samples sublimed r a p i d l y and presumably a small amount of the o r i g i n a l decrease was due to cumulative sample l o s s by sublimation. A s l i g h t l y concave p o r t i o n of the I ( V Q ^ ( H D O ) ) betx<reen 110° and 140°K i n d i c a t e d f i r s t a more r a p i d and then a l e s s r a p i d decrease i n hydrogen bond energy.  Some unusual heat capacity e f f e c t s were noticed near 110°K  but i t i s not c e r t a i n that the e f f e c t s are r e l a t e d .  (82),  159  B.  Dependence of HgO and DgO Bands on Temperature  ( i ) Fundamental L a t t i c e Mode Temperature Dependences (a) The Rr>0 t r a n s l a t i o n a l mode.  Cubic i c e I (Fd3m) has two mole-  c u l e s per u n i t c e l l which provide s i x t r a n s l a t i o n a l modes, of which three are  zero frequency t r a n s l a t i o n s of the whole f i n i t e c r y s t a l .  B e r t i e ( 8 7 , 8 8 ) developed  a  Whalley and  theory f o r hexagonal and cubic i c e I which  incorporates proton o r i e n t a t i o n a l disorder i n the d e s c r i p t i o n of v^. They deduced from an approximate density of states r e l a t i o n that points of i n f l e c t i o n , m i n i m a and shoulders, as w e l l as peaks, are associated w i t h s p e c i f i c branches of the o p t i c a l and a c o u s t i c a l modes. The l a t t i c e modes o f hexagonal i c e I were a l s o observed by neutron i n e l a s t i c s c a t t e r i n g (92, 93).  Our observed v (H 0 ) s t r u c t u r a l absorption features were given  i n Table I l l . I X b along w i t h some previous r e s u l t s  (88,92,93).  d e f i n i t i o n of the absorption features (other than the 2 2 9 cm  1  The poor peak maxi-  mum) made i t impossible t o f o l l o w t h e i r temperature dependences.  The  f e a t u r e s recorded here at 83°K agreed w i t h the mull r e s u l t s of B e r t i e and Whalley ( 8 8 ) and the condensation r e s u l t s of Giguere and Arraudeau ( 8 9 ) . The lowest temperature i n d i c a t e d by the (Au-Co) / (Ag-Au) thermocouple f o r t h i s experiment was 25°K, probably due t o some s o l i d i f i e d N  2  (gj used  t o p r e c o o l the helium dewar. The low temperature (25°K) l i m i t i n g values of the h i b i t e d no s p e c i a l behaviour.  From 2 5 ° t o 70°K the  features ex-  maximum underwent  a stage of i n v a r i a n t frequency up t o 5 5 t 5°K, and an apparent s h i f t by 2 cm  -1  t o lower frequency between  55  +  5°  and  70  +  5°K.  From  70°  t o 90°K  v,p was r e l a t i v e l y constant i n frequency, while above 90°K v had a con-  i6o  t i n u o u s , near l i n e a r s h i f t towards lower frequency of Above  l60°K  (max.) remained constant at  Zimmermann and Pimentel's from 90°K t o 250°K.  (97)  i  221  0.5  cm \  data i n d i c a t e d a slope of  The dependence(rate of change) of v  bond energy was l e s s than f o r the molecular modes, i_.e_.  v  R  or the molecular modes.  In comparison, cm~^~/°K  on the hydrogen  T  a  /°K.  -  -0.081  hydrogen bond energy had 0.5 t o 0 . 3 times the e f f e c t on v v  cm  -0.093  given change i n T  as i t d i d on  The s e n s i t i v i t y (minimum- detectable change) of  t o hydrogen bond energy changes.was the same as f o r v , v , v_ and v , n  o  i_.e_.  s e n s i t i v e t o changes of ±  A/°K i n  0.0001  The o r i g i n of the sharp s h i f t near  55°K  R(0-\--0).  i s unknown, but i t may have  a r i s e n from a change i n the c r y s t a l s t r u c t u r e (and hence the u n i t c e l l and B r i l l o u i n zone),  o r  a  change i n proton ordering.  A similar effect  was observed f o r HDO s t r e t c h i n g modes and i t was c o r r e l a t e d to the p r e d i c t e d (70) ordering near 70°K. (b) The HgO and DgO l i b r a t i o n s .  The low temperature l i m i t i n g  v^CHgO) frequency ( 8 3 2 cm ) and v^DgO) frequency ( 6 3 0 cm"*") e x h i b i t e d no 1  -  s p e c i a l behaviour a t t r i b u t a b l e t o e x c i t e d state depopulation, ordering of protons, or decreased anharmonicity.  From h2° t o 7 0 ± 10°K the frequency  s c a t t e r of data p o i n t s was l a r g e , ± 5 cm V^(D20)  (Fig.' 3.13).  was constant.  1  f o r v^HgO) and i 3 cm  1  for  W i t h i n these frequency l i m i t s the absorption maximum  The f r e e z e - i n temperature f o r ^(H^O) and  v^(D20)  was  70'  ± 10°K and agreed w i t h other H 2 O and D 2 O bands but d i d not conform t o our more p r e c i s e measurements on HDO peaks. t o changed hydrogen bond energy through  The s e n s i t i v i t y of AR(0  , ,  '"0)  v^(H20  and  D2O)  was l a r g e r than HDO, i_.e_.  l 6 l  >  0.0001  o A/°K.  Between 70°K and l 8 0 ° K v ( H 0 and R  -1  temperature dependences of - 0 . 1 8 cm  2  exhibited linear  D 0) 2  /°K and - 0 . 1 1 cm  -1  /°K r e s p e c t i v e l y .  Again the frequency s c a t t e r of points was large and a c u r v i l i n e a r dependence may be t r u e , as was i n d i c a t e d f o r v^HDO) ( F i g . 3.7).  Liquid  n i t r o g e n and l i q u i d helium c e l l data agreed i n t h e i r overlap region f o r v (H 0). R  Zimmermann and Pimentel's (97) data f o r v ( H 0 ) i n d i c a t e d a  2  R  2  s l i g h t l y c u r v i l i n e a r temperature dependence of about - 0 . 2 2 cm /°K. -1  points, were approximately 1 0 cm  1  higher i n frequency than ours:  Their  They  chose the band center and ignored any v band structure ( i n d i c a t e d i n D  t h e i r s p e c t r a ) . D e t a i l s of the o r i g i n s , p o s s i b l e t h e o r e t i c a l treatments, and the nature of the  modes w i l l be given i n s e c t i o n h.h.  ( i i ) Fundamental Molecular Mode Temperature Dependences (a) The v-j_ and frequencies f o r v  ±  (2413) cm  1  and v  respectively.  s t r e t c h i n g modes. 3  The low temperature  of H 0 and D 0 were 3133 (2320) c m 2  2  -1  limiting and 320U  As f o r HDO t h a t e x t r a p o l a t i o n t o 0°K may not  have been v a l i d , but the thermodynamic data was r e g u l a r down t o 2°K (83). The e f f e c t s of proton ordering should not be seen since the time f o r such a process i s very long below 60°K (70).  As w e l l , t r a n s l a t i o n a l , l i b r a t i o n a l  and v i b r a t i o n a l e x c i t e d l e v e l s are a l l depopulated at 5°K: Further e f f e c t s from depopulation should-have been n e g l i g i b l e .  A l s o , nuclear spin and  e l e c t r o n spin perturbations (i_.e_. as i n ortho-para hydrogen) were expected t o be very small.  No changes i n hydrogen bonding were expected since the  l a t t i c e was no longer c o n t r a c t i n g . From 4.2°K t o 60°K, v-^ and v w i t h i n the e r r o r s of measurement.  3  ( H 0 and D 0 ) absorptions were i n v a r i a n t 2  2  Over that temperature range the c r y s t a l  162  o expanded very s l o w l y , l e s s than 0.0001 A/°K. Accompanying changes i n and  R{0''•'0)  technique.  or  were too small t o "be detected by t h i s i r absorption  The large frequency s c a t t e r i n points was pre-determined by  the u n c e r t a i n t y i n peak and shoulder p o s i t i o n s .  The v^HgO) data from  l i q u i d helium and nitrogen c e l l s d i d not completely agree ( F i g . 3 . 1 0 ) . L i q u i d nitrogen c e l l data i n d i c a t e d a " f r e e z e - i n " frequency near 3215 cm . 1  L i q u i d helium c e l l data i n d i c a t e d a " f r e e z e - i n " frequency near 320k cm . 1  The data were c o l l e c t e d during warm-up from 77°K and h.2°K The discrepancy may be explained i f the  respectively.  absorption peak underwent a  type of " h y s t e r e s i s " during c o o l i n g from 77°K t o U.2°K, frequency lagged behind temperature decrease. h:2°K  shift  Since the samples were always held at  f o r three hours, s u f f i c i e n t time may have been given f o r completion  of the h y s t e r e s i s loop before warm-up observations began:  Observations of  frequency s h i f t during a c o o l i n g c y c l e are r e q u i r e d t o t e s t that; p o s s i bility.  Data from the same two c e l l s f o r v (R\p0) ( F i g . 3.11) a l s o suggested  h y s t e r e s i s although the separation of points was not as w e l l defined. ;Only the r e s u l t s from the l i q u i d helium c e l l were obtained f o r v^ and v^ of DgO. Above 60°K the  and v^ modes underwent r e g u l a r s h i f t s t o the  ;  p r o g r e s s i v e l y higher frequencies associated with p r o g r e s s i v e l y decreased hydrogen bond strengths.  The explanation f o l l o w s that of v (HDO)., On The i r high temperature dependences of v and v_ f o r cubic i c e I ! 1 J .  agree with the Raman observations of Val'kov and Maslenkova (90). The Raman and i r  (H^O and DgO) observations concurred d i r e c t l y .  However,  the v^HgO and D^O) Raman observations were a l l s h i f t e d (by 5 5 and 32 cm r e s p e c t i v e l y ) t o lower frequency than the i r observations. constant value of - 55 cm  1  t o the v^HgO) and of 32 cm  1  By adding a  t o the V-^DgO)  1  163  Raman data at a l l temperatures, then the Raman and i r data agreed. The following temperature dependences were observed by Val'kov and Maslenkova (90):  Raman cm-l/°K  AT  H 0 2  Av  IR cm-l/°K  0.25U  0.26  0.2U6  0.24  0.222  0.20  0.198  0.22  0  AT A(v + v ) x  T  AT Av. D 0  — -  2  AT Av, 0.143  AT AT  =  203 - T7°K  =  0.14  126°K.  The equivalence of Raman and IR temperature dependences f o r v^ and v^ shows that the hydrogen bond coupling of neighbours was independent of the applied electromagnetic r a d i a t i o n . There i s a p o t e n t i a l l y i n t e r e s t i n g extension of these cubic i c e I temperature dependences t o hexagonal i c e I . I t i s known that the l i n e a r thermal expansion c o e f f i c i e n t s of hexagonal i c e I are not equal ( 6 0 ) and that the 0  -  -  ,  *0  distances p a r a l l e l and n o n - p a r a l l e l t o the c-axis are not  equal, F i g . 4.3. Hence, the temperature dependences o f R(0* • • *0) ,. i^.e_. p a r a l l e l t o the c - a x i s , and R ( 0 * * 0 ) are not equal and the single,.crystal , -  a  spectra o f the ac face of hexagonal i c e I , p o l a r i z e d p a r a l l e l and perpen-  164 d i c u l a r to the c - a x i s , should be d i s t i n g u i s h a b l e .  For example, consider the  s i x p o s s i b l e arrangements of the four protons about any one oxygen atom i n hexagonal i c e ,  H  H  H  H  H H  4  .  H  'I c - axis  H  Then the three arrangements 4,5 and 6 have both protons along the shorter 0****0 distances and w i l l give one band of frequencies. The 1,2 and 3 arrangements, however, have asymmetric 0-H bond lengths leading to a d i s t o r t e d p o t e n t i a l and frequencies d i s t i n c t from cases 4,5 and 6.  The  frequencies observed p a r a l l e l to the c-axis should be intermediate between those observed perpendicular to c and those expected i f both protons the R ( 0 " " 0 ) along c.  had  164a One can p r e d i c t the values and temperature dependences f o r v^R^O and V^O) of 0-H stretches p a r a l l e l and n o n - p a r a l l e l to the hexagonal c - a x i s . From the temperature dependences of v^CH^O) and v^CD^O) ( F i g . 3.10) and the temperature dependence of R(0**'"0) i n cubic i c e I ( F i g . 4.3), one can determine the R(0*'"0) - v  3  c o r r e l a t i o n s f o r H 0 and D 0, F i g . 4.12. Then 2  knowing the hexagonal R(0'*' 0) and R ( 0 c  , , , -  0)  2  parameters as a f u n c t i o n o f a  temperature one can obtain a set of v^O^O) and  v^(T)^0)  frequencies  parallel  and n o n - p a r a l l e l to the c - a x i s , F i g . 4.13. For v^O^O) of hexagonal i c e one sees that a t 150°K the asymmetric s t r e t c h i n g frequencies would be 3214 and 3229 cm  1  p a r a l l e l and n o n - p a r a l l e l  to the c - a x i s , while a t 100°K the values would be 3202 and 3225 cm . 1  S i m i l a r l y f o r v ( D 0 ) the 150°K values are 2417 and 2429 cm" , and the 100 K 1  3  e  2  values a r e 2411 and 2425 cm . 1  Ockman (108) was not able to detect the  d i f f e r e n c e s a t 139°K probably because of the breadth of the bands, i.e.. because Av^ i s probably greater than 100 cm  and because of the r e l a t i v e l y  small s p l i t between the bands. In contrast the bands due to d i l u t e concentrations J)^0 are narrower and absorptions c-axis should be separable.  of HDO i n H^O or  p a r a l l e l and n o n - p a r a l l e l to the hexagonal  Sets or predicted v (HD0) and v^(HDO) f r e QH  quencies i n the two d i r e c t i o n s were determined as above (i..e_. from F i g s . 3.6 and 4.3) and are p l o t t e d i n F i g . 4.14. Thus a t 150°K v (HD0) along QH  a and a should be separated by 16 cm  1  and at 100°K by 26 cm  VQp(HDO) along c and a would be separated by 11 cm  1  and 18 cm  while 1  respectively.  Accurate measurement of the d i f f e r e n c e s i n the a and c temperature, dependences  165  ICE 2410 -I  I  C o  20  2.746 H  3200  ICE  Fig.  U.12  (DO)cm-  tj  2  1  30  1  1  1  ,  10  20  I ^ (H 0) c m c  3  2  —  , 30  1  The c o r r e l a t i o n s of V3 of, H 2 O and DpO t o the 0 - • • - 0 distances as a function of common temperature. The frequency data were uncorrected f o r source beam heating.  166  ICE  I  h  2410  4.13  3  2  20  ICE  Fig.  z, (D 0) c m -  I  h  1  30  z/ (H Q) c m 3  2  1  The c a l c u l a t e d frequencies of H2O and D 0. i n hexagonal i c e I along the c and a axis as a function of temperature. 2  167  ICE  I h  cm-  1  OD  2 0  2410  ICE  g. k.lk  (HDO)  is  3 0  I  v  h  (HDO)  cm-  1  The c a l c u l a t e d v (HDOl and v CHDO) frequencies f o r HDO i n hexagonal i c e I and along the c and a axis as a function of temperature. OH  OD  168  should y i e l d valuable information on the a n i s o t r o p i c deformation of the hydrogen bond i n hexagonal i c e I . —1  (b) The v bending mode. Absorptions near 2  cm  l600  —1  and  1200  cm  i n cubic i c e I (HgO and D 2 O ) were very near the corresponding vapour phase v  2  fundamental absorptions of 1 5 9 5 cm ^ and 1 1 7 9 cm ^ r e s p e c t i v e l y .  Doubts  arose i n the previous l i t e r a t u r e assignments (Tables I I I . X I and I I I . X I I I ) of these i c e frequencies to e i t h e r V 2 or 2 v p , which should nearly c o i n c i d e . In f a c t , these absorptions i n i c e appear to be composite overlapping V 2 and 2vj; peaks as was p r e v i o u s l y described (page 1 1 2 ) .  The inconsistency  between the l i q u i d helium and l i q u i d nitrogen c e l l V 2 data ( F i g . 3 . 1 2 ) may have a r i s e n from a temperature h y s t e r e s i s , i^.e_. the lagging o f frequency s h i f t behind the temperature drop during c o o l i n g . (97)  r e s u l t s (Fig.  3.12)  Zimmermann and Pimentel'  tend to discount that p o s s i b i l i t y f o r  V2(H 0). 2  Their r e s u l t s from l i q u i d nitrogen experiments agree w i t h the present r e s u l t s from l i q u i d helium experiments.  Much of the d i s p a r i t y i n the pre-  sent r e s u l t s probably arose from reference beam uncompensation f o r the l i q u i d nitrogen c e l l data. below  1595  cm  and above  The strong atmospheric water vapour absorption  l6l5  cm ^ may have d i s t o r t e d the  band severely, while a gap i n the vapour spectrum between may have presented an a r t i f i c i a l  V2(H2 ) U  i  c  e  maximum.  V2(H"20) 1595  V2(H20)  l6l5  cm  However, such a  maximum would be independent of the i c e sample temperature. For  and  ice  . -• ; -  the l i q u i d nitrogen c e l l data i n d i c a t e d a low temperatur  l i m i t i n g frequency of  l605  cm  , while the l i q u i d helium c e l l data i n d i -  cated a low temperature l i m i t i n g v frequency of 1 5 6 0 cm ^: 2  and Pimentel's data were extrapolated to near 1 5 7 0 cm \  Zimmermann  Whalley ( 9 6 )  found the Vp maxima i n high pressure H 2 O ices were above 1 6 8 0 cm ^ /and  169  argued that V 2 ( i c e ) > V2(vapour). However, 2 v p may be more intense than V2 i n these cases.  Whalley's ( 9 6 )  frequency f o r cubic and hexagonal  ice I at 110°K i n an isopentane mull was more than 2 5 cm  1  higher than  observed here, or by Ockman ( 1 0 8 ) ( V 2 = 1 5 8 0 cm ) and Hornig ( 1 0 6 ) -1  (v  2  =  1585  cm ) .  The r e f l e c t i v i t i e s of Whalley's  1  (95,96)  mulled samples  may have been s i g n i f i c a n t l y d i f f e r e n t than f o r our condensed leading t o h i s higher apparent maxima. (0.5%)  samples  However, Ockman found only a small  increase i n the one percent general r e f l e c t i v i t y of c r y s t a l l i n e i c e -1  over the range 1 5 0 0 cm 1 5 7 5 cm  at 110°K.  1  -1  t o 1 7 0 0 cm  , the maximum r e f l e c t i v i t y was at  I t i s also p o s s i b l e that sample formation by vapour  condensation accentuated the r e f l e c t i v i t y , c r e a t i n g an a r t i f i c i a l low frequency maximum i n our r e s u l t s . For D2O the l i q u i d helium c e l l data i n d i c a t e d a low temperature l i m i t i n g V g frequency of 1 1 8 9 cm ^, however the B^O l i q u i d nitrogen ,-cell experiments were not attempted.  The region near 1 2 0 0 cm  1  was free *from  atmospheric HgO vapour attenuations and the recorded D2O spectrum was free of atmospheric absorption d i s t o r t i o n s .  The  D2O  observation of  i s greater than the D2O vapour frequency, 1 1 7 9 cm (106)  and Ockman  1210 cm  -1  (108)  observed  at 1 0 0 t 10°K.  v (D20) 2  II89  cm  1  In c o n t r a s t , Hornig  t o be even h i g h e r , i_.e_.  near  These D 0 r e s u l t s were contrary t o our v ( H 0 ) 2  2  2  helium data as w e l l as the nitrogen data of o t h e r s , as noted above. P o s s i b l y i n DgO the r e l a t i v e p o s i t i o n s of 2 v ^ and  are a l t e r e d from that  of H 2 O , g i v i n g a d i f f e r e n t peak maximum r e l a t i v e t o the vapour. Maximum range 5°K t o  70  V2/2v-^(H20)  absorption was constant over the temperature  - 10°K, while maximum  V2/2vp(D20)  absorption was constant  170  over the temperature range 5°K t o 5 0 t 10°K. temperature of I  v /2vp 2  The low D 0 " f r e e z e - i n " 2  was probably due to i n s u f f i c i e n t data.  50°K  The cubic i c e  band e x h i b i t e d the same dependence as the s t r e t c h i n g modes i n  t h i s low temperature range, constancy w i t h i n ± 8 cm"*". As a check on -  hysteresis i n t h i s temperature range, d e t a i l e d observations should be made during f a s t and slow c o o l i n g , i_.e_. c o o l i n g i n 1 0 - 2 0 min. and 1 5 0 - 2 0 0 min. r e s p e c t i v e l y .  The  absorption also e x h i b i t e d the same s e n s i -  V /2VR 2  t i v i t y to changes i n hydrogen bond length (energy) as d i d the s t r e t c h i n g modes, i_.e_.  i t was s e n s i t i v e to changes i n R(O----O) greater than  0.0001  A/°K. The question of whether v ( i c e ) i s l e s s than or greater than v 2  (vapour) i s s t i l l unanswered. due t o more intense v  I f the  was the more intense t r a n s i t i o n then v (D 0) 2  2  2  t r a n s i t i o n s then v  2  i c e may be l e s s than v  ice  2  2VR(E 0) 2  vapour.  2  absorption maximum was  V /2VR(D 0) 2  dence i n d i c a t e d the peak maximum was v  2  > v  ice  2  vapour.  >v (D 0) 2  2  If  v /2vpj H 0 2  2  v (H 0) 2  2  and 2VR must be masked.  than or l e s s than Maximum  v (H 0) 2  2  V /2VR(H 0 2  2  P o s i t i v e high temperature depenand not 2VR, since  (and pre-  D 0) 2  Whether  v (H 0) 2  2  i c e was greater determined.  absorptions had approximately l i n e a r ,  p o s i t i v e temperature dependences of 0 . 3 7 cm "V°K t i v e l y over the temperature range from data of Zimmermann and Pimentel  The tempera-  The maximum of absorption must  vapour could not be unambiguously and  2  absorption was also p o s i t i v e f o r e i t h e r  l i q u i d helium or l i q u i d nitrogen data. then be  2v^(D 0)  vapour and  sumably 2VR) had a negative frequency temperature dependence. ture dependence of the  2  (97)  60°  to  and 0 . 1 5 cm~"'"/K respec-  l80°K.  0  In contrast the  i n d i c a t e d a slope of  0.28l  H 0  cm •^/°K  2  171  i n the range from 90°K t o 253°K.  The r e l a t i v e l y small temperature depen-  dence of V2/2VR(D20) may have r e s u l t e d from the c l o s e r coincidence of V2(D2°)  and  - 2v (D 0) than i n HgO. R  I f the H 2 O and D 0 bands had the same  2  2  structure then t h e i r temperature dependences should have been simply r e l a t e d since t h e i r changes i n R(O----O) were nearly the same. ( i i i ) The Combination and Overtone Mode Temperature Dependences (a) The 3 v or ( v + v ) mode. R  cm  1  and 1635 cm  1  2  R  Broad weak absorptions near 2235  i n H 0 and D 0 cubic i c e I e x h i b i t e d temperature depen2  2  dences of -O.lU cm /°K and -0.15 cm /°K r e s p e c t i v e l y over the temperature 1  1  range from 30° t o l80°K.  