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Vibrations of ice I and some clathrate-hydrates below 200°K 1970

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THE VIBRATIONS OF ICE I AND SOME CLATHRATE-HYDRATES BELOW 200°K fey Arvid Holger Hardin B.Sc.(Hons.), The University of 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 thesis as conforming to the required, standard THE UNIVERSITY OF BRITISH COLUMBIA Ju l y , 1970 In present ing th is thesis in p a r t i a l f u l f i lmen t of the requirements for an advanced degree at the Un ivers i t y of B r i t i s h Columbia, I agree that the L ibrary sha l l make i t f r ee l y ava i l ab le for reference and Study. I further agree that permission for extensive copying of th is thesis for s cho la r l y purposes may be granted by the Head of my Department or by his representat ives . It is understood that copying or pub l i ca t i on of th is thes,is for f i nanc i a l gain sha l l not be allowed without my wr i t ten permiss ion. The Un ivers i ty of B r i t i s h Columbia Vancouver. 8, Canada Date ABSTRACT The vibrations of H2O, HDO and D 20 molecules p a r t i c i p a t i n g i n the hydrogen bonding of vitreous 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 halides and halogens encaged i n these s o l i d s , were studied by infrared spectroscopy between h.2 and 200°K over the iiOOO to l 6 0 cm-"1" frequency range. Four kinds of 0-H* , , -0 hydrogen bonding l a t t i c e s were investigated, vitreous and annealed (cubic) ice I and vitreous and annealed clathrate-hydrate mixtures. In vitreous ice I the effects on the molecular and l a t t i c e vibrations were observed i n d e t a i l for H2O between 77 and l80°K during the phase transformation to cubic ice I , and the results of the transformation for HDO and D2O were recorded. As w e l l , the effects on the molecular and : l a t t i c e vibrations of H 20, D 20, H 20 ( 5 - 9 W HDO), and D 20 (h.00% HDO) cubic ices I were studied during warming from h.2 to 200°K. Similar studies were made for the vibrations of H 20, HDO, D 20 and guest molecules, during the vi 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 resu l t i n g \ annealed mixtures. For ice I the method involved condensation of the vapour at 77°K, observation of the spectra during warming i n stages to 185 1 5°K, cooling to k.2°K, and observation of the cubic sample spectra during warming to 200°K. The results were plotted as a function of temperature and were correlated to calculated distances and RMS amplitudes of tr a n s l a t i o n . As well four models for molecular l i b r a t i o n were investigated. Three approaches were taken to the clathrate-hydrate problem. In p a r a l l e l to the ice I method gaseous stoichiometric mixtures were con- densed, observed during transformation, cooled to h.2°K and observed during warm-up. Other gaseous clathrate mixtures were condensed i n an isolat e d sample chamber, to prevent sample fra c t i o n a t i o n , and treated 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 results show that on warming the ice I phase transformation occurred between 120 ± 5 and 135 - 5°K and required, less than 18 minutes at 135 i 3°K. Weak peaks due to oligomeric H2O and D2O units disappeared during annealing, while a l l hydrogen bonded H2O molecular modes shifted to lower frequency and a l l l a t t i c e modes shifted to higher frequency. The half-height widths of the composite H2O band ( v 2 / 2 v p ) appeared to increase upon annealing and to decrease upon warming while the (V R , V R + vp) and ( v l , V 3 , v i + vrp) bands had the opposite behaviour. This was interpreted, as indicating a weak 2v^ band underlying the stronger \>£ absorption near 1 6 0 0 cm - 1. The frequency-temperature dependences of a l l cubic ice I bands were interpreted on a b i l i n e a r , high and low temperature basis (the l a t t i c e modes shifted to lower frequency and the molecular modes to higher frequency with increasing temperature). For HDO above 8 6 ° K Av / A T was 0.200 1 0.005 cm-1/°K, Av /AT was 0.123 + 0.005 cm-1/°K, the frequencies were "frozen-in" at 80 ± 5°K and 65 ± 5°K and had irregular 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 for the apparent displacement of the HDO stretching frequencies from the H2O and D2O frequencies. The HDO results also permitted the accurate determination of -1 0 -1 0 Av / A R ( O 0) as 1921 cm /A and Av / A R as 128l cm /A above 150°K and i v -1 ° -1 ° as 8202 cm /A and 6629 cm /A below 100°K. As w e l l , the HDO stretching frequencies gave an anharmonicity which increased from h.2 to 80°K and then decreased between 80 and 200°K. 1 The clathrate-hydrate mixtures transformed on warming i n the temper- ature range 125 - 5 to 1U5 + 5°K and required less than l 8 minutes at 135°K as for ice I. S i m i l a r l y , the weak oligomeric and guest absorptions disap- peared upon annealing. From the comparison of the three sets of "clathrate" results and the behaviour of annealed sample peaks we concluded that cubic ice 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 i x L i s t of Figures x i Acknowledgements x i v INTRODUCTION 1 Hydrogen Bonding 1 A. Theories of Hydrogen Bonding 2 B. Spectroscopic Manifestations of Hydrogen Bonding . . . 6 Clathrate-Hydrates 12 A. The Clathrate-Hydrate Problem 12 B. The Structures of the Clathrate-Hydrates 12 C. Formation of Clathrate-Hydrates 17 D. Previous Investigations of the Clathrate-Hydrates. . . 18 E. The Present Approach to the Clathrate-Hydrate Problem 19 Ice • 20 A. The Ice Problem 20 B. Non-Spectroscopic Investigations of Ice 20 C. Spectroscopic Investigations of Ice 27 D. The Present Approach to the Ice Problem 37 CHAPTER ONE: APPARATUS 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 Liquid Nitrogen C e l l 1+2 1.5 The Duerig-Mador Liquid Helium C e l l 1+5 1.6 The Metal Liquid Nitrogen C e l l *+5 v i PAGE CHAPTER TWO: METHODS AND MATERIALS hi 2.1 Water Samples and Clathration Materials ^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 Infrared Specimens 52 A. Low Temperature Mulling 52 B. Isolated Chamber Condensation 53 C. Open Chamber Condensation 5*+ 2.5 D e v i t r i f i c a t i o n 55 2.6 Temperature Variation Methods 56 CHAPTER THREE: ICE I: EXPERIMENTAL AND RESULTS 58 3.1 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 3.2 Temperature Dependence of Cubic Ice I Absorptions. .... 69 A. Temperature Dependence of HDO Absorptions 69 B. Temperature Dependence of H 20 and D 20 Absorptions. .. 79 3.3 The H 20, D 20 and HDO Ice I Absorptions at 83°K 95 A. Experimental 95 B. Results at 83°K 95 3. U Summary of Ice I Results 1 0 1 A. Vitreous-Cubic Ice I Transformation 1 0 1 B. . HDO i n Cubic Ice I . . 102 C. H 20 and D 20 i n Cubic Ice I 102 v i i PAGE CHAPTER FOUR: DISCUSSION OF ICE I 103 k.l The Ice I Vitreous-Cubic Phase Transformation 103 A. General Discussion 10k B. Fundamental Lattice Mode Transformations 107 C. Fundamental Molecular Mode Transformations I l l D. Combination and Overtone Mode Transformation . . . . 117 . E. Confidence i n the Cubic Ice I Samples 118 h.2 Temperature Dependence of Cubic Ice I Absorptions. . . . 120 A. Dependence of HDO Bands on Temperature 1 2 1 B. Dependence of H 2 O and D 20 Bands on Temperature . . . 159 it. 3 Assignments of the Cubic Ice I Absorption Bands 175 A. The Fundamental La t t i c e Modes 175 B. The Fundamental Molecular Modes 1 7 7 C. The Overtone and Combination Modes 186 it .U The L'ibration of HDO, H 20 and D 20 187 A. The Moments-of-Intertia Models 187 B. The H 2 0 3 Model of Ice ; 198 C. A Summary of H 2 O , HDO and D 2 O Librations 2 1 1 CHAPTER FIVE: CLATHRATE-HYDRATE EXPERIMENTAL DETAILS AND RESULTS 2lh 5.1 The Vitreous-Crystalline 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 2 l 6 5.2 ClathrateMixture Guest Absorptions, 228 A. Condensation i n an Open Chamber 229 B. Condensation i n an Isolated Chamber 233 C. Low Temperature Mulls 233 5.3 Temperature Dependence of the Cr y s t a l l i n e Clathrate Mixture Absorptions 23^ A. Temperature Dependence of the EDO Absorptions. . . . 23** B. Temperature Dependence of the H 2 O and D 2 O Absorptions 239 v i i i PAGE CHAPTER SIX: DISCUSSION OF THE CLATHRATE MIXTURES 2*+7 6:1 The Clathrate Mixture Vitreous-Crystalline Phase Transformation 2*+7 A. General Discussion 2^7 B. Annealing C 1 2 ' 7 . 6 7 H 2 0 on Csl 21*8 C. Oligomeric H 20 Absorptions 2 5 1 D. Unannealed Sample Guest Absorptions 2 5 1 6.2 Guest Species Absorptions 255 A. Isolated Chamber Condensation 256 B. Low Temperature Mulls 257 C. Summary 258 6.3 The Temperature Dependences of Cry s t a l l i n e Clathrate Mixture Absorptions 259 A. HDO i n Clathrate Mixtures 259 B. H 20 and D 20 i n Clathrate Mixtures 2 6 l CHAPTER SEVEN: SUMMARY 26k 7.1 Suggestions for Further Work 26k A. Clathrate Mixtures 2.6k B. Ice Systems 265 C. Other Chemical Systems 267 7.2 Conclusions 268 A. Annealing Ice I T 268 B. HDO Studies 268 C. The H 20 and D 20 Studies 270 D. Clathrate Mixture Annealing 272 REFERENCES . . . . . 273 LIST OF TABLES TABLE PAGE 0.1 Typical clathrate-hydrates and t h e i r properties l U 0.2 Clathrate-hydrate unit c e l l dimensions, guest sizes and f i l l e d c a vities l 6 0.3 Stable temperature ranges of vitreous, cubic and hexagonal ice I 23 O.k Some physical properties of the ices 25 0.5 H 20 vapour, l i q u i d and ice I frequencies and assignments . 29 I I I . I Cubic and vitreous ice I frequencies at 82°K 62 I I I . I I Vitreous ice I oligomeric absorptions 65 I I I . I l l H 20 composite band half-height widths 68 III.IV The behaviour of HDO stretching modes i n cubic ice I . . . 72 III.V The behaviour of HDO l i b r a t i o n a l modes i n cubic ice I. . . 7*+ III.VI HDO stretching modes half-height widths 76 III.VII HDO stretching modes peak heights 77 I I I . V I I I Ice I sample h i s t o r i e s 80 III.IX Cubic ice I H 20 and D 20 absorptions 83 III.X Cubic ice I v T(H 20) absorptions 91 III.XI (a) Fresent and previous H 20 assignments for cubic ice I . 96 (b) Present and previous frequencies for v T ( H 2 0 ) 97 I I I . X I I Present and previous HDO frequencies for cubic ice I . . . 98 I I I . XIII Present and previous D 20 assignments for cubic i c e I . . . 99 IV. I Calculated and observed RMS amplitudes of tran s l a t i o n for H 20 and D 2 O 1^9 IV.II H 20, HDO and D 20 moments-of-inertia 190 I V . I l l Symmetric G-matrix elements for H 2 O 3 2 0 1 X TABLE PAGE IV. IV HgCg and D 20 3 force constants for ice 1 208 V. I The clathrate-mixture sample h i s t o r i e s 215 V.II RV,0 frequencies i n unannealed and annealed CH-^Cl• 7• 67H 20 . 221 V.III Oligomeric frequencies at 83°K i n unannealed clathrate- mixtures 223 V.IV. Temperature dependences of oligomeric frequencies i n unannealed clathrate mixtures 22k V.V The stable temperature ranges of the oligomer peaks. . . . 225 V.VI The a l k y l halide guest absorptions i n unannealed clathrate mixtures at 83°K 230 V.VII The temperature dependence of the guest frequencies during annealing 231 V.VIII The stable temperature ranges for the guest absorptions. . 232 V.IX The behaviour of HDO stretching modes for annealed clathrate mixtures 237 V.X HDO l i b r a t i o n s for three annealed clathrate mixtures . . . 2^1 V.XI Average H20 and D20 frequency-temperature data for annealed clathrate mixtures 2kk V. XII Data for Cl2'7.67H 20 and Br 2-8.6H20 on Csl and AgCl. . . . 2^5 VI. I H20 frequencies for hydrated a l k a l a i halide s a l t s 250 VI.II Oligomeric H20 and D20 peaks i n clathrate mixtures and rare gas matrices | 252 V I . I l l A l k y l halide frequencies i n pure solids and clathrate mixtures 25^ LIST OF FIGURES FIGURE PAGE 1.1 The stainless s t e e l deposition tube kk 1.2 The isolated sample chamber k6 3.1 Representative spectra of vitreous and cubic ices 60 3.2 Frequency s h i f t s during phase transformation . . . 6 1 3.3 Oligomeric H 20 and D 20 absorptions i n vitreous ice I . . . . 6k 3.k Half-height width s h i f t s for ( v R , v R + v T) and ( v l 5 v 3 , v1 + v T) 66 3.5 Half-height width s h i f t s for ( v 2 , 2 v R ) 67 3.6 HDO stretching frequency s h i f t s for cubic ice 1 71 3.7 HDO l i b r a t i o n a l frequency s h i f t s for cubic ice I 73 3.8 HDO stretching mode half-height width s h i f t s for cubic ice 1 75 3.9 HDO stretching mode peak height s h i f t s for cubic ice I . . . 78 3.10 The s h i f t s of cubic ice I v 3 82 3.11 The s h i f t s of cubic ice I vj_ 85 3.12 . The s h i f t s of cubic ice I v 2 • 86 3.13 The s h i f t s of cubic ice I v R 88 3.1k The cubic ice I v T ( H 2 0 ) band at 83°K 89 3.15 The shifts- of cubic ice I v T . 90 3.16 The s h i f t s of cubic ice I ( v i + v T) . . . 92 3.17 The s h i f t s of cubic ice I 3 v R 93 3.18 The s h i f t s of cubic ice I ( v R + v T) 9k x i i FIGURE P A G E h.l The calculated l i n e a r thermal expansion c o e f f i c i e n t of cubic ice I 128 it. 2 The calculated cubic ice I l a t t i c e parameter as a function of temperature 129 U.3 The calculated 0-••-0 distance for cubic ice I as a function of temperature 131 k.h Cubic ice I HDO stretching frequencies as a function of R(0 0) 132 U.5 Comparison of observed and predicted v (HDO) - R(0-*--0) dependence 13T k.6 The calculated cubic ice I harmonic HDO frequency as a function of temperature 1^3 it. 7 The calculated HDO anharmonicity ihk It.8 A plot 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 A plot of<Ar 2^> against R(0 0) 1 5 1 it. 11 A plot of v^CHDO) and v^(HDO) ag a i n s t < A r 2 > 152 Un OD it.12 The cubic ice I dependences on RCO'^'O) 165 4.13 The calculated hexagonal ice I V 3 dependence on R(0 0) . . 1 6 6 it.lU The calculated hexagonal ice I v Q H(HD0) and vor)(HDO) dependences on R ( 0 , , , , 0 ) l 6 T it. 15 H 2 O , HDO and D20 vapour and cubic ice I phase frequencies . . 180 it. 16 The effects of uncoupling on the HDO stretching frequencies • l 8 U it. IT The p r i n c i p a l axes of H 20, HDO and D20 189 it. 18 The H 20 3 model of H20 i n ice 199 it. 19 The inte r n a l coordinates of H 2 O 3 . . .- 202 it.20 The symmetry coordinates of H 2 O 3 203 x i i i FIGURE PAGE 5.1 Clathrate-mixture frequency shifts during transformation . 217 5.2 Typical annealing spectra for C H 3 C I , CH^Br and CH^I clathrate-mixtures 218 5.3 Typical annealing spectra for C H C I 3 and C2H5Br clathrate-mixtures 2 1 9 5.U Typical annealing spectra for Br 2 and C l 2 clathrate- mixtures 220 5.5 Consecutive spectra for annealing C12*7.67H20 on Csl . . . 227 5.6 Frequency shifts for v (HDO) of annealed CH^Br•7.67D20 (k.00% HDO) 235 5.7 Frequency shifts for v (HDO) of annealed CH 3Br•7.67H 20 (5.9W HDO) 2 3 6 5.8 The half-height width shifts for and v of several clathrate-mixtures 238 5.9 The shift of vR(HD0) in annealed CH^Br•7.67D20 (k.00% HDO) 2i+0 5.10 Shifts of v 1 ( D 2 0 ) for annealed CH^Br•7.67D2O 2^2 5.11 Shifts of .v3(D20) for annealed CH3Br• 7.67D20 2^3 ACKNOWLEDGEMENTS To Professor K.B. Harvey who has the assured f a i t h i n graduate students to allow them to choose and pursue a range of interests 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 action. To Professors R.F. Snider and A. Bree who as members of my committee were also w i l l i n g to discuss problems related to t h i s work. To the members of the mechanical, glass blowing and electronics workshops for t h e i r excellent craftsmanship and cheerful aid. To Raymond Green and other students and faculty for the many opportunities to discuss diverse problems and for the ready mutual exchange of ideas. And to my wife and family for t h e i r special help and the joy they provide. DEDICATION: To my parents Karl Johan F r i t h i o f Hardin and Beatrice Mary (.Trojanoski) Hardin INTRODUCTION The phenomenon of hydrogen bonding has played an increasingly impor- tant role i n the theories of certain chemical and bio-chemical systems for more than three decades. Several models, depending on the physical proper- ty investigated, have been proposed to explain the experimental r e s u l t s . However, for crystals a u n i f i e d hydrogen bond model has "not yet developed which i s consistent with a l l the chemical and physical properties of the s o l i d state. The present work i s a spectroscopic investigation of s o l i d state hydrogen bonding i n vitreous and cubic ice I and i n vitreous and c r y s t a l l i n e clathrate-hydrate mixtures; the nature of the clathrate-hydrate solids formed by vapour condensation i s uncertain. A detailed study of the large changes ( r e l a t i v e to non-hydrcgen-bonded solids) i n the infrared, ( i r ) absor- tions as a function of temperature provides information on changes i n hydrogen bonding as a function of the oxygen-oxygen nearest-neighbour distance (R(0''-'0)) both for i n d i v i d u a l molecules and for the c o l l e c t i v e s o l i d arrays. These data help to describe precisely changes i n one so l i d ' s molecular p o t e n t i a l and should aid i n the development of a u n i f i e d hydrogen bond model. Hydrogen Bonding The main effects 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) alterations i n i n t e n s i t y , 3) increased band width, and k) the appearance of new bands associated with the deformation of the hydrogen bond. The general phenomenon of hydrogen bonding has been reviewed by Pimentel and McClellan ( l ) , Sokolov and Tschulanovski ( 2 ) , and by Hadzi and Thompson (3). Recently Hamilton and Ibers (h) discussed the roles of hydrogen bonding i n chemical structures. The s p e c i f i c effects of hydrogen bonds on the chemical and physical proper- t i e s of ice are treated 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 theories f a l l into two c l a s s e s — c l a s s i c a l and quan- tum mechanical; the l a t t e r includes three separate approaches—valence bond (VB), charge transfer (CT) and molecular o r b i t a l (MO) representations. The conclusions drawn from a l l the theories are that both e l e c t r o s t a t i c , charge migration and short range repulsion give concerted effects 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 theories are based on Pauling's (8) des- c r i p t i o n which assumed the H atom could form a single covalent "bond only. . (a)- Point charge models. In the early 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 clathrate-hydrate systems with 0-H««--0 "bonds, h electrons (2 i n the 0-H bond and 2 i n the 0 lone pair) were considered and the remaining electrons and protons were assumed to form the molecular core. The charges were located so that the correct 0-H and lone pair dipole moments were obtained. The i n t e r a c t i o n energy of the hydrogen bond, calculated by assuming a simple Coulomb p o t e n t i a l , was then 6 kcal/mole. The theories have successfully explained the lengthening of the X-H bond (r(Xr--H)) and the X-H stretching 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 indicated by the decreasing bond strength with decreasing electronegativity of the proton acceptor and proton donor. Secondly, e l e c t r o s t a t i c energy causes at least part of A R ( X * , - , Y ) and Av v r r. An (b) Continuous charge d i s t r i b u t i o n model. This model was presented i n 1964 by Bader (13) for the 0-H-••-0 system t y p i c a l of ice and clathrate- hydrates. He considered a l l the electrons, by methods developed for hydrides and binary hydrides (lU,15), i n spherical charge di s t r i b u t i o n s and calculated the el 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 interpretation of Bader's model are the same as for the point charge model. (c) Summary of the c l a s s i c a l theories. The e l e c t r o s t a t i c theories ignore four important facts about hydrogen bonding. For example, hydrogen bonds may not be completely ionic since there i s no correlation 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 electronic charge distri b u t i o n s are undistorted by the formation of a hydrogen bond. Another point to consider i s that the X - . . . Y distances are much less than the covalent 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 el e c t r o s t a t i c theories cannot explain the increase of intensity of the X-H stretching mode. ( i i ) Quantum Mechanical Theories The f i r s t quantum mechanical theory of the hydrogen bond was published i n 1952 by Sokolov . ( l 6 ) , although such methods have become p r a c t i c a l only recently. Since the results of t h i s thesis are not interpreted i n d e t a i l by the quantum theories, they w i l l only be outlined and t h e i r results w i l l be stated. k (a) Valence bond theories. The VB calculations (16,17) did not give exact physical solutions since the method has a largely empirical 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 effects contribute to the hydrogen bond, and that the agreement of the e l e c t r o s t a t i c model with experiment may be fortuitous since the three non-electrostatic effects may cancel each other. The four energies contributing to 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 repulsion energy, 3) the dispersion energy, and k) the d e r e a l i z a t i o n energy due to CT. Tsubomura characterized effects 2, 3 and k e x p l i c i t l y . He assumed there were 5 contributing resonant structures: *1 Xr--|H Y covalent X-H *2 X - H + Y pure ionic Y 3 X + H~ Y pure ionic X" H| «Y + covalent H-Y CT V H~ covalent X-Y CT Tsubomura's cal c u l a t i o n showed that the de l o c a l i z a t i o n energy amounts to 8.1 kcal/mole—about 1.5 times larger than the e l e c t r o s t a t i c energy. The repulsion energy and dispersion energy are of opposite sign to the d e l o c a l i - zation energy and appear to cancel i t . The VB method has received more recent treatments (19,20). Hasegawa, Daiyasu and Yomosa (20)reported a four electron VB ca l c u l a t i o n of the hydro- gen bond p o t e n t i a l energy. They used Tsubomura's ( l 8 ) 5 resonant struc- tures and constructed the contributing ^-functions from t r i g o n a l or t e t r a - hedral plater atomic o r b i t a l s . The proton p o t e n t i a l was calculated as a function of R(0 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 calculations of Hasegawa et a l . ignored the contributions of the CT structures, 1 ^ and IJJ^-, and resulted i n an . asymmetric,.single minimum po t e n t i a l . They deduced that to account for Ar(O-H) and Av_„ the p o l a r i z a - t i o n of the surroundings must be considered, i_.e_. ip^ and must be included. When that was done a double minimum po t e n t i a l resulted. t One can summarize the VB theories by stating the following conclusions l ) i n addition to e l e c t r o s t a t i c forces other forces are important—dispersion exchange repulsion 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 for short bonds but may be for long bonds, 3) the amount of CT changes very ra p i d l y as a function of r(X-H) and r(X-Y)(the contribution of ^ r i s e s much faster (10 times) than the contributions of ipg, ^ and ^ ^ ) . (b) Charge transfer theories. Since a w e l l developed theory for CT e x i s t s , several workers applied these techniques to the hydrogen bond (21, 22,23). Bratoz (22) applied 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 p a i r . o r b i t a l The conclusions Bratoz (7) reached from these CT theories are: l ) the VB picture of the hydrogen bond i s v a l i d , 2) since the H atom'is small, the short range repulsive forces are small and the H atom has a special r o l e for t h i s kind 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 electron exists i n the OH antibonding o r b i t a l , reducing the bond strength and allowing longer r(X-Y) and weaker X-H force constants, k\ CT theories predict an increased p o l a r i t y i n the O-H-'-'O complex and therefore an i n - creased infrared v n w i n t e n s i t y . '(c) Molecular o r b i t a l theories. 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 to physical s i z e , bond length and number of electrons. Larger systems such as (Ĥ O),.,, (HF),_>, and (HgS)^ cannot be treated exactly since drastic approximations must be made. For O-H'-'-O Weissmann and Cohen (2k) found a very asymmetric single minimum p o t e n t i a l , i n contrast to the empirical double minimum resu l t of Lippincott and Schroeder ( 2 5 ) . Weissmann's res u l t s predicted an Ĥ 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 less successful i n pre- d i c t i n g the r(X-H) and r(X-Y) distances. More recently, Rein, Clarke and Harris ( 2 6 ) studied the hydrogen bond of water by MO methods. The important point of t h i s work i s that the atomic charges and overlap populations i n d i - cate a substantial CT across the hydrogen bond. . . Molecular o r b i t a l theories so far indicate 2 properties of hydrogen bonds: l ) formation of a hydrogen bond induces electron charge migration from the molecular core to the external region and 2 ) the H 2p^ atomic o r b i t a l contribution to 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 of TT character i n the hydrogen bond. B. Spectroscopic Manifestations of Hydrogen Bonding As early as 1933 Bernal and Fowler (9) recognized i n Ĥ O the large s h i f t i n v..,, ( A v ^ = v O T J(vapour) - v r t T I (hydrogen bonded)) caused by hydrogen Un Un Un Un bonding. Infrared techniques s t i l l remain the most v e r s a t i l e t o o l to i n - vestigate the hydrogen bonds i n vapours, l i q u i d s and s o l i d s . However, the r e l a t i v e l y large electron migrations induced by hydrogen bonds give large 7 changes i n nuclear shielding 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 with the i r manifestations of hydrogen bonding i n the 0-H -,,"0 system ice I and i n clathrate-hydrates. ( i ) The' General Effects of Hydrogen Bonding The four main spectroscopic effects i n hydrogen bonded solids are often large i n contrast to the small effects found between the vapour and s o l i d phases of molecules incapable of hydrogen bonding. The f i r s t c o r r e l a - t i o n made from the experimental data was the rela t i o n s h i p between R(X***-Y) and the v^.TT s h i f t s from the monomer frequency i n the bonded complex. Gener-An 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 vVXJ depends on An the strength of the hydrogen bond. Those properties are largest for 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 larger. The four effects w i l l now be considered i n d e t a i l . (a) Frequency s h i f t s . Wot a l l of the molecular v i b r a t i o n frequencies are strongly affected by hydrogen bonding. The X-H stretching frequency i s shi f t e d to 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 to higher frequency. The novelty of the large stretching mode s h i f t s can be grasped by comparing non-hydrogen bonding and hydrogen bonding molecules. (a) no hydrogen bonding (b) hydrogen bonding i ) FHF (b) CO CHT Vapour 1285 291k cm" So l i d cm 1 1285 cm - 1 2906 cm"1 AV -1 0 cm 8 cm"1 HF vapour (HF) Ca) KHF, Cal VHF Av R(F-••-F) klhO cm -1 3UU0 cm 1 -700 cm"1 2.55 X -1 1U50 cm -2690 cm _ 1 2.26 £ (a) Nakamoto et a l . , Ref. 27- 0>). C0 2 bonding mode. .8 Tables and plots of v„TT as a function of R(X....Y) were compiled by Art Nakamoto, Margoshes and Rundle (27) for the FHF, OHO, NHF, OHN, NHO, NHN, 0HC1 and NHC1 f a m i l i e s of hydrogen bonding compounds. For small R(X....Y) the v vs. R relationships are lin e a r as Pimentel and Sederholm (28) proposed. For large R(X....Y) the v vs. R relationship i s non-linear: the behaviour o over a l l R(X....Y) suggested an asymptotic relationship. (b) Band broadening. An incresed half-height width (Av 2) i s found for v and i t s overtones i n hydrogen bonded systems (29). In contrast An the effect i s much smaller on the width of the R-X-H bending modes. In the early work the explanation for braodening was thought to l i e i n the form of the intermolecular potential perturbation. Such an explanation i s s u f f i c i e n t only for weak or moderate strength hydrogen bonds, but not for 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 arises from the anharmonicity perturbations and changes or differences i n the anharmonicity over many molecules. Generalizing 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 often increase many-fold upon hydrogen bond formation. Also the overtones of h v decrease i n i n t e n s i t y . The apparent relationships among Av, Av and An i n t e n s i t y (large s h i f t , broad band, large intensity) do not necessarily hold for 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 integrated i n t e n s i t i e s due to experi- mental d i f f i c u l t i e s , however, early work by Huggins and Pimentel (29) esta- blished that hydrogen bonded complexes which show no increase i n the i n t e n s i t y of v V T J appeared to have non-linear hydrogen bonds. XH 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 theories of the hydrogen bond: El e c t r o s t a t i c s requires that both v v t r and increase i n i n t e n s i t y . However, An n CT theories predict that only increases i n i n t e n s i t y . (d) New absorptions. For X-H , - ,*Y systems new bands appear i n the spectra associated with the deformation of the hydrogen bond. In ice the hydrogen bond stretch and hydrogen bond bend correspond to molecular trans- l a t i o n (v„) and molecular l i b r a t i o n (v_) modes, the so-called l a t t i c e modes, i n ( i i ) The 0-H 0 Hydrogen Bond Effects The discussions here have so far been concerned with correlations among diff e r e n t hydrogen bonding f a m i l i e s . However, there i s a very big problem involved i n such comparisons, the diff e r e n t X-H,,,*Y systems have differences 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 , sizes 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 tionships among Av v u, i n t e n s i t y and R(X**''Y). These parameters i n An An cubic ice I and the clathrate-hydrates can best be compared to other 0-H'-'*0 systems and preferably to other Ĥ O allo t r o p e s , i_.e_. , the high pressure ices. In order to study v V T J as a function of R ( 0 - - , * 0 ) , Nakamoto et a l . (27) An compiled AvOTJ and R(0'*'"0) data for 26 compounds. As w e l l , they correlated On R(0** , ,0) to r(O-H) from neutron d i f f r a c t i o n data. The resu l t s indicate 10 that as R(0 - -**0) decreases then r(O-H) increases l i n e a r l y for long hydrogen bonds and exponentially for strong (short) hydrogen bonds. They f e l t that inclusion of covalency i n the hydrogen bond was important, as i n Tsubomura's ( 1 8 ) work. In order to understand the potential energy of the proton as a func- t i o n of R ( 0 * - * * 0 ) , Lippincott and Schroeder (25) constructed a one dimen- sional model of the hydrogen bond. By applying the conditions of equilibrium, they obtained relations for Av ̂ , r(O-H) , hydrogen bond energy and force constants as a function of R ( 0 , , - - 0 ) . Their results agree we l l with experi- o ment: for i c e , where R(0 >- , ,0) = 2.76 * 0.1 A, t h e i r relationship between v and R(0'* -0) i s l i n e a r . Unfortunately t h e i r formulas are not good for predicting the v,-„ of ice over a small range of R(0-«--0) since there i s some arbitrariness i n defining the hydrogen bond dissociation energy. Reid (31) constructed the potential surface for simultaneous H and 0 motion i n 0-H-,**0 hydrogen bonds over a wide range of R ( 0 - - , - 0 ) and r(O-H). He modified the Lippincott-Schroeder potential by changing the hydrogen bond dissociation energy from molecule to molecule, i^.e_. , with changing R ( 0 - , - * 0 ) . Reid used his potential functions to interpret the changes i n i r results 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 to i t s strong dependence OH on R(0-- , ,0). During any v^ vibration many R(0 - -**0) distances occur and many v Q J J ' s a r e observed. Recently Bellamy and Pace (32) reviewed the relations among Av„TT An and R(X-•••Y). They deduced that X and Y can approach only to the. combined van der Waal's r a d i i , further 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 closest approach distance of 3.6 A. The weakest o \ hydrogen bond has an R(O----O) of 3.36 A, therefore R ( 0 - - - - 0 ) contracts upon formation of the hydrogen bond. Extrapolations of the X-Y plots of Wakamoto et_ al_. indicated 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 including H: o o FHF" intercept 2.7 A (calc. 2.7 A) o o OH 0 intercept 2.8*1 A (calc. 2.8 A) This suggested that i n hydrogen bonds the H o r b i t a l disappears or i s com- pletely overlapped and that there i s no repulsion due to i t . Bellamy and Owen ( 3 3 ) extended t h i s idea and proposed that the rate of increase of repulsion i s proportional to the rate of increase i n lone pair - lone pair repulsions. They adopted the 6-12 potential to describe the repulsive terms from lone pairs i n X and Y and f i n a l l y obtained an ex- pression r e l a t i n g A v ^ and R ( X - , - , Y ) . For 0-H----0 t h i s has the form An 12 6 3.35 3.35 A VOH =• 5 0 [ ( i r } - < R > I- This relationship give's good agreement with the work of Nakamoto et_ a l . However by inspection of Nakamoto's work one sees that no unique v - R ( 0 * 4 " " 0 ) r e l a t i o n exists for the 0-H*••*0 family. There are too many On variables. I t seems more reasonable to study one molecular system l i k e H 2 O i n a variety of c r y s t a l habits and to attempt to vary only R ( 0 - - , , 0 ) i n some way. For example, a study of H 2 O i n a l l 9 ice phases and i n clathrate- hydrates as a function of temperature may provide useful r e s u l t s . 12 Clathrate-Hydrates A.- The Clathrate-Hydrate Problem Quantized rotation 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 ( 3 ^ , 3 5 ) and nmr ( 3 6 , 3 7 ) studies. Now detailed i r assignments of the guest rotations and the i r behaviour i n the host cavity are required to determine the form of the potential well surrounding the guest molecules. In order to determine the changes i n the interactions of the guest molecules with the host l a t t i c e and the height of the barrier to guest rotations, i t i s necessary to know pre- c 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 inclusion compound i n which one stable mole- cule 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 cavities i s ca l l e d the host and the enclosed molecule i s ca l l e d the guest.) A common property of some im- portant clathrate compounds i s hydrogen bonding. Some examples of c l a t h - rates are: 1) g-quinol clathrates, 0 .Jk Kr-3 CgH^(.0H)2 2) gas hydrates, Ar*7.67 Ĥ O 3) tetraalkylammonium clathrates, salt hydrates [(n - C^H9)UN] C 6H 5C0 2-39.5 Ĥ O U) Ni(CN) 2NH 3-C 6Hg . 13 A clathrate-hydrate i s a clathrate compound formed with an Ĥ O host l a t t i c e i n which a variety of small atoms and covalent molecules are trapped. The clathrate-hydrates can be separated into two classes: The gas hydrates are clathrates formed between Ĥ O (host) and small, covalent gases (guests, G) and l i q u i d hydrates are clathrates formed between Ĥ 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 structures have been found for the clathrate-hydrates. The so-called gas hydrate clathrates, Type I , are cubic and have maximum i d e a l stoichiometries of SG'^HgO or 6G-U6H20. The so-called l i q u i d clathrate- hydrates, Type I I , are also cubic and have maximum i d e a l stoichiometries of 8G-136H 20 or l6G'-8G - 1 3 6 H 20. Bromine l i q u i d clathrate-hydrate, Type I I I , i s tetragonal and has a maximum i d e a l stoichiometry of 20G*172H20. (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 unit c e l l edge and U6 HgO molecules i n a unit 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 linked by the remaining 6 Ĥ O molecules to form 6 tetrakaidecahedra, giving a t o t a l of 8 c a v i t i e s per unit c e l l . In Type I clathrate-hydrates the nearly spherical pentagonal dodeca- o hedra have free diameters of ,3.95 A and the spheroidal tetrakaidecahedra have o o free diameters of 5-8 A (for a 12.0 A unit c e l l ) . Molecules and atoms whose o maximum dimensions are less 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 clathrate stoichiometry of SG'^H^O (i..e_. G = Ar, CH^, H ^ S ) . Molecules and atoms whose maximum dimensions are less than 5.8 A but are larger 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 clathrates and t h e i r properties, P,. gives the clathrate decomposition pressure at 0°C, diss ' T gives the maximum stable temperature of the clathral Tiq gives b o i l i n g temperature of pure guest.* Type Clathrate diss at 0°C max G (cubic) I I [cubic] I I I (tetrag) 8G'U6H20 Ar Kr Xe H2S 6G-1*6H20 C I 2 CH3C1 CH^Br S0„ 8G-136H2O CH 3I CHC13 C 2H 5Br CH 2C1 2 C3 H8 C 2H 5C1 20G-1T2H20 Br„ o A 11.97 12.00 1 2 . 0 3 12.00 1 2 . 0 9 1 1 . 9 ^ n.ik 17-30 17.26 17.31 17.ho 17.30 a 23.8 o c Q 12.2 95.5 atm lh.5 1.15 698 Torr 252 311 187 297 50 155 116 {l.lh atm) 201 U3.90 29.5 28.7 2.1 1U.5 12.1 U.3 1.6 1.7 5.69 It.8 5.81 83 1 2 1 166 213 239 2U9 277 263 316 33U 311 315 228 286 332 Reference kO x 5 6G ' U 6H 2 0 stoichiometry ( C l ^ , SO^, Ĉ Ĥ -). Some properties of the clathrates formed i n these two ra t i o s are given i n Table 0.1. One may also 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 In the p r a c t i c a l s i t u a t i o n the unit c e l l dimension varies according to the size of the guest species, Table 0.2. ( i i ) Type I I Clathrate-Hydrates o These compounds form a cubic c r y s t a l of Fd3m (38) symmetry with a IT A unit c e l l edge and 136 Ĥ O molecules i n a unit 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 hexakaideca- o hedral c a v i t i e s i n one unit c e l l . The free diameters are 5.0 and 6.T A o respectively (for a 17.h A unit c e l l ) . o Molecules which have a maximum dimension greater than 5>8 A and less o than 6.7 A cannot form Type I clathrates, but do form Type I I clathrates. That implies they occupy only the hexakaidecahedr.a with an i d e a l s t o i c h i o - metry of 8G'136H£0. Some Type I I clathrates, the guest s i z e s , and the unit 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 clathrate-hydrate of Br^ was o r i g i n a l l y thought to be of Type I I . However, work by A l l e n and Je f f r e y (1*1) has shown that i t forms a tetragonal o c r y s t a l of symmetry k/xamm with a = 23.8 and c = 12.2 A unit c e l l edges and 172 HgO molecules i n a unit c e l l . They reported 20 polyhedral c a v i t i e s large enough to accomodate Br^ molecules, 10 small pentagonal dodecahedra, 16 tetrakaidecahedral and k pentakaidecahedral. The id e a l stoichiometry i s then 20Br -1T2H 0. 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 sizes and unit c e l l dimensions of t y p i c a l clathrate-hydrates. f Type Clathrate ao Guest Allowed occupancy of c a v i t i e s . co size V Ik 15 16 8G'ii6H 20 0 A 0 A Ar 3.76 2(2)* 6(6) Kr k.ok 2 6 Xe a Q 11.97 k.ko 2 6 I H 2S 12.00 k.ho 2 • 6 6G-U6H2O (cubic) CI 12.03 5.17 0(2) 6 CH3CI 12.00 5.06 0 6 CH 3Br 12.09 5.33 0 6 S0 2 11.9h 5.00 0 . 6 8G-I36H2O CH3I YJ.lh 5.TO 0(16) 8(8) I I CHCI3 17.30 6.kh 0 8 (cubic) C 2H 5Sr 17.26 6 M 0 8 CH2C12 17 • 31 6.08 0 •8 C3H8 17.^0 • 6.28 0 8 C2H5CI 17.30 , 6.20 0 . 8 20G-1T2H20 0(10) 16(16) . k(k) I I I B r 2 a 0 23.8 5-68 (tetrag) c 0 12.2 V^ 2 pentagonaldodecahedron, V.^ ̂ . ̂  - t e t r a k a i , pentakai, hexakaidodecahedrons. * - numbers i n brackets show maximum number of cavi t i e s per unit c e l l . 1 H 17 Since the present experiments attempt to accurately correlate v and OH R(0 0) for seven Type I , II., and I I I clathrate-hydrates, the R(O----O) distances are required. However, the structures were determined by assuming o constant R(O--'-O) throughout the unit c e l l , e_.g_. 2.8l A for a Type I o o o clathrate (12.0 A unit c e l l ) and 2.78 A for a Type I I clathrate (17-3 A unit c e l l ) . In order to accomodate the pentagonal dodecahedra and other polyhedra i n the unit c e l l , the 0-0-0 angles were distorted from tetrahedral. Von Stackelberg (38) reported angles from 100.0° to 12k.6°. I t seems l i k e l y that i n r e a l i t y the 0 - - , - 0 distances are also irregular and a range of R(0--«0) exist for each clathrate-hydrate. That w i l l unfortunately broaden the i r results even more than i n ice I. Indeed for Type I clathrate-hydrates (cubic, Pm3n) the Ĥ O oxygen atoms l i e on 3 unit 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- ditions to permit formation of clathrate-hydrates, r a i s i n g the pressure of G to form either guest G(gas) or G(liquid) plus hydrate. I f the p a r t i a l pressure of guest applied to the sample i s less than the equilibrium dissociation par- t i a l pressure then the clathrate dissociates. In a recent review Byk and Fomina (it2) discussed the conditions for 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 clathrate formation at low temperatures. 18 S p e c i f i c a l l y , they investigated the formation of clathrate-hydrate from ice and Ar, Kr and Xe gases at 90°K and 195°K. Their technique involved depositing a t h i n layer of Ĥ O i n a glass bulb at TT°K. The sample was warmed to 195°K and either Ar, Kr or Xe ( 1 9 0 Torr) was admitted. The gas uptake as a function of time was measured. They found that Kr and Xe, but not Ar, reacted with ice at 195°K. Ar was found to react slowly at 90°K at 190 Torr. Their results suggested the ready formation of clathrate-hydrates at low temperatures with a c r i t i c a l formation pressure of less than 190 Torr. D. Previous Investigations of the Clathrate-Hydrates Contemporary interest i n clathrates has been centered on the motion of the guest molecules i n the host l a t t i c e s . Thus the methods of d i e l e c t r i c relaxation (1+1+-1+6), x-ray d i f f r a c t i o n (38,1+7), nmr (1+8-51), thermodynamics ( 3 8 ) , and i r spectroscopy ( 5 2 - 5 7 , 3l+) have been applied to quinol clathrates and clathrate-hydrates to discover whether guest rotations are free ,or res- t r i c t e d , how fast they rotate, and what are the barriers to free rotation. S i m i l a r l y , deductions with respect to hindered translations ( 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). He studied the three Type I clathrate-hydrates of Ar,; Kr., and S O 2 . The main points of his thesis were: l ) there was an E^O host band at 21+25 cm i n addition to the w e l l known ice absorptions, 2) the v R band was shifted -50 cm from ice I , 3) the 1 6 0 0 cm ^ and 2210 cm absorptions of the host were v (HOH bending) and v 0 .