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Vibrations of ice I and some clathrate-hydrates below 200°K Hardin, Arvid Holger 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 British Columbia, 1963 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of Chemistry We accept this thesis as conforming to the required, standard THE UNIVERSITY OF BRITISH COLUMBIA July, 1970 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and Study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thes,is for financial gain shall not be allowed without my written permission. The University of British Columbia Vancouver. 8, Canada Date ABSTRACT The vibrations of H2O, HDO and D20 molecules participating in the hydrogen bonding of vitreous and crystalline solids, and some alkyl halides and halogens encaged in these solids, were studied by infrared spectroscopy between h.2 and 200°K over the iiOOO to l60 cm-"1" frequency range. Four kinds of 0-H*,,-0 hydrogen bonding lattices 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 lattice vibrations were observed in detail 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 well, the effects on the molecular and : lattice vibrations of H20, D20, H20 (5-9W HDO), and D20 (h.00% HDO) cubic ices I were studied during warming from h.2 to 200°K. Similar studies were made for the vibrations of H20, HDO, D20 and guest molecules, during the vitreous-crystalline phase transformation of seven clathrate-hydrate mixtures and during warming of the resulting \ annealed mixtures. For ice I the method involved condensation of the vapour at 77°K, observation of the spectra during warming in 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 translation. As well four models for molecular libration were investigated. Three approaches were taken to the clathrate-hydrate problem. In parallel 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 in an isolated sample chamber, to prevent sample fractionation, and treated as before. Finally, low temperature mulls of solid 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 all hydrogen bonded H2O molecular modes shifted to lower frequency and all lattice modes shifted to higher frequency. The half-height widths of the composite H2O band (v2/2vp) appeared to increase upon annealing and to decrease upon warming while the (VR, VR + vp) and (vl, V3, vi + vrp) bands had the opposite behaviour. This was interpreted, as indicating a weak 2v^ band underlying the stronger \>£ absorption near 1600 cm-1. The frequency-temperature dependences of all cubic ice I bands were interpreted on a bilinear, high and low temperature basis (the lattice modes shifted to lower frequency and the molecular modes to higher frequency with increasing temperature). For HDO above 86°K Av /AT 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 in both modes. An explanation is 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 /AR(O 0) as 1921 cm /A and Av /AR as 128l cm /A above 150°K and iv -1 ° -1 ° as 8202 cm /A and 6629 cm /A below 100°K. As well, 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 in the temper ature range 125 - 5 to 1U5 + 5°K and required less than l8 minutes at 135°K as for ice I. Similarly, 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 ii Table of Contents v List of Tables x List of Figures xi Acknowledgements xiv INTRODUCTION 1 Hydrogen BondingA. Theories of Hydrogen Bonding 2 B. Spectroscopic Manifestations of Hydrogen Bonding ... 6 Clathrate-Hydrates 12 A. The Clathrate-Hydrate Problem 1B. 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 2B. Non-Spectroscopic Investigations of Ice 20 C. Spectroscopic Investigations of Ice 27 D. The Present Approach to the Ice Problem 3CHAPTER 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 Cell 1+2 1.5 The Duerig-Mador Liquid Helium Cell 1+5 1.6 The Metal Liquid Nitrogen Cell *+vi 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 Solid Samples ^9 B. Preparation of Stoichiometric Gaseous Mixtures ... 50 2. h Preparation of Infrared Specimens 52 A. Low Temperature Mulling 5B. Isolated Chamber Condensation 53 C. Open Chamber Condensation 5*+ 2.5 Devitrification 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 5B. Results of Devitrification 59 3.2 Temperature Dependence of Cubic Ice I Absorptions. .... 69 A. Temperature Dependence of HDO Absorptions 69 B. Temperature Dependence of H20 and D20 Absorptions. .. 79 3.3 The H20, D20 and HDO Ice I Absorptions at 83°K 95 A. Experimental 9B. Results at 83°K 5 3. U Summary of Ice I Results 101 A. Vitreous-Cubic Ice I Transformation 101 B. . HDO in Cubic Ice I . . 102 C. H20 and D20 in Cubic Ice I 10vii 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 Ill D. Combination and Overtone Mode Transformation .... 117 . E. Confidence in the Cubic Ice I Samples 118 h.2 Temperature Dependence of Cubic Ice I Absorptions. . . . 120 A. Dependence of HDO Bands on Temperature 121 B. Dependence of H2O and D20 Bands on Temperature . . . 159 it. 3 Assignments of the Cubic Ice I Absorption Bands 175 A. The Fundamental Lattice Modes 17B. The Fundamental Molecular Modes 7 C. The Overtone and Combination Modes 186 it.U The L'ibration of HDO, H20 and D20 187 A. The Moments-of-Intertia Models 18B. The H203 Model of Ice ; 198 C. A Summary of H2O, HDO and D2O Librations 211 CHAPTER FIVE: CLATHRATE-HYDRATE EXPERIMENTAL DETAILS AND RESULTS 2lh 5.1 The Vitreous-Crystalline Clathrate-Mixture Phase Transformation 2lh A. ExperimentalB. Results of Devitrification 2l6 5.2 ClathrateMixture Guest Absorptions, 228 A. Condensation in an Open Chamber 229 B. Condensation in an Isolated Chamber 233 C. Low Temperature Mulls 235.3 Temperature Dependence of the Crystalline Clathrate Mixture Absorptions 23^ A. Temperature Dependence of the EDO Absorptions. . . . 23** B. Temperature Dependence of the H2O and D2O Absorptions 239 viii PAGE CHAPTER SIX: DISCUSSION OF THE CLATHRATE MIXTURES 2*+7 6:1 The Clathrate Mixture Vitreous-Crystalline Phase Transformation 2*+A. General Discussion 2^7 B. Annealing C12'7.67H20 on Csl 21*8 C. Oligomeric H20 Absorptions 251 D. Unannealed Sample Guest Absorptions 256.2 Guest Species Absorptions 255 A. Isolated Chamber Condensation 256 B. Low Temperature Mulls 257 C. Summary 258 6.3 The Temperature Dependences of Crystalline Clathrate Mixture Absorptions 259 A. HDO in Clathrate Mixtures 25B. H20 and D20 in Clathrate Mixtures 26l 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 IT 26B. HDO Studies 26C. The H20 and D20 Studies 270 D. Clathrate Mixture Annealing 272 REFERENCES ..... 273 LIST OF TABLES TABLE PAGE 0.1 Typical clathrate-hydrates and their properties lU 0.2 Clathrate-hydrate unit cell dimensions, guest sizes and filled cavities l6 0.3 Stable temperature ranges of vitreous, cubic and hexagonal ice I 23 O.k Some physical properties of the ices 25 0.5 H20 vapour, liquid and ice I frequencies and assignments . 29 III.I Cubic and vitreous ice I frequencies at 82°K 62 III.II Vitreous ice I oligomeric absorptions 65 III.Ill H20 composite band half-height widths 8 III.IV The behaviour of HDO stretching modes in cubic ice I . . . 72 III.V The behaviour of HDO librational modes in cubic ice I. . . 7*+ III.VI HDO stretching modes half-height widths 76 III.VII HDO stretching modes peak heights 77 III.VIII Ice I sample histories 80 III.IX Cubic ice I H20 and D20 absorptions 83 III.X Cubic ice I vT(H20) absorptions 91 III.XI (a) Fresent and previous H20 assignments for cubic ice I . 96 (b) Present and previous frequencies for vT(H20) 97 III.XII Present and previous HDO frequencies for cubic ice I . . . 98 III. XIII Present and previous D20 assignments for cubic ice I . . . 99 IV. I Calculated and observed RMS amplitudes of translation for H20 and D2O 1^9 IV.II H20, HDO and D20 moments-of-inertia 190 IV.Ill Symmetric G-matrix elements for H2O3 201 X TABLE PAGE IV. IV HgCg and D203 force constants for ice 1 208 V. I The clathrate-mixture sample histories 215 V.II RV,0 frequencies in unannealed and annealed CH-^Cl• 7• 67H20 . 221 V.III Oligomeric frequencies at 83°K in unannealed clathrate-mixtures 223 V.IV. Temperature dependences of oligomeric frequencies in unannealed clathrate mixtures 22k V.V The stable temperature ranges of the oligomer peaks. . . . 225 V.VI The alkyl halide guest absorptions in 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 librations 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 Cl2'7.67H20 and Br2-8.6H20 on Csl and AgCl. ... 2^5 VI. I H20 frequencies for hydrated alkalai halide salts 250 VI.II Oligomeric H20 and D20 peaks in clathrate mixtures and rare gas matrices | 252 VI.Ill Alkyl halide frequencies in pure solids and clathrate mixtures 25^ LIST OF FIGURES FIGURE PAGE 1.1 The stainless steel deposition tube kk 1.2 The isolated sample chamber k6 3.1 Representative spectra of vitreous and cubic ices 60 3.2 Frequency shifts during phase transformation . . . 61 3.3 Oligomeric H20 and D20 absorptions in vitreous ice I . . . . 6k 3.k Half-height width shifts for (vR, vR + vT) and (vl5 v3, v1 + vT) 66 3.5 Half-height width shifts for (v2, 2vR) 67 3.6 HDO stretching frequency shifts for cubic ice 1 71 3.7 HDO librational frequency shifts for cubic ice I 73 3.8 HDO stretching mode half-height width shifts for cubic ice 1 75 3.9 HDO stretching mode peak height shifts for cubic ice I . . . 78 3.10 The shifts of cubic ice I v3 82 3.11 The shifts of cubic ice I vj_ 5 3.12 . The shifts of cubic ice I v2 • 86 3.13 The shifts of cubic ice I vR 88 3.1k The cubic ice I vT(H20) band at 83°K 89 3.15 The shifts- of cubic ice I vT . 90 3.16 The shifts of cubic ice I (vi + vT) . .  