Both the H 0 and D 0 bands were l e s s than one-half 2  as intense as their, corresponding v / 2 v 2  absorption at 2238 cm ^.  2  R  bands.  F i r s t consider the. R"0 i c e 2  I f the absorption arose from a v  + \) transi-  2  R  t i o n then the temperature dependence should have been p o s i t i v e , i_.e^. Av /AT = R  -0.17  = +0.19 cm negative.  cm /°K and Av /AT = +0.36 cm /°K, therefore ( A v + A v ) / T -1  _1  2  /°K.  2  R  However, the temperature dependence was observed t o be  I f the absorption arose from a 3 v t r a n s i t i o n then the temperaR  ture dependence should have been negative, i_.e_. A(3v )/AT = -0.51 cm "V°K. R  As was seen i n F i g . 3.17, Pimentel's data (97) agrees w e l l with ours, h i s slope was -0.12 cm /°K compared t o our measured value of -0.15 cm /°K. 1  1  The measured A ( 3 v ) / T = -0.15 cm /°K was nearly the same as A V R / A T 1  R  -0.17 cm "V°K and one-third the predicted rate of -0.51 cm " /°K. L  =  Anhar-  monicity increases from the l a r g e r amplitudes at increased temperature, could not be the source of t h i s r e s u l t . E i t h e r the 2235 cm  1  H 0 absorption was a v 2  R  fundamental, or the  3VR anharmonicity was decreasing with increased temperature, or energy l e v e l population r e d i s t r i b u t i o n was a f f e c t i n g the r e s u l t s .  Such a.high  172  frequency fundamental l a t t i c e mode seems u n l i k e l y , as do such large e f f e c t s from p o p u l a t i o n a l r e d i s t r i b u t i o n . 3v  and v  R  R  A l t e r n a t e l y decreased anharmonicity of  from decreased hydrogen bond energy may be l a r g e r than the i n -  creased anharmonicity a r i s i n g from increased amplitude of l i b r a t i o n at higher temperatures. Consider the apply as f o r H 2 O .  absorption at 1 6 3 7 cm  where the same considerations  Absorption a r i s i n g from D 0 ( v 2  + v ) t r a n s i t i o n s - would obs. obs.  2  R  e x h i b i t zero temperature dependence; A ( v 2 + v )/AT = (AV2/AT) +  (Av^/AT)  R  = + 0 . 1 5 cm ^/°K - 0 . 1 5 cm "V°K to be d i s t i n c t l y negative,  = 0.  -0.15  The temperature dependence was observed  cm "V°K.  In f a c t V R ( D 0 ) and the  D2O band had the same observed temperature  dependences.  Low temperature l i m i t i n g 3VR absorption was 2235 cm  (from v  = 6 2 7 cm ) -1  R  2  and  2  anharmonicity f o r 3VR(H20) (from 2  for H 0  That implied an approximate H 0 low temperature l i m i t i n g  1 6 3 5 cm ^ f o r DgO.  (D 0)  cm ^  1637  2  =  833  of - 2 5 3 cm .  considerable i s o t o p i c s h i f t :  of  cm  -258  and f o r  The apparent HgO and D 0 3 v  -1  anharmonicities were nearly equal.  cm  2  3y  R  R  Now the parent t r a n s i t i o n s underwent  vp(H 0) = 8 3 3 cm  1  2  and v ( D 0 ) = 6 2 7 cm " . L  R  2  The H 0 anharmonicity of - 2 5 8 cm ^ represented 1 1 . 5 percent of the observed 2  absorption band frequency, 2235 cm ^~.  The increased DgO percent anharmon-  i c i t y was unexpected f o r the mass s u b s t i t u t i o n made. vapour phase the anharmonicity of H 0 2  x  33  =  cm \  -^6.4 x 3 3  cm  (x-^ = -43.8 cm  i s almost halved i n D 0  -22.8  =  2  = -24.9  cm  D 0 motion are smaller. 2  f o r v^, v^, and  (l2h)  9  For example, i n the -1  , x  cm  2 2  = - 1 9 - 5 cm  , x 2  =  2  -1  ,  -10...hk  since the amplitudes of  S i m i l a r behaviour was expected f o r the s o l i d , but  the observed 3 v ( . D 0 ) anharmonicity was not one- h a l f that of 3 v ( H 0 ) . , R  2  R  2  Thus the large s h i f t s of 3 v below the expected frequencies cannot /be simply R  173 explained as anharmonicities. The large s h i f t s of (3v  R  2  2  observed = 2235 cm , 3 ( v ) = -1  R  below the expected frequencies  3 v ( H 0 , D 0) R  3(833)  =  cm ) may a r i s e from d i f -1  21+99  ferent maximum t r a n s i t i o n moments f o r the band of ground state l i b r a t i o n a l energies f o r the v^ and 3 v t r a n s i t i o n s .  The extreme case i s :  R  molecules  occupying the higher energies of the band have maximum t r a n s i t i o n moments f o r (0 -> l ) t r a n s i t i o n s and minimum t r a n s i t i o n moments f o r ( 0 -* 3 ) t r a n s i t i o n s , while molecules occupying the lower energies of the band have minimum t r a n s i t i o n moments f o r ( 0 -»- l ) t r a n s i t i o n s and maximum t r a n s i t i o n moments f o r ( 0  3) transitions.  The maximum of the ( 0 -> 1.) v  R  transition  would occur above the center of the energy band and the maximum of the (0  3 ) v t r a n s i t i o n would occur below the center of the energy band. R  In support of t h i s r e c a l l that the v  R  absorption had a A v  2 R  of about ;  1 2 5 cm ^, i n d i c a t i n g a very large l i b r a t i o n a l energy range. Data on 3 v  from spectra recorded during warm-up from 5°K t o 60°K  R  showed that the 3 v  R  energy l e v e l had the same s e n s i t i v i t y t o hydrogen-bond  changes as the i n t e r n a l modes, i_.e_. i t was i n s e n s i t i v e t o changes i n hydrogen-bond o A/°K.  energy from changes i n R ( 0 :  - -  **0)  that were l e s s than  0.0001  Data from the l i q u i d nitrogen and l i q u i d helium c e l l s agreed s a t i s -  factorily.  The 3 v f r e e z e - i n temperatures f o r H 0 and D 0 , 7 0 ± 10°K, R  2  2  concurred w i t h previous data. (b) The (v + v,p) band.  The high frequency shoulder on the icubic  i c e I s t r e t c h i n g band had low temperature l i m i t s of for H 0 and DgO r e s p e c t i v e l y (Table I I I . I X ) . 2  and ikh cm  1  333U  and  cm  2h6k  1  Those frequencies are 2 0 1  higher than the low temperature l i m i t i n g low frequency  shoulders at 3133 and  2320  cm  1  respectively.  The high temperature depen-  dences of the high frequency shoulders were 0.20 and 0 . 1 7 cm /°K, compared 1  :  17k  to 0.3k and 0 . 1 9 cm"" /°K f o r the low frequency shoulders (Table I I I . I X ) . 1  I f the high frequency shoulders are i n f a c t due to (v^ + v ) t r a n s i t i o n s then the v^ to (v 2 0 1 cm ^) f o r H^O  + v ) displacement should have been 2 2 9 cm ^ (observed and the temperature dependence of (v^ + v ) of H^O  should have been approximately (Av /AT) + (A(v cm  -1  /°K.  That value of 0.2k cm  -1  + v )/AT) or ( 0 . 3 ^ - 0 . 1 0 )  /°K agrees w e l l with the observed v^ + v^  value of 0 . 2 0 cm "*"/°K. For D 0 the high frequency shoulder appears to be 2  composed of v ^ ( D 0 ) and the LA t r a n s l a t i o n a l mode near 1 6 0 cm"'". The tem-  2  perature dependence of v ^ ( D 0 ) i s not known however. 2  ( i v ) The Half-Height Widths Temperature Dependences The temperature dependence of the composite s t r e t c h i n g r e g i o n band half-height width was p o s i t i v e (page 6 6 ), as expected. two sources of the i n c r e a s i n g width.  One obvious e f f e c t common t o a l l the  modes was the increase i n the amplitudes of v i b r a t i o n . broadening arose from increasing 0  -  ,  ,  *0  R(0*'*"0):  A second source of  The increasing range of ,  distances gave a l a r g e r range of hydrogen bond energies and a  broader range of possible t r a n s i t i o n s . A(V-^,  There appear to be  V^?  pronounced  V-^ +  Vrp)  Above l 6 0 ° K ( F i g . 3.k)  the  ^ data are not r e l i a b l e since sample sublimation had a  effect.  The observed temperature dependence of A ( v , V R  may have been anomalous.  R  + Vrp)  ( F i g . 3.k)  The s c a t t e r of data p o i n t s was nearly as large  as the range of p o i n t s between 10°K  and 200°K:  The high temperature data  was j u s t outside the error l i m i t s of the low temperature data. the temperature dependence of A ( V R , V  r  + vip)  would be i n t e r e s t i n g to study the o r i g i n of v  As w e l l ,  seems to be too small. ; I t R  i n the s o l i d , l i q u i d and  175  vapour phases about the t r i p l e point as w e l l as the o r i g i n of \^ as the c r i t i c a l point i s approached from the vapour phase. i.  The temperature of A ( V g , 2 v )  ( F i g . 3 . 5 ) was opposite t o that, of  2  R  A(vp, v + R  phases.  Vrp) " 3  5  and A(v^, V ^ ,  + v ^ ) ^ i n the amorphous and cubic i c e I  An explanation was given i n s e c t i o n U . l C ( i ) (page H I ) . k.3  Assignments of the Cubic Ice I Absorption Bands  A.  The Fundamental L a t t i c e Modes  ( i ) The T r a n s l a t i o n a l Modes Two peaks 296  (l62  and  227.8  cm ) and three shoulders -1  cm ) were observed at 93°K f o r 1  H" 0 2  ( 1 9 1 , 267  and  cubic i c e I . The features of the  band d i f f e r e d only s l i g h t l y from those of B e r t i e and Whalley ( 8 8 ) .  In this  work no c a l c u l a t i o n s were made which disagreed w i t h the assignments of B e r t i e and Whalley. ( i i ) The L i b r a t i o n a l Modes The low temperature l i m i t i n g frequencies- of the observed l i b r a t i o n s are i n the r a t i o , v / ( v R  in  H 0 2  and  D 0 2  R  + v^) =  of:0.9lAU  and  That compares t o the same r a t i o s  O.963.  0.953  r e s p e c t i v e l y . The peak t o shoulder  separations at 10°K were: [(v  R  + v ) - v ]H 0  =  5 0 ± 5 cm"  I(v  R  + v ) _ v ]HD0  =  3 3 + 1 . 5  + v ) _ v ]D 0  =  31 ± 5 cm"  I(v  R  T  T  T  R  2  R  R  2  1  cm" 1  1  '  I  -  176  •  I f the shoulder d i d a r i s e by a combination t r a n s i t i o n of v (HDO) and v,p(host), R  then the value of  t o apply t o HDO i s that of the host DgO since at a  concentration of k.0% HDO i n D 0 the l a t t i c e dynamics must surely be domin2  ated by the D 0 molecules f o r any reasonable model.  The f a c t that the  2  D 0 peak t o shoulder separation i s 31 cm 2  1  supports t h i s conclusion.  As  w e l l , the peak t o shoulder separations of pure D 0 and of HDO i n D 0 agree 2  well.  2  Presumably HDO i n H 0 should have a v-p peak to ( v + \J ) shoulder 2  separation of about 5 0 cm . 1  R  t  However, that has not been observed yet by  any workers. Recent work by Trevino ( 9 3 ) quoted experimental data of neutron i n e l a s t i c s c a t t e r i n g from hexagonal i c e I and compared that data t o the r e s u l t s of a t h e o r e t i c a l model based on cubic i c e I . His hypothesis noted that the Raman and i r observations from 50 to 3500 cm  1  are the same f o r  cubic and hexagonal i c e I , and assumed that the basic dynamical l a t t i c e u n i t of cubic i c e (one 0 atom surrounded t e t r a h e d r a l l y by k others) was a s u i t a b l e model f o r hexagonal i c e . That i s supported by the f a c t that the nearest-neighbour configurations'are the same.  Trevino's ( 9 3 ) theory also  assumed that the protons are i n ordered p o s i t i o n s , which they are not. However, the basic t r a n s l a t i o n a l u n i t i n i c e i s the 0 atom and the o r i e n t a t i o n of protons i s r e l a t i v e l y i n s i g n i f i c a n t i n t h i s case.  }  For hexagonal i c e I at 150°K the neutron i n e l a s t i c s c a t t e r i n g experiments ( 9 3 ) demonstrated l a t t i c e maxima at 6 3 c m the assignment of peaks.  (TA) depending on  Other workers ( 9 2 ) found ( f o r H 0 hexagonal'ice  I at 2 6 l ° K ) l a t t i c e modes at  2  60  and  70  cm \  C l e a r l y there e x i s t s a high  density of H 0 t r a n s l a t i o n a l states near 50 - 1 0 cm 2  -1  1  at 150°K f o r hexa- .  gonal H 0 i c e I . The corresponding modes f o r D 2 O cubic i c e I at 10°K may 2  be lower than 50 cm  1  since the mass d i f f e r e n c e would s h i f t the frequency  177 to O.9484 x 5 0 c m  =47.5  -1  cm . -1  The observed neutron hand width i n H 0 was 50 cm"*". Of the broad -  2  band of r e a l t r a n s l a t i o n a l frequencies, the maximum t r a n s i t i o n moments do not have t o occur over the same sections of the band f o r i r absorption and neutron i n e l a s t i c s c a t t e r i n g .  The i r t r a n s i t i o n moment maximum may l i e at  lower frequencies than the neutron s c a t t e r i n g t r a n s i t i o n moment maximum. Further, the overlap i n the i r of v  and ( v + Vrp) brings the instrumentally  R  R  traced, summed absorptions c l o s e r together, i_.e_. i f v  and ( v + VIJ) could  R  R  be resolved completely t h e i r peak p o s i t i o n s would be separated by more^ than 50, 33 and 31 cm  1  f o r H 0, HDO and D 0 r e s p e c t i v e l y . 2  2  One may conclude  that a s i n g l e l i b r a t i o n a l mode and a combination l i b r a t i o n a l - t r a n s l a t i o n a l mode were observed f o r HDO.  Since v  and v . are expected t o be about  R x  Ry  equally intense, and since only one band was observed, then v must be exactly or nearly degenerate.  R x  and. v y R  The same conclusions seem appropriate  for H 0 and D 0. 2  2  B.  The Fundamental Molecular Modes  ( i ) The Stretching Modes There are many c o n f l i c t i n g assignments of the three main i r absorpt i o n features near 3200 c m  -1  f o r H 0 and 2400 cm" f o r D 0. 1  2  2  Ockman (108)  assigned the low frequency shoulder t o v-j_, the main peak t o v , and the 3  high frequency shoulder t o ( v + v ) , while Hornig et_ a l . (105) assigned 3  T  the three bands as 2 v , v , and v-j_. 2  3  I n c o n t r a s t , B e r t i e and Whalley (.95)  assigned the low frequency shoulder and the main peak as a p a i r of bands ;  composed of coupled  - v v i b r a t i o n s , and they eliminated the d i s t i n c t i o n 3  1  178  between v-j_ and  absorption bands of H 0 and D 2 O .  We propose that the low  2  frequency shoulder i s v-^, the main peak i s  and the high frequency shoulder  i s (v-^ + v ) i n agreement with the Raman r e s u l t s of Val'kov and Maslenkova T  (99) and as Ockman ( 1 0 8 ) i n t e r p r e t e d them. The s t r e t c h i n g frequencies of HDO do not l i e at the p o s i t i o n s expected on the b a s i s of H 0 and D 0 s h i f t s i n cubic i c e I . 2  2  This r e s u l t w i l l  be discussed i n terms o f a theory proposed by Pimentel and Hrostowski ( l O l ) and Hornig and Hiebert (102) i n the e a r l y 1950's:  They suggested t h a t the  two major e f f e c t s on molecular v i b r a t i o n s i n s o l i d s , c r y s t a l - f i e l d perturbations and inter-molecular c o u p l i n g , were separable by d i l u t e i s o t o p i c substitution. (a) The H 0 and D 0 s t r e t c h i n g modes. 2  2  For the Raman spectra^ of  hexagonal i c e I Val'kov and Maslenkova (99) found peaks at 3088', 3210 and -1 3321 cm  -1 of r e l a t i v e i n t e n s i t i e s 10:4:2.  The 3088 cm  peak had a, p o l a r i -  zation, r a t i o of l e s s than 0.75, while the 3210 cm" peak was depolarized. 1  The 3088 cm  1  Raman peak was unambiguously of a^ symmetry, i_.e_. the. v-^  symmetric s t r e t c h mode. The suggestion of B e r t i e and Whalley  (95,96)  that v-j_ and vg are  coupled and i n d i s t i n g u i s h a b l e cannot be e n t i r e l y c o r r e c t .  I f the  .and  bands of coupled v i b r a t o r s were l a r g e l y mixed i n t o two bands equally of V]_ and  character, then the same set of energy l e v e l s would have been  present f o r both the Raman and i r t r a n s i t i o n s , however the s e l e c t i o n r u l e s would change.  For the mixed energy l e v e l s one would expect equally intense  peaks at 3088 and 3210 cm ratio.  contrary t o the 10 t o h observed  intensity  Hence the v-^ and V 3 energy l e v e l s appear t o be separated (lack of  179  non-resonant coupling) while  -  and  -  resonance coupling of  neighbours may s t i l l be e f f e c t i v e . There remains the problem of the d i s p a r i t y between the v-^ i r and Raman frequencies, at 1 0 0 t 10°K, i_.e_. 3088  cm  -1  at  Similarly i n  10°K.  100 ±  and 2 2 9 1 cm r e s p e c t i v e l y .  v-^(ir) = 3 1 ^ 9 c m D 0 2  i c e I the  v  ±  -1  and v^(Raman) =  r e s u l t s were 2321  R e c a l l that both the symmetric and asymmetric  1  s t r e t c h i n g modes appear t o be very broad bands due t o v-[_ - v-^ and V 3 resonance coupling.  Of the complete set of v-^ energy l e v e l s , the same  portions of the band need not be both Raman and i r a c t i v e nor with the same i n t e n s i t y f a c t o r .  Thus f o r the Raman s c a t t e r i n g only a narrow band i n  the lower one-half of the v-^ band was a c t i v e while f o r the i r a large range of frequencies was observed and the maximum i n t e n s i t y occurred at a higher frequency.  For the asymmetric  mode the same portions of the band o f  frequencies was i r and Raman a c t i v e . ference i n  - v^ and  -  This may i n d i c a t e a fundamental d i f -  resonance coupling.  Thus the Raman s c a t t e r i n g from hexagonal i c e I i n d i c a t e d that i n the i r absorption spectra the low frequency shoulder was peak was v^, .i.e.. v-^HgO) = 3 2 1 0 cm and v-^d^O) 1  that the two is  O.85U6  for  =  and the main  2 U 1 3 cm . -1  By, assuming  assignments are c o r r e c t , then the r a t i o of v^Cice^v^Cvapour) H2O  and  0.8655  for  D 0. 2  are the same on a l l 0-H bonds, then  I f the e f f e c t s of hydrogen bonding and  are expected t o be i n the  same order as i n the vapour phase and should have the same r e l a t i v e d i s placements from the vapour phase frequencies, F i g . i c e I absorption (3756  cm ). -1  (3210  U.15.  The  \>3(H 0) 2  cubic  cm ) i s O.85U6 times the V3(.H 0) vapour frequency -1  2  In order t o preserve the displacement due t o hydrogen bonding  180  4000-  3756  3500:  3340 3266  l  \32l6*x , 3 , 4 9 ^  (31681  (3125 )  3000-  2788 3  2727 . 2672  2500-  *•.  *  2465 •..2416 , \ 2 4 I 3 7  ( 2 3 6 0 ) ' ...2321 (2313)  2000  HDO  H 0 2  VAPOUR F i g . 4.15  D O  HDO  z  ^ 1  D O ; 2  J  SOLID  3  ICE  The ohserved vapour phase and cubic i c e I phase. H 2 O , HDO and D 0 frequencies are shown as s o l i d h o r i z o n t a l l i n e s . The r a t i o s of V3(ice)/v (vapour) are shown on the diagonal s o l i d l i n e s . The H 0 , HDO and D 2 O i c e frequencies p r e d i c t e d with those r a t i o s are shown as dotted h o r i z o n t a l l i n e s . 2  3  2  181  then the v -^(^O) i c e (where p stands f o r predicted) frequency would have t o he  0.85U6  x  365T  cm  -1  = 3125 cm , -1  compared to the observed v^RVjO) f r e -  quency of 31^9 cm . By s i m i l a r arguments v^ (l>20) = p  2313 cm  O.8655  compared to the observed value of 2321 cm . -1  x  2671  cm"  =  The p r e d i c t e d v-^  frequencies, which preserved the r e l a t i v e e f f e c t s of hydrogen bonding on and v j , agree very w e l l with the observed i r r e s u l t s .  The agreement i s  probably b e t t e r than i n d i c a t e d since the observed i r V j band was s h i f t e d t o higher frequency by overlap with the adjacent v^ band. The a l t e r n a t e assignment of observed i c e peaks which also r e t a i n s the v-j_ - V 3 order i s v-^ = 3210 c m  -1  v g ( i c e ) / ^ ( v a p o u r ) i s then  and the p r e d i c t e d v-^ frequency i s  O.8858  and  = 3 3 ^ 0 cm . -1  cm \ compared t o the i r r e s u l t , v-^ = 3210 cm . -1  The r a t i o < of 3253  Neither the v-^HgO) nor  the v-^(D20) frequency was a good approximation t o an observed i r band. The second assignments of v-^ and  were r e j e c t e d .  The reasonable assumption of equal e f f e c t s on v^ and  due .to  hydrogen bonding gives p r e d i c t e d frequencies i n good agreement w i t h observed features.  The accepted assignments were  = 31^9 cm and 1  = 3210 cm ^~,  while the 3 3 ^ 0 cm shoulder was probably (v^ + Vrp). 1  (b) The HDO s t r e t c h i n g modes.  Use of d i l u t e i s o t o p i c s u b s t i t u t i o n  to separate the c r y s t a l f i e l d and resonance coupling perturbations  (101,102)  was o r i g i n a l l y suggested f o r studying the molecular v i b r a t i o n s of DC1  under'  the influence of an HC1 c r y s t a l f i e l d , but i n the absence of intermolecular resonance coupling. The extensions of that concept to polyatomic molecules, which have more than one normal coordinate and where r a p i d i s o t o p i c exchange may occur, has l e d to some m i s i n t e r p r e t a t i o n s of experimental r e s u l t s , i_.e_. as i n  H2O  in  D2O  •.( 1 0 6 , 9 5 ) • Because of the r a p i d i s o t o p i c exchange i t  182  i s impossible t o i s o l a t e D 0 i n H 0 or H 0 i n D 0 at low concentrations. 