+ . v,, respectively, h) S 0 o absorbed at 2^+55 cm and 3570 cm ^ (a weak shoulder on v and v_, the symmetric and 19 assymetric stretches,, of Ĥ O) i n the clathrate-hydrate. Shurvell (57) followed up the above work by observing SO^, H^S, and Kr Type I clathrate hydrates (SG-UeH^). For S0 2'7 -67H 20 Shurvell reported: l ) that v_, (H O0) was ho cm-"'" less than that of i c e , 2) that the 1600 cm "*" band of ice was at 1.6k0 cm "*" i n the clathra.te and was therefore rather than 2v T 3, 3) that the 2230 cm-"1" was v_ •+• . v , and k) that HO i n clathrates had. a new feature at 2^10 cm "*" i n addition to the ice bands. As w e l l , he found that the v^SO^) had a central peak and 2 wings, 1336, 13^2 and 13U8 cm-"*". There was no s p l i t t i n g of v^tso,.,) as i n the pure SO^ s o l i d and the clathrated SO^ bands were broadened by " r a t t l i n g " and r o t a t i o n a l fine struc- ture . The wings were thought to be due to combinations with l i b r a t i o n s (hindered rotations) and transl a t i o n s . Both McCourt (56) and Shurvell (57) formed the clathrate-hydrates by condensation of stoichiometric gas mixtures on Csl windows at 77°K. Shurvell reported his samples were annealed to d e v i t r i f y the condensed phase. The r e s u l t s of these preliminary investigations on Type I clathrate-hydrates were summarized by Harvey, McCourt and Shurvell (3k). '• E. The Present Approach to the Clathrate-Hydrate Problem Three facets of the clathrate-hydrate i r absorptions were studied i n t h i s work. F i r s t , i n order to analyze previous work (.56,57), the forms of the clathrate-hydrate absorptions were determined from low temperature mulls of s o l i d clathrate samples. Secondly, the v i t r e o u s - c r y s t a l l i n e phase trans- formation was observed by i r spectroscopy as a function of temperature for clathrate-hydrates (types I , I I and I I I ) condensed from gaseous stoichiometric 20 mixtures. T h i r d l y , the temperature dependences were determined for the i r absorption of d e v i t r i f i e d "clathrate" samples. Ice A. The Ice Problem Many theories have been proposed to explain the origins of the f r e - quency s h i f t s , the 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 either support an existing theory or which w i l l suggest some modifications to the theory. S p e c i f i c a l l y , the correlations of absorption band frequencies, widths and heights to AR(O-'-'O) are required for i c e I. B. Non-Spectroscopic Investigations of Ice ( i ) S t r u c t u r a l Studies Ice exists i n at least twelve s t r u c t u r a l allotropes above TT°K and at pressures of up to 25,000 atmospheres. The ice phases stable at 1 atmosphere are a l l c a l l e d i c e I. In f a c t , there are three allotropes of ice I , the vitreous or amorphous, the cubic and the hexagonal phases ( i v , Ic and Ih). The i c e I s t r u c t u r a l r e s u l t s up to 1 9 5 8 were summarized by Lonsdale ( 5 8 ) and Owston ( 5 9 ) . Recently, 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 the i c e Ih l a t t i c e parameters between 1 5 ° and 200°K. As w e l l , Arnold, Finch, Rabideau and Wenzel ( 6 l ) reported a neutron d i f f r a c t i o n study of ice I c . (a) Hexagonal ice I. The ordinary phase of ice at S.T.P. i s hexagonal ice I (ih) i n which the oxygen atoms form a P62/mmc unit c e l l with h molecules. * Assuming s o l i d polywater i s a unique s o l i d of H2O. 2 1 The unit c e l l dimensions are ( 6 2 ) ; ao co H 20 (l63°K) k.H93 A 7.337 A D 20 (ll+3°K) 1+.1+95 7.335 o The oxygen-oxygen nearest-neighbour distances ( R ( 0 • • • • 0 ) ) i n Ĥ O are 2.76 A at l63°K. The molecules are hydrogen bonded to 1+ nearest-neighbours i n layers of hexagonal, puckered rings. The open structure has channels p a r a l l e l and perpendicular to the c Q axis. There i s s t i l l some uncertainty about the unit c e l l dimensions of ice Ih. The disagreement between Lonsdale's ( 5 8 ) expansion c o e f f i c i e n t s and the direct dilatometric measurements seems to arise from differences 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 with Dantl's (6I4) direct thermal expansion measurements: La Placa and Post's ( 6 3 ) work was confirmed by B r i l l e and Tippe ( 6 0 ) . The l a t t e r found that the c/a r a t i o i s temperature independent, not reaching 1.633 even at 15°K; they found c/a = 1 . 6 2 8 0 ± 0 . 0 0 0 2 . (b) Amorphous ice I . This phase i s formed by the slow condensation of vapour onto a cold surface. Beaumount, Chihara and Morrison ( 6 5 ) found that amorphous ice I was formed when the deposition rate at 135°K was less than 0.0U g/cm^/hour. The x-ray and electron d i f f r a c t i o n patterns are diffuse and the samples are c l e a r , transparent f i l m s . The samples have consequently been variously described as vitreous, amorphous or microcry'stalline. V i r t u a l l y nothing i s known about the structure of amorphous ice I. (c) Cubic ice I. Ice Ic can be formed by the i r r e v e r s i b l e transfor- mation of amorphous ice I or from the high pressure ic e s . The vftreous-cubic ice I transformation has been reported to star t as low as 110°K and as high 22 . i as 153°K by various authors, Table 0.3. The high pressure ice-cubic ice transformations have been studied by B e r t i e , Calvert and Whalley ( 6 6 ) at T7°K by release of pressure. Cubic ice I can also be formed by vapour con- densation between 133° and 153°K. When warmed above 210°K cubic ice I transforms irrevers i b l y to hexagonal ice I with a small enthalpy change, iLe_. <1.5 cal/gm (65). The c r y s t a l structure of the oxygen atoms i n cubic ice I i s the "diamond" structure, Fd3m with 8 molecules per unit c e l l . The oxygens are arranged i n a sim i l a r fashion to that of hexagonal ice i n layers of puckered hexagonal rings. However, the s i x 0 atoms adjoining 2 nearest-neighbours are eclipsed i n cubic ice I and staggered i n hexagonal ice I. The l a t t i c e o o parameters ( 6 2 ) at li+3°K are a o(H 20) = 6.350 A and a o(D 20) = 6.351 A. (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 at 1.01 A. They asserted that the DOD angle = 000 angle and, therefore, that the hydrogen bonds are l i n e a r . Their r e s u l t s were the same at 123° and 223°K, indicating no ordering of the l a t t i c e down to 123°K. Pauling predicted a residual entropy at 0°K of Rln 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 calculated value. Nagle ( 6 8 ) found by l a t t i c e s t a t i s t i c s that the t h e o r e t i c a l value i s O.81U5 t 0.0002 e.u., compared to an experimental value of 0.82 i 0.15 e.u. Disorder i n cubic ice I was confirmed by electron : d i f f r a c t i o n ( 6 9 ) . P i t z e r and Po l i s s a r ( 7 0 ) discussed the order-disorder problem i n ice I and concluded that the ordered structure i s more stable 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 vitreous, cubic and hexagonal ice I by several experimental methods. Technique Low Temperature Phase and Range °K Cubic Phase Range °K Hexagonal Phase Range °K Workers heat capacity 77 - Ikk c r y s t a l l i n e ihh 2T3 Pryde et_ a l . (a) amorphous (b) e l e c t . d i f f r a c . TT - 1 0 T 10T - 190 190 - 273 Hon jo et_ a l . calorimetry TT - ( 1 5 0 t 1 0 ) c r y s t a l l i n e 150 2T3 de Wordwall et al. ( c ) amorphous (d) e l e c t . d i f f r a c . TT - 1 5 1 1 5 1 - 173 173 - 2 T 3 Blackman et a l . amorphous x-ray d i f f r a c . TT - HO 113 - 1U3 lh3 - 2 T 3 Dowell et a l . (e) amorphous diff.therm, anal. TT - lk9 lk9 - 186 186 - 2T3 McMillan et a l . (f) glass x-ray d i f f r a c . TT -(1U8 + 8) (1U8 + 8) - ( 2 2 0 1 2 0 ) 2 2 0 ± 2 0 - 2T3 Beaumont et_ a l . (g) amorphous thermal analysis TT - 15U 15U - 208 208 - 2T3 Ghormley (h) amorphous calorimetry TT - 135 135 - 160 160 - 2 T 3 Sugisaki et_ a l . ( i ) amorphous (a) Ref. 7 1 , (b) Ref. 6 9 , (c) Ref. 7 2 , (d) Ref. 7 3 , (e) Ref. 7^, (f) Ref. 7 5 , (g) Ref. 6 5 , (h) Ref. 7 6 , ( i ) page 3 2 9 , Ref. 6. 24 also estimated the Curie point to be near 60°K. (e) High pressure ices. The aliotropes of ices I I through IX may not consitute a l l p o s s i b i l i t i e s . More allotropes may exist below 77°K and at higher pressures. Some of the crystallographic properties and struc- t u r a l parameters of the i c e allotropes are given i n Table 0.4. Phases I I , VIII and IX are ordered and a l l others are disordered with respect to proton position. The higher densities of the high pressure ices derive not from shorter R(0....)) but from distorted hydrogen bonds. The di s t o r t i o n s r e s u l t o o i n much closer (3.2 A) next-nearest-neighbours compared to ice Ih(4.5 A). There i s considerable d i s t o r t i o n of the HOH angles: Ice I I has 18 HOH angles between 80° and 128°. ( i i ) E l e c t r i c a l Properties of Ice 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). In general, they found that ice I has a large r e c i p r o c a l d i e l e c t r i c relaxation constant (about 10"* reorientations per T - l i second), and that the disordered high pressure ices have even larger ^ s. The ^'s of ordered i c e s , however, are small (no reorientations). The T ^ of i c e I increases very rapidly with decreasing temperature due to the increasing e l e c t r i c f i e l d of the approaching neighbouring molecules: T ^ ̂ i s 2000 times larger at 208°K than at 273°K. An accepted mechanism of re- orientation invokes the migration of Bjerrum (79) D- and L- defects. ( i i i ) Thermodynamic Properties of Ice There i s support for some ordering i n i c e Ih from heat capacity (Cp) and e l e c t r i c i t y measurements. Helmreich and Riehl (80) deduced from elec- t r i c i t y measurements that the proton disorder i s p a r t i a l l y removed as \ Table O.U Physical properties of the ice s . ICE Ih Ic I I I l l . IV V VI VII VIII IX Crystal System Hexag Cub. Rhomb. Tetrag. Monocl. Monocl. Tetrag. Cub. Cub. Tetrag. Space Group P63/mmc Fd3m R3 pit ? 2 r 1 r A2/a A2/a p l * 2 / m m c Im3n Im3m Vk.2 2 1 1 Z k 8 12 28 28 0 2 2 12 Density g/cm^ 0.9k — 1.17 1.1k 1.23 1.31 1.50 No.n-neighbours k . k k k % k k 8 8 k R n-neighbours 2.1k 2.15 2.15 2.76 •• 2.76 2.81 2.86 2.86 0 A R n.n-neighbours 0 A k.k9 U.50 -2.8U 3.2U -2.80 3.U7-. • -2.87 3.28 3.1*6 3.51 2.86 2.86 deg 1 0 9 . 5 1 0 9 . 5 80 -128 87 -li+1 8U -135 . 76 . -128 100.5 1 0 9 . 5 - k positions disord. disord. ord. disord. ord. disord.. disord. disord. ord. ord. * Table from ref. (5). 26 temperature decreases. The effects found were small and they therefore deduced a small f r a c t i o n of the sample was ordered: A f i n i t e number of ordered domains i n a disordered continuum. Pick ( 8 l ) also suggested that regions of short-range ordering are formed as the temperature of ice I i s lowered. However, he pointed out that the D- and L- defects responsible for reorientation (ordering) decrease i n number exponentially with decreasing temperature. Hence .the time for establishing an ordered c r y s t a l increases exponentially as temperature decreases. The heat capacity of ice Ih above 15°K was f i r s t investigated by Giauque and Stout ( 8 2 ) . They found that the samples attained thermodynamic equilibrium 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 ice Ih Cp below 15°K. They found Cp extrapolates to zero at 0°K and i s consistent with a continu- ous decrease. As w e l l they pointed out that the t r a n s l a t i o n a l , librati.onal 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 contribution to Cp i s explained well by an average frequency for Ĥ O of 620 cm' Leadbetter ( 8 U ) , i n a comprehensive interpretation of the ice I , thermodynamics, explained Cp i n terms of the excitation 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) vibrations. Below 80°K, Cp was derived e n t i r e l y from excitations of v m, while above 150°K v~ gave a s i g n i f i c a n t contribution. He also predicted that between 0° and 273°K the frequency shifts...by 8 + 2$ and that v R s h i f t s by 6 ± 2% for H g0 (for D g0 ±0 ± 2% and 8. + 2% respectively). Blue's ( 8 5 ) elementary treatment of Cp gave a surprisingly good;value for the l i b r a t i o n a l average frequency, 660 cm ^. He also gave a convenient formula for 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 axis n i n gm/cm , k. i s the force constant re s t r a i n i n g atom i from ro t a t i o n about axi i n n i n dynes/cm, • ' - r. i s the normal distance of atom i to axis n i n cm, The effects 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 electronic state or i n the excited state. In nmr spectra the proton signals of (H atoms in) hydrogen bonded molecules are s h i f t e d to a lower f i e l d than for the non- hydrogen bonded molecule. In i c e , nmr has been used to f i n d proton separa tions and to 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 ice have been made by neutron i n e l a s t i c scattering, Raman, and infrared spectroscopy. The previous work w i l l be considered i n two sections, modes occurring below and above 1000 cm (the fundamental l a t t i c e and molecular mode regions ). The r e s u l t s of previous works are tabulated i n Chapter 3 for comparison to the r e s u l t s of the present work. respectively). In cubic ice I (Fd3m) with 2 molecules per primitive unit c e l l (Z = 2) there are (3n)Z (where n i s the number of atoms/molecule) c.v i n 6 i s the v e l o c i t y of l i g h t cm/sec. C. Spectroscopic Investigations of Ice The Ĥ O molecule has 3 molecular v i b r a t i o n s ; a symmetric and an •asymetric stretch and a symmetric HOH bend (v (a^), v„(b ) and. y~(a-j_) 28 18 c r y s t a l vibrations. Of those, (3n-6)Z or 6 of these are molecular v i b r a - tions, 3Z or 6 are rotatory i n nature, 3(Z-1) or 3 are translatory vibrations and 3 are simple translations of the complete unit c e l l . Hence i n a mole (N) of unit c e l l s there are 6N molecular v i b r a t i o n s , 6N rotatory v i b r a t i o n s , 3N o p t i c a l translations and 3N acoustical translations. Ice spectra are characterized by 5 very broad bands. Two bands occur below 1000 cm ^ i n the ^ 0 ices. A band with at least 6 features and centred near 230 cm i s attributed to hydrogen bond stretching modes, the l a t t i c e t r a n s l a t i o n a l modes v̂ ,. A band with from 3 to 16 features and cen- tered near 830 cm ^ i s attributed 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. The band near 1630 cm ^ has been attributed to Iv*., v 0 or to overlapping 2v D/v 0. The band near 2200 cm ^ has been assigned to v 0 + v n or 3V,,. The features of the ^ /, K K 3200 cm band have been assigned by various authors to: 1) 2^2* v 3 ' v l (105), 2) v r \>y v 3 + v T (108), and 3) a l l as v Q H(H 20) (95). The vapour, l i q u i d and i c e I frequencies, with the various assignments are given i n Table 0.5. The analysis of the vibrations of c r y s t a l l i n e materials usually begins with a factor group analysis 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 positions are averaged i n the time of a d i f f r a c t i o n experiment, while i n v i b r a t i o n spectroscopy the instantaneous symmetry of the unit c e l l i s important, ( i ) The L a t t i c e Modes (a) Translations. For ices Ih and Ic the factor group analysis, based on symmetric -̂H positions and the above d i f f r a c t i o n symmetries, pre- Table 0.5 Ĥ O vapour, l i q u i d and ice Ih infrared absorption frequencies, half-height widths and i n t e n s i t i e s and the divergent assignments made to the bands of i c e . (a) (D) (c) (d) (d) Vapour Liquid Ice I Ice Ice Av^ Peak Heii -1 -1 -1 -1 cm cm cm cm 1 6 0 232 weak ( 1 7 0 ) ( 2 1 8 ) 6 5 0 800 2 0 0 strong ( 5 0 0 ) . ( 5 9 0 ) 1595 1 5 7 0 , 1 6 U 5 161+0 250 med. ( 1 1 7 8 ) ( 1 1 6 0 , 1 2 1 0 ) ( 1 2 1 0 ) ( 1 5 0 ) 2130 2 2 2 5 2 0 0 weak ( 1 6 2 0 ) ( 1 6 2 0 ) ( 1 8 0 ) 3657 3219 311+2 ( 2 6 7 1 ) ( - ) (231+7) very- 3756 31+1+5 3252 300 strong ( 2 7 8 8 ) ( 2 5 0 0 ) (2440) ( 2 5 0 ) 3 352 . ( 2 5 1 4 ) 8 1 0 * weak (6oo)<* 3707 31+05 3275 80 very ( 2 7 2 7 ) ( 2 5 2 0 ) (21+16) • ( 2 ) strong (c) (e) (f) (g) Ockman Hornig Pimentel Whalley 1957 1958 1959 1961+ H20 (D 90) HDO V2 + VR v l v 3 + v T R V2 3v 2v, R VR v OH "0D V2 3vT R V 2 V • 3 V V 2 + VR v O H(H 20) v Q H(H 20) VR VR V0H V0D (a) Ref. 1 1 6 , (b) Ref. 9 8 , (c) Ref. 1 0 8 , (d) Ref. 1 0 6 , (e) Ref. 1 0 5 , (f) Ref. 9 7 , (g) Ref. 95- ro 30 diets 9 o p t i c a l modes for Ih (Ajg, B l g, E l g , ̂ 2g' a n ^ E2u^ a n < i o p t i c a l modes for Ic (Fig). The normal k_ = 0 selection rules predict that a l l these modes are i r inactive and that a l l g modes are Raman active. However, i r t r a n s l a t i o n a l absorption (v^) _is_ observed ( 8 6 ) for both Ih and Ic i c e s . In fact the absorptions are nearly i d e n t i c a l . The factor group analysis f a i l s for Vfj of hexagonal and cubic i c e s , as wel l as for the other disordered i c e s , V and VI ( 8 6 ) . In contrast, the factor group analysis works well for of ices I I and V I I I , the ordered H atom ices ( 8 6 ) . The H atoms i n ice 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 perfe c t l y ordered, with 2 near and 2 away from each 0 atom, the c r y s t a l symmetry of ice Ic could not be Fd3m since the symmetry would be destroyed. One'might expect ice Ic to order i t s e l f i n a sub-group of Fd3m or simi l a r to one of the structures i n ices I I , VIII or IX (R3, Im3n or P, „ - ) . Then the v m modes may not be a l l inactive i n ^ l 2 i 2 T the i r . I f short range ordering i s present (as suggested before) then the ef 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 eff e c t i v e p o t e n t i a l at the central molecule. (h) Disorder theory. Whalley and Bertie ( 8 7 ) proposed a theory to explain 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 crys- t a l s . They considered ice Ic to have (near) p o s i t i o n a l symmetry (order) of the 0 atoms but or 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 effect 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 , therefore the t r a n s l a t i o n a l modes are mechanically regular. However, since i n the course of a vi b r a t i o n Ay_ varies according to the l o c a l molecular orientations, then the. c r y s t a l t r a n s l a t i o n a l vibrations are e l e c t r i c a l l y i r r e g u l a r . 31 Whalley and Bertie ( 8 7 ) assumed that the dipole derivative could be s p l i t into a symmetric part, M', (corresponding to 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 part, M'', due to the H atom disorder. Then they showed that the molecular i n t e n s i t y of absorption has a part for 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 for a l l k 0 t r a n s i t i o n s due to M'1. Therefore they deduced that a l l t r a n s l a t i o n a l vibrations are i r active. In a subsequent paper Bertie and Whalley ( 8 8 ) used the above theory to describe the density of states i n of ices Ih and Ic. They assigned the 2 2 9 . 2 cm-"*" peak to degenerate longitudinal and transverse o p t i c a l modes at the zone center, the l 6 0 cm-"1" peak to the longitudinal acoustical mode of a zone boundary, and the 1 9 0 cm shoulder to the longitudinal o p t i c a l mode at the same zone boundary. They showed a density of states curve for ices Ih and I c . As w e l l , Bertie and Whalley ( 8 8 ) . found that v^RgO) shifted by 7 cm - 1 to lower frequency upon r a i s i n g the temperature from 100° to l68°K. They attrib u t e d the red s h i f t to exc i t a t i o n of hot bands. The r e s u l t s of v^H^O) for vitreous ice I are c o n f l i c t i n g ( 8 8 , 8 9 ) . Giguere and Arraudeau ( 8 9 ) indicated considerable band structure." (c) Raman spectra. Scattering from v^H^O) was reported by Val'kov and Maslenkova ( 9 0 ) with a medium in 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 Ih, I c , I I , I I I and I I . They reported a peak at -1 ' -1 225 cm i n ices Ic and Ih and at 151 cm i n ice I I . Cd.) Neutron i n e l a s t i c scattering. Spectra were reported by Prask and Boutin ( 9 2 ) for ice Ih and Trevino ( 9 3 ) and Renker and Blanckenhagen 32 (9*0 calculated the v spectra of ice I. The frequency di s t r i b u t i o n s c a l - culated and observed i n neutron work agree quite well with Bertie and Whalley's ( 8 8 ) predictions from the i r . (e) Libration. Hydrogen bonding also gives r i s e to hindered r o t a t i o n a l transitions i n the ices. For Ĥ O t h i s absorption i s seen from 1000 - hOO cm 1 -1 -1 and for D o0 from 750 cm to 350 cm . The r a t i o of v 0 for H-0 and D o0 would d a d d i d e a l l y be 1.1*1 for purely r o t a t i o n a l motion and 1.05 for purely t r a n s l a t i o n a l motion: The observed values l i e closer to 1.35• Blue's ( 8 5 ) treatment of Ĥ 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 interactions were considered. In such an approximation the l i b r a t i o n about the axis i s i r inactive. 2v Bertie and Whalley ( 9 5 ) , i n contrast, pointed out that the very existence of the v bands i s due to the strong coupling of the 3N l i b r a t i o n s of N molecules i n a mole of unit 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 ice 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 active. 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 necessarily the shape of the c r y s t a l l i n e vibration band. Bertie and Whalley ( 9 5 ) reported that the v absorptions of ices Ic and Ih are i d e n t i c a l . For HO they observed 5 features on v n between 900 and d R 555 cm for D̂ O they observed 3 features between 675 and 1+25 cm \, (However, the mulling agent used obscured the results i n some areas.) Similar bands were observed i n the high pressure ices ( 9 6 ) . 33 The ordered ice I I appears to obey the factor group s p l i t t i n g pre- d i c t i o n s with respect to v_. Bertie C86) suggested 12 v i r active modes. In f a c t , 16(9] features were observed between kJ5 and 1066 cm-"1" with a band center at 800 (593) cm - 1. As w e l l , Bertie and Whalley (96) suggested that a mode v D +• v may be active i n ice I I . - The l i b r a t i o n a l absorptions of vitreous, hexagonal and cubic ice I were reported also by Giguere and Arraiideau (89). For vitreous ice they re- ported features at 8 0 0 ( 6 0 0 ) , 8^0(635) and 900 (675) cm - 1. . In cubic and hexagonal ice I they observed only two features, 835(625) and 890(673) cm 1 . The two c r y s t a l l i n e modes were assigned to and + v^. For vitreous ice they suggested the C l i b r a t i o n was active due to the asymmetric e l e c t r i c f i e l d . The observed frequency of 800(600) cm 1 i s i n good agreement with the predictions 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 analysis based on an Ĥ Ô  model they deduced that the hydrogen bond bending force constant varies from 0.095 to 0 . 0 8 5 x 1 0 ^ dynes/cm between 93° and 273°K. This agrees with 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 previously by at least 5 groups. Giguere and Harvey (98) reported frequencies for v^, v 0 and v_ at 1 0 3 ° , 217° n d 3 and 268°K for Ĥ O and D̂ O. They observed solids formed by condensing the l i q u i d or vapour phase. Ice Ih (H^O'^nd D̂ O) single c r y s t a l Raman spectra were reported by Val'kov and Maslenkova (99) for several temperatures above 77°K. On the I 3 k basis of intense a^ Raman scattering and the s i m i l a r i t y to vapour phase scattering, they assigned i n d i v i d u a l and ice frequencies. That i s i n direct contrast to more recent work ( 9 5 ) which strongly coupled and into two separate but equally mixed bands. Val'kov and Maslenkova suggested that the r a t i o ^ o r ^ n ^ e so-^a- should be the same as for the vapour, as well as for D̂ O. They also observed other l i n e s i n the stretching region which may have arisen from combinations with l a t t i c e modes. Zimmermann and Pimentel ( 9 7 ) also reported the temperature dependences of and 3v R above 93°K. As the temperature was increased from 9 3 ° ; to 273°K they found that v and 3v^ decreased and v increased i n frequency. Thus the l 6 0 0 cm ^ ice band could not be 2 v n . As w e l l , they found that at n 93°K v 2 ( s o l i d ) < v 2(vapour). The most accurate study of temperature dependences i n ice was recently reported by Ford and Falk (100) for the vQH(HDO) and vor)(HDO) modes.? By pre- 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 Falk observed r e l a t i v e l y sharp HDO bands, the half-height width (Av ) was about 18 cm - 1 for v O T J(KD0) at 97°K. That i s s t i l l much wider than for ice, II:, On h i Av = 5 cm , where the H atoms are ordered. , • The widths of HDO bands i n ice I I are due to hot bands, overtones, and sum and difference bands. (Hot and difference bands should be removed near 10°K.) The widths of the HDO bands i n ice Ih are due to the above effects plus H atom disorder (irregular Hydrogen bond po t e n t i a l s ) . The problem of forming hydrated s a l t windows and not ice I was d i s - covered by Mutter, Mecke and Lutke (103) and was c l a r i f i e d by Schiffer-(104). Hydrated salt window absorptions are r e a d i l y distinguished from those of i c e . 35 (b) Infrared absorption' spectra. The' spectra of Ĥ O, HDO and D̂ O were studied i n d e t a i l by Hornig, White and Reding (105), Table 0.5. The fundamentals and were assumed to have reversed order i n energy from the vapour phase-order because of the stretch-stretch interaction constant. They also estimated that the b a r r i e r to proton jumping was 27 kcal/mole. Unfortunately, i t now appears t h e i r samples were of amorphous and not c r y s t a l l i n e i c e . (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 to anneal s o l i d samples formed by vapour condensation. They demonstrated the i r effects of annealin amorphous i c e , but did not study the phase transformation i n d e t a i l . Ice Ih spectra of Ĥ O, D̂ O and HDO were obtained by Haas and Hornig (106) at 83°K. They observed 2vOTI(HD0) and suggested that the b a r r i e r to On proton transfer exceeded 23 kcal/mole. However, they suggested that proton tunneling may occur, leading to broad HDO bands. On the other hand, they used very high concentrations (8-10%) of HDO i n Ĥ O and D̂ 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 pair of shoulder one on either side of the main HDO stretching band. Their r e s u l t s showed that the width of hydrogen bonded 0-JI stretching 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 Bertie and Whalley (95) i s the most comprehensive study of cubic and hexagonal (HO, HDO and D 20) ice I. Their re s u l t s were obtained at 110°K by the low temperature mulling 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-ray diffraction.--- 36 Bertie and Whalley reported that the i r spectra of ice Ih and Ic -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 to the absence of amorphous i c e . They rejected the interpretation of the bands i n terms of v^, v^, and v R on the basis of strong intermolecular coupling. For example, i n ice crystals the neighbouring vibrations were -assumed to couple with ,each other to form one broad, symmetric band: S i m i l a r l y a broad symmetric band formed. F i n a l l y they suggested the coupled-band could interact with the physically and energetically adjacent coupled-band to give two broad bands which were equal admixtures of v_L and v^; two hybrid v^-v^ bands. Bertie and Whalley suggested that different portions of these coupled, broad bands were i r and Raman active, accounting for the differences between the i r and Raman res u l t s . With respect to the widths of the ice I absorptions, they suggested that H atom disorder leads to l o c a l variations i n 0 atom positions 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 ) . Three other causes of the broad bands were also reviewed ( 9 6 ) . These were: 1) the occurrence of sum, difference and hot bands with l a t t i c e modes, 2) the occurrence of proton tunnelling and the re 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. Bertie and Whalley ( 9 5 ) discussed the 1 6 5 0 cm ̂  absorption as ar i s i n g from combined 2 v „ and v_ vibrations, but they pointed out that discussion i n terms of a unimolecular mode i s not meaningful. One must consider the Nv„ modes/mole of c r y s t a l . 37 D. The Present Approach, to the Ice Problem Three facets of the ice 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 results for ice 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 vitreous ice absorptions were observed and the vitreous-cubic phase transformation was characterized. Secondly, the temperature dependences of cubic ice I absorptions were observed i n order to make spe c i f i c corre- lations of v to R(0* •••()) and to discover the contributions of.hot olK bands to the band widths. Thirdly, data from the two above methods were used to confirm previous ice I band assignments-. ; CHAPTER ONE APPARATUS 1.1 The Perkin-Elmer 112-G Spectrophotometer The Perkin-Elmer 112-G instrument i s a high resolution single "beam spectrophotometer based on a double pass (model 9 9 ) grating monochromator. The monochromator employs a 75 lines/mm r e p l i c a echelette grating which i s blazed to r e f l e c t maximum int e n s i t y at 12u 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 situated between a glober source and the grating monochromator. The fore-prism f i l t e r monochromator consists of a 6 0 ° KBr prism mounted i n Littrow configuration. This monochromator arrangement gives an instrument resolving power of 0.5 cm or better. Spectral s l i t widths [calculated by Siegler's method ( 1 0 9 ) ] , are indicated on the appropriate spectra. Thermal radiation i s detected by a thermocouple or PbS sensor. However, only 2 n d pass radiation i s chopped at 13 cps and amplified..in a standard model 107 amplifier. The 13 cps e l e c t r i c a l signal 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. signal i s applied.to a conventional 10 mv Speedomax-G recorder. In the experiments to be described, the P.E. 112-G was used from 5000 to 550 cm-"'' with thermocouple detection i n a l l regions. The instrument was calibrated at each use with atmospheric H 90 and CO or with NH (g). 39 Low temperature experiments on ice are hampered i n the P.E. 112-G by the small sampling area and severe atmospheric absorption. The spectro- photometer was modified considerably to eliminate or reduce these and other d i f f i c u l t i e s . At the PbS detector mount a simple ellipsoidal-plane mirror system i s placed which produces a monochromatic source image i n free' space 50.5 cm from the exit s l i t s . A second detection unit (thermocouple,' focussing optics and pre-amplifier) i s mounted i n series with the added, o p t i c a l system. These modifications offer several advantages over standard P.E. 112-G sampling f a c i l i t i e s . For example, beam vignetting losses may be reduced and smaller samples may be used by placing the sample at the source image i n the new sample area. Also, concurrent c a l i b r a t i o n and sample observation i s possible 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 free 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 radiation striking,samples mounted i n the monochromatorexit beam. Tests indicate a 5% energy loss between the standard and modified detector configurations. The complete instrument, excluding the new thermocouple detector u n i t , i s placed i n a metal-plexiglass drybox to reduce background atmospheric attenuation from Ĥ O and CO^. The new detector unit has i t s own chamber, and sampling accessories are used to couple the two chambers. Spectrophoto- meter controls are easily operated outside the drybox by simple mechanical extensions. However, the grating drive and transmission are now located at the front of the instrument outside the drybox. A standard drybox a i r lock and rubber gloves permit the introduction and manipulation of conven- t i o n a l i r accessories i n the primary sample mount. The N 2(g) drybox 1+0 atmosphere i s circulated 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 ) to remove residual Ĥ O and CO^. When the c i r - culating 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 eliminates absorption from atmospheric Ĥ O but i s less effective i n reducing atmospheric CO^ absorption. To achieve maximum performance for fore-prism/grating monochromator assemblies of the P.E. 112-G type the two monochromators must transmit the id 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 just separate the various grating orders. 'This allows the grating monochromator to be scanned with reasonable performance over varying, li m i t e d frequency ranges which depend on the region of the spectrum. A mechanical servo system was designed to l i n k the two mono- chromators permitting them to be scanned i n near resonance. Lengths of certain scans (at acceptable energy levels) can be doubled by th i s arrange- ment. The design uses a variable r a t i o , b a l l and disc gearbox, reduction gears, and l i n k i n g driveshafts. A more powerful motor replaces the.- standard grating drive motor to compensate for 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 dispersion, the modification: improves the scanning cha 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 resolution ( l cm , double beam, n u l l recording grating spectrophotometer of conventional design.. A Nernst glower source and thermocouple detector are used I n con- junction with i n t e r f e r e n c e . f i l t e r s (which eliminate unwanted orders) and a Hi single pass grating monochromator. Two removable, self-contained mono- ehromators are rea d i l y interchanged, permitting rapid conversion of the scanned frequency range. Each interchange comprises the appropriate i n t e r - ference f i l t e r s and- a pair of gratings mounted back-to-back on a cosecant drive: One interchange i s used from H000 - 530 cm 1 and the other from 2000 - 220 cm 1. Grating 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. Spectral s l i t widths [calculated by the method of Roche ( l l O ) ] are indicated on the appropriate spectra. Some minor up-dating modifications have been made, i_.e_. i n s t a l l a t i o n of a larger ( 0 . 8 amp) Nernst glower and a l t e r a t i o n of the grating switching mechanism to prevent arcing. A l o c a l modification i s the provision of i n l e t and exhaust ports, i n the monochromator and source housings respectively, permitting the use of a c i r c u l a t i n g dryer (manufactured by P.E. Bodenseewerk for the P.E. 225 spectrophotometer). This drying unit i s remarkably effec- t i v e i n reducing atmospheric Ĥ O absorptions but i s less e f f e c t i v e with respect to CO,-,. The P.E. k21 was operated under the normal, recommended conditions. Specific conditions of operation are l i s t e d with the r e s u l t s . General con- ditions of operation are l i s t e d below. The automatic s l i t program was set at 2 x 10.00 which gave spectral —1 — 1 s l i t widths of 3.86 and 2.22 cm at 3300 and 800 cm respectively. Spectra were recorded on U.B.C. Chemistry Department charts, which were printed on Rolland Colonial Bond rag content paper. The charts have an inaccurate frequency scale but frequency markers were applied with the absorbance scale expansion switch to coincide with the frequency readout drum. The drum was read to ± 0 .05 cm 1 and the marker was applied to within + 0.1 cm 1 - 1 - 1 but could be read from the charts to ± 1.0 cm for 100 cm / i n . recording. U2 1.3 The Perkin-Elmer 301 Spectrophotometer The Perkin-Elmer 301 grating 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 to cover the instrument range from 650 cm "*" to lh cm-"'". Combinations of interference f i l t e r s , scatter plates and c r y s t a l choppers (Csl or BaF2) are used to 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, single pass model 210 grating monochromator i s used with 3 pairs of complementary, r e a d i l y ex- changeable 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 necessi- tates a defector with a large target. A golay sensor i s suitable and i s used over the f u l l instrument range. Signal to noise r a t i o s may be doubled i f the instrument i s operated i n the single beam mode by replacing a s p l i t aperature (l/2 image) I-Io mirror with a f u l l apperature I or Io mirror. An advantage of the P.E. 301 i s the chopping of source rad i a t i o n before i t enters the sample chamber. Therefore radiation o r i g i n a t i n g at the sample i s not amplified. 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 the 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 Liquid Nitrogen C e l l The low temperature c e l l which proved most useful for 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 previously h3 (112, 57) has a glass body and r e s e r v o i r , a brass sample block, and Csl or AgCl windows. Thermal contact between the sample window and sample block was improved with layers of s i l v e r conductive paint on contact surfaces. Temperature was measured with a fused Cu-constantan thermocouple soldered "to the brass sample holder base. Thermocouple wires and c e l l windows were sealed to the c e l l with Cenco soft-seal 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 for vacuum sealing when extremely low pressure i s not required. Although l i q u i d nitrogen coolant comes into direct contact with the brass sample block, the spectrophotometer source beam radiation raised the "block temperature to 83 t 3°K. Because of non-ideal thermal contact and low sample window thermal conductivity, sample temperature was considerably above that of the block. From melting point observations the sample window temperature was estimated to be 10°K higher than that of the sample block. Unless otherwise stated, a l l temperatures quoted i n t h i s work are not corrected for source heating. Two sample deposition tubes were used with t h i s c e l l , one of a l l - glass and the other of metal construction. Both were mounted with t h e i r t i p s 7mm from the sample window surface. At such a distance there are large heat losses (from the sample tube t i p to the window and cooling block) permitting sample condensation at the cold t i p s . Dangers of selective IL̂ O condensation or f r a c t i o n a t i o n of clathrate mixtures at the tube t i p s were avoided by using external heating on the stainless s t e e l tube, F i g . 1.1. B F i g . 1.1 The stainless steel- sample deposition tube: A - pyrotenax heater, B - Cu-Constantan thermocouple, C - deposition tube t i p , D - B - 1 9 a conical 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 . I 1+5 1.5 The Duerig-Mador Liquid 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 (112, 57) and i s similar i n design to that of Duerig and Mador (113). A p r i n c i p a l modification 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 to be rotated through 9 0 ° for sample deposition. Thermal contact between sample windows (Csl or polyethylene) and the Cu sample block was improved by painting the contact surfaces with s i l v e r conductive paint. Sample block temperature was measured with a Au-Co/Ag-Au thermocouple. . The thermocouple was calibrated at h.2°K and with 9 b o i l i n g l i q u i d s or slushes from 77° to 273°K. Actual sample window temperature was estimated to be 10°K higher than the temperature indicated with the thermocouple. 1.6 The Metal Liquid 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 to achieve the i d e a l clathrate condensation a l i q u i d nitrogen c e l l was constructed containing an evacuable sample chamber, Fig. 1.2. To help prevent fractionation i n the sample chamber, one window-is embedded i n the cold block and the other i s thermally insulated from the f i r s t by a stainless steel spacer ri n g (which provided the chamber body) and two t e f l o n gaskets. Only one window i s cooled to refrigerant 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 isolated sample chamber: A - Cu cooling block and "cold 1 window, B - Cu-Constantan thermocouple, C r- pyrotenax heater D - coolant reservoir, E - deposition and evacuation tube, F - pyrotenax heater, G - pressure, plate and stainless s t e e l screws, H - sample window and holder, I - sample chamber, sample port and t e f l o n gaskets. CHAPTER TWO METHODS AND MATERIALS 2.1 Water Samples and Clathration Materials Clathrate-hydrate guest molecules were either Matheson compressed gases, Fisher c e r t i f i e d reagents, or B r i t i s h Drug House analar reagents. Bromomethane ( 9 9 . 5 % pure), trichlorofluoromethane (99%), dichloro- difluoromethane ( 9 9 . 0 % ) , chlorotrifluoromethane ( 9 9 . 0 % ) and chlorine ( 9 9 « 9 % ) were used d i r e c t l y from t h e i r lecture b o t t l e s . Chloromethane ( 9 9 . 5 % ) was supplied i n a No. h cylinder 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, 9 9 . 9 % p u r i t y ) , iodomethane (C.R. 9 9 - 9 % ) , and broriioethane (C.R. 9 9 - 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 freezing and pumping off non-condensible impurities. .Bromine l i q u i d (Analar Reagent, 9 9 . 0 % ) was also p a r t i a l l y p u r i f i e d by freezing and pumping. Guest compound, purity was checked by i r vapour phase absorption spectra. Clathrate-hydrate host and ice I compounds used were Ĥ O, D̂ O, H 20 ( 5 . 9 % HDO), and D 20 {k.0% EDO). Before use the HgO water was d i s t i l l e d , de-ionized and f i n a l l y degassed by several cycles of freezing and pumping. D̂ 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 of 9 9 - 7 % ; D̂ O was degassed i n the usual way. Mixtures of D̂ O or H 20 with HDO were made by mixing 1*9.0 ml D g0 with 1.0 ml HgO and 1*9.0 ml HgO with 1.5 ml DgO. In both cases the isotopic impurity was almost a l l present as HDO at equilibrium. Residual H 20 (or D 20) was spectroscopically undetected. No quantitative analyses of the isotopic mixtures were under- taken. 1+8 2.2 Infrared Windows and Sample Mounts Choice of window material i s tempered by the necessary application of thermal stress and essential non-reactivity with applied samples. The l a t t e r property i s important i n studies of water containing compounds since, as Mecke (103) found and Schiffer (104) proved, t h i n hydrated layers may form on a l k a l i halide c r y s t a l s . Csl i s suitable for a l l cryostats used here since i t i s r e l a t i v e l y soft and d u c t i l e and accepts the considerable thermal shock. Only C l ^ * T^THgO samples reacted detectably with Csl windows. That experiment was repeated using an AgCl sample mount. S i l v e r chloride does not transmit as widely as cesium iodide over our range of i n t e r e s t , however AgCl i s soft and e a s i l y withstands thermal shocks. Also, i t i s apparently non-reactive to chlorine and bromine. C e l l windows and a sample support used i n the P.E. 301 v̂ , experiment were cut d i r e c t l y from commercial high density polyethylene (A powdered polyethylene was also available).. The windows were only used from 650 cm to 160 cm and through the temperature range 5°K to 200°K. The polyethylene was apparently non-reactive to the clathrate-hydrate mixtures investigated. 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 conductivity i s low and source heating may be high. To counteract source heating, sample supports were pressed from powdered polyethylene embedded with a brass or copper g r i d . The method consisted of placing a wire g r i d between two l i g h t l y pressed (7000 p s i , unheated) 0.20 g d i s c s , heating to the polyethylene flow temperature (130 t 5°K) under l i g h t pressure (1000 psi) and pressing to 15,000 p s i while cooling to less than 35°C. The r e s u l t was a low scattering p e l l e t with 58% transmission at 36l cm h9 and 1 7 1 cm \ Energy transmission could "be improved by reducing the effec- 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 Preparation of Clathrate-hydrates A. Preparation of Solid Samples Clathrate-hydrates with stoichiometries 1M'17 Ĥ 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 stoichiometric 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 1.2 cm test tube was added 0.01 moles of l i q u i d guest compound. The mixture was agitated and success- i v e l y immersed for about 30 sec i n an ice-water-sodium chloride bath ( 2 6 5 °K) and 30 sec i n a l i q u i d nitrogen bath. The sample was then warmed to a viscous state. The procedure was repeated u n t i l a uniform, white s o l i d formed—about 5 repetitions for each sample. Samples were stored over dry ice for a short time before use. Clathrate-hydrate samples were prepared by two other methods, but such samples were not investigated spectroscopically. For clathrates 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 ) was used with some modification: a preparation c e l l similar to Allen's was constructed. For clathrates 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 modifications.; A preparation c e l l of similar dimensions to the one above, but with provision for mechanical s t i r r i n g and l i q u i d guest addition, was constructed. Samples prepared by these two methods were also stored over dry ice and were analyzed with a gas burette. .• 50 B. Preparation of Stoichiometric Gaseous Mixtures There are a number of 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 ice phase must form a stable thermodynamic system i n the region k.2° to 200°K. Also, the method must maintain the clathrate stoichiometry, avoiding guest mole- cule loss by di f f u s i o n and d i s s o c i a t i o n — t h e equilibrium dissociation . 