92 3.17 The shifts of cubic ice I 3vR 93 3.18 The shifts of cubic ice I (vR + vT) 9k xii FIGURE PAGE h.l The calculated linear thermal expansion coefficient of cubic ice I 128 it. 2 The calculated cubic ice I lattice 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 T 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 translationfCAr^> 150 it. 10 A plot of<Ar2^> against R(0 0) 151 it. 11 A plot of v^CHDO) and v^(HDO) against<Ar2> 152 Un OD it.12 The cubic ice I dependences on RCO'^'O) 165 4.13 The calculated hexagonal ice I V3 dependence on R(0 0) . . 166 it.lU The calculated hexagonal ice I vQH(HD0) and vor)(HDO) dependences on R(0,,,,0) l6T it. 15 H2O, HDO and D20 vapour and cubic ice I phase frequencies . . 180 it. 16 The effects of uncoupling on the HDO stretching frequencies • l8U it. IT The principal axes of H20, HDO and D20 189 it. 18 The H203 model of H20 in ice 19it. 19 The internal coordinates of H2O3. . .- 202 it.20 The symmetry coordinates of H2O3 203 xiii FIGURE PAGE 5.1 Clathrate-mixture frequency shifts during transformation . 217 5.2 Typical annealing spectra for CH3CI, CH^Br and CH^I clathrate-mixtures 218 5.3 Typical annealing spectra for CHCI3 and C2H5Br clathrate-mixtures 219 5.U Typical annealing spectra for Br2 and Cl2 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 CH3Br•7.67H20 (5.9W HDO) 236 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 v1(D20) 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 faith in graduate students to allow them to choose and pursue a range of interests in vibrational spectroscopy, and who instills a beneficial but often frustrating independence of thought and action. To Professors R.F. Snider and A. Bree who as members of my committee were also willing to discuss problems related to this work. To the members of the mechanical, glass blowing and electronics workshops for their 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 their special help and the joy they provide. DEDICATION: To my parents Karl Johan Frithiof Hardin and Beatrice Mary (.Trojanoski) Hardin INTRODUCTION The phenomenon of hydrogen bonding has played an increasingly impor tant role in 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 results. However, for crystals a unified hydrogen bond model has "not yet developed which is consistent with all the chemical and physical properties of the solid state. The present work is a spectroscopic investigation of solid state hydrogen bonding in vitreous and cubic ice I and in vitreous and crystalline clathrate-hydrate mixtures; the nature of the clathrate-hydrate solids formed by vapour condensation is uncertain. A detailed study of the large changes (relative to non-hydrcgen-bonded solids) in the infrared, (ir) absor-tions as a function of temperature provides information on changes in hydrogen bonding as a function of the oxygen-oxygen nearest-neighbour distance (R(0''-'0)) both for individual molecules and for the collective solid arrays. These data help to describe precisely changes in one solid's molecular potential and should aid in the development of a unified hydrogen bond model. Hydrogen Bonding The main effects manifested by the hydrogen bond (A-X-H••••Y-B) on the ir spectra are: l) large frequency shifts, 2) alterations in intensity, 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 in chemical structures. The specific effects of hydrogen bonds on the chemical and physical proper ties of ice are treated in books by Eizenberg and Kaufmann (5) and by Riehl, Bullemer and Engelhardt (6). A. Theories of Hydrogen Bonding Hydrogen bonding theories fall into two classes—classical and quan tum mechanical; the latter includes three separate approaches—valence bond (VB), charge transfer (CT) and molecular orbital (MO) representations. The conclusions drawn from all the theories are that both electrostatic, charge migration and short range repulsion give concerted effects and both are concurrently important (7). (i) Classical Theories The classical electrostatic theories are based on Pauling's (8) des cription which assumed the H atom could form a single covalent "bond only. . (a)- Point charge models. In the early work (1933-1957) the charge distribution was approximated "by a set of point charges (9-12). For the ice and clathrate-hydrate systems with 0-H««--0 "bonds, h electrons (2 in the 0-H bond and 2 in 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 interaction energy of the hydrogen bond, calculated by assuming a simple Coulomb potential, 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 shift. 3 Two conclusions have been drawn from the simple electrostatic model. First, electrostatic energy is important in hydrogen bonding as is indicated by the decreasing bond strength with decreasing electronegativity of the proton acceptor and proton donor. Secondly, electrostatic energy causes at least part of AR(X*,-,Y) and Avvrr. An (b) Continuous charge distribution model. This model was presented in 1964 by Bader (13) for the 0-H-••-0 system typical of ice and clathrate-hydrates. He considered all the electrons, by methods developed for hydrides and binary hydrides (lU,15), in spherical charge distributions and calculated the electrostatic force by classical electrostatic methods. The conclusions and interpretation of Bader's model are the same as for the point charge model. (c) Summary of the classical theories. The electrostatic theories ignore four important facts about hydrogen bonding. For example, hydrogen bonds may not be completely ionic since there is no correlation between di-pole moments and hydrogen bond strengths in the hydroxides. As well, both the point and continuous charge distribution models assume the electronic charge distributions are undistorted by the formation of a hydrogen bond. Another point to consider is that the X-...Y distances are much less than the covalent van der Waal's radii suggesting that forces other than.re pulsion are important. Finally, the electrostatic theories cannot explain the increase of intensity of the X-H stretching mode. (ii) Quantum Mechanical Theories The first quantum mechanical theory of the hydrogen bond was published in 1952 by Sokolov .(l6), although such methods have become practical only recently. Since the results of this thesis are not interpreted in detail by the quantum theories, they will only be outlined and their results will 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 origin. As in the elementary electrostatic models only four electrons were considered. Later Tsubomura (l8) showed that four effects contribute to the hydrogen bond, and that the agreement of the electrostatic 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 electrostatic energy, 2) the short-range repulsion energy, 3) the dispersion energy, and k) the derealization energy due to CT. Tsubomura characterized effects 2, 3 and k explicitly. He assumed there were 5 contributing resonant structures: *1 Xr--|H Y covalent X-H *2 X- H+ Y pure ionic Y3 X+ H~ Y pure ionic X" H| «Y+ covalent H-Y CT V H~ covalent X-Y CT Tsubomura's calculation showed that the delocalization energy amounts to 8.1 kcal/mole—about 1.5 times larger than the electrostatic energy. The repulsion energy and dispersion energy are of opposite sign to the delocali zation energy and appear to cancel it. The VB method has received more recent treatments (19,20). Hasegawa, Daiyasu and Yomosa (20)reported a four electron VB calculation of the hydro gen bond potential energy. They used Tsubomura's (l8) 5 resonant struc tures and constructed the contributing ^-functions from trigonal or tetra-hedral plater atomic orbitals. The proton potential was calculated as a function of R(0 0) and r(O-H). As well, the shifts in r(0-H) and v 5 upon hydrogen bonding were studied. The calculations of Hasegawa et al. ignored the contributions of the CT structures, 1^ and IJJ^-, and resulted in an . asymmetric,.single minimum potential. They deduced that to account for Ar(O-H) and Av_„ the polariza-tion of the surroundings must be considered, i_.e_. ip^ and must be included. When that was done a double minimum potential resulted. t One can summarize the VB theories by stating the following conclusions l) in addition to electrostatic forces other forces are important—dispersion exchange repulsion and delocalization, 2) CT from Y to X is not negligible for short bonds but may be for long bonds, 3) the amount of CT changes very rapidly as a function of r(X-H) and r(X-Y)(the contribution of ^ rises much faster (10 times) than the contributions of ipg, ^ and ^^). (b) Charge transfer theories. Since a well developed theory for CT exists, 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 in three orbitals, the OH bonding and antibonding orbitals and the 0 lone pair.orbital The conclusions Bratoz (7) reached from these CT theories are: l) the VB picture of the hydrogen bond is valid, 2) since the H atom'is small, the short range repulsive forces are small and the H atom has a special role for this kind of intermolecular interaction, 3) a fraction of an electron exists in the OH antibonding orbital, reducing the bond strength and allowing longer r(X-Y) and weaker X-H force constants, k\ CT theories predict an increased polarity in the O-H-'-'O complex and therefore an in creased infrared vnw intensity. '(c) Molecular orbital theories. The FHF anion has been examined in detail since it is relatively small with respect to physical size, bond length and number of electrons. Larger systems such as (H^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 potential, in contrast to the empirical double minimum result of Lippincott and Schroeder (25). Weissmann's results predicted an H^O dipole moment of 2.k0 D in ice, in good agreement with the experimental value of Eisenberg (5), 2.U0-2.87 D, however., the method was less successful in pre dicting the