2  2  2  2  One obtains a d i l u t e s o l u t i o n of HDO and very, very d i l u t e residues of H 0 or D 0 . 2  2  Now HDO has Cg molecular symmetry and three i n t e r n a l coordin-  ates, an OH s t r e t c h , an 0-D s t r e t c h and an HOD bend.  I t i s unreasonable  to expect both of the HDO s t r e t c h i n g modes t o be completely uncoupled from the s t r e t c h i n g modes of the H 0 or D 0 l a t t i c e . 2  2  Just such an assumption  by Hornig et a l . ( 1 0 6 ) and by B e r t i e and Whalley ( 9 5 ) has r e s u l t e d i n misi n t e r p r e t a t i o n of the i c e I HDO i r r e s u l t s . As a f i r s t approximation  t o i c e I , consider the i r observations f o r  HDO, H 2 O and D 2 O i n the vapour phase, F i g . H . 1 5 . One HDO s t r e t c h i n g mode l i e s almost exactly midway between V3 and v-j_ of H 2 O , while the other HDO of D 0 .  s t r e t c h i s observed nearly midway between V 3 and e n t i r e l y understandable  That i s  2  since the symmetric and asymmetric H 0 modes may 2  be considered as constructed from a basis of two i s o l a t e d 0-H (HDO) stretches which i n t e r a c t weakly.  Hornig ejt a l .  (105,106)  claimed that such a p i c t u r e  of the H 0 and D 2 O p o t e n t i a l s should extend t o the s o l i d as w e l l , i_.e_. i n 2  i c e I they expected the HDO modes t o l i e between the v-^/vj modes of H 2 O and  D 0. 2  For i c e I ( F i g .  features, while ture.  VQ^(HDO)  U.15)  VQ^HDO)  was observed between two i r  was almost coincident with a c e n t r a l i r  D 0 2  H 0 2  fea-  Ignoring the weight of Raman data t o the contrary, Hornig et a l .  assigned them at of the  V3(H 0) 2  3275  to  cm +.  VQ^(HDO)  3210  cm  1  and v^(HgO) t o  3360  cm  1  with  v^ (HD0) H  between  Their c e n t r a l aim appears t o have been the preservation  observed p o s i t i o n between  V3  and v-j_ of  H 0. 2  B e r t i e and Whalley's ( 9 5 ) d i s c u s s i o n of the r e l a t i o n s h i p s between HDO, H 0 and D 0 stretches was confusing. 2  the H-OD  2  (in  D 0) 2  They a l s o assumed the nature of  s t r e t c h was the same as the  H-0H(in  H2O)  stretch.  183  The above r a t i o s of v^(ice)/v^(vapour) f o r  and D 0 ( F i g . h. 1 5 ) 2  y i e l d i n t e r e s t i n g r e s u l t s when applied t o HDO (vapour) frequencies. observed vapour phase frequencies of HDO s t r e t c h i n g are The predicted HDO frequencies using the HpO and D 0.8655)  are v  P QH  (HD0) =  3l68  cm  -1  and v  observed HDO frequencies o f 3 2 6 3 cm  1  P Qr)  (HD0) =  and 2 U l 3 c m  the predicted frequencies l i e close t o the with the concept of Hornig et_ a l .  2  -  (105,106),  ratios cm  2360  -1  and 2 7 2 7 cm \  3707  0  -1  The  (0.85^6  and  compared t o the  r e s p e c t i v e l y . .Thus mid-points, i n agreement  but do not agree with the  observed HDO frequencies. On the basis of our assignments the observed v^. (HD0) s t r e t c h rr  Un  (Fig. k.l6) was outside and above the respondingly, the  -  i n t e r v a l of pure H 0. 2  Cor-  s t r e t c h was j u s t above v ^ ( D 0 ) , F i g . k.l6.  VQ^(HDO)  2  A  c l e a r explanation of the m i s p o s i t i o n i n g of the HDO stretches can be found by considering the coupling of HDO t o H 0 and D 0 l a t t i c e s . 2  2  Consider the case of k.0% HDO i n a D 0 cubic i c e I l a t t i c e . , . Of the 2  two HDO stretches only V Q ^ ( H D O ) can undergo reasonably strong near-resonance coupling t o v (Do0): v~„(HD0) i s "uncoupled" from the l a t t i c e v i b r a t i o n s . 3 . OH o  One then compares the observed v„„(HD0) t o v. and v„ of H 0 on the assumpUn X 3 d. t i o n of equal hydrogen bond e f f e c t s , F i g . h.l6. However, v (HD0) l i e s On o  OTJ  86 cm  1  above the  - v^(H 0) midpoint. 2  A p o s s i b l e explanation i s a  lengthened D0-H-'--0H distance due t o the very process o f uncoupling. 2  For example the covalent character of the hydrogen bond i s dependent upon an equal sharing o f e~ among the overlapped o r b i t a l s .  I f the o r b i t a l  f o l l o w i n g o f e~ about v i b r a t i n g n u c l e i i s not at the same rate then the hydrogen bond may .be weakened.  18U  3250+ 8 6  "Ms  32CO 3150  , Z /  1  -73 O  3100 -  o c CD  CT 2450 • LL  OD  24 OO  +49  2350 -  - 5 8  2300-  HQ 2  1+.16  HDO in Dp HDO in H0 2  DQ 2  The. r e l a t i v e p o s i t i o n s o f the observed H 2 O , HDO and D 0 s t r e t c h i n g v i b r a t i o n s are shown as h o r i z o n t a l s o l i d , l i n e s . The expected p o s i t i o n s of the. HDO absorptions before and a f t e r the e f f e c t s of uncoupling, are shown as dotted h o r i z o n t a l l i n e s 2  185  From s e c t i o n 4 . 2 A ( i i ) we found that Hence, a A v  of 8 6 cm  Q H  -1  0) =  AV.^/ARCO  On  implies the D0H-D 0 R ( 0  - , , -  2  cm  1,921  -1 ° /A.  0 ) distance was longer  o  than "expected" by 0.0^5 A.  Correspondingly the H0D-D 0 R(0 ci  tance should have been shorter than expected by D 0) would have been 58 cm  l y i n g under v ( D 0 ) ) , at 2311 cm . -1  2367  cm  1  2  f o r H 0 and D 0 2  For  5.9W  the center of  A and v (HDO i n QI)  (The  -  midpoints are 3180 and  respectively.)  2  HDO i n H 0 v (HD0) was found at 2hl6 2  QI)  cm , -1  cm  U9  -1  above  - v^DgO) f o r cubic i c e I , F i g . U . l 6 . That implies the  uncoupling had lengthened R ( 0 R(0  O.OH5  lower than expected (but i t was unobservable  1  2  1  0) d i s -  2  0) f o r DO-H  o  0) f o r HO-D  H 0 by 0.038 A.  Similarly  2  o  H 0 must have been shorter by 0.038 A and v (HD0) 2  QH  would have been lower than normal by 73 cm \  at 3107 near v^(H 0).. 2  For HDO i n H 0 and D 0 the point i s that one HDO mode was coupled 2  2  to the l a t t i c e and the other was uncoupled: the hydrogen bond, lengthened one R ( 0 R(0'*-*0) of HDO.  - - - -  The act of uncoupling weakened  0 ) and shortened the other three  Consequently the uncoupled frequency was s h i f t e d t o  higher frequency and the other was s h i f t e d t o lower frequency. Our explanation of the observed p o s i t i o n s of HDO frequencies i n r e l a t i o n t o the H 0 and D 0 frequencies cannot be r e a d i l y confirmed by any 2  2  meaningful c a l c u l a t i o n or conceived experiment.  However i t serves to.  point out an important f a c t i n d i l u t e i s o t o p i c s u b s t i t u t i o n studies i n solids:  The molecules of mixed analogues are not a l l uncoupled from the  lattice.  The method i s not generally u s e f u l nor a p p l i c a b l e to molecules  with mixed isotopes unless one recognizes that unusual e f f e c t s can occur.  186  ( i i ) The Bending Mode The p o s i t i o n of the 1570  cm  (l60H)  H0  -1  (Table I I I . X I ) i n d i c a t e s i t could be e i t h e r v lapping v / 2 v 2  cm .  R  absorptions.  cubic i c e I absorption  2  2  or 2v  and p o s s i b l y over-  R  The vapour phase v ( H 0 ) frequency i s 1595 2  2  The frequency s h i f t upon annealing was t o lower frequency  1  a c h a r a c t e r i s t i c of molecular modes and thus favours the v  2  ( F i g . 3.2)  assignment.  As w e l l , the cubic i c e I frequency s h i f t was t o higher frequency and s i m i l a r l y favoured \Jg.  However the h a l f - h e i g h t width increased upon annealing  and f o r cubic i c e I i t decreased with i n c r e a s i n g temperature (Figs. and 3.5 and page 67). The v  2  That data favours a combined v / 2 v 2  absorption was more intense than the underlying 2v -1  bably centered below 1595 cm R  C. ( i ) The 3v  R  R  absorption. and was  pro-  -1 , i_.e_. near 1570 cm  the v / 2 v band was found at 119k 2  R  3.12  .  Similarly for  D0 2  cm . -1  The Overtone and Combination Modes  Modes  The 2235 cm preted as both 3v  R  1  H0  and 1635 cm  2  and v  2  + v  R  D0  1  2  absorptions have been i n t e r -  (Table 0.5).  The bands s h i f t e d t o higher  frequency upon annealing and as cubic i c e I. the frequencies s h i f t e d down (Figs. 3.2 and 3.17):  Both of those f a c t s i n d i c a t e a l a t t i c e mode and  assign the absorption to 3v . R  we  However, there i s at l e a s t one d i s c o n c e r t i n g  f a c t o r , the r e l a t i v e i n t e n s i t i e s of v , 2v R  R  and 3v  R  that were observed.  One expects the overtone i n t e n s i t i e s to f a l l very r a p i d l y and thus the i n t e n s i t y of 3v  R  should be much l e s s than 2v . R  However the 3v  i s only about 1/k l e s s intense than the combined v / 2 v 2  R  R  absorption  absorption, and  187  that i n d i c a t e s t h a t 2 v i s l e s s intense than 3 v . However, the i n t e r p r e R  R  t a t i o n i n terms of i n d i v i d u a l molecular l i b r a t i o n s i s weak and a complete s o l i d s t a t e treatment i s necessary. ( i i ) The (v + v ) Mode  ••' •  T  The shoulder at 33h0 cm  in  has been v a r i o u s l y assigned as v-^,  and  H 0 2  +  cm  2I+65  in  -1  D 0 2  cubic i c e I  and v-^ + Vrj-i (Table 0 . 5 ) .  Our  previous d i s c u s s i o n on the s t r e t c h i n g modes o f H 0 , D 0 and HDO (page 181) 2  eliminated the  assignment.  "v^ + Vrp") i s 1 3 0 cm  1  The peak t o high-shoulder separation (v^ t o  while the low t o high frequency shoulder separation  (V-L t o "v + v " ) i s 1 9 1 cm ±  2  T  . The l a t t e r separation l i e s c l o s e r t o our  observed vrp(H 0) band maximum and favours the v-j_ + Vrp assignment. 2  t i o n , the Raman data ( 9 9 ) favours a  + Vrp assignment on the b a s i s o f  frequency separation and r e l a t i v e i n t e n s i t i e s , i_. e_. the r e l a t i v e v  l  +  V  T  In a d d i -  ,  to  i " t e n s i t i e s are 1 0 : i t : 2. n  k.h  The L i b r a t i o n s of HDO, H 0 and D 0 2  A.  2  The Moments-of-Iriertia Models  Past treatments of the l i b r a t i o n a l l a t t i c e modes of the i c e s have dwelt upon the a s s o c i a t i o n of the l i b r a t i o n s t o free r o t a t i o n of o r i e n t e d gas or gas phase molecules  (85,89).  I m p l i c i t i n such treatments have been  comparisons of the moments-of-inertia ( i ) about the three p r i n c i p a l axes of H 0 , HDO and D 0 . Blue ( 8 5 ) was the f i r s t t o evaluate the l i b r a t i o n a l 2  2  frequencies through moments-of-inertia.  We have extended the c a l c u l a t i o n s  188  to include weighted lone-pair o r b i t a l c o n t r i b u t i o n s to the moments. ( i ) The Non-Interacting  Molecules Model  The molecular parameters and the p o s i t i o n s of the p r i n c i p a l axes are shown i n F i g . U.17-  The moments-of-inertia are given i n Table IV.II  as w e l l as the differences between the HDO, H2O and D2O moments.  Under  the molecular symmetries, l i b r a t i o n s about the H2O and D2O z-axes are i r i n a c t i v e , while l i b r a t i o n of HDO about z i s i r a c t i v e due to the l o s s of symmetry and the o r i e n t a t i o n of the molecular dipole at  C2v  z-axis.  However,  VR (HD0) Z  0-H-••-0  1  to the  i s expected t o be weak compared t o v y and v R  due to the small dipole r e o r i e n t a t i o n . m e t r i c a l l y bent  17°5 +'  and  0-D  - - ,  *0  R x  Notice that v (HDO) gives asymRx  hydrogen bonds.  o  The D atom sweeps  o  0.00U A/deg arc while the H atom sweeps 0 . 0 1 2 A/deg arc i n a c l a s s i c a l approach. The HDO moments are s p l i t between the H 2 O and D 2 O moments-of-inerti Table I V . I I .  Hornig et_ a l . (105) pointed out that on the basis of• moments  o f - i n e r t i a the observed HDO l i b r a t i o n s would be expected t o s p l i t between the H 2 O and D 2 O l i b r a t i o n a l frequencies. moments one sees that  I (HD0) X  and Iy(HDO) i s midway between  From the differences i n the  i s nearer T^^O, Iy(H20)  and  I (HD0) Z  Iy(D 0). 2  i s nearer  I^(D20),  I t does not n e c e s s a r i l  f o l l o w that the HDO l i b r a t i o n a l frequencies w i l l be observed i n a corresponding manner. HDO l i b r a t i o n a l absorption was observed here only f o r HDO i n a D 2 O matrix: cm  1  One peak and one shoulder were observed at 8 2 3 cm and 8 5 6  r e s p e c t i v e l y (page  1  7 ^ ) . Assuming that the l i b r a t i o n a l  frequencies  for HDO, H 2 O and D 2 O can be defined by a s i n g l e function such as Blue's  z  Z  H 0 2  z HDO  F i g  -  ' ''  1+  P r i n c i p a l axes of H 0, HDO and D 0 and t h e i r molecular parameters. The angles were assumed t o be t e t r a h e d r a l .  r  71:16  2  2  X  H  Cpage 2 7 ) then v (HD0) should be r e l a t i v e l y weakly coupled t o any l i b r a Rx  t i o n of the D 0 l a t t i c e since the HDO and D 0 2  2  librational.frequencies  observed were about 9 0 % separated. One of the absorptions at 8 5 6 and 8 2 3 cm V  n (HD0) i s  it  n c e  n a s  x  V  R  must contain at l e a s t  "the lowest moment-of-inertia and i s expected t o be  c l o s e s t t o the H 0 values. 2  1  The other feature above cannot be due t o  (HDO) nor p (HD0) since the peak-shoulder separation was too s m a l l , v  z  190  Table IV.II  The moments-of-inertia of H 0, HDO and D 0 and a comparison of HDO t o H 0 and D 0. The parameters used to c a l c u l a t e the p r i n c i p a l moments-of-inertia are given i n the t e x t . 2  2  2  2  H0  D0  2  HDO  2  0.89 x i o -  • 1.61 x  h o  io'  1,.08 x 1 0  h o  2.91  5.63  h..23'  2.01  1+.02  3..15  4  0  u n i t s gms-cm / molecule 2  Comparison of moments -1+0 0.53 x 10  I (HD0) - I ( H 0 ) == 0.19 x 10~ °  I ( D 0 ) - I (HD0) =  Iy(HDO) - I ( H 0 ) == 1.32  I ( D 0 ) - Iy(HDO)  =  1.1+0  I (HD0) - I ( H 0 ) == 1.1k  I ( D 0 ) - I (HD0) =  0.87  x  x  y  z  z  h  2  2  2  x  y  z  2  x  2  2  z  I 33 cm" . As mentioned e a r l i e r , the shoulder appears t o be due t o (.v + v^) R  absorption. A l t e r n a t e l y the peak and shoulder may have r e s u l t e d from nearly degenerate V ( H D 0 ) and v-py(HDO) absorptions. R x  Such an event implies that  e i t h e r I and I of H D O are degenerate through coupling, or that the x  y  brations cannot be treated on the basis of moments-of-inertia. these p o s s i b i l i t i e s w i l l be t r e a t e d i n d e t a i l .  li-  Both of :  191  Assume t h a t the l i b r a t i o n s of HDO,  H0  and D 0  2  can be simply r e -  2  l a t e d t o the p r i n c i p a l moments-of-inertia by Blue's (85) formula (page 27). S i n c e the oxygen atoms l i e c l o s e to each of the p r i n c i p a l axes then the r  2  are a l l s m a l l and since the r e s t o r i n g forces on the oxygen atoms are °n a l l s m a l l then Blue's equation reduces t o : R  V  ( c m n  where:  —1 "  )  1 1 2^l7T 2  =  C  ( k H  2 ln Hm r  2 +  k  H n H r  2  ) ] 2 n  1/2 .  [ k ]  i s the l i b r a t i o n a l frequency about a x i s n kjj^  and '  r H  kn  =  n  =  2n  ^Hn  *  o n  tiasis of symmetry  n e  i s the distance of atom H  2  ln  n 1  normal t o a x i s n.  U s i n g the c a l c u l a t e d moments-of-inertia from Table I V . I I one obtains the l i b r a t i o n a l frequencies i n terms of the k g  V  R  f o r c e constants:  R x  =  H0 2.1*5 k  H  HDO . 2.60 k '  D0 1.83 k  D  y  =  2.77 k  H  2.33 k '  1.99  k  D  =  2.90 k  H  2.23 k '  2.05  k  D  2  v  n  ^2  2  H  H  H  I t i s i m p l i c i t i n t h i s treatment t h a t the three l i b r a t i o n s of each molecule are non-degenerate.  On the b a s i s of the above equations the  lowest observed frequencies of H 0 2  and D 0 must be a s s o c i a t e d w i t h the 2  Vp 's since they have the lowest force constant c o e f f i c i e n t s : x  V g ( H 0 ) = 833 cm , -1  x  2  and ]R (D 0) v  x  2  =  627 cm . -1  Thus  Using those frequencies  t h e f o r c e constants are :  k ( H 0 ) = (1.15 t 0.03) 1 0 H  k ( D 0 ) = (1.17 t 0.03) 1 0 D  F o r HDO,  v  R  (HDO)  5  dynes/cm  5  dynes/cm  2  2  has the smallest force constant c o e f f i c i e n t and we assign  t h a t (on a t r i a l b a s i s ) t o the 819 cm  1  peak.  Then the HDO  f o r c e constant,  192  kg' , i s ( l . 2 k 1 0.03)10^ dynes/cm, i n reasonable agreement with the and D 0  force constants.  2  By applying the above three force constants t o  the remaining functions one obtains the f o l l o w i n g set of frequencies:  H0  v  % V  R  cm  833  Rx  HDO  '  2  -1  D0 2  cm  916  -1  627  9h0  819  682  98U  785  702  cm  -1  Z  where the observed frequencies which were used t o define the force cons t a n t s are underlined.  Since l i b r a t i o n about the y p r i n c i p a l axis e n t a i l s  a greater d i s t o r t i o n of one HDO then the s l i g h t l y l a r g e r HDO  hydrogen bond than f o r v  force constant i s  R x  of H 0 2  and  D0 2  understandable.  Of the nine frequencies l i s t e d above three were assigned from experimental observation.  From the remaining s i x frequencies, two were ex-  pected t o be i r i n a c t i v e (i_.e_. v ( H 0 ) and v ( D 2 0 ) ) while a t h i r d R z  (VR (HD0)) 2  2  Rz  i s expected to be very weak.  quencies to compare with experiment:  v  That leaves three p r e d i c t e d f r e (H 0)  R  2  ,v  R  y Only the p r e d i c t i o n of the D 0 2  cubic i c e I band at 6 6 l cm . -1  out by more than 2 0 cm near the 9^0 cm V  R (HD0) x  ( D 0 ) at 6 8 2 cm 2  and  V R  (D 0) 2  (HDO)  and v  (D 0).  R  2  y 1  l i e s near an observed band,  However, even that p r e d i c t i o n i s  As w e l l , there were no observed absorptions .  Therefore, V R ( H 0 ) , y are e i t h e r weak or i n a c t i v e i r absorptions. A l t e r -  or 9 l 6 cm  1  one  1  p r e d i c t e d frequencies.  2  y n a t e l y those modes may be i r a c t i v e and strong but degenerate with the other l i b r a t i o n a l modes.  193 The conclusion must he that I mula i s i n v a l i d .  and Iy are degenerate or Blue's f o r -  x  The moments-of-inertia can be made n e a r l y degenerate by  considering the masses of the detached (more d i s t a n t ) two protons as being attached to the lone-pair o r b i t a l s .  As w e l l , Blue's formula ( 8 5 ) over-  s i m p l i f i e s the problem since i t ignores the motion of the four adjacent molecules through the hydrogen bonds. ( i i ) The Weighted Lone-Pairs Model Consider one R2O molecule as being suspended with n e u t r a l d e n s i t y i n a cubic i c e I l a t t i c e .  The supporting l a t t i c e can be considered as  having two p r i n c i p a l e f f e c t s .  F i r s t , the p r i n c i p a l moments of the two  protons attached t o the c e n t r a l molecule (0-H* •••()) are decreased through reduction of t h e i r :real masses t o an e f f e c t i v e mass by the "buoyancy" of the surrounding l a t t i c e through the hydrogen bonds.  The mass " l o s t " by  the two c e n t r a l protons i s gained i n the lone-pair o r b i t a l s of two neighboring molecules. ' S i m i l a r l y , the two lone-pair o r b i t a l s of the c e n t r a l molecule gain an e f f e c t i v e mass from the two detached protons ( 0 - - * H - 0 ) ,  associated with the c e n t r a l molecule hydrogen bonds.  Hence the lone-pair  e f f e c t i v e masses restore the moments-of-inertia to near t h e i r i n i t i a l values. The second e f f e c t on the moments-of-inertia which a r i s e s from hydrogen bonding i s the movement of the two attached protons away from, and the two detached protons c l o s e r t o the c e n t r a l oxygen atom.  Notice that  cooling the sample decreases R(0*•••()) and tends to c e n t r a l i z e the four protons f u r t h e r .  I f the four protons were centered between  0"-* 0 ,  and had  masses equally shared by the p a i r s of oxygen atoms, then the molecules would be r e s t r a i n e d s p h e r i c a l tops, I  x  = l  v  = l . z  19h  A pseudo-symmetric top i s approximated by smaller masses working at longer d i s t a n c e s , i_.e_. weighted l o n e - p a i r s a c t i n g at the detached proton o  distance of 1 . 7 9 A and a reduced protonic mass a c t i n g at the 0-H distance o  of 0 . 9 5 A. The point i s that i f the moments-of-inertia I and I y are equal x  for H 0 and DgO then by Blue's ( 8 5 ) formula v 2  R x  and v  should be degener-  R y  ate .  . Consider the e f f e c t o f reduced protonic masses and e f f e c t i v e lone-  p a i r masses where the molecular parameters w i l l be assumed t o be: r  0H  =  r  0D  °-  =  9 5 0  ^ o  R(6  H) = R(0- --D)  = 1.790 A  :  mass of oxygen =  15.999  gms/mole  the attached protons are Hj_ and Hg the detached protons are H 3 and H^ the masses of H j and H =  0.75(1.008)  2  =0.756  the masses of  and H^ =  H3  0.25  =  0.252  gms/mole  gms/mole (1.008)  gms/mole  gms/mole  (This i s c a l l e d the (3/h, 1/h) e f f e c t i v e mass option.)  