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 extinction 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 less. Deposition of water vapour or a gaseous stoichiometric clathrate mixture on a cold sample mount gives samples which s a t i s f y some of these c r i t e r i a (^3). The quantity of a stoichiometric 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 saturation vapour pressure of Ĥ O at the given temperature and the mixing bulb volume. The calibrated mixing bulb (including a side bulb) had a volume of 3.853 1 and contained 2.76 millimoles of HgO at 293°K and 1 7 - 5 3 Torr H 20. I f uniformly deposited on a t y p i c a l window with a surface area of 7 cm2, 2.76 m moles of Ĥ O would form a layer approximately 70y thick. A 3.853 1 mixing bulb obviously.- supplies enough sample for several deposits. I o The molar r a t i o s for the 12 A cubic structure are 1 guest: 5..75. Ĥ O and 1 guest: 7-67 H 20, while the corresponding r a t i o s for the tetragonal o and 17 A,cubic structures are 1 guest*8.6 HgO and 1 guest*17 Ĥ O. Clearly the numbers of guest mmoles required to combine with 2.76 m moles of H 20 are very small. Measurement of at best one-fifth of 2.76 ( 0 . U 8 ) mmoles of gas i n 3.853 1 at 20°C i s impractical due to the large error i n measuring 51 small pressure differences. Gaseous guest aliquots 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 into 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 for four clathrate structures. Clathrate mmole X P a r t i a l Pressure of Guest X : 2.76mm H20 3.853 1 bulb 0.1039 1 bulb 1 X • 5-75 H"20 0.48 3.05 Torr 117.10 Torr 1 X " 7.67 H~20 0.36 2.28 87.5I+ 1 X • 8.60 H20 0.32 2.01+ 78.32 1 X -17.0 H20 0.16 1.03 39.55 After the guest sample was expanded into the mixing bulb at 20°C, the chamber was saturated with E^0 vapour from l i q u i d previously isola t e d and degassed i n a side bulb. The system was equilibrated i n that state for ten minutes before the l i q u i d H20 was again isola t e d from the mixing chamber. Since the densities -of the gases i n the bulb varied over the range from 17.3 x 10 g/cm3 for H"20 to 13.3 x 10 g/cm for B r 2 and 6.30 x 10 g/cm3 for 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- tained for a minimum of 30 minutes before sample deposition. Suitably ; mixed gases were used either d i r e c t l y from the mixing chamber, for deposi- t i o n i n the isolated chamber of the metal l i q u i d nitrogen cryostat, or were transferred to a portable 3.0 l i t e r bulb and attached to a Duerig-Mador or Hornig-Wagner cryostat. 52 2.h Preparation of Infrared Specimens A. Low Temperature Mulling Clathrate-hydrates decompose i f mounted at 293°K by the usual spec- troscopic means, but they are metastable at 7T°K. Low temperature mulls of the clathrate-hydrates were prepared by an adaptation of the method Bertie and Whalley ( 1 0 7 ) used for the high pressure ices. Preparation of a suitable spectroscopic sample required approximately 0.5h. A few grams of s o l i d clathrate were placed in. l i q u i d nitrogen i n ; a mortar at 77°K and ground manually for 10 minutes. A small portion 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 to prepare a uniform suspen- sion. A second window was placed over the sample and secured i n place by a retaining ri n g . The window assembly was placed i n the sample block of a standard Wagner-Hornig nitrogen cryostat. The assembled cryostat was immediately evacuated. , Contamination of the sample by condensed atmospheric CO2 and H2O i s most l i k e l y to occur during cryostat assembly. Blank runs, and runs; with mulling agent only, made i t clear that l i t t l e impurity absorption was found even for the most intense Ĥ O stretching band [see also Whalley ( 1 0 7 ) ] . Recalling that the transmission spectrum of a mulled sample can :be distorted from the idealized absorption spectrum, one can have confidence i n the low temperature mull spectra only i f d i s t o r t i o n i s minimized,by • attention to the p a r t i c l e size of the sample and the re f r a c t i v e index of the mulling agent. Whalley ( 1 0 7 ) found that even for the most intense R̂ O stretching frequencies, where r e f l e c t i v i t y i s greatest, the spectra; of 5 mulls were i n good agreement with those of th i n films. 53 B. Isolated Chamber Condensation The sample chamber designed for approximate comparison of absorp- t i o n i n t e n s i t i e s of clathrate-hydrates was described i n d e t a i l i n section 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 to the sample were degassed by heating to 393°K while evacuating to 2.0 x 1 0 - ^ Torr for two hours.. Sample block temperatures from 300°K to a maximum of 393°K could be maintained with the coolant reservoir empty. Several blank spectroscopic runs were made to ensure that no impurities were being deposited. The sample tube heater was l e f t on but the sample cooling block heater was shut o f f , while l i q u i d nitrogen coolant was added to the reservoir. Twenty minutes after the coll e c t o r plate window had recooled to 83°K, the background spectra were recorded from 550 cm to 4000 cm \ No impurity absorptions were observed. For deposition the gaseous sample was expended i n short bursts ;down the heated sample tube into the sample chamber which was held at 83°K . after the method of Barrer and Ruzicka ( 4 3 ) . With the sample tube ;at . 3^3 0K and the sample tube heaters on, some heating of the stainless s t e e l spacer occurred which aided the thermal insulation of the second, "hot" window. The Csl 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 to 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 into clusters or diffusion out of the l a t t i c e completely. Subsequently, samples were annealed to temperatures between 1 6 0 - l80°K for 5 to 10 minutes. The sample chamber was not subject to pumping 5H and the sample tube was warmed to 3H3°K prior to annealing. The sample block heater was used only i n the i n i t i a l stages of annealing, ji.e_. up to 100°K. The warming was completed by passing a stream of dry, room tempera- ture Ng gas through the coolant reservoir. The rates of warming and re- cooling are described i n section 2.5. After recooling the sample block to 83°K, the sample tube heaters were shut off and the spectra were observed i n the desired range. The s p e c i f i c instrument conditions are l i s t e d with the r e s u l t s . •: C. Open Chamber Condensation Deposition of gaseous samples on a cold substrate, which was-., exposed to the cryostat c e l l body,. was used for both the Wagner-Hornig cryostat and the Duerig-Mador cryostat for observation on either the P.E. h21 or P.E. 301 spectrophotometers. Gases used were either vapours evaporated d i r e c t l y from l i q u i d Ĥ O, D̂ O or Ĥ O/D̂ O mixtures or were water/guest mix- tures prepared as described i n section 2 . 3 . Cryostats were degassed by evacuation for a minimum of 10 hours before cooling with l i q u i d nitrogen to 83°K. To ensure a minimum col l e c t o r plate temperature, the source beam was blocked and the cryostat was allowed to equilibrate for 15 to 20 minutes. Typic a l l y , samples were deposited as follows. Ten ml of sample (at a pressure at 8.7 Torr), were isolated i n the sample deposition tube. Several of these aliquots were passed i n bursts onto the colle c t o r plate at 83°K. The cryostat vacuum jacket was isolated from the pumping station during sample deposition to minimize d i s t o r t i o n of the sample gas stream. The HO v stretching region was monitored b r i e f l y after each burst ..to 55 determine the in t e n s i t y of absorption. We estimated that the sample thicknesses ranged from 0.6u for very t h i n samples to several microns for thick samples. The rates of deposition were estimated as 0.04 g/cm -h. Such deposits were subsequently annealed by the standard procedure. 2.5 D e v i t r i f i c a t i o n As was discussed i n the introduction, deposition of water vapour on. a l k a l i halide substrates held near 80°K has led to doubts of sample c r y s t a l l - i n i t y and confusion i n the interpretation of the various i r r e s u l t s . The situa t i o n was c l a r i f i e d by Beaumont, Chihara and Morrison ( 6 5 ) through cor- related heat capacity/x-ray d i f f r a c t i o n studies. Their work accentuated the differences i n sample c r y s t a l l i n i t y among the i r ice spectra of various authors ( 1 0 5 , 1 0 6 , 9 5 , 97) 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 ice I allotropes. ; In order to make comparative i r studies of ice I and clathrate-.; hydrates as a function of temperature i n t h i s work, one had to reproducibly form the ice I allotropes. However, no attempt was made to r e s t r i c t s e l f - annealing by l i m i t i n g deposition rates to that recommended by Beaumont et a l . — 0.04 g/h-cm^. That the samples did not undergo a high degree of self-annealing was demonstrated by the broad, featureless i r absorption bands observed immediately after deposition. Attention was i n i t i a l l y directed to annealing condensed, vitreous samples to the common ice phase, hexagonal ice I , whose transition-tempera- ture from cubic ice I l i e s between 200 and 250°K. The vitreous sample was warmed to the hexagonal t r a n s i t i o n at 5-0 to 1 2 . 5 deg/min from 83°K to 205 - 5°K (with the sample source beam off and no pumping i n the sample chamber). I t was recooled to 83°K at 50 deg/min after being held for 56 2 to 3 min at the maximum annealing temperature. Unfortunately, the samples were unstable above 195°K with respect to 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 to hexagonal i c e , further attempts to devit- r i f y at 205 ± 5°K were abandoned. Further extensive tests showed that t h i n films of Ĥ O could be annealed under vacuum to 185 + 5°K from 83 t 5°K (at between 5 and 1 2 . 5 deg/min with no pumping and the source beam off) , and maintained stable at l85°K for up to 5 minutes. The samples were successfully recooled at 5.0°K/min with l i t t l e loss of sample as detected by s l i g h t l y diminished absorption. According to the data of Beaumont e_t_al_. ( 6 5 ) t h i s should give a w e l l developed po l y c r y s t a l l i n e cubic ice sample, since the t r a n s i t i o n temperature was w e l l exceeded and the rate 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;; tempera- ture, 150°K. Before spectroscopic investigations began, the t h i n films were thermally equilibrated for 20 minutes with the sample source beam on. Discussion of the nature of samples formed,, by condensing and anneal- ing stoichiometric gaseous mixtures i s l e f t u n t i l Chapter 6. : 2.6 Temperature Variation Methods The purposes of t h i s work are to study the variations of ice and clathrate spectra as a function of temperature and to show that gas con- densation and d e v i t r i f i c a t i o n gives legitimate c r y s t a l l i n e samples. The same sample heating and i r observation techniques were used for both vitreous and c r y s t a l l i n e sample studies. : 57 A l l the samples studied.as a function of temperature were formed i n either 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 section 2.4(c). The nitrogen c e l l was mounted only i n the P.E. 421 and was used for preliminary observations between 8 3 ° and 200°K. The helium c e l l was mounted either i n the P.E. 301 or i n the P.E. 421 spectro- photometer, and was used for the detailed studies between 4 . 2 ° and 200°K. Two methods of warming these cryostats were used: l ) natural, unforced warming due to radiative and conductive heating, and 2) warming with a stream of N (g). The helium c e l l was allowed to warm from 4? to 83°K by the natural heat i n f l u x after 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 reservoir. The nitrogen c e l l was held at 4 to 8 constant tem- peratures (± 3°K) for d e v i t r i f i c a t i o n studies (at 83°K Ng(liq) was used and at higher temperatures 1-2 ml of N 2 ( l ) were added to the empty reservoir at appropriate intervals ) . Sets of spectra were obtained by continuously recycling the spectro- meters over the spectral range desired as the c e l l warmed continuously, or spectra were recorded at certain successively higher constant (t 3°K) tem- peratures. Some sets of spectra were also recorded at successively cooler constant temperatures (t 3°K) from 190 - 10°K to 83°K after d e v i t r i f i c a t i o n 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 . CHAPTER THREE ICE I: EXPERIMENTAL AND RESULTS This chapter i s comprised of four main sections. The f i r s t section contains the results from temperature v a r i a t i o n studies of vitreous ice I — observations of the vitreous-cubic phase transformation. The second section contains the results from temperature v a r i a t i o n studies of cubic ice I — observations of Av/AR for c r y s t a l l i n e i c e . The t h i r d section uses the results of sections one and two as an aid i n assigning the> ice 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 vitreous-cubic phase transformations: exhibited diminishing oligomeric peak heights (I) and i r r e v e r s i b l e peak frequency and half-height width s h i f t s . A. Experimental Two vitreous ice 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 (section l.h) Sample A was deposited on Csl at 82 - 3°K, warmed from 8 2 ° to l69°K i n f i v e stages over 105 min and was annealed to a maximum temperature of 185 t 3°K. Sample B was deposited on Csl at 8 l ± 3°K, warmed from 8 l ° to l 6 l ° K i n four stages over 120 min and was annealed to a maximum temperature of 182 i 3°K. Seven spectra were recorded for each of samples A and B during d e v i t r i f i - cation. 59 The basic spectrophotometer conditions were described previously (section 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 with 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 also purged. B. Results of D e v i t r i f i c a t i o n Infrared absorption spectra representative of samples A and B are shown i n F i g . 3.1 (top). Frequency and half-height width (Av ) data were derived independently, but by the same methods, for the two sets of spectra. Peak absorptions were determined (to within i l O cm "*") at the intersection of l i n e s along the band sides, while shoulders were determined (to within i l 4 cm at the point of minimum slope. Band heights were measured on the absorbance scale ( i ) from the baseline and Av^ was measured at (1/2). ( i ) The Effect of D e v i t r i f i c a t i o n on the Peak Maxima The vitreous Ĥ O ice I absorption maxima are plotted i n F i g . 3.2 as a function of increasing 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 D̂ O ic e and HDO bearing ice were not observed i n d e t a i l , data from such samples, immediately before and after d e v i t r i f i c a t i o n , are included i n Table I I I . I for comparison to Ĥ O data. In F i g . 3.2, the transformation temperature ranges are indicated for v^, and + v^,. Transformation was assumed to have begun at the onset of peak s h i f t and was assumed to have finished upon reversal of peak s h i f t d i r e c t i o n . 4 0 0 0 3 0 0 0 2 0 0 0 Frequency c m - 1 i 1000 F i g . 3.1 Representative spectra of vitreous and cubic ices at various temperatures. - Top:.. . A....-, ..cryostat.. background at 83°K.. (compensated),. B - H 20 ice I y at 8 3 ° , C - sample B annealed to l85°K and recooled to 83°K (cubic i c e ) , D - sample ' G at T°K, -and E -- cubic ice' C H 2 0 ( 5 . 9 W HDO)) at 83°K; - Bottom: A - cryostat background, B - D 20 (U.0% HDQ) vitreous ice at 83°K, C - sample B annealed to 185°K, cubic ice at 83°K. 0 rr D H '< tK l±J UJ I80- 140- IOO- 180 ' 140- IOO 2 2 2 0 2 2 3 0 3 3 3 0 3 3 5 0 OA 1590 16IO 1630 1 6 5 0 1570 32IO 3 2 3 0 1 8 0 - 140 IOO 8 0 0 8 2 0 8 4 0 3145 F R E Q U E N C Y C M 3165 3 3 7 0 3 2 5 0 3185 -I F i g . 3.2 Shifts of Ĥ O frequencies during the vitreous-cubic ice phase transformation and. subsequent behaviour of cubic i c e . The f u l l c i r c l e s and triangles 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 after annealing. OA H 62 Table I I I . I The frequencies of cubic and vitreous ice I at 82°K, t h e i r differences, the transformation range and the cubic ice absorptions temperature dependences. H20 (D20) Ice Iv 82°K Ice Ic 82°K Av Ic-Iv 82°K Transformation Temperature Range Ice I c Av/AT -1 cm -1 cm -1 cm + 5°K cm -1/°K V1 + VT 3367 ± (2k99) 7 331*0 + (21*65) 7 -27 (-3U) 130 - 11*5 0.26 + 0.05 (0.16) V3 3253 ± (2436) 5 3217 ± (21*13) 5 -36 (-23) 125 - ll*5 0.20 (0.13) v l 3191 ± (2372) 7 311*9 ± (2321) 7 -1+2 (-51) 120 - ll*5 0.25 (0.18) 3v R 2220 + ( 1 6 1 7 ) 5 .2235 ± .(1635) 5 +15 (+18) 115 - 130 -0.11 (-0.11) 1660 ± 5 ; l60l+ + 5 -56 115 - 130 0.36 v 2 1570 (1212) 1570 (1191*) (-18) (0,11*) V 81*6 1 ( - - ) 7 881 + :(66l) 7 +35 (--) 115 - 130 - 0 . 1 9 (-0.16) VR 802 ± ( 6 0 0 ) 5 833 ± ( 6 2 7 ) .780 + 5 7 +31 (+27) 115 - 130 - 0 . 1 8 (-0.12) 675 ± 7 . : 690 ± 7 +15 535 ± 7 570 ± 7 +35 Vip 212.8 + 1 .227.8 + 5 +15 HDO v OH 3301* + 1 (21*37) 792 ± 1 : 3266 + 1 -38 (2kh2) (21*16) (-21) ( 2 3 9 2 ) •• 85!+ ± 1 . 5 — 819 + 0 . 5 +27 0.20 ± 0.005 (0.123 ± 0.005) -O.I5I+ t 0.022 -0.11*7 ± 0.012 63 There are f i v e important effects to notice: l ) between 1 1 5 ° and l45°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 reversal 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 vitreous ice 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 ice I. These effects can be seen i n Fig. 3.2 for the v^(E^O) data. The f r e - quency was constant up to 125 i 5°K, and shifted i r r e v e r s i b l y by 36 * 2 cm - 1 to lower frequency between 125 t 5 and 142 t 5°K. The frequency attained a po s i t i v e , reversible temperature dependence of +0.23 cm~V°K above l42°K. Subsequent warming and cooling cycles revealed a sample with an approximately linear frequency-temperature dependence between 82°K and l80°K. The'remain- ing absorptions of ice 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 exhibited p o s i t i v e , and a l l l i b r a t i o n a l modes exhibited negative temperature dependences after d e v i t r i f i c a t i o n . ( i i ) Oligomeric H 2 O Absorptions In addition to a l l the expected vitreous ice I absorptions, weak ab- sorptions were observed near the frequencies previously reported ( 1 1 5 ) for oligomeric HgO and D 2 O . Weak peaks ( 0 . 0 1 abs units) were found near 3 6 9 0 cm - 1 i n H 20 and 2720 cm - 1 i n D 20 and HgO shoulders near 3647 cm - 1 (Fig. 3 . 3 ) . They persisted only up to 125 1 5°K and did not reappear upon recooling the sample. Half-height widths were between 15 and 20 cm No detailed study was made for oligomers, but data from several samples are compiled i n Table I I I . I I . F R E Q U E N C Y C M " 1 3 9 0 0 3 7 0 0 3 5 0 0 o . o - 0.4- 0.5- 2 9 0 0 2 8 0 0 2 7 0 0 2 6 0 0 2 5 0 0 F R E Q U E N C Y C M " 1 Fig. 3 .3 Oligomeric HgO and D 2 O absorptions i n vitreous ice I at 83°K: l ) vitreous H 2 O i c e , 2 ) cubic H 2 O i c e , 3) vitreous D 2 O i c e , h) cubic D 2 O i c e . The features were more or less accentuated depending on the deposition rate. 65 Table I I I . I I Oligomeric HvpOCDgO) and V3 i r absorptions seen for vitreous ice I samples before and during warm-up. The V3(H"20) absorptions were weak peaks and the v;j_(H20) and V3(D20) absorptions were weak shoulders. One V3(D20) absorption i s given i n brackets. H 20 (D 20) Temperatur e of Observation, °K 82 85 94 110 125 140 -1 -1 -1 -1 -1 -1 cm cm cm cm cm cm V 3 3692 3 6 8 7 ( 2 7 2 4 ) 3689 3690 3690 — 3677 3658 3674 V 1 — 3637 3650 3647 — — — — 3640 • ( i i i ) The Effect 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 > + VT^' ^ V 2 ' ^ V F J a n <^ ̂ VR' VR + VT^ a r e s n a r P e r i n cubic ice I than i n vitreous ice I. Half-height widths for these com- posite bands from the sets of H 2 O spectra (samples A and B) were measured as a function of temperature, Figs. 3 . 4 and 3 . 5 . [The large scatter i n the data arises from several sources: l ) the choice of baseline (± 2 cm "*"), 2) the error i n assessing I and TJ- I f° r intense .peaks (± 5 cm "*"), and 3) atmospheric attenuation or d i s t o r t i o n of the V2 band.] The parameters are compiled i n Table I I I . I I I . LLJ D h < LLJ Q_ LLJ h Az/ 2 150 - 1 0 0 - 7 0 180 A A A z / A O A A Q O 1,3 , H - T A A • « 4 o May 2 9 A May 3 0 2 0 0 2 2 0 ~i r 2 7 0 3 0 0 I ' 1 1 1 1 3 5 0 4 0 0 H A L F - H E I G H T W I D T H C M " 1 F i g . 3.H The s h i f t s of H20 half-height widths for the composite H20 bands (v R , vp+vrp.) and ( v l s V3. V I + V T ) during the vitreous-cubic ice transformation' and subsequent" to"'annealing. Solid c i r c l e s and triang l e s are for the" uhannealed sample warm-up. Open 'circles and triangles are for the annealed sample warm-up. A z / 2 ( z / 2 / 2 z / R ) - A 50 - A ••. .AO A *\o '• A .•j OO - •"" A A • -/ * ^ / O / 4/ / / A / / / - O May 2 9 A May 3 0 •• * A / • A A A O TO - 1 I " - T i - - T — r 1 —1 1 1 1 280 300 350 H A L F - H E I G H T W I D T H C M " 1 g. 3.5 The s h i f t s of half-height width for the composite H 20 (v 2, 2V R) hand during the vitreous-cubic phase transfor- mation and subsequently for cubic ice I. S o l i d points were obtained during vitreous sample warm-up from 8 3 ° to l85°K. Open points were obtained from annealed samples. 68 Table I I I . I l l The half-height widths of the vitreous and cubic R̂ O ice composite bands at 82°K and t h e i r temperature dependences for cubic ice I. Composite Vitreous Cubic Difference Transition Band A J-/2 A vL/2 A vL/2 Temperature 82°K . 82°K 82°K . Range H 2 0 cm -1 -1 cm -1 cm °K ( v 1 , v 3 , v x + v T) 322 + 7 287 ± 5 -35 115 ± 5 - 130 + 5 ( v 2 , 2 v R ) .350 10 365 ± 10 +15 115 ± 5 - 140 5 ( VR' VR + V 220 + 5 1 9 5 + 3 -25 115 ± 5 - 150 + 5 During warming from 82°K the half-height widths of vitreous ice 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 cycles showed that the cubic ice spectra half-widths s h i f t e d r e v e r s i b l y and that the vitreous and cubic data agreed above 150°K. There are s p e c i f i c differences among the three sets of composite bands (see Figs. 3.4 and 3.5). These are as follows: l ) the stretching band Av ̂ increased, 2) the bending band Av^ decreased and 3) the l i b r a t i o n a l band Av 3 5 appeared to increase with increasing temperature. Also, the half-height 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 to decrease. Annealing effects on v^HgO) were not observed i n d e t a i l , but the differences between vitreous and cubic i c e at 83°K were measured. The data are 62.8 cm and 23.2 cm for vitreous and cubic i c e . Also, the 69 absorbance of Vp(cubic), I = 1.285, was almost exactly double that of Vrp(vit.). The vitreous V^(H 20) absorption features were: a peak at 2 1 2 . 8 t 0.5 cm"1'and fa i n t shoulders centered at 301 t 3 and 271 + 3 cm"1'. 3.2 Temperature Dependence of Cubic Ice I Absorptions A. Temperature Dependence of HDO Absorptions The four observed HDO absorptions provided the best measurements of band parameters as a function of increasing temperature i n cubic ice I. ( i ) Experimental • Three samples of D20(4.00% HDO) and two samples of H20 (5-9W HDO) were prepared (section 2.4(c)) and observed i n the l i q u i d helium c e l l (section 1.5). Samples C(l,2,3) were deposited at 85 1 3°K on C s l , warmed from 8 5 ° to l87°K i n 9 minutes, annealed at 187 t 3°K for 2 minutes and were recooled to 84°K i n 4 minutes. The r e s u l t i n g cubic C samples were then cooled to 4.2°K and observed for 3 hours before warming began: Warming from k.2°K to 200°K required 6-8 hours. Samples D(l,2) (5-94$ HDO i n H 20) were deposited at 83 t 3°K on C s l , warmed to 188 ± 3°K i n 8 minutes, annealed at 188 ± 3°K for 4 minutes and rap i d l y recooled to 83°K. Samples Dl and D2 were then treated as i n C above. During warming sets of P.E. 421 spectra were recorded for each sample under i d e n t i c a l spectrophotometer conditions. The basic spectrometer con- ditions were the same as those for samples A and B (section 3.1 a) with small var i a t i o n s . For example, HDO peaks were recorded at 20 cm "Vin or 2 cm "VdiVj and a 10 cm path gas c e l l ( i n the reference beam) was used with the Bodenseewerk unit for e f f e c t i v e instrument purging. Among the three TO sets of C sample spectra, frequencies were reproduced to within t 2 cm 1 at 1T0°K and ± 1 cm - 1 at h°K, 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 l 6 0 ° or h°K. Typical HDO spectra were shown i n F i g . 3.1. ( i i ) Results of Warming Cubic Ice Containing HDO Frequencies, half-height widths and absorbances were obtained as i n section 3.1(b). However, to i n h i b i t personal systematic bias the spectra were analyzed randomly with respect to temperature and during analysis no reference to temperature was permitted. Because of 2 cm ^/div recording, HDO peak frequencies were- read to ± 0.5 cm 1. No attempt was made to subtract the 3v (HpO) weak absorption from v (HDO) absorption and consequently K ^ OD V Q^(H D O) frequencies- are s l i g h t l y low. Baselines for absorbances and h a l f - height widths were drawn from 3391* to 31^0 cm - 1 for v Q H(HD0) and from 2H80 cm"1 to 23^0 cm - 1 for v Q r )(HD0). (a) HDO frequencies. The behaviour of vr,TJ(HD0) frequency with i n - creasing temperature i s shown i n Fig. 3.6. The data were derived from one set of spectra during a single warming period. Errors i n instrumentation and i n the methods of data evaluation l i m i t e d the precision to t 1 cm 1. Pertinent parameters from Fig. 3.6 are compiled i n Table III.IV., The low temperature l i m i t i n g frequency was obtained by extrapolating the data to 0°K. Although the data are non-linear, they can be approximated by two straight 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 "freeze-in" temperature was chosen as t h e i r point of intersection. There i s a s l i g h t indication of irregular behaviour between U5° and 70°K (Fig.3.6). Sample sublimation above l80°K did not appear to affect the frequency data. z^(HOD) Frequency cm-1 3 2 6 0 3 2 7 0 3 2 8 0 3 2 9 0 3 3 0 0 2 8 0 - 6 0 - 4 0 - 2 0 - > CD 2 0 0 - :̂ CO 8 0 - CD CD 6O- C N CD Q 4 0 - CD 2 0 - D O I O O - _̂ CD A C 8 0 - TE N 6O- 4 0 - 2 0 - O - •4 ^ D ( H O D ) o this work ° Ford and .Falk • this work • Ford and Falk 2 4 I O 2 4 2 0 2 4 3 0 2 4 4 0 2 4 5 0 CHOD) Frequency cm -1 Fig. 3.6 The s h i f t s of HDO stretching frequencies for cubic ice I. The temperatures are not corrected for 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 for comparison. —1 H 72 Table I I I . I V The low temperature behaviour of the HDO stretching modes i n the H 20 and D 20 environments of cubic ice I , v Q H ( H D 0 ) v 0 D ( H D 0 ) Low Temperature Limit -1 cm 3263.5 - 1 2 4 1 2 . 0 + 1 Ratio v 0 H / v Q r ) 1.354 + 0.001 Linear Low Temperature Dependence cm _ 1/ 0K 0.047 ± 0.005 0.04T-± 0.005 Linear High Temperature Dependence cm _ 1/ 0K . 0.200 t 0.005 0.123 ± 0.005 "Freeze-in" Temperature °K 80 + 5 68 + 5 I r r e g u l a r i t i e s °K 45 : - 70 ^60 Behaviour of V Q D ( H D 0 ) i s shown i n F i g . 3.6 and some parameters are compiled i n Table I I I . I V . The comments made above concerning V Q ^ ( H D O ) apply equally well to v^(HDO). The peak and shoulder near 800 cm i n the samples of DgO (4.0% HDO) [tracing C, bottom of Fi g . 3.1] were assigned to HDO l i b r a t i o n s , v R ( H D 0 ) and v o ( H D 0 ) + v m(D o0) respectively. (For ease of notation v_ + v_ i s designated R 1 2 n 1 v '.) Temperature variations 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 positions are z/j Frequency cm-1 2 2 0 2 2 5 2 3 0 180- • 1 „ 1 — . 60- • 0 • 40- . 0 • • c > Kel  20- • 0 • • • en • • 0 • Q) • • Q) _̂ 100- • 0 • cn Q) • 0 • O • 0 0 CD • 0 • 80-ur • 0 0 • • • • 0 °0 • CD 60- • 0 0 • a • 0 0 • E • • 0 •• Te • • 0 0 • • 4 0 - • 0 0 • • 0 • - 0 • % g o g • 20- • ^ T ( H z O ) • a • - z/ R ( H O D ) - i / R l ( HOD ) •• 1 1 O - 1 , , 1 -1 1 1 T • • 1 u i  1 1 1 1  1 1   1 8 0 0 8 IO 8 2 0 8 3 0 8 4 0 8 5 0 86C vR Frequency cm-1 Fig. 3.7 The s h i f t s of v R ( H D O ) , v r ' ( K D 0 ) and V T(H20) for cubic ice I during, warm-up. The l i b r a t i o n a l shoulder v R ' ( H D O ) i s assigned as v R ( H D O ) + V T(E>2 u)' Temperatures are uncorrected for source heating. 74 Table III.V The low temperature behaviour of the HDO l i b r a t i o n a l modes in cubic ice I for d i l u t e solutions of HDO i n H 2 O and D 2 O . vR(HDO) vR(HDO) + v T(D 20) Low Temperature Limit cm 1 8 2 3 . 3 ± 0 . 5 856.2 ±1.5 Linear Low Temperature Dependence cm" /°K < -0.02 < -0.04 Linear High Temperature Dependence cm /°K -0_.l4T ± 0.012 -0.154 ± 0.022 "Freeze-in" Temperature °K 55 t 5 65 ± 5 I- I r r e g u l a r i t i e s °K. 105 - 120 d i f f i c u l t to determine accurately, v ' data have a higher error than v„—in th i s case ± 1.5 cm Spectra and data were obtained as i n section'3.1. (b) HDO half-height widths. The v^„(HD0) and v.^(HDO) half-height OH OD widths, Fig. 3.8, were obtained from the same sets of spectra as were the frequencies i n the preceding section. Details of the plots are compiled i n Table III . V I . h -1 Errors i n Av.^HDO) (± 0.75 cm ) resulted from l ) inaccuracies-in OH assigning baselines (± 0.005 absorbance), 2) errors i n estimating 1/2 I for I = 1.0 absorbance (± 0.01 absorbance), and 3) errors i n estimating.widths 2 8 0 6 0 1 4 0 2 0 > CD en CD Q 2 0 0 H 8 0 j 6 0 - 4 0 - 2 0 • CD D O IOC- CD Q. 8 0 -E 6 0 H 4 0 - 2 0 - o- 2 0 • • i ? AZ/o20(HOD) 3 0 * (HOD) O H 4 0 M [o] Sublimation • • Ford and Falk • o this work 5 0 6 0 Half-height width cm-1 Fig'. 3.8 The s h i f t s of HDO stretching-modes half--height widths during warm-up of-cubic ice I. These data were obtained from the same spectra as were the frequencies of Fig. 3.6. Temperatures are uncorrected. 76 Table III.VI The low temperature behaviour of the HDO stretching modes half-height widths for HDO i n H20 and D20 cubic ice I. vOH(HDO) v 0 D(HD0) ; Low Temperature Limit -1 cm 35.5 t 0.75 23.5 ± 0.75 Ratio Av Q H/Av 0 D 1.51 Linear Low Temperature Dependence cm_1/°K < 0.02 ' < 0.03 Linear High Temperature Dependence cm_1/°K 0.066 '+ 0.005 O.Okk t 0.005 "Freeze-in" Temperature °K 87 ± 5 105 ± 5 (t 0.5 cm ). Because of sample sublimation, data for A V Q ^ ( H D O ) obtained above 190°K do not extrapolate into those obtained at lower temperatures. h —1 Errors i n AvQI)(HD0) (estimated to be ± 1.0 cm ) resulted from l ) inaccuracies i n assigning baselines due to an underlying 3v̂ (H,_,0) absorption (t 0.01: absorbance),, 2) errors i n estimating 1/2 I for I = 0.70 absorbance (t 0.005 absorbance), and 3) errors i n estimating widths (±0.5 cm - 1). In both cases above the H D O half-height widths were quoted and plotted only to 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 errors of ± 0.01 and ± 0.005 abs. units respectively) from consistent baselines on the same sets of spectra as were frequency and h a l f - height width. Absorbance data ( i ) are plotted 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 underwent a r e l a t i v e l y smooth, continuous decrease from 28° to l'90°K. Data obtained with the sample above l'90°K indicate a sharp decrease i n I as the sample sublimed. No estimate was made of cummu- l a t i v e sample loss due to sublimation during the whole experiment. A s l i g h t , concave discontinuity centered at 125°K appears i n an otherwise convex curve for- -these data. The data appear constant below 35°K in d i c a t i n g I (v^(HDO)) varied by less than -0.24 x 10 absorbance/°K. Table I I I . V I I The low temperature behaviour of the HDO stretching modes peak heights for cubic ice I . . l(v_„(HD0)) I(v--CHDO)) Low Temperature Limit absorbance Linear Low Temperature Dependence absorbance/°K Linear High Temperature Dependence absorbance/°K "Freeze-in" Temperature °K I r r e g u l a r i t i e s °K 0.945 -O.69 x 10' -2.26 x 10 79 ± 5 130(?) . 0.540. -0.24 x 10' -1.07 x 10 7 6 + 5 125 200- [•] [•] o 150- LLI c r D < 100- UJ a. LLI h 50- O o I (z/ (HDO )) O D • I (zv (HDO)) O H ' o o f . o 0.2 0.4 0.6 0.8 I A B S O R B A N C E F i g . 3.9 The s h i f t s of the HDO stretching mode peak heights or absorbances ( i ) during warm-up of a cubic ice I sample. The I data were obtained from the same spectra as were the frequencies and Av of Figs. 3.6 and. 3.8. 79 B. Temperature Dependence of H20 and D20 Absorptions Eight HgO and D20 absorptions provided less accurate measures of the primary spectral parameters than the three HDO absorptions, but they did y i e l d information on cubic ice I. ( i ) Experimental Five sets of spectra from f i v e specimens were recorded on the P.E. 421 or P.E. 301 spectrophotometers i n the l i q u i d helium dewar. Details of sample composition and preparation are given i n Table I I I . V I I I . General H20 absorptions were: observed i n samples E and F and t h e i r results were combined with those of cubic samples A and B. General D20 absorptions, were observed i n samples H and I and t h e i r results were combined with those of sample C. Samples E, F, H and I were observed on Csl i n the P.E-. 4 2 1 . The v^HgO) absorptions were observed i n a separate sample (G) with;, poly- ethylene windows on the P.E. 301. c P.E. 421 function settings were again i d e n t i c a l within one set pf spectra and as consistent as possible between samples. Specific conditions were given i n section 3.1. Only small alterations i n instrument purging, reference beam attenuation and o p t i c a l wedge settings were made. The P.E. 301 was used i n the I / I Q mode between 666 cm 1 and ;l60, : cm 1 with Bodenseewerk purging and no evacuated reference c e l l . Spectra were scanned at 40 cm "Vmin. and recorded at 4.4 cm "Vdiv. Spectral s l i t widths varied but were usually less than 4 cm \ 4 Table I I I . V I I I Details of depositing and annealing of H 2 O , D 2 O and HDO bearing ice I samples. Sample ;, 1 E H 20 F H 20(D 20) G H 20 H D 20 I D 20(H 20) Deposition Temperature (°K) 85 85 85 85 85 Time to warm from 85°K to l85°K (min.) ••. 12 15 17 17 15 Maximum annealing Temperature (°K) 186 183 187 185 180 Time maintained at maximum annealing temperature (min.) 2 3 2 1 2 ' Time to cool from l85°K to 85 °K (min.) 5 4 4 5 6 Time to cool from 85°K to 8°K (min.) 30 24 18 (25°K) . 21 18 Time maintained at 8°K (min.). 245 170 269 (25°K) 210 1 2 3 Length of warmup run (min.) 243 166 433 920 348 Co o 81 ( i i ) Results of Warming H 20 and :D20 .Cubic :Ice I Frequency data were obtained as i n section 3.IB. The sets of spectra were analyzed randomly with respect to temperature as i n section 3 . 2 A ( i i ) . Each complete set of spectra was analyzed one band at a time. Because of the breadth of H 20 and D 20 bands, frequency data were accurate only to t 2.5 -1 cm (a) Fundamental H 20 and DgO frequencies. The v-j frequencies are plotted as a function of temperature i n F i g . 3.10 and some plot parameters are compiled i n Table I I I . I X . From F i g . 3.10 and Table I I I . I X i t i s apparent that l i q u i d nitrogen 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 5 1 ° and 83°K since a sudden s l i g h t r i s e i n cryostat pressure (from traces of condensed residua l 0 2 and N 2) caused heat losses between the nitrogen sh i e l d and the helium dewar. - 6 - 6 Although the pressure rose only from 6.8 x 10 Torr to 15 x 10 Torr and -6 dropped to 8.2 x 10 i n 2 - 3 minutes, the pressure r i s e was s u f f i c i e n t to rapid l y warm the helium dewar and sample block. The frequency variations during sample warming are plotted i n F i g . 3.11 and some d e t a i l s of the behaviour are given i n Table I I I . I X . For V 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 20) a high scatter of points did not permit evaluation of low temperature depen- dence. No data was obtained between 5 1 ° and 83°K for the same reasons as with v^, a rapid pressure r i s e . Helium and nitrogen c e l l v 2 data do not agree (Fig. 3 . 1 2 ) . Details of the plots are given i n Table I I I . I X . Data for three helium c e l l "samples and two nitrogen c e l l samples are plotted (including unannealed sample data at 2 0 0 ' o 150 UJ cr D <t IOO or uj n UJ 5 0 h z/ ( H O) 3 2 o o 82 3 2 3 0 2 0 0 0 150 111 or D £ , 0 ° ' or UJ o. UJ h 5 0 - o- ^3(D20) 24IO 2 4 2 0 2 4 3 0 FREQUENCY CM - i F i g . 3.10 The s h i f t s of cuMc ice I during warm-up. open c i r c l e s represent data from experiments between 8 3 ° For H 20 the and l80°K on a Hornig-Wagner a l l - g l a s s c e l l , are uncorrected for source beam heating. Temperatures Table III.IX The temperature dependences of cubic ice I H?0 and Dp0 vib r a t i o n a l absorptions. Low temperature Low temperature High temperature Freeze-in l i m i t dependences dependences temperature H20 -1 cm cm  1/°K cm 1/°K °K V + VT 333*+ + k •• 0.08 ± 0.05 + 0.20 ± 0.08 80 + 10 V 3 320*1 ( 3 2 1 5 + + 2 5) 0.03 ± 0.03 + 0.17 ± 0.05 (+ 0.19 ± 0.0*0 70 + 10 V l 3133 + 3 + 0.3k ± 0.03 65 + 5 3 VR 2 2 3 9 + 3 < - 0 . 0 9 - 0.12 ± 0.03 70 + 10 v 2 / 2 v R 1562 ( 1 6 0 5 + + h 10) < 0.1k ( 0 . 3 6 ± 0.10) v ' R 8 8 1 + 7 — - 0.19 ± 0.08 80 + 20 V R 832 + 5 — - 0.18 ± 0.06 75 + 10 VT 2 2 9 . £ ! ± 0.75 - 0.102 ± 0.012 95 + 5 CO OO Table III.IX (Continued) Low temperature low temperature High temperature Freeze-in l i m i t dependences dependences temperature D 20 -1 " cm cm  1/°K cm 1/°K °K V l + VT 2464 + 3 — 0.17 ± 0.05 80 + 30 V 3 2 4 1 3 + 4 < 0.06 0.13 ± 0 . 0 4 100 + 20 V l 2320 + 5 — 0.19 ± 0.03 70 + 10 3 vR 1 6 3 7 + 3 <-0.07 -0.11 ± 0.03 60 + 5 V 2 v R 1 1 8 9 + 2 0.13 ± 0.03 0.08 ± 0.05 50 + 10 V 663 + 6 — - 0 . 1 0 ± 0.05 100 + 10 VR 630 + 4 — - 0 . 1 1 ± 0.04 65 + 15 CO Fig. 3.11 The 'shifts of cubic ice I v during warm-up. For R^O t y p i c a l annealing run data are included for pre- and post-annealing behaviour (open c i r c l e s and squares). 0 _ | , , — , I I 8 0 I I 9 0 . I 2 0 0 I 2 I O FREQUENCY CM"' Fig. 3.12 The s h i f t s of i n cubic ice I during warm-up. For comparison to the helium c e l l data, nitrogen c e l l data for pre and post- annealing behaviour are included.' Pimentel and Zimmerman's (97) data are also included for hexagonal ice I. Temperatures are uncorrected. 87 83°K for the helium runs). The-v 2(D 20) data were not obtained from the same set of spectra as the more intense and absorption data. Data r e l a t i n g the v frequency temperature dependence are plotted i n F i g. 3.13 and important parameters obtained from the figure are l i s t e d i n Table III.IX. For v (H o0) , helium and nitrogen c e l l data are i n good K d. agreement. Because the v band i s broad the maximum was d i f f i c u l t to deter- n mine accurately. 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 20 absorptions i s shown i n F i g . ,3.lH. The peak frequency temperature dependence i s given i n F i g . 3.15. An irr e g u l a r s h i f t of 1.5 cm 1 occurs between 55 and 60°K and the frequency i s invariant from 1 5 5 ° to 200°K. The de t a i l s of the graph are l i s t e d i n Table II I . I X . Several features of v^(E^O) were observed. The intersection of two lines along peak sides was read to * 0.50 cm 1 while shoulder positions, were estimated to within ± 3 cm The peak near 165 cm 1 i s distorted because of the rapid energy drop at the end of a grating range. Frequencies of peaks, minima, shoulder edges and baseline at 25°K are l i s t e d i n Table III.X. ' (b) Overtone and combination frequencies. The (v + v^) data are plotted i n Fig. 3 . l 6 and summarized i n Table II I . I X : One can see that the helium and nitrogen c e l l data agree. However, the data are too poor to permit an approximation of a l i n e a r low temperature dependence. Both the H o0 and D o0 3v^. frequencies (Fig. 3.17) decrease with i n -d d K creasing temperature at rates indicated i n Table II I . I X . Again the.helium and nitrogen c e l l data agree near 80°K. 88 2 8 0 - 6 0 - 4 0 - 2 0 - 2 0 0 - 8 0 - 6 0 - z 4 a " > 2 0 - _ l LU 100 8 0 - 00 LU 6 0 - LU (T 40- O LU 20 Q O o- 8OO o .R(HaO) V W on A V V A A A A LU DC l8°i D I— 60 < r r 4 O H ; LU Q_ 20 LU 1 0 0 h - 8 0 - 6 0 4 0 - 2 0 • ~I 8 2 0 8 3 0 o A 610 6 2 0 6 3 0 6 4 0 F R E Q U E N C Y C M -1 Fig. 3.13 The s h i f t s of v R for cubic ice I during warm-up. For H2O Pimentel and Zimmerman's (97) data and l i q u i d nitrogen c e l l data are included for comparison. 89 Fig. 3.14 The cubic ice 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"! arises from a f i l t e r change. 200 z/ ( H O ) T 2 150- 100- 50 A 4 1 A o- -T 1 r 225 220 ~* 1 1 230 F R E Q U E N C Y C M ' 1 3.15 The s h i f t s of v-d^O) for cubic ice I during warm-up. The sample was mounted on a polyethylene window 0.25 cm thick. The c e l l temperature did not reach helium temperature with the source on or off after 3 hours of cooling. Temperature are uncorrected for source heating. 91 Table III.X The interpretation of the v^RgO) features for comparison to previous r e s u l t s . T 2 Description Frequency Feature -1 cm A peak < l 6 l B minimum 176.5 ± 1 C shoulder edge 193 ± 3 D shoulder edge 21k ± 3 E peak 2 2 9 . 6 ± .5 F shoulder edge 2U6 ± 3 G shoulder edge 272 ± 3 H shoulder edge 286 ± 3 I shoulder edge 295 ± 3 J baseline 331+ ± 3 The (v + v ) data are plotted i n Fig. 3.18 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 to within ± 7 cm 1. Helium and nitrogen c e l l data are not i n good agreement. Low temperature dependences could not be defined. , (c) H 20 and DgO half-height widths. Data for cubic ice I (H 20) were plotted i n Figs. 3.k and 3.5 of section 3.1. The half-height widths of the composite stretching band and the composite l i b r a t i o n a l band increased with increasing temperature. However, the composite ( v 0 , 2 v r a ) band half-height I 2 R width decreased with increasing T. \ 200 o UJ or UJ Q_ LU h o LU D Q: LU 0. UJ h 150 H IOO H 5 0 H o 200 (zf + z/ T ) (H z O) o 0 o o o o o oo A o o A * • A A A A A 3320 3340 3360 I50H 50 IOO H 2460 2470 2480 F R E Q U E N C Y C M " 1 Fig. 3.16 The s h i f t s of (v + the nitrogen cell'data are included, uncorrected. v,p) for cubic ice I during.-warm-up. | For " ' . ., „ , Temperatures aire 93 2 8 0 . 6 0 4 0 2 0 2 0 0 80H ~Z_ 6 0 4 0 \ £ 2 0 CO 1 0 0 UJ 8°-1 LT C9 6 0 Ld Q 4 0 UJ 2 0 cr D a: L±J 6 0 Q_ •̂ r 4 0 O 2 2 1 0 h- 2 0 - 1 0 0 - 8 0 6 0 4 0 2 0 i o 1610 O 3 v or O * V K A A 2 2 2 0 o 2 2 3 0 2 2 4 0 3vR or 2 2 5 0 - 2 +- R(D 20) 8 o o o I — 1 6 2 0 1 6 3 0 1 6 4 0 1 6 5 0 FREQUENCY CM Fig 3.IT The s h i f t s of 3v R for cubic ice I during -warm-up. For H20 annealing data and data of Pimentel and Zimmerman (97) are included. Temperatures are uncorrected. 2 0 0 0 l 5 ° H LU D h IOO- < Q: LU n >̂ 5 0 - LU h o- • O • (z/ + z/ T)(H 20) oa • o a • ° A A a 8 a ± A £ A i i 1 1 : I I I I 1 1 | T 1 1 1 8 6 6 8 7 6 8 8 6 2 0 0 o I 5 0 - LU cr D h IOO- < LU d LU h 5 C H o- — I i 6 5 0 A A A A * (z/ + z/)(D 20) A A A A ^ I I 6 6 0 T T 1 r 6 7 0 F R E Q U E N C Y CM Fig. 3.18 The s h i f t s of (v^ + v^) for cubic ice I during warm-up. Nitrogen and helium c e l l data are included for R̂ O. 95 3.3 The H 20, DgO and HDO Ice I Absorptions at 83°K In t h i s section are l i s t e d the details of the H2O, D 20 and HDO vitreous and cubic ice I"absorptions at 83°K for comparison i n Chapter h to the l i t e r a t u r e values. A. Experimental Typical spectra of vitreous and cubic ice were shown i n F i g . 3.1: v,p(H20) was shown i n F i g . 