r(X-H) and r(X-Y) distances. More recently, Rein, Clarke and Harris (26) studied the hydrogen bond of water by MO methods. The important point of this work is that the atomic charges and overlap populations indi cate a substantial CT across the hydrogen bond. . . Molecular orbital 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 orbital contribution to the ground state is not negligible—there is a small amount of TT character in the hydrogen bond. B. Spectroscopic Manifestations of Hydrogen  Bonding As early as 1933 Bernal and Fowler (9) recognized in H^O the large shift in v..,, (Av^ = vOTJ(vapour) - vrtTI (hydrogen bonded)) caused by hydrogen Un Un Un Un bonding. Infrared techniques still remain the most versatile tool to in vestigate the hydrogen bonds in vapours, liquids and solids. However, the relatively large electron migrations induced by hydrogen bonds give large 7 changes in nuclear shielding and shifts in the nmr transitions. The present work is concerned only with the ir manifestations of hydrogen bonding in the 0-H-,,"0 system ice I and in clathrate-hydrates. (i) The' General Effects of Hydrogen Bonding The four main spectroscopic effects in hydrogen bonded solids are often large in contrast to the small effects found between the vapour and solid phases of molecules incapable of hydrogen bonding. The first correla tion made from the experimental data was the relationship between R(X***-Y) and the v^.TT shifts from the monomer frequency in the bonded complex. Gener-An ally it is found that the shift, breadth and intensity 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 in the weak UK* * • 'II systems since the II van der Waal's radii are larger. The four effects will now be considered in detail. (a) Frequency shifts. Wot all of the molecular vibration frequencies are strongly affected by hydrogen bonding. The X-H stretching frequency is shifted to lower frequency by 10-50% of the vapour phase frequency and the R-X-H bending vibration experiences a relatively smaller shift to higher frequency. The novelty of the large stretching mode shifts 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" Solid 5 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 al., Ref. 27- 0>). C02 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 families of hydrogen bonding compounds. For small R(X....Y) the v vs. R relationships are linear as Pimentel and Sederholm (28) proposed. For large R(X....Y) the v vs. R relationship is non-linear: the behaviour o over all R(X....Y) suggested an asymptotic relationship. (b) Band broadening. An incresed half-height width (Av2) is found for v and its overtones in hydrogen bonded systems (29). In contrast An the effect is much smaller on the width of the R-X-H bending modes. In the early work the explanation for braodening was thought to lie in the form of the intermolecular potential perturbation. Such an explanation is sufficient only for weak or moderate strength hydrogen bonds, but not for strong hydrogen bonds. Strong hydrogen bonds give broad bands in the vapour phase as well as in the liquid and solid phases. Hence the breadth is inde pendent of the non-hydrogen bond intermolecular forces to the first order. Bratoz and Hadzi (30) and Reid (31) suggested that the breadth arises from the anharmonicity perturbations and changes or differences in the anharmonicity over many molecules. Generalizing the discussions of ice they suggested that in all X-H....Y systems the breadth of the v absorption An arises from a group of closely spaced bands. (c) Band intensity. The integrated intensity coefficients often increase many-fold upon hydrogen bond formation. Also the overtones of h v decrease in intensity. The apparent relationships among Av, Av and An intensity (large shift, broad band, large intensity) do not necessarily hold for all types of hydrogen bonding complexes. There is little reliable data on integrated intensities due to experi mental difficulties, however, early work by Huggins and Pimentel (29) esta blished that hydrogen bonded complexes which show no increase in the intensity of vVTJ appeared to have non-linear hydrogen bonds. XH The increased intensity of vXH and the unaffected intensity of vR cannot be explained by electrostatic theories of the hydrogen bond: Electrostatics requires that both vvtr and increase in intensity. However, An n CT theories predict that only increases in intensity. (d) New absorptions. For X-H,-,*Y systems new bands appear in the spectra associated with the deformation of the hydrogen bond. In ice the hydrogen bond stretch and hydrogen bond bend correspond to molecular trans lation (v„) and molecular libration (v_) modes, the so-called lattice modes, i n (ii) The 0-H 0 Hydrogen Bond Effects The discussions here have so far been concerned with correlations among different hydrogen bonding families. However, there is a very big problem involved in such comparisons, the different X-H,,,*Y systems have differences in molecular polarizability, van der Waal's radii, sizes of orbitals, dispersion forces, etc. Therefore one must expect different rela ys tionships among Avvu, intensity and R(X**''Y). These parameters in An An cubic ice I and the clathrate-hydrates can best be compared to other 0-H'-'*0 systems and preferably to other H^O allotropes, i_.e_. , the high pressure ices. In order to study vVTJ as a function of R(0--,*0), Nakamoto et al. (27) An compiled AvOTJ and R(0'*'"0) data for 26 compounds. As well, they correlated On R(0**,,0) to r(O-H) from neutron diffraction data. The results indicate 10 that as R(0--**0) decreases then r(O-H) increases linearly for long hydrogen bonds and exponentially for strong (short) hydrogen bonds. They felt that inclusion of covalency in the hydrogen bond was important, as in Tsubomura's (18) work. In order to understand the potential energy of the proton as a func tion 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 well with experi-o ment: for ice, where R(0>-,,0) = 2.76 * 0.1 A, their relationship between v and R(0'*-0) is linear. Unfortunately their formulas are not good for predicting the v,-„ of ice over a small range of R(0-«--0) since there is some arbitrariness in defining the hydrogen bond dissociation energy. Reid (31) constructed the potential surface for simultaneous H and 0 motion in 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 in ir results with changes in crystalline lattice dimensions. He proposed that the breadth of v was due to its strong dependence OH on R(0--,,0). During any v^ vibration many R(0--**0) distances occur and many vQJJ's are 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 radii, further approach of X and Y is permitted only if 11 hydrogen bonding occurs. For example in the 0-H'*'*0 system the van der o Waal's radii 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 limiting R(X-• •-Y) is the sum of X and Y van der Waal's radii 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 in hydrogen bonds the H orbital disappears or is com pletely overlapped and that there is no repulsion due to it. Bellamy and Owen (33) extended this idea and proposed that the rate of increase of repulsion is proportional to the rate of increase in lone pair - lone pair repulsions. They adopted the 6-12 potential to describe the repulsive terms from lone pairs in X and Y and finally obtained an ex pression relating Av^ and R(X-,-,Y). For 0-H----0 this has the form An 12 6 3.35 3.35 AVOH =•50 [(ir } - < R > I-This relationship give's good agreement with the work of Nakamoto et_ al. However by inspection of Nakamoto's work one sees that no unique v - R(0*4""0) relation exists for the 0-H*••*0 family. There are too many On variables. It seems more reasonable to study one molecular system like H2O in a variety of crystal habits and to attempt to vary only R(0--,,0) in some way. For example, a study of H2O in all 9 ice phases and in clathrate-hydrates as a function of temperature may provide useful results. 12 Clathrate-Hydrates A.- The Clathrate-Hydrate Problem Quantized rotation or libration of trapped (guest) molecules in the (host) lattice cavities has been suggested by previous ir (3^,35) and nmr (36,37) studies. Now detailed ir assignments of the guest rotations and their behaviour in the host cavity are required to determine the form of the potential well surrounding the guest molecules. In order to determine the changes in the interactions of the guest molecules with the host lattice and the height of the barrier to guest rotations, it is necessary to know pre cisely how the guest molecule absorptions and host lattice absorptions vary as a function of temperature. B. The Structures of the Clathrate-Hydrates Clathrates are a type of inclusion compound in 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 lattice which contains the cavities is called the host and the enclosed molecule is called the guest.) A common property of some im portant clathrate compounds is hydrogen bonding. Some examples of clath rates are: 1) g-quinol clathrates, 0 .Jk Kr-3 CgH^(.0H)2 2) gas hydrates, Ar*7.67 H^O 3) tetraalkylammonium clathrates, salt hydrates [(n - C^H9)UN] C6H5C02-39.5 H^O U) Ni(CN)2NH3-C6Hg . 13 A clathrate-hydrate is a clathrate compound formed with an H^O host lattice in 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 H^O (host) and small, covalent gases (guests, G) and liquid hydrates are clathrates formed between H^O (host) and molecules of volatile liquids (guests, G). Three crystal structures have been found for the clathrate-hydrates. The so-called gas hydrate clathrates, Type I, are cubic and have maximum ideal stoichiometries of SG'^HgO or 6G-U6H20. The so-called liquid clathrate-hydrates, Type II, are also cubic and have maximum ideal stoichiometries of 8G-136H20 or l6G'-8G-136H20. Bromine liquid clathrate-hydrate, Type III, is tetragonal and has a maximum ideal stoichiometry of 20G*172H20. (i) Type I Clathrate-Hydrates These compounds form a cubic crystal of Pm3n symmetry (38,39) with a o 12.A unit cell edge and U6 HgO molecules in a unit cell. Two pentagonal dodecahedrons are formed by 20 HgO molecules each. Those two cavities are linked by the remaining 6 H^O molecules to form 6 tetrakaidecahedra, giving a total of 8 cavities per unit cell. 