The moments-of-  i n e r t i a of H 0 *-*H are: #  2  2  I ' =  3.1+3 x 1 0  Iy' =  3.15  I  3.30 x 10  x  z  =  x  10  gm-cm /molecule 2  -1+0 -ho  S u b s t i t u t i n g those'values of the moments i n t o Blue's ( 8 5 ) formula,  [h],  where the contributions of the oxygen force constants are s t i l l s m a l l , then:  195  3A,lA) =  X(H 0,  2.87(0.282  k  R (H 0,3/l+,l/4)  = 2.99(0.602  k  R (H 0,3/1+,1/1+)  =  k  2  V  y  V  Z  2  2  2.92(0.902  + 2.14  k^)  H  +  kg)  1.10  constant  and  force  constant.  k j j i s t h e 0' **H-0 b e n d i n g -  By s o l v i n g t h e f i r s t  .and  v  and v  R  S e  °  o f H 0 a r e degenerate  R  at 833  2  y  two e x p r e s s i o n s above one f i n d s  \-Yi ~  0.60 x 1 0 ^ dynes/cm  kg  0 . 2 1 x 1 0 ^ dynes/cm.  =  U s i n g t h o s e v a l u e s o f k^ a n d kjj i n t h e t h i r d Rz  H  force  x  V  ki)  w h e r e k^ i s t h e 0-H----0 b e n d i n g  Our m o d e l s u p p o s e s t h a t cm \  + 3.20  H  (H 0,3/1+,1/1+) i s 8 3 1 cm 2  which  e x p r e s s i o n above, then  i s degenerate  with  v  a n d _^_ w i t h i n V  R  x  R  error. How w e l l do k ( H 0 ) a n d k ^ ( H 0 ) a p p l y t o D 0 H  2  2  above m o l e c u l a r p a r a m e t e r s  and deuterium  gms/mole f o r t h e a t t a c h e d p a i r mole f o r t h e detached  pair  D ?  2  2  e f f e c t i v e masses  ( D j a n d D ) and masses 2  Using t h e o f 0.75(2.011+)  o f 0 . 2 5 ( 2 . 0 1 1 + ) gms/  ( D ^ a n d D^) t h e n t h e D 0 - - ' ' D 2  2  moments-of-  inertia are:  and  I  x  = 6.8H(l0 ^)  I  y  =  6.28(10"^°)  =  6.59(l0  l  gm-cm /molecule 2  -  z  - 1 + 0  ).  The c o r r e s p o n d i n g s e t o f e x p r e s s i o n s f r o m B l u e ' s  formula a r e :  196  :  (D 0,3A.1/U) 2  = 2.03(0.268 k  v c a l c ( D 0 , 3 A , l- /M X U) = ?  2  —  H  2.12(0.902  k  2.07(0.602  k  H  + 3 . 2 0 k^}  + 1.13  . i , kg)  = 586  ^oo cm"- 1  =  588  =  591  'r  s  v calc(D 0,3/U,lA) ?  R  =  H  + 2.lk k')  cm"  1  H z  where k^ and k j j of R^O were used.  The three DpO l i b r a t i o n a l frequencies  are reasonably degenerate and l i e 6% below the main observed band at 6 2 7 cm .  This i s as much accuracy as can be expected from so simple a model.  1  By invariance of the p o t e n t i a l energy t o symmetry operations kj^O^-H-^ • • * 0 ) -  2  kj^Oj-Hg  =  and k j ^ O ^ H g " • -  0 ) 3  not f o l l o w that k ( 0 - H j H  2*'"' ) u  *0^)  =  kntO-j-H^  k j j ( 0 * ' "'H3 ^ - 0 )  =  O5).  However, i t does  , since they are not  interchangeable by s i t e or point symmetry. 1  That basis. to 0  ,  ,  ,  is  0.309  times  kg  may be r a t i o n a l i z e d on the f o l l o w i n g  The p o t e n t i a l f o r l i b r a t i o n i s the same i n a l l d i r e c t i o n s normal  R(0 -  kjj  , - ,  *0),  axis.  0  i_.e_. the " p o t e n t i a l " has a c o n i c a l c r o s s - s e c t i o n along the While the shape of the p o t e n t i a l i s the same at protons H j  and Hg as w e l l as being the same at H^ and H^, only the moments of the forces a c t i n g at the two protonic distances must be equal.  Since the  o  O-H-j^ g  a n  d O-'-'H^ ^ distances are 0 . 9 ^ and 1 . 7 9 A r e s p e c t i v e l y , then the !  2  2  r a t i o ( r ^ ) / R ( 0 ' H ) = 0 . 3 ^ 5 . The moment' of the force a c t i n g at H and OH i H i s kjjr 2 = 0 . 5 3 x 1 0- 1 1 dyne-cm compared t o the moment a c t i n g at. H^ , , -  2  and H4, k ^ O  H ) = 0.67 x 1 0 2  -  1  1  dyne-cm.  There i s at l e a s t one d i s c o n c e r t i n g f a c t about t h i s model that i s seen f o r the case of h.0% HDO i n D 2 O . The e f f e c t i v e masses added t o the HDO lone-pairs are 0 . 2 5 times the deuterium mass not the protonic•mass. Thus HDO l i b r a t i o n a l frequencies would be c a l c u l a t e d nearer t o the D^O values than the H 2 O values, contrary t o our observations.  197  Another weighted l o n e - p a i r s option was i n v e s t i g a t e d , the ( H 0 , 1 , 2  l/U) option.  In t h i s model the two attached protons were assigned  full  protonic masses, while the two detached protons were assigned masses of 0.25  times the f u l l mass.  sums are not conserved.  Such a model seems unreasonable  By the same treatment as above one f i n d s :  k (H 0,l,lA)  =  0.783  kfl(H 0,1,1/1+)  =  0.213 x  H  2  2  x  The p r e d i c t e d v ( H 0 ) frequency i s 8 2 9 cm R z  dicted 1/1+)  D0 2  10  582,  592  and  5  105  1  2  frequencies are  model.  586  dynes/cm dynes/cm. f o r t h i s model and the pre-  c m , much as f o r the -1  (3/1+,  Notice that the moments of the forces a c t i n g at H^ ^ and —11  are now nearly equal, O.69 x 1 0 pectively, In  since the mass'  ^  —11  dyne-cm and O.67 x 1 0  dyne-cm r e s -  x  summary l e t us consider the r e s u l t s of the two models considered  F i r s t , Blue's ( 8 5 ) formula f o r n o n - i n t e r a c t i n g molecules gave three nondegenerate, widely  separated frequencies f o r the three l i b r a t i o n s .  That  i s contrary t o the observed spectra and must be r e j e c t e d . Secondly, f o r degenerate v  and v  R  the moments-of-inertia must be equal.  R  Using a  weighted l o n e - p a i r s model i t was necessary t o consider two kinds of hydrogen bond bending force constants, which were not a c c u r a t e l y t r a n s f e r able between H 0 and D 0 molecules. 2  2  As w e l l , the hydrogen bond bending  force constants c a l c u l a t e d were about as l a r g e as the molecular H0H bendin force constant, i_.e_. Zimmermann and Pimentel ( 9 7 ) found the H0H bending force constant i n i c e t o be 0.1+9 x 1 0 ^ dynes/cm.  The value of 0 . 6 0 x 1 0 ^  dynes/cm seems t o be an u n s a t i s f a c t o r i l y high 0-H*••*0 bending f o r c e constant .  198  B.  The  H 0 2  3  Model.of Ice  An a l t e r n a t e approach t o the l i b r a t i o n s of H 0 , HDO and D 0 2  2  molecules i n i c e i s the normal coordinate a n a l y s i s of an extended molecule HgO-j. Fig.  The s t r u c t u r e and parameters of the U.l8.  H 0 2  molecule are shown i n  3  For a f r e e l y r o t a t i n g and t r a n s l a t i n g  H 0 2  3  molecule there are  nine degrees of freedom and nine i n t e r n a l coordinates (R) are defined as: R-L  = Ar]_  R  2  =Ar  R  3  = Ar  R5  = A<(>  R  =  6  A6i  2  R  3  =  R  = A6  7  8  =  A  6  2  1  \.- ^  A s i m i l a r model was studied by Zimmermann and Pimentel ( 9 7 ) i n order t o c a l c u l a t e the hydrogen bond bending and s t r e t c h i n g force constants  asso-  c i a t e d w i t h molecular l i b r a t i o n and t r a n s l a t i o n . With Cp^. point symmetry the H^O^ s e n t a t i o n composed of 5 ^  2a  2  molecule has the r e d u c i b l e repre-  5b^_ and 3 b  2  i r r e d u c i b l e representations.  The representations of v i b r a t i o n , t r a n s l a t i o n and r o t a t i o n of the  H 0 2  3  molecule, as w e l l as the representations of the.sets of symmetry coordina t e s , are shown below:  199  F i g . k.18  The H 0 model of H 0 i n i c e I . The 000 and HOH angles were assumed t o be t e t r a h e d r a l . The hydrogen bond bending coordinates 6-j_ and 0 are i n the HOH plane and 8-|_ and 6^ are perpendicular t o them. 2  3  2  2  E  c  1  1  .1  1  1  1  -1  -1  °i  1  -1  1  -1  b  1  -1  -1  1  Ty * R  r(H o )  15  -1  5  1  5ai  +  r(Rot.)  • 3  -1  -1  -1  a  +  2v  C  a  l  2  2  3  2  °xz  a yz a  R  T  xx' y y z z a  z Ry  X  2  a  a  xy  a  xz  "y?  X  2a  +  2  \  +  5b  D  x  3  -1  1  1  a-|_ +  b  x  +  b  r(vib.)  9  1  7  -1  l+a +  a  2  +  3b]_  2  0  2  0  a-^ +  2  0  2  0  aj +  1  1  1  1  ru(R ,R )  2  0  2  0  l a-^ +  T (R ,R )  2  0  -2  0  a  ri(R ,R ) 1  2  r (R ) 3  5  6  5  8  7  Q  b  l  *1  a  2  +  l b b  2  +  3b  +  b  2  2  r(Trans.)  1  ,  2  2  200  The symmetry coordinates of HgO^ are S  1  S  2  S  h  =  1//2  (R^ + R )  =  1//2  (R +  =  R.  =  1//2  g  R^)  3  (R  1  1//2  "(R  3  -  1//2  (R  5  -  V  (Rg  -  v  S  6  =  S  7  =  S  8  =  1//2  9  =  1//2  a. (R + R ) 6  1//2  ?  S  (RQ  -  +  V  ]  \  V  J  v  a  2  b  2  In matrix n o t a t i o n the transformation from i n t e r n a l t o symmetry coordinates is S  =  p  where S_ and R_ are column m a t r i c i e s of symmetry and i n t e r n a l coordinates , and U i s an orthogonal matrix.  The s o l u t i o n of the secular equation i s simpler  i n symmetry coordinates and the F_ and G 'matrices must a l s o he transformed from i n t e r n a l coordinates (J(S))  (F_(R)  and  G_(R))  t o symmetry coordinates  (F_(S)  and  by the transformations F(S)  =  U  F(R)  U  T  G(S)  =  U  G(R)  U  T  The F ( S ) and G_(S) m a t r i c i e s each are d i a g o n a l i z e d i n t o block form c o n t a i n i n g a (k x l O a j , a(3 x 3)b^, a ( l x l ) a and a ( l x l ) b block. 2  2  The form of  G_(S) i n terms o f G_(R) elements and the numerical values o f the G_(s) blocks are given i n Table I V . I I I .  The form of the F _ ( S ) elements i n terms of F ( R )  elements i s the same as shown i n Table I V . I l l f o r  G_(S).  Before proceeding f u r t h e r w i t h the normal coordinate a n a l y s i s , the normal modes of v i b r a t i o n , r o t a t i o n and t r a n s l a t i o n of H 0 i n i c e I must 2  be assigned t o the i n t e r n a l v i b r a t i o n s o f the H 03 molecule as represented 2  201  Table XV.III.  ai G(S)  g  l l  +  E  13  +  2g  S  1 7  S  13 3 3  g  2 g  +  ll-  s  S  13  g  l 6 "  G(S) b  12  1 5  s  G(S) =  The symmetric G matrix elements i n terms of the i n t e r n a l coordinates and t h e i r numerical values f o r the HgO^ model i n u n i t s of (gm~^- A2 moles).  g  l 6  S  12  s  3h  8  +  +  S  13  S  33"  g  36  8 8  =  8 8  g  S  S  = [g  2  5  3 6  g  17  3  2g  lU  s  +  g  2  37  3U  g  1 5  35  s  l 6  S  3 6  +  +  2g  55 56  g  66  g  l 6 " ' 17  g  36  g  6 6 "•  +  l 7  g  s  37  56 g  76  1.03^  0  992  0.992  1  055  -,g ] =  g  76  088  0.062  D  0  0.088  0  2  393  2. 511  0.062  0  2  511  2.733  1.076  0  992  0.062  0.992  1  055  0  g  =  0  0.062  0  2.595  2.595  89  2  G(S)  [g  +  g  8 9  ]  =  2.733  by the symmetry coordinates above.  The displacement vectors o f each k i n d  of i n t e r n a l HgO^ coordinate are shown i n F i g . h.19.  The corresponding  displacement vectors of the symmetry coordinates constructed from those i n t e r n a l coordinates are shown i n F i g . h.20.  The RgO i c e I normal mode  associated with each HgOg i n t e r n a l v i b r a t i o n i s l i s t e d i n F i g . k.20. The symmetry coordinates vR , and z  , Sg and  , which correspond t o R t> v  x  r e s p e c t i v e l y , are of p a r t i c u l a r i n t e r e s t f o r t h i s discussion.  / /  R =A<£ 5  6 F i g . 4.19  The i n t e r n a l coordinates of the H2O3 model shown as. symmetrically equivalent p a i r s . The displacement vectors are not to scale and give only an approximate representation of the coordinates.  Fig.  U.20  The symmetry coordinates of the H 2 O 3 model were constructed as simple l i n e a r combinations of the i n t e r n a l coordinates. Each symmetry coordinate was assigned t o an HgO i c e I normal mode simply on the basis of the diagramatic representation.  Inspection of  , Ggg and G . i n Table I V . I l l shows that the two l i b r a t i o n s QG  ("Rx and v ) are " k i n e t i c a l l y " degenerate and that v p v  R z  degenerate with them:  v  i s very nearly  20k  G  G  G  77  =  88  5 3  99  =  -  % 6  S  6  V  T  §66  +  g  R  V  § 6 6 ~ 667  v  67  R  R  X  Z  y  I f the forces r e s t r a i n i n g l i b r a t i o n about x and y are equal (which they are for HyjCU by symmetry) then v -J  x  R  i s degenerate w i t h V R . y  The secular equation can be solved f o r the diagonal symmetry f o r c e constants by an i t e r a t i o n formula given by Green k*?  =  1  A.{ G. . +  £  ( G  iJ  iJ  ) 2 k  }  _  (.125):  [ 5 ] .  1  The b block i s t r i v i a l and gave the s o l u" t i o n of k 1  j  2  when  was assigned t o the peak at 8 3 3 cm ^.  =  Q Q  x  O.IH9  5 10  dyne-cm  The a block i s a l s o 2  t r i v i a l and gave the s o l u t i o n kgg = 0 . 1 5 7 x 1 0 ^ dyne-cm, i n good agreement with k ( T ?  and  v  V  n q  were assumed t o be degenerate at 8 3 3 cm " "). -  R  For the ( 3 x 3 ) b ^ block the S^, Sg and associated with  ^ 2 ^ 2 ° ^ '  V  &T1  T ^ 2 ^ H  G  X  ^  V  R ^ 2 ^> H  u  y  1  symmetry coordinates were respectively.  Applying  the i t e r a t i o n formula: 4  = 5  5  \  (G„ 5  55  ( +  0  -  9  —5; • 5  A  A  where  A. = 1  1  (v./1303-l)  9  6  2  )  2  -  -  k  6 6  r 6  X  1 +  ^ •  0  6  2  A  )  2  k  7 7  5; 5 "  1  }  1  7 7  5  7 - S  . I n i t i a l force constants k?. = 11  1.000  and the formulas converged t o t 0 . 0 0 1 i n eleven i t e r a t i o n s . constants determined were:  _  were assumed  The force  205  k,.,. =  5.U81 x 1 0 ^ dynes/cm  kgg  =  0 . 1 9 2 x 1 0 dynes/cm  k  =  0 . 1 5 U x 1 0 ^ dyne-cm  5  Notice that the symmetry force constant associated with v K  x 1 0 ^ dynes/cm, does not agree with those of v  and  V  R  x  R  n  y  , k„„ = 0 . 1 5 ^ 77  . z  F i n a l l y the (h x U)a^ block was solved f o r the HgO^ symmetry force constants. v-^HgO),  The S^, Sg,  and  symmetry coordinates were assigned t o  TgCHgO), vgCHgO) and v^HgO) r e s p e c t i v e l y . The symmetry coor-  dinate was assumed t o be a redundant, non-genuine HgO bending mode, although i t was a genuine mode of HgO^.  As a redundant coordinate terms due t o  i n F(s) and G_(s) were set equal t o zero.  Then the symmetry block reduced  to a (3 x 3)aj_ matrix. Using the observed V]_, Vip and V g frequencies of HgO (Table I I I . X I ) and i n i t i a l force constants of k.. =  then the three i t e r a t i o n  1.000,  11  formulas converged i n f i f t e e n steps t o : k^  =  5-369  k  =  0 . 2 3 1 x 1 0 dynes/cm  2 2  k ^ =  x  dynes/cm  10^  5  0 . 6 0 1 x 1 0 dyne-cm 5  With b e t t e r choices of i n i t i a l force constants, the formulas converged i n four t o f i v e steps t o ± 0 . 0 0 1 x 1 0 ^ dynes/cm. and k  To convert k ^ 5 y y ' 8 8 k  k  u n i t s from dyne-cm t o dynes/cm i t i s only necessary t o d i v i d e by  the lengths of the arms forming the bending coordinates. i n t e r n a l mode force, constants were estimated:  The set o f HgO  206  l l  k  k  (  V  =  '  5  3 6 9  (v )  =  5.H82  k (v )  =  0.666  5 5  3  3 3  2  x  10  dynes/cm  5  Of the three p o s s i b l e H 0 t r a n s l a t i o n s only two force constants were 2  estimated: k (T )  = 0.231  kgg(T )  =  2 2  z  y  0 . 1 9 2 x 1 0 dynes/cm. 5  F i n a l l y , three force constants associated with the three p o s s i b l e l i b r a t i o n s were estimated: k (R )  =  k (R )  = , 0.091  9 9  x  7 7  k  y  88^ z^ R  0.088  =  °-°9  2  x  l  o  dynes/cm.  5  The above symmetry force constants were transformed back t o i n t e r n a l coordinates force constants f o r comparison t o those of other workers. For example, the symmetry force constants i n terms o f i n t e r n a l force constants are: k  ll^ l^ V  k^(v )  =  k  r  +  k  (r]_r ) 2  - kCr-ji^)  k Co)*)  =  3  3  r  k(rir-]_)  =  3  k 3(v )  ^ l l ^  k  9 9  ( x^ R  = k(eie'i)+  k(e|e ) 2  k ( R y ) = k ( . e e ) - kCe^g) T T  = k ( r r ) + k(r r )k (R )  k (T ) 2 2  k  6 6  3  z  (  V  1  =  k  (  r  3 3 r  3  3  )  -  k ( r  1 +  3*V  8 8  z  1  = kCe^e^)-  k(e{e ) 2  207  Thus one found that the i n t e r n a l coordinates f o r c e constants f o r H 0 are 2  ( i n 1 0 ^ dynes/cm): internal  translational (0 0 stretch)  k ( r r ) = 5-425 1  k  1  k(r-Lr ) =  -O.O56  kU<j>)  0.666  2  =  ^  r  3  r  3^  =  °-  H^r^)=  lie-rational ( 0 - H 0 bend) kCe^)  2 1 2  0.019  =  0.090  k(0-[0 ) =  -0.002  *k(e e ) =  0.093  *k(e e ) =  -0.002  2  1  1  1  2  Since the other symmetry coordinate i n v o l v i n g 0^ and 0^ was assumed redundant and e l i m i n a t e d , then k(9^0^) could only be evaluated by assuming that k(0 0 ) 1  2  =  k(6J0 ) = 2  -0.002  x  10  5  dynes/cm.  A set of D 0 force constants was estimated i n the same way (from 2  LV>0 ) 3  as f o r  H 0. 2  The r e s u l t s of the  H 0 2  and D  2  0  i c e I f o r c e constant  :  models are l i s t e d i n Table IV.IV along with the r e s u l t s of Zimmermann and Pimentel ( 9 7 ) and Trevino ( 9 3 ) . .  I  Our k(0^9-^) i s an in-plane hydrogen bond  ! .  bend while k(0^0^) i s the out-of-plane bend.  Our in-plane hydrogen bond  bend i s approximately 1.5 times Trevino's value:  Part o f the d i f f e r e n c e  i s probably due t o d i f f e r e n c e s i n the models, Trevino's ( 9 3 ) was extended f u r t h e r and i n a three-dimensional l a t t i c e while ours was planar. The f o l l o w i n g comments can be made about the H 0 f o r c e constants 2  estimated using the HgO^ model and equation [ 5 ] :  • •  - the OH s t r e t c h i n g force constant (k(r-j_r^) = 5 . ^ 2 5 x 1 0 ^ dynes/cm) i s l e s s than the gas phase value and i s i n the region p r e d i c t e d from the r a t i o o f frequencies f o r harmonic o s c i l l a t o r s ,  208  Table 17.IT  The force constants o f i c e I from the HgO^ and D 0 models as w e l l as the r e s u l t s of Pimentel and Zimmerman and Trevino.  Force Constant  Associated Motion  2  H 0  D 0  2  2  Pimentel ' (a) i.r.  This Work (f) i.r. (a)  Cd)  k(r r 1  1  kCr^  5 . 7 H  5.U25  0-H, 0-H  -0.0U9  -O.0H9  0.225  0.212  0.023  0.019  k(r r  3  k( r r  u  k(e e  1  0-  k(e e  2  0  3  1  1  HH  •0  str,  0.178  0 , H-••-0  interaction (b) ••• -H-0 i .p.b.  0.093  * W k(0^0  0-  2  k(<M>)  (d) 5.52  0.25  0.06  H-0, 0- • •  H-0 i n t e r a c t i o n  (9  Trevino (e) neutron  (d)  0-H s t r .  interaction  3  This Work (f) i.r..  -H-0  (c) o.p.b.  (-0.002)  0.095  interaction  HOH bending  0.h9  0.099  0.090  -0.002  -0.002  0.730  0.666  0.08  0.62  (a) Pimentel and Zimmerman, Ref. 9 7 (b) i.p.b. = in-plane ( l i n e a r ) bend, (c) o.p.b. = out-of-plane ( l i n e a r ) bend. lO^ dynes/cm. H 0 2  3  model.  (d) a l l force constants are  (e) Trevino, Ref. 9 3 . ( f ) This  work, Green's formula,  209  - the'hydrogen-bond s t r e t c h i n g force constant ( k l r ^ r ^ l - = 0 . 2 1 2 . x 1 0 ^ dynes/cm) i s o f the order of magnitude expected on the b a s i s t h a t the hydrogen bond s t r e n g t h ( 5 - 1 0 Kcal/mole) i s about o f the 0-H bond s t r e n g t h ,  l/25th  - the H-O-H bending f o r c e constant (k^^ = k(<j><j>) =  0.666  x  10^  dynes/cm) i s s l i g h t l y decreased from the gas phase value ( 0 . 6 9 x 1 0 ^ dynes/cm) as expected from the s h i f t .in frequency, and - the out-of-plane hydrogen bond bending (O'-'-H-O) f o r c e constant (kfe^Gj) =  0.090  x  10^  dynes/cm) i s very s m a l l , t h i s may be  i n t e r p r e t e d as i n d i c a t i n g the hydrogen bond i s r e l a t i v e l y i n s e n s i t i v e t o bending through small angles. I t i s i n t e r e s t i n g t o n o t i c e that f o r every d i a g o n a l , i n t e r n a l coordinate force constant the DgO values a r e ' l a r g e r than the H2O values by 5 t o 10$.  The source o f t h i s e f f e c t i s i n the nature o f the force constant model.  Green's ( 1 2 5 ) formula [ 5 ] assumes a diagonal f o r c e f i e l d and a harmonic o s c i l l a t o r approach.  Since D 0 energy l e v e l s are lower, and since D 0 2  2  i n t e r n a l coordinates displacements are smaller than H 0 displacements, 2  then our D 0 "sees" a lower, more symmetric p o r t i o n of the "true" poten2  t i a l curve.  The simulated D 0 parabola i s thus narrower and steeper than 2  the simulated H 0 parabola and consequently the D 0 force constants are 2  2  l a r g e r than the H 0 force constants. 2  H 02 2  and D  2  0  3  I t i s obvious t h a t such diagonal  models assumed no anharmonicity i n i c e . Such a case seems  h i g h l y u n l i k e l y i n view o f the strong neighbour-neighbour through strong hydrogen bonds.  interaction  I n s p i t e o f t h i s o v e r s i m p l i f i c a t i o n , the  force constants appear t o give a f a i t h f u l r e p r e s e n t a t i o n o f the spectrum.  210  The t e s t of any set of. force constants, however, ll.es. i n i t s a b i l i t y t o reproduce the observed frequencies of i s o t o p i c analogues. To check the force constants derived from RVjO-g f o r the H 0 i n t e r n a l , 2  t r a n s l a t i o n a l and l i b r a t i o n a l v i b r a t i o n s i n i c e , the frequencies of D Q 2  i c e frequencies were c a l c u l a t e d .  