3.1*+. The samples, spectra and methods of t r e a t - ment were described i n sections 3.1 and 3.2. B. Results at 83°K Vitreous and cubic ice I have the same ske l e t a l absorption spectra (Fig. 3.1) but are ea s i l y distinguished i n d e t a i l s of band structure, frequency and width. Frequencies observed for the H 20, HDO and D 20 systems 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 respectively. Results of previous workers are included for comparison. ( i ) H 20 Absorptions at 83°K Spectra of vitreous and cubic ice I obtained i n t h i s work are i n sharp contrast and•exhibit features not previously observed. The stretching band of cubic ice I i s composed of one peak and two well defined shoulders—33*+0 (2*+42) (sh)cm - 1, 3210(2*116) cm - 1 and 31*+9 (2392)(sh)cm \ (D 20 data are given i n brackets.) In contrast, vitreous ice I has very weak absorptions at 3 6 8 6 ( 2 7 2 0 ) cm 1 and 36UO cm - 1 i n addi- tion to a peak at '3253(2*+36) cm 1 and two poorly defined shoulders at Table I l l . X l ( a ) The frequencies and assignments for cubic and.hexagonal ice I of the present and previous workers. Assignment This Vitreous 93°K Work Cubic 93°K Whalley and Bertie(a) 100°K Hornig and Haas (b) 83°K Giguere and Harvey(c) 100°K Val'kov and Maslenkova(d) 77°K Ockman (e) 100°K -1 -1 -1 -1 -1 -1 -1 cm cm cm cm cm cm cm v 3 o l i g 3686 vw — v± olig 3640 vw — v l + VT ^3367 sh 3340 ssh 3350 shs ( v x ) 3 3 6 0 Msh 3321 (2) .3340 v3 3253 vs 3210±5 vs 3220±5 s (v J 3210 vs 3260 3210 (4) 3224 (3217±5)* v l ^3191 sh 3149 ssh 3140 shs (2v2)3125 Msh 3088 (10) 3140 2220 w 2235 w 2266±20 vbw .2225 s 2250 2235 v? 1 6 6 0 m 1570+10 m l650±30 vbw 1585 s 1580 ( 1 6 0 4 5)* 1570 sh — — (1130 msh) *# 846 ssh 8 8 1 ssh 900 sh VR 802 s 833 s 840 s 850 850 846 — ^ 7 8 0 sh 770 sh ^675 sh ^696" . sh 660 sh VR" VT 535 msh 570" msh 555 sh * data from sample A section 3 . 1 ; ** observed only in samples annealed above 200°K. (a) Ref. 95 (b) Ref. 106 (c) Ref. 98 (d) Ref. 99 (e) Ref. 1 0 8 . O N Table III.XI(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 vitreous, cubic and hexagonal ice I. v T(H 20) This Work 93°K 93°K Vitreous Cubic Giguere and Arraudeau(a) 113°K 173°K Vitreous Cubic Whalley(b) 100°K Hexag.& Cub. Pimentel(c) 93°K Hexag. cm-! cm--'- high frequency l i m i t 326 + 3 33U ± 3 ^328 (330)* shoulder 301 296 295 293 300-310 ( 3 0 5 ) shoulder 2 7 1 267 259 257 ^275 ( 2 7 5 ) change of slope 2U6 ^2k0 peak 2 1 2 . 8 ± 0 . 5 2 2 7 . 8 ± 0 . 5 225 (ms) 223 m 229.2 229 change of slope 2 1 1 220 change of slope 197 200 shoulder 1 9 1 190 188 190 minimum 173 180.5 peak 162 15U (m) 152 l6h * taken from F i g . 3 of Ref. ( 9 7 ) . (a) Ref, 89 (b) Ref. -95 (c) Ref. 97- Table I I I . X I I Comparison of the present and previous HDO vibration frequencies near 90°K. Assignment This work 93°K Whalley and Hornij I and Ford and Hornig Vitreous Cubic Bertie (a) 100 °K Haas (b) 83°K Falk (c) 93°K et al.(d) 83°K -1 cm - 1 cm -1 cm -1 cm -1 cm - 1 cm V OH HDO i n D 20 3304 m 3266 s 3277 ± 4 s 3275 vs 3270 ± 5 3300 V OD — ( 2 4 4 2 ) wsh 2445 msh 2442 s HDO i n H 20 2437 m 2 4 l 6 s 2 4 2 1 ± 4 s 2 4 l 6 vs 2418 ± 3 2440 ( 2 3 9 2 ) wsh 2395 msh 2393 1975 s w ^2(HDO) 1490 s 1 4 7 0 V + V R T — 854 wsh HDO i n D 20 VR HDO i n D 20 792 w 819 mw 822 ± 6 m 800 620 HDO i n H 20 515 i 1 0 m "(a) Ref." '95 (b) Ref. T0'6 '(c) Ref. 100 (d) Ref. 1 0 5 . MO CO Table I I I . X I I I The frequencies and assignments of D 20 ice I (vitreous, cubic, hexagonal) near 90°K for the present and previous workers. This work 93°K . Whalley and . Hornig and Giguere and Val'kov and Assignment Vitreous Cubic Bertie (a) 100°K •Haas (b) Harvey (c) 83°K 100°K Maslenkova (d) 100°K hex.and cub. cubic hexagonal hexagonal cm 1 cm cm--'- cm-! cm-^ - 1 cm o l i g 2720 v o l i g — — v l + VT 21*99 ssh 21*65 21*85 ± 10 msh ( v 1 , 2 v 2 ) + 2 l + 9 5 msh 251*2 ( 0 . 5 ) V 3 21*36 s 21*13 21+25 ± 5 s (v 3) 21*32 vs 21*50 2l*2l* ( 3 ) V l 2372 ssh 2 3 2 1 2332 ± 5 s 221*0 vwsh (v l S2v 2)"2336 s 2 2 9 1 ( 1 0 ) 3 \ 1617 w 1 6 3 5 1650 ± 30 1635 s 1630 v 2 1212 m 1191* 1 2 1 0 ± 10 1210 s 1210 M.2l*0 v R + v T ssh 6 6 1 675 sh VR 600 s 627 61*0 s 630 VR ~ VT 1*25 sh "(a)""Ref. 95 '(b) Ref. 1 0 6 (c) Ref. 98 (d) Ref. 9 9 . VO 100 3367(21+99) cm - 1 and 3191(2372) cm - 1. For H~20 cubic ice. I , the l i q u i d helium and l i q u i d nitrogen experimental data do not agree at 83 PK (Fig. . 3.10). •Two d i s t i n c t values of v^HgO) are indicated among l i q u i d helium /V''' experiments and some l i q u i d nitrogen experiments. A l l helium runs ,and some nitrogen runs gave v 2(83°K) at 1570 cm - 1. A few nitrogen runs with t h i n samples gave v 2(83°K) at l6oU cm - 1. Atmospheric H 20 absorptions may have attenuated the weak v 2(H 2 0 ) absorptions of t h i n samples. 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. The former gave spectra with a d i s t i n c t shoulder at 1130 cm 1 (on the side of v 2 ) . As w e l l , a deep minimum appeared between the 1130 cm 1 shoulder and the v R band. Pimentel's (97) spectra showed the same features although he offered no explanations for them. Inspection of the cubic ice I H 20 v T band (Fig. 3.11+) shows, two peaks and three shoulders. However, Whalley's (87) theory showed that additional v T features y i e l d important information on the densities of phonon states. Accordingly, ten features of v^(E^O) at 93°K were reported i n Table III.X. In contrast, the vitreous ice I band had no low f r e - quency shoulder or peak. As well the 267 cm - 1 shoulder was poorly defined. ( i i ) D 20 Absorptions at 83°K DgO ice I has the same sets of spectral features as H 20 ice I. Vitreous B^O ice spectra have a weak oligomeric absorption at 2720 cm 1 which has not been reported previously for ic e . Oligomeric absorptions are absent i n cubic D,_,0 sample spectra. As i n E^O ice I , the stretching band shoulders are.better defined i n cubic than i n vitreous i c e . The 1 0 1 problems caused by atmospheric Ĥ O attenuations encountered i n Ĥ O ice I • w e r e eliminated 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 . In vitreous samples the three absorptions were broad, r e l a t i v e l y weak and without shoulders. In cubic samples the v_„ band On h a d no shoulders, the v band had two shoulders and the v band had one OD n shoulder. No v^(HDO) absorption was observed near 6 0 0 cm"1 for HDO i n Ĥ O. 3.h Summary of Ice I Results A. Vitreous-Cubic Ice I Transformation 1. 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 It5°K; i n t e r n a l modes s h i f t to lower frequencies while l a t t i c e modes s h i f t t o higher frequencies. 2. A b o v e 150°K, vitreous and cubic frequency data concur and s h i f t r e v e r s i b l y with respect to temperature. 3. Oligomeric Ĥ 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 , shar- p e n e d a n d better defined. 5. D̂ O and HDO absorptions appear to have the same behaviour as t h o s e of H 20. 6. Composite-band half-height widths exhibited unusual behaviour i n t h e case of ( v Q , 2 v p ) . 102 B. HDO i n Cubic Ice I 1. Dilute concentrations of HDO i n Ĥ O and D̂ O gave accurate measures of frequency, half-height widths and absorbances as a function of temperature. 2. Plots 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 indications of irregular behaviour. 3. A new absorption was observed as a shoulder on v (HDO) and i s K designated v^HDO) + v m(DJD) or v '(HDO). n I d n h. Internal mode cubic ice I HDO absorptions s h i f t reversibly to 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 to lower frequencies as a function of increasing temperature. 5. HDO stretching mode half-height widths increased as a function of increasing temperature. 6. HDO stretching mode absorbances decreased as a function of i n - creasing temperature. C. H20 and D20 i n Cubic Ice I These results provided measures of eight Ĥ O and seven D̂ O absorptions that were less accurate, but of the same nature, as those from HDO. CHAPTER FOUR DISCUSSION OF ICE I The data from cubic and vitreous ice I i r spectra contribute to detailed understandings of: l ) the origins of the absorptions, 2 ) the process of the vitreous-cubic phase transformation, and 3) the effects of increasing temperature, increasing R(0*••-0) and decreasing hydrogen bond strength on the R 20, D 2 O , and HDO vibrations and potential w e l l . 4.1 The Ice I Vitreous-Cubic Phase Transformation The x-ray and electron d i f f r a c t i o n experiments ( 5 8 ) indicated that the structure of the s o l i d formed by condensing H 2 O vapour at low tempera- tures depended on the rate of deposition and the substrate temperature: Amorphous, cubic and hexagonal ices were observed. The thermodynamic studies of the i r r e v e r s i b l e phase transformations indicated varying trans- formation temperature ranges and degrees of c r y s t a l l i n i t y . The confusion with respect to vitreous, cubic and hexagonal sample formation i s reflected i n the variations among the i r spectra of various authors ( 9 5 , 9 7 , 9 8 , 1 0 5 ) . Bertie and Whalley ( 8 8 , 9 5 ) 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 "recipe" 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 solids condensed from the vapour. While they were t h e . f i r s t to 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 vitreous and cubic i c e , they did 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 i r absorption except v (H 0 ) , but the results of the transformation for a l l H2O, HDO and D 20 bands were recorded. The spectra gave four concurrent 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 rate. The studies showed that cubic samples formed by transformation of the vitreous 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 be- haviour before, during and after the vitreous-cubic phase transformation. Between 83 ± 3°K and-120 ± 10°K a l l H 20 band maxima had constant frequencies (Fig. 3.2). The absence.of frequency s h i f t s i s indicative 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 to allow molecular reorientation, softening of the glass, and hydrogen bond formation. The H 20 band maxima a l l shifted i r r e v e r s i b l y during the vitreous- cubic transformation. However, the data (page 6 2 ) indicated different, transformation temperature ranges for different bands: Ranges from 1 1 5 i 5 ° to 130 + 5°K and 130 ± 5° to IH5 + 5°K were found for v R and v± + v T. The differences appear to be caused by the increasing period the sample was held at one temperature while the spectra were recorded. t , For example, frequencies plotted i n F i g . 3.2 show that v R was constant up to 100°K and was completely shifted to the cubic frequency at 125°K. 105 That indicates, on f i r s t inspection, that the transformation for v~(Rn0) n d started at 115 1 5°K, about 10°K lower than for other bands. Such a con- clusion i s incorrect. S p e c i f i c a l l y consider the positions of the data indicated by s o l i d triangles ( • ) at 125°K i n F i g . 3.2 for a l l s i x bands. The data were ob- tained from one sample during one run at constant temperature. At 125°K the Vl + VT b a n d- w a s unshifted from the vitreous frequency, the and bands were only s l i g h t l y s h i f t e d , the 3v R band was shifted approximately one-half the t o t a l s h i f t towards 3v cubic, the v band was shift e d three-quarters the i\ d t o t a l s h i f t and v R was completely shifted. .The amount of s h i f t i s propor- t i o n a l to the time the sample was held at 125°K. In t h i s work, spectra were, scanned from 4000 to 530 cm - 1 i n 20 minutes. Thus for + v^, v^, v^, 3^, and the vitreous sample had been progressively annealed at 125°K for 3.7, 4.4, 4.7, 10.2, 13.4 and 18.3 minutes respectively. By the time was recorded the sample had completely transformed. I f the transforma- t i o n rate i s assumed to be l i n e a r , then a plot of (v^ - v^^/Cv^ - v c ) t _ m (where t i s the time at 125°K and t = 0 0 i s maximum annealing s h i f t ) against -2 -1 time i n minutes gives the transformation rate 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 for v + v , v , v , 3v 0 and v 0 were a r t i f i c i a l l y elevated,by X 1 3 1 K d the recording technique. The transformation temperature range for a l l bands must be consistent, 120 - 135 - 5°K (corrected for sample window heating). During the transformation the l a t t i c e modes v and 3v shifted i r r e - n R vers'ibly to higher frequency while the molecular modes shifted i r r e v e r s i b l y to lower frequency due to large alterations to 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 attained s u f f i c i e n t thermal k i n e t i c energy to permit molecular reorientation, the low polymers were then free to form long chains with complete hydrogen bonding, four per molecule. The complete sets of strong hydrogen bonds hindered l i b r a t i o n and tr a n s l a t i o n and increased the frequencies of those bands. After 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 reversible 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' 185 ± 5°K for 2 - 5 minutes , followed by recooling to 83°K. r At 83°K the effects of reorientation and hydrogen bond formation (lengthening r(O-H) and o r b i t a l rehybridization) were measured for H 20, D 20 and HDO. I f the frequency s h i f t s between cubic and vitreous ice did r i s e from hydrogen bond formation, then the r e l a t i v e effects on H 20, D20 and HDO frequencies should have been the same provided a l l the vitreous 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 s h i f t s would i d e a l l y be i n the r a t i o Av^(H20) /Av^(D20) near 1.*+, where Av.̂ v^(cubic) - (vitreous) for the i - t h v i b r a t i o n a l mode. Only the peaks and v R give reasonable agreement with the id e a l r a t i o , i_.e_. 1.6 t 0,> 3 and 1.1 ± 0.30 respectively. A l l the other bands were poorly defined and the ratios range from 0.79 ± 0.5 to 3.1 ± 0.5 for v.̂  + v T and respectively. A modified product rule AvjAv 2(H 20) /Av^Avg^giO) does not improve the r a t i o . For 4.00 % HDO i n D20 AvR(HD0) = Av R(D 20) = +27 cm - 1, Av^HgO) ./ AvOTJ(HD0) = 0.94 and Av o(D o0) /Av--(HDO) = 1.1: None of these are ; i n agree-On 3 uu ment with the ideal r a t i o . The r a t i o for Av (HDO) /Av (HDO) = 1.8 i s much 1 0 7 higher than 1.4. The observed-ratios of the cubic ice I fundamental frequen- cies are near 1.35 and one deduces that Av (HDO) i s too large, Av.^HDO) i s On OD too small (compared to pure H2O and D 20) or both. However, since samples were not i d e n t i c a l l y deposited, they would have had different degrees of self-annealing, and different frequency displacements from the cubic ice values. Each band w i l l now be considered i n turn. B. Fundamental La t t i c e Mode Transformations ( i ) The v^HgO) Transformation The v band had remarkable differences between the vitreous and cubic samples at 83°K: The vitreous band was broad and featureless while the cubic band was narrow and had nine features. That i s understandable from the very different nature of the two so l i d s . For example, since the positions of the atoms i n a vitreous 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 irregular and the normal vibrations of the s o l i d are also irregular ( 8 7 ) . The resu 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 tran 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 selection rules ( 8 7 ) , a very broad i r . (vitreous) band i s expected and observed. In contrast, cubic ice I has regular, long range ordering of oxygen atoms, but i r r e g u l a r , short range ordering of the protons (orientational disorder). Whalley ( 8 7 ) has shown that the orientational disorder does not have a s i g n i f i c a n t irregular effect on the mechanical vibrations of cubic i c e , but that i t does affect the; l o c a l e l e c t r i c o s c i l l a t i o n s . Consequently, one obtains a structured (cubic) band whose features are indicative of the c r y s t a l l i n e state. I t i s suf- 108 f i c i e n t here to compare our vitreous and cubic v̂ , data (83°K) to those of Whalley (88) and Giguere (89). Consider the v̂ , data given on pages 89, 90, and 91 of Chapter 3. That v^, (cubic), 227.8 cm \ was 7% higher than (vitreous) i s understandable simply on the basis of the increased number of hydrogen bonds, the deepened hydrogen bond potential and increased force constants, and the increased hinderance to t r a n s l a t i o n . These effects resulted from extension of hydrogen bonding closer to the l i m i t (4 bonds/molecule), reduction of the mean 0 0 distance, and a change i n the density i n cubic c r y s t a l s . However, i n r e a l i t y the explanation for the frequency s h i f t may not be so simple. Formation of a w e l l defined B r i l l o u i n zone i n cubic samples may e n t a i l complex changes i n the densities of states and selection rules from those of the vitreous sample. The half-height width of 'V (vitreous) was 62.8 an \ i n sharp con- t r a s t to that of v̂ , (cubic) which was very nearly one-third of that value, 2 3 . 2 cm Increases i n the densities of states at the B r i l l o u i n zone boun- daries probably accounts for t h i s dramatic change. That the peak height of ^ (cubic), 1.285 absorbance, was almost exactly double that of (vitreous) i s probably due to two effects. 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 for ]c_ = 0 t r a n s i t i o n s . The second effect arises 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 dipoles i n p a r t i a l l y hydrogen bonded glasses. The Vj, ( v i t . ) band of t h i s work compares very well with Whalley's (88 ) vtj, ( v i t . ) but not with Giguere's (89) v ( v i t . ) . The v̂ , ( v i t . ) band had no 162 cm 1 peak or 173 cm 1 minimum, as Whalley (88) also reported. 109 However, Whalley's (vitreous) peak was 9 cm higher than observed here, 2 1 2 . 8 cm He did not l i s t the positions of other vitreous band features and i t i s hard to determine i f the difference i s only due to c a l i b r a t i o n errors. [On the basis of the two sets of v T (cubic) features, the l a t t e r seems unlikely.] In contrast Giguere's ( 8 9 ) v T ( v i t . ) band showed too much structure and suggested a largely c r y s t a l l i n e sample. The present work supports Whalley's observations of v̂ , ( v i t . ) . For \> (cubic) the results of t h i s work agree i n general features with both Whalley (88) and Giguere ( 8 9 ) . However the two peaks in:, the present work are nearly 2 cm 1 lower than Whalley reported, probably due to a c a l i b r a t i o n error. Whalley found that a l l cubic samples, either condensed from the vapour or formed under pressure and mulled, gave the same absorp- tions. Since v observed i n t h i s work agrees with his 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 legitimate cubic ice I samples with respect to v^. , ( i i ) The v R Transformation At 83°K vitreous ice vj^HgO) had two d i s t i n c t and two f a i n t features: 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 (535 cm "*"), and two fain t shoulders (846 cm 1 and 675 cm 1 ) . However, vitreous ice V R ( H D O ) and Vp>(Dg0) each had only a single feature. In contrast, cubic ice v R ( H 2 0 ) had five features (one peak and four shoulders) while V R (H D O ) and vR(D2.Q) had 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 previously reported. Changes i n frequency and half-height width between the vp> bands of vitreous and cubic H 2 O ice samples were shown i n Figs. 3.2 and 3 . 4 (pages 6 l and 66) and the results of d e v i t r i f i c a t i o n for v R(H 20, D 20, HDO) were given i n 110 Table I I I . I (page 6 2 ) . After the vitreous sample was annealed at 185 i 5°K for 2 - 3 minutes and recooled to 83°K, one found a l l the v R features had shif t e d to higher frequency and that three new features appeared. P r e c i s e l y , v R(Hg0) s h i f t e d by +31 cm - 1, vR(HD0) by +27 cm - 1 and v R(D 20) by +27 cm - 1. As for v T , the v R s h i f t to higher frequency may be simply understood on the basis of hydrogen bonding. Cubic ice has more and stronger hydrogen bonds than vitreous i c e . The results are a deeper hydrogen bond p o t e n t i a l , larger hydrogen bond force constants, increased.hinderance to l i b r a t i o n and i n - creased absorption frequency. However, as for 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 , densities of states and selection rules. 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 with the l a t t i c e v i b r a t i o n theory. The plot of half-height widths (Av R ) of the composite band ( v R , v R + v T) was shown i n F i g . 3.h (page 6 6 ) . I t also indicated a "de- pressed" v R transformation temperature range ( 1 1 5 - 130 ± 5°K). However, the low range may be explained as i n section k.lA (page IO5) for v^ f f r e q . ) . One also sees that the behaviour of Av 0 above 130°K did not conform to n the reversible behaviour of f u l l y annealed cubic samples, i_*e_* the h a l f - height width continued to decrease. F i n a l l y , on completing the annealing and recooling of the sample to 83°K, one found that the disorder broadening due to i r r e g u l a r 0 positions was removed but that there remained the orien- t a t i o n a l disorder broadening. The half-height widths at 83°K decreased i n the following way: I l l H 20 HDO D 20 H 20/D 20 Av ( v i t . ) 2 2 0 cm - 1 88. cm"1 ^ 2 0 0 cm"1 1.10 Av (cub.) 1 9 5 51 140 "1.30 Av^cub.) 0.89 0.58 ^ 0 . 7 0 1.27 A v ^ v i t . ) The differences may be due simply to errors i n determining baselines, inten- s i t i e s and widths, or may aris e from differences i n m i c r o c r y s t a l l i n i t y among the three vitreous samples formed. C. Fundamental Molecular Mode Transformations ( i ) The v 2 / 2 v R Transformation Absorptions between 1 0 0 0 and 1 8 0 0 cm 1 i n H 20 ice have been variously assigned to 2V R or v 2- A l l previous workers ( 9 5 , 9 7 ,105 ,106,108) reported only a single feature i n t h i s range for both H 20 and D 2 0 ices (vitreous or cubic). However, Zimmermann and Pimentel's ( 9 7 ) F i g . 1 for cubic ice has shoulders at 1 1 0 0 and 1 5 3 0 cm - 1 and a peak at l 6 l 5 cm"1:. They treated the l 6 l 5 cm 1 peak and 1 5 3 0 cm 1 shoulder as one band centered at 1 5 8 0 cm"1 (83°K) i n cubic H 20 i c e . Most thick vitreous H 20 i c e spectra recorded i n t h i s work had two features, a peak at 1 6 6 0 t 10 cm"1 and a shoulder at 1 5 7 0 ± 20 cm"1. In contrast, cubic samples annealed below 190°K only had a peak at 1 5 7 0 + 1 0 cm \ Cubic samples annealed to 205°K had a peak at 1 5 7 0 t 1 0 cm - 1 a shoulder at 1130 cm and a deep minimum at 1 0 5 0 cm - 1, much l i k e Zimmermann and Pimentel's ( 9 7 ) spectra. While the f i n a l assignments of the bands are l e f t 112 u n t i l section k.3 (page 1 7 5 ) , i t seems l o g i c a l to consider the vitreous 1570 cm 1 shoulder and the 1 6 6 0 cm 1 peak as being either v_ or 2v . Cor- d K responding features were not observed i n vitreous DgO ice I. The reasons for s h i f t s to lower frequencies, Av^CH^O) = .56 Cm 1 and A V^CD ^ O ) = -18 cm ^, have been explained by Zimmermann and Pimentel .(97) on the basis of a weakened molecular potential and decreased force constants. However, the large differences between s h i f t s for Ĥ O and D̂ O, observed here, i s not understood. In F i g . 3.5 (page 67 ) one saw that the vitreous h -1 -1 AVg was constant at 350 cm up to 115 ± 5°K and broadened to 390 cm at 12.5 - 5°K. Above 125°K Av 2 had a negative, reversible temperature depen- dence, -1.6k cm 1/°K. A l l other vitreous Ĥ O, HDO and D̂ O bands were narrower after the transformation and subsequently broadened with increasing temperature i n the cubic phase. The anomalous behaviour of Av^ (H^O) may be explained i f the vitreous ice band i s composed of a medium absorption s l i g h t l y below 1 5 7 0 cm 1 and a 2v absorption s l i g h t l y above 1660 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 1570 cm 1 y i e l d i n g a net broader v /2v band. For t h i s explanation i t i s also neces- d a sary that the peak absorbance of 2v decrease i n the cubic phase. The negative temperature dependence of the band results from the s h i f t of a weak underlying 2 v R to lower frequency (towards 1600 cm 1 ) and the s h i f t of Vg to higher frequency (towards 1 6 0 0 cm 1 ) . w i t h increasing temperature. As the two absorptions further coalesce, the composite band becomes narrower. However, the frequency dependence of the cubic band i s determined by the more intense absorption. The Vg frequencies obtained for c r y s t a l l i n e ice formed from the vapour 113 (this work, 9 7 , 1 0 5 , 1 0 6 ) do not agree with Whalley's ( 9 5 ) work. For a l l phases of ice Whalley found to be higher than 1 6 5 0 cm - 1. The results of t h i s work support Ockman's ( 1 0 8 ) observations for samples formed from the l i q u i d . Ockman's ( 1 0 8 ) r e f l e c t i o n spectra indicated a weak maximum at 1 6 0 0 cm 1. I t i s possible that Whalley's ( 9 5 ) mulling technique gave a different r e f l e c t i o n spectrum than occurs for t h i n films and enhanced the high f r e - quency portion of his v^. His results showed the mulling agent decreased r e f l e c t i o n and scattering compared to powder spectra. On the other hand, r e f l e c t i o n and scattering may be severe for 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 1 and 1 0 5 0 cm "*") may have arisen from a strong Christiansen f i l t e r effect on the high, f r e - quency side of v . ( i i ) The v___ Transformations Din In the region from 3000 to 4000 cm 1 one observes the symmetric and asymmetric 0-H stretching frequencies from Ĥ O molecules i n various degrees of polymerization and the combinational absorption of with the l a t t i c e modes. The corresponding 0-D stretches are found betweeen 2000-2800 cm Data for and of Ĥ O, HDO and D̂ O i n the vitreous and cubic phases, were shown i n Figs. 3.2 and 3.4 (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 vitreous ice (3191 - 15 cm 1 ) but was better defined i n cubic ice (3149 - 10 cm ^ ) . In contrast, for D^0 ice the shoulder was well defined for both vitreous and cubic ice I (2372 ± 10 cm - 1 and 2321 cm 1) 114 Like other molecular modes, shifted to lower energy because of weaker molecular bonds, a shallower potential well and weaker force constants. (b) The peak. The vitreous ice stretching band frequency at 83°K was 3253 cm 1 while for cubic ice was 3217 cm - 1, a s h i f t of -36 cm - 1 (AV^CD^O) = -23 cm ~̂) . The explanation for a negative s h i f t follows from above. (c) The HDO modes. The vitreous ice HDO absorptions were l i s t e d i n Table I I I . I , v_ n = 2437 cm - 1 and v n r i = 3304 cm - 1. The cubic ice HDO f r e -UD Un. quencies were shifted -21 and -38 cm 1 respectively from t h e i r vitreous values. Reference to Table I I I . I shows that these s h i f t s correspond very well to the s h i f t s of D̂ O and Ĥ O respectively. The vitreous-cubic trans- formation had the same effect on v (asymm.) or v (asymm.) of HO,-HDO and OD OH <L DgO molecules whether they were i n an Ĥ O or D̂ O l a t t i c e . There appear to be no differences among the couplings of HDO, HgO and D̂ O molecules for either vitreous or cubic ice I. F i n a l l y , the explanation for the direc t i o n of s h i f t follows from previous discussion. The HDO stretch half-height widths sharpened from 77 to 23.5, cm - 1 and 115 to 35.5 cm 1 between the vitreous and cubic phases (at 83°K). In vitreous ice both the 0 po s i t i o n a l disorder and proton orientational disorder c o n t r i - buted to the widths. In cubic ice the 0 positions were ordered, but the proton disorder broadening remained. Even i n the cubic phase the uncoupled HDO molecules had Av values about twice as large as expected for ordered solids. For example, Whalley ( 9 6 ) found Av (EDO) data of 8 - 13 cm - 1 for an ordered high pressure i c e . The HDO peaks were uninhibited by band overlap and provided ,an ex- cellent probe for making accurate transformation rate studies of vitreous 115 ice. The dil u t e H / D isotopic substitution should be employable i n rate studies of other disordered systems. (d) The oligomeric modes. A l l vitreous HgO and D̂ O ice samples observed i n t h i s work had very weak absorptions between 3600 and 3 7 0 0 cm 1 i n HgO (near 2620 cm 1 i n D^O). Typical E^O peaks were shown i n F i g . 3-3 (page 6k) and the frequencies were l i s t e d i n Table I I I . I I (page 6 5 ) . These absorptions occurred quite close to the vapour phase monomeric frequencies. Shurvell ( 1 1 5 ) and Van Thiel et_ a l . ( 1 1 7 ) studied the absorptions from d i l u t e concentrations of Ĥ O and D̂ O i n various matrices. Van Thiel et_ a l . assigned the (v^s v^) monomeric, dimeric and trimeric Ĥ O ( i n an N matrix at 20°K) absorptions to ( 3 7 2 5 and 3625 cm - 1), ( 3 6 9 1 and 35^6 cm - 1), and(3510 and- 3355 cm ̂ ) respectively. For D̂ O Shurvell reported (v^s v^) monomer and dimer absorptions for an matrix at ( 2 7 6 5 and 2655 cm 1 ) and ( 2 7 2 5 and 2 6 5 0 cm 1) respectively. Our frequencies appear to r i s e from dimeric systems.• We observed half-height widths of 15 - 20 cm 1 which were s l i g h t l y smaller than i n matrix i s o l a t i o n , 20 - 30 cm Their oligomeric peaks were stable up to the softening temperatures of the matrix used, generally less than 30°K. Oligomeric absorptions observed i n t h i s work were stable up to the softening temperature of the Ĥ O glassy matrix, 125°K. That corresponds to the temperature of onset of peak s h i f t i n other bands, i_.e_. the temperature of molecular reorientation. The high softening temperature i s consistent with the increased van der Waals forces i n molecular solids compared to 1 rare gas sol i d s . For example, Shurvell ( 1 1 5 ) observed that Ĥ O oligomers were stable up to 80°K i n a CCl^ matrix. 1 1 6 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 reorientation r e s u l t i n g i n progressively higher polymerization. The monomeric, oligomeric and medium polymers disappear as we l l as t h e i r absorptives. The high frequency side of the v g T R hand was greatly 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 absorbances for dimeric and f u l l y polymerized Ĥ O i s 1 to TO. 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 Ferriso and Ludwig ( 1 1 9 ) on the vapour phase (monomeric H^O) showed that the extinction 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. Thus one finds 1 part of monomeric-dimeric Ĥ O to 2.3 parts of completely polymerized HgO. There re- mains an unknown portion of the sample i n intermediate stages of polymeriza- t i o n . However, while t h i s estimate seems to be very high, the point, is- that a considerable amount of oligomeric Ĥ O and DgO sample was formed by our condensation technique. i (e) The Av 3 5 of the band ( v ^ v^, v 1 + v T ) . The half-height width h (Av ) of the composite band (v^, v^, (v^ + v^)) sharpened from 325 i 10 cm 1 to 285 t 10 cm 1 (83°K) between vitreous and cubic i c e . The band t sharpened i r r e v e r s i b l y between 115 i 5°K and 125 ± 5°K by the s p e c i f i c loss of approximately 2 0 % of the high frequency absorption. Such absorption arises from medium length Ĥ O and D̂ O polymers with incomplete hydrogen bonding. In addition, 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 potential energies. 117 D. Combination and Overtone Mode Transformations ( i ) The 3VR Transformation Absorption near 2200 cm - 1 i n HgO ice and near 1 6 0 0 cm - 1 i n DgO ice has been variously assigned to 3VR a n d v 2 + V R . S p e c i f i c a l l y , the H20 absorption had a single feature, a peak at 2 2 2 0 or 2235 cm 1 i n vitreous or cubic i c e . The s h i f t upon annealing was to higher frequency, and was also found for V R and VIJI. The nature of the s h i f t was given i n F i g . 3.2 (page 6 l ) while data was given i n Table I I I . I (page 6 2 ) . Cubic ice absorptions, 2 2 3 5 and 1 6 3 5 cm"1 for H20 and D20 (at 83°K), agreed very w e l l with the single c r y s t a l observations of Ockman ( 1 0 8 ) , Table I I I . X I . As w e l l , Haas and Hornig's ( 1 0 6 ) and Giguere and Harvey's ( 9 8 ) re- sults were comparable. However, Whalley's ( 9 5 , 9 6 ) results were consistently higher. As for v 2 , the differences i n Whalley's results may have arisen from changes i n the r e f l e c t i o n spectrum caused by the mulling agents. The s h i f t by + 15 cm 1 (for H 20) to higher frequency upon d e v i t r i f i - cation may provide a clue to the o r i g i n of t h i s band. I f the band i s V2 + V R then one would expect the s h i f t A ( v 2 + V R ) to be proportional to Av2 + A V R = (-56 + 31) = -25 cm 1 for H20. I f the band i s 3VR then one. would expect A ( 3 V R ) to be proportional to 3(A V R ) = +93 cm - 1. The observed s h i f t to higher frequency by +15 cm - 1 i n H20 and +18 cnT^ i n D20 supports 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 results are consistent with results from c r y s t a l l i n e samples prepared from the l i q u i d , i_.e_. the resu l t s of Ockman (108) and Giguere ( 9 8 ) . 118 ( i i ) The (v + v ) Transformation The high frequency shoulder (v + v ) was very poorly defined i n vitreous i c e , but was well defined i n cubic i c e . As for other molecular modes, (v + v^) shifted i r r e v e r s i b l y towards lower frequency (-27 cm 1 for HgO and -34 cm 1 for D̂ O) between 130 and 145 i 5°K. Comments made above with respect to the o r i g i n of the molecular mode s h i f t s and the temperatures of transformation also apply to (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 vitreous-cubic transformation took only a few minutes to f i n i s h even at 150°K. As wel l they found that vitreous ice transformed cleanly to cubic i c e . On the other hand, Dowell and Rinfret (74) estimated only a 30 per cent conversion to cubic ice and an average -cubic o c r y s t a l l i t e size (embedded i n the remaining 60% vitreous ice) of 400 A. The results of Dowell and Rinfret (74) necessitate a heat of cubic-hexagonal phase transformation of 24 cal/gm. Such an evolution of heat was unobserved at higher temperatures by Beaumont et a l . In fact they estimated the ,heat of cubic-hexagonal transformation to be less than 1.5 cal/gm. ; I f the samples i n the present work were only 30% cubic ice with 60% vitreous ice remaining, then the spectra of annealed samples should .have been characteristic of vitreous ice and might have exhibited separate maxima from cubic and vitreous i c e . Only one stretching peak was observed and the bands matched very closely the spectra of hexagonal ice I ( 9 5 ) - These facts support Beaumont's interpretation of the vitreous-cubic transformation. 1 1 9 . The 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 t r a n s f o r m e d f u l l y t o c u b i c i c e I . The p r e s e n c e o f s i g n i f i c a n t amounts o f r e s i d u a l v i t r e o u s i c e w o u l d have bro a d e n e d t h e 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 , g i v i n g a t a i l on t h e h i g h f r e q u e n c y s i d e . The h a l f - h e i g h t w i d t h s and band shapes o f s p e c t r a i n F i g . 3.1 compared v e r y f a v o u r a b l y w i t h s p e c t r a o f h e x a g o n a l i c e I formed f r o m t h e l i q u i d . D e p o s i t i o n r a t e s 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 by Beaumont e t a l . ( 6 5 ) — 0 . 0 k gm/cm^/hour. Assuming a v-^HgO) e x t i n c t i o n c o e f f i c i e n t o f lkO f o r h e x a g o n a l i c e I ( 1 1 9 ) t h e sample t h i c k n e s s was 0.5 - -h 3 1.0 m i c r o n s . The volume o f i c e I sample was a t l e a s t 1.4 x 10 cm . A t a d e n s i t y o f 0.924 gm/cm^ one had a minimum sample o f 1.3 x 10 gms.• Such samples were a p p l i e d i n two b u r s t s , o f two seconds d u r a t i o n e a c h , o n t o a window i n i t i a l l y a t 83°K. By assuming a 1.0 crn^ image, t h e r a t e of- d e p o s i - t i o n was a t l e a s t 0.04 gm/cm2/hour. -k D u r i n g t h e d e p o s i t i o n , 1.3 x 10 gms o f H^O v a p o u r r e l e a s e 0-09 c a l (assuming t h e h e a t s o f s u b l i m a t i o n o f amorphous and h e x a g o n a l i c e I r a r e t h e same). There was s u f f i c i e n t h e a t o f c o n d e n s a t i o n t o i n d u c e l o c a l i z e d h e a t i n g and t o p e r m i t d i f f u s i o n o f i n d i v i d u a l m o l e c u l e s . The e x t e n t o f h e a t i n g and d i f f u s i o n , o r t h e amount o f s e l f - a n n e a l i n g , depended on t h e r a t e of; d i s s i - p a t i o n o f heat a t t h e window-sample s u r f a c e . S e v e r a l a t t e m p t s , under v a r i o u s c o n d i t i o n s , were made t o f o r m h e x a g o n a l i c e . 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 a l m o s t i n s t a n t a n e o u s s u b l i m a t i o n s i n c e t h e samples were u n c o v e r e d . Such s u b l i m a t i o n has a l s o been t h e e x p e r i e n c e o f o t h e r w o r k e r s ( 1 2 0 ) . The e x t e n s i v e s h a r p e n i n g and a l t e r a t i o n o f t h e bands between v i t r e o u s and c u b i c i c e I was due t o two e f f e c t s . The f i r s t was t h e d i f f u s i o n and 1 2 0 reorientation of indiv i d u a l molecules into l a t t i c e s i t e s i n the cubic unit c e l l . The cubic unit 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 vibrations were broadened by asymmetries in proton orientation at equivalent unit c e l l s i t e s . The second effect was the extension of low, medium, and high;polymer H 2 O clusters of the vitreous phase into 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 clusters amal- gamated into larger units where the deformed or absent hydrogen bonds at the contact surfaces between clusters (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 i n H>>0, D 2 0 and HDO spectra between h°K and 2 0 0°K permit accurate correla- tions of the s h i f t s to changes i n R ( 0 * • • - 0 ) and changes i n hydrogen bond strength. In t h i s section values of R ( 0 , - , * 0 ) for cubic ice I are calculated over the range 1 0 ° - 200°K and plotted against v . T J ( H D 0 ) and v.̂ (HDO') . , That On OD plot i s compared to the predictions of an empirical equation which relates v^(HDO) to R ( 0 0 ) . In addition, values of < T T ( H D 0 ) and X ^ T T ( H D 0 ) are Un Un Un calculated from v (HDO) and v (HDO) as a function of temperature. A. Dependence of HDO Bands on Temperature 121 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 extrapolation to Q°K simply as a matter of convenience. The ind i v i d u a l frequencies had v i r t u a l l y the same values when extrapolated to 5° or 0°K. There i s the danger that the properties of ice are irregular below 5°K. However, Flubacher et_ al_. (83) proved that the thermodynamics of ice I are well behaved down to 2°K. The low temperature l i m i t i n g frequencies, half-height widths and peak heights are for E^O molecules at the distance of minimum approach. The' 0 - , , ,H potential i s deepest and the 0-H potential i s shallowest. The conditions at minimum approach permit the largest o r b i t a l overlap and degree of hydrogen bond covalency, the largest e l e c t r o s t a t i c e f f e c t s , and the largest 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 for minimum root-mean-squared (RMS) amplitudes of HgO tran s l a t i o n and 0-H vibr a t i o n . F i n a l l y , the contours of the;bands are least distorted by hot bands and v i b r a t i o n a l perturbations of the , potential. :.< As the temperature was raised the ice I sample expanded, giving; increasing R ( 0 - , , - 0 ) and resulted i n the weakening of the 0-*-,H bonds and a strengthening of the 0-H bonds. Hence the l a t t i c e mode and molecular mode force constants could be understood to decrease and increase respectively, i_.e_. the frequencies respectively decreased and increased. While the crystals expanded.continuously and non-linearly during warm-up, the frequency- temperature dependence was approximated by two straight l i n e s . The, lines 122 corresponded to regions of slow and fast c r y s t a l expansions. Below 50°K the effects of AR(O'--'O), changes i n RMS amplitude of tr 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 disc o n t i n u i t i e s i n the temperature dependences indicate possible 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). A f u l l discussion of the o r i g i n and nature n K of the l i b r a t i o n a l modes i s given i n section U . U . As expected, the temper- ature dependences were negative for both bands, -0.02 cm 1/°K below 55°K and -O.lUT cm-1/°K above 55°K. Below 55°K the effects of vra and v m hot bands should have been ne g l i g i b l e . Above 55°K, however, v and v hot bands, may have contributed s i g n i f i c a n t l y to the changes i n band frequency, width and height. For v (HDO) (Fig. 3.7) one saw an apparent discontinuity between 1 0 5 ° n and 120°K. The change i n slope may have arisen 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) vrtTI(HD0) from h.00% HDO i n D o0. The shallow molecular potential On d i s demonstrated by the low temperature l i m i t i n g v (HDO) frequency, i . e . On 3263.5 cm - 1 at 0°K compared to 3268 cm - 1 and 3288 cm - 1 at 8 0 ° and l80°K respectively. The HDO frequency-temperature plot (.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. Since there i s l i t t l e point i n doing a least-mean-squares f i t to some arb i t r a r y function, the data were approximated on a b i l i n e a r basis. Up to 45 * 5°K v (HDO) was constant within the random On point scatter, + 0.T5 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 to changes i n un R(0"*'*0) and the effects 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 for v (HDO) below 80°K On (+0.0U7 t 0.005) cm-1/°K. Above lt5°K one saw a d e f i n i t e effect due.to.in- creasing R ( 0 - - - " 0 ) , the s h i f t of frequency exceeds the point scatter. .Thus the thermal expansion data of B r i l l e and Tippe ( 6 0 ) suggest that when o AR(0 0)> ± 0 . 0 0 0 1 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 for v (HDO) between On 8 0 ° and 190°K, i_.e_. +0.200 t 0.005 cm-1/°K. Data of t h i s work are i n good agreement with the data of Ford and Falk ( 1 0 0 ) . Their data were shown i n Fig. 3.6 and were obtained from the best straight l i n e through t h e i r F i g . 2. One sees that the steadily increasing R ( 0 * - - , 0 ) i n a cubic ice l a t t i c e yields a steadily increasing v (HDO) frequency. 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 following 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 vOTI(HD0) between *t5°K and 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 to a p a r t i a l order- disorder phase transformation predicted i b be near 60°K by P i t z e r and , Polissar ( 7 0 ) . However, they pointed out probably greater than 2h hours. That peiiod i s far i n excess of our very that the period of t r a n s i t i o n was rapid cooling time of 15 - 20 minutes. P. a order-disorder phase transfor- mation i s also unsupported by any compara'lle s h i f t i n half-height 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 arisen from a transformation from an as yet uncharacterized low temperature ice phase, or from one of the disordered high pressure ices. A low temperature phase transformation i n ice 1^ was not indicated 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 contribute l i t t l e to Cp. (c) VQp(HDO) from 5-9^% HDO i n Ĥ O. The general comments made above with respect to V Q J J ( H D O ) apply as we l l to V Q ^ H D O ) : However, there are differences i n d e t a i l s . Specific differences can be seen i n F i g . 