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 cell). Molecules and atoms whose o maximum dimensions are less than 5.1 A can fill all 8 cavities and would have an ideal 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 will fill only the 6 tetrakaidecahedra and would have Table 0.1 Some typical clathrates and their properties, P,. gives the clathrate decomposition pressure at 0°C, diss ' T gives the maximum stable temperature of the clathral Tiq gives boiling temperature of pure guest.* Type Clathrate diss at 0°C max G (cubic) II [cubic] III (tetrag) 8G'U6H20 Ar Kr Xe H2S 6G-1*6H20 CI2 CH3C1 CH^Br S0„ 8G-136H2O CH3I CHC13 C2H5Br CH2C12 C3H8 C2H5C1 20G-1T2H20 Br„ o A 11.97 12.00 12.03 12.00 12.09 11.9^ n.ik 17-30 17.26 17.31 17.ho 17.30 a 23.8 o cQ 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 83 121 166 213 239 2U9 277 263 316 33U 311 315 228 286 332 Reference kO x5 6G'U6H20 stoichiometry (Cl^, SO^, C^H^-). Some properties of the clathrates formed in these two ratios are given in 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 2262 In the practical situation the unit cell dimension varies according to the size of the guest species, Table 0.2. (ii) Type II Clathrate-Hydrates o These compounds form a cubic crystal of Fd3m (38) symmetry with a IT A unit cell edge and 136 H^O molecules in a unit cell (i_>e_- G = CH^I, CHCl^, C^H^Br). There are 16 pentagonal dodecahedral cavities and 8 hexakaideca-o hedral cavities in one unit cell. The free diameters are 5.0 and 6.T A o respectively (for a 17.h A unit cell). 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 II clathrates. That implies they occupy only the hexakaidecahedr.a with an ideal stoichio metry of 8G'136H£0. Some Type II clathrates, the guest sizes, and the unit cell dimensions are given in Tables 0.1 and 0.2. (iii) Type III Clathrate-Hydrates The clathrate-hydrate of Br^ was originally thought to be of Type II. However, work by Allen and Jeffrey (1*1) has shown that it forms a tetragonal o crystal of symmetry k/xamm with a = 23.8 and c = 12.2 A unit cell edges and 172 HgO molecules in a unit cell. They reported 20 polyhedral cavities large enough to accomodate Br^ molecules, 10 small pentagonal dodecahedra, 16 tetrakaidecahedral and k pentakaidecahedral. The ideal stoichiometry is then 20Br -1T2H 0. Some data are given in Tables 0.1 and 0.2. Table 0.2 The types of cavities, the maximum allowed occupancy, guest sizes and unit cell dimensions of typical clathrate-hydrates. f Type Clathrate ao Guest Allowed occupancy of cavities. co size V Ik 15 16 8G'ii6H20 0 A 0 A Ar 3.76 2(2)* 6(6) Kr k.ok 2 6 Xe aQ 11.97 k.ko 2 6 I H2S 12.00 k.ho 2 • 6 6G-U6H2O (cubic) CI 12.03 5.17 0(2) 6 CH3CI 12.00 5.06 0 6 CH3Br 12.09 5.33 0 6 S02 11.9h 5.00 0 .6 8G-I36H2O CH3I YJ.lh 5.TO 0(16) 8(8) II CHCI3 17.30 6.kh 0 8 (cubic) C2H5Sr 17.26 6M 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) III Br2 a0 23.8 5-68 (tetrag) c0 12.2 V^2 pentagonaldodecahedron, V.^ ^. ^ - tetrakai, pentakai, hexakaidodecahedrons. * - numbers in brackets show maximum number of cavities per unit cell. 1 H 17 Since the present experiments attempt to accurately correlate v and OH R(0 0) for seven Type I, II., and III clathrate-hydrates, the R(O----O) distances are required. However, the structures were determined by assuming o constant R(O--'-O) throughout the unit cell, e_.g_. 2.8l A for a Type I o o o clathrate (12.0 A unit cell) and 2.78 A for a Type II clathrate (17-3 A unit cell). In order to accomodate the pentagonal dodecahedra and other polyhedra in the unit cell, the 0-0-0 angles were distorted from tetrahedral. Von Stackelberg (38) reported angles from 100.0° to 12k.6°. It seems likely that in reality the 0--,-0 distances are also irregular and a range of R(0--«0) exist for each clathrate-hydrate. That will unfortunately broaden the ir results even more than in ice I. Indeed for Type I clathrate-hydrates (cubic, Pm3n) the H^O oxygen atoms lie on 3 unit cell sites (k, i, and c). - Consequently, there are it- types of hydrogen bonds; k-k, k-i, k-c, i-i. It seems reasonable that these may;not be identical in the real crystal. C. Formation of Clathrate-Hydrates A general phase diagram was proposed by Roozeboom and is shown in von Stackelberg's work (38). At constant temperature there are 2 boundary con ditions to permit formation of clathrate-hydrates, raising the pressure of G to form either guest G(gas) or G(liquid) plus hydrate. If the partial pressure of guest applied to the sample is less than the equilibrium dissociation par tial pressure then the clathrate dissociates. In a recent review Byk and Fomina (it2) discussed the conditions for formation and the thermodynamics of formation. As well, Barrer and Ruzicka (it3) studied the kinetics of rare gas clathrate formation at low temperatures. 18 Specifically, 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 thin layer of H^O in a glass bulb at TT°K. The sample was warmed to 195°K and either Ar, Kr or Xe (190 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 critical formation pressure of less than 190 Torr. D. Previous Investigations of the Clathrate-Hydrates Contemporary interest in clathrates has been centered on the motion of the guest molecules in the host lattices. Thus the methods of dielectric relaxation (1+1+-1+6), x-ray diffraction (38,1+7), nmr (1+8-51), thermodynamics (38), and ir spectroscopy (52-57, 3l+) have been applied to quinol clathrates and clathrate-hydrates to discover whether guest rotations are free ,or res tricted, how fast they rotate, and what are the barriers to free rotation. Similarly, deductions with respect to hindered translations (rattling) of the guest have been made (1+8-51). The first work on clathrate-hydrates in the ir was reported by McCourt (56). He studied the three Type I clathrate-hydrates of Ar,; Kr., and SO2. The main points of his thesis were: l) there was an E^O host band at 21+25 cm in addition to the well known ice absorptions, 2) the vR band was shifted -50 cm from ice I, 3) the 1600 cm ^ and 2210 cm absorptions of the host were v (HOH bending) and v0 .+ . v,, respectively, h) S0o absorbed at 2^+55 cm and 3570 cm ^ (a weak shoulder on v and v_, the symmetric and 19 assymetric stretches,, of H^O) in the clathrate-hydrate. Shurvell (57) followed up the above work by observing SO^, H^S, and Kr Type I clathrate hydrates (SG-UeH^). For S02'7-67H20 Shurvell reported: l) that v_, (HO0) was ho cm-"'" less than that of ice, 2) that the 1600 cm "*" band of ice was at 1.6k0 cm "*" in the clathra.te and was therefore rather than 2vT3, 3) that the 2230 cm-"1" was v_ •+• . v , and k) that HO in clathrates had. a new feature at 2^10 cm "*" in addition to the ice bands. As well, he found that the v^SO^) had a central peak and 2 wings, 1336, 13^2 and 13U8 cm-"*". There was no splitting of v^tso,.,) as in the pure SO^ solid and the clathrated SO^ bands were broadened by "rattling" and rotational fine struc ture. The wings were thought to be due to combinations with librations (hindered rotations) and translations. 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 devitrify the condensed phase. The results 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 ir absorptions were studied in this work. First, in order to analyze previous work (.56,57), the forms of the clathrate-hydrate absorptions were determined from low temperature mulls of solid clathrate samples. Secondly, the vitreous-crystalline phase trans formation was observed by ir spectroscopy as a function of temperature for clathrate-hydrates (types I, II and III) condensed from gaseous stoichiometric 20 mixtures. Thirdly, the temperature dependences were determined for the ir absorption of devitrified "clathrate" samples. Ice A. The Ice Problem Many theories have been proposed to explain the origins of the fre quency shifts, the large band widths and the large intensities in ice. Now data are required which will either support an existing theory or which will suggest some modifications to the theory. Specifically, the correlations of absorption band frequencies, widths and heights to AR(O-'-'O) are required for ice I. B. Non-Spectroscopic Investigations  of Ice (i) Structural Studies Ice exists in at least twelve structural allotropes above TT°K and at pressures of up to 25,000 atmospheres. The ice phases stable at 1 atmosphere are all called ice I. In fact, there are three allotropes of ice I, the vitreous or amorphous, the cubic and the hexagonal phases (iv, Ic and Ih). The ice I structural results up to 1958 were summarized by Lonsdale (58) and Owston (59). Recently, Brille and Tippe (60) measured by x-ray diffraction the ice Ih lattice parameters between 15° and 200°K. As well, Arnold, Finch, Rabideau and Wenzel (6l) reported a neutron diffraction study of ice Ic. (a) Hexagonal ice I. The ordinary phase of ice at S.T.P. is hexagonal ice I (ih) in which the oxygen atoms form a P62/mmc unit cell with h molecules. * Assuming solid polywater is a unique solid of H2O. 21 The unit cell dimensions are (62); ao co H20 (l63°K) k.H93 A 7.337 A D20 (ll+3°K) 1+.1+95 7.335 o The oxygen-oxygen nearest-neighbour distances (R(0••••0)) in H^O are 2.76 A at l63°K. The molecules are hydrogen