Formula 15] was i n v e r t e d and solved:-  2 A. = k. ,. LG.. [G„ ++ . , j1. i ji jj j , ]1,1 1 11 11 lyCJ . . ' i~h are taken from HgOCHgO^) G  [6]  k  A  where k.., k  A. i s taken t o be the observed value, and J A. i s t o be c a l c u l a t e d . I  The a  2  and b  2  blocks are e a s i l y solved of course since they reduce t o the  form - A. l  = k..G.. n n  i n the absence of off-diagonal G_(S) elements.  The (3 x 3)b^ block and  the (3 x 3)a^ (reduced from (H x k) by e l i m i n a t i o n of the redundant coordinate) y i e l d two quadratic and one cubic equation each.  The frequen-  cies of the normal.modes of D 0 i c e I were found and are compared t o the 2  observed values below: v  3 l v v v  2  X v ~ H  R  vj  T x  (a)  VR J X  calc. -1 cm 2325 2258 1138 595 nn), 59^  v  obs. -1 cm 2^13 2321 119k  V  £o-Aai 627 r  601  627  229 232  220£ j 220^'  vp and  (b) Reference 9 6 .  VR  L  &  1  (b) b  z  calc.  obs. -1 cm -88 -63 -56 -32 -33 -26  +9  +12  are assumed t o be degenerate  V  211  The D 0 i c e i n t e r n a l mode frequencies CyijVgj'V^l- c a l c u l a t e d from formula 2  [6]  using  H2OC.H2O3}  force constants were a l l too low-  - 8 8 cm "*") by 3 to 5%.  cm , -1  The modes of i n t e r e s t , f o r which the  culated frequencies were also too low by 5 - 6%. D0 2  frequencies from the  as those predicted f o r HgO and D 0 2  1  H 0 2  3  Their c a l -  I t i s i n t e r e s t i n g that  model are nearly the.same  i n the weighted-lone-pair, moment-of-  i n e r t i a model p r e v i o u s l y discussed. 586 cm "*", 5 8 8 cm  cm/*'",  2  model was constructed, are the l i b r a t i o n a l l a t t i c e modes.  the l i b r a t i o n a l  -56  The D 0 t r a n s l a t i o n a l l a t t i c e frequencies c a l c u l a t e d  i n the same way were too high by 5%. HpO^  C-6"3  There the frequencies c a l c u l a t e d were  and 5 9 1 cm "*" f o r v p , Vp  and v p r e s p e c t i v e l y .  x  z  y One can conclude that the  ;  basis f o r  H2O/D2O  H2O3  normal coordinate a n a l y s i s , as a  i c e l i b r a t i o n s o f f e r s no improvement over a weighted  lone-pairs moment-of-inertia model.  The HgO^  model does give reasonable  i n t e r n a l and l a t t i c e , mode frequencies and reasonable i c e force constants. C.  A Summary of H 2 O , HDO  and D 2 O L i b r a t i o n s  Three models, of i c e l i b r a t i o n were presented:  Blue's ( 8 5 ) harmonic,  hindered o s c i l l a t o r model using moments-of-inertia, a weighted lone-pairs moments-of-inertia model, and a normal coordinate a n a l y s i s of the tended molecule.  Blue's formula [k] gave widely dispersed Vp  frequencies i n H 2 O : and D 2 O , jL.e_. separation of about 1 0 0 cm \ not conform to the observed i r absorption.  x  H2O3  and Vp^. This d i d  The l a s t two models were  discussed on the assumptions that the l i b r a t i o n a l modes were degenerate or nearly degenerate and that V R and vp^. are of equal i n t e n s i t y while x  vp  z  was weak or i n a c t i v e .  ex-  212  Transfering e f f e c t i v e mass from a nearest-neighbour proton t o the c e n t r a l molecule's l o n e - p a i r o r b i t a l s produced a nearly s p h e r i c a l t o p . The three p r i n c i p a l moments-of-inertia d i f f e r e d by only ± 5 percent f o r the ( H 0 ,  3/4,1/4)  2  option.  The force constants f o r molecular l i b r a t i o n were k  = 0.60 x 1 0 ^  n  dynes/cm at the attached proton and k^' = 0 . 2 1 x 10-* dynes/cm at the detached proton. [k]  These two force constants were deduced from Blue's formula  assuming v p =  [h]  =  x  8 3 2 cm \  A p p l i c a t i o n of k^ and k^' t o formula  i n D 0 parameters p r e d i c t e d D 0 frequencies o f : 2  2  v  R y  =  586  cm  588  cm  591  cm  -1  -1 -1  The D 0 frequencies' are reasonably degenerate, but l i e s i x percent below 2  the observed band maximum. 1,1/U)  Analogous r e s u l t s were obtained f o r an ( H 0 ,  e f f e c t i v e mass option.  2  T r a n s f e r a b i l i t y o f force constants among  i s o t o p i c analogues was v i o l a t e d i n the e f f e c t i v e mass model, force constants estimated from HgO and D2O frequencies d i d not agree. Normal coordinate analysis of the HgO-^ extended molecule  '; produced  very good valence force constants and hydrogen-bond force constants. However, the H 0 force constants d i d not d u p l i c a t e the D 0 frequencies.. 2  2  The d i s p e r s i o n was explained by considering the d i f f e r e n c e i n shape of harmonic p o t e n t i a l simulated by formula 15].  Degeneracy of the l i b r a t i o n a l  modes was acceptable i n t h i s model w i t h respect t o force constant evaluation.  213  Further improvements i n the analysis of i c e may be found by t r e a t ing i t as an extended three dimensional polymer. coordinate a n a l y s i s of polymers are now expanding.  Techniques of normal Zerbi's review  (12,6)  o u t l i n e s the approach, a m o d i f i c a t i o n of the t r a d i t i o n a l Wilson FG method, and l i s t s some references.  CHAPTER FIVE CLATHRATE-HYDRATE EXPERIMENTAL DETAILS AND RESULTS 5.1  The V i t r e o u s - C r y s t a l l i n e Clathrate-Mixture Phase Transformation A.  Experimental  Warm-up studies of the i r absorptions of v i t r e o u s , condensed mixtures of H 0 and guest species were completed i n the l i q u i d nitrogen 2  c e l l (page k2).  Stoichiometric gaseous mixtures corresponding t o the  three classes of clathrate-hydrate were prepared and condensed i n the same manner as the i c e samples (page 58).  Samples studied i n the f i r s t  c l a t h r a t e class (page 13) 6G-1+6H 0 were G = CH3CI, CH Br and C l , while 2  3  2  for the second c l a t h r a t e c l a s s (page 15) SG'ISSHgO the samples were f o r G = CH3I, CHCI3 and C H^Br. 2  Only one sample from the t h i r d class,.  20G*1T2H 0 (page 15), was studied, i_.e_. G = B r . 2  2  The conditions of  sample formation and annealing are l i s t e d i n Table V.I.  In order t o •  avoid separation of the c l a t h r a t e mixture, a l l these samples were depos i t e d through the heated metal deposition tube (page kh). As with the H 0, HDO and D 0 2  2  samples, the source beam was blocked  when the c l a t h r a t e mixture samples were warmed above l80°K, i n order to prevent sublimation. above l60°K.  As w e l l , the c e l l chamber was not pumped when  The temperatures quoted here are those which were measured  by the copper-constantan thermocouple attached t o the brass sample", block: heating.  The sample temperatures were 10°K higher due t o source beam However, the maximum annealing temperatures do not need t o be  corrected i n that way since the source beam was o f f then.  Table V.I.  The d e p o s i t i o n  The c l a t h r a t e mixture sample h i s t o r i e s f o r the deposition and annealing procedures, temperature r e f e r s t o the.sample block temperature.with the source o f f .  CI (CU)  B2  Molar gas r a t i o  D  ICH3CI:  lCH^Br:  ICH3I:  1CHC1-:  lC H Br:  1C1 :  7 H0  7 H0  17H 0  17H 0  17H 0  7  sec  3 sec  2  Deposition Rate  10  Sample Substrate  Csl  sec  2  1.5  min  Csl  Deposition Temperature 83  81*  139  265  200  199  12  U5  2  sec ( -- ) 5  Csl  83 (83)  2  2  2  Maximum Annealing Temperature Time at Maximum Temperature  Min  98 (105) • 188 (189)  5  2  Csl  Csl  83  81  172  170  189  189  15  16  °K Annealing Time  Fl (F6)  E  2  H0 2  3 sec ' (2 min) Csl 81 (82)  103 (25) 189 (190)  G3  1C1 : 2  7  H0 2  lBr : 2  8. 6H~ 0 2  3 sec  3 sec  AgCl  AgCl  83  83  . 15  2k0  190  200  °K Min  16 (18)  12 (15)  11  25  ro H  216  A l l annealing processes were observed on the P.E. h21 spectrophotometer during warm-up from 8 5 t 5°K t o 1 8 0 t 10°K.  Spectrophotometer  controls were set f o r optimum response and were the same as f o r i c e I (page 5 9 ) with small v a r i a t i o n s .  The spectra were recorded at 8 5 t 5°K  immediately a f t e r deposition and at several temperatures between 8 5 l80°K.  Peaks and shoulders were assigned as f o r i c e I (page  B.  0  and  59).  Results of D e v i t r i f i c a t i o n  While the degree of c r y s t a l l i n i t y of the samples condensed from the vapour phase depended upon the sample h i s t o r y , the basic r e s u l t s f o r a l l the  unannealed, vitreous.samples were the same.  Consequently, only one set  of normal annealing r e s u l t s w i l l be discussed i n d e t a i l . were observed f o r  6Cl2'46R"20  condensed and annealed on a C s l window.:  r e s u l t s w i l l be discussed separately. (v]_ + vp),  v  3»  v  l» 3 R» y  V2/2.Vp  Some i r r e g u l a r i t i e s  and v  absorptions which were observed.  R  Each of the H^O  Those  s k e l e t a l bands  was analyzed, as were those guest  No d i s t i n c t i o n between the classes^ of.  c l a t h r a t e s was noticed i n t h i s work. ( i ) The E f f e c t of D e v i t r i f i c a t i o n on the L a t t i c e Peak Maxima For  the seven samples l i s t e d previously (page 2 1 5 ) only the r e s u l t s  of the chloromethane c l a t h r a t e mixture w i l l be given. The s i x other samples ( i n c l u d i n g C l on C s l ) had the same behaviour w i t h i n the l i m i t s of 2  error.  The frequency-temperature dependences of the main H 0 2  skeletal  features are shown i n F i g . 5 - 1 . The absorption spectra of some unannealed and annealed samples ( a l l at 8 3 ± 3°K) are shown i n F i g s . 5 . 2 , 5-3 and 5 - 4 . Some d e t a i l s of the CHjCl'T^THgO c l a t h r a t e mixture annealing ( F i g . 5 - l ) are  • 8  200 -  0  • 7  UJ D h  ^3  •5  150-  •5 • 4  • 4  <  Q: UJ Q_ LU  • 3  • 6  •1  I 3150  '  l l 3170  1  1  •1  1 3220  • 8  o  i  1 3240  •8  • 7  LU  • 7 • 5  150 -  • 5  • 4  <  LU Q.  • 2  • 6  200  h  • 3  • 2  IOO -  70  D  217  •7  • 4 •3 • 2  IOO  LU  • 6  h  70  i  •3 •2 • 1  • 1 i 3360  i  i 3370  i  i  •  i  i  • 8  200-  o  • 6 I 2220  i 2230  • 8 •7  LU  DC D h  •5  I5Q-  • 4  <  LU CL  •5 • 4-  •3  • 3 • 2  IOO-  LU  • 6  h  70  i 1610  •2  i  i 1630  i  i i 1650  i  i 790  FREQUENCY F i g . 5.1  • 6  •1  •f  i  CM  1 810  i  i 830  -1  The s h i f t s of the unannealed c l a t h r a t e mixture ( C B ^ C l ^ ^ R ^ O ) H 0 peaks during warming from 83 ± 3°K t o 200 ± 5°K. The data are t y p i c a l of a l l the c l a t h r a t e mixtures and appear t o be the same as f o r i c e Iv. The data are numbered i n the order of observation. 2  A.B  •4000  A.B  1000  3000  3000  4COO  500 A.B  A.B  2000  FREQUENCY  IOOO  500  CM"  F i g . 5.2 The i n f r a r e d absorption spectra of some c l a t h r a t e mixtures. In. a l l cases spectra numbered "A" are backgrounds through the low temperature c e l l , (a) C H 3 C I • 7 . 6 7 H 0 unannealed at 8 3 ± 3°K ( B ) , at 8 3 ± 3°K but annealed t o l 6 0 ± 3°K ( C ) , and at 200°K (D). (b) CH^Br• 7 . 6 7 H 0 . unannealed at 8 3 ± 3°K ( B ) , at 8 3 ± 3°K but annealed t o 1 5 8 + 3°K (C) and at 1 8 9 + 3°K (D). (c) C H I - 1 7 H 0 unannealed at 8 3 ± 3°K (B), annealed t o 1 9 0 ± 5°K but observed at 8 3 ± 3°K ( O and at .188 + 3°K (D). The same frequency scale applies t o a l l of the spectra, i . e . f o r each absorbance s c a l e . 2  2  3  2  Fig.  5-3  The e f f e c t s of annealing c l a t h r a t e mixtures of C H C I 3 and C^^Br" 17H 0. (a) C H C 1 - 1 7 H 0 unannealed at 8 3 ± 3°K (B), at 1 2 9 ± 3°K 2  3  2  (c), at ll+9 i 3°K (D) and at 1 8 9 t 5°K (E) .  unannealed and at 1 8 9 absorbance f o r D than  (h) C H B r • 1 7 H 0 2  5  2  at 8 3 ± 3°K ( B ) , at 1 2 9 i 3°K lc\ at 1kg ± 3°K (D) i 3°K (E). The same frequency scale applies t o each s c a l e , i_.e_. a shorter span of frequencies i s shown f o r E. t  A.B  A,B  2000  3000  4000  FREQUENCY  F i g . 5.U  1000  CM"  Ca) B r ' 8 . 6 HgO on AgCl unannealed at 8 3 ± 3°K (B,C), at 1 3 0 + 3°K (D,E) and at 1 7 0 + 3°K (F)... Spectra B and. C were recorded s i x hours apart while spectra D and E were recorded t h i r t y minutes apart. (b) C 1 - 7 . 6 7 H 0 on AgCl unannealed a t 8 3 ± 3°K (B) and at 8 3 ± 3°K but annealed t o 1 9 0 + 5°K Cc). (c) C 1 - 7 . 6 T H 0 on C s l unannealed at 8 3 + 3°K (.B) and at 8 3 ± 3°K but annealed t o 1 9 0 ± 5°K f o r 1 5 minutes (C). 2  2  2  2  2  500  221  i n Table V . I I .  As f o r i c e I , the frequency s h i f t s of the v i t r e o u s sample  peaks were i r r e v e r s i b l e .  The points i n F i g . 5 . 1 are numbered i n the  sequence i n which they were obtained f o r each band.  The s i x t h point was  obtained by c o o l i n g the sample t o 8 3 - 3°K a f t e r annealing i t at 1 6 0 ± 3°K for 2 0 minutes and before warming t o higher  Table.V.II  The R" 0 frequencies of the CH C1*7.67H 0 c l a t h r a t e mixture before ( v ) and a f t e r ( v ) annealing t o 2 0 0 ± 5°K. The transformation temperature range and the temperature dependence a f t e r annealing are shown. 2  3  u  82°K  unannealed v •• u  v  + v  V  3  v  l  3v  D  T  temperatures.  2  a  82°K  annealed va  82°K  Transformation  Av v - v  Temperature Range  a  cm  u  a  AT  cm  cm  3382±5  3361+  _ i 8  (lUO-170) ±10  0.10  3258±3  3219  -39  (lHO-l6o)±10  0.12  3195±5  311+6  -1+9  (130-155) ±10  0.25  2209±5  2227  +18  (125-155)±10  l65l+'±3  1610  -1+1+  (125-Il+0)±10  792±1+  823  +31  (I15-ll+0)±10  1  °K  .  cm ""V°K  -0.09  R  v  V  2  R  0.18  -0.l6  222  The f i v e conclusions made w i t h respect t o the i c e I d e v i t r i f i c a t i o n (page 6 3 ) apply t o RgO i n these c l a t h r a t e mixtures a l s o . • T y p i c a l v i s u a l observations of the annealing process are i l l u s t r a t e d by those f o r  CH3CI'7.67^0:  - at 8 3 i 3°K (before' annealing) a transparent f i l m around a t r a n s l u c e n t , milky-white mass about 0 . 2 5 inches i n diameter, - at 1 6 8 i 3°K an opaque white mass opposite the nozzle  surrounded  by a t h i n transparent f i l m , and - at 1 8 8 t 3°K the sample appeared t o be t o t a l l y white and opaque. In g e n e r a l , the source image was centered on the thinner p o r t i o n of the sample.  The  Br2'8.6H20  mixtures were not white, but were orange and  yellow-orange depending on the t h i c k n e s s . ( i i ) The E f f e c t s o f D e v i t r i f i c a t i o n on the Oligomeric HpO Bands Weak peaks and shoulders on the high frequency side of the s k e l e t a l unannealed HgO s t r e t c h i n g band had the same appearance as f o r v i t r e o u s i c e I ( F i g . 3 . 3 ) and can be seen i n F i g s . 5 . 2 , 5.3 and 5 . ^ .  The p o s i t i o n s of  these oligomeric H 2 O absorptions f o r various unannealed c l a t h r a t e mixtures at 8 3 ± 3°K immediately a f t e r d e p o s i t i o n are given i n Table V . I I I : some cases a number o f specimens were observed. depend  In  The p o s i t i o n s of the peaks  on the r a t e of sample d e p o s i t i o n . For example, the three CH^Br  sets o f r e s u l t s were obtained from mixtures deposited through a needle valve i n ^.5> 1.5 and 1 1 minutes r e s p e c t i v e l y .  The temperature  of the H 2 O oligomeric absorptions from a number of c l a t h r a t e given i n Table V.IV.  dependences  mixtures are  With a s i n g l e exception t h e oligomeric HgO "absorptions  began t o d i m i n i s h i n peak height between below 170°K, Table V.V.  120  and  129°K  and had disappeared  Table V . I I I  CR£1  CH Br  CH3I  3  '7.67H 0 2  1"5  The frequencies a t 8 3 ± 3°K o f the weak peaks and shoulders associated with oligomeric H2O u n i t s i n s e v e r a l unannealed c l a t h r a t e mixtures.  cm """  365h  (vw)  3583  (w)  7-67H 0 2  -1 ±5 cm 3 6 U 5 (vw) 3 6 0 5 (vw)  "17H 0 2  ±5  Br  •17H 0  •17H 0  *8.6H 0  2  cm  3580  C H^Br 2  ±5  (w)  2  cm """  3689 3639  (ww) (vw)  ±5  2  C  +5  1  c i  2  ±5  36k3  (vw)  3 6 9 1 (ww)  3689  3565  (w)  3612  3672  (vw)  3635 3687 3670 3617  3620  (v)  3687  (vw)  3668  (ww)  3673  (w)  36U8  (ww)  3636  (vw)  3625  (ww)  3638  36k2 3690  (vw)  (vw)  (w)  -1  cm (ww) (vw) (w) (ww) (vw) (w)  ±5  cm """  3635  3689  3690 3671 36lU  (vw)  ±5  v  cm  1  3687 3658 3637  3623  3620  ice I  2  2  cm """  H20  2  •7.67H 0  *7.67H 0  2  cm *""  AgCl  Csl  CHCI3  (vw)  (ww) (w) (ww) (vw) (w)  362k (vw)-  ro ro  22h  The temperature dependences of the oligomeric H 2 O absorption frequencies of some c l a t h r a t e mixtures and unannealed i c e I .  Table V.IV  85±3°K  Ice I  H 0 2  v  -1  cm  9 +±3°K  110±3°K  125±3°K ,  3687  3689  3690  3690  3658  367I+  3637  3650  3  H 0 2  cm ^  3689  (sh)  3639(0.11)  83±3°K  C H Br'17 H 0 2  5  2  361+3  (wsh)  -1  cm  3565  (msh)  8l±3°K  Cl -7.67 2  H 0 2  -1  cm  2  -1  cm  H 0 2  109±3°K  3687  (sh)  361+0 ( 0 . 1 0 )  110±3°K  3669  (wsh)  3638  (wsh)  3569  (msh)  129±3°K  ll+9±3°K  3673  3672  (sh)  3652  (sh)  (sh)  361+0(0.06)  363l+(0.0U)  129±3°K  150±3°K  3658  (wsh)  3563  (msh)  ll+9±3°K  129±3°K  109±3°K  (vw)  3688  (vw)  3688  (vw)  3672  (vw)  3675  (vw)  3669  (vw)  3635  (wsh)  3630  (wsh)  3636  (wsh)  3689  83±3°K  Br -8.6  361+7  36k0  83±3°K  CHC1 '1T  i  130i3°K  3691(0.02)  3693(0.02)  3612(0.10)  3616(0.08)  130±3°K  1 7 0 ± 3 °K  83±3°K  +0.5 hours 3609(0.06) 3563  (sh)  3528  (sh  225  Table V.V  The temperatures at which the oligomeric peak heights began to decrease (T-.) and the maximum temperature at which they were observed ( T ) 2  Guest  T  l  T  ±5°K  CH3CI  2  ±5°K  120  120  CH Br  120  <  138  CH3I  120  <  iho  ikg  <  169  125  <  150  —  >  185  129  <  lh9  3  CHC1  3  C H Br 2  Br  5  2  Cl (Csl) 2  H0 2  ice I  v  110  125  For the B r ^ S ^ H g O mixture the oligomeric absorptions were observed at 170 t 3°K during annealing and even at 8 3 t 3°K a f t e r annealing, F i g . 5.4.  The v i s u a l appearance of the B r ' 8 . 6 H 0 sample changed markedly during 2  2  annealing above 1 8 5 t 3°K (with the source beam o f f ) :  The sample was  annealed f o r 1 0 minutes at 1 8 5 ± 3°K, 1 0 minutes at 1 9 0 ± 3°K and f o r 3 minutes at 2 0 0 ± 3°K. A f t e r 1 minute at 2 0 0 ± 3°K the sample changed from orange-brown t o a rusty-brown surface l a y e r . 2 0 0 ± 3°K the rusty-brown l a y e r had sublimed o f f .  A f t e r 3 minutes at  226  ( i i i ) The E f f e c t s of D e v i t r i f i c a t i o n on Gl -7.6THpO Mixtures 2  Gaseous mixtures of Cl2"7-67 H 2 O condensed on C s l and annealed f o r long periods appeared to react with the C s l . H0 2  Consequently  the Cl '7-67 2  mixture was studied on two s u b s t r a t e s , i_.e_. C s l and AgCl, samples F  and G r e s p e c t i v e l y .  In a l l s i x samples were studied on C s l and three on  AgCl. (a) C1 '7.67H 0 on C s l (sample F ) . 2  2  The i r absorption spectra of  Cl2*7.67H 0 at 83 ± 3°K before and a f t e r annealing to l89°K were shown i n 2  F i g . 5.*+ H0 2  (sample F j ) , while the temperature-frequency  dependences of the  s k e l e t a l absorptions were the same as f o r CH3CI•7•67H 0 2  (Fig.5-1).  The  e f f e c t of annealing Cl2"7.67H 0 to p r o g r e s s i v e l y higher temperatures i s 2  shown i n F i g . 5-5 (sample Fg). and during annealing  The v i s u a l appearance of sample F-^ before  was:  - (between 83 t 3 and 110 i 3°K) a cone of opaque white m a t e r i a l which became g r a d u a l l y more transparent at the base of the cone, - (at 169 t 3°K) a generally opaque white sample 0.5 inches i n diameter, and - (at 83 ± 3°K a f t e r annealing) a uniformly white opaque sample. The v i s u a l appearance of sample Fg before and during annealing was  the  same as f o r sample F]_. By v i s u a l observation no d i s t i n c t i o n could be drawn between the samples annealed to 170 ± 3, 180 ± 3 and 190 ±  3°K  although t h e i r spectra d i f f e r e d . In the spectrum of sample Fg the absorption between 3000 cm 2^00  cm"*" increased as the sample was annealed t o higher -  and  temperatures.  Also n o t i c e the dramatic e f f e c t on the s t r e t c h i n g band due to annealing to  E.F  4000  E.F  3000  2000  FREQUENCY  IOOO  CM  F i g . 5.5 Spectra o f one sample of Cl2 T.67H 0 on C s l at 83°K with various successive annealing times: (A) Unannealed, (B) annealed t o 170°K f o r 1 5 minutes, (C) annealed a f t e r (B) to l 8 0 ° K f o r 1 5 minutes, (D) then annealed t o 190°K f o r 1 5 minutes, (E) then annealed t o 190°K f o r 30 minutes, and ( F ) , background through low temperature c e l l at 83°K. ,  2  ro ro  —]  228  190 ± 2°K, i_-e_. the i n t e n s i t y of the low frequency shoulder increased and Annealing t o 1 7 0 + 2°K or 1 8 0 t  a new high frequency shoulder appeared.  gave only the c h a r a c t e r i s t i c sharpening i n t o 1 peak and 2 shoulders. w e l l , the nature of the v (b)  C1 *7.67H 0 2  2  2  2°K  As  absorption changed.  