3.6 and Table III.IV (pages 71 and 72). The low temperature l i m i t i n g v Q D(HDO) f r e - quency was 2412.0 - 1 cm The r a t i o of HDO frequencies, v ^ / v ' , i s U n U D 1.35^ - 0.001. That r a t i o i s the same as reported by Whalley (96) for ices I , I I and I I I and i s very close to the vapour phase r a t i o of 1.360. From the r a t i o s one can show that the HDO anharmonicity, as discussed by Whalley (96), 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% larger 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 section. . The temperature dependence of V Q ^ ( H D O ) was different from that of v^^XHDO) i n several ways. The v__(HD0) data were constant within the point U n U D scatter up to 30 t 5°K i n contrast to 45 ± 5°K for v_„(HD0). The low U n temperature dependences of v and were the same.. However, the high temperature dependence of vnT. was (+0.123 - 0.005) cm "V°K (Av^/AT was U D U n I.626 times higher, 0.200 cm~'1"/0K). The differences i n the high temperature dependences probably arose from differences i n the physical properties of 125 the two mediums. The v data are from HDO i n DO 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 for the asymmetric stretches i n HDO, D̂ O and Ĥ O, T _ 0 percentage s h i f t = VSTR VSTR x 1 0 0 v STR T where v i s the stretching frequency at temperature T, bin and v^ m T 3 i s the low temperature l i m i t i n g frequency, bin One might have expected i n Ĥ O and D̂ O to s h i f t by the same percentage of the low temperature frequencies. However, between 1 0 ° and l60°K the —2 -2 s h i f t s of H 2 0 and D G 0 increased from 0 . 6 x 1 0 % to 82 x 1 0 % and 0 . 0 $ to _;2 36 x 1 0 % respectively. The stretching frequencies do not s h i f t propor- t i o n a l l y . The s h i f t s of v . ^ C H D O ) and v (HDO) are not proportionally the un uv same, nor do they compare to the percentage s h i f t s of i n Ĥ O and D̂ O. The VQ ^ (H D O ) s h i f t was faster than for v^D^O) at a l l temperatures,, while the v O I J ( H D 0 ) shifted proportionally faster than v_(H O 0 ) only below 100°K. On 3 d The percentage s h i f t from the low temperature l i m i t i n g frequencies were: Temperature °K Percentage S h i f t x 102 V O H ' ( H D O ) v Q D ( H D 0 ) v 3 ( H 2 0 ) v 3 ( D 2 ( 2 0 0 .9 0 .1+ 0 . .6 0 1+0 2 • 5 3 • 7 1 , .8 1 . 2 60 7 . 0 9 . 1 1+, . 0 3 .7 80 ll+. .1+ 17 .1+ 9. .3 7 . 0 1 0 0 23 .6 26 . 1 2 1 . . 2 1 1 .6 2 0 35 . 2 36 . 1 37. .1+ 17 . 0 1+0 1+6 • 9 1+6 . 0 60. .5 '25 . '2 60 59 .1+ 57 .6 81. .7 36 . 0 80 73 . 2 70 .1 — 55 .9 2 0 0 89 . 2 81+ . 2 — — 126 Dantl (6h) found the thermal expansion co e f f i c i e n t s for H 20 and D 20 l a t t i c e s were the same above 120°K. Hence, differences i n A R / A T seem to be an u n l i k e l y source of the dispersion. The difference i n temperature depen- dences may arise from differences i n HDO coupling to H 20 and D 20 lattices.. I f HDO coupling to D 20 decreases faster than to H 20 then the OH (HDO.) hydrogen bond to DpO must weaken faster and the vOTI(HDO) frequency must s h i f t faster On than v Q D(HDO). The v (HDO) data are not i n as good agreement with the data; of^ Ford and Falk ( 1 0 0 ) as for v_„(nT)0). Again t h e i r data are from the best Un straight l i n e through t h e i r F i g . 2. The v slopes agree but their.data are displaced 2 cm 1 to lower frequency. This i s probably due to d i f f e r - ences i n instrument c a l i b r a t i o n . ( i i ) Dependence of HDO Frequencies on R ( 0 , , , ' 0 ) The relationship between v and R ( 0 ' , - , 0 ) for a large family of Un molecules was studied by various authors (27-30) and several empirical r e l a - tionships were proposed ( 2 8 , 2 9 , 3 2 ) by neglecting s p e c i f i c differences i n molecular properties. The empirical relationships give only an average v /R(O--'-O) behaviour. The HDO frequencies observed i n t h i s work permit Un the v / R ( 0 * - - * 0 ) dependence for one molecular system to be accurately eva-Un luated. (a) Observed HDO frequency dependence on calculated R ( 0 « ' * 0 ) . The observed HDO frequencies are known as a function of temperature (page 71 ) 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 ice I as a function of temperature. A detailed study of the temperature dependence of the l a t t i c e para- meters of cubic ice I has not been reported i n the l i t e r a t u r e . However, the 127 cubic ice I l a t t i c e parameter was given by Wyckoff (62) for lU3°K, o o a o(H 2 0) = 6.350 ± 0.008 A and a o(D 2 0) = 6.351 - 0.008 A. For hexagonal ice I , B r i l l e and Tippe (60) made a detailed study of the l a t t i c e parameters between 13° and 193°K: a Q , c Q and the linea r thermal expansion coef f i c i e n t s were evaluated every 20° from 13° to 193°K. In addition, x-ray d i f f r a c t i o n (58) and i r (95) studies indicated that the nature of the hydrogen bonding and the nearest-neighbour configurations are the same i n hexagonal and cubic ice I. On that basis we assumed the linea r thermal expansion c o e f f i c i e n t of cubic ice I (aa,o^' ) "to be the average of the expansion co e f f i c i e n t s of hexa- , hex hex gonal ice I (ct a o (T) + cxcQ (T)), _i.e. cub/ x 1 / hex, , hex a a (T) = 2-(cxa0 (T) + a c 0 (T)) at temperature T.. cub Values of a a Q (T) were determined every 10°K i n the i n t e r v a l 10° to 200°K by the following method. B r i l l e and Tippe's (60) ten a Q and c Q para- hex meters were plotted as a function of temperature. Twenty values of aa Q (T) hex n o and a.c0 (T) were determined at ten temperatures between 20 and 200 K, two values at each temperature. The pairs of co e f f i c i e n t s at each temperature were obtained from intervals of 2 ° above and below that temperature, JL.e_. a h e X ( l 50°K) = I [ a h e X ( l 4 8 ° - 1 5 0 ° ) + a h e X ( 1 5 0 ° - 1 5 2 ° ) ] a 0 2 a Q a Q In the same way ac^ X(T) was evaluated. From the ten values of ̂ ao^T1) and CCQ X(T) , ten values of were obtained, F i g . h.l. Using Wyckoffs (62) ao U b(H" 20) at l43°K (6.350 A) and the li n e a r thermal expansion coef f i c i e n t s i n F i g . U.l, the cubic ice I l a t t i c e para- meter aQ U b(T) was calculated every 2°K down from lh3° to 10°K and every 2°K up from lh3° to 200°K, aQ U b(T) i s shown i n F i g . h.2. [Since the a^tn^O) and a^ u b(D Q 0) l a t t i c e parameters were the same within experimental error, 6 0 -1 5 0 - 4 0 - 3 0 - 2 0 - 10 - O i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 — — i 1 1 O 5 0 1 0 0 T 5 0 2 0 0 T E M P E R A T U R E ° K Fig." h.l—The'"'"llne"ar- thermal""expansion coefficient of cubic ice I as a function of temperature calculated from the hexagonal ice I data of B r i l l e and Tippe ( 6 0 ) . ^ CO 2 0 0 H Y. o LU D h < Ld CL UJ h 50H 100 H 50 - O 129 i r 6.345 6.350 6.355 r 6.360 6.365 a C U B I C ICE i ! Fig. k.2 The cuhic ice I l a t t i c e parameter as a function of temperature. The values were calculated from the experimental a Q at l43°K and the calculated thermal expansion c o e f f i c i e n t s . 130 only the a^^CHgO) parameter vas evaluated.] For the cubic ice I unit c e l l the distance R(0 0) = ( J$~t'/k)a^°{T). The r e s u l t i n g cubic ice I 0 0 distances are plotted i n F i g . U.3 as a function of temperature. HDO stretching frequencies from section 3.2A are plotted as a function of R(0**' -0) i n F i g . k.k. Frequency and R ( 0 , , , - 0 ) were correlated as a function of common temperature. The frequencies were plotted as a function of the experimentally measured temperature, uncorrected for source beam heating (+10°K at 83°K) since the error may not be a l i n e a r function of tem- peratures. Both the v^„(HD0) and v^(HDO) plots were l i n e a r from 150° to 200°K: Un 01) Av (HDO) — — = 1.921 x 10 J cm AR(0 0) I and A V 0 D ( H D 0 ) 1 p f l l i n 3 -1 = 1.2ol x 10 cm AR(0 0) A However, the v (HDO) frequency should be plotted as a function of R(0'" -"0) for D20 ice I , since the v data were obtained from a sample of k.0% HDO i n Dg,0. There i s no experimental evidence to 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 D20 ices are d i f f e r e n t . However, i t may be incorrect to assume the same behaviour since the amplitudes of trans- l a t i o n , l i b r a t i o n and vibrati o n are d i f f e r e n t . From F i g . h.k one sees that the frequency—R(0 , , ,*0) dependence i s also l i n e a r between 30° and 100°K: 250 2 0 0 H 0 UJ ^ 150 h < w IOO Q_ (- 50 H o o • o • o • o o • o • • o o C - AXIS ICE I © A - AXIS J • A - AXIS ICE I h O T 1 1 1 1 1 1 1 1 1 r 2.755 2.760 "1 1 1 2.765 2.745 -T 1 r-2.750 R (O O ) A F i g . h.3 "The calculated 0•••-0 distance In" cubic' ice I as" a function•of" temperature compared to hexagonal ice I 0*••*0 distances from experimental data. H 132 u y u z UJ Z) o UJ or LL o Q i O O CD CM r o o 00 C\J r o O CM r o O CO CM r o oo CvJ OJ 30i oiano (o --o) d F i g . h.k The HDO stretching frequencies i n cubic ice I as a function of R(O--'-O). 'Frequency and R(0 -••*0) were correlated at common temperature. 133 • ̂  = 8.202 x 10 3 cm"1/! AR(0 0) Av 0 D(HD0) 0 = 6.629 x 10 cm /A AR(0 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 ction of the low and high temperature l i n e a r dependences were at 125°K o (2.748.7A) for both v.„(HD0) and v.^(HDO). Un. OD - 1 ° For 100°K Whalley (95) assumed a Av/AR dependence of 3000 cm /A to support his argument that the deviation 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 disorder was only a few hundreths of an angstrom. The tangent to v.u(HD0) vs. R ( 0 " " 0 ) at 100°K i n F i g . 4.4 has Av/A R equal Un 3 —1 ° to 6.750 x 10 cm /A, showing that Whalley's estimate was low by a factor of about two. As w e l l , Whalley (96) found that the most intense v (HDO) bands for O H ices I I , I I I and V were 3323, 3318 and 3350 cm"1 respectively. Using Av/AR above, then the displacements of 51, 46 and 78 cm 1 from i c e I vriu(HD0) U n (3272 cm were caused by larger 0''*'0 distances. S p e c i f i c a l l y , the most intense v (HDO) absorptions i n ices I I , I I I and V had R(0'"*0)'s larger U n o than cubic i c e I (100°K) by 0.008, 0.007 and 0.012 A. Ice I I also had two other v„u(HD0) absorptions (3357 and 3373 cm ^) which suggest two other U n o sets of 0 " " 0 distances. They are longer than R(0 0) cubic (2.748 A) o by 0.013 and 0.015 A respectively. Thus ice I I appears to have three d i s - t i n c t O 0 bond lengths, 2.756, 2.761 and 2.763 A. 13h Ice I I I had one additional peak at 100°K, 3 3 2 6 cm 1. That could be due t o a second d i s t i n c t '0*••*0 distance, which i s longer than R(0 0) o cubic by 0.008 A . Thus ice I I I has two sets of 0 # , , , 0 distances, 2.755 and 2.756 A. o • Ice V has only a single 0"'*'0 distance, 2.760 A. How well the Av/AR relationships of ice I apply to other ices i s not cer t a i n . The estimates of RCO-'-'O) above are only approximate. At 0°K the half-height width for v.^CHDO) i n D o0 cubic ice I was found to be 35.5 cm That indicates that the 0'"''0 distances vary by o less than 1 0.00U A from the average value i n cubic ice I at 0°K. The S. - l AvOTI(HD0) rose to U2.5 cm at l80°K. Thus the R(0 0 ) deviation must OH o 3j have been less than 0.022 A. Since the observed Av data were twice the expected width f o r an ordered phase ( 9 6 ) , then the deviations 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 disorder were less than 1/2 the above values, o ± 0.002 and ± 0.011 A for 0 ° and l80°K respectively. S i m i l a r l y by using Av0r>(HD0) and. Av Q D/AR one finds dispersions i n R(O--'-O) of ± 0.002 and o " ' • ± 0.010 A at 0 ° and l80°K. .. As one would expect the dispersions of R(0*••'0) i n Ĥ O and D̂ O are equal but the changes i n force constants are related by approximately 1 y~2. Clearly one does not expect the HDO frequencies to be a l i n e a r func- t i o n of 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 of the hydrogen bond should increase as (l/R(0'••*0)1^as temper- ature i s increased. Correspondingly the covalent nature of the bond w i l l 135 change non-linearly. The effects of such changes i n hydrogen bond strength are seen i n the observed non-linear behaviour and i n the four-fold i n - crease i n Av/AR. (b) Comparison of observed and empirical Av/AR rel a t i o n s . The detailed study of vr.tI(HDO) absorption as a function of temperature and i t s On correlation to R(O----O) permitted detailed checks of empirical relations between stretching frequencies and hydrogen bond lengths i n ice I. Many workers ( 2 7 , 2 8 , 3 3 ) have made correlations from data of large numbers of compounds i n different hydrogen bonding families. The lin e a r relationship of Pimentel and Sederholm ( 2 8 ) , 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 ice 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) to a maximum effec t i v e hydrogen bond length and the measured 0 , * ' - 0 distance: = k.h3 ( 1 0 3 ) (2.8U-R) cm' -1 Av st r = c [ ( f ) 1 2 - ( | ) 6 ] where Av str s h i f t of the stretching 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 o i n Angstroms (d = 3.35 A), R the 0*-,'0 distance i n Angstroms, and C the constant of proportionality between the potential 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""1. Their predicted Av , agreed SX>TC very well with the observed values, particularly at long 0'-«-0 lengths, for a family of 0-H-''*0 systems. By using the R(O--'-O) values determined in section (a) above for 10°K and 130°K, two values of the constant C were determined for ice I: C(10°K) = 58.890 cm"1. C(130°K) = 57.767 cm" 9 -1 The constants were determined by substituting the Av , values between S X/± V Q H ( H D 0 ) of the vapour phase ( 3 7 5 7 . 5 cm "*") and the cubic ice I values (10°K 3 2 6 3 . 8 cm - 1 and 130°K 3 2 7 6 . 8 cm - 1). The constants were then used to calculate A.v . (R). Since the thermal expansion of cubic ice I is only small between 10°K and 200°K, Bellamy and Owen:.';s(33) formula could only be checked over a small range of 0*••-0 distances. The predictions of Bellamy and Owen's formula and the observed Av/AR relation are shown in Fig. U.5. For the constant determined at 130°K the predicted behaviour was good above 130°K but did not follow the observed trend below 130°K. Over o o the 0 0 range 2.7^70 A to 2.7570 A Bellamy and Owen's formula predicted _1 O -I o o Av/AR = 2 , 2 6 3 cm /A. Experimentally Av/AR = 7,360 cm /A from 2.7^70 A O n O O O to 2.7U80 A ( 1 0 ° to 110°K) and Av/AR = 2,lhk cm /A from 2.7U85 A to 2.7570 A (130° to 200°K). Thus above 130°K Bellamy and Owen's formula reproduces the ice I experimental behaviour well. Below 130°K (R(0'*-'6) less than o 2.7U85 A) their formula f a i l s . Bellamy and Owen ( 3 3 ) started from the Lippincott-Schroeder potential and made certain assumptions about the intermolecular interaction. The Lippincott-Schroeder potential ( 2 5 ) consists of four terms, one term being 137 0 < 2 . 7 5 5 - o 6 *—* o LU 5̂  2 . 7 5 0 2 . 7 4 6 - • — 2 0 0 ° K 150 ° K mu* I O O ° K ^ 5 0 0 K A ' - IO°K 3 2 6 0 7 0 8 0 9 0 F R E Q U E N C Y C M Fig. 4.5 The stretching frequency—R(O----O) dependence. The observed frequencies are plotted against the' R(O-'--O) distances e s t i - mated for cubic ice I from hexagonal ice I linear thermal expansion coefficients and are indicated 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 triangles ( • , • ). due to van der Waals repulsive forces. Bellamy and Owen investigated the van der Waals repulsion on the basis of a Lennard-Jones 6-12 potential by assuming the interaction of non-bonding f i l l e d o r b i t a l s was similar to that of non-polar spherical atoms. Bellamy and Pace (32) suggested that i f the van der Waal's repulsion originates largely i n the lone-pair/lone-pair repulsions of the two oxygen atoms then the 6-12 provides a good distance/ energy r e l a t i o n . The re l a t i o n between the potential energy and the frequency 138 s h i f t was assumed to be l i n e a r . From our resu l t s the assumptions of Bellamy and Pace (32) and Bellamy and Owen (33) are not contradicted between 130° and 200°K, but are contra- dicted below 130°K. That suggests that the van der Waals repulsion does not originate only i n the lone-pair/lone—pair repulsions below 130°K, or that 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 resulted i n a s h i f t to higher frequency as temperature was lowered, i n opposition to the observed increase i n s h i f t to lower frequency. I t i s possible that the 0-H stretching amplitude affects the strength 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 po 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 to increase above 130°K and did not reach a l i m i t i n g value, i_^e_. between 73° o and 173°K the RMS amplitude of 0-H stretch 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 that the modulation of the p o t e n t i a l energy did not approach a l i m i t i n g value. The Bellamy and Owen (33) formula reproduced the Av/AR re s u l t s for a large number of molecules observed near 300°K, while our resu l t s were ob- tained below 200°K. One i s tempted to look for a property common to a l l samples above 130°K. Such properties may be the population of t r a n s l a t i o n a l 139 hot bands and large amplitudes of tra n s l a t i o n . Molecular tr a n s l a t i o n would modulate the 0-**-0 distance and hence the hydrogen bond energy. Larger amplitudes of tran s l a t i o n would resu l t i n increased modulation of the poten- t 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 to 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). According to Ki b l e r and Pimentel ( l 2 l ) the anharmonicity X O T I of HDO i n the vapour phase, i s . On 91.2 cm \ For cubic ice I Haas and Hornig ( 1 0 6 ) predicted X (from On overtone data) to be 125 cm 1 while Bertie and Whalley ( 9 6 ) estimated i t to be 100 cm 1 (by a modified product r u l e ) . While Bertie 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 did 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 Bertie and Whalley ( 9 6 ) . •, Application of free molecule theory to 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 yields useful q u a l i t a t i v e i n f o r - mation. For a free, bent XY 2 molecule one finds that ; v l = u l ~ 2 X 1 1 ~ X 1 2 " X13 v 2 = u 2 - 2 X 2 2 - X 2 1 " x 2 3 v 3 = o>3 - 2X 3 3 - X 3 1 - X 3 2 . iko I f X. . ( i ~f j} are assumed to be small and are neglected then V l = <°1 - 2 X 1 1 ' v 2 = co2 - 2X 2 2 V 3 = "3 ~ 2 X 3 3 - For isotopic substitution one can employ the Teller-Redlich product rule i i i p = a i> e . over 1 symmetry representation . w a u>b w e and by analogy to the diatomic case one also knows that x 1 1 1 A i i l i l t Id For of H20 and D^O the application i s straightforward since v^ and v 2 are of a^ symmetry while v^ i s of b j symmetry (assuming the C 2 v point group) Then ' • » ' ^ - and p. - \ ±f - > . Hence, one can write for HgO V 3 = W 3 " 2 X 3 3 " x " 2 and for DgO v 3 = ^3 ~ 2 X 3 3 = p (°3 ~ 2 p X33 By assuming that p of the vapour phase (say from Nibler and Pimentel's harmonic data) applies also to the s o l i d and by using the observed H20 and D20 frequencies, then the two equations can be solved for w? and X-^ of i c e I. l U l For H D O the prohlem i s more complex. The s t r i c t product rule would he V O D ^ H O D V ^ X h d o P = • 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 not), the product rule i s s t i l l complex " O H W H O D W1 W3 W2 As an approximation we can treat the problem as a diatomic molecule H -(0D) with the isotopic analogue D - ( O H ) . Then the product rule i s W0D P = " O H The expected value of p i s given by 1 W0H IG _ - r M D + t m 0 + M H ' 1 " O H I I mH + (mQ + mD) = 0.T2T8 . From the vapour data of Nibler and Pimentel ( 1 2 1 ) one finds p= 0.'726l. B r i e f l y the method of Bertie and Whalley ( 9 6 ) involved assuming such a modified product rule for H D O , where P W 0 D ( i c e ) u Q D(vapour) cjjQH(ice) <u (vapour) and OD 2 X — = p X0H 1U2 Then v OH OH - 2X. OH and ' v OD OH - 2p 2X, OH where p = O.72608 of the vapour phase. The anharmonicity of the HDO s t r e t - ching vibrations i n ice I was then given by Hence the anharmonicity can be determined as a function 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 Figs, 4.6 and 4.7 respectively. While the magnitude of the calculated anharmonicity i s not accurate, the trend i n X o u(T) indicates some fundamental changes i n the hydrogen bonded system. Be-On tween 1 0 ° and 80°K X.„ underwent a regular increase of k% and from 8 0 ° to On 200°K X_„ underwent a regular decrease of k%. The low temperature(limiting On -1 -2 anharmonicity was 105.6 cm , the low temperature dependence was 3.25 x 10 -1 -2 -1 cm /°K, and the high temperature dependence was - 3 . 7 5 x 10 cm /°K:. The anharmonicity reached a maximum at 80°K. The temperature dependence of to was 0.138 cm "V°K i f i t was assumed to be l i n e a r . The maximum i n the ; anharmonicity i s also seen i n the harmonic frequency. The anharmonicity was also plotted as a function of R ( 0 , , , - 0 ) , Fig. 4 . 8 . That plot looks surpris- ingly l i k e a Lennard-Jones 6-12 potential energy curve. • •, The harmonic HDO frequency and the anharmonicity of HDO stretches as a function of temperature were estimated from, observed v (HDO) and On v_^(HD0) frequencies. Hence, the variations of uin„ and X„ T as a function OD On On of temperature arise from a l l sources present i n the cubic ice I c r y s t a l s . There appear to be two major sources of changes i n the anharmonicity as a function of temperature. As the c r y s t a l i s cooled from 200°K to;5°K i t contracts and R ( 0 - * * - 0 ) decreases. The hydrogen bond energy increases, 2p (1 - p) 11+3 O i i i 1 1 \ 1 3475 3485 3495 3505 co (HDO) c m - 1 Fig. h.6 The harmonic HDO stretching frequency for cubic ice I as a function of temperature. The w^CHDO) was estimated from observed HDO cubic ice I frequencies. Ikh . 1 Fig. h.l The HDO cubic ice I anharmonicity as a function of temperature The X values were estimated from observed HDO stretching frequencies and the p value of the vapour phase. Hence one would expect a steady increase i n the contribution of increasing hydrogen bond energy to the t o t a l anharmonicity down to about 80°K (the 1U6 R(O-'--O) freeze-in 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 to changes i n the amplitudes of 0-H stretch and HDO t r a n s l a t i o n . The 0-H stretching 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 state. As was indicated previously, the 0-H ampli- tudes have been measured experimentally (ref. 5, page 78) and increased from o o 0.150 A at 1°K to 0.221 A at 200°K i n H 20 ice Ih. Corresponding 0-D, ampli- o o tudes for D 20 were 0.129 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 to decrease below 200°K. .As w e l l , the RMS amplitude of tran s l a t i o n decreases from 200°K to 1°K. Since v , X , and oi are a l l strongly coupled to the instantaneous On OH On R(O----O), then decreases i n the range of R ( 0 , , - , 0 ) through decreased ampli- tudes of tran s l a t i o n w i l l give a smaller range of X_.„ and a net. smaller: Un X0H' We suggest that: l ) below 80°K AX n T J from changes i n amplitudes i s On greater than AX due to changes i n hydrogen bond energy, 2) at 80°K the Un two kinds of AX.„ are equal, and 3) that above 80°K AX (hydrogen bond OH On energy) i s greater than AX.^ (amplitude.). On (d) Correlation of the HDO stretching frequencies to the RMS.ampli- tudes of tran s l a t i o n . Since the HDO stretching frequencies are a function of R(0'--*0) 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 interesting to consider the relationship between v and<Ar^> 2 as a function of temperature. l V f Decius (122).gave the mean-square displacement from the equilibrium distance between two atoms resulting from a l l modes of vib r a t i o n as: < f i r 2 > = 2 L 2 k < o 2 > [ l ] k where o Ar^. = the displacement distance of in t e r n a l coordinate t due to a l l normal coordinates, k, = the element of the matrix transforming normal coordinate k into internal coordinate t , and 0̂ . = "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 hcv k <Qv > = o 2 coth ±L r o l K OTT^CV^ 2kT L 2 J where v, = 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 i n degrees Kelvin, c = the vel o c i t y of l i g h t , and h = Planck's constant. The formulas [ l ] and [2] were derived for the'isolated, free molecule case. In a rigorous treatment of ice i t would be necessary to consider a l l in t e r n a l and l a t t i c e modes i n the sum over k. Cubic ice I has two HgO molecules per primitive unit 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 si x in t e r n a l v i b r a t i o n a l modes. I f the pair of HgO molecules i s considered as a weakly bonded diatomic molecule, (HgO)••'*(H20), then there i s one normal mode of v i b r a t i o n , the IkQ R(0-•••(}) stretch. The mean-square amplitude of tran s l a t i o n between two molecules can then be estimated. Equations [ l ] and [ 2 ] give h <AR^> = < A r ^ > = LL'T^ coth he 71 C VT 2kT and for the (H^cOg "diatom" LL' = G, which i s ea s i l y evaluated for HgO or DgO. The RMS amplitude of displacement i s then given by h < A r 2 > = hcvm coth i - mi U T T 2 C V T 2kT 2 ^ .3] where m̂  i s the mass of H ^ O or D 2 0 , and the vari a t i o n of<[Ar ) as a function of temperature can be calculated by using the observed v^CH^O) frequencies. y o h Two sets of <Ar^) were calculated between 1 0 ° and 200°K. In both cases the v^HgO) frequencies used were from the best smooth curve through the experimental points (Fig. 3 . 1 5 ) . Since the v ^ H ^ O ) frequency varied by less than 5% between 10°K and 2 0 0°K, one set of <Ar2>'5 was calculated at constant v t L-OL' V I J = 2 2 7 . 0 cm 1 at 80°K. That i s reasonable since l/T dominates the function. A corresponding set of ( A r 2 ) for E>20 were calcu- lated using the H 2 0 frequencies and D 2 0 masses. These data are compiled i n Table IV.I and are plotted i n Fig. k.9. For comparison, a set of HgO (Ar 2} 3" 2 were calculated using the f u l l range of observed frequencies..' Those data'are also compiled i n Table IV.I. The only s i g n i f i c a n t change was a sligh t decrease i n the low temperature values and a s l i g h t increase,- i n the high temperature values. Plots of R C 0 - - - " 0 ) against ( A r 2 ) at equal temperatures and of v 0 H ( H D 0 ) and V Q ^ H D O ) against ( A r 2 ) 3 5 are given i n Figs, k.10 and U . . 1 1 res- pectively. TABLE IV. I The RMS amplitudes' of tr a n s l a t i o n calculated from H20 v T and compared to r e s u l t s of-thermodynamic calculations. <Ar 2> 1 5 <Ar 2> h <Ar 2> 35 <Ar2> Temperature H20 • v \ D20 H20 const. Vrp v TtT) COnSt . Vrp (a) (a) o o 0 0 9 0 _ 0 °K xl O 2 A xlO^ A x l O 2 A xlO^ A xlO^ A 1 9.2 9.0 10 9.08 9.01+ 8.61 20 9.08 8.61 30 9.08 9.01+ 8.61 1+0 9.08 8.62 50 9.10 9.06 8.63 60 9.12 8.65 70 9.IT 9.11+ 8.TO 80 9.25 8.TT 90 9.33 • 9.32 8.85 100 9.1+1+ . 8.95 13.2 10 9.57 : 9-59 9-0T 20 9-TO 9.20 IH.5 30 9.81+ 9.96 9.31+ 1+0 10.0 9-̂ 9 50 10.2 10.1+ 9.65 60 10.1+ 9.82 TO 10.5 10. T 9-99 80 10. T 10.1 - 90 10.9 11.2 10.3 200 11.1 10.5 18.5 223 19.5 2T3 21.5 21.1+ (a) Ref. 81+. D O < A r 2 > 2 A x l O 2 8.6 9.0 9 5 IO.O 2 0 0 H 5 C H IOO-1 50 10.5 9.0 9.5 IO.O H O W z f A x IO: ;. U.9 The RMS amplitudes of H20 and DpO translation calculated with a constant v T(H 20) assuming an (H 20) 2 diatomic unit c e l l model. i— 1 O 200 0K t O 0<[ 2.755-1 jo X 2.750- 2.746 I50°K IOO°K 50°K 1 O l o o o o ° IO°K "i r 9.0 9.5 IO.O L o "i i | i r I0.5 H 0 < A r 2 ) 2 A x l O ' i — i I.O Fig. U.10 The correlat i o n of RMS amplitude of translation to the calculated 0 f , , , 0 distance i n cubic ice I. " ' R(0-• •'i0)" and ̂ Ar2) !s were correlated as a'function of common temperature. H 3 2 9 0 - O o Q I 3 2 8 0 - 3 2 7 0 - 3 2 6 0 - 2 0 0 0 K i • I 5 0 0 K A I A I 5 0 0 K I • • • I O O ° K A I • I O O ° K - A - 5 0 ° K I | 0 0 K - 4 0 ° K O > — 5 0 ° K O ° K 2 0 0 ° K I - 2 4 4 0 2 4 3 0 Q ys ( A r 2 ) 2 D O I O ° K . Z / V S ( A r 2 ) 2 H O O D — X 2 2 4 2 0 2 4 I O 8 . 6 9 . 0 9 . 5 I O . O 1 0 . 5 I I . O 0 O H p < A r 2 > " A x lO 2 Fig. h.ll The dependence of the observed HDO stretching frequencies' on the RMS amplitudes of tr a n s l a t i o n w of HgO and D20. The frequencies continued to decrease although the ̂ Ar2^ 3 s became constant at low temperatures. 1 5 3 From Table TV.I one sees that the RMS amplitudes of tran s l a t i o n for HgO and D 20 agree at low temperatures, i_.e. below- 10°K, quite well with those calculated by Leadbetter ( 8 U ) from thermodynamic data. His data appears to be linea r i n temperature over the whole range, 1 ° to 273°K. . However, the temperature dependences of our calculated (Ar2) ̂ are non- linear and are much smaller than h i s . Between 1 0 0 ° and 200°K his RMS -h ° -1 , -k amplitude increased by 5-3 x 10 A/cm while ours increased by 1.6 x 10 o _-. o A/cm . For HgO ice I at 200°K we calculated RMS amplitudes of 0.111 A while- o he calculated 0.185 A. There are probably several reasons for 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 larger amplitudes of molecules i n excited t r a n s l a t i o n a l states must certainly 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 excited states. The contribution of the l a t t i c e fundamental at l 6 0 cm 1 to the ind i v i d u a l molecular amplitude must be even larger than for the 229 cm 1 fundamental chosen above, although the apparent density of states i s l e s s . The plot of < A r 2 ) ^ against R(0 0) i n Fig. k.10 showed that below 50°K our calculated RMS amplitude was constant although our calculated 0'"''0 distance was s t i l l decreasing. As w e l l , below 50°K the frequencies continued to decrease. These results also support the conclusion that below 100°K factors other than R(0 0 ) affected the HDO stretching frequencies. 15 *»• ( i i i ) HDO Stretch 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 for v (HDO) and v w(HD0) were 23.5 cm" and 35.5 cm" res- ujj oh. \ i % j pectively. At 100°K Av^(HDO) was 23.5 cm and Av^(HDO) was 35-5 cm 01) On which compared very well with the data of Ford and Falk (lOO) (23.5 cm"1 and 33 cm 1 respectively) at similar temperatures. Ford, and-Falk (100). took great care to ensure they had very low and well known concentrations of* HDO in D20 and H20. For the di l u t e samples of HDO i n HgO and D20 used i n t h i s work, care was taken to prevent accumulative exchange between atmospheric H20 and D20 l i q u i d during handling. In our HDO i n D20 samples, exchange of D2.0 with unwanted H20 absorbed on preparative surfaces or H20 vapour i n the atmosphere enriched the concentration of HOD. The fact that our Av^T(HD°) On was somewhat larger than Ford and Falk's (100) indicated our HD0/D2Q con- is centration was more than the k.00% intended. Our Av (HDO) was probably On broader than Falk's, due to increased coupling. Our widths were s t i l l much h ; -1 narrower than those observed by Whalley ( 9 6 ) , i . e . Av (HDO) = 50 cm . and — — OH h -1 Av (HDO) = 30 cm . It i s important to recognize that the coupling-broadening does not necessarily originate from HDO-HDO pairs. Since at least one HDO stretching frequency i s always coupled to the host, even at low concentration, and since the (H20 or D20) bands are both very broad d i s t r i b u t i o n s of frequencies, then HDO may have a quite broad range of interaction energies with H20.and D20 neighbouring molecules.. The consequent range of perturbations i n f l i c t e d on the isolated 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 to 155 a -wider range of perturbations giving increased AA> even i n the absence of HDO-HDO pairs. Clearly, the number of HDO molecules coupled to the fewer l a t t i c e molecules with stretching 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 central 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 for V Q D ( H D O ) from 5 . 9 W D 2 O i n H 2 O showed good agreement since exchange with atmospheric HgO was only very slow and tended to deplete HDO rather than increase i t . Half-height widths of stretching modes i n the high pressure ices, were . . L \ n —1 indicated by Whalley ( 9 6 ) to be: AvSL = 5 cm and A v ^ = l o cm for ices I I and I I I . There was obviously a dramatic change i n the ice c r y s t a l i n transforming between ice I and ices I I or I I I . Whalley ( 9 6 ) and others ( 1 0 0 , 1 0 5 , 106) suggested a number of reasons for the observed ice band widths. The postulates can be condensed into four main mechanisms. The f i r s t mechanism was f i r s t mentioned by Hornig ( 1 0 6 ) , but Bertie and Whalley ( 9 6 ) have described i t i n more d e t a i l . The mechanism suggested the band width arose from closely spaced transitions between a range of closely spaced ground state energies and corresponding, closely 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 state, but that over the whole c r y s t a l the sets of equivalent molecules sat i n sites of varying 0-H-*-*0 energies. The va r i a t i o n of 0-H*••'0 energies arose from the variation i n 0----0 distances prescribed at equivalent oxygen site s by disorder allowed i n the proton orientations. A result of the proton orien- t a t i o n a l disorder at.equivalent oxygen positions i n the set of unit c e l l s 156 was the loss of s i t e symmetry. Consequently, a l l vibrations became a or a' and the selection rules collapsed to one general selection rule allowing transitions between a l l forms of combination and overtone l e v e l s . The second mechanism of stretching region broadening was.through Fermi resonance of any fundamental (or the fundamental sum and difference bands with low frequency l a t t i c e modes) with other overtone and combination bands such, as 2Vg» ^ VR' A N ^ v2 + 2 VR' Notice that because of the lack of s i t e symmetry through proton orientational disorder, Fermi resonance between any two near- degenerate levels was possible, not just between 2v^ and as was expected from c r y s t a l s i t e symmetry. The t h i r d mechanism invoked Heisenberg's un- certainty p r i n c i p l e . S p e c i f i c a l l y , the energy l e v e l uncertainty, AE,, was J, increased by a shortened h a l f - l i f e , At , of the upper state by either proton tunnelling to an ionized state or by resonance interaction between the ,. excited fundamental vibration and overtones of l a t t i c e modes giving the ground state, fundamental int e r n a l mode and excited l a t t i c e vibrations.. Both proton tunnelling and ejection from the excited vibration to nearby upper l a t t i c e modes constituted radiationless t r a n s i t i o n s . The fourth 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 difference bands as sources of broadening are not s i g n i f i - cant. I f the observed stretching modes were broadened by difference and hot bands involving l a t t i c e modes, then the stretching modes should have,; under- gone s i g n i f i c a n t sharpening once the higher l a t t i c e energy levels were 157 depopulated at low temperatures: The.stretching modes were not s i g n i f i - cantly sharpened as far down as 10°K. A simple calculation of the ra t i o s of numbers of molecules i n the ground, 1 s t , 2 n d and 3 r d excited states for —1 —1 v T( = 229 cm ) and v R C = 832 cm ] showed that at 10°K a l l upper levels were e f f e c t i v e l y depopulated. These observations removed mechanism four from consideration as a source of broadening. The observed "freeze-in" of half-height width supported mechanism one, the proton orientational disorder mechanism. For that mechanism, as the sample was cooled and the l a t t i c e contracted, the mean deviation from the ideal symmetry s i t e of the oxygen atoms decreased. Since the mean deviation of O-'-'O distances was also a measure of the range of hydrogen bond energies and the range of stretching frequencies, then as R ( 0 - - - , 0 ) decreased and ^ A r 2 ) 3 5 decreased so should the stretching band width. Once the 0'*'*0 d i s - tances were invariant, so was the half-height width. A further modification to the stretching 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. Ideally one wanted to.compare the uncoupled OH stretch to the coupled OH stretch 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 stretch to coupled OH stretch i n i d e n t i c a l electron d i s t r i b u t i o n s . However, the periodic modulation of the electrons by l a t t i c e modes was, different for 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 effect of broadening of OH(HDO) stretch by the D̂ O l a t t i c e was different than the broadening of OHvHgO) stretch by the HgO l a t t i c e since H 2 O and DgO have different l a t t i c e , funda- mental frequencies and amplitudes. i 158 The half-height widths had a near-linear temperature dependence of 13.5 x l ( f 2 cm - 1/°K for v„„(HDO) and 7.0 x 10~ 2 cm _ 1/°K for v._(HD0) i n the U n U D high temperature range from 100° to 190°K. Those data compare wel l with our interpretation of the data of Ford and Falk (100) i n the temperature i- - 2 - 1 range 100° to 200°K,Av^HDO) changed by 4.5 x 10 cm /°K. In the temper- ature range from 100° to 273°K we deduced from Falk's data that the slope ofAvJf(HDC)) = 16.2 x 1 0 _ 2 cm" 1/^ and o£Wn(HD0)« 10.7 (10 _ 2) cm_1/°K. U n . U l J Our experimental data l i e w i t h i n th e i r r e s u l t s , and our scatter 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 stretching mode peak heights (I) and half-height widths were used to approximate the area of v (HDO) as a function of temperature. Simple U n triangles were constructed which had heights equal to the peak height on a l i n e a r absorbance scale and a base at 1/2 of %(A.v 2) . The area of two such t r i a n g l e s , extended to the baseline, was assumed to represent the integrated int e n s i t y (A) approximately. Typical r e s u l t s are given below: Temperature Av I A ° -1 2 K cm absorbance cm 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 with the concept of a weakening hydrogen bond and a decrease i n molecular dipole with increasing R(0....)) as temperature increases. Above 190°K the samples sublimed ra 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 loss by sublimation. A s l i g h t l y concave portion of the I ( V Q ^ (H D O ) ) betx<reen 110° and 140°K indicated f i r s t a more rapid and then a less rapid decrease i n hydrogen bond energy. Some unusual heat capacity effects were noticed near 110°K (82), but i t i s not c e r t a i n that the effects are related. 1 5 9 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 ice I (Fd3m) has two mole- cules per unit 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 translations of the whole f i n i t e c r y s t a l . Whalley and Be r t i e ( 8 7 , 8 8 ) developed a theory for hexagonal and cubic ice I which incorporates proton o r i e n t a t i o n a l disorder i n the description of v^. They deduced from an approximate density of states r e l a t i o n that points of inflection,minima and shoulders, as w e l l as peaks, are associated with s p e c i f i c branches of the o p t i c a l and acoustical modes. The l a t t i c e modes of hexagonal ice I were also observed by neutron i n e l a s t i c scattering ( 9 2 , 9 3 ) . 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 with some previous results ( 8 8 , 9 2 , 9 3 ) . The poor d e f i n i t i o n of the absorption features (other than the 2 2 9 cm 1 peak maxi- mum) made i t impossible to follow t h e i r temperature dependences. The features recorded here at 83°K agreed with the mull re s u l t s of Bertie and Whalley ( 8 8 ) and the condensation results of Giguere and Arraudeau ( 8 9 ) . The lowest temperature indicated by the (Au-Co) / (Ag-Au) thermocouple f o r t h i s experiment was 25°K, probably due to some s o l i d i f i e d N 2 (gj used t o precool the helium dewar. The low temperature (25°K) l i m i t i n g values of the features ex- h i b i t e d no special behaviour. From 2 5 ° to 70°K the maximum underwent a stage of invariant frequency up to 55 t 5°K, and an apparent s h i f t by 2 cm - 1 to lower frequency between 55 + 5 ° and 70 + 5°K. From 7 0 ° to 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- i 6 o tinuous, near l i n e a r s h i f t towards lower frequency of - 0 . 0 9 3 cm- /°K. Above l60°K (max.) remained constant at 2 2 1 i 0.5 cm \ In comparison, Zimmermann and Pimentel's ( 9 7 ) data indicated a slope of - 0 . 0 8 1 cm~^~/°K from 90°K to 250°K. The dependence(rate of change) of v T on the hydrogen bond energy was less than for the molecular modes, i_.e_. a given change i n hydrogen bond energy had 0.5 to 0.3 times the effect on v T as i t did on v R or the molecular modes. The s e n s i t i v i t y (minimum- detectable change) of v to hydrogen bond energy changes.was the same as for v , v n , v_ and v , o i_.e_. sensitive to changes of ± 0 . 0 0 0 1 A/°K i n R ( 0 - \ - - 0 ) . The o r i g i n of the sharp s h i f t near 55°K i s unknown, but i t may have arisen from a change i n the c r y s t a l structure (and hence the unit c e l l and B r i l l o u i n zone), o r a change i n proton ordering. A sim i l a r effect was observed for HDO stretching modes and i t was correlated to the predicted (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 1 ) and v^DgO) frequency ( 6 3 0 cm-"*") exhibited no sp e c i a l behaviour attributable to excited state depopulation, ordering of protons, or decreased anharmonicity. From h2° to 70 ± 10°K the frequency scatter of data points was large, ± 5 cm 1 for v^HgO) and i 3 cm 1 for V ^ ( D 2 0 ) (Fig.' 3.13). Within these frequency l i m i t s the absorption maximum was constant. The freeze-in temperature for ̂ (H^O) and v ^ ( D 2 0 ) was 70' ± 10°K and agreed with other H 2 O and D 2 O bands but did not conform to our more precise measurements on HDO peaks. The s e n s i t i v i t y of v ^ ( H 2 0 and D 2 O ) to changed hydrogen bond energy through A R ( 0 , , ' " 0 ) was larger than HDO, i_.e_. l 6 l o > 0 . 0 0 0 1 A/°K. Between 70°K and l80°K v R ( H 2 0 and D 20) exhibited l i n e a r - 1 -1 temperature dependences of - 0 . 1 8 cm /°K and - 0 . 1 1 cm /°K respectively. Again the frequency scatter of points was large and a cur v i l i n e a r depen- dence may be true, as was indicated for v^HDO) (Fig. 3.7). Liquid nitrogen and l i q u i d helium c e l l data agreed i n t h e i r overlap region for v R ( H 2 0 ) . Zimmermann and Pimentel's (97) data for v R ( H 2 0 ) indicated a s l i g h t l y c u r v i l i n e a r temperature dependence of about -0.22 cm-1/°K. Their points, were approximately 10 cm 1 higher i n frequency than ours: They chose the band center and ignored any v D band structure (indicated i n t h e i r spectra). Details of the o r i g i n s , possible 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 section h.h. ( i i ) Fundamental Molecular Mode Temperature Dependences (a) The v-j_ and stretching modes. The low temperature l i m i t i n g frequencies for v± and v 3 of H 20 and D 20 were 3133 (2320) cm - 1 and 320U (2413) cm 1 respectively. As for HDO that extrapolation to 0°K may not have been v a l i d , but the thermodynamic data was regular down to 2°K (83). The effects of proton ordering should not be seen since the time for 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 excited levels are a l l depopulated at 5°K: Further effects from depopulation should-have been n e g l i g i b l e . Also, nuclear spin and electron spin perturbations (i_.e_. as i n ortho-para hydrogen) were expected to be very small. No changes i n hydrogen bonding were expected since the l a t t i c e was no longer contracting. From 4.2°K to 60°K, v-̂  and v 3 (H 20 and D 20) absorptions were invariant within the errors of measurement. Over that temperature range the c r y s t a l 162 o expanded very slowly, less than 0.0001 A/°K. Accompanying changes i n R{0''•'0) and or were too small to "be detected by t h i s i r absorption technique. The large frequency scatter i n points was pre-determined by the uncertainty i n peak and shoulder positions. The v^HgO) data from l i q u i d helium and nitrogen c e l l s did not completely agree (Fig. 3 . 