bonded to 1+ nearest-neighbours in layers of hexagonal, puckered rings. The open structure has channels parallel and perpendicular to the cQ axis. There is still some uncertainty about the unit cell dimensions of ice Ih. The disagreement between Lonsdale's (58) expansion coefficients and the direct dilatometric measurements seems to arise from differences in crystal-linity among the worker's samples. The x-ray diffraction work of La Placa and Post (63) agrees well with Dantl's (6I4) direct thermal expansion measurements: La Placa and Post's (63) work was confirmed by Brille and Tippe (60). The latter found that the c/a ratio is temperature independent, not reaching 1.633 even at 15°K; they found c/a = 1.6280 ± 0.0002. (b) Amorphous ice I. This phase is formed by the slow condensation of vapour onto a cold surface. Beaumount, Chihara and Morrison (65) 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 diffraction patterns are diffuse and the samples are clear, transparent films. The samples have consequently been variously described as vitreous, amorphous or microcry'stalline. Virtually nothing is known about the structure of amorphous ice I. (c) Cubic ice I. Ice Ic can be formed by the irreversible transfor mation of amorphous ice I or from the high pressure ices. The vftreous-cubic ice I transformation has been reported to start 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 Bertie, Calvert and Whalley (66) 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 ibly to hexagonal ice I with a small enthalpy change, iLe_. <1.5 cal/gm (65). The crystal structure of the oxygen atoms in cubic ice I is the "diamond" structure, Fd3m with 8 molecules per unit cell. The oxygens are arranged in a similar fashion to that of hexagonal ice in layers of puckered hexagonal rings. However, the six 0 atoms adjoining 2 nearest-neighbours are eclipsed in cubic ice I and staggered in hexagonal ice I. The lattice o o parameters (62) at li+3°K are ao(H20) = 6.350 A and ao(D20) = 6.351 A. (d) Disorder in Ice I. The neutron diffraction work of Peterson and Levy (quoted in Lonsdale (58)) 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 linear. Their results were the same at 123° and 223°K, indicating no ordering of the lattice 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 (67) showed that Pauling's result is only the lower bound to the true calculated value. Nagle (68) found by lattice statistics that the theoretical value is O.81U5 t 0.0002 e.u., compared to an experimental value of 0.82 i 0.15 e.u. Disorder in cubic ice I was confirmed by electron : diffraction(69). Pitzer and Polissar (70) discussed the order-disorder problem in ice I and concluded that the ordered structure is more stable at low temperatures However, they estimated that the transformation time may exceed a day. They Table 0.3 Temperature ranges of stability 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 crystalline ihh 2T3 Pryde et_ al. (a) amorphous (b) elect.diffrac. TT - 10T 10T - 190 190 - 273 Hon jo et_ al. calorimetry TT -(150 t 10) crystalline 150 2T3 de Wordwall et al.(c) amorphous (d) elect.diffrac. TT - 151 151 - 173 173 - 2T3 Blackman et al. amorphous x-ray diffrac. TT - HO 113 - 1U3 lh3 - 2T3 Dowell et al. (e) amorphous diff.therm, anal. TT - lk9 lk9 - 186 186 - 2T3 McMillan et al. (f) glass x-ray diffrac. TT -(1U8 + 8) (1U8 + 8) - (220120) 220±20 - 2T3 Beaumont et_ al. (g) amorphous thermal analysis TT - 15U 15U - 208 208 - 2T3 Ghormley (h) amorphous calorimetry TT - 135 135 - 160 160 - 2T3 Sugisaki et_ al. (i) amorphous (a) Ref. 71, (b) Ref. 69, (c) Ref. 72, (d) Ref. 73, (e) Ref. 7^, (f) Ref. 75, (g) Ref. 65, (h) Ref. 76, (i) page 329, Ref. 6. 24 also estimated the Curie point to be near 60°K. (e) High pressure ices. The aliotropes of ices II through IX may not consitute all possibilities. More allotropes may exist below 77°K and at higher pressures. Some of the crystallographic properties and struc tural parameters of the ice allotropes are given in Table 0.4. Phases II, VIII and IX are ordered and all 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 distortions result o o in much closer (3.2 A) next-nearest-neighbours compared to ice Ih(4.5 A). There is considerable distortion of the HOH angles: Ice II has 18 HOH angles between 80° and 128°. (ii) Electrical Properties of Ice Recently dielectric constant work was reported by Wilson et al. (77) and by Whalley and Heath (78). In general, they found that ice I has a large reciprocal dielectric relaxation constant (about 10"* reorientations per T -li second), and that the disordered high pressure ices have even larger ^ s. The ^'s of ordered ices, however, are small (no reorientations). The T^ of ice I increases very rapidly with decreasing temperature due to the increasing electric field of the approaching neighbouring molecules: T^ ^ is 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. (iii) Thermodynamic Properties of Ice There is support for some ordering in ice Ih from heat capacity (Cp) and electricity measurements. Helmreich and Riehl (80) deduced from elec tricity measurements that the proton disorder is partially removed as \ Table O.U Physical properties of the ices. ICE Ih Ic II Ill . 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 pl*2/mmc 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 109.5 109.5 80 -128 87 -li+1 8U -135 . 76 . -128 100.5 109.5 -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 fraction of the sample was ordered: A finite number of ordered domains in a disordered continuum. Pick (8l) also suggested that regions of short-range ordering are formed as the temperature of ice I is lowered. However, he pointed out that the D- and L- defects responsible for reorientation (ordering) decrease in number exponentially with decreasing temperature. Hence .the time for establishing an ordered crystal increases exponentially as temperature decreases. The heat capacity of ice Ih above 15°K was first investigated by Giauque and Stout (82). They found that the samples attained thermodynamic equilibrium in the range 85° to 115°K only slowly. The reason is not under stood. Recently Flubacher et_ al. (83) studied the ice Ih Cp below 15°K. They found Cp extrapolates to zero at 0°K and is consistent with a continu ous decrease. As well they pointed out that the translational, librati.onal and internal energies are separable and that the librational contribution to Cp is explained well by an average frequency for H^O of 620 cm' Leadbetter (8U), in a comprehensive interpretation of the ice I , thermodynamics, explained Cp in terms of the excitation of translational (v^) and librational (VR) vibrations. Below 80°K, Cp was derived entirely from excitations of vm, while above 150°K v~ gave a significant contribution. He also predicted that between 0° and 273°K the frequency shifts...by 8 + 2$ and that vR shifts by 6 ± 2% for Hg0 (for Dg0 ±0 ± 2% and 8. + 2% respectively). Blue's (85) elementary treatment of Cp gave a surprisingly good;value for the librational average frequency, 660 cm ^. He also gave a convenient formula for deducing the set of ir librational frequencies: 27 :1 [1] 2TTCI. n where In is the moment of inertia about axis n in gm/cm , k. is the force constant restraining atom i from rotation about axi in n in dynes/cm, • ' - r. is the normal distance of atom i to axis n in cm, The effects of hydrogen bonding have been observed in 3 fields of spectroscopy; electronic, nmr and vibrational. For example, both red and blue shifts (from the non-hydrogen bonded frequency) are observed dependin on whether the hydrogen bond is stronger in the ground electronic state or in the excited state. In nmr spectra the proton signals of (H atoms in) hydrogen bonded molecules are shifted to a lower field than for the non-hydrogen bonded molecule. In ice, nmr has been used to find proton separa tions and to determine charge redistributions. Vibrational studies of ice have been made by neutron inelastic scattering, Raman, and infrared spectroscopy. The previous work will be considered in two sections, modes occurring below and above 1000 cm (the fundamental lattice and molecular mode regions ). The results of previous works are tabulated in Chapter 3 for comparison to the results of the present work. respectively). In cubic ice I (Fd3m) with 2 molecules per primitive unit cell (Z = 2) there are (3n)Z (where n is the number of atoms/molecule) c.v in 6 is the velocity of light cm/sec. C. Spectroscopic Investigations of Ice The H^O molecule has 3 molecular vibrations; a symmetric and an •asymetric stretch and a symmetric HOH bend (v (a^), v„(b ) and. y~(a-j_) 28 18 crystal vibrations. Of those, (3n-6)Z or 6 of these are molecular vibra tions, 3Z or 6 are rotatory in nature, 3(Z-1) or 3 are translatory vibrations and 3 are simple translations of the complete unit cell. Hence in a mole (N) of unit cells there are 6N molecular vibrations, 6N rotatory vibrations, 3N optical translations and 3N acoustical translations. Ice spectra are characterized by 5 very broad bands. Two bands occur below 1000 cm ^ in the ^0 ices. A band with at least 6 features and centred near 230 cm is attributed to hydrogen bond stretching modes, the lattice translational modes v^,. A band with from 3 to 16 features and cen tered near 830 cm ^ is attributed to hydrogen bond bending modes, the lattice hindered rotational modes, vw. Between 1000 and 4000 cm ^ 3 bands are observed. The band near 1630 cm ^ has been attributed to Iv*., v0 or to overlapping 2vD/v0. The band near 2200 cm ^ has been assigned to v0 + vn or 3V,,. The features of the ^ /, K K 3200 cm band have been assigned by various authors to: 1) 2^2* v3' vl (105), 2) vr \>y v3 + vT (108), and 3) all as vQH(H20) (95). The vapour, liquid and ice I frequencies, with the various assignments are given in Table 0.5. The analysis of the vibrations of crystalline materials usually begins with a factor group analysis based on the known diffraction symmetry, jL.ji. based on oxygen atoms and -|H atoms. Now the disordered H positions are averaged in the time of a diffraction experiment, while in vibration spectroscopy the instantaneous symmetry of the unit cell is important, (i) The Lattice Modes (a) Translations. For ices Ih and Ic the factor group analysis, based on symmetric -^H positions and the above diffraction symmetries, pre-Table 0.5 H^O vapour, liquid and ice Ih infrared absorption frequencies, half-height widths and intensities and the divergent assignments made to the bands of ice. (a) (D) (c) (d) (d) Vapour Liquid Ice I Ice Ice Av^ Peak Heii -1 -1 -1 -1 cm cm cm cm 160 232 weak (170) (218) 650 800 200 strong (500) .