on AgCl (sample G).  D e t a i l e d studies of the  annealing process of amorphous s o l i d C l - 7 HgO on an AgCl substrate were 2  not made.  Spectra were recorded at 8 3 ± 3°K before and a f t e r annealing to  various temperatures.  The v i s u a l appearances were as before, i_.e_. a c l e a r  and transparent sample except f o r one spot opposite the nozzle before annealing and a uniform opaque white sample a f t e r annealing. absorption as might be expected was not observed and the H 0 2  Cl  2  guest  skeletal  absorption was shown i n F i g . 5 . ^ . None of our attempts t o s p l i t the C1 '7-67H 0 s t r e t c h i n g band i n t o 1 2  2  peak and 3 shoulders succeeded f o r samples on an AgCl window. nature of the v 3000 cm  -1  2  band changed.  and 2 ^ 0 0 cm  -1  Nor was the  As w e l l , no increased absorption between  was observed.  The p o s i t i o n s of the C1 '7.67H 0 2  2  bands on C s l and AgCl w i l l be discussed i n section 5-3 (page 23*0.  5-2  C l a t h r a t e Mixture Guest Absorptions  , •  The i r absorptions due to the guest molecules which were expected to be trapped i n the cages of the- H 0 host l a t t i c e were formed and observed 2  by three techniques.  In the f i r s t method (section 5 - l ) the s t o i c h i o m e t r i c  gaseous mixtures were condensed r a p i d l y onto a substrate h e l d at 8 3 i 3°K i n an open chamber (section 2.kc).  To ensure that the guest molecules  were not d i f f u s i n g out of the host l a t t i c e , a second and a t h i r d method  229  were i n v e s t i g a t e d .  The second method was condensation o f the mixtures i n  an i s o l a t e d chamber (section 2.4B), and the t h i r d method was the preparat i o n and observation of low temperature mulls ( s e c t i o n 2.kA) o f s o l i d c l a t h r a t e mixtures (section  2.3A).  Of the seven c l a t h r a t e mixtures studi<  Clg'T-STHpO and Brp'S^RgO should have no guest i r absorptions.  A.  Condensation i n an Open Chamber  During d e v i t r i f i c a t i o n of these samples the temperature at which the guest absorption peak heights began t o diminish and the temperature at which they were absent v a r i e d considerably from sample t o sample. However, since the behaviours were generally the same only one or two cases w i l l be described i n d e t a i l . For example, the 2957  cm  1  CH3CI'7.67^0  guest absorptions were observed at  (m), lkk3 (m), 1U37 ( s h ) , 1347 (w) 1338 (vw), 1 0 2 1 (vw) and ( F i g . 5 . 2 ( a ) ) near the s o l i d  CH3CI  absorptions.  700  (ms)  They were observed  up t o 1 0 0 ± 3°K with undiminished i n t e n s i t y and up t o l 6 0 ± 3°K with diminishing i n t e n s i t y .  I n contrast CH^I'^^O guest absorptions"were  undiminished up t o 138 +2°K and n i l at f o r a second specimen the  CH3Br  168 +  2°K f o r one specimen, w h i l e  absorptions were s l i g h t l y diminished at  1 1 0 + 3°K and slowly diminishing up to 1 8 9 ± 3°K (the 1235 c m s t i l l present).  - 1  peak was  The guest absorptions from a number of unannealed  c l a t h r a t e mixtures at 8 3 t 3°K, immediately a f t e r d e p o s i t i o n , are l i s t e d i n Table V.VI. The v a r i a t i o n s of those guest absorptions as a function of temperature are given i n Table V.VII and the temperatures o f the onset of a l t e r a t i o n , i n guest absorptions and the maximum temperature at which they were observed are given i n Table V.VIII.  Table V.VI The a l k y l h a l i d e guest absorptions at 8 3 t 3°K i n a number of a l k y l halide c l a t h r a t e mixtures before annealing began  CH^Br  CH3CI •T.67H 0 2  cm 2957  (m)  lhk3 (m) 1^37  (sh)  CH I  -7.67H 0  -17H 0  cm l  cm-l  2  1  CgH^Br  3  -  C H C 1  2  cm"-1  • 3020' (sh) ' 2965  (sh)  2950  (w)  2936 2915  (vvw) (ww) 1 2 0 0 (sh)  (ww) (ww)  3  cm l -  3020 (m)  '  1  T  H  -X7H20  2 °  cm~l 301U  (sh)  cm~l 3016  cm~l  (sh) 2985  (vw)  125^  (vw)  1292 1338  (w) (vw)  1021  (vw)  13^7  700  (ms)  1218  750  (s)  (w) 12kk (sh) 1233 (sh) 123U (w) 1238  121U  (sh) (w)  105U  (vw)  1238  12U1 1216  (ww) (vw)  1238 12ll|  (ww) (vw)  755  (ms)  752  (ms)  752  (ms)  665  (w)  665  (w)  663  (w)  12k2 (vw) 955  (w)  760  (sh)  ro o  231  Table V.VII  The temperature dependences o f the guest absorptions during the annealing of c l a t h r a t e mixtures. These data are t y p i c a l of a l l samples.  . 83±3°K CH.3I • 17H 0 2  110±3°K  2950  Cw)  1238  Cw) (sh)  1233  (ww)  2  5  2  2939  (ww)  2915  (ww) 12kh ( s h ) 123-4 (w)  (ww) 1244 ( s h ) 1 2 3 6 (w)  83±3°K  110±3°K  +2  C H Br'lTH 0  Csh)  139±3°K  83±3°K 2936  2960  1247 (w) 1240 (vw)  cm  -1  2917  +2  cm"  (vw)  2981  (vw) 1245 (w) 9 5 6 (w) 760 (sh)  1252  (vw) (sh) (vw) (vw) (sh)  ±2  (vw)  2983  1254 (vw)  1255  2985 12U2 ' 955 760  (vw) (w) (sh)  150±3°K  129±3°K  cm"  1  12U5 952 763  1  ±2  cm"  1258  (sh)  1  1245 ( w w  I  232  Table V.VIII  The temperature at which the guest absorptions peak heights began t o decrease ( T ^ ) , and tbe maximum temperature at which they were observed ( T ) . 2  Guest  T  l  T  2  G-7.6TH 0  ±3°K  ±3°K  CH C1 3  100  160  CH Br  138  <  170  138  <  168  110  >  189  129  <  189  >  169  <  170  2  3  G'1TH 0 2  CH I 3  CHC1  3  C H Br 2  110  5  The guest frequencies s h i f t e d very l i t t l e , i f at a l l , upon warming f o r d e v i t r i f i c a t i o n , however the peaks d i d sharpen near 1 2 5 1 5°K. For example, i n annealing CHC1 '17H 0 (Fig.5.3(a)) the absorptions near 1200 3  cm  sharpened at 1 2 9 - 3°K.  1223 and 1203 c m  -1  2  In fact i t s p l i t i n t o two d i s t i n c t peaks at  and a shoulder at 1 2 l U cm . -1  As w e l l the guest absorp-  t i o n s near 3000 cm ^ and 750 cm "^sharpened at 129 ± 3°K. Although the two CHC1 peaks at 1223 and 1203 c m 3  -1  were observed as high as lh9 ± 3°K,  the point i s that they were unobserved a f t e r annealing.  233  B.  Condensation in'an'Isolated'Chamber  The condensation apparatus and the technique were described i n sect i o n s 1.6 and 2.UB r e s p e c t i v e l y .  S t o i c h i o m e t r i c mixtures of C l  2  "7.67^0,  S 0 - 7 . 6 7 H 0 , CH C1-7.67D 0, CH C1-7.67H 0, CH Br•7•67H 0, CC1 F'17H 0, and 2  2  3  2  3  2  3  2  3  2  CH I'17H 0 were condensed r a p i d l y i n a precooled chamber and annealed t o 3  2  I85 i 5°K f o r 2 - 5 minutes.  Spectra were subsequently recorded at 83 i 3°K  on the P.E. 112-G- spectrophotometer. The r e s u l t s of t h i s method were the same as f o r condensation and d e v i t r i f i c a t i o n i n an open chamber.  No guest absorptions were observed  i n the annealed samples, while the H 0 "host" absorptions were the same as 2  f o r s e c t i o n 5.1 but w i t h considerably more s c a t t e r i n g . samples had spectra much l i k e cm  -1  (on C s l ) between 3000 and 2200  C1 '7.67H 0 2  As w e l l these  2  ( F i g . 5.4(c)).  C.  Low Temperature M u l l s  The technique was described i n s e c t i o n 2.kA on the P.E. 421 spectrophotometer.  and spectra were recorded  The present samples were mulled from  ground s o l i d s prepared by freezing-warming cycles on s t o i c h i o m e t r i c l i q u i d At 83 + 3°K CH I'17H 0 and CC1 F-17H 0 had no guest absorptions  mixtures.  3  2  3  2  and the R"0 s k e l e t a l absorptions were l i k e those reported i n s e c t i o n 5.1 2  f o r annealed samples.  However, the s c a t t e r i n g was greater than i n methods  5.2A or 5.2B. Some guest absorptions may have been masked by the C Hg and CC1F 3  3  m u l l i n g agent absorptions, but i t seems u n l i k e l y that a l l the CH I peaks 3  would be masked by both agents.  S e v e r a l thicknesses o f samples and amounts  of m u l l i n g agent, were t r i e d , a l l w i t h the same r e s u l t s .  23h  5.3  Temperature Dependence of the C r y s t a l l i n e Clathrate Mixture Absorptions  The r e s u l t s of warming annealed samples of c l a t h r a t e mixtures from k.2°K  or TT°K t o 200°K are i n general the same as f o r cubic i c e I , .i.e..  only the H 0 i r absorptions were observed.  Thus only a few t y p i c a l c l a t h -  2  rate mixture r e s u l t s w i l l be quoted and the remaining c l a t h r a t e mixture r e s u l t s w i l l be given i n t a b u l a r form or as an average over a l l samples..  A.  Temperature Dependence of the HDO Absorptions  ( i ) Experimental The data reported here f o r v ^ H D O ) i n CH C1-7.67D 0, CHgBr • 7 • 6 7 D 0 3  and  CH I-1TD 0, for V 3  2  2  2  (HDO) i n C H B r • 7 . 6 T H 0 , and f o r v (HDO) i n 3  2  R  CH Br•7•6TD 0 were obtained from gaseous samples condensed i n an open 3  2  chamber followed by d e v i t r i f i c a t i o n (section 5 - l ) .  The observations were  made w i t h the l i q u i d . h e l i u m dewar and the P.E. h21 spectrophotometer. D e t a i l s of the sample h i s t o r i e s were t y p i c a l of those f o r i c e I (page 6 9 ) as were d e t a i l s of spectrophotometer  operating c o n d i t i o n s . The HDO peak  maxima were determined as before (page 6 9 ) and were estimated t o w i t h i n :  ±0.5  cm . -1  ( i i ) Results of Warming Clathrate Mixtures Containing HDO (a) The HDO.stretching bands.  These bands appeared t o be the same  as i n cubic i c e I ( F i g . 3 . l ) and t y p i c a l spectra w i l l not be reproduced. The temperature dependences o f ^ ( H D O ) and v (HDO) f o r CHoBr•7.67H 0 On , OD are shown i n Figs.. 5-6 and 5.7: They are t y p i c a l of the other c l a t h r a t e ?  J  iI 1  2 0 0 235  150  X.  o  A  <D  D  o iooa  i  E' • O  •  5 0 -  #  o-  3 2 6 2  A  A  Z/ (HDO) OH  A  6 •  •  A  •  e  A  A  A  •  A A |  A  70  3 2 9 0  8 0  Frequency c m - 1 F i g . 5 - 6 The temperature dependence of v (HDO) f o r CH Br-7D 0 (k.0Q% HDO) a f t e r annealing. This was t y p i c a l of a l l the annealed c l a t h r a t e mixtures of the a l k y l h a l i d e s . 3  2  200 236  I5CH  o CD  D O  IOOH  Cl  E  50  (HDO) O  o 2412  Fig.  5.7  20  D  2430  Frequency c m -1  The temperature dependence of v CHDO) f o r C H ^ B r • 7 • 6 7 H 0 (5.9W ' HDO) a f t e r annealing. This behaviour was t y p i c a l of other a l k y l halide c l a t h r a t e mixtures. 2  mixtures and are very s i m i l a r t o cubic i c e I . The d e t a i l s of the frequencytemperature dependences f o r a l l c l a t h r a t e mixtures containing HDO are given i n Table V.IX.  The samples were prepared from the same H 0 (5-9^% HDO) and 2  D 0 (h.00% HDO) specimens as were the cubic i c e I samples. 2  The peak  heights and h a l f - h e i g h t widths f o r HDO i n these c l a t h r a t e mixtures behaved h  i n ,the same way as f o r HDO i n cubic i c e I . Some Av  data are given m F i g .  5.8. Table V.IX Some parameters derived from the. p l o t s of (HDO) and. ( H D 0 ) against temperature f o r four annealed c l a t h r a t e mixtures. v  v  OH  Clathrate Guest G  CH C1 3  Mode Observed Low Temperature Limit  Low Temperature Dependence  High Temperature Dependence  CH Br 3  v (HDO) v (HD0) QH  -1 cm  -1 cm °K  -1 cm °K  Av  1+6.5+1 1+7.0±1.5  0.0375 ±0.020  0.0507 10.027  —  —  CH Br 3  v (HD0)  v (HD0)  3265.Oil.0  21+15.010.5  '1+1+.Oil.5  61.012.0  0H  0.0368 10.03  0D  0.031+3 10.02  13  V  32  —  —  0.166 io.o6o 0.11+8 10.026  0.191+ 10.09  0.109 10.013  0.074 ±o.oU6  0.162 ±0.039 0.11+8 ±0.030  0.152 10.060  0.080 10.025  75±5  75+5 90110  8715  68i5  100±20  10015 0.1+±5  9515  8515  63-75  52-57  0.183 ±0.012  V  V  1+9.8 ±2.3  3261*. 0+1  CH3I  h  Av  Av  Irregularities i n Frequency S h i f t , °K  55  V  Av  "Freeze-in" Temperature, °K  3263.9  V  QH  QD  1+2-48  1+2-65 1+5-67  1  CI - 7.67 H O  o = A z y ^ (HDO) C H OH  2 0 0  i  3  A--A^ (HDO) CH  ^  I - 17 H  2  OH  2  3  O  2  ISP-  CD -t—  ••  o iooCD  a £  ^  i=Az/ A  50-  A  • A  OD  • •  CH  A  AA  O 40  A  a  eo  9  • •  50  •<  •  3  (HDO)  Br - 7.67H  2  O  M  60  70  Half-height widths A z / c m 2  _ 1  F i g . 5.8 The h a l f - h e i g h t widths f o r V Q ^ C H D O ) and v ( H D O ) i n several c l a t h r a t e mixtures a f t e r annealing These data were almost twice as large as f o r the cubic i c e I data. IV) CO  239  Data f o r v (HDO) of CH^Br•7.67D 0 (k.0% HDO) are  Cb) HDO l i b r a t i o n s .  R  2  given as a function of temperature i n F i g . 5.9other c l a t h r a t e mixtures as w e l l .  This data i s t y p i c a l o f  The d e t a i l s of the temperature dependences  are given i n Table V.X.  B.  Temperature Dependence of the H20 and D 2 O Absorptions  ( i ) Experimental The H 0 and D 0 absorption features f o r the annealed c l a t h r a t e mixtures 2  2  were observed by the same methods as were cubic i c e I samples (page 79). Seven HgO absorptions were observed f o r each of the seven samples (v  l  + v l  o  v  l  v  .  3v , v /2v K ^ K  , v ' and v ). However f o r D 0 c l a t h r a t e mixK r( d o  tures the s t r e t c h i n g band was studied i n d e t a i l f o r CH^I • ITD^O, 0^01*7.67 DpO and CH Br'7.67Do0, and the (v ' v V band was studied only i n CH_Br-7-67 0  D^O..  A l l mixtures except C l ^ and B r ^ were studied between U.2°K and 200°K,  while C l ^ and Br,, were observed only above 77°K.  Sample h i s t o r i e s and  spectrometer conditions were t y p i c a l of the i c e experiments. ( i i ) Results of Warming C l a t h r a t e Mixtures Containing H 0 and D 0 2  2  The temperature dependences of the H 0 and D 0 absorptions i n the 2  2  annealed c l a t h r a t e mixtures were the same as f o r cubic i c e I .  Typical  spectra f o r v^ and v^. of CH^Br•7.67D. 0 are given i n F i g s . 5-10 and 2  5.11.  The d e t a i l s of these samples were averaged f o r CH^Cl, CH^Br, CH3I, CHCl^ and C H^Br mixtures and are compiled i n Table V.XI. The d e t a i l s of 2  several C1 '7.67H 0 and B r ' 8 . 6 H 0 mixtures above 83 ± 3°K are given i n 2  Table V.XII.  2  2  2  The spectra and p l o t s were t r e a t e d i n the same manner as f o r  2h0  180  i  •  150  -  Y.  o  CD -4—  1 0 0 -  CD a  o e  5 0 -  1/ ( H D O ) R  • •  o-  795  8 0 0  ^  #  A  8 2 0  810  Frequency c m F i g . 5.9  •  - 1  The temperature dependence of V C H D 0 ) f o r annealed CHgBr*7•6TD 0 (k.00% EDO) c l a t h r a t e mixture.. This data i s t y p i c a l of other a l k y l h a l i d e c l a t h r a t e mixtures. R  2  Table V.X  The parameters f o r the HDO l i b r a t i o n s of three annealed c l a t h r a t e mixtures.  CH Br-7.6TD 0 3  2  ( k.00% H D O ) v (HDO)  Low Temperature Limit  cm  1  8lU.0±2.0  CH  Br-7.67D 0 (k.00% HDO)  3  v  (HDO)  '817.8+1.0  I-17D 0 {k.00% H D O ) v (HDO)  CH  2  8l6.3±1.3  Br'7.67I> 0 (k.00% H D O ) v (HDO) + v  CH  2  853.3±2.8  Low Temperature Dependence  High Temperature Dependence  cm" °K c  m  < -0.03  -  l  _ .061|±0.031 0  < -0.03  -0.135±0.055  —  -0.l6U±0.045  < -0.09  -0.125±0.028  °K "Freeze-in" Temperature  °K  75±10  70±5  62±5  Irregularities i n Frequency s h i f t s  °K  H8-58  Vf-57  56-72  80±5  ro  H  2h2  I8O-1  z,(D 0) 2  150 -  X.  o  0) >_  D  l O O -  -t—  2 cu a  a B  E  B° B  a a  B '"  H  B  A A  A  A  •  A  *  O -  2410  2420  Frequency c m F i g . 5.10  2430  2440  - 1  The temperature dependence of v^DgO) f o r annealed CH^Br*7.cJD^O. Data from two specimens which had s i m i l a r sample h i s t o r i e s are given.  i c e I t o determine the d e t a i l s of tine samples behaviours. The l i q u i d helium and l i q u i d nitrogen c e l l frequency data d i d not always coincide w i t h i n the errors of the two experiments.  In general, the  l i q u i d helium c e l l data have been quoted i n regions of doubt.  However, the  frequency-temperature dependences were equal f o r both sets of data. For  the Sv^CHgO) region considerable error was introduced by atmos-  pheric COp absorption and the r e s u l t i n g instrument imbalance near 2300 cm , 1  2k3  \80-{  o W  1  D  2  O  )  o  CD =5  o  o o  100H  o o  o,  C D  a  0  o  o ° o O o  o  2310  • • o  I 20  1  1  30  40  1 —  60  2350  Frequency c m -1  F i g . 5 . 1 1 The temperature dependence of v (D 0 ) f o r annealed CH3Br-T.6TD20. Data from the same two experiments as i n F i g . 5 . 1 0 are shown. The best study of 3VRCH"201  w a s  m a (  i e f o r a t h i c k sample of Br2*8.6H 0. 2  The  frequency-temperature dependence was d i s t i n c t l y negative. Samples of G l 2 * 7 . 6 7 H 0 on C s l support windows gave anomalous behaviour 2  a f t e r annealing t o 1 9 0 ± 5°K. The s t r e t c h i n g band s p l i t i n t o two peaks and three shoulders, F i g . 5•^Cc1.  A sharp weak band and a v e r y , very weak  shoulder appeared on top of the general, broad V 2 absorption:' A peak at 1628 cm  -1  and a shoulder near 1 6 2 0 cm" . 1  Samples of Cl 7.67-H20 on AgCl  support windows di'd not e x h i b i t such behaviour.  2  The high frequency absorp-  Table V-.-XI- The temperature dependences-of H20.(D20 i n brackets) modes averaged over the f i v e a l k y l h a l i d e annealed c l a t h r a t e mixtures.  Low Temperature Limit  H  2°  Low Temperature Dependence  cm" '  cm /°K *  1  -1  High Temperature Dependence  Freeze-in Temperature  cm /°K _1  3  K  (D 0) 2  v  + v v  V  J  v /2v„ 0  R R  <0.06 (0.06±0.O3)  0.17±0.05 (0.lU±0'.06)  (93±15)  3208±3 (vs) (2l+l6±2)  <0.06 (0.05±0.03)  0.19±0.05 (0..12±0.0U)  8l±15 (88±10)  0.24±0.05 (0.2U±0.05)  85±20 (86±10)  0.36±0.15  80±15  312T±5 (sh) (23l6±2)  l  c.  3331±5 (sh) (2l+40±5)  K  1588±6  (m)  896±5 (6T7±3)  (sh)  831±5  (s)  (6U6±3)  <0.15 (<0.08) <0.2  82±10  -0.07±0.01 (<0.03)  -0.l8±0.05  83±15  (-0.15±0.07)  (80±10)  -0.05 ±0.01 (<-0.02)  -0.l4±0.06  85±17  (-0.15±0.07)  (90±10)  ro -pp-  Table-V,XII  0 on AgCl and C s l The frequencies at. 80°K-and the h i*h ^ temperature dependences of C l •T.67H ' and of Br -8.6H 0 on C s l . ' 2  2  Host L a t t i c e  H0 2  Guest Species  Clg  Sample Support Window Frequency  +  V  T 1  -5  V  at 80°K  from  3  R od  3v  Extrapolated  v  V  Linear Dependence  cm  V  -1  Frequency  V  l  R  +  J.  V  T  1  Dependence on  Csl 3368 3218 311+5 2220±10 l628±2  ci  2  q-z—  V  R  2  Br  2  Csl  3365 3215 3119  3338  3333 3222  3332  —  162U±5  3221  311+7 2225 1609  2226 1622  31 vr  886 8Ul  887 8^2  -0.12  -0.20  0.13  0.12  0.32 0.22 0.21+  0.26 0.16 0.18  -0.09 -0.17  2  AgCl  895 83U  -0.06  Br  AgCl  891+ 839  —  4'  ci  Csl  0.19 -1  Temperature  2  2  —  <±o.o6 -0.18 -0.15  -0.18  0.1+6  -0.12  0.19  3216 311+7 2211+ 1579 (1619) 898 831  0,.28 0 , .17 0,.21  -0.  .01+  0 , .1+0  .05  -0.10  -0.20  -0,  -0.20  -0.16  -0, .13  -p-  V71  2h6  t i o n a t t r i b u t e d ' t o . C^i + v l was a.peak near 336.5 cm*" T  Csl.  That was about 30 cm  2  ,  2  A l s o , the frequency-temperature  dependence of (v^ + v ^ l (JH^Ol from samples of C l g ^ ^ H ^ O on C s l was tive. dence.  2  higher than the shoulder observed i n other  samples and f o r C1 7.67H 0 on AgCl. 2  f o r C1 "7.67H 0 on  nega-  In other samples Cv-j_ + vij>l (K^Ol had a p o s i t i v e temperature depenThe'H"2 ' features from Cl •7•67H2O on C s l and AgCl windows at'83°K 0  2  were: C s l Window 3H12  Csh)  3368  (s)  3285  Csh) Cvs)  3218  31U5 2220 .  1883 1628  c.a.  1600  "  89^ 839  The sharp peak at 1 6 2 8 cm temperature dependence.  AgCl Window cm ^  (sh) (w) (w) (sharp, weak) (broad, m.) (sh) (m)  3338  —  3221 . 31U? 2225  — —  1609  886 8U1  Csh)  cm'  Cvs)  (sh) (w) (broad, (sh) (m)  from the C s l window experiment e x h i b i t e d no  CHAPTER SIX DISCUSSION OF THE CLATHRATE MIXTURES 6.1  The Clathrate Mixture V i t r e o u s - C r y s t a l l i n e Phase Transformation  A.  General Discussion  The nature of the samples formed by r a p i d condensation of c l a t h r a t e mixtures was probably much the same as f o r v i t r e o u s i c e I . Thus much of the discussion on annealing i c e I applies here a l s o , jL_.e_. the onset o f c r y s t a l l i z a t i o n , the e f f e c t s on the i r spectra and the processes involved i n reorientation.  As before the H 0 l a t t i c e modes s h i f t e d t o higher frequency 2  and the molecular modes s h i f t e d t o lower frequency. and had b e t t e r defined features a f t e r annealing.  The H 0 bands sharpened 2  The transformation temper-  ature range began at 115 - 5°K (uncorrected f o r source beam heating) and took about 18 minutes at 125°K.  However, the range f o r the c l a t h r a t e mix-  tures seemed t o be extended t o higher temperatures by about 10°K. The v i t r e o u s samples s h i f t e d i r r e v e r s i b l y below 150°K and r e v e r s i b l y once warmed above 150°K.  I t was not c l e a r that annealing v i t r e o u s c l a t h r a t e mixtures o  o  produced the desired cubic 12 A or 17 A u n i t c e l l s t r u c t u r e s .  