1 0 ) . Liquid nitrogen c e l l data indicated a "freeze-in" frequency near 3215 cm 1. Liquid helium c e l l data indicated a "freeze-in" frequency near 320k cm 1. The data were collected during warm-up from 77°K and h.2°K respectively. The discrepancy may be explained i f the absorption peak underwent a type of "hysteresis" during cooling from 77°K to U.2°K, frequency s h i f t lagged behind temperature decrease. Since the samples were always held at h:2°K for three hours, s u f f i c i e n t time may have been given for completion of the hysteresis loop before warm-up observations began: Observations of frequency s h i f t during a cooling cycle are required to test that; possi- b i l i t y . Data from the same two c e l l s for v (R\p0) (Fig. 3.11) also suggested hysteresis although the separation of points was not as wel l defined. ;Only the results from the l i q u i d helium c e l l were obtained for v^ and v^ of DgO. Above 60°K the and v^ modes underwent regular s h i f t s to the ; progressively higher frequencies associated with progressively decreased hydrogen bond strengths. The explanation follows that of v (HDO)., On The i r high temperature dependences of v and v_ for cubic ice 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 D̂ O) Raman observations were a l l shifted (by 55 and 32 cm 1 respectively) to lower frequency than the i r observations. By adding a constant value of - 55 cm 1 to the v^HgO) and of 32 cm 1 to the V-^DgO) 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 ( 9 0 ) : H 20 AT Av 0 Raman IR cm-l/°K cm-l/°K 0.25U 0.26 0.2U6 0.24 AT A(v x + v T) AT Av. AT Av, 0.222 0.20 D 20 — - 0.198 0.22 0.143 0.14 AT AT = 203 - T7°K = 126°K. The equivalence of Raman and IR temperature dependences for v^ and v^ shows that the hydrogen bond coupling of neighbours was independent of the applied electromagnetic radiation. There i s a po t e n t i a l l y interesting extension of these cubic ice I temperature dependences to hexagonal ice I. I t i s known that the li n e a r thermal expansion coefficients of hexagonal ice I are not equal ( 6 0 ) and that the 0 - - , * 0 distances p a r a l l e l and non-parallel to the c-axis are not equal, Fig. 4.3. Hence, the temperature dependences of R(0* • • *0) ,. i^.e_. p a r a l l e l to the c-axis, and R ( 0 , - * * 0 ) a are not equal and the single,.crystal spectra of the ac face of hexagonal ice I , polarized p a r a l l e l and perpen- 164 dicular to the c-axis, should be distinguishable. For example, consider the s i x possible arrangements of the four protons about any one oxygen atom i n hexagonal i c e , H H H 4 . H H H H H 'I c - ax is 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 distorted potential 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 had the R ( 0 " " 0 ) along c. 164a One can predict the values and temperature dependences for v^R^O and V^O) of 0-H stretches p a r a l l e l and non-parallel to the hexagonal c-axis. From the temperature dependences of v^CH^O) and v^CD^O) (Fig. 3.10) and the temperature dependence of R(0**'"0) i n cubic ice I ( F i g . 4.3), one can determine the R(0*'"0) - v 3 correlations for H20 and D 20, F i g . 4.12. Then knowing the hexagonal R(0'*' 0) and R ( 0 , , , - 0 ) parameters as a function of c a temperature one can obtain a set of v^O^O) and v^(T)^0) frequencies p a r a l l e l and non-parallel to the c-axis, F i g . 4.13. For v^O^O) of hexagonal i c e one sees that at 150°K the asymmetric stretching frequencies would be 3214 and 3229 cm 1 p a r a l l e l and non-parallel to the c-axis, while at 100°K the values would be 3202 and 3225 cm 1. Si m i l a r l y for v 3(D 20) the 150°K values are 2417 and 2429 cm"1, and the 100eK values are 2411 and 2425 cm 1. Ockman (108) was not able to detect the differences at 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 of HDO i n Ĥ O or J)^0 are narrower and absorptions p a r a l l e l and non-parallel to the hexagonal c-axis should be separable. Sets or predicted v Q H(HD0) and v^(HDO) f r e - quencies i n the two directions were determined as above (i..e_. from Figs. 3.6 and 4.3) and are plotted i n F i g . 4.14. Thus at 150°K v Q H(HD0) along a and a should be separated by 16 cm 1 and at 100°K by 26 cm while VQp(HDO) along c and a would be separated by 11 cm 1 and 18 cm 1 respectively. Accurate measurement of the differences i n the a and c temperature, dependences 165 I C E I tj ( D O ) c m - 1 C o 2 2 4 1 0 2 0 3 0 -I 1 1 2 . 7 4 6 H 1 , — , 3 2 0 0 10 2 0 3 0 I C E I c ^ 3 ( H 2 0 ) c m - 1 Fig. U . 1 2 The correlations of V3 of, H 2 O and DpO to the 0 - • • - 0 distances as a function of common temperature. The frequency data were un- corrected for source beam heating. 1 6 6 I C E I h z , 3 (D 2 0) c m - 1 2410 20 30 I C E I h z / 3 ( H 2 Q ) c m - 1 Fig. 4.13 The calculated frequencies of H2O and D20. i n hexagonal ice I along the c and a axis as a function of temperature. 167 ICE I is (HDO) cm-1 h O D 2 4 1 0 2 0 3 0 ICE Ih v (HDO) cm-1 g. k.lk The calculated v O H(HDOl and vODCHDO) frequencies for HDO i n hexagonal ice I and along the c and a axis as a function of temperature. 1 6 8 should y i e l d valuable information on the anisotropic deformation of the hydrogen bond i n hexagonal ice I. —1 —1 (b) The v 2 bending mode. Absorptions near l 6 0 0 cm and 1 2 0 0 cm i n cubic ice 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 ̂  respectively. Doubts arose i n the previous l i t e r a t u r e assignments (Tables III.XI and II I . X I I I ) of these ice frequencies to either V2 or 2 v p , which should nearly coincide. In f a c t , these absorptions i n ice appear to be composite overlapping V2 and 2vj; peaks as was previously 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 V2 data (Fig. 3.12) may have arisen from a temperature hysteresis , i^.e_. the lagging of frequency s h i f t behind the temperature drop during cooling. Zimmermann and Pimentel' ( 9 7 ) results (Fig. 3.12) tend to discount that p o s s i b i l i t y for V 2 ( H 2 0 ) . Their results from l i q u i d nitrogen experiments agree with the present results 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 results probably arose from reference beam uncompensation for the l i q u i d nitrogen c e l l data. The strong atmospheric water vapour absorption below 1595 cm and above l 6 l 5 cm ̂  may have distorted the V2(H"20) i c e band severely, while a gap i n the vapour spectrum between 1 5 9 5 and l 6 l 5 cm may have presented an a r t i f i c i a l V 2 ( H 2 U ) i c e maximum. However, such a maximum would be independent of the ice sample temperature. .- •;- For V 2 ( H 2 0 ) the l i q u i d nitrogen c e l l data indicated a low temperatur l i m i t i n g frequency of l 6 0 5 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 2 frequency of 1 5 6 0 cm ̂ : Zimmermann and Pimentel's data were extrapolated to near 1 5 7 0 cm \ Whalley ( 9 6 ) found the Vp maxima i n high pressure H 2 O ices were above 1680 cm ̂  /and 169 argued that V2(ice) > V2(vapour). However, 2 v p may be more intense than V2 i n these cases. Whalley's ( 9 6 ) frequency for cubic and hexagonal ice I at 110°K i n an isopentane mull was more than 25 cm 1 higher than observed here, or by Ockman ( 1 0 8 ) (V2 = 1580 cm - 1) and Hornig ( 1 0 6 ) ( v 2 = 1585 cm 1 ) . The r e f l e c t i v i t i e s of Whalley's ( 9 5 , 9 6 ) mulled samples may have been s i g n i f i c a n t l y different than for our condensed samples leading to his higher apparent maxima. However, Ockman found only a small ( 0 . 5 % ) 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 ice -1 -1 over the range 1 5 0 0 cm to 1 7 0 0 cm , the maximum r e f l e c t i v i t y was at 1575 cm 1 at 110°K. I t i s also possible that sample formation by vapour condensation accentuated the r e f l e c t i v i t y , creating an a r t i f i c i a l low frequency maximum i n our re s u l t s . For D2O the l i q u i d helium c e l l data indicated a low temperature l i m i t i n g Vg frequency of 1189 cm ^, however the B̂ 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 di s t o r t i o n s . The D2O observation of I I 8 9 cm 1 i s greater than the D2O vapour frequency, 1179 cm In contrast, Hornig ( 1 0 6 ) and Ockman ( 1 0 8 ) observed v 2 ( D 2 0 ) to be even higher, i_.e_. near 1210 cm - 1 at 100 t 10°K. These D 20 results were contrary to our v 2 ( H 2 0 ) helium data as well as the nitrogen data of others, as noted above. Possibly i n DgO the r e l a t i v e positions of 2 v ^ and are altered from that of H2O, giving a different peak maximum r e l a t i v e to the vapour. Maximum V2/2v-^(H20) absorption was constant over the temperature range 5°K to 70 - 10°K, while maximum V 2 / 2 v p ( D 2 0 ) absorption was constant 1 7 0 over the temperature range 5°K to 50 t 10°K. The low D 2 0 "freeze-in" temperature of 50°K was probably due to i n s u f f i c i e n t data. The cubic ice I v 2 / 2 v p band exhibited the same dependence as the stretching modes i n th i s low temperature range, constancy within ± 8 cm-"*". As a check on hysteresis i n t h i s temperature range, detailed observations should be made during fast and slow cooling, i_.e_. cooling i n 10 - 20 min. and 150 - 200 min. respectively. The V2/2VR absorption also exhibited the same sensi- t i v i t y to changes i n hydrogen bond length (energy) as did the stretching modes, i_.e_. i t was sensitive to changes i n R(O----O) greater than 0.0001 A/°K. The question of whether v 2 ( i c e ) i s less than or greater than v 2 (vapour) i s s t i l l unanswered. I f the V 2/2VR(D 20) absorption maximum was due to more intense v 2 transitions then v 2 ice > v 2 vapour. I f 2 v ^ ( D 2 0 ) was the more intense t r a n s i t i o n then 2VR(E 20) ice > v 2 ( D 2 0 ) vapour and v 2 ( D 2 0 ) ice may be less than v 2 vapour. Positive high temperature depen- dence indicated the peak maximum was v 2 and not 2VR, since (and pre- sumably 2VR) had a negative frequency temperature dependence. The tempera- ture dependence of the v 2/2vpj H 2 0 absorption was also positive for either l i q u i d helium or l i q u i d nitrogen data. The maximum of absorption must then be v 2 ( H 2 0 ) and 2VR must be masked. Whether v 2 ( H 2 0 ) ice was greater than or less than v 2 ( H 2 0 ) vapour could not be unambiguously determined. Maximum V 2/2VR(H 20 and D 2 0 ) absorptions had approximately l i n e a r , positive temperature dependences of 0.37 cm "V°K and 0.15 cm~"'"/0K respec- t i v e l y over the temperature range from 6 0 ° to l80°K. In contrast the H 2 0 data of Zimmermann and Pimentel ( 9 7 ) indicated a slope of 0 . 2 8 l cm •̂ /°K 171 i n the range from 90°K to 253°K. The r e l a t i v e l y small temperature depen- dence of V2/2VR(D20) may have resulted from the closer coincidence of V 2 ( D 2 ° ) a n d- 2v R(D 20) than i n HgO. I f the H 2 O and D20 bands had the same structure then t h e i r temperature dependences should have been simply related 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 3v R or ( v 2 + v R) mode. Broad weak absorptions near 2235 cm 1 and 1635 cm 1 i n H20 and D20 cubic ice I exhibited temperature depen- dences of -O.lU cm 1/°K and -0.15 cm 1/°K respectively over the temperature range from 30° to l80°K. Both the H20 and D20 bands were less than one-half as intense as their, corresponding v 2/2v R bands. F i r s t consider the. R"20 ice absorption at 2238 cm ^. I f the absorption arose from a v 2 + \) R t r a n s i - t i o n then the temperature dependence should have been p o s i t i v e , i_.e^. AvR/AT = -0.17 cm-1/°K and Av2/AT = +0.36 cm_1/°K, therefore (Av 2 + Av R)/ T = +0.19 cm /°K. However, the temperature dependence was observed to be negative. I f the absorption arose from a 3v R t r a n s i t i o n then the tempera- ture dependence should have been negative, i_.e_. A(3v R)/AT = -0.51 cm "V°K. As was seen i n Fi g . 3.17, Pimentel's data (97) agrees well with ours, his slope was -0.12 cm 1/°K compared to our measured value of -0.15 cm 1/°K. The measured A(3v R)/ T = -0.15 cm 1/°K was nearly the same as AVR/AT = -0.17 cm "V°K and one-third the predicted rate of -0.51 cm "L/°K. Anhar- monicity increases from the larger amplitudes at increased temperature, could not be the source of t h i s r e s u l t . Either the 2235 cm 1 H20 absorption was a v 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 affecting the re 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 effects from populational r e d i s t r i b u t i o n . Alternately decreased anharmonicity of 3v R and v R from decreased hydrogen bond energy may be larger 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 absorption at 1 6 3 7 cm where the same considerations apply as for H 2 O . Absorption a r i s i n g from D 2 0 ( v 2 + v R) transitions- would obs. obs. exhibit zero temperature dependence; A(v2 + v R)/AT = (AV2/AT) + (Av^/AT) = +0.15 cm ^/°K - 0.15 cm "V°K = 0. The temperature dependence was observed to be d i s t i n c t l y negative, -0.15 cm "V°K. In fact VR(D 20) and the 1637 cm ^ D2O band had the same observed temperature dependences. Low temperature l i m i t i n g 3VR absorption was 2235 cm for H 20 and 1635 cm ^ for DgO. That implied an approximate H 2 0 low temperature l i m i t i n g anharmonicity for 3VR(H20) (from = 833 cm of - 2 5 8 cm and for 3 y R (D 20) (from v R = 627 cm - 1) of - 2 5 3 cm - 1. The apparent HgO and D 20 3 v R anharmonicities were nearly equal. Now the parent transitions underwent considerable isotopic s h i f t : vp(H 20) = 833 cm 1 and v R ( D 2 0 ) = 627 cm "L. The H 20 anharmonicity of - 2 5 8 cm ^ represented 11.5 percent of the observed absorption band frequency, 2235 cm ~̂. The increased DgO percent anharmon- i c i t y was unexpected for the mass substitution made. For example, i n the -1 -1 vapour phase the anharmonicity of H 20 (x-^ = -43.8 cm , x 2 2 = - 1 9 - 5 cm , x 3 3 = -^6.4 cm i s almost halved i n D 20 = -22.8 cm , x 2 2 = -10...hk cm \ x 3 3 = -24.9 cm for v^, v^, and (l2h)9 since the amplitudes of D 20 motion are smaller. Similar behaviour was expected for the s o l i d , but the observed 3v R(.D 20) anharmonicity was not one- half that of 3 v R ( H 2 0 ) . , Thus the large s h i f t s of 3 v R below the expected frequencies cannot /be simply 173 explained as anharmonicities. The large s h i f t s of 3 v R ( H 2 0 , D 20) below the expected frequencies ( 3 v R observed = 2235 cm - 1, 3(v R) = 3 ( 8 3 3 ) = 21+99 cm - 1) may arise from d i f - ferent maximum t r a n s i t i o n moments for the band of ground state l i b r a t i o n a l energies for the v^ and 3 v R t r a n s i t i o n s . The extreme case i s : molecules occupying the higher energies of the band have maximum t r a n s i t i o n moments for (0 -> l ) transitions and minimum t r a n s i t i o n moments for ( 0 -* 3) trans- 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 for ( 0 -»- l ) transitions and maximum t r a n s i t i o n moments for (0 3) t r a n s i t i o n s . The maximum of the ( 0 -> 1.) v R t r a n s i t i o n would occur above the center of the energy band and the maximum of the ( 0 3) v R t r a n s i t i o n would occur below the center of the energy band. In support of th i s r e c a l l that the v R absorption had a Av R 2 of about ; 125 cm ^, indicating a very large l i b r a t i o n a l energy range. Data on 3 v R from spectra recorded during warm-up from 5°K to 60°K 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 to hydrogen-bond changes as the in t e r n a l modes, i_.e_. i t was insensitive to changes i n hydrogen-bond energy from changes i n R ( 0 - - * * 0 ) that were less than 0.0001 o : A/°K. 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 - f a c t o r i l y . The 3 v R freeze-in temperatures for H 20 and D 20, 70 ± 10°K, concurred with previous data. (b) The (v + v,p) band. The high frequency shoulder on the icubic ice I stretching band had low temperature l i m i t s of 333U and 2h6k cm 1 for H 20 and DgO respectively (Table I I I . I X ) . Those frequencies are 2 0 1 and ikh cm 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 0.17 cm 1/°K,:compared 17k to 0.3k and 0.19 cm""1/°K for the low frequency shoulders (Table I I I . I X ) . I f the high frequency shoulders are i n fact due to (v^ + v ) tra n s i t i o n s then the v^ to (v + v ) displacement should have been 229 cm ^ (observed 201 cm ^) for Ĥ O and the temperature dependence of (v^ + v ) of Ĥ O should have been approximately (Av /AT) + (A(v + v )/AT) or ( 0 . 3 ^ - 0.10) -1 -1 cm /°K. That value of 0.2k cm /°K agrees we l l with the observed v^ + v^ value of 0.20 cm "*"/°K. For D 20 the high frequency shoulder appears to be composed of v^(D 20) and the LA t r a n s l a t i o n a l mode near 160 cm-"'". The tem- perature dependence of v^(D 20) i s not known however. (iv) The Half-Height Widths Temperature Dependences The temperature dependence of the composite stretching region band half-height width was positive (page 66 ), as expected. There appear to be two sources of the increasing width. One obvious effect common to a l l the modes was the increase i n the amplitudes of v i b r a t i o n . A second source of broadening arose from increasing R ( 0 * ' * " 0 ) : The increasing range of , 0 - , , * 0 distances gave a larger range of hydrogen bond energies and a broader range of possible t r a n s i t i o n s . Above l60°K (Fig. 3.k) the A ( V - ^ , V ^ ? V-^ + Vrp) ^ data are not r e l i a b l e since sample sublimation had a pronounced effect. The observed temperature dependence of A(v R, V R + Vrp) (Fig. 3.k) may have been anomalous. The scatter of data points was nearly as large as the range of points between 10°K and 200°K: The high temperature data was just outside the error l i m i t s of the low temperature data. As w e l l , the temperature dependence of A ( V R , V r + vip) seems to be too small. ; I t would be interesting to study the o r i g i n of v 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 wel 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 R ) 2 (Fig. 3.5) was opposite to that, of A(vp, v R + Vrp) 3" 5 and A(v^, V ^ , + v ^ ) ^ i n the amorphous and cubic ice I phases. An explanation was given i n section U.lC(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 Translational Modes Two peaks ( l 6 2 and 2 2 7 . 8 cm - 1) and three shoulders ( 1 9 1 , 267 and 296 cm 1) were observed at 93°K for H"20 cubic ice I. The features of the band diffe r e d only s l i g h t l y from those of Bertie and Whalley ( 8 8 ) . In t h i s work no calculations were made which disagreed with the assignments of Bertie and Whalley. ( i i ) The Li 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 R / ( v R + v^) = O.963. That compares to the same r a t i o s i n H 20 and D 20 o f : 0 . 9 l A U and 0.953 respectively. The peak to shoulder separations at 10°K were: [ ( v R + v T) - v R]H 20 = 50 ± 5 cm"1 I ( v R + v T) _ vR]HD0 = 3 3 + 1 . 5 cm"1 I ( v R + v T) _ v R]D 20 = 31 ± 5 cm"1 ' I - 176 • I f the shoulder did arise by a combination t r a n s i t i o n of vR(HDO) and v,p(host), then the value of to apply to HDO i s that of the host DgO since at a concentration of k.0% HDO i n D 20 the l a t t i c e dynamics must surely be domin- ated by the D 20 molecules for any reasonable model. The fact that the D 2 0 peak to shoulder separation i s 31 cm 1 supports t h i s conclusion. As w e l l , the peak to shoulder separations of pure D 20 and of HDO i n D 20 agree well. Presumably HDO i n H 20 should have a v-p peak to ( v R + \Jt) shoulder separation of about 5 0 cm 1. 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 scattering from hexagonal ice I and compared that data to the results of a theoretical model based on cubic ice I. His hypothesis noted that the Raman and i r observations from 50 to 3500 cm 1 are the same for cubic and hexagonal ice I , and assumed that the basic dynamical l a t t i c e unit of cubic ice (one 0 atom surrounded tetrahedrally by k others) was a suitable model for hexagonal i c e . That i s supported by the fact that the nearest-neighbour configurations'are the same. Trevino's ( 9 3 ) theory also assumed that the protons are i n ordered positions, which they are not. However, the basic t r a n s l a t i o n a l unit i n ice i s the 0 atom and the orien- 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 ice I at 150°K the neutron i n e l a s t i c scattering ex- periments ( 9 3 ) demonstrated l a t t i c e maxima at 63 cm - 1 (TA) depending on the assignment of peaks. Other workers ( 9 2 ) found (for H20 hexagonal'ice I at 26l°K) l a t t i c e modes at 60 and 70 cm \ Clearly there exists a high density of H 20 t r a n s l a t i o n a l states near 50 - 10 cm 1 at 150°K for hexa- . gonal H 20 ice I. The corresponding modes for D 2 O cubic ice I at 10°K may be lower than 50 cm 1 since the mass difference would s h i f t the frequency 177 to O.9484 x 50 cm - 1 =47.5 cm - 1. The observed neutron hand width i n H20 was 50 cm-"*". Of the broad 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 to occur over the same sections of the band for i r absorption and neutron i n e l a s t i c scattering. 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 scattering t r a n s i t i o n moment maximum. Further, the overlap i n the i r of v R and ( v R + Vrp) brings the instrumentally traced, summed absorptions closer together, i_.e_. i f v R and ( v R + VIJ) could be resolved completely t h e i r peak positions would be separated by more^ than 50, 33 and 31 cm 1 for H 20, HDO and D20 respectively. One may conclude that a single 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 for HDO. Since v R x and v R y. are expected to be about equally intense, and since only one band was observed, then v R x and. v Ry must be exactly or nearly degenerate. The same conclusions seem appropriate for H20 and D20. 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 absorp- t i o n features near 3200 cm - 1 for H20 and 2400 cm"1 for D20. Ockman (108) assigned the low frequency shoulder to v-j_, the main peak to v 3 , and the high frequency shoulder to ( v 3 + v T ) , while Hornig et_ a l . (105) assigned the three bands as 2v 2, v 3 , and v-j_. In contrast, Bertie and Whalley (.95) assigned the low frequency shoulder and the main peak as a pair of ;bands composed of coupled - v 3 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 1 178 between v-j_ and absorption bands of H20 and D2O. We propose that the low frequency shoulder i s v-̂ , the main peak i s and the high frequency shoulder is (v-^ + v T) i n agreement with the Raman results of Val'kov and Maslenkova (99) and as Ockman ( 1 0 8 ) interpreted them. The stretching frequencies of HDO do not l i e at the positions ex- pected on the basis of H20 and D20 s h i f t s i n cubic ice I. This res u l t w i l l be discussed i n terms of a theory proposed by Pimentel and Hrostowski (lOl) and Hornig and Hiebert (102) i n the early 1950's: They suggested that the two major effects on molecular vibrations i n s o l i d s , c r y s t a l - f i e l d per- turbations and inter-molecular coupling, were separable by d i l u t e isotopic substitution. (a) The H20 and D20 stretching modes. For the Raman spectra^ of hexagonal ice I Val'kov and Maslenkova (99) found peaks at 3088', 3210 and -1 -1 3321 cm 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 less than 0.75, while the 3210 cm"1 peak was depolarized. The 3088 cm 1 Raman peak was unambiguously of a^ symmetry, i_.e_. the. v-̂ symmetric stretch mode. The suggestion of Bertie and Whalley ( 9 5 , 9 6 ) that v-j_ and vg are coupled and indistinguishable cannot be en t i r e l y correct. I f the .and bands of coupled vibrators were largely mixed into two bands equally of V]_ and character, then the same set of energy levels would have been present for both the Raman and i r t r a n s i t i o n s , however the selection rules would change. For the mixed energy levels one would expect equally intense peaks at 3088 and 3210 cm contrary to the 10 to h observed intensity r a t i o . Hence the v-̂  and V3 energy levels appear to be separated (lack of 179 non-resonant coupling) while - and - resonance coupling of neighbours may s t i l l be eff e c t i v e . There remains the problem of the dis p a r i t y between the v-̂  i r and Raman frequencies, at 100 t 10°K, i_.e_. v-^(ir) = 31^9 cm - 1 and v^(Raman) = 3088 cm - 1 at 100 ± 10°K. S i m i l a r l y i n D 20 ice I the v± results were 2321 and 2291 cm 1 respectively. Recall that both the symmetric and asymmetric stretching modes appear to be very broad bands due to v-[_ - v-̂  and V3 - 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 active nor with the same intensity factor. Thus for the Raman scattering only a narrow band i n the lower one-half of the v-̂  band was active while for the i r a large range of frequencies was observed and the maximum int e n s i t y occurred at a higher frequency. For the asymmetric mode the same portions of the band of frequencies was i r and Raman active. This may indicate a fundamental d i f - ference i n - v^ and - resonance coupling. Thus the Raman scattering from hexagonal ice I indicated that i n the i r absorption spectra the low frequency shoulder was and the main peak was v^, .i.e.. v-^HgO) = 3 2 1 0 cm 1 and v-^d^O) = 2 U 1 3 cm - 1. By, assuming that the two assignments are correct, then the r a t i o of v^Cice^v^Cvapour) i s O.85U6 for H2O and 0.8655 for D 20. I f the effects of hydrogen bonding are the same on a l l 0-H bonds, then and are expected to 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 ig. U . 1 5 . The \>3(H20) cubic ice I absorption ( 3 2 1 0 cm - 1) i s O.85U6 times the V3(.H20) vapour frequency ( 3 7 5 6 cm - 1). In order to preserve the displacement due to hydrogen bonding 4 0 0 0 - 3 7 5 6 3 5 0 0 - 3 0 0 0 - 2 5 0 0 - 2 0 0 0 3 2 7 2 7 2 7 8 8 . 2 6 7 2 H 2 0 H D O D z O J 180 : 3 3 4 0 3 2 6 6 \ 3 2 l 6 * x , 3 , 4 9 ^ l (31681 (3125 ) * • . * 2 4 6 5 •. .2416 7 , \ 2 4 I 3 3 ( 2 3 6 0 ) ' . . .2321 ^ (2313) 1 H D O D O 2 ; V A P O U R S O L I D ICE Fig. 4.15 The ohserved vapour phase and cubic ice I phase. H 2 O , HDO and D 2 0 frequencies are shown as s o l i d horizontal l i n e s . The ra t i o s of V3(ice)/v 3(vapour) are shown on the diagonal s o l i d l i n e s . The H 2 0 , HDO and D 2 O ice frequencies predicted with those ratios are shown as dotted horizontal l i n e s . 1 8 1 then the v -^(^O) ice (where p stands for predicted) frequency would have to 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 similar arguments v^p(l>20) = O.8655 x 2 6 7 1 cm" = 2313 cm compared to the observed value of 2321 cm - 1. The predicted v-̂ frequencies, which preserved the r e l a t i v e effects of hydrogen bonding on and v j , agree very well with the observed i r r e s u l t s . The agreement i s probably better than indicated since the observed i r V j band was shifted to higher frequency by overlap with the adjacent v^ band. The alternate assignment of observed ice peaks which also retains the v-j_ - V3 order i s v-̂  = 3210 cm - 1 and = 33^0 cm - 1. The r a t i o < of vg(ice)/^(vapour) i s then O.8858 and the predicted v-^ frequency i s 3253 cm \ compared to the i r r e s u l t , v-̂  = 3210 cm - 1. Neither the v-^HgO) nor the v-^(D20) frequency was a good approximation to an observed i r band. The second assignments of v-̂  and were rejected. The reasonable assumption of equal effects on v^ and due .to hydrogen bonding gives predicted frequencies i n good agreement with observed features. The accepted assignments were = 31^9 cm 1 and = 3210 cm ̂~, while the 33^0 cm 1 shoulder was probably (v^ + Vrp). (b) The HDO stretching modes. Use of d i l u t e isotopic substitution to separate the c r y s t a l f i e l d and resonance coupling perturbations ( 1 0 1 , 1 0 2 ) was o r i g i n a l l y suggested for studying the molecular vibrations 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 rapid isotopic exchange may occur, has led to some misinterpretations of experimental r e s u l t s , i_.e_. as i n H 2 O i n D 2 O •.( 106,95) • Because of the rapid isotopic exchange i t 1 8 2 i s impossible to i s o l a t e D 2 0 i n H 2 0 or H 2 0 i n D 2 0 at low concentrations. One obtains a d i l u t e solution of HDO and very, very d i l u t e residues of H 2 0 or D 2 0 . Now HDO has Cg molecular symmetry and three i n t e r n a l coordin- ates, an OH stretch, an 0-D stretch and an HOD bend. I t i s unreasonable to expect both of the HDO stretching modes to be completely uncoupled from the stretching modes of the H 2 0 or D 2 0 l a t t i c e . Just such an assumption by Hornig et a l . ( 1 0 6 ) and by Bertie and Whalley ( 9 5 ) has resulted i n mis- interpretation of the ice I HDO i r r e s u l t s . As a f i r s t approximation to ice I , consider the i r observations for HDO, H 2 O and D 2 O i n the vapour phase, Fig. H . 1 5 . One HDO stretching mode l i e s almost exactly midway between V3 and v-j_ of H 2 O , while the other HDO stretch i s observed nearly midway between V3 and of D 2 0 . That i s enti r e l y understandable since the symmetric and asymmetric H 2 0 modes may be considered as constructed from a basis of two isolated 0-H (HDO) stretches which interact weakly. Hornig ejt a l . ( 1 0 5 , 1 0 6 ) claimed that such a picture of the H 2 0 and D 2 O potentials should extend to the s o l i d as w e l l , i_.e_. i n ice I they expected the HDO modes to l i e between the v-^/vj modes of H 2 O and D 2 0 . For ice I (Fig. U . 1 5 ) V Q ^ H D O ) was observed between two i r H 2 0 features, while V Q ^ ( H D O ) was almost coincident with a central i r D 2 0 fea- ture. Ignoring the weight of Raman data to the contrary, Hornig et a l . assigned V3(H 2 0) to 3 2 1 0 cm 1 and v^(HgO) to 3 3 6 0 cm 1 with v ^ H ( H D 0 ) between them at 3 2 7 5 cm +. Their central aim appears to have been the preservation of the V Q ^ ( H D O ) observed position between V 3 and v-j_ of H 2 0 . Bertie and Whalley's ( 9 5 ) discussion of the relationships between HDO, H 2 0 and D 2 0 stretches was confusing. They also assumed the nature of the H-OD (in D 2 0 ) stretch was the same as the H - 0 H ( i n H 2 O ) stretch. 1 8 3 The above r a t i o s of v^(ice)/v^(vapour) for and D 20 (Fig. h. 1 5 ) y i e l d interesting results when applied to HDO (vapour) frequencies. The observed vapour phase frequencies of HDO stretching are 3707 and 2 7 2 7 cm \ The predicted HDO frequencies using the HpO and D 20 r a t i o s ( 0 . 8 5 ^ 6 and 0.8655) are v Q H P(HD0) = 3 l 6 8 cm - 1 and v Q r ) P(HD0) = 2360 cm - 1 compared to the observed HDO frequencies of 3263 cm 1 and 2 U l 3 cm - 1 respectively. .Thus the predicted frequencies l i e close to the - mid-points, i n agreement with the concept of Hornig et_ a l . ( 1 0 5 , 1 0 6 ) , but do not agree with the observed HDO frequencies. On the basis of our assignments the observed v^.rr(HD0) stretch Un (Fig. k.l6) was outside and above the - i n t e r v a l of pure H 20. Cor- respondingly, the V Q ^ ( H D O ) stretch was just above v ^ ( D 2 0 ) , Fig. k.l6. A clear explanation of the mispositioning of the HDO stretches can be found by considering the coupling of HDO to H 20 and D 2 0 l a t t i c e s . Consider the case of k.0% HDO i n a D 20 cubic ice I lattice.,. Of the two HDO stretches only V Q ^ ( H D O ) can undergo reasonably strong near-resonance coupling to v o(Do0): v~„(HD0) i s "uncoupled" from the l a t t i c e vibrations. 3 . OH One then compares the observed v„„(HD0) to v. and v„ of H o0 on the assump- Un X 3 d. t i o n of equal hydrogen bond e f f e c t s , Fig. h.l6. However, vOTJ(HD0) l i e s On 86 cm 1 above the - v^(H 20) midpoint. A possible explanation i s a lengthened D0-H-'--0H2 distance due to the very process of uncoupling. For example the covalent character of the hydrogen bond i s dependent upon an equal sharing of e~ among the overlapped o r b i t a l s . I f the o r b i t a l following of e~ about vibrating nuclei i s not at the same rate then the hydrogen bond may .be weakened. 18U 3250- + 8 6 32CO - "Ms 3150 , Z / 1 -73 O 3100 - o c CD CT 2450 • LL 24 OO 2350 - 2300- - 5 8 OD + 4 9 H2Q HDO in Dp HDO in H20 D2Q 1+.16 The. r e l a t i v e positions of the observed H2O, HDO and D 20 stretching vibrations are shown as horizontal solid, l i n e s . The expected positions of the. HDO absorptions before and after the effects of uncoupling, are shown as dotted horizontal l i n e s 185 -1 ° From section 4 . 2 A ( i i ) we found that A V . ^ / A R C O 0) = 1,921 cm /A. On Hence, a Av Q H of 86 cm - 1 implies the D0H-D20 R ( 0 - , , - 0 ) distance was longer o than "expected" by 0.0^5 A. Correspondingly the H0D-D20 R(0 0) d i s - ci tance should have been shorter than expected by O.OH5 A and vQI)(HDO i n D20) would have been 58 cm 1 lower than expected (but i t was unobservable lying under v 1 ( D 2 0 ) ) , at 2311 cm - 1. (The - midpoints are 3180 and 2367 cm 1 for H20 and D20 respectively.) For 5 . 9 W HDO i n H20 vQI)(HD0) was found at 2hl6 cm - 1, U9 cm - 1 above the center of - v^DgO) for cubic ice I , Fig. U.l6. That implies the o uncoupling had lengthened R(0 0) for HO-D H20 by 0.038 A. S i m i l a r l y o R(0 0) for DO-H H20 must have been shorter by 0.038 A and v Q H(HD0) would have been lower than normal by 73 cm \ at 3107 near v^(H20).. For HDO i n H20 and D20 the point i s that one HDO mode was coupled to the l a t t i c e and the other was uncoupled: The act of uncoupling weakened the hydrogen bond, lengthened one R ( 0 - - - - 0 ) and shortened the other three R(0'*-*0) of HDO. Consequently the uncoupled frequency was shifted to higher frequency and the other was shifted to lower frequency. Our explanation of the observed positions of HDO frequencies i n re l a t i o n to the H20 and D20 frequencies cannot be re a d i l y confirmed by any meaningful calculation or conceived experiment. However i t serves to. point out an important fact i n d i l u t e isotopic substitution studies i n so l i d s : The molecules of mixed analogues are not a l l uncoupled from the l a t t i c e . The method i s not generally useful nor applicable to molecules with mixed isotopes unless one recognizes that unusual effects can occur. 186 ( i i ) The Bending Mode The position of the 1570 ( l 6 0 H ) cm - 1 H20 cubic ice I absorption (Table III.XI) indicates i t could be either v 2 or 2v R and possibly over- lapping v 2/2v R absorptions. The vapour phase v 2(H 20) frequency i s 1595 cm 1. The frequency s h i f t upon annealing was to lower frequency (Fig. 3.2) a characteristic of molecular modes and thus favours the v 2 assignment. As w e l l , the cubic ice I frequency s h i f t was to higher frequency and simi- l a r l y favoured \Jg. However the half-height width increased upon annealing and for cubic ice I i t decreased with increasing temperature (Figs. 3.12 and 3.5 and page 67) . That data favours a combined v 2/2v R absorption. The v 2 absorption was more intense than the underlying 2v R and was pro- -1 -1 bably centered below 1595 cm , i_.e_. near 1570 cm . S i m i l a r l y for D20 the v 2/2v R band was found at 119k cm - 1. C. The Overtone and Combination Modes (i ) The 3v R Modes The 2235 cm 1 H20 and 1635 cm 1 D20 absorptions have been i n t e r - preted as both 3v R and v 2 + v R (Table 0.5). The bands shifted to higher frequency upon annealing and as cubic ice I. the frequencies shifted down (Figs. 3.2 and 3.17): Both of those facts indicate a l a t t i c e mode and we assign the absorption to 3v R. However, there i s at least one disconcerting factor, the r e l a t i v e i n t e n s i t i e s of v R , 2v 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 rapidly and thus the intensity of 3v R should be much less than 2v R. However the 3v R absorption i s only about 1/k less intense than the combined v 2/2v R absorption, and 187 that indicates that 2 v R i s less intense than 3v R. However, the interpre- 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 state treatment i s necessary. ( i i ) The (v + v T) Mode ••' • The shoulder at 33h0 cm i n H 20 and 2I+65 cm - 1 i n D 20 cubic i c e I has been variously assigned as v-̂ , + and v-̂  + Vrj-i (Table 0 . 5 ) . Our previous discussion on the stretching modes of H 20, D 20 and HDO (page 181) eliminated the assignment. The peak to high-shoulder separation (v^ to "v^ + Vrp") i s 1 3 0 cm 1 while the low to high frequency shoulder separation (V-L to "v± + v T") i s 1 9 1 cm . The l a t t e r separation l i e s closer to our observed vrp(H20) band maximum and favours the v-j_ + Vrp assignment. In addi- t i o n , the Raman data ( 9 9 ) favours a + Vrp assignment on the basis of 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 , to v l + VT i n " t e n s i t i e s are 10:it: 2. k.h The Librations of HDO, H 20 and D 20 A. 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 ices have dwelt upon the association of the l i b r a t i o n s to free rotation of oriented- gas or gas phase molecules ( 8 5 , 8 9 ) . 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 20, HDO and D 20. Blue ( 8 5 ) was the f i r s t to evaluate the l i b r a t i o n a l frequencies through moments-of-inertia. We have extended the calculations 188 to include weighted lone-pair o r b i t a l contributions to the moments. (i ) The Non-Interacting Molecules Model The molecular parameters and the positions 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 well 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 active due to the loss of C 2 v symmetry and the orientation of the molecular dipole at 17°5 1+' to the z-axis. However, V R Z ( H D 0 ) i s expected to be weak compared to v Ry and v R x due to the small dipole reorientation. Notice that vRx(HDO) gives asym- metrically bent 0-H-•• - 0 and 0 - D - - , * 0 hydrogen bonds. The D atom sweeps o 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 IV.II. 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 to 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. From the differences i n the moments one sees that I X ( H D 0 ) i s nearer T^^O, I Z ( H D 0 ) i s nearer I ^ ( D 2 0 ) , and Iy(HDO) i s midway between I y ( H 2 0 ) and I y ( D 2 0 ) . It does not necessaril follow that the HDO l i b r a t i o n a l frequencies w i l l be observed i n a corres- ponding manner. HDO l i b r a t i o n a l absorption was observed here only for HDO i n a D 2 O matrix: One peak and one shoulder were observed at 8 2 3 cm 1 and 856 cm 1 respectively (page 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 single function such as Blue's Z H 2 0 z z H D O F i g - 1+'r'' 7 1 : 1 6 P r i n c i p a l axes of H 20, HDO and D20 and t h e i r molecular parameters. The angles were assumed to be tetrahedral. X H Cpage 27) then v R x(HD0) should be r e l a t i v e l y weakly coupled to any l i b r a - t i o n of the D20 l a t t i c e since the HDO and D20 librational.frequencies observed were about 9 0 % separated. One of the absorptions at 856 and 823 cm 1 must contain at least Vn x(HD0) s i - n c e i t n a s "the lowest moment-of-inertia and i s expected to be closest to the H20 values. The other feature above cannot be due to V R (HDO) nor vp z(HD0) since the peak-shoulder separation was too small, 190 Table IV.II The moments-of-inertia of H 20, HDO and D20 and a comparison of HDO to H20 and D20. The parameters used to calculate the p r i n c i p a l moments-of-inertia are given i n the text. H20 D20 HDO 0.89 x i o - h o • 1.61 x i o ' h o 1, .08 x 1 0 4 0 2.91 5.63 h. .23' 2.01 1+.02 3. .15 units gms-cm2 / molecule Comparison of moments Ix(HD0) - I x(H 20) = = 0.19 x 10~h° I x(D 20) - I x(HD0) = -1+0 0.53 x 10 Iy(HDO) - I y(H 20) = = 1.32 I y(D 20) - Iy(HDO) = 1.1+0 I z(HD0) - I z(H 20) = = 1.1k I z(D 20) - I z(HD0) = 0.87 I 33 cm" . As mentioned e a r l i e r , the shoulder appears to be due to (.vR + v^) absorption. Alternately the peak and shoulder may have resulted from nearly de- generate V R x ( H D 0 ) and v-py(HDO) absorptions. Such an event implies that either I x and I y of H D O are degenerate through coupling, or that the l i - brations cannot be treated on the basis of moments-of-inertia. Both of these p o s s i b i l i t i e s w i l l be treated i n d e t a i l . : 191 Assume that the l i b r a t i o n s of HDO, H 20 and D20 can be simply re- l a t e d to the p r i n c i p a l moments-of-inertia by Blue's (85) formula (page 27). Since the oxygen atoms l i e close to each of the p r i n c i p a l axes then the 2 r are a l l small and since the restoring forces on the oxygen atoms are °n a l l small then Blue's equation reduces to: —1 1 1 2 2 1/2 V R n ( c m "  ) = 2 ^ l 7 T C2 ( k H l n r H m + k H 2 n r H 2 n ) ] . [ k ] where: i s the l i b r a t i o n a l frequency about axis n k j j ^ n = kn2n = ^Hn o n * n e tiasis of symmetry and r 2 i s the distance of atom Hn normal to axis n. ' H l n 1 Using the calculated moments-of-inertia from Table IV.II one obtains the l i b r a t i o n a l frequencies i n terms of the k g n force constants: H 20 HDO . D20 v R x = 2.1*5 k H 2.60 k H' 1.83 k D V R y = 2.77 k H 2.33 k H' 1.99 k D ^2 = 2.90 k H 2.23 k H' 2.05 k D I t i s i m p l i c i t i n t h i s treatment that the three l i b r a t i o n s of each molecule are non-degenerate. On the basis of the above equations the lowest observed frequencies of H 20 and D 20 must be associated with the Vp x's since they have the lowest force constant c o e f f i c i e n t s : Thus Vg x(H 20) = 833 cm - 1, and v]R x(D 20) = 627 cm - 1. Using those frequencies the force constants are : k H(H 20) = (1.15 t 0.03) 10 5 dynes/cm k D(D 20) = (1.17 t 0.03) 10 5 dynes/cm For HDO, v R (HDO) has the smallest force constant c o e f f i c i e n t and we assign that (on a t r i a l basis) to the 819 cm 1 peak. Then the HDO force constant, 192 kg' , i s ( l . 2 k 1 0.03)10^ dynes/cm, i n reasonable agreement with the and D20 force constants. By applying the above three force constants to the remaining functions one obtains the following set of frequencies: H 20 ' HDO D 20 vRx 8 3 3 cm - 1 916 cm - 1 6 2 7 cm - 1 % 9h0 819 682 V R Z 98U 785 7 0 2 where the observed frequencies which were used to define the force con- stants 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 hydrogen bond than for v R x of H 20 and D 20 then the s l i g h t l y larger HDO force constant i s understandable. Of the nine frequencies l i s t e d above three were assigned from ex- perimental observation. From the remaining s i x frequencies, two were ex- pected to be i r inactive (i_.e_. v R z ( H 2 0 ) and v R z(D20)) while a t h i r d one ( V R 2 ( H D 0 ) ) i s expected to be very weak. That leaves three predicted f r e - quencies to compare with experiment: v R (H 20) , v R (HDO) and v R ( D 2 0 ) . y y Only the prediction of (D 20) at 682 cm 1 l i e s near an observed band, the D 20 cubic i c e I band at 6 6 l cm - 1. However, even that prediction i s out by more than 20 cm As w e l l , there were no observed absorptions . near the 9^0 cm 1 or 9 l 6 cm 1 predicted frequencies. Therefore, V R (H 20) , y V R x ( H D 0 ) and V R (D 20) are either weak or inactive i r absorptions. A l t e r - y nately those modes may be i r active 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 x and Iy are degenerate or Blue's f o r - mula i s i n v a l i d . The moments-of-inertia can be made nearly degenerate by considering the masses of the detached (more distant) 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- si 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 neutral density i n a cubic ice 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 effects. F i r s t , the p r i n c i p a l moments of the two protons attached to the central molecule (0-H* •••()) are decreased through reduction of t h e i r :real masses to an effective 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 central protons i s gained i n the lone-pair o r b i t a l s of two neigh- boring molecules. ' S i m i l a r l y , the two lone-pair o r b i t a l s of the central molecule gain an effective mass from the two detached protons (0--* ,H-0) associated with the central molecule hydrogen bonds. Hence the lone-pair effective masses restore the moments-of-inertia to near t h e i r i n i t i a l values. The second effect on the moments-of-inertia which arises from hy- drogen bonding i s the movement of the two attached protons away from, and the two detached protons closer to the central oxygen atom. Notice that cooling the sample decreases R(0*•••()) and tends to centralize the four protons further. I f the four protons were centered between 0"-* ,0 and had masses equally shared by the pairs of oxygen atoms, then the molecules would be restrained spherical tops, I x = l v = l z . 