(590) 1595 1570,16U5 161+0 250 med. (1178) (1160,1210) (1210) (150) 2130 2225 200 weak (1620) (1620) (180) 3657 3219 311+2 (2671) ( - ) (231+7) very-3756 31+1+5 3252 300 strong (2788) (2500) (2440) (250) 3352 . (2514) 810* weak (6oo)<* 3707 31+05 3275 80 very (2727) (2520) (21+16) • (2) strong (c) (e) (f) (g) Ockman Hornig Pimentel Whalley 1957 1958 1959 1961+ H20 (D90) HDO V2 + VR vl v3 + vT R V2 3v 2v, R VR v OH "0D V2 3vT R V2V • 3VV2 +VR vOH(H20) vQH(H20) VR VR V0H V0D (a) Ref. 116, (b) Ref. 98, (c) Ref. 108, (d) Ref. 106, (e) Ref. 105, (f) Ref. 97, (g) Ref. 95-ro 30 diets 9 optical modes for Ih (Ajg, Blg, Elg, ^2g' an^ E2u^ an<i optical modes for Ic (Fig). The normal k_ = 0 selection rules predict that all these modes are ir inactive and that all g modes are Raman active. However, ir translational absorption (v^) _is_ observed (86) for both Ih and Ic ices. In fact the absorptions are nearly identical. The factor group analysis fails for Vfj of hexagonal and cubic ices, as well as for the other disordered ices, V and VI (86). In contrast, the factor group analysis works well for of ices II and VIII, the ordered H atom ices (86). The H atoms in ice Ic are not symmetrically placed along R(O----O) in the unit cell. Even if the H atoms were perfectly ordered, with 2 near and 2 away from each 0 atom, the crystal symmetry of ice Ic could not be Fd3m since the symmetry would be destroyed. One'might expect ice Ic to order itself in a sub-group of Fd3m or similar to one of the structures in ices II, VIII or IX (R3, Im3n or P, „ -). Then the vm modes may not be all inactive in ^l2i2 T the ir. If short range ordering is present (as suggested before) then the effective crystal symmetry may be a.subgroup of Sg, 0^ or Dli, since the nearest molecules determine the effective potential at the central molecule. (h) Disorder theory. Whalley and Bertie (87) proposed a theory to explain the activity of lattice modes in orientationally disordered crys tals. They considered ice Ic to have (near) positional symmetry (order) of the 0 atoms but orientational disorder of the H atoms. They suggested that the result is a small effect on the mechanical form of the translational vibrations, therefore the translational modes are mechanically regular. However, since in the course of a vibration Ay_ varies according to the local molecular orientations, then the. crystal translational vibrations are electrically irregular. 31 Whalley and Bertie (87) assumed that the dipole derivative could be split into a symmetric part, M', (corresponding to diffraction symmetry part) and an asymmetric, irregular part, M'', due to the H atom disorder. Then they showed that the molecular intensity of absorption has a part for zero wave vector (k_ = 0) transitions, which are the normal symmetry allowed transitions, and a finite intensity for all k 0 transitions due to M'1. Therefore they deduced that all translational vibrations are ir active. In a subsequent paper Bertie and Whalley (88) used the above theory to describe the density of states in of ices Ih and Ic. They assigned the 229.2 cm-"*" peak to degenerate longitudinal and transverse optical modes at the zone center, the l60 cm-"1" peak to the longitudinal acoustical mode of a zone boundary, and the 190 cm shoulder to the longitudinal optical mode at the same zone boundary. They showed a density of states curve for ices Ih and Ic. As well, Bertie and Whalley (88). found that v^RgO) shifted by 7 cm-1 to lower frequency upon raising the temperature from 100° to l68°K. They attributed the red shift to excitation of hot bands. The results of v^H^O) for vitreous ice I are conflicting (88,89). Giguere and Arraudeau (89) indicated considerable band structure." (c) Raman spectra. Scattering from v^H^O) was reported by Val'kov and Maslenkova (90) with a medium intensity peak at 230 cm "*" and weak features at 291 and 310 cm As well, Taylor and Whalley (91) reported the Raman spectra of ices Ih, Ic, II, III and II. They reported a peak at -1 ' -1 225 cm in ices Ic and Ih and at 151 cm in ice II. Cd.) Neutron inelastic scattering. Spectra were reported by Prask and Boutin (92) for ice Ih and Trevino (93) and Renker and Blanckenhagen 32 (9*0 calculated the v spectra of ice I. The frequency distributions cal culated and observed in neutron work agree quite well with Bertie and Whalley's (88) predictions from the ir. (e) Libration. Hydrogen bonding also gives rise to hindered rotational transitions in the ices. For H^O this absorption is seen from 1000 - hOO cm 1 -1 -1 and for Do0 from 750 cm to 350 cm . The ratio of v0 for H-0 and Do0 would d adideally be 1.1*1 for purely rotational motion and 1.05 for purely translational motion: The observed values lie closer to 1.35• Blue's (85) treatment of H^O libration was based on the assumption of three uncoupled, degenerate librators. 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 libration about the axis is ir inactive. 2v Bertie and Whalley (95), in contrast, pointed out that the very existence of the v bands is due to the strong coupling of the 3N librations of N molecules in a mole of unit cells. The crystal field and hydrogen-bond coupling yield a broad band of crystal frequencies. Since ice Ic is: dis ordered and has only symmetry E, all the crystal frequencies are ir active. However, the distribution of ir intensities across the band of crystal fre quencies is unknown, and the shape of the ir absorption band is not necessarily the shape of the crystalline vibration band. Bertie and Whalley (95) reported that the v absorptions of ices Ic and Ih are identical. For HO they observed 5 features on vn between 900 and d R 555 cm for D^O they observed 3 features between 675 and 1+25 cm \, (However, the mulling agent used obscured the results in some areas.) Similar bands were observed in the high pressure ices (96). 33 The ordered ice II appears to obey the factor group splitting pre dictions with respect to v_. Bertie C86) suggested 12 v ir active modes. In fact, 16(9] features were observed between kJ5 and 1066 cm-"1" with a band center at 800 (593) cm-1. As well, Bertie and Whalley (96) suggested that a mode vD +• v may be active in ice II. -The librational absorptions of vitreous, hexagonal and cubic ice I were reported also by Giguere and Arraiideau (89). For vitreous ice they re ported features at 800(600), 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 crystalline modes were assigned to and + v^. For vitreous ice they suggested the C libration was active due to the asymmetric electric field. The observed frequency of 800(600) cm 1 is in 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 H^O^ model they deduced that the hydrogen bond bending force constant varies from 0.095 to 0.085x10^ dynes/cm between 93° and 273°K. This agrees with the concept of a weakening hydrogen bond as R(0* •••()) increases. (ii) Modes Above 1200 cm"1 (a) Temperature dependences of the modes. Temperature dependences of the ice absorptions have been observed previously by at least 5 groups. Giguere and Harvey (98) reported frequencies for v^, v0 and v_ at 103°, 217° n d 3 and 268°K for H^O and D^O. They observed solids formed by condensing the liquid or vapour phase. Ice Ih (H^O'^nd D^O) single crystal Raman spectra were reported by Val'kov and Maslenkova (99) for several temperatures above 77°K. On the I 3k basis of intense a^ Raman scattering and the similarity to vapour phase scattering, they assigned individual and ice frequencies. That is in direct contrast to more recent work (95) which strongly coupled and into two separate but equally mixed bands. Val'kov and Maslenkova suggested that the ratio ^or ^n ^e so-^a- should be the same as for the vapour, as well as for D^O. They also observed other lines in the stretching region which may have arisen from combinations with lattice modes. Zimmermann and Pimentel (97) also reported the temperature dependences of and 3vR above 93°K. As the temperature was increased from 93°; to 273°K they found that v and 3v^ decreased and v increased in frequency. Thus the l600 cm ^ ice band could not be 2vn. As well, they found that at n 93°K v2(solid) < v2(vapour). The most accurate study of temperature dependences in ice was recently reported by Ford and Falk (100) for the vQH(HDO) and vor)(HDO) modes.? By pre paring a dilute concentration of HDO in HgO or DgO one maintains a constant crystal field, but removes the dynamical intermolecular coupling of one.HDO mode to the surrounding lattice (101, 102). Consequently, Ford and Falk observed relatively sharp HDO bands, the half-height width (Av ) was about 18 cm-1 for vOTJ(KD0) at 97°K. That is still much wider than for ice, II:, On hi Av = 5 cm , where the H atoms are ordered. , • The widths of HDO bands in ice II 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 in ice