We suspect  that not a c l a t h r a t e s t r u c t u r e , but cubic i c e I was probably formed.  The  longer t r a n s i t i o n temperature range suggested the v i t r e o u s c l a t h r a t e mixtures were more stable than the v i t r e o u s H 0 or D 0 i c e samples. 2  2  While the mechanism f o r H 0 or D 0 frequency s h i f t was the same as 2  2  i n i c e I (the formation of a f u l l y hydrogen bonded network of each oxygen to four nearest-neighbour oxygen atoms at about the same distance as i n i c e I ) there should be a fundamental d i f f e r e n c e f o r the i r spectra of clathrate-hydrates.  X-ray crystallography had shown that the a l k y l h a l i d e  2kQ  and halogen c l a t h r a t e s had varying cage s i z e s and varying (Table 0 . 2 ) .  Peak p o s i t i o n s of annealed c l a t h r a t e samples should have  v a r i e d r e g u l a r l y as a function of u n i t c e l l s i z e . d i d not support t h i s concept, but r e s u l t s on H 0 2  large e r r o r s .  HDO  Samples of  190 or  200°K  for  The annealing r e s u l t s and D 2 O were subject t o  r e s u l t s were b e t t e r and are discussed i n section  B.  •  distances  0*-'-0  Annealing Cl -7.6TH 0 on C s l 2  C1 *7.67H 0 2  10  6.3A.  2  2  which were deposited on C s l and annealed to  to 15 minutes gave unique  H0 2  spectra ( F i g s . 5-^(c)  and 5.5), while the same samples annealed t o only 180 ± 3°K gave t y p i c a l H0 2  spectra ( F i g . 5-5) • As w e l l , the spectra from samples of  annealed on AgCl windows to 190 or as were the spectra of  CH3CI,  200°K  CH^Br,  C1 *7-67H20 2  f o r long times were t y p i c a l of i c e ,  CHCI3  and  C2H^Br  c l a t h r a t e mixtures  annealed on C s l at 195°K f o r more than 1 0 minutes. Cl2'7.67H 0  The  2  on C s l samples had f i v e s t r e t c h i n g band features  (three shoulders at 3^12, 3285 and 31^5 cm""" and two peaks at 3368 and 1  3218 cm ^) compared to three features i n i c e I and other annealed c l a t h r a t e mixtures  (two shoulders at 3338 and 31^7 cm  Cl2"7.67H 0 on AgCl). 2  and a peak at 3221 cm  1  As w e l l there appeared a weak, sharp peak and  adjacent shoulder (1628 and l607 cm" ) 1  absorption.  1  for an  on top of the broad v^H^O)  The weak peak and shoulder frequencies were independent of  temperature.  Other absorption features which arose were a peak at 1883  a d i s t i n c t shoulder at 1 1 0 0 cm  •  -1  and 3000 cm  The l a s t e f f e c t may  -1  ( F i g . 5-^Cc)).  cm  and pronounced absorption between 2300 cm  -1  have been due to increased  s c a t t e r i n g losses i f the substrate surface became p i t t e d by the sample, while  2h9  the shoulder at 11Q0. cm~ may- have heen due t o a C h r i s t i a n s e n f i l t e r e f f e c t . Me eke et a l . (103) observed four w e l l defined bands i n t h e i r " i c e 1^" spectra on NaCl windows (Table V I . I ) .  However, S c h i f f e r (.104) studied a  number of dihydrated sodium halides and showed that Mecke's " i c e " was NaCl-2H 0.  The data of Table V I . I suggest that the C 1  2  2  condensed  '7.67H 0 2  and annealed on C s l may have formed a hydrated cesium h a l i d e l a y e r on the substrate, i_.e_. CsI'xH 0, CsCl-xH 0 or C s I C l ' x H 0 . 2  2  2  2  The presence of hydrated cesium h a l i d e substrate was supported by the appearance of the sharp, weak peak at 1 6 2 8 cm" and a shoulder at 1 6 0 7 cm  1  i n the spectra of C1 '7.6"7H 0 on C s l . These were s i m i l a r t o peaks 2  2  observed by Mecke et_ a l . (103) and S c h i f f e r (.104) , Table V I . I . That substrate hydration d i d not occur f o r for  CH^Br, CH-^I,  CH3CI,  prising.  For AgCl and  CHCI3  C1 "7.67H 0 2  2  on AgCl nor  and C H^Br c l a t h r a t e mixtures i s not sur2  C1 '7.67H 0 2  2  i t i s probable that the C l does not 2  oxidize AgCl, whereas i t may o x i d i z e C s l . As w e l l , AgCl i s chemically more r e s i s t a n t t o hydration. I t i s possible that C l reacted with C s l t o form CsCl and IC1 or 2  else C s I C l . 2  halide s a l t s .  Intermediate steps may have allowed the formation of hydrated Although hydrates of C s C l , C s l and C s I C l  2  are not stable at  20°C, they may be stable at 200°K and lower. •  0  We have already estimated that our samples were about l y (10,000 A) thick.  From the r e l a t i v e i n t e n s i t i e s of the i c e I and hydrated s a l t  absorptions one might expect 10% or more of the H 0 i n the o r i g i n a l sample 2  to be attached as water of hydration. Thus the formation of several hundred monolayers of C s I C l  2  i s u n l i k e l y since I C 1 i s too long t o f i t 2  250  Table V I . I  The i r absorptions due t o RgO stretches i n dihydrated s a l t s , "Mecke's i c e " , and annealed C l " 7 . 6 7 K 0 on C s l ( a l l at 83 i 3°K. 0  C1 *7.67H 0  Ice on  on C s l  NaCl  2  2  cm  -1  31*12  (sh)  3368  (ms)  3285  (sh)  cm 3555  (vw) 1607 (sh)  161+5  (s) (vs) 31+05 (vs) 3310 (ww) 3 2 6 5 (mw) 321+2 (mw)  (m)  (m) '  I6l6  (m)  Ref. 103  2  Cc)  (vs)  3538  3539  (s)  3568  (sh)  35^9  3U68  31+69  (vs)  3506  (s)  3I+06  (vs)  31+61  (s)  31+96 (s)  3360  (sh)  31+37  (sh)  31+21  (vs)  161+3 1615  (s) (s)  (b) Ref. 101+  into an.interior I l a t t i c e site: -  site.  CaSOi,-2H 0  2  ,  •  321+5 (w)  1628  Cb)  -1  3^07 (s)  (s) 311+5 (sh)  (a)  2  (b)  3^71 (s)  3218  NaI-2H 0 Cb)  NaBr•2H2O  NaCl•2R 0  ( a )  2  1635 16H+  (s) (s)  (c) Ref.  1626  (sh)  I6l3  (s)  31+01+  (vs)  321+2 (m)  127  I t may however occupy an I  -  surface l a t t i c e  As w e l l i t seems u n l i k e l y that a s o l i d - s o l i d r e a c t i o n would l e a d t o  deep p e n e t r a t i o n o f C l o r C l ~ i n t o C s l since Harrison et a l . ( 1 2 8 ) found 2  some a l k a l i Cl  2  h a l i d e s i n g l e c r y s t a l s were'very r e s i s t i v e t o exchange w i t h  even at room temperature. The o r i g i n o f the new absorption at 1 8 8 3 cm  1  i s not known.  It lies  w e l l above the c a l c u l a t e d v^HgO) p o s i t i o n o f Hornig ejfc_ al_. ( 1 0 5 ) , 1 7 8 0 cm . -1  I t may be due t o C v + v ) f o r the hydrated s a l t v ( H 0 ) and the H 0 l a t t i c e 2  T  2  2  2  251  C.  Oligomeric K Q Absorptions 2  A l l the'"unannealed c l a t h r a t e mixtures e x h i b i t e d very weak peaks or shoulders i n the region  were found f o r H 0 and D 0 i c e I 2  cm" , Table V I . I I . 1  3500-3700  2  v  and the c l a t h r a t e mixture peaks were a l s o  assigned t o oligomeric H 0 and D 0 u n i t s . 2  S i m i l a r absorptions  2  As was shown f o r CH^Br•7•67H 0 2  (Table V . I I l ) i n three d i f f e r e n t specimens the p o s i t i o n s , i n t e n s i t y and number of oligomeric features were dependent on the r a t e o f sample deposition.  The  3690  cm  1  peak was obtained from a CH^Br•7•67H 0 sample deposited 2  i n 11 minutes, while the in  1.5  3620  cm  1  peak was obtained from a sample deposited  minutes and the peaks at 3 6 h 5 and 3 6 0 5 c m  samples deposited i n 4.5 minutes.  -1  were obtained from  Fast d e p o s i t i o n produced more l o c a l i z e d  heating and H 0 polymerization than slow d e p o s i t i o n . Van T h i e l et_ al_. (117) 2  suggested monomeric, dimeric and t r i m e r i c (3691  and  35^+6),  and  (3510  and  3355)  cm  H 0 2  absorbed at  respectively.  1  (.3725  and  3625),  On that b a s i s we  appear t o have formed r e s i d u a l dimeric H 0 i n the unannealed c l a t h r a t e 2  mixtures. The presence o f oligomeric H 0 and D 0 suggests a low m o b i l i t y o f 2  molecules during condensation. does not n e c e s s a r i l y f o l l o w .  2  However, low m o b i l i t y of guest  molecules  F i n a l l y , i t may be p o s s i b l e t o f o l l o w the  rate of c r y s t a l l i z a t i o n i n i c e I and c l a t h r a t e mixtures by f o l l o w i n g the peak heights of oligomeric H 0 . 2  D.  Unannealed Sample Guest Absorptions  Guest absorptions i n unannealed c l a t h r a t e mixtures due t o a l k y l h a l i d e s were observed f o r a l l specimens.  During annealing the general experience was  Table V I . I I  M  The weak peaks and shoulders a t t r i b u t e d t o oligomeric some c l a t h r a t e mixtures and i n some i n e r t m a t r i c i e s .  CH3CI  CH Br  1  1  Moles M Moles R  7.67  cm  CH3I  3  7.67  C H Br 2  5  1  1  1  17  17  17  3687  3689  3668  365h  361+8  361+5 3620  X  3639  R is  1  1  7.67  7.67  17  261+1+  26U7  D 0 2  2626  (a) Ref.  2  1  7.67  8.6  3690  3691  Ar(a)  Kr(a)  300  380  21+0  1000  1  1  1  1  N (a) 2  CCll^a)  3708  3700  3699  3687  3686  363k  3631+ 3617 3612  3580  1  26U8  1  Br  361+3  3625  3683  Moles R  2  3670  3605  Moles M  Cl  3725  R is 2  3  2  -1 3690*  H 0  CHC1  and D 0 vj_ and V3 s t r e t c h i n g modes i n  3565  3574  3570  210  210  21+0  1000  1  1  1  1  2637  2635  2655  261+3  2635  2632  2650  2622  2625  2639  2615  2611+  2617  26ll+  2610  26ll+  115  * Very slow deposit  X  f a s t deposit  .  M  ro  253 that guest absorptions were observed with undiminished peak heights up to' 120 i 5°K, but they were unobserved above 170 1 5°K or a f t e r r e c o o l i n g the samples to 83 - 3°K.  The peak heights of bands i n d i f f e r e n t c l a t h r a t e  types decreased at d i f f e r e n t r a t e s , w h i l e the peak heights of several  speci-  mens of one c l a t h r a t e mixture (i.e_. CH^Br • 7.67^0) decreased at about the same r a t e .  As one might expect the drop i n guest peak heights began at the  same temperature as the oligomeric H^O disappeared (near 130 + 10°K). Frequencies of guest absorptions i n the unannealed clathrate-hydrates and of pure, s o l i d guest molecules ( a l l at 83 ± 3°K) are l i s t e d i n Table VI.III.  For unannealed c l a t h r a t e mixtures of CH C1, CHCl^ and C ^ B r a l l 3  strong and medium i n t e n s i t y absorptions of the pure s o l i d were observed. In c o n t r a s t , f o r CH^Br and CH^I unannealed c l a t h r a t e mixtures, only some of the pure s o l i d absorptions were observed.  Strong unannealed c l a t h r a t e guest  absorptions expected near 3050, 1420, 895 or 964, and 596 cm served.  1  were unob-  Also i n the CH^Br *7.67^0 sample, peaks were observed i n the  c l a t h r a t e (1218, 1200, and 750 cm ) which were unobserved i n the pure 1  solid.  The c l a t h r a t e guest peaks were s h i f t e d only s l i g h t l y from the pure  s o l i d peaks.  However, where the pure s o l i d had m u l t i p l e t s of peaks the  c l a t h r a t e peaks were s i n g l e t s . We can o f f e r no explanation f o r the missing CH I and CH Br peaks nor 3  f o r the extra CH^Br peaks.  J  The l o s s of guest band s p l i t t i n g between the pure  s o l i d and c l a t h r a t e was not unexpected, the s p l i t t i n g of degeneracies i n pure c r y s t a l s being l o s t due to the range of absorption frequencies a r i s i n g from the inhomogeneity among the guest s i t e s i n the v i t r e o u s mixtures. There are at l e a s t three explanations of the l o s s of the c l a t h r a t e guest absorptions i n the annealed samples.  F i r s t , there was too much guest i n  Table V I . I l l  CH3CI  Unann. Clath. cm 2957  _  m  A l k y l h a l i d e i r absorptions i n the pure s o l i d state and i n some unannealed c l a t h r a t e mixtures at 8 3 ± 3°K.  .  CH Br  solid(a)  2950  CH3I  3  w  Unann. Clath.  Solid(a)  3020 sh 2 9 6 5 sh  295H  3036  2846 2830 Ikkk  m 1437 sh  lkk3  lkk3 lkkl 1U36  sh s sh m  m s m m  Unann. Clath.  2936 2915  WW WW  Solid(b)  3035 m 2935 s  2803  1436 1426 1420 1401  1432 vs 1 U 1 7 vs  1396  13^7 1338  W vw  13^5 1336  m m  1293 1292 1218 1200  1021  vw  1020  m  vvw WW sh  1291  sh vs  1244 sh 123k w  1 2 kl 1236  Solid(c)  C H Br Unann. Clath. Solid(a)  3012  2985  CHCI3  Unann. Clath.  3016  sh  955  vw vs  589  sh  585  vs m  895 888  5  vw  m m ms s ms s vs vs vs vs  2984  w  2921  m  2859  v  WW 1214 vw 1238  1235 1220  752  m  vw 1242 vw 1254  767  748  955  w  lkk8 lkk6  sh m  lkkO  m  1433 sh 1376 m 1371 m 1255 m 1242 s 1232 m 960 961  700  s  700 697 692  vs sh s  750  s  (a) This work  (b) Ref. 129  (c) Ref. 130  s sh  663 785  570  m  2963  1459 w  1218 962  2  760  sh  762 735  w s v  ro -p-  255  the unannealed.mixture formed, on the window.:'.. The excess guest d i f f u s e d . o u t . and sublimed o f f the'-window; during annealing, w h i l e .the remainder. was, too small t o detect.  Secondly, a l l of the guest molecules may have d i f f u s e d out  .of the H 2 O l a t t i c e and sublimed o f f the window.  T h i r d l y , the guest molecules  may have been present but i r i n a c t i v e due to some cage e f f e c t .  The t h i r d  p o s s i b i l i t y i s u n l i k e l y since cage p e r t u r b a t i o n s are more l i k e l y t o induce anharmonicities, peak s h i f t s or even enhance the i n t e n s i t i e s .  The  first  explanation also seems u n l i k e l y since H 2 O condenses at a much higher temperature than most of the guests, i f anything the samples may have been d e f i c i e n t i n guest.  The expulsion of a l l guest molecules from the H 0 2  seems most probable.  lattice  ,  Further work, to be described l a t e r , was done t o check which of the above reasons was most probable.  One f u r t h e r l o g i c a l method t o use (which we  d i d not) i s observing clathrate-hydrates i n Raman spectroscopy.  There the  H2O bands are sharp, w h i l e most a l k y l h a l i d e bands are i r and Raman a c t i v e and thus the bulk samples may be prepared and observed, i n contrast to the t h i n f i l m s o f our i r technique.  6.2  Guest Species Absorptions  I t was suggested i n s e c t i o n 6.1 that sample condensation and annealing i n an open c e l l chamber leads t o expulsion of the f o r e i g n guest molecules from the H 0 or D 0 l a t t i c e i n the absence of the e q u i l i b r i u m d i s s o c i a t i o n p r e s 2  2  sure of the c l a t h r a t e .  Two f u r t h e r experiments t e s t e d the p o s s i b i l i t i e s of  sample f r a c t i o n a t i o n between the sample deposition tube and the substrate s u r f a c e , and simple sample d i s s o c i a t i o n .  256  A.  I s o l a t e d Chamber Condensation  Gaseous c l a t h r a t e mixtures condensed i n an i s o l a t e d chamber ( F i g . 1.2) and unannealed e x h i b i t e d guest absorptions with approximately the same i n t e n s i t i e s r e l a t i v e t o H 2 O bands as open chamber samples.  Therefore  we concluded that the open chamber samples d i d not f r a c t i o n a t e during deposition.  The design of the closed chamber c e l l ensured that a l l o f the  gaseous sample condensed on one window while f o r open chamber condensation the heated deposition tube ensured that no H 2 O or guest molecules condensed on the deposition tube t i p . Clathrate mixtures condensed i n a closed chamber, but annealed t o I85 i 5°K and recooled t o 83°K, e x h i b i t e d no guest absorptions: The same behaviour exhibited by open chamber samples.  That was contrary t o Shurvell's  ( 5 7 ) r e s u l t s and probably arose from the differences i n maximum annealing temperature:  He annealed only t o 1 ^ 5 ± 5°K. The annealing process was not  followed i n d e t a i l ( s p e c t r o s c o p i c a l l y ) f o r closed chamber samples, but the annealed sample spectra f o r 83°K appeared the same as those i n s e c t i o n and i n i c e I .  :  6.1  -  The same spectroscopic r e s u l t s were obtained f o r unannealed or annealed samples whether they were observed i n open or closed sample chambers.  The guest molecules must have been expelled from the H 2 O or D 2 O  l a t t i c e i n the closed chamber, due t o the absence of a p o s i t i v e c l a t h r a t e s t a b i l i z i n g pressure of guest vapour at 1 8 5 ± 5°K.  257  B.  Low Temperature Mulls  The obvious a l t e r n a t i v e was to form clathrate-hydrate samples i n bulk and observe t h e i r spectra by- low temperature m u l l i n g .  I t was  diffi-  c u l t t o g r i n d the samples at 77°K t o a v e r y f i n e powder and considerable s c a t t e r i n g was observed from the large p a r t i c l e s i z e . . Whalley C 9 5 ) obtained much b e t t e r spectra (of i c e ) apparently w i t h f i n e r powders.  The i n d i c e s of  r e f r a c t i o n of the m u l l i n g agents and i c e agreed f a i r l y w e l l i n the v i s i b l e r e g i o n , but the i n d i c e s  change very r a p i d l y over absorption bands and t h i s  seems t o induce considerable s c a t t e r i n g between to 3000  t o 2000'cm " " and -  1700  1  2300  .  cm . -1  I t was of course unnecessary t o anneal mulled samples since the c r y s t a l l i n e samples were i n i t i a l l y cooled from 273°K t o 83°K at of N ( g ) . 2  atmosphere  However, no guest absorptions were observed f o r e i t h e r the m u l l  of C H I - 1 7 H 0 or 3  1  CC1 F-17H 0.  2  3  2  Most of the CH I or 3  CCI3F  guest absorptions  should have been observed i n e i t h e r the C H8 or CC1F m u l l i n g agent. 3  Two explanations are p o s s i b l e .  3  F i r s t , during t r a n s f e r a l o f sample  from the preparation tube t o the mortar and p e s t l e the sample was warmed t o 2T3°K momentarily and i t may have d i s s o c i a t e d .  However, the CH I and C C 1 F 3  3  c l a t h r a t e s were chosen s p e c i f i c a l l y f o r t h e i r guests l i q u i d states and low vapour pressures at 273°K and t h e i r c l a t h r a t e s low d i s s o c i a t i o n pressures. Secondly, the CH I and 3  CCI3F  molecules may have been very soluble i n l i q u i d  C H8 and l i q u i d CCIF^ even at low temperature. 3  However, the c l a t h r a t e  samples were not observed t o d i s s o l v e i n the'mulling agents.  I f the guests  d i d d i s s o l v e i n the m u l l i n g agent then they should s t i l l have been observed i n the spectra as a s o l i d s o l u t i o n .  258  We could not e s t a b l i s h with, confidence that the c l a t h r a t e samples had not decomposed during preparation of the m u l l .  The samples may have  d i s s o c i a t e d e i t h e r during trans-fer t o the p e s t l e or during evacuation o f the cryostat (.with the sample temperature between 100. and 150°K) .  No  attempts were made t o analyze the small q u a n t i t i e s of vapour evolved a f t e r warm-up of the c e l l t o room temperature. The H2O s k e l e t a l absorptions observed i n mulls were much l i k e previous cases:  S c a t t e r i n g d i s t o r t e d the bands considerably.  occur, however, the v  One d i f f e r e n c e d i d  absorption was w e l l defined at 1 5 7 0 cm"" at 83°K. -  2  In most spectra the region from  1600  to  3000  cm  1  1  was j u s t one broad band  which s t e a d i l y increased i n i n t e n s i t y .  C.  Summary  Infrared observations by Hexter and Goldfarb ( 5 3 ) on H C 1 , H S, C 0 2  and S 0  2  2  c l a t h r a t e d i n hydroquinone demonstrated that f o r weakly absorbing  guests the guest absorption was unobserved i n the c l a t h r a t e , but strong absorbers l i k e C 0 and S 0 were e a s i l y observed. 2  2  They pointed out that i n  the amount of HCl-quinone c l a t h r a t e used f o r the i r observations, only about 5% of the H C 1 needed f o r a reasonable HCl(g) spectrum was present.  Davies  and C h i l d ( 5 5 ) also observed i r absorption by guests i n quinone c l a t h r a t e s . They suggested that the s h i f t s i n guest frequencies were no l a r g e r than f o r solutions of guests i n CCl^.  Their conclusion was that the cage had p e r t u r -  bing influences no l a r g e r than a non-polar  solvent.  We deduce that i n our  annealed clathrate-hydrate mixtures the guests a l l could not have been present and i r i n a c t i v e .  259  We concluded that f o r unannealed c l a t h r a t e mixtures, since there was no f i n e structure associated w i t h the guest absorptions, guest r o t a t i o n and t r a n s l a t i o n was hindered.  I f the binding i n the unannealed samples was not  p h y s i c a l , but chemical, then we expected new guest f u n c t i o n a l group frequencies.  The evidence i n d i c a t e s our methods were i n s u f f i c i e n t to form c l a t h r a t e -  hydrates .  6.3  The Temperature Dependences of C r y s t a l l i n e Clathrate Mixture Absorptions  A.  HDO i n Clathrate Mixtures  Discussion of the r e s u l t s from annealed clathrate-hydrate mixtures collapses to a d i s c u s s i o n of cubic i c e I : We assume the guest was a l l d i s persed and a cubic i c e I l a t t i c e formed at 1 8 5 ± 5°K.  The c l a t h r a t e studies  became independent checks of the r e p r o d u c i b i l i t y of cubic i c e I experiments. Consider the v^(HDO) frequencies from CH^Cl, CH^Br and C ^ I mixtures with D 0 2  (h.00% HDO).  Except f o r one set of CH Br r e s u l t s , the c l a t h r a t e 3  mixture low temperature l i m i t s , low temperature dependences, high temperature, dependences, " f r e e z e - i n " temperatures and i r r e g u l a r i t i e s i n frequencytemperature s h i f t s agreed, w i t h i n e r r o r , w i t h HDO cubic i c e I data. Clathrate mixture  M^CHDO)  frequency l i m i t , temperature dependences,  "freeze-  i n " temperatures, etc. , agreed, w i t h i n e r r o r , w i t h v^(HDO) of cubic i c e I . Half-height width data from clathrate-mixtures d i d not agree with cubic i c e I HDO data.  J. Both Av~, 2  r  Oil  L and Av„Z  25 percent l a r g e r than i n cubic i c e I .  OD  from c l a t h r a t e s were at l e a s t  Contrary t o cubic i c e I , Av . nT  was  260  30. percent l a r g e r than AvJ^.. UH  One can understand the increased A v A Oh.  oyer  cubic i c e I on the basis of further'H^O exchange i n t o the'D^OCH/pO) mixture as the sample aged, i n s p i t e of precautions. Av p Q  One cannot r a t i o n a l i z e increased  i n that way. Notice that i f a true c l a t h r a t e had been formed from the CH^Br mix-  t u r e , f o r example, then the v  (HDOl frequency would have been expected at  a much higher frequency than observed.  Since CH^Br forms a cubic type I o  c l a t h r a t e ( C H ^ B r • 7 . 6 7 H 0 i d e a l stoichiometry) w i t h a 1 2 . 0 9 A c e l l 2  o  parameter  (Table 0.2) then the average 0 0 distance must be 2 . 8 0 9 A at 273°K. For ° -1 R(0 0) = 2 . 7 5 5 A i n cubic i c e I we found v (HDO) = 3 2 9 0 cm ( F i g . 5-12) UrL  _n  O  O  and Av/AR = 1 9 2 1 cm /A. Since the 0 0 distances d i f f e r e d by 0.05^ A we expected a Av of 1 0 U cm . Thus CH3Br'7.67D20(H 0) c l a t h r a t e should have -1  2  had v^ (HD0) absorbing near OH TT  339^  cm ( 2 7 3 ° K ) . 1  Assuming the same frequency-  temperature dependence as i n i c e then at 83°K v at  339^  cm  -1  - 190°K ( 0 . 2 0 0 cm /°K) = _1  3356  (HDO)  cm" .  should have absorbed  The absence of such  1  absorption also supported the conclusion that c l a t h r a t e s d i d not form.  The  same p r i n c i p l e s could be a p p l i e d to CH I-17D 0(HD0) and CH Br•7.67H2O(HDO) 3  2  3  mixtures. The d i s t r i b u t i o n of 0*---0 distances i s much greater i n c l a t h r a t e s than i n i c e I due to four unique d i s t a n c e s , each of which must have an ice-like distribution.  One would expect considerably broader HDO bands i n  clathrates. L i b r a t i o n s of HDO  i n c l a t h r a t e mixtures and cubic i c e I a l s o agreed  w i t h i n e r r o r with respect to high temperature frequency dependence, "freezei n " temperature and frequency s h i f t i r r e g u l a r i t i e s . l i m i t s d i d not agree w i t h i n our stated e r r o r s .  The low temperature  The disagreement was not  26l  s u f f i c i e n t t o suggest c l a t h r a t e had formed, i_.e_. increased c l a t h r a t e s suggested a s h i f t o f ' ( 1 5  -  20)  cm  1  R(0**"'0)  in  from cubic i c e I .  The i r r e g u l a r i t i e s observed i n frequency s h i f t s with i n c r e a s i n g temperature were discontinuous s h i f t s by 2 - 3 cm , generally t o higher f r e 1  quency i n the case of stretches and t o lower frequency i n the case o f librations.  Another break i n the curves appeared near 80°K.  These breaks  may have been r e l a t e d t o p a r t i a l ordering, as was suggested before.  B.  H2O and D 0 i n Clathrate Mixtures 2  Discussion of H 0 and D 0 absorptions i n annealed clathrate-hydrate 2  2  mixtures also reduces t o a discussion of cubic i c e I . The behaviour of H 0 and D 0 c l a t h r a t e mixture absorption frequencies, h a l f - h e i g h t widths 2  2  and temperature dependences were the same as i n cubic i c e I . I f true c l a t h r a t e hydrates had formed.on annealing then low temperature l i m i t s and h a l f - h e i g h t widths should have been s i g n i f i c a n t l y from i c e :  They were not.  different  The low temperature l i m i t s of each i n d i v i d u a l  H 0 or D 0 absorption agreed w i t h i n e r r o r , Table V.XI, f o r the set of 2  2  c l a t h r a t e mixture data.  The average f o r each band, over a l l c l a t h r a t e  mixtures, agreed with the observed H 0 and D 0 i c e I data. 2  ceptions were f o r  + v  T  2  ( D 0 ) , v p ' ( D 0 ) and v ( D 0 ) . 2  2  R  2  The only ex-  Those three sets  of data were obtained from broad shoulders or i l l - d e f i n e d peaks, both of which were hard t o define c o n s i s t e n t l y .  High temperature frequency.depen-  dences f o r each clathrate-mixture band agreed w i t h i n e r r o r , Table V.XI, over  262  the set o f c l a t h r a t e mixtures.  The " f r e e z e - i n " temperature data were a l s o  compatible. There were two s p e c i a l p o i n t s t o consider, the negative temperature dependence o f  + v^, from  o f the weak 1 6 2 8 cm  1  CI^'7.67R2O  on C s l and zero temperature dependence  (CsI^R^O ?) band.  was c h a r a c t e r i s t i c of l a t t i c e modes. was u n l i k e l y , the 3 3 6 8 cm  Negative temperature dependence  Since such an intense l a t t i c e overtone  band may have been a combination o f  overtone of a low frequency l a t t i c e " mode (say  2v '). T  w i t h an  The s h i f t o f  +v  T  t o higher frequency by 30 cm was understood i n terms o f the smaller overlap 1  with  than i n i c e I .  I n s e n s i t i v i t y o f the weak, sharp 1 6 2 8 c m  -1  absorption  t o temperature i s c h a r a c t e r i s t i c o f non-hydrogen-bonded-lattice IL^O: supports i t s assignment t o  That  of,say, C s T ^ ^ O .  Results o f s e c t i o n 5.3 on H2O and D2O i n annealed c l a t h r a t e mixtures d i f f e r e d from those o f McCourt ( 5 6 ) and S h u r v e l l ( 5 7 ) . t h e i r a d d i t i o n a l 3 V R absorption near 2 ^ 0 0 cm \  However, we experienced  problems from instrument imbalance through atmospheric 2360  cm  As w e l l , attempts t o d u p l i c a t e t h e i r  We f a i l e d t o detect  C0  2  between  ( 5 6 , 5 7 ) SO2  2280  and'  results failed.  McCourt's samples do not appear t o have been annealed, as suggested by the shape and p o s i t i o n s o f the H2O absorptions. I n s p e c t i o n o f McCourt's ( 5 6 ) and S h u r v e l l ' s ( 5 7 ) o r i g i n a l background spectra revealed s l i g h t , 0 . 0 2 abs. u n i t s , negative  CO2  absorptions from  2280  t o 2 3 6 0 ' cm  For t h i c k samples,  r e q u i r i n g extensive reference beam a t t e n u a t i o n and very small instrument source s i g n a l s , the negative CO2 absorption would be p r o p o r t i o n a l y greater and could give the appearance o f 2 ( 3 V R ) bands i n s t e a d o f one.  The p o s i t i o n  o f the minimum between t h e i r 2 ( 3 V R ) peaks corresponds c l o s e l y t o the C O 2 (gas) maximum. There was also evidence of oligomeric H 2 O absorption i n  263 t h e i r o r i g i n a l spectra.  We concluded t h e i r samples were unannealed and  vitreous and that no extra 3v  R  (H2O) absorption appeared.  F i n a l l y , the  nearly i d e n t i c a l spectra of the various i c e s suggests that s i m i l a r spectra should be expected f o r the c l a t h r a t e s .  CHAPTER SEVEN SUMMARY  7.1  Suggestions  f o r Further Work  Extensions and new a p p l i c a t i o n s of t h i s work are proposed under three headings:  f u r t h e r work i n the  H2O-HDO-D2O  i c e systems, a p p l i c a t i o n s  of i s o t o p i c s u b s t i t u t i o n t o other chemical systems, and f u r t h e r work on clathrate-hydrates.  A.  Clathrate Mixtures  We recommend observation of bulk clathrate-hydrate samples i n glass preparation tubes by l a s e r Raman spectroscopy.  S h i f t s o f peak frequency,  h a l f - h e i g h t width and i n t e n s i t y as a f u n c t i o n of temperature should be e a s i l y followed.  I t i s important t o choose guest species which are strong  Raman s c a t t e r e r s and whose frequencies are widely separated from the H 2 O frequencies.  In that case the guest frequencies would be perturbed the  l e a s t by coupling t o the H 0 l a t t i c e . 2  As an extension of the e f f e c t of the l a t t i c e , one could study clathrates whose guests frequencies are close t o H 0 frequencies and would 2  be expected t o couple (to ^ ( ^ 0 )  say, which i s weak i n the Raman e f f e c t ) .  One could also study the perturbing e f f e c t of the l a t t i c e on the guest by observing the D 2 O c l a t h r a t e analogues.  265  F i n a l l y , c a r e f u l technique should permit one t o grow c l a t h r a t e hydrate s i n g l e c r y s t a l s i n glass tubes, simultaneously allowing one t o confirm the c l a t h r a t e s t r u c t u r e by x-ray crystallography and t o observe p o l a r i z e d Raman spectra. We also recommend f u r t h e r attempts t o observe low temperature mulls of clathrate-hydrates whose structures are confirmed by x-ray powder diffraction.  Use of clathrate-hydrates which are more stable under am-  bient conditions (i_.e_. tetrahydrofuran hydrate) should f a c i l i t a t e mull preparation, but may make the spectroscopy more complicated.  B.  Ice Systems  Some extentions of t h i s work which should be completed are l i s t e d below. 1.  Use d i l u t e HDO frequencies t o f o l l o w the annealing or vitreous-cubic i c e I transformation i n d e t a i l .  2.  Determine the rates of transformation at various  constant  temperatures by f o l l o w i n g the s h i f t s i n HDO frequencies as a function of time. 3.  Study v  2  and A v  2  i n d e t a i l f o r l i q u i d helium and l i q u i d  nitrogen experiments t o resolve the  v  h.  Check cubic i c e I cooling and warming curves f o r h y s t e r e s i s under slow and f a s t cooling  5.  - 2 p dilemma. v  2  ( 0 . 5 - 2 0 hours).  Investigate hydration o f sample windows by Cl ,and H 0 . 2  Some other projects r e l a t e d t o t h i s work are included below.  2  266  1.  C a r e f u l l y check the properties of cubic i c e I i n the temperature range ko  -  70°K  by Raman s c a t t e r i n g , i n f r a r e d  absorption and n.m.r. of HDO i n D 0 considering the s h i f t 2  i n s t r e t c h i n g frequency i n that range. 2.  Investigate the behaviour o f HDO frequencies below 10°K to check the e x t r a p o l a t i o n of our data.  3.  Study HDO absorptions i n the family o f high pressure i c e s as a f u n c t i o n of temperature over t h e i r s t a b l e ranges. This w i l l permit the extension of hydrogen-bond force constants over a wider range of R(O--'-O) i n s i m i l a r e l e c t r o n i c environments.  k.  Obtain d e t a i l e d l i n e a r expansion c o e f f i c i e n t s of cubic i c e I down t o lt°K.  5.  Study the o r i g i n of  as the H 0 t r i p l e point i s approached 2  from the three phases. 6.  Use our EDO frequencies, tong and X ^ t o i n v e s t i g a t e various models of hydrogen-bonding as a f u n c t i o n of  R(0-**-0)  and  attempt t o r e l a t e Av t o changes i n the covalent and e l e c t r o s t a t i c nature of the hydrogen-bond. 7.  Study the anisotropy of hexagonal i c e I s i n g l e - c r y s t a l s by observing d i f f e r e n c e s i n HDO frequencies and Av/AR (as a function of temperature) along the a  8.  D  and c  Q  axes.  Determine the proton jump energy by observing at what temperature during warm-up a t h i n l a y e r of D 0 embedded between 2  t h i c k layers of v i t r e o u s H 0 leads t o the formation of 2  c h a r a c t e r i s t i c HDO peaks.  Deposition rates would have t o  267  be extremely slow at  h.2°K.  Heat of sublimation may be too  large t o permit i s o l a t i o n of a few mono-layers of D 0 on H 0. 2  C.  Other Chemical Systems  Several possible applications  of the d i l u t e i s o t o p i c  substitution  and temperature v a r i a t i o n technique are l i s t e d below. 1.  Study s i n g l e - c r y s t a l s of organic a c i d s , whose c r y s t a l structures  and l i n e a r expansion c o e f f i c i e n t s are known,  as a function of temperature and r e l a t e R(0*'*"0) t o better characterize  VQ^CHDO)  to  the hydrogen-bond  potential. 2.  Study carbohydrates, hydrogen-bonding polymers and long chain molecules t o determine the nature and v a r i a t i o n of 0-H*••*0 hydrogen bonding.  3.  Use d i l u t e i s o t o p i c s u b s t i t u t i o n i n b i o l o g i c a l systems generally  since the H 0 medium masks spectroscopic obser2  vations of H 0. 2  h.  2  Use d i l u t e HDO and temperature v a r i a t i o n t o study the nature of hydrogen bonding i n poly-water.  268  7.2  A.  Conclusions  Annealing Ice I  v  Our, i n f r a r e d r e s u l t f o r the transformation temperature range (120 135 i 5°K corrected f o r source beam heating) does not agree completely with the ranges of some other workers (Table 0.3).  Our range seems t o agree  best with that of Dowell and R i n f r e t (7M and perhaps that of Sugisaki et_ a l . (6).  However, these i r r e s u l t s do not support Dowell's ( 7 ^ ) conclusion  that only 30% of the v i t r e o u s i c e I was transformed t o cubic i c e I .  However,  t h e i r r e s u l t s may i n d i c a t e that only 30% of t h e i r o r i g i n a l sample was vitreous.  The i r r e v e r s i b l e transformation frequency s h i f t s (at ll+5°K)  were: Avj_ = -h2, Av^ = -36, A v = -56, A v = +31 and 2  R  AVIJ  = +12 cm . 1  The  transformation temperature range was independent of deposition r a t e , but transformation frequency  s h i f t s were not, f a s t e r depositions gave smaller  shifts. Oligomeric (probably dimeric and t r i m e r i c ) H 0 and D 0 were present 2  2  i n considerable concentration i n amorphous i c e I : Slower depositions gave higher concentrations of oligomers.  The oligomers were s t a b l e u n i t s up t o  135 I 5°K. As much as 30% of the amorphous sample may have been i n the form of oligomers.  B.  HDO Studies  The assumption that d i l u t e concentrations of HDO i n H 2 O or D 2 O gave completely uncoupled HDO v i b r a t o r s i s i n v a l i d . i s coupled t o a parent H 0 or D 0 2  2  frequency.  At l e a s t one HDO  frequency  269  The low temperature l i m i t s o f v (HDO) and v._(HDO) were 3263.5 cm  1  OTI  On  and  cm  2412.0  respectively.  1  OD  The low temperature dependences o f v  and On  v  were both 0.0^7 cm /°K between 10°K and 80°K.  The high temperature  _1  Q D  dependences o f v.„ and v ^ were 0.200 and 0.123 cm~""/K between 80°K and 1  Un  OT OD  0  u  200°K.  Insofar as u in  and X ^ were a measure, the p o t e n t i a l of HDO molecules  l a t t i c e s changed i t s shape i r r e g u l a r l y with temperature, i_.e_. the  H2O/D2O  changes i n to  were not l i n e a r as temperature increased.  On  Hot bands and d i f f e r e n c e bands d i d not contribute s i g n i f i c a n t l y t o the breadth of v or D 2 O .  and v^(HDO) and, by extension, not t o stretches i n H 2 O  Half-height width data supported the o r i e n t a t i o n a l l y disordered  proton theory of Whalley ( 8 8 ) . The temperature dependences o f Av  (HDO) and Av  Un  200°K were 0.135 and 0.070 cm /°K. -1  technique, v  On  (HDO) and v  OD  (HDO) from 100° -  OD  Within the l i m i t s of the i n f r a r e d  (HDO) peak frequencies were s e n s i t i v e t o changes  o i n R(0'••'0) greater than 0.0001 A.  HDO s t r e t c h i n g absorptions were not  l i n e a r functions of R(0'**"0) over the whole temperature range 10° - 200°K. 3 -1 The low temperature dependences A v / A R and A v / A R were 8.202 x lO-'cm /A 0  OH  OD  3 -1 and 6.629 x 10 cm /A from 10° - 100°K, while the high temperature depen3 -1 ^ -1 dences A v / A R and A v / A R were 1.921 x 10 cm /A and 1.283 x 10 cm /A 0  0  0  J  On  OD  from 150 - 200°K. The c a l c u l a t e d low temperature l i m i t o f R C 0 o o was 2.753 A assuming a = 6 . 3 5 0 A e x a c t l y at l43°K.  , , , ,  Q  0 ) f o r cubic i c e I  The c a l c u l a t e d changes 6  i n R(0  0 ) , with temperature were AR/AT = 8.28 x 10 -6  and 10.52 x 10  0  A/°K from 130° - 200°K.  0  A/°K from 0° - 80°K  270  Bellamy and Owen's ( 3 3 ) formula gave a good approximation t o the r e l a t i o n between  and v  R(0--*-0)  (HDO) i n the temperature range 130°K  On  to 200°K with the constant set at  cm . -1  57-77  Anharmonicity c o r r e c t i o n , X  On  , had a low temperature l i m i t of 1 0 5 . 6  cm , a low temperature ( 0 - 60°K) dependence of +0.032 cm /°K, a high -1  -1  temperature dependence of 1 0 8 . 7 c m  -1  (100°  200°K)  -  of - 0 . 0 3 8 cm" / !^, and a maximum value 1  0  at 80°K.  The HDO harmonic s t r e t c h i n g frequency had a low temperature l i m i t at 3^73.7  cm , a temperature dependence (30°K - 200°K) of + 0 . 1 3 8 cm /°K and a -1  _1  maximum displacement of h cm  had a low temperature l i m i t of  Vp''(HD0)  (assigned t o ( v  from l i n e a r i t y at 80°K.  1  , T R  823  cm  -1  and the shoulder  + Vrp)) had a low temperature l i m i t of 8 5 6 cm .  Various  -1  calculations indicated v ,. V Rx  and non-degenerate f o r HDO.  R  v  and v  were degenerate f o r H2O and D 0  R z  2  The negative temperature dependence of l a t t i c e  modes was understood i n terms of a shallower p o t e n t i a l and i n c r e a s i n g excited state populations as temperature increased.  C.  The H 0 and.D 0 Studies 2  The order of v-j_ and same:  2  i n the gas and cubic i c e I phases was the  Hydrogen bonding a f f e c t e d v-|_ and  s h i f t i n g them down p r o p o r t i o n a l l y . coupling of v-j_ t o v ^ and ice I , \) and  of the gas phase e q u a l l y ,  We conclude that the molecule-molecule  t o V 3 were s i m i l a r i n nature and that i n cubic  were d i s t i n c t t r a n s i t i o n s .  The assignments of major H 0 2  and D 0 absorptions at 0°K were v-j_ + Vrp = 3 3 3 ^ , 2  3v  R  = 2239, v = 2  1562,  v  R  + v  T  =  881,  v = R  832,  = 320U, v-j_ = 3133, and v = T  229-2  cm" f o r 1  271  H 0 2  and v  v = 2k6h, v =  +  T  3  VR + Vrp = 6 6 3 , and v = 6 3 0 cm  3v  R  =  1637,  v =  II89,  2  f o r D 0 , i n b a s i c agreement with previous  1  R  authors.  v = 2320,  2Ul3,  2  The absorption near 1 6 0 0 cm  i n R~ 0 d e f i n i t e l y had a 2 v under-  1  2  R  l y i n g absorption. Temperature dependence o f v 100°K)  3  and v-j_ i n absorptions f o r H 0 (above 2  confirmed the Raman temperature  dependence o f Val'kov  (99).  The  data of HDO a p p l i e d t o H 0 and D 0 as w e l l . 2  2  Blue's ( 8 5 ) formula l e d t o anomalous r e s u l t s when a p p l i e d t o simple H0 2  and D 0 molecules i n i c e . Assuming e f f e c t i v e masses f o r two attached 2  and two detached protons and a l s o assuming that the three l i b r a t i o n s were degenerate or near-degenerate,  then reasonable hydrogen bond bending force  constants were c a l c u l a t e d by Blue's method. we found k(0-H dynes/cm.  0 ) = 0.60 x 1 0  5  From the (Hr>0, 3/h,l/k)  dynes/cm and k ' ( 0 H  option  H-0) = 0 . 2 1 x 1 0  5  These force constants p r e d i c t e d nearly degenerate D 0 l i b r a t i o n s 2  ( 5 8 6 , 5 8 8 and 5 9 1 cm ) about 6% below the observed value. -1  The e f f e c t i v e  mass concept d i d not apply w e l l t o HDO. An H 0 2  3  model of i c e gave a set o f H 0 i n t e r n a l and l a t t i c e force 2  constants i n good agreement with those deduced by Trevino ( 9 3 ) and poorer agreement with Pimentel's r e s u l t s ( 9 7 ) .  That k ^ ( v ) ( 0 . 6 6 x 1 0 ^ dynes/cm) 0  Cj)<j>  d  was smaller than the gas phase value was consistent w i t h the lower i c e frequency.  H 0 2  3  force constants were used t o p r e d i c t D 0 frequencies: 2  I n t e r n a l mode D 0 frequencies were 2-3%  too low and l a t t i c e mode D 0  2  frequencies were h - 6% too high.  2  The v ( D 0 ) c a l c u l a t e d were about the  same as from the e f f e c t i v e mass model.  R  2  272  D.  Clathrate Mixture Annealing  Condensation of a gaseous, s t o i c h i o m e t r i c mixture o f R"0 or D 0 2  2  and guests, followed by annealing t o 185 ± 5°K, d i d not form c r y s t a l l i n e clathrate-hydrate compounds.  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