19h A pseudo-symmetric top i s approximated by smaller masses working at longer distances, i_.e_. weighted lone-pairs acting at the detached proton o distance of 1.79 A and a reduced protonic mass acting at the 0-H distance o of 0.95 A. The point i s that i f the moments-of-inertia I x and Iy are equal for H 20 and DgO then by Blue's ( 8 5 ) formula v R x and v R y should be degener- ate . . Consider the effect of reduced protonic masses and effect i v e lone- pair masses where the molecular parameters w i l l be assumed to be: r0H = r0D = ° - 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 H3 and H^ the masses of Hj and H 2 = 0 . 7 5 ( 1 . 0 0 8 ) gms/mole = 0 . 7 5 6 gms/mole the masses of H3 and H^ = 0.25 ( 1 . 0 0 8 ) gms/mole = 0.252 gms/mole (This i s cal l e d the (3/h, 1/h) effective mass option.) The moments-of- i n e r t i a of H 20 #*-*H 2 are: I x ' = 3.1+3 x 10 gm-cm2/molecule Iy' = 3.15 x 10 -1+0 -ho I z = 3.30 x 10 Substituting those'values of the moments into Blue's ( 8 5 ) formula, [h], where the contributions of the oxygen force constants are s t i l l small, then: 195 X ( H 2 0 , 3 A , l A ) = 2 . 8 7 ( 0 . 2 8 2 k H + 3.20 ki) S e° V R y ( H 2 0 , 3 / l + , l / 4 ) = 2 . 9 9 ( 0 . 6 0 2 k H + 2.14 k^) VR Z(H 20,3/1+,1/1+) = 2 . 9 2 ( 0 . 9 0 2 k H + 1.10 kg) where k^ i s t h e 0-H----0 b e n d i n g f o r c e c o n s t a n t and kjj i s t h e 0' -**H-0 b e n d i n g f o r c e c o n s t a n t . Our model supposes t h a t v R and v R o f H 2 0 a r e d e g e n e r a t e a t 833 x y cm \ By s o l v i n g t h e f i r s t 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 .and k g = 0.21 x 1 0 ^ dynes/cm. U s i n g t h o s e v a l u e s o f k^ and kjj i n t h e t h i r d e x p r e s s i o n above, t h e n V R z (H 20,3/1+,1/1+) i s 831 cm w h i c h i s d e g e n e r a t e w i t h v R x and VR_^_ w i t h i n e r r o r . How w e l l do k H ( H 2 0 ) and k ^ ( H 2 0 ) a p p l y t o D 20 D 2? U s i n g t h e above m o l e c u l a r p a r a m e t e r s and d e u t e r i u m e f f e c t i v e masses o f 0.75(2.011+) gms/mole f o r t h e a t t a c h e d p a i r ( D j and D 2) and masses o f 0.25(2.011+) gms/ mole f o r t h e d e t a c h e d p a i r (D^ and D^) t h e n t h e D 20--''D 2 moments-of- i n e r t i a a r e : I x = 6 . 8 H ( l 0 - ^ ) gm-cm 2/molecule I y = 6 . 2 8 ( 1 0 " ^ ° ) and l z = 6 . 5 9 ( l 0 - 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 f o r m u l a a r e : 196 : ( D 2 0 , 3 A . 1 / U ) = 2 . 0 3 ( 0 . 2 6 8 k H + 3.20 k^} = 586 ? c a l c ( D 2 0 , 3 A , l / U ) = 2 . 1 2 ( 0 . 9 0 2 k H + 1.13 k g ) = 588 cm" v - M X — . i , ^oo -1 s'r v calc(D ?0,3/U,lA) = 2 . 0 7 ( 0 . 6 0 2 k H + 2.lk k') = 591 cm"1 R z H where k^ and k j j of R̂ 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 1. This i s as much accuracy as can be expected from so simple a model. By invariance of the potential energy to symmetry operations kj^O^-H-^-• • * 0 2 ) = kj^Oj-Hg 0 3 ) and kj^O^Hg" - • *0^) = kntO-j-H^ O 5 ) . However, i t does not follow that k H ( 0 - H j 2 * ' " ' u ) = k j j ( 0 * ' "'H3 ̂ - 0 ) , since they are not interchangeable by s i t e or point symmetry. 1 That k j j i s 0.309 times k g may be rat i o n a l i z e d on the following basis. The potential for l i b r a t i o n i s the same i n a l l directions normal to R ( 0 , - , * 0 ) , i_.e_. the "potential" has a conical cross-section along the 0 , - , , 0 axis. While the shape of the potential i s the same at protons Hj and Hg as well as being the same at H^ and H^, only the moments of the forces acting at the two protonic distances must be equal. Since the o O-H-ĵ  g a n d O-'-'Ĥ  ̂  distances are 0.9^ and 1.79 A respectively, then ! the 2 2 r a t i o ( r ^ ) /R(0' , , -H) = 0.3^5. The moment' of the force acting at H and OH i 2 -11 H 2 i s kjjr = 0.53 x 10 dyne-cm compared to the moment acting at. H^ and H4, k ^ O H) 2 = 0.67 x 1 0 - 1 1 dyne-cm. There i s at least one disconcerting fact about t h i s model that i s seen for the case of h.0% HDO i n D 2 O . The effective masses added to the HDO lone-pairs are 0.25 times the deuterium mass not the protonic•mass. Thus HDO l i b r a t i o n a l frequencies would be calculated nearer to the D̂ O values than the H 2 O values, contrary to our observations. 197 Another weighted lone-pairs option was investigated, the (H 20, 1, l/U) option. In t h i s model the two attached protons were assigned f u l l protonic masses, while the two detached protons were assigned masses of 0.25 times the f u l l mass. Such a model seems unreasonable since the mass' sums are not conserved. By the same treatment as above one finds: k H ( H 2 0 , l , l A ) = 0.783 x 1 0 5 dynes/cm kfl(H 20,1,1/1+) = 0.213 x 105 dynes/cm. The predicted v R z ( H 2 0 ) frequency i s 829 cm 1 for t h i s model and the pre- dicted D 20 frequencies are 5 8 2 , 592 and 586 cm - 1, much as for the (3/1+, 1/1+) model. Notice that the moments of the forces acting at H^ ^ and ^ — 1 1 — 1 1 are now nearly equal, O.69 x 10 dyne-cm and O.67 x 10 dyne-cm res- pectively, x In summary l e t us consider the results of the two models considered F i r s t , Blue's ( 8 5 ) formula for non-interacting molecules gave three non- degenerate, widely separated frequencies for the three l i b r a t i o n s . That i s contrary to the observed spectra and must be rejected. Secondly, for degenerate v R and v R the moments-of-inertia must be equal. Using a weighted lone-pairs model i t was necessary to consider two kinds of hy- drogen bond bending force constants, which were not accurately tr a n s f e r - able between H 20 and D 20 molecules. As w e l l , the hydrogen bond bending force constants calculated were about as large as the molecular H0H bendin force constant, i_.e_. Zimmermann and Pimentel ( 9 7 ) found the H0H bending force constant i n ice to be 0.1+9 x 1 0 ^ dynes/cm. The value of 0.60 x 1 0 ^ dynes/cm seems to be an u n s a t i s f a c t o r i l y high 0-H*••*0 bending force con- stant . 1 9 8 B. The H 2 0 3 Model.of Ice An alternate approach to the l i b r a t i o n s of H 20, HDO and D 20 molecules i n i c e i s the normal coordinate analysis of an extended molecule HgO-j. The structure and parameters of the H 2 0 3 molecule are shown i n F i g . U . l 8 . For a fr e e l y rotating and t r a n s l a t i n g H 2 0 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]_ R5 = A<(> R 2 = A r 2 R 6 = A6i R 3 = A r 3 R 7 = A6 2 = R 8 = A 6 1 \.- ^ A s i m i l a r model was studied by Zimmermann and Pimentel ( 9 7 ) i n order to c a l c u l a t e the hydrogen bond bending and stretching force constants asso- c i a t e d with molecular l i b r a t i o n and t r a n s l a t i o n . With Cp̂ . point symmetry the Ĥ Ô  molecule has the reducible repre- sentation composed of 5 ^ 2 a 2 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 2 0 3 molecule, as w e l l as the representations of the.sets of symmetry coordin- ates, are shown below: 199 Fig. k.18 The H 20 3 model of H20 i n ice I. The 000 and HOH angles were assumed to be tetrahedral. The hydrogen bond bending coor- dinates 6-j_ and 0 2 are i n the HOH plane and 8-|_ and 6̂  are perpendicular to them. C 2 v E c 2 °xz a yz a l 1 1 .1 1 a x x ' a y y a z z 1 1 -1 -1 R z axy °i 1 -1 1 -1 T X Ry axz b 2 1 -1 -1 1 Ty * R X "y? , r(H 2o 3) 15 -1 5 1 5 a i + 2 a 2 + 5 b x + 3 b 2 r(Rot.) • 3 -1 -1 -1 a 2 + \ + D 2 r(Trans.) 3 -1 1 1 a-|_ + b x + b 2 r(vib.) 9 1 7 -1 l+a1 + a 2 + 3b]_ + b 2 r i ( R 1 , R 2 ) 2 0 2 0 a-̂  + b l 2 0 2 0 aj + * 1 r 3 ( R 5 ) 1 1 1 1 a l ru(R 6,R 7) 2 0 2 0 a-̂  + b l T 5(R 8,R Q) 2 0 -2 0 a 2 + b 2 2 0 0 The symmetry coordinates of HgO^ are S1 = 1//2 (R^ + R g) S 2 = 1//2 (R 3 + R ^ ) = R. Sh = 1//2 (R 6 + R ?) a. 1//2 (R 1 - V ] S 6 = 1//2 " ( R 3 - V \ S 7 = 1//2 ( R 5 - V J S 8 = 1//2 (Rg - v a 2 S 9 = 1//2 ( R Q + v b 2 In matrix notation the transformation from i n t e r n a l to symmetry coordinates i s S = p where S_ and R_ are column matricies of symmetry and i n t e r n a l coordinates , and U i s an orthogonal matrix. The solution of the secular equation i s simpler i n symmetry coordinates and the F_ and G 'matrices must also he transformed from i n t e r n a l coordinates ( F _ ( R ) and G _ ( R ) ) to symmetry coordinates ( F _ ( S ) and ( J ( S ) ) by the transformations F ( S ) = U F ( R ) U T G ( S ) = U G ( R ) U T The F ( S ) and G_(S) matricies each are diagonalized into block form contain- ing a (k x l O a j , a(3 x 3)b^, a ( l x l ) a 2 and a ( l x l ) b 2 block. The form of G_(S) i n terms of G_(R) elements and the numerical values of 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 for G _ ( S ) . Before proceeding further with the normal coordinate analysis, 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 H20 i n ice I must be assigned to the i n t e r n a l vibrations of the H203 molecule as represented 2 0 1 Table XV.III. The symmetric G matrix elements i n terms of the in t e r n a l coordinates and t h e i r numerical values for the HgO^ model i n units of (gm~^- A2 moles). a i G(S) G(S) = g l l + S 1 2 S 1 3 + s l U 2 g 1 5 s l 6 + g l 7 1.03^ 0 992 0 088 0.062 E 1 3 + g 3 3 + 83h 2 g 3 5 S 3 6 + s 3 7 0.992 1 055 0 D 2 g 1 5 2 g 3 5 S 5 5 2g 56 0.088 0 2 393 2. 511 s 1 7 + g l 6 g 3 6 + S 3 7 2 g 5 6 g 6 6 + g 7 6 0.062 0 2 511 2.733 s l l - S 1 2 S 1 3 g l 6 " ' g 1 7 1.076 0 992 0.062 S 1 3 S 3 3 " g 3 U g 3 6 = 0.992 1 055 0 g l 6 " s 1 7 g 3 6 g 6 6 " • g 7 6 0.062 0 2.595 G(S) = [ g 8 8 -,g 8 9] = 2.595 b 2 G(S) = [ g 8 8 + g 8 9 ] = 2.733 by the symmetry coordinates above. The displacement vectors of each kind of i n t e r n a l HgO^ coordinate are shown i n Fig. h.19. The corresponding displacement vectors of the symmetry coordinates constructed from those int e r n a l coordinates are shown i n Fig. h.20. The RgO ice I normal mode associated with each HgOg in t e r n a l vibration i s l i s t e d i n Fig. k.20. The symmetry coordinates , Sg and , which correspond to vRxt> vR z, and respectively, are of par t i c u l a r interest for t h i s discussion. / / R 5 = A < £ 6 Fig. 4.19 The in t e r n a l coordinates of the H2O3 model shown as. symmetrically equivalent pairs. The displacement vectors are not to scale and give only an approximate representation of the coordinates. Fig. U.20 The symmetry coordinates of the H2O3 model were constructed as simple lin e a r combinations of the in t e r n a l coordinates. Each symmetry coordinate was assigned to an HgO ice I normal mode simply on the basis of the diagramatic representation. Inspection of , Ggg and GQG. i n Table I V . I l l shows that the two l i b r a t i o n s ("vRx and v R z ) are " k i n e t i c a l l y " degenerate and that vp v i s very nearly degenerate with them: 20k G 7 7 = % 6 - S 6 T V R X G 8 8 5 3 § 6 6 ~ 667 VR Z G 9 9 = § 6 6 + g 6 7 vR y I f the forces restraining l i b r a t i o n about x and y are equal (which they are for HyjCU by symmetry) then v R i s degenerate with V R . - J x y The secular equation can be solved for the diagonal symmetry force constants by an i t e r a t i o n formula given by Green (.125): k*? 1 = A.{ G. . + £ ( G i J ) 2 k i J } _ 1 [ 5 ] . 1 " j 5 The b 2 block i s t r i v i a l and gave the solution of k Q Q = O.IH9 x 10 dyne-cm when was assigned to the peak at 833 cm ̂ . The a 2 block i s also t r i v i a l and gave the solution kgg = 0.157 x 1 0 ^ dyne-cm, i n good agreement with k n q ( v T ? and V R were assumed to be degenerate at 8 3 3 cm-"1"). For the ( 3 x 3)b^ block the S^, Sg and symmetry coordinates were associated with ^ 2 ^ 2 ° ^ ' V T X ^ H 2 G ^ &T1^ V R y ^ H 2 u ^ > respectively. Applying the i t e r a t i o n formula: 4 = \ (G„ + ( 0 - 9 9 2 ) 2 k 6 6 1 + ^ • 0 6 2 ) 2 k 7 7 1 } _ 1 5 5 5 55 — 5 ; r 5; 7 • 5 - 6 A 5 " 7 A 6 - X 5 A 7 - S where A. = ( v . / 1 3 0 3 - l ) . I n i t i a l force constants k?. = 1.000 were assumed 1 1 11 and the formulas converged to t 0.001 i n eleven i t e r a t i o n s . The force constants determined were: 205 k,.,. = 5.U81 x 1 0 ^ dynes/cm kgg = 0.192 x 1 0 5 dynes/cm k = 0.15U x 1 0 ^ dyne-cm Notice that the symmetry force constant associated with v n , k„„ = 0 . 1 5 ^ K y 77 x 1 0 ^ dynes/cm, does not agree with those of v R and V R . x z F i n a l l y the (h x U)a^ block was solved for the HgO^ symmetry force constants. The S^, Sg, and symmetry coordinates were assigned to v-^HgO), TgCHgO), vgCHgO) and v^HgO) respectively. The symmetry coor- dinate was assumed to be a redundant, non-genuine HgO bending mode, although i t was a genuine mode of HgO^. As a redundant coordinate terms due to i n F(s) and G_(s) were set equal to zero. Then the symmetry block reduced to a (3 x 3)aj_ matrix. Using the observed V]_, Vip and Vg frequencies of HgO (Table III.XI) and i n i t i a l force constants of k.. = 1 . 0 0 0 , then the three i t e r a t i o n 11 formulas converged i n f i f t e e n steps to: k ^ = 5-369 x 1 0 ^ dynes/cm k 2 2 = 0.231 x 1 0 5 dynes/cm k ^ = 0.601 x 1 0 5 dyne-cm With better choices of i n i t i a l force constants, the formulas converged i n four to fi v e steps to ± 0.001 x 10 ̂  dynes/cm. To convert k ^ 5 k y y ' k88 and k units from dyne-cm to dynes/cm i t i s only necessary to divide by the lengths of the arms forming the bending coordinates. The set of HgO internal mode force, constants were estimated: 206 k l l ( V = 5 ' 3 6 9 k 5 5 ( v 3 ) = 5.H82 k 3 3 ( v 2 ) = 0.666 x 1 0 5 dynes/cm Of the three possible H20 translations only two force constants were estimated: k 2 2 ( T z ) = 0.231 kgg(T y) = 0.192 x 1 0 5 dynes/cm. F i n a l l y , three force constants associated with the three possible l i b r a t i o n s were estimated: k 9 9 ( R x ) = 0.088 k 7 7 ( R y ) = , 0.091 k 8 8 ^ R z ^ = ° - ° 9 2 x l o 5 dynes/cm. The above symmetry force constants were transformed back to in t e r n a l coordinates force constants for comparison to those of other workers. For example, the symmetry force constants i n terms of in t e r n a l force constants are: k l l ^ V l ^ = k ^ r l r l ^ + k ( r ] _ r 2 ) k ^ ( v 3 ) = k(rir-]_) - k C r-ji^) k 3 3 ( v 3 ) = k Co)*) k 9 9 ( R x ^ = k(eie ' i ) + k(e|e 2) k T T(Ry) = k(.e 1e 1)- kCe^g) k 2 2 ( T z ) = k ( r 3 r 3 ) + k ( r 3 r 1 + ) k 8 8 ( R z ) = kCe^e^)- k(e{e 2) k 6 6 ( V = k ( r 3 r 3 ) - k ( r 3 * V 207 Thus one found that the i n t e r n a l coordinates force constants for H 20 are (in 1 0 ^ dynes/cm): in t e r n a l t r a n s l a t i o n a l lie-rational ( 0 0 stretch) (0-H 0 bend) k ( r 1 r 1 ) = 5-425 k ^ r 3 r 3 ^ = °- 2 1 2 k C e ^ ) = 0.090 k(r-Lr 2) = -O.O56 H ^ r ^ ) = 0.019 k(0-[02) = - 0 . 0 0 2 kU<j>) = 0.666 *k(e 1e 1) = 0.093 *k(e 1e 2) = - 0 . 0 0 2 Since the other symmetry coordinate involving 0̂  and 0̂  was assumed redun- dant and eliminated, then k(9^0^) could only be evaluated by assuming that k(0 10 2) = k(6J0 2) = -0.002 x 1 0 5 dynes/cm. A set of D 20 force constants was estimated i n the same way (from LV>03) as for H 20. The results of the H 20 and D 20 ice I force constant : models are l i s t e d i n Table IV.IV along with the results of Zimmermann and Pimentel ( 9 7 ) and Trevino ( 9 3 ) . Our k(0^9-^) i s an in-plane hydrogen bond . I ! . 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 of the difference i s probably due to differences i n the models, Trevino's ( 9 3 ) was extended further and i n a three-dimensional l a t t i c e while ours was planar. The following comments can be made about the H 20 force constants estimated using the HgO^ model and equation [ 5 ] : • • - the OH stretching force constant (k(r-j_r^) = 5.^25 x 1 0 ^ dynes/cm) i s less than the gas phase value and i s i n the region predicted from the r a t i o of frequencies for harmonic o s c i l l a t o r s , 208 Table 17.IT The force constants of ice I from the HgO^ and D 20 models as well as the results of Pimentel and Zimmerman and Trevino. Force Constant Associated Motion D 20 Pimentel This Work ' (a) (f) i . r . i . r . H 20 This Work (f) i . r . . Trevino (e) neutron k ( r 1 r 1 k C r ^ k ( r 3 r 3 k( r 3 r u k ( e 1 e 1 k ( e 1 e 2 *(9W k(0^0 2 0-H s t r . 0-H, 0-H interaction H- •0 s t r , Cd) 0.178 H 0, H-••-0 interaction (b) 0- ••• -H-0 i .p.b. 0 H-0, 0- • • H-0 interaction (c) 0- -H-0 o.p.b. 0.095 interaction (a) 5 . 7 H - 0 . 0 U 9 0 . 2 2 5 0 . 0 2 3 0.099 -0.002 (d) 5 . U 2 5 -O.0H9 0.212 0.019 0.093 (-0.002) 0.090 -0.002 (d) 5.52 0.25 0.06 0.08 k(<M>) HOH bending 0.h9 0 . 7 3 0 0.666 0.62 (a) Pimentel and Zimmerman, Ref. 97 (b) i.p.b. = in-plane (linear) bend, (c) o.p.b. = out-of-plane (linear) bend. (d) a l l force constants are lO^ dynes/cm. (e) Trevino, Ref. 93. (f) This work, Green's formula, H 2 0 3 model. 2 0 9 - the'hydrogen-bond stretching force constant ( k l r ^ r ^ l - = 0.212 . x 1 0 ^ dynes/cm) i s of the order of magnitude expected on the basis that the hydrogen bond strength ( 5 - 1 0 Kcal/mole) i s about l / 2 5 t h of the 0-H bond strength, - the H-O-H bending force constant (k^^ = k(<j><j>) = 0.666 x 1 0 ^ 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) force constant (kfe^Gj) = 0.090 x 1 0 ^ dynes/cm) i s very small, t h i s may be interpreted as ind i c a t i n g the hydrogen bond i s r e l a t i v e l y insen- s i t i v e to bending through small angles. I t i s i n t e r e s t i n g to notice that for every diagonal, i n t e r n a l coor- dinate force constant the DgO values are'larger than the H2O values by 5 to 1 0 $ . The source of t h i s effect i s i n the nature of the force constant model. Green's ( 1 2 5 ) formula [ 5 ] assumes a diagonal force f i e l d and a harmonic o s c i l l a t o r approach. Since D 20 energy l e v e l s are lower, and since D 20 i n t e r n a l coordinates displacements are smaller than H 20 displacements, then our D 20 "sees" a lower, more symmetric portion of the "true" poten- t i a l curve. The simulated D 20 parabola i s thus narrower and steeper than the simulated H 20 parabola and consequently the D 20 force constants are larger than the H 20 force constants. I t i s obvious that such diagonal H 202 and D 2 0 3 models assumed no anharmonicity i n i c e . Such a case seems highly u n l i k e l y i n view of the strong neighbour-neighbour in t e r a c t i o n through strong hydrogen bonds. In spite of 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 to give a f a i t h f u l representation of the spectrum. 210 The test of any set of. force constants, however, ll.es. i n i t s a b i l i t y to reproduce the observed frequencies of isotopic analogues. To check the force constants derived from RVjO-g for the H20 i n t e r n a l , 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 vibrations i n i c e , the frequencies of D2Q ice frequencies were calculated. Formula 15] was inverted and solved:- 2 , [G„ + , 1 G i j k j j ] [6] A. = k. . LG.. . j . i  ,1,1 1 11 11 lyCJ . . where k.., k are taken from HgOCHgO^) ' A i ~ h A. i s taken to be the observed value, and J A. i s to be calculated. I The a 2 and b 2 blocks are easily solved of course since they reduce to the form - A. = k..G.. l 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 elimination of the redundant coordinate) y i e l d two quadratic and one cubic equation each. The frequen- cies of the normal.modes of D20 ice I were found and are compared to the observed values below: v c a l c . vobs. V c a l c . Vobs. v3 v l v 2 -1 -1 -1 cm cm cm 2325 2^13 -88 2258 2321 -63 1138 119k -56 595 -32 H X nn), £o-Aai v R~ 59^ 627 r -33 vj 601 6 2 7 L & 1 -26 (b) 232 2 2 0 ^ ' +12 T x 229 220£bj +9 (a) V R X J vp and V R z are assumed to be degenerate (b) Reference 9 6 . 2 1 1 The D 20 i c e i n t e r n a l mode frequencies CyijVgj'V^l- calculated from formula [ 6 ] using H2OC.H2O3} force constants were a l l too low- C-6"3 cm - 1, -56 cm/*'", -88 cm "*") by 3 to 5%. The D 20 t r a n s l a t i o n a l l a t t i c e frequencies calculated i n the same way were too high by 5%. The modes of i n t e r e s t , for which the HpO^ model was constructed, are the l i b r a t i o n a l l a t t i c e modes. Their c a l - culated frequencies were also too low by 5 - 6%. I t i s interesting that the l i b r a t i o n a l D 20 frequencies from the H 2 0 3 model are nearly the.same as those predicted for HgO and D 20 i n the weighted-lone-pair, moment-of- i n e r t i a model previously discussed. There the frequencies calculated were 586 cm "*", 588 cm 1 and 591 cm "*" for vp x, Vp and vp z respectively. y ; One can conclude that the H 2 O 3 normal coordinate analysis, as a basis for H 2 O / D 2 O ice l i b r a t i o n s offers no improvement over a weighted lone-pairs moment-of-inertia model. The HgO^ model does give reasonable int e r n a l and l a t t i c e , mode frequencies and reasonable ice force constants. C. A Summary of H 2 O , HDO and D 2 O Librations Three models, of ice 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 analysis of the H 2 O 3 ex- tended molecule. Blue's formula [k] gave widely dispersed Vp x and Vp̂ . frequencies i n H 2 O : and D 2 O , jL.e_. separation of about 1 0 0 cm \ This did not conform to the observed i r absorption. 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 x and vp^. are of equal i n t e n s i t y while vp z was weak or inactive. 212 Transfering effective mass from a nearest-neighbour proton to the central molecule's lone-pair o r b i t a l s produced a nearly spherical top. The three p r i n c i p a l moments-of-inertia dif f e r e d by only ± 5 percent for the (H 20, 3 / 4 , 1 / 4 ) option. The force constants for 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^' = 0.21 x 10-* dynes/cm at the de- tached proton. These two force constants were deduced from Blue's formula [k] assuming vp x = = 832 cm \ Application of k^ and k^' to formula [h] i n D 20 parameters predicted D 20 frequencies of: 586 -1 cm v R y = 588 -1 cm 591 -1 cm The D 20 frequencies' are reasonably degenerate, but l i e s i x percent below the observed band maximum. Analogous results were obtained for an (H 20, 1,1/U) effective mass option. Transf e r a b i l i t y of force constants among isotopic analogues was violated i n the effective mass model, force con- stants estimated from HgO and D2O frequencies did not agree. '; Normal coordinate analysis of the HgO-̂  extended molecule produced very good valence force constants and hydrogen-bond force constants. However, the H 20 force constants did not duplicate the D 20 frequencies.. The dispersion was explained by considering the difference i n shape of harmonic potential 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 with respect to force constant evalua- ti o n . 213 Further improvements i n the analysis of ice may be found by t r e a t - ing i t as an extended three dimensional polymer. Techniques of normal coordinate analysis of polymers are now expanding. Zerbi's review (12,6) outlines the approach, a modification 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 Vitreous-Crystalline Clathrate-Mixture Phase Transformation A. Experimental Warm-up studies of the i r absorptions of vitreous, condensed mix- tures of H20 and guest species were completed i n the l i q u i d nitrogen c e l l (page k2). Stoichiometric gaseous mixtures corresponding to the three classes of clathrate-hydrate were prepared and condensed i n the same manner as the ice samples (page 58). Samples studied i n the f i r s t clathrate class (page 13) 6G-1+6H20 were G = CH3CI, CH3Br and C l 2 , while for the second clathrate class (page 15) SG'ISSHgO the samples were for G = CH3I, CHCI3 and C2H^Br. Only one sample from the t h i r d class,. 20G*1T2H20 (page 15), was studied, i_.e_. G = B r 2 . The conditions of sample formation and annealing are l i s t e d i n Table V.I. In order to • avoid separation of the clathrate mixture, a l l these samples were depo- sited through the heated metal deposition tube (page kh). As with the H 20, HDO and D20 samples, the source beam was blocked when the clathrate mixture samples were warmed above l80°K, i n order to prevent sublimation. As w e l l , the c e l l chamber was not pumped when above l60°K. The temperatures quoted here are those which were measured by the copper-constantan thermocouple attached to the brass sample", block: The sample temperatures were 10°K higher due to source beam heating. However, the maximum annealing temperatures do not need to be corrected i n that way since the source beam was off then. Table V.I. The clathrate mixture sample h i s t o r i e s for the deposition and annealing procedures, temperature refers to the.sample block temperature.with the source o f f . The deposition Molar gas r a t i o Deposition Rate Sample Substrate Deposition Temperature °K Annealing Time Min Maximum Annealing Temperature °K Time at Maximum Temperature Min B2 I C H 3 C I : lCH^Br: CI (CU) I C H 3 I : 10 sec 1.5 min Csl 83 139 200 12 Csl 81* 265 1 9 9 U5 5 sec ( -- ) Csl 83 ( 8 3 ) 98 ( 1 0 5 ) • 188 ( 1 8 9 ) 16 ( 1 8 ) D 1CHC1-: 7 H20 7 H20 17H20 17H20 2 sec Csl 83 172 189 15 E lC 2H 5Br: 17H20 3 sec Csl 81 170 189 16 F l (F6) 1C1 2: 7 H20 3 sec ' (2 min) Csl 81 ( 8 2 ) 103 ( 2 5 ) 189 ( 1 9 0 ) 12 (15) G3 1C1 2: 7 H20 3 sec AgCl 83 . 15 1 9 0 11 l B r 2 : 8. 6H~20 3 sec AgCl 83 2k0 200 25 ro H 2 1 6 A l l annealing processes were observed on the P.E. h21 spectrophoto- meter during warm-up from 85 t 5°K to 180 t 10°K. Spectrophotometer controls were set for optimum response and were the same as for ice I (page 59) with small variations. The spectra were recorded at 85 t 5°K immediately after deposition and at several temperatures between 8 5 0 and l80°K. Peaks and shoulders were assigned as for ice I (page 5 9 ) . B. 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 hi s t o r y , the basic results for a l l the unannealed, vitreous.samples were the same. Consequently, only one set of normal annealing results w i l l be discussed i n d e t a i l . Some i r r e g u l a r i t i e s were observed for 6 C l 2 ' 4 6 R " 2 0 condensed and annealed on a Csl window.: Those results w i l l be discussed separately. Each of the Ĥ O s k e l e t a l bands (v]_ + vp), v 3 » vl» 3 yR» V2/2.Vp and v R was analyzed, as were those guest absorptions which were observed. No d i s t i n c t i o n between the classes^ of. clathrates was noticed i n t h i s work. ( i ) The Effect of D e v i t r i f i c a t i o n on the Lattice Peak Maxima For the seven samples l i s t e d previously (page 2 1 5 ) only the results of the chloromethane clathrate mixture w i l l be given. The s i x other samples (including C l 2 on Csl) had the same behaviour within the l i m i t s of error. The frequency-temperature dependences of the main H 20 s k e l e t a l features are shown i n F i g . 5-1. The absorption spectra of some unannealed and annealed samples ( a l l at 83 ± 3°K) are shown i n Figs. 5.2, 5-3 and 5 - 4 . Some det a i l s of the CHjCl'T^THgO clathrate mixture annealing (Fig. 5 - l ) are 0 UJ D h < Q: UJ Q_ LU 2 0 0 - o LU D h < LU Q. LU h o LU DC D h < LU CL LU h 150- IOO - 7 0 2 0 0 150 - IOO 7 0 2 0 0 - I 5 Q - I O O - 7 0 • 8 ^ 3 • 7 • 7 • 5 • 4 • 3 • 2 • 5 • 4 • 3 • 2 • 6 • 1 • 6 • 1 I ' l l 1 3 1 5 0 3 1 7 0 1 1 i 1 3 2 2 0 3 2 4 0 • 8 • 8 • 7 • 5 • 4 • 3 • 2 • 7 • 4 • 3 • 2 • 5 • 6 • 1 • 1 • 6 i i 3 3 6 0 i i i i 3 3 7 0 • i i I 2 2 2 0 i 2 2 3 0 • 8 • 8 • 7 • 5 • 4 • 3 • 2 • 5 • 4- • 3 • 2 • 6 • f •1 • 6 i i i i i i 1610 1 6 3 0 1 6 5 0 i i i 1 7 9 0 8 1 0 i i 8 3 0 217 F R E Q U E N C Y C M -1 Fig. 5.1 The s h i f t s of the unannealed clathrate mixture (CB^Cl^^R^O) H20 peaks during warming from 83 ± 3°K to 200 ± 5°K. The data are t y p i c a l of a l l the clathrate mixtures and appear to be the same as for ice Iv. The data are numbered i n the order of observation. A.B A.B •4000 3000 1000 A . B 4COO 3000 2000 F R E Q U E N C Y CM" IOOO 500 A . B 500 Fig. 5.2 The infrared absorption spectra of some clathrate mixtures. In. a l l cases spectra numbered "A" are backgrounds through the low temper- ature c e l l , (a) C H 3 C I • 7 . 6 7 H 2 0 unannealed at 83 ± 3°K (B), at 83 ± 3°K but annealed to l 6 0 ± 3°K (C), and at 200°K (D). (b) CH^Br• 7.67H 20. unannealed at 83 ± 3°K (B), at 83 ± 3°K but annealed to 158 + 3°K (C) and at 189 + 3°K (D). (c) CH 3I-17H 20 unannealed at 83 ± 3°K (B), annealed to 190 ± 5°K but observed at 83 ± 3°K (O and at .188 + 3°K (D). The same frequency scale applies to a l l of the spectra, i . e . for each absorbance scale. F i g . 5-3 The effects of annealing clathrate mixtures of C H C I 3 and C^^Br" 17H 20. (a) C H C 1 3 - 1 7 H 2 0 unannealed at 83 ± 3°K (B), at 129 ± 3°K (c), at ll+9 i 3°K (D) and at 189 t 5°K (E) . (h) C 2H 5Br• 1 7 H 20 unannealed at 83 ± 3°K (B), at 129 i 3°K lc\t at 1kg ± 3°K (D) and at 189 i 3°K (E). The same frequency scale applies to each absorbance scale, i_.e_. a shorter span of frequencies i s shown for D than for E. A . B A , B 4 0 0 0 3 0 0 0 2 0 0 0 1 0 0 0 F R E Q U E N C Y C M " 5 0 0 Fig. 5.U Ca) B r 2 ' 8 . 6 HgO on AgCl unannealed at 83 ± 3°K (B,C), at 130 + 3°K (D,E) and at 170 + 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 2 - 7 . 6 7 H 2 0 on AgCl unannealed at 83 ± 3°K (B) and at 83 ± 3°K but annealed to 190 + 5°K Cc). (c) C 1 2 - 7 . 6 T H 20 on Csl unannealed at 83 + 3°K (.B) and at 83 ± 3°K but annealed to 190 ± 5°K for 15 minutes (C). 2 2 1 i n Table V.II. As for ice I , the frequency s h i f t s of the vitreous 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 for each band. The sixt h point was obtained by cooling the sample to 83 - 3°K after annealing i t at 160 ± 3°K for 20 minutes and before warming to higher temperatures. Table.V.II The R"20 frequencies of the CH 3C1*7.67H 20 clathrate mixture before (v u) and after (v a) annealing to 200 ± 5°K. The transformation temperature range and the temperature depen- dence after annealing are shown. 82°K 82°K 82°K Transformation . a unannealed annealed Av Temperature v u • • va v a - v u Range AT cm cm cm 1 °K cm ""V°K v + v T 3 3 8 2 ± 5 3361+ _ i 8 (lUO-170) ±10 0.10 V3 v l v 2 VR 3258±3 3219 -39 (lHO-l6o)±10 0.12 3195±5 311+6 -1+9 (130-155) ±10 0.25 3v D 2 2 0 9 ± 5 2227 +18 ( 1 2 5 - 1 5 5 ) ± 1 0 - 0 . 0 9 R l65l+'±3 1 6 1 0 -1+1+ ( 1 2 5 - I l + 0 ) ± 1 0 0.18 792±1+ 823 +31 ( I 1 5 - l l + 0 ) ± 1 0 - 0 . l 6 222 The f i v e conclusions made with respect to the ice I d e v i t r i f i c a t i o n (page 6 3 ) apply to RgO i n these clathrate mixtures also. • Typical 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 for C H 3 C I ' 7 . 6 7 ^ 0 : - at 83 i 3°K (before' annealing) a transparent f i l m around a translucent, milky-white mass about 0.25 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 188 t 3°K the sample appeared to be t o t a l l y white and opaque. In general, the source image was centered on the thinner portion of the sample. The B r 2 ' 8 . 6 H 2 0 mixtures were not white, but were orange and yellow-orange depending on the thickness. ( i i ) The Effects of 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 stretching band had the same appearance as for vitreous ice I (Fig. 3.3) and can be seen i n Figs. 5.2, 5.3 and 5.^. The positions of these oligomeric H2O absorptions for various unannealed clathrate mixtures at 83 ± 3°K immediately after deposition are given i n Table V . I I I : In some cases a number of specimens were observed. The positions of the peaks depend on the rate of sample deposition. For example, the three CH^Br sets of re s u l t s were obtained from mixtures deposited through a needle valve i n ̂ .5> 1.5 and 1 1 minutes respectively. The temperature dependences of the H2O oligomeric absorptions from a number of clathrate mixtures are given i n Table V.IV. With a single exception the oligomeric HgO "absorptions began to diminish i n peak height between 1 2 0 and 129°K and had disappeared below 170°K, Table V.V. Table V.III The frequencies at 83 ± 3°K of the weak peaks and shoulders associated with oligomeric H2O units i n several unannealed clathrate mixtures. Csl AgCl CR£1 CH3Br CH3I CHCI3 C2H^Br B r 2 C 1 2 c i 2 H20 ' 7 . 6 7 H 2 0 7 - 6 7 H 2 0 "17H20 •17H20 •17H20 *8.6H20 * 7 . 6 7 H 2 0 • 7 . 6 7 H 2 0 ice I v 1"5 cm """ ±5 -1 cm ± 5 cm ± 5 cm """ ± 5 cm *"" +5 cm """ ± 5 -1 cm ± 5 cm """ ± 5 cm  1 36U5 (vw) 3 5 8 0 (w) 3 6 8 9 (ww) 36k3 (vw) 3691 (ww) 3689 (ww) 3635 (vw) 3 6 8 7 365h (vw) 3605 (vw) 3 6 3 9 (vw) 3565 (w) 3612 (vw) 3672 (vw) 3 6 5 8 3583 (w) 3635 (w) 3 6 3 7 3687 (ww) 3670 (vw) 3617 (w) 3 6 8 7 (vw) 3 6 6 8 (ww) 3 6 7 3 (w) 3 6 2 3 (vw) 36U8 (ww) 3 6 3 6 (vw) 3 6 2 0 (v) 3 6 2 5 (ww) 3 6 3 8 (vw) 3689 (ww) 36k2 (w) 3620 (w) 3 6 9 0 (vw) 3690 (ww) 362k (vw)- 3671 (vw) 3 6 l U (w) ro ro 22h Table V.IV The temperature dependences of the oligomeric H 2 O absorption frequencies of some clathrate mixtures and unannealed ice I. 85±3°K 9i+±3°K 110±3°K 125±3°K , H 20 Ice I v -1 cm 3687 3658 3637 3689 367I+ 3650 36k0 3690 361+7 3690 83±3°K 109±3°K 129±3°K ll+9±3°K CHC13'1T H 20 cm ̂ 3689 (sh) 3 6 3 9 ( 0 . 1 1 ) 3 6 8 7 (sh) 361+0 ( 0 . 1 0 ) 3 6 7 3 (sh) 361+0(0.06) 3 6 7 2 (sh) 3652 (sh) 363l+(0.0U) 83±3°K 110±3°K 129±3°K 150±3°K C 2H 5Br'17 H 20 -1 cm 361+3 (wsh) 3565 (msh) 3669 (wsh) 3638 (wsh) 3569 (msh) 3658 (wsh) 3563 (msh) 8l±3°K 109±3°K 129±3°K ll+9±3°K C l 2 - 7 . 6 7 H 20 -1 cm 3689 (vw) 3672 (vw) 3635 (wsh) 3688 (vw) 3675 (vw) 3630 (wsh) 3688 (vw) 3669 (vw) 3636 (wsh) 83±3°K 130i3°K 130±3°K 1 7 0 ± 3 +0.5 hours °K 83±3°K B r 2 - 8 . 6 H 20 -1 cm 3 6 9 1 ( 0 . 0 2 ) 3 6 1 2 ( 0 . 1 0 ) 3 6 9 3 ( 0 . 0 2 ) 3 6 1 6 ( 0 . 0 8 ) 3 6 0 9 ( 0 . 0 6 ) 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 2 C H 3 C I ±5°K 120 ±5°K 120 CH3Br 120 < 138 C H 3 I 1 2 0 < iho CHC13 ikg < 169 C 2H 5Br 125 < 150 B r 2 — > 185 C l 2 ( C s l ) 1 2 9 < lh9 H 20 ice I v 1 1 0 125 For the Br^S^HgO mixture the oligomeric absorptions were observed at 170 t 3°K during annealing and even at 83 t 3°K after annealing, Fig. 5 . 4 . The v i s u a l appearance of the Br 2'8.6H 20 sample changed markedly during annealing above 185 t 3°K (with the source beam o f f ) : The sample was annealed for 10 minutes at 185 ± 3°K, 10 minutes at 190 ± 3°K and for 3 minutes at 200 ± 3°K. After 1 minute at 200 ± 3°K the sample changed from orange-brown to a rusty-brown surface layer. After 3 minutes at 200 ± 3°K the rusty-brown layer had sublimed o f f . 226 ( i i i ) The Effects of D e v i t r i f i c a t i o n on Gl2-7.6THpO Mixtures Gaseous mixtures of Cl2"7-67 H 2 O condensed on Csl and annealed for long periods appeared to react with the Csl. Consequently the Cl 2'7-67 H20 mixture was studied on two substrates, i_.e_. Csl and AgCl, samples F and G respectively. In a l l s i x samples were studied on Csl and three on AgCl. (a) C1 2'7.67H 20 on Csl (sample F). The i r absorption spectra of Cl2*7.67H 20 at 83 ± 3°K before and after annealing to l89°K were shown i n Fig. 5.*+ (sample F j ) , while the temperature-frequency dependences of the H20 skeletal absorptions were the same as for CH3CI•7•67H 20 (Fig.5-1). The effect of annealing Cl2"7.67H 20 to progressively higher temperatures i s shown i n Fig. 5-5 (sample Fg). The v i s u a l appearance of sample F-̂  before and during annealing was: - (between 83 t 3 and 110 i 3°K) a cone of opaque white material which became gradually 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 after 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 for 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 differed. In the spectrum of sample Fg the absorption between 3000 cm and 2^00 cm-"*" increased as the sample was annealed to higher temperatures. Also notice the dramatic effect on the stretching band due to annealing to E.F E.F 4 0 0 0 3 0 0 0 2 0 0 0 IOOO F R E Q U E N C Y C M Fig. 5.5 Spectra of one sample of Cl2 ,T.67H 20 on Csl at 83°K with various successive annealing times: (A) Unannealed, (B) annealed to 170°K for 15 minutes, (C) annealed after (B) to l80°K for 15 minutes, (D) then annealed to 190°K for 15 minutes, (E) then annealed to 190°K for 30 minutes, and (F), background through low temperature c e l l at 83°K. 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 a new high frequency shoulder appeared. Annealing to 170 + 2°K or 1 8 0 t 2°K gave only the characteristic sharpening into 1 peak and 2 shoulders. As w e l l , the nature of the v 2 absorption changed. (b) C1 2*7.67H 20 on AgCl (sample G). Detailed studies of the annealing process of amorphous s o l i d C l 2 - 7 HgO on an AgCl substrate were not made. Spectra were recorded at 83 ± 3°K before and after annealing to various temperatures. The v i s u a l appearances were as before, i_.e_. a clear and transparent sample except for one spot opposite the nozzle before annealing and a uniform opaque white sample after annealing. C l 2 guest absorption as might be expected was not observed and the H 20 s k e l e t a l absorption was shown i n F i g . 5.^. None of our attempts to s p l i t the C1 2'7-67H 20 stretching band into 1 peak and 3 shoulders succeeded for samples on an AgCl window. Nor was the nature of the v 2 band changed. As w e l l , no increased absorption between 3000 cm - 1 and 2^00 cm - 1 was observed. The positions of the C1 2'7.67H 20 bands on Csl and AgCl w i l l be discussed i n section 5-3 (page 23*0. 5-2 Clathrate 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 20 host l a t t i c e were formed and observed by three techniques. In the f i r s t method (section 5 - l ) the stoichiometric gaseous mixtures were condensed rapidly onto a substrate held at 83 i 3°K i n an open chamber (section 2.kc). To ensure that the guest molecules were not dif 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 investigated. The second method was condensation of the mixtures i n an isolated chamber (section 2.4B), and the t h i r d method was the prepara- t i o n and observation of low temperature mulls (section 2.kA) of s o l i d clathrate mixtures (section 2 . 3 A ) . Of the seven clathrate 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 to diminish and the temperature at which they were absent varied considerably from sample to 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 C H 3 C I ' 7 . 6 7 ^ 0 guest absorptions were observed at 2957 (m), lkk3 (m), 1U37 (sh), 1347 (w) 1338 (vw), 1 0 2 1 (vw) and 700 (ms) cm 1 (Fig. 5.2(a)) near the s o l i d C H 3 C I absorptions. They were observed up to 100 ± 3°K with undiminished i n t e n s i t y and up to l 6 0 ± 3°K with diminishing in t e n s i t y . In contrast CH^I'^^O guest absorptions"were undiminished up to 138 +2°K and n i l at 168 + 2°K for one specimen, while for a second specimen the CH3Br absorptions were s l i g h t l y diminished at 110 + 3°K and slowly diminishing up to 189 ± 3°K (the 1235 cm - 1 peak was s t i l l present). The guest absorptions from a number of unannealed clathrate mixtures at 83 t 3°K, immediately after deposition, are l i s t e d i n Table V.VI. The variations of those guest absorptions as a function of temperature are given i n Table V.VII and the temperatures of the onset of alteration, 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 halide guest absorptions at 83 t 3°K i n a number of a l k y l halide clathrate mixtures before annealing began C H 3 C I CH^Br CH 3I CgH^Br •T.67H 20 - 7 . 6 7 H 2 0 - 1 7 H 2 0 C H C 1 3 ' 1 T H 2 ° -X7H20 cm 1 cm -l cm-l cm" -1 cm -l cm~l cm~l cm~l 2957 (m) • 3020' (sh) ' 3020 (m) 301U (sh) 3016 (sh) 2965 (sh) 2 9 5 0 (w) 2936 (ww) 2985 (vw) lhk3 (m) 2915 (ww) 1^37 (sh) 1292 (vvw) 13^7 (w) 1218 (ww) 1 2 3 8 (w) 12kk (sh) 1 2 3 8 (sh) 12U1 (ww) 1238 (ww) 1 2 5 ^ (vw) 1 3 3 8 (vw) 1 2 0 0 (sh) 1233 (sh) 123U (w) 121U (w) 1216 (vw) 1 2 l l | (vw) 12k2 (vw) 1 0 2 1 (vw) 105U (vw) 955 (w) 700 (ms) 750 (s) 755 (ms) 752 (ms) 752 (ms) 760 (sh) 665 (w) 665 (w) 663 (w) ro o 231 Table V.VII The temperature dependences of the guest absorptions during the annealing of clathrate mixtures. These data are t y p i c a l of a l l samples. . 83±3°K 110±3°K CH.3I • 17H20 2950 Cw) 1238 Cw) 1233 ( s h ) 2960 Csh) 1247 (w) 1240 (vw) 83±3°K 139±3°K 2936 ( w w ) 2915 ( w w ) 12kh ( s h ) 123-4 (w) 2 9 3 9 ( w w ) 2917 ( w w ) 1244 ( s h ) 1 2 3 6 (w) 83±3°K 110±3°K 129±3°K 150±3°K +2 cm - 1 ± 2 cm"1 +2 cm"1 ± 2 cm"1 C 2H 5Br'lTH 20 2985 (vw) 1254 (vw) 12U2 (vw) ' 955 (w) 760 ( s h ) 2 9 8 3 (vw) 1255 (vw) 1245 (w) 956 (w) 760 ( s h ) 2981 (vw) 1 2 5 2 ( s h ) 12U5 (vw) 952 (vw) 763 ( s h ) 1 2 5 8 ( s h ) 1245 ( w w I 232 Table V.VIII The temperature at which the guest absorptions peak heights began to decrease (T^), and tbe maximum temperature at which they were observed ( T 2 ) . Guest T l T 2 G-7.6TH 20 ±3°K ±3°K CH3C1 1 0 0 160 CH3Br 138 < 170 G'1TH 20 CH 3I 138 < 1 6 8 110 > 1 8 9 CHC13 1 2 9 < 1 89 > 1 6 9 C 2H 5Br 110 < 170 The guest frequencies shifted very l i t t l e , i f at a l l , upon warming for d e v i t r i f i c a t i o n , however the peaks did sharpen near 125 1 5°K. For example, i n annealing CHC1 3'17H 20 (Fig.5.3(a)) the absorptions near 1200 cm sharpened at 129 - 3°K. In fact i t s p l i t into two d i s t i n c t peaks at 1223 and 1203 cm - 1 and a shoulder at 1 2 l U cm - 1. As well the guest absorp- tions near 3000 cm ̂  and 750 cm "^sharpened at 129 ± 3°K. Although the two CHC13 peaks at 1223 and 1203 cm - 1 were observed as high as lh9 ± 3°K, the point i s that they were unobserved after annealing. 233 B. Condensation in'an'Isolated'Chamber The condensation apparatus and the technique were described i n sec- tions 1.6 and 2.UB respectively. Stoichiometric mixtures of C l 2 " 7 . 6 7 ^ 0 , S0 2-7.67H 20, CH3C1-7.67D20, CH 3C1-7.67H 20, CH 3Br•7•67H 20, CC13F'17H20, and CH 3I'17H 20 were condensed rap i d l y i n a precooled chamber and annealed to 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 re s u l t s of t h i s method were the same as for 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 H20 "host" absorptions were the same as fo r section 5.1 but with considerably more scattering. As w e l l these samples had spectra much l i k e C1 2'7.67H 20 (on Csl) between 3000 and 2200 cm - 1 (Fig. 5.4(c)). C. Low Temperature Mulls The technique was described i n section 2.kA and spectra were recorded on the P.E. 421 spectrophotometer. The present samples were mulled from ground s o l i d s prepared by freezing-warming cycles on stoichiometric l i q u i d mixtures. At 83 + 3°K CH3I'17H20 and CC1 3F-17H 20 had no guest absorptions and the R"20 s k e l e t a l absorptions were l i k e those reported i n section 5.1 for annealed samples. However, the scattering was greater than i n methods 5.2A or 5.2B. Some guest absorptions may have been masked by the C3Hg and CC1F3 mulling agent absorptions, but i t seems u n l i k e l y that a l l the CH 3I peaks would be masked by both agents. Several thicknesses of samples and amounts of mulling agent, were t r i e d , a l l with 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 results of warming annealed samples of clathrate mixtures from k.2°K or TT°K to 200°K are i n general the same as for cubic ice I , .i.e.. only the H 20 i r absorptions were observed. Thus only a few t y p i c a l c l a t h - rate mixture results w i l l be quoted and the remaining clathrate mixture results w i l l be given i n tabular form or as an average over a l l samples.. A. Temperature Dependence of the HDO Absorptions ( i ) Experimental The data reported here for v^HDO) i n CH 3C1-7.67D 20, CHgBr • 7 • 67D 20 and CH 3I-1TD 20, f o r V (HDO) i n CH 3Br•7.6TH 20, and for vR(HDO) i n CH 3Br•7•6TD 20 were obtained from gaseous samples condensed i n an open 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 with the liquid.helium dewar and the P.E. h21 spectrophotometer. Details of the sample h i s t o r i e s were t y p i c a l of those for ice I (page 69) as were de t a i l s of spectrophotometer operating conditions. The HDO peak maxima were determined as before (page 69) and: were estimated to within ± 0 . 5 cm - 1. ( i i ) Results of Warming Clathrate Mixtures Containing HDO (a) The HDO.stretching bands. These bands appeared to be the same as i n cubic ice I (Fig. 3.l) and t y p i c a l spectra w i l l not be reproduced. The temperature dependences of ̂ (HDO) and v (HDO) for CHoBr•7.67H?0 On , OD J are shown i n Figs.. 5-6 and 5.7: They are t y p i c a l of the other clathrate i- I 1 2 0 0 235 1 5 0 X. o <D D o ioo- a E' 5 0 - A i •  A O A • • A • A e A 6 A • A # • A A | A Z / ( H D O ) O H o- 3 2 6 2 7 0 8 0 3 2 9 0 Frequency cm -1 Fig. 5-6 The temperature dependence of v (HDO) for CH3Br-7D20 (k.0Q% HDO) after annealing. This was t y p i c a l of a l l the annealed clathrate mixtures of the a l k y l halides. 2 0 0 I 5 C H o CD D O Cl E I O O H 5 0 2 3 6 ( H D O ) O D o 2412 2 0 2 4 3 0 Frequency cm -1 Fig. 5.7 The temperature dependence of v CHDO) for CH^Br•7•67H 20 (5.9W ' HDO) after annealing. This behaviour was t y p i c a l of other a l k y l halide clathrate mixtures. mixtures and are very similar to cubic ice I. The det a i l s of the frequency- temperature dependences for a l l clathrate mixtures containing HDO are given i n Table V.IX. The samples were prepared from the same H20 (5-9^% HDO) and D20 (h.00% HDO) specimens as were the cubic ice I samples. The peak heights and half-height widths for HDO i n these clathrate mixtures behaved h i n ,the same way as for HDO i n cubic ice I. Some Av data are given m Fig. 5.8. Table V.IX Some parameters derived from the. plots of v O H(HDO) and. v Q D(HD0) against temperature for four annealed clathrate mixtures. Clathrate Guest G CH3C1 CH3Br CH3I CH3Br Mode Observed vQH(HDO) v Q H(HD0) v 0 H(HD0) v 0 D(HD0) Low Temperature Limit -1 cm V Av 5 5 3263.9 1+9.8 ±2.3 3261*. 0+1 1+6.5+1 1+7.0±1.5 3265.Oil.0 '1+1+.Oil.5 21+15.010.5 61.012.0 Low Temperature Dependence -1 cm °K V 0.0375 ±0.020 0.0507 10.027 0.0368 10.03 0.031+3 10.02 h Av — — — — High Temperature Dependence -1 cm °K V 0.183 ±0.012 0.166 io.o6o 0.11+8 10.026 0.191+ 10.09 0.109 10.013 Av 1 3 0.074 ±o.oU6 0.162 ±0.039 0.11+8 ±0.030 0.152 10.060 0.080 10.025 "Freeze-in" Temperature, °K V 75±5 75+5 90110 8715 68i5 Av 3 2 100±20 10015 0.1+±5 9515 8515 I r r e g u l a r i t i e s i n Frequency S h i f t , °K V 1+2-48 1+2-65 1+5-67 63-75 52-57 1 2 0 0 i o = A z y ^ (HDO) C H CI - 7.67 H O O H 3 2 A - - A ^ 2 ( H D O ) C H I - 17 H O O H 3 2 ^ ISP- CD -t— o ioo- CD a £ ^ 5 0 - • • A • A • A • A i = A z / ( H D O ) O D C H B r - 7 . 6 7 H O 3 2 O A A A a eo 9 • • • < • M 4 0 5 0 6 0 7 0 Half-height widths A z / 2 c m _ 1 Fig. 5.8 The half-height widths for V Q ^ C H D O ) and v ( H D O ) i n several clathrate mixtures after annealing These data were almost twice as large as for the cubic ice I data. IV) C O 239 Cb) HDO l i b r a t i o n s . Data for vR(HDO) of CH^Br•7.67D20 (k.0% HDO) are given as a function of temperature i n Fig. 5.9- This data i s t y p i c a l of other clathrate mixtures as we l l . 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 20 and D 20 absorption features for the annealed clathrate mixtures were observed by the same methods as were cubic ice I samples (page 79). Seven HgO absorptions were observed for each of the seven samples (v + v v v 3v , v /2v , v ' and v ). However for D o0 clathrate mix-l l o l . K ^ K K r( d tures the stretching band was studied i n d e t a i l for CH^I • ITD^O, 0^01*7.67 DpO and CH0Br'7.67Do0, and the (v ' v V band was studied only i n CH_Br-7-67 D̂ O.. A l l mixtures except C l ^ and Br^ 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 ice experiments. ( i i ) Results of Warming Clathrate Mixtures Containing H 20 and D20 The temperature dependences of the H20 and D 20 absorptions i n the annealed clathrate mixtures were the same as for cubic ice I. Typical spectra for v^ and v̂ . of CH^Br•7.67D.20 are given i n Figs. 5-10 and 5.11. The details of these samples were averaged for CH^Cl, CH^Br, CH3I, CHCl^ and C2H^Br mixtures and are compiled i n Table V.XI. The d e t a i l s of several C1 2'7.67H 20 and Br 2'8.6H 20 mixtures above 83 ± 3°K are given i n Table V.XII. The spectra and plots were treated i n the same manner as for 2h0 1 8 0 i • 1 5 0 - Y. o CD -4— CD a 1 0 0 - 5 0 - o- 7 9 5 o e 1/ ( H D O ) R • • • ^ # A 8 0 0 8 1 0 Frequency c m - 1 8 2 0 Fig. 5.9 The temperature dependence of V R C H D 0 ) for annealed CHgBr*7•6TD 20 (k.00% EDO) clathrate mixture.. This data i s t y p i c a l of other a l k y l halide clathrate mixtures. Table V.X The parameters for the HDO l i b r a t i o n s of three annealed clathrate mixtures. C H 3 B r - 7 . 6 T D 2 0 C H Br-7.67D 0 C H I-17D20 C H Br'7.67I>20 ( k.00% H D O )  3(k.00% HDO) {k.00% H D O ) (k.00% H D O ) v ( H D O ) v ( H D O ) v ( H D O ) v ( H D O ) + v Low Temperature Limit c m 1 8 l U . 0 ± 2 . 0 '817.8+1.0 8 l 6 . 3 ± 1 . 3 8 5 3 . 3 ± 2 . 8 Low Temperature Dependence cm" < -0.03 < -0.03 — < - 0 . 0 9 °K High Temperature c m - l _ 0.061|±0.031 -0.135±0.055 -0.l6U±0.045 - 0 . 1 2 5 ± 0 . 0 2 8 Dependence °K "Freeze-in" Temperature °K 7 5 ± 1 0 7 0 ± 5 6 2 ± 5 8 0 ± 5 I r r e g u l a r i t i e s i n Frequency s h i f t s °K H8-58 Vf-57 56-72 ro H 2h2 I 8 O - 1 150 - X. o 0) >_ D -t— 2 cu a E l O O - O - z,(D20) B H B B° A B a A A A a • a A B ' " * 2410 2 4 2 0 2 4 3 0 Frequency c m - 1 2 4 4 0 Fig. 5.10 The temperature dependence of v^DgO) for annealed CH^Br*7.cJD^O. Data from two specimens which had similar sample h i s t o r i e s are given. ice I to determine the details 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 did not always coincide within 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 for both sets of data. For the Sv^CHgO) region considerable error was introduced by atmos- pheric COp absorption and the resu l t i n g instrument imbalance near 2300 cm 1, 2k3 \80-{ W D O ) 1 2 o CD =5 100H o C D a o o o, o o o 0 o ° • • o o o 2 3 1 0 O o o I 1 1 1 — 2 0 3 0 4 0 2 3 5 0 -1 6 0 Frequency cm Fig. 5.11 The temperature dependence of v (D 0) for annealed CH3Br-T.6TD20. Data from the same two experiments as i n Fig. 5.10 are shown. The best study of 3VRCH"201 w a s m a ( i e for a thick sample of Br2*8.6H20. The frequency-temperature dependence was d i s t i n c t l y negative. Samples of Gl2*7.67H 20 on Csl support windows gave anomalous behaviour after annealing to 190 ± 5°K. The stretching band s p l i t into two peaks and three shoulders, Fig. 5•^Cc1. A sharp weak band and a very, very weak shoulder appeared on top of the general, broad V 2 absorption:' A peak at 1 6 2 8 cm - 1 and a shoulder near 1 6 2 0 cm"1. Samples of Cl27.67-H20 on AgCl support windows di'd not exhibit such behaviour. 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 halide annealed clathrate mixtures. v V l Low Temperature Low Temperature High Temperature Freeze-in Limit Dependence Dependence Temperature H2° cm"1 ' cm-1/°K * cm_1/°K (D 20) v + v 3331±5 (sh) <0.06 0.17±0.05 82±10 (2l+40±5) (0.06±0.O3) (0.lU±0'.06) ( 9 3 ± 1 5 ) 3K 3208±3 (vs) <0.06 0 . 1 9 ± 0 . 0 5 8l ± 1 5 J (2 l+l6±2) ( 0 . 0 5 ± 0 . 0 3 ) (0. .12±0.0U) (88±10) 312T±5 (sh) <0 .15 0.24±0.05 85±20 ( 2 3 l 6±2) (<0 . 0 8 ) ( 0 . 2 U ± 0 . 0 5 ) (86±10) v 0 / 2 v „ 1 5 8 8 ± 6 (m) <0.2 0 . 3 6 ± 0 . 1 5 8 0 ± 1 5 c. K R R 896±5 (6T7±3) 831±5 ( 6 U 6 ± 3 ) (sh) (s) -0.07±0.01 (<0.03) -0.05 ±0.01 (<-0.02) - 0 . l 8 ± 0 . 0 5 ( - 0 . 1 5 ± 0 . 0 7 ) - 0 . l 4 ± 0 . 0 6 ( - 0 . 1 5 ± 0 . 0 7 ) 8 3 ± 1 5 ( 8 0 ± 1 0 ) 8 5 ± 1 7 ( 9 0 ± 1 0 ) ro -p- p- Table-V,XII The frequencies at. 80°K-and the hi^ and of Br 2-8.6H 20 on Csl.' *h temperature dependences of C l 2 ' •T.67H20 on AgCl and Csl Host La t t i c e H20 Guest Species Clg c i 2 c i 2 B r 2 B r 2 Sample Support Window Csl Csl AgCl AgCl Csl Frequency at 80°K from Extrapolated Linear Dependence cm - 1 + V T 3368 3365 3338 3333 3332 1 V-5 3218 3215 3221 3222 3216 3 311+5 3119 311+7 31 vr 311+7 3 vR vo 2220±10 — 2225 2226 2211+ l628±2 162U±5 1609 1622 1579 d (1619) V VR 891+ 895 886 887 898 839 83U 8Ul 8̂ 2 831 Frequency V l + V T - 0 . 1 2 - 0 . 2 0 0.32 0.26 0 , . 2 8 J . 1 0 . 1 3 0 . 1 2 0.22 0.16 0 , .17 Dependence on 0.19 0.21+ 0.18 0 , . 2 1 - 1 — — -0.18 - 0 . 1 2 - 0 . .01+ Temperature q-z— -0.06 <±o.o6 0.1+6 0.19 0 , .1+0 4' VR - 0 . 0 9 -0.18 - 0 . 1 0 - 0 . 2 0 - 0 , .05 - 0 . 1 7 -0.15 - 0 . 2 0 -0.16 - 0 , . 1 3 -p- V71 2h6 t i o n attributed'to. C^i + v T l was a.peak near 336.5 cm*" for C12"7.67H20 on Csl. That was about 30 cm higher than the shoulder observed i n other samples and for C12,7.67H20 on AgCl. Also, the frequency-temperature dependence of (v^ + v ^ l (JH^Ol from samples of C l g ^ ^ H ^ O on Csl was nega- t i v e . In other samples Cv-j_ + vij>l (K^Ol had a positive temperature depen- dence. The'H"20' features from Cl2•7•67H2O on Csl and AgCl windows at'83°K were: Csl Window AgCl Window 3H12 Csh) cm ^ 3368 (s) 3 3 3 8 Csh) cm' 3285 Csh) — 3218 Cvs) 3221 Cvs) 31U5 (sh) . 31U? (sh) 2 2 2 0 (w) 2225 (w) . 1 8 8 3 (w) — 1628 (sharp, weak) — c.a. 1600 (broad, m.) 1 6 0 9 (broad, " 8 9 ^ (sh) 886 (sh) 839 (m) 8U1 (m) The sharp peak at 1628 cm from the Csl window experiment exhibited no temperature dependence. CHAPTER SIX DISCUSSION OF THE CLATHRATE MIXTURES 6.1 The Clathrate Mixture Vitreous-Crystalline Phase Transformation A. General Discussion The nature of the samples formed by rapid condensation of clathrate mixtures was probably much the same as for vitreous ice I. Thus much of the discussion on annealing ice I applies here also, jL_.e_. the onset of c r y s t a l l i z a t i o n , the effects on the i r spectra and the processes involved i n reorientation. As before the H20 l a t t i c e modes shifted to higher frequency and the molecular modes shifted to lower frequency. The H20 bands sharpened and had better defined features after annealing. The transformation temper- ature range began at 115 - 5°K (uncorrected for source beam heating) and took about 18 minutes at 125°K. However, the range for the clathrate mix- tures seemed to be extended to higher temperatures by about 10°K. The vitreous samples shifted i r r e v e r s i b l y below 150°K and reversibly once warmed above 150°K. I t was not clear that annealing vitreous clathrate mixtures o o produced the desired cubic 12 A or 17 A unit c e l l structures. We suspect that not a clathrate structure, but cubic ice I was probably formed. The longer t r a n s i t i o n temperature range suggested the vitreous clathrate mix- tures were more stable than the vitreous H20 or D20 ice samples. While the mechanism for H20 or D20 frequency s h i f t was the same as in ice 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 ice I) there should be a fundamental difference for the i r spectra of clathrate-hydrates. X-ray crystallography had shown that the a l k y l halide 2kQ and halogen clathrates had varying cage sizes and varying 0*-'-0 distances (Table 0 . 2 ) . Peak positions of annealed clathrate samples should have varied regularly as a function of unit c e l l size. The annealing results did not support t h i s concept, but results on H 20 and D 2 O were subject to large errors. HDO results were better and are discussed i n section 6.3A. B. Annealing Cl 2-7.6TH 20 on Csl • Samples of C 1 2 * 7 . 6 7 H 2 0 which were deposited on Csl and annealed to 190 or 200°K for 10 to 15 minutes gave unique H 20 spectra (Figs. 5-^(c) and 5.5), while the same samples annealed to only 180 ± 3°K gave t y p i c a l H 20 spectra (Fig. 5-5) • As w e l l , the spectra from samples of C1 2*7-67H20 annealed on AgCl windows to 190 or 200°K for long times were t y p i c a l of i c e , as were the spectra of C H 3 C I , CH^Br, C H C I 3 and C 2 H^Br clathrate mixtures annealed on Csl at 195°K for more than 10 minutes. The C l 2 ' 7 . 6 7 H 2 0 on Csl samples had f i v e stretching band features (three shoulders at 3^12, 3285 and 31^5 cm""1" and two peaks at 3368 and 3218 cm ^) compared to three features i n ice I and other annealed clathrate mixtures (two shoulders at 3338 and 31^7 cm 1 and a peak at 3221 cm 1 for Cl2"7.67H20 on AgCl). As w e l l there appeared a weak, sharp peak and an adjacent shoulder (1628 and l607 cm"1) on top of the broad v^H^O) absorption. The weak peak and shoulder frequencies were independent of temperature. Other absorption features which arose were a peak at 1883 cm • -1 -1 a d i s t i n c t shoulder at 1100 cm and pronounced absorption between 2300 cm and 3000 cm - 1 (Fig. 5-^Cc)). The l a s t effect may have been due to increased scattering 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 to a Christiansen f i l t e r effect. Me eke et a l . (103) observed four well defined bands i n t h e i r "ice 1^" spectra on NaCl windows (Table VI.I). However, Schiffer (.104) studied a number of dihydrated sodium halides and showed that Mecke's " i c e " was NaCl-2H20. The data of Table VI.I suggest that the C1 2'7.67H 20 condensed and annealed on Csl may have formed a hydrated cesium halide layer on the substrate, i_.e_. CsI'xH 20, CsCl-xH 20 or CsICl 2'xH 20. The presence of hydrated cesium halide substrate was supported by the appearance of the sharp, weak peak at 1628 cm" and a shoulder at 1 6 0 7 cm 1 i n the spectra of C12'7.6"7H20 on C s l . These were sim i l a r to peaks observed by Mecke et_ a l . (103) and Schiffer (.104) , Table VI.I. That substrate hydration did not occur for C1 2"7.67H 20 on AgCl nor for C H 3 C I , CH^Br, CH-^I, C H C I 3 and C2H^Br clathrate mixtures i s not sur- p r i s i n g . For AgCl and C1 2'7.67H 20 i t i s probable that the C l 2 does not oxidize AgCl, whereas i t may oxidize C s l . As w e l l , AgCl i s chemically more resistant to hydration. It i s possible that C l 2 reacted with Csl to form CsCl and IC1 or else C s I C l 2 . Intermediate steps may have allowed the formation of hydrated halide s a l t s . Although hydrates of CsCl, Csl 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 ice I and hydrated salt absorptions one might expect 10% or more of the H20 i n the o r i g i n a l sample to be attached as water of hydration. Thus the formation of several hun- dred monolayers of C s I C l 2 i s u n l i k e l y since IC1 2 i s too long to f i t 250 Table VI.I The i r absorptions due to RgO stretches i n dihydrated s a l t s , "Mecke's i c e " , and annealed C l 0 " 7 . 6 7 K 2 0 on C s l ( a l l at 83 i 3°K. C1 2*7.67H 20 on C s l Ice on N a C l ( a ) NaCl•2R 20 (b) NaBr•2H2O Cb) , NaI-2H20 Cb) CaSOi,-2H20 Cc) -1 -1 cm cm • 31*12 (sh) 3 5 5 5 (m) 3 5 3 8 (s) 3 5 3 9 (s) 3568 (sh) 3 5 ^ 9 (vs) 3 3 6 8 (ms) 3^71 (s) 3U68 (vs) 31+69 (vs) 3 5 0 6 (s) 31+96 (s) 3 2 8 5 (sh) 3^07 (s) 31+05 (vs) 3I+06 (vs) 31+61 (s) 31+01+ (vs) 3 2 1 8 (s) 321+5 (w) 3310 (ww) 3 3 6 0 (sh) 31+37 (sh) 321+2 (m) 311+5 (sh) 3 2 6 5 (mw) 31+21 (vs) 321+2 (mw) 1 6 2 8 (vw) 161+5 (m) ' 161+3 (s) 1 6 3 5 (s) 1 6 2 6 (sh) 1607 (sh) I 6 l 6 (m) 1 6 1 5 (s) 16H+ (s) I 6 l 3 (s) (a) Ref. 103 (b) Ref. 101+ (c) Ref. 1 2 7 into a n .interior I - l a t t i c e s i t e : I t may however occupy an I - surface l a t t i c e s i t e . As well i t seems u n l i k e l y that a s o l i d - s o l i d reaction would lead to deep penetration of C l 2 or C l ~ into Csl since Harrison et a l . ( 1 2 8 ) found some a l k a l i halide single c r y s t a l s were'very r e s i s t i v e to exchange with C l 2 even at room temperature. The o r i g i n of the new absorption at 1 8 8 3 cm 1 i s not known. I t l i e s w e l l above the calculated v^HgO) pos i t i o n of Hornig ejfc_ al_. ( 1 0 5 ) , 1 7 8 0 cm - 1. I t may be due to Cv 2 + v T) for the hydrated s a l t v 2 ( H 2 0 ) and the H 20 l a t t i c e 2 5 1 C. Oligomeric K2Q Absorptions A l l the'"unannealed clathrate mixtures exhibited very weak peaks or shoulders i n the region 3 5 0 0 - 3 7 0 0 cm"1, Table V I . I I . Similar absorptions were found for H 20 and D 20 ice I v and the clathrate mixture peaks were also assigned to oligomeric H 20 and D 20 units. As was shown for CH^Br•7•67H 20 (Table V.IIl ) i n three different specimens the positions, i n t e n s i t y and number of oligomeric features were dependent on the rate of sample deposi- t i o n . The 3690 cm 1 peak was obtained from a CH^Br•7•67H20 sample deposited i n 11 minutes, while the 3620 cm 1 peak was obtained from a sample deposited i n 1.5 minutes and the peaks at 36h5 and 3605 cm - 1 were obtained from samples deposited i n 4.5 minutes. Fast deposition produced more l o c a l i z e d heating and H 20 polymerization than slow deposition. Van Thiel et_ al_. (117) suggested monomeric, dimeric and trimeric H 20 absorbed at (.3725 and 3 6 2 5 ) , ( 3 6 9 1 and 35^+6), and ( 3 5 1 0 and 3 3 5 5 ) cm 1 respectively. On that basis we appear to have formed residual dimeric H 20 i n the unannealed clathrate mixtures. The presence of oligomeric H 20 and D 20 suggests a low mobility of molecules during condensation. However, low mobility of guest molecules does not necessarily follow. F i n a l l y , i t may be possible to follow the rate of c r y s t a l l i z a t i o n i n ice I and clathrate mixtures by following the peak heights of oligomeric H 20. D. Unannealed Sample Guest Absorptions Guest absorptions i n unannealed clathrate mixtures due to alkylhalides were observed for a l l specimens. During annealing the general experience was Table VI.II The weak peaks and shoulders attributed to oligomeric and D20 vj_ and V3 stretching modes i n some clathrate mixtures and i n some inert matricies. M C H 3 C I CH3Br C H 3 I C H C 1 3 C 2H 5Br C l 2 B r 2 Ar(a) Kr(a) N 2(a) CCll^a) Moles M 1 1 1 1 1 1 1 300 380 21+0 1000 Moles R 7.67 7.67 17 17 17 7.67 8.6 1 1 1 1 R i s H 20 -1 cm 3 6 9 0 * 3687 3689 3690 3691 3708 3700 3725 365h 3683 361+5 3 6 2 0 X 3605 3668 361+8 3625 3 5 8 0 3 6 3 9 361+3 3565 3670 3617 3612 3699 3631+ 3574 3687 3570 3686 363k Moles M 1 1 1 210 210 21+0 1000 Moles R 7.67 7.67 17 1 1 1 1 R i s D 20 26U8 261+1+ 26U7 2 6 2 6 2637 2635 2622 2615 26ll+ 2635 2632 2625 2611+ 2610 2655 2650 2639 2617 26ll+ 261+3 (a) Ref. 115 * Very slow deposit X fast 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 after recooling the samples to 83 - 3°K. The peak heights of bands i n d i f f e r e n t clathrate types decreased at d i f f e r e n t rates, while the peak heights of several speci- mens of one clathrate mixture (i.e_. CH^Br • 7.67^0) decreased at about the same rate. As one might expect the drop i n guest peak heights began at the same temperature as the oligomeric Ĥ 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 V I . I I I . For unannealed clathrate mixtures of CH3C1, CHCl^ and C ^ B r a l l strong and medium in t e n s i t y absorptions of the pure s o l i d were observed. In contrast, for CH^Br and CH^I unannealed clathrate mixtures, only some of the pure s o l i d absorptions were observed. Strong unannealed clathrate guest absorptions expected near 3050, 1420, 895 or 964, and 596 cm 1 were unob- served. Also i n the CH^Br *7.67^0 sample, peaks were observed i n the clathrate (1218, 1200, and 750 cm 1) which were unobserved i n the pure s o l i d . The clathrate guest peaks were shifted 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 multiplets of peaks the clathrate peaks were s i n g l e t s . We can o f f e r no explanation for the missing CH I and CH Br peaks nor 3 J for the extra CH^Br peaks. The loss of guest band s p l i t t i n g between the pure s o l i d and clathrate 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 vitreous mixtures. There are at least three explanations of the loss of the clathrate 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 A l k y l halide i r absorptions i n the pure s o l i d state and i n some unannealed clathrate mixtures at 83 ± 3°K. C H 3 C I . CH3Br C H 3 I C H C I 3 C 2H 5Br Unann. Unann. Unann. Unann. Unann. Clath. solid(a) Clath. Solid(a) Clath. Solid(b) Clath. Solid(c) Clath. Solid(a) _ cm 3020 sh 3036 m 3035 m 3016 sh 3012 2985 vw 2984 m 2 9 5 7 m 2 9 5 0 Ikkk lkk3 w sh s 2965 sh 295H 2 8 4 6 2 8 3 0 s m m 2936 2915 WW WW 2935 2803 1436 1426 s m m ms 2 9 6 3 w 2 9 2 1 m 2859 v 1459 w lkk8 sh lkk6 m lkk3 m lkkl sh 1432 vs 1420 s lkkO m 1437 sh 1U36 m 1U17 vs 1401 1 3 9 6 ms s 1433 sh 1 3 7 6 m 13^7 W 13^5 m 1 2 9 3 sh 1244 sh 12 kl vs 1238 WW 1235 1 3 7 1 m 1338 vw 1 3 3 6 m 1292 1218 1200 vvw WW sh 1 2 9 1 vs 123k w 1 2 3 6 vs 1214 vw 1 2 2 0 1 2 1 8 1 2 5 4 1242 vw vw 1 2 5 5 m 1242 s 1232 m 1 0 2 1 vw 1 0 2 0 m 962 955 vw vs 895 888 vs vs 752 m 767 748 955 w 960 s 9 6 1 sh 700 s 700 697 692 vs sh s 750 s 589 585 570 sh vs m 663 760 sh 785 w 762 s 735 v (a) This work (b) Ref. 129 (c) Ref. 130 ro -p- 255 the unannealed.mixture formed, on the window.:'.. The excess guest diffused.out . and sublimed o f f the'-window; during annealing, while .the remainder. was, too small to detect. Secondly, a l l of the guest molecules may have diffused out .of the H 2 O l a t t i c e and sublimed o f f the window. Thirdly, the guest molecules may have been present but i r inactive due to some cage effect. 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 perturbations are more l i k e l y to 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 f i r s t explanation also seems u n l i k e l y since H 2 O condenses at a much higher tempera- ture than most of the guests, i f anything the samples may have been d e f i - cient i n guest. The expulsion of a l l guest molecules from the H 20 l a t t i c e seems most probable. , Further work, to be described l a t e r , was done to check which of the above reasons was most probable. One further l o g i c a l method to use (which we did not) i s observing clathrate-hydrates i n Raman spectroscopy. There the H2O bands are sharp, while most a l k y l halide bands are i r and Raman active and thus the bulk samples may be prepared and observed, i n contrast to the t h i n films of our i r technique. 6.2 Guest Species Absorptions I t was suggested i n section 6 . 1 that sample condensation and annealing i n an open c e l l chamber leads to expulsion of the foreign guest molecules from the H 2 0 or D 20 l a t t i c e i n the absence of the equilibrium d i s s o c i a t i o n pres- sure of the clathrate. Two further experiments tested the p o s s i b i l i t i e s of sample frac t i o n a t i o n between the sample deposition tube and the substrate surface, and simple sample di s s o c i a t i o n . 2 5 6 A. Isolated Chamber Condensation Gaseous clathrate mixtures condensed i n an isolated chamber (Fig. 1.2) and unannealed exhibited 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 to H 2 O bands as open chamber samples. Therefore we concluded that the open chamber samples did not fractionate during deposition. The design of the closed chamber c e l l ensured that a l l of the gaseous sample condensed on one window while for 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 to I85 i 5°K and recooled to 83°K, exhibited no guest absorptions: The same behaviour exhibited by open chamber samples. That was contrary to Shurvell's ( 5 7 ) results and probably arose from the differences i n maximum annealing temperature: He annealed only to 1^5 ± 5°K. The annealing process was not followed i n d e t a i l (spectroscopically) for closed chamber samples, but the annealed sample spectra for 83°K appeared the same as those i n section 6.1 and i n ice I. : - The same spectroscopic results were obtained for 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 to the absence of a positive clathrate s t a b i l i z i n g pressure of guest vapour at 185 ± 5°K. 257 B. Low Temperature Mulls The obvious alternative was to form clathrate-hydrate samples i n bulk and observe t h e i r spectra by- low temperature mulling. I t was d i f f i - c ult to grind the samples at 77°K to a very fine powder and considerable scattering was observed from the large p a r t i c l e size.. Whalley C95) obtained much better spectra (of ice) apparently with f i n e r powders. The indices of r e f r a c t i o n of the mulling agents and ice agreed f a i r l y w e l l i n the v i s i b l e region, but the indices change very rapidly over absorption bands and t h i s seems to induce considerable scattering between 1 7 0 0 to 2000'cm-"1" and 2 3 0 0 . to 3000 cm - 1. I t was of course unnecessary to 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 to 83°K at 1 atmosphere of N 2(g). However, no guest absorptions were observed for either the mull of CH 3I-17H 20 or C C 1 3 F - 1 7 H 2 0 . Most of the CH 3I or C C I 3 F guest absorptions should have been observed i n either the C3H8 or CC1F3 mulling agent. Two explanations are possible. F i r s t , during t r a n s f e r a l of sample from the preparation tube to the mortar and pestle the sample was warmed to 2T3°K momentarily and i t may have dissociated. However, the CH 3I and C C 1 3 F clathrates were chosen s p e c i f i c a l l y for 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 clathrates low dis s o c i a t i o n pressures. Secondly, the CH 3I and C C I 3 F molecules may have been very soluble i n l i q u i d C3H8 and l i q u i d CCIF^ even at low temperature. However, the clathrate samples were not observed to dissolve i n the'mulling agents. I f the guests did dissolve i n the mulling agent then they should s t i l l have been observed i n the spectra as a s o l i d solution. 258 We could not establish with, confidence that the clathrate samples had not decomposed during preparation of the mull. The samples may have dissociated either during trans-fer to the pestle or during evacuation of the cryostat (.with the sample temperature between 100. and 150°K) . No attempts were made to analyze the small quantities of vapour evolved after warm-up of the c e l l to 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: Scattering distorted the bands considerably. One difference did occur, however, the v 2 absorption was well defined at 1 5 7 0 cm-"1" at 83°K. In most spectra the region from 1 6 0 0 to 3000 cm 1 was just one broad band which steadily increased i n intensity. C. Summary Infrared observations by Hexter and Goldfarb ( 5 3 ) on H C 1 , H2S, C 0 2 and S 0 2 clathrated i n hydroquinone demonstrated that for weakly absorbing guests the guest absorption was unobserved i n the clathrate, but strong absorbers l i k e C 0 2 and S 0 2 were easily observed. They pointed out that i n the amount of HCl-quinone clathrate used for the i r observations, only about 5% of the HC1 needed for a reasonable HCl(g) spectrum was present. Davies and Child ( 5 5 ) also observed i r absorption by guests i n quinone clathrates. They suggested that the s h i f t s i n guest frequencies were no larger than for solutions of guests i n CCl^. Their conclusion was that the cage had pertur- bing influences no larger 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 inactive. 259 We concluded that for unannealed clathrate mixtures, since there was no fine structure associated with the guest absorptions, guest rotation and translation was hindered. I f the binding i n the unannealed samples was not physical, but chemical, then we expected new guest functional group frequen- cies. The evidence indicates our methods were i n s u f f i c i e n t to form clathrate- 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 results from annealed clathrate-hydrate mixtures collapses to a discussion of cubic ice I: We assume the guest was a l l d i s - persed and a cubic ice I l a t t i c e formed at 185 ± 5°K. The clathrate studies became independent checks of the r e p r o d u c i b i l i t y of cubic ice I experiments. Consider the v^(HDO) frequencies from CH^Cl, CH^Br and C ^ I mixtures with D20 (h.00% HDO). Except for one set of CH3Br r e s u l t s , the clathrate- mixture low temperature l i m i t s , low temperature dependences, high tempera- ture, dependences, "freeze-in" temperatures and i r r e g u l a r i t i e s i n frequency- temperature s h i f t s agreed, within error, with HDO cubic ice I data. Clathrate mixture M ^ C H D O ) frequency l i m i t , temperature dependences, "freeze- i n " temperatures, etc. , agreed, within error, with v^(HDO) of cubic ice I. Half-height width data from clathrate-mixtures did not agree with J. L cubic ice I HDO data. Both Av~,2r and Av„Z from clathrates were at least Oil OD 25 percent larger than i n cubic ice I. Contrary to cubic ice I , AvnT. was 260 30. percent larger than AvJ^.. One can understand the increased AvA oyer UH Oh. cubic ice I on the basis of further'H^O exchange into the'D^OCH/pO) mixture as the sample aged, i n spite of precautions. One cannot r a t i o n a l i z e increased Av Qp i n that way. Notice that i f a true clathrate had been formed from the CH^Br mix- ture, for 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 clathrate (CH^Br•7.67H 20 id e a l stoichiometry) with a 1 2 . 0 9 A c e l l parameter o (Table 0.2) then the average 0 0 distance must be 2.809 A at 273°K. For ° -1 R(0 0) = 2.755 A i n cubic ice I we found v (HDO) = 3 2 9 0 cm (Fig. 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 10U cm - 1. Thus CH3Br'7.67D20(H20) clathrate should have had v^TT(HD0) absorbing near 3 3 9 ^ cm 1 ( 2 7 3 ° K ) . Assuming the same frequency-OH temperature dependence as i n ice then at 83°K v (HDO) should have absorbed at 3 3 9 ^ cm - 1 - 190°K (0.200 cm_1/°K) = 3356 cm"1. The absence of such absorption also supported the conclusion that clathrates did not form. The same principles could be applied to CH 3I-17D 20(HD0) and CH3Br•7.67H2O(HDO) mixtures. The d i s t r i b u t i o n of 0*---0 distances i s much greater i n clathrates than i n ice I due to four unique distances, each of which must have an i c e - l i k e d i s t r i b u t i o n . One would expect considerably broader HDO bands i n clathrates. Librations of HDO i n clathrate mixtures and cubic ice I also agreed within error with respect to high temperature frequency dependence, "freeze- i n " temperature and frequency s h i f t i r r e g u l a r i t i e s . The low temperature l i m i t s did not agree within our stated errors. The disagreement was not 2 6 l s u f f i c i e n t to suggest clathrate had formed, i_.e_. increased R(0**"'0) i n clathrates suggested a s h i f t o f ' ( 1 5 - 2 0 ) cm 1 from cubic ice 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 increasing tem- perature were discontinuous s h i f t s by 2 - 3 cm 1 , generally to higher f r e - quency i n the case of stretches and to lower frequency i n the case of l i b r a t i o n s . Another break i n the curves appeared near 80°K. These breaks may have been related to p a r t i a l ordering, as was suggested before. B. H2O and D 20 i n Clathrate Mixtures Discussion of H 20 and D 20 absorptions i n annealed clathrate-hydrate mixtures also reduces to a discussion of cubic ice I. The behaviour of H 20 and D 20 clathrate mixture absorption frequencies, half-height widths and temperature dependences were the same as i n cubic ice I. I f true clathrate hydrates had formed.on annealing then low tempera- ture l i m i t s and half-height widths should have been s i g n i f i c a n t l y d ifferent from i c e : They were not. The low temperature l i m i t s of each i n d i v i d u a l H 20 or D 20 absorption agreed within error, Table V.XI, for the set of clathrate mixture data. The average for each band, over a l l clathrate mixtures, agreed with the observed H 20 and D 20 ice I data. The only ex- ceptions were for + v T ( D 2 0 ) , vp'(D 20) and v R ( D 2 0 ) . 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 to define consistently. High temperature frequency.depen- dences for each clathrate-mixture band agreed within error, Table V.XI, over 262 the set of clathrate mixtures. The "freeze-in" temperature data were also compatible. There were two special points to consider, the negative temperature dependence of + v^, from CI^'7.67R2O on Csl and zero temperature dependence of the weak 1 6 2 8 cm 1 (CsI^R^O ?) band. Negative temperature dependence was c h a r a c t e r i s t i c of l a t t i c e modes. Since such an intense l a t t i c e overtone was u n l i k e l y , the 3 3 6 8 cm band may have been a combination of with an overtone of a low frequency l a t t i c e " mode (say 2 v T ' ) . The s h i f t of + v T to higher frequency by 30 cm 1 was understood i n terms of the smaller overlap with than i n ice I. I n s e n s i t i v i t y of the weak, sharp 1 6 2 8 cm - 1 absorption to temperature i s c h a r a c t e r i s t i c of non-hydrogen-bonded-lattice IL^O: That supports i t s assignment to of,say, CsT^^O. Results of section 5.3 on H2O and D2O i n annealed clathrate mixtures d i f f e r e d from those of McCourt ( 5 6 ) and Shurvell ( 5 7 ) . We f a i l e d to detect t h e i r additional 3 V R absorption near 2^00 cm \ However, we experienced problems from instrument imbalance through atmospheric C 0 2 between 2 2 8 0 and' 2 3 6 0 cm As w e l l , attempts to duplicate t h e i r ( 5 6 , 5 7 ) SO2 results f a i l e d . McCourt's samples do not appear to have been annealed, as suggested by the shape and positions of the H2O absorptions. Inspection of McCourt's ( 5 6 ) and Shurvell's ( 5 7 ) o r i g i n a l background spectra revealed s l i g h t , 0.02 abs. u n i t s , negative CO2 absorptions from 2 2 8 0 to 2360' cm For thick samples, requiring extensive reference beam attenuation and very small instrument source s i g n a l s , the negative CO2 absorption would be proportionaly greater and could give the appearance of 2 ( 3 V R ) bands instead of one. The posi t i o n of the minimum between t h e i r 2 ( 3 V R ) peaks corresponds closely to the CO2 (gas) maximum. There was also evidence of oligomeric H2O 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 ices suggests that si m i l a r spectra should be expected for the clathrates. CHAPTER SEVEN SUMMARY 7.1 Suggestions for Further Work Extensions and new applications of t h i s work are proposed under three headings: further work i n the H2O-HDO-D2O ice systems, applications of isotopic substitution to other chemical systems, and further work on clathrate-hydrates. A. Clathrate Mixtures We recommend observation of bulk clathrate-hydrate samples i n glass preparation tubes by laser Raman spectroscopy. Shifts of peak frequency, half-height width and intensity as a function of temperature should be easily followed. I t i s important to choose guest species which are strong Raman scatterers and whose frequencies are widely separated from the H 2 O frequencies. In that case the guest frequencies would be perturbed the least by coupling to the H 20 l a t t i c e . As an extension of the effect of the l a t t i c e , one could study clathrates whose guests frequencies are close to H 20 frequencies and would be expected to couple (to ^ ( ^ 0 ) say, which i s weak i n the Raman e f f e c t ) . One could also study the perturbing effect of the l a t t i c e on the guest by observing the D 2 O clathrate analogues. 265 F i n a l l y , careful technique should permit one to grow clathrate- hydrate single crystals i n glass tubes, simultaneously allowing one to confirm the clathrate structure by x-ray crystallography and to observe polarized Raman spectra. We also recommend further attempts to observe low temperature mulls of clathrate-hydrates whose structures are confirmed by x-ray powder d i f f r a c t i o n . 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 to follow the annealing or vitreous-cubic ice I transformation i n d e t a i l . 2. Determine the rates of transformation at various constant temperatures by following the s h i f t s i n HDO frequencies as a function of time. 3. Study v 2 and Av 2 i n d e t a i l for l i q u i d helium and l i q u i d nitrogen experiments to resolve the v 2 - 2 vp dilemma. h. Check cubic ice I cooling and warming curves for hysteresis under slow and fast cooling ( 0 . 5 - 20 hours). 5. Investigate hydration of sample windows by Cl 2,and H 20. Some other projects related to th i s work are included below. 2 6 6 1. Carefully check the properties of cubic ice I i n the temperature range ko - 70°K by Raman scattering, infrared absorption and n.m.r. of HDO i n D 20 considering the s h i f t i n stretching frequency i n that range. 2. Investigate the behaviour of HDO frequencies below 10°K to check the extrapolation of our data. 3. Study HDO absorptions i n the family of high pressure ices as a function of temperature over t h e i r stable ranges. This w i l l permit the extension of hydrogen-bond force constants over a wider range of R(O--'-O) i n similar electronic environments. k. Obtain detailed l i n e a r expansion coefficients of cubic ice I down to lt°K. 5. Study the o r i g i n of as the H 20 t r i p l e point i s approached from the three phases. 6. Use our EDO frequencies, tong and X ̂  to investigate various models of hydrogen-bonding as a function of R(0-**-0) and attempt to relate Av to changes i n the covalent and electro- s t a t i c nature of the hydrogen-bond. 7. Study the anisotropy of hexagonal ice I single-crystals by observing differences i n HDO frequencies and Av/AR (as a function of temperature) along the a D and c Q axes. 8. Determine the proton jump energy by observing at what tem- perature during warm-up a th i n layer of D 20 embedded between thick layers of vitreous H 20 leads to the formation of characteristic HDO peaks. Deposition rates would have to 267 be extremely slow at h.2°K. Heat of sublimation may be too large to permit i s o l a t i o n of a few mono-layers of D20 on H20. C. Other Chemical Systems Several possible applications of the d i l u t e isotopic substitution and temperature v a r i a t i o n technique are l i s t e d below. 1. Study single-crystals of organic acids, whose c r y s t a l structures and l i n e a r expansion coefficients are known, as a function of temperature and relate VQ^CHD O) to R(0*'*"0) to better characterize the hydrogen-bond potential. 2. Study carbohydrates, hydrogen-bonding polymers and long chain molecules to determine the nature and va r i a t i o n of 0-H*••*0 hydrogen bonding. 3. Use d i l u t e isotopic substitution i n b i o l o g i c a l systems generally since the H20 medium masks spectroscopic obser- vations of H20. h. Use d i l u t e HDO and temperature v a r i a t i o n to study the nature of hydrogen bonding i n poly-water. 268 7.2 Conclusions A. Annealing Ice I v Our, infrared result for the transformation temperature range (120 - 135 i 5°K corrected for source beam heating) does not agree completely with the ranges of some other workers (Table 0.3). Our range seems to agree best with that of Dowell and Rinfret (7M and perhaps that of Sugisaki et_ a l . (6). However, these i r results do not support Dowell's ( 7 ^ ) conclusion that only 30% of the vitreous ice I was transformed to cubic ice I. However, the i r results may indicate 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, Av 2 = -56, Av R = +31 and A V I J = +12 cm 1. The transformation temperature range was independent of deposition ra t e , but transformation frequency s h i f t s were not, faster depositions gave smaller s h i f t s . Oligomeric (probably dimeric and trimeric) H20 and D20 were present i n considerable concentration i n amorphous ice I: Slower depositions gave higher concentrations of oligomers. The oligomers were stable units up to 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 vibrators i s i n v a l i d . At least one HDO frequency i s coupled to a parent H20 or D20 frequency. 269 The low temperature l i m i t s of vOTI(HDO) and v._(HDO) were 3263.5 cm 1 On OD and 2 4 1 2 . 0 cm 1 respectively. The low temperature dependences of v and On v Q D were both 0.0^7 cm_1/°K between 10°K and 80°K. The high temperature dependences of v.„ and v O T^ were 0.200 and 0.123u cm~"1"/0K between 80°K and Un OD 200°K. Insofar as u and X ̂  were a measure, the pot e n t i a l of HDO molecules i n H 2 O / D 2 O 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 changes i n to were not li n e a r as temperature increased. On Hot bands and difference bands did not contribute s i g n i f i c a n t l y to the breadth of v and v^(HDO) and, by extension, not to stretches i n H 2 O or D 2 O . Half-height width data supported the or i e n t a t i o n a l l y disordered proton theory of Whalley ( 8 8 ) . The temperature dependences of Av (HDO) and Av (HDO) from 100° - Un OD 200°K were 0.135 and 0.070 cm-1/°K. Within the l i m i t s of the infrared technique, v (HDO) and v (HDO) peak frequencies were sensitive to changes On OD o i n R(0'••'0) greater than 0.0001 A. HDO stretching absorptions were not line a r functions of R(0'**"0) over the whole temperature range 10° - 200°K. 3 -1 0 The low temperature dependences Av/AR and Av/AR were 8.202 x lO-'cm /A OH OD 3 -1 0 and 6.629 x 10 cm /A from 10° - 100°K, while the high temperature depen- 3 -1 0 ^ -1 0 dences Av/AR and Av/AR were 1.921 x 10 cm /A and 1.283 x 10Jcm /A On OD from 150 - 200°K. The calculated low temperature l i m i t of R C 0 , , , , 0 ) for cubic ice I o o was 2.753 A assuming a Q = 6.350 A exactly at l43°K. The calculated changes 6 0 i n R(0 0), with temperature were AR/AT = 8.28 x 10 A/°K from 0° - 80°K -6 0 and 10.52 x 10 A/°K from 130° - 200°K. 270 Bellamy and Owen's ( 3 3 ) formula gave a good approximation to the rel a t i o n between R(0--*-0) and v (HDO) i n the temperature range 130°K On to 200°K with the constant set at 57-77 cm - 1. Anharmonicity correction, X , had a low temperature l i m i t of 1 0 5 . 6 On cm - 1, a low temperature (0 - 60°K) dependence of +0.032 cm-1/°K, a high temperature dependence ( 1 0 0 ° - 200°K) of - 0 . 0 3 8 cm"1/0!^, and a maximum value of 108.7 cm - 1 at 80°K. The HDO harmonic stretching frequency had a low temperature l i m i t at 3^73.7 cm - 1, a temperature dependence (30°K - 200°K) of +0.138 cm_1/°K and a maximum displacement of h cm 1 from l i n e a r i t y at 80°K. Vp''(HD0) had a low temperature l i m i t of 823 cm - 1 and the shoulder (assigned to ( v R , T + Vrp)) had a low temperature l i m i t of 856 cm - 1. Various calculations indicated v R x,. V R v and v R z were degenerate for H2O and D 20 and non-degenerate for HDO. The negative temperature dependence of l a t t i c e modes was understood i n terms of a shallower po t e n t i a l and increasing excited state populations as temperature increased. C. The H20 and.D20 Studies The order of v-j_ and i n the gas and cubic ice I phases was the same: Hydrogen bonding affected v-|_ and of the gas phase equally, s h i f t i n g them down proportionally. We conclude that the molecule-molecule coupling of v-j_ t o v ^ and to V3 were similar i n nature and that i n cubic ice I , \) and were d i s t i n c t t r a n s i t i o n s . The assignments of major H20 and D20 absorptions at 0°K were v-j_ + Vrp = 3 3 3 ^ , = 320U, v-j_ = 3133, 3 v R = 2239, v 2 = 1 5 6 2 , v R + v T = 8 8 1 , v R = 8 3 2 , and v T = 229-2 cm"1 for 271 H 20 and v + v T = 2k6h, v 3 = 2 U l 3 , v = 2320, 3 v R = 1 6 3 7 , v 2 = I I 8 9 , V R + Vrp = 6 6 3 , and v R = 6 3 0 cm 1 for D 20, i n basic agreement with previous authors. The absorption near 1 6 0 0 cm 1 i n R~20 d e f i n i t e l y had a 2 v R under- ly i n g absorption. Temperature dependence of v 3 and v-j_ i n absorptions for H 20 (above 100°K) confirmed the Raman temperature dependence of Val'kov ( 9 9 ) . The data of HDO applied to H 20 and D 20 as w e l l . Blue's ( 8 5 ) formula led to anomalous results when applied to simple H 20 and D 20 molecules i n i c e . Assuming effe c t i v e masses for two attached and two detached protons and also 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 calculated by Blue's method. From the (Hr>0, 3/h,l/k) option we found k(0-H 0) = 0.60 x 1 0 5 dynes/cm and k ' ( 0 H-0) = 0.21 x 1 0 5 H dynes/cm. These force constants predicted nearly degenerate D 20 l i b r a t i o n s ( 5 8 6 , 588 and 591 cm - 1) about 6% below the observed value. The effect i v e mass concept did not apply w e l l to HDO. An H 2 0 3 model of ice gave a set of H 20 i n t e r n a l and l a t t i c e force constants i n good agreement with those deduced by Trevino ( 9 3 ) and poorer agreement with Pimentel's results ( 9 7 ) . That k ^ ( v 0 ) ( 0 . 6 6 x 1 0 ^ dynes/cm) Cj)<j> d was smaller than the gas phase value was consistent with the lower ice frequency. 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