Ih are due to the above effects plus H atom disorder (irregular Hydrogen bond potentials). The problem of forming hydrated salt windows and not ice I was dis covered by Mutter, Mecke and Lutke (103) and was clarified by Schiffer-(104). Hydrated salt window absorptions are readily distinguished from those of ice. 35 (b) Infrared absorption' spectra. The' spectra of H^O, HDO and D^O were studied in detail by Hornig, White and Reding (105), Table 0.5. The fundamentals and were assumed to have reversed order in energy from the vapour phase-order because of the stretch-stretch interaction constant. They also estimated that the barrier to proton jumping was 27 kcal/mole. Unfortunately, it now appears their samples were of amorphous and not crystalline ice. (Many of their conclusions are still valid however.) Zinnnermann and Pimentel (97) pointed out the need to anneal solid samples formed by vapour condensation. They demonstrated the ir effects of annealin amorphous ice, but did not study the phase transformation in detail. Ice Ih spectra of H^O, D^O and HDO were obtained by Haas and Hornig (106) at 83°K. They observed 2vOTI(HD0) and suggested that the barrier 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 in H^O and D^O. The resulting HDO-HDO coupling (neighbours) gave wider bands as well as a pair of shoulder one on either side of the main HDO stretching band. Their results showed that the width of hydrogen bonded 0-JI stretching bands was not a characteristic of the 0-H-'•-0 bond but arose from extensive molecule-molecule coupling of 0-H motions. The work of Bertie and Whalley (95) is the most comprehensive study of cubic and hexagonal (HO, HDO and D20) ice I. Their results were obtained at 110°K by the low temperature mulling techniques developed by them (107). The cubic or hexagonal crystallinities of their samples were confirmed by x-ray diffraction.---36 Bertie and Whalley reported that the ir spectra of ice Ih and Ic -were identical. As -well, they obtained much sharper spectra than the previous workers (97, 105, 106, 108) due to the absence of amorphous ice. They rejected the interpretation of the bands in terms of v^, v^, and vR on the basis of strong intermolecular coupling. For example, in ice crystals the neighbouring vibrations were -assumed to couple with ,each other to form one broad, symmetric band: Similarly a broad symmetric band formed. Finally 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 ir and Raman active, accounting for the differences between the ir and Raman results. With respect to the widths of the ice I absorptions, they suggested that H atom disorder leads to local variations in 0 atom positions and vari ations in the local potential, as earlier suggested by Reid (3l). Three other causes of the broad bands were also reviewed (96). These were: 1) the occurrence of sum, difference and hot bands with lattice modes, 2) the occurrence of proton tunnelling and the resulting increase in the width of the energy level by a decreased lifetime, and 3) Fermi resonance between the fundamental modes and overtones or combinations. Bertie and Whalley (95) discussed the 1650 cm ^ absorption as arising from combined 2v„ and v_ vibrations, but they pointed out that discussion in terms of a unimolecular mode is not meaningful. One must consider the Nv„ modes/mole of crystal. 37 D. The Present Approach, to the Ice Problem Three facets of the ice problem were.studied in this work. First, to help clarify the discrepancies among ir and Raman results for ice I samples •condensed from the vapour or crystallized from the liquid, 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 in order to make specific 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 is a high resolution single "beam spectrophotometer based on a double pass (model 99) grating monochromator. The monochromator employs a 75 lines/mm replica echelette grating which is blazed to reflect maximum intensity at 12u in the first diffraction order and has a grating-ghost between 1000 and 1070 cm \ Unwanted orders are eliminated by a fore-prism monochromator situated between a glober source and the grating monochromator. The fore-prism filter monochromator consists of a 60° KBr prism mounted in Littrow configuration. This monochromator arrangement gives an instrument resolving power of 0.5 cm or better. Spectral slit widths [calculated by Siegler's method (109)], are indicated on the appropriate spectra. Thermal radiation is detected by a thermocouple or PbS sensor. However, only 2nd pass radiation is chopped at 13 cps and amplified..in a standard model 107 amplifier. The 13 cps electrical signal is mechanically rectified synchronously with the optical chopper. This d.c. signal is 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 in all regions. The instrument was calibrated at each use with atmospheric H90 and CO or with NH (g). 39 Low temperature experiments on ice are hampered in 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 difficulties. At the PbS detector mount a simple ellipsoidal-plane mirror system is placed which produces a monochromatic source image in free' space 50.5 cm from the exit slits. A second detection unit (thermocouple,' focussing optics and pre-amplifier) is mounted in series with the added, optical system. These modifications offer several advantages over standard P.E. 112-G sampling facilities. For example, beam vignetting losses may be reduced and smaller samples may be used by placing the sample at the source image in the new sample area. Also, concurrent calibration and sample observation is possible when a calibration gas is placed at the standard sample mount and the sample is placed at the new sampling area. In .addi tion, there is 15 cm of optical path length and ample surrounding free space for mounting bulky accessories, i_.e_. low temperature cells. A more impor tant advantage is the decreased range of thermal radiation striking,samples mounted in the monochromatorexit beam. Tests indicate a 5% energy loss between the standard and modified detector configurations. The complete instrument, excluding the new thermocouple detector unit, is placed in a metal-plexiglass drybox to reduce background atmospheric attenuation from H^O and CO^. The new detector unit has its 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 air lock and rubber gloves permit the introduction and manipulation of conven tional ir accessories in the primary sample mount. The N2(g) drybox 1+0 atmosphere is circulated through one of two parallel molecular sieve columns (Linde 13X l/l6 in. pellets) to remove residual H^O and CO^. When the cir culating system is in use one column is on-line while the other is regenerated by combined evacuation and heating. This system eliminates absorption from atmospheric H^O but is less effective in 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 identical frequencies. Normally, the fore-prism monochromator slits 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, limited frequency ranges which depend on the region of the spectrum. A mechanical servo system was designed to link the two mono chromators permitting them to be scanned in near resonance. Lengths of certain scans (at acceptable energy levels) can be doubled by this arrange ment. The design uses a variable ratio, ball and disc gearbox, reduction gears, and linking driveshafts. A more powerful motor replaces the.-standard grating drive motor to compensate for the added load. Despite the difficulty in maintaining exact fore-prism/grating monochromator resonance, because of non-linear prism dispersion, the modification: improves the scanning characteristics. 1.2 The Perkin-Elmer 1+21 Spectrophotometer The Perkin-Elmer 1+21 instrument is a moderate resolution (l cm , double beam, null recording grating spectrophotometer of conventional design.. A Nernst glower source and thermocouple detector are used In con junction with interference.filters (which eliminate unwanted orders) and a Hi single pass grating monochromator. Two removable, self-contained mono-ehromators are readily interchanged, permitting rapid conversion of the scanned frequency range. Each interchange comprises the appropriate inter ference filters and- a pair of gratings mounted back-to-back on a cosecant drive: One interchange is used from H000 - 530 cm 1 and the other from 2000 - 220 cm 1. Grating and filter operations are automated by pre-programed mechanical and' electrical servo systems. Spectral slit widths [calculated by the method of Roche (llO)] are indicated on the appropriate spectra. Some minor up-dating modifications have been made, i_.e_. installation of a larger (0.8 amp) Nernst glower and alteration of the grating switching mechanism to prevent arcing. A local modification is the provision of inlet and exhaust ports, in the monochromator and source housings respectively, permitting the use of a circulating dryer (manufactured by P.E. Bodenseewerk for the P.E. 225 spectrophotometer). This drying unit is remarkably effec tive in reducing atmospheric H^O absorptions but is less effective with respect to CO,-,. The P.E. k21 was operated under the normal, recommended conditions. Specific conditions of operation are listed with the results. General con ditions of operation are listed below. The automatic slit program was set at 2 x 10.00 which gave spectral —1 —1 slit 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 /in. recording. U2 1.3 The Perkin-Elmer 301 Spectrophotometer The Perkin-Elmer 301 grating instrument is a far-infrared, 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 filters, scatter plates and crystal choppers (Csl or BaF2) are used to reduce scattered radiation and to' eliminate the energy of unwanted diffraction orders. A standard, single pass model 210 grating monochromator is used with 3 pairs of complementary, readily ex changeable gratings which are mounted back-to-back on kinematic mounts. The P.E. 301 optical design produces a large image at the detector and necessi tates a defector with a large target. A golay sensor is suitable and is used over the full instrument range. Signal to noise ratios may be doubled if the instrument is operated in the single beam mode by replacing a split aperature (l/2 image) I-Io mirror with a full apperature I or Io mirror. An advantage of the P.E. 301 is the chopping of source radiation before it enters the sample chamber. Therefore radiation originating at the sample is not amplified. The P.E. 301 was modified by installing inlet and exhaust ports for the P.E. Bodenseewerk". dryer. Severe background atmospheric water problems can be almost completely eliminated by using this dryer. l.k The Hornig-Wagner Liquid Nitrogen Cell The low temperature cell which proved most useful for obtaining spectra above 80°K was constructed from a design originally given by Wagner and Hornig (ill). Our cell, which has been described previously h3 (112, 57) has a glass body and reservoir, a brass sample block, and Csl or AgCl windows. Thermal contact between the sample window and sample block was improved with layers of silver conductive paint on contact surfaces. Temperature was measured with a fused Cu-constantan thermocouple soldered "to the brass sample holder base. Thermocouple wires and cell windows were sealed to the cell with Cenco soft-seal Tackiwax. This wax is- slightly plastic at room temperature, flows well and is ideal for vacuum sealing when extremely low pressure is not required. Although liquid 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, all temperatures quoted in this work are not corrected for source heating. Two sample deposition tubes were used with this cell, one of all-glass and the other of metal construction. Both were mounted with their tips 7mm from the sample window surface. At such a distance there are large heat losses (from the sample tube tip to the window and cooling block) permitting sample condensation at the cold tips. Dangers of selective IL^O condensation or fractionation of clathrate mixtures at the tube tips were avoided by using external heating on the stainless steel tube, Fig. 1.1. B Fig. 1.1 The stainless steel- sample deposition tube: A - pyrotenax heater, B - Cu-Constantan thermocouple, C - deposition tube tip, D - B-19a conical glass joint, a Kovar metal glass joint, and a brass cap, E - needle valve and "swage-lok" fittings. I 1+5 1.5 The Duerig-Mador Liquid Helium Cell Spectra of samples below 83°K were observed through a liquid helium cell which is described elsewhere (112, 57) and is similar in design to that of Duerig and Mador (113). A principal modification incorporated in our cell is the use of a vacuum seal/bearing which permits the helium container and sample holder to be rotated through 90° for sample deposition. Thermal contact between sample windows (Csl or polyethylene) and the Cu sample block was improved by painting the contact surfaces with silver 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 boiling liquids 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 Cell To prepare clathrate-hydrates by deposition from the gas phase one must first ensure that the guest and host components condense in the proper stoichiometries. In an attempt to achieve the ideal clathrate condensation a liquid nitrogen cell was constructed containing an evacuable sample chamber, Fig. 1.2. To help prevent fractionation in the sample chamber, one window-is embedded in the cold block and the other is thermally insulated from the first by a stainless steel spacer ring (which provided the chamber body) and two teflon gaskets. Only one window is cooled to refrigerant tempera ture during the cell 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 "cold1 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 steel screws, H - sample window and holder, I - sample chamber, sample port and teflon gaskets. CHAPTER TWO METHODS AND MATERIALS 2.1 Water Samples and Clathration Materials Clathrate-hydrate guest molecules were either Matheson compressed gases, Fisher certified reagents, or British Drug House analar reagents. Bromomethane (99.5% pure), trichlorofluoromethane (99%), dichloro-difluoromethane (99.0%), chlorotrifluoromethane (99.0%) and chlorine (99«9%) were used directly from their lecture bottles. Chloromethane (99.5%) was supplied in a No. h cylinder and was used without purification. Trichloromethane (Certified Reagent, 99.9% purity), iodomethane (C.R. 99-9%), and broriioethane (C.R. 99-9%) were partially repurified before each use by freezing and pumping off non-condensible impurities. .Bromine liquid (Analar Reagent, 99.0%) was also partially purified by freezing and pumping. Guest compound, purity was checked by ir vapour phase absorption spectra. Clathrate-hydrate host and ice I compounds used were H^O, D^O, H20 (5.9% HDO), and D20 {k.0% EDO). Before use the HgO water was distilled, de-ionized and finally degassed by several cycles of freezing and pumping. D^O was supplied by Merck, Sharpe and Dohme in 100g lots and had a stated purity of 99-7%; D^O was degassed in the usual way. Mixtures of D^O or H20 with HDO were made by mixing 1*9.0 ml Dg0 with 1.0 ml HgO and 1*9.0 ml HgO with 1.5 ml DgO. In both cases the isotopic impurity was almost all present as HDO at equilibrium. Residual H20 (or D20) 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 is tempered by the necessary application of thermal stress and essential non-reactivity with applied samples. The latter property is important in studies of water containing compounds since, as Mecke (103) found and Schiffer (104) proved, thin hydrated layers may form on alkali halide crystals. Csl is suitable for all cryostats used here since it is relatively soft and ductile and accepts the considerable thermal shock. Only Cl^ * T^THgO samples reacted detectably with Csl windows. That experiment was repeated using an AgCl sample mount. Silver chloride does not transmit as widely as cesium iodide over our range of interest, however AgCl is soft and easily withstands thermal shocks. Also, it is apparently non-reactive to chlorine and bromine. Cell windows and a sample support used in the P.E. 301 v^, experiment were cut directly 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 is not an entirely satisfactory sample support' since its thermal conductivity is low and source heating may be high. To counteract source heating, sample supports were pressed from powdered polyethylene embedded with a brass or copper grid. The method consisted of placing a wire grid between two lightly pressed (7000 psi, unheated) 0.20 g discs, heating to the polyethylene flow temperature (130 t 5°K) under light pressure (1000 psi) and pressing to 15,000 psi while cooling to less than 35°C. The result was a low scattering pellet with 58% transmission at 36l cm h9 and 171 cm \ Energy transmission could "be improved by reducing the effec tive reflecting surface area of the metal with finer gauge wire. 2.3 Preparation of Clathrate-hydrates A. Preparation of Solid Samples Clathrate-hydrates with stoichiometries 1M'17 H^O, and whose guest molecules formed liquids at room temperature, were prepared by repeated cycles of cooling and warming stoichiometric liquid mixtures between 77°K and 265°K. To 3g HO (0.17 moles) in a 10 cm by 1.2 cm test tube was added 0.01 moles of liquid guest compound. The mixture was agitated and success ively immersed for about 30 sec in an ice-water-sodium chloride bath (265 °K) and 30 sec in a liquid nitrogen bath. The sample was then warmed to a viscous state. The procedure was repeated until a uniform, white solid 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 ordinarily gases, the method of Allen (ll4) was used with some modification: a preparation cell similar to Allen's was constructed. For clathrates whose guest molecules are ordinarily liquids, the basic method of Allen (114) was used but with major modifications.; A preparation cell of similar dimensions to the one above, but with provision for mechanical stirring and liquid 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 criteria which must be satisfied in forming a stablesuitable sample. For example, the clathrate-hydrate or ice phase must form a stable thermodynamic system in the region k.2° to 200°K. Also, the method must maintain the clathrate stoichiometry, avoiding guest mole cule loss by diffusion and dissociation—the equilibrium dissociation . pressure of guest molecules must remain negligible. As well, since ice has very large 0-H extinction coefficients (VL^O) the samples must be thin— 3 microns or less. Deposition of water vapour or a gaseous stoichiometric clathrate mixture on a cold sample mount gives samples which satisfy some of these criteria (^3). The quantity of a stoichiometric gas mixture which can be prepared in a vacuum system is clearly limited by the saturation vapour pressure of H^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 17-53 Torr H20. If uniformly deposited on a typical window with a surface area of 7 cm2, 2.76 m moles of H^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 ratios for the 12 A cubic structure are 1 guest: 5..75. H^O and 1 guest: 7-67 H20, while the corresponding ratios for the tetragonal o and 17 A,cubic structures are 1 guest*8.6 HgO and 1 guest*17 H^O. Clearly the numbers of guest mmoles required to combine with 2.76 m moles of H20 are very small. Measurement of at best one-fifth of 2.76 (0.U8) mmoles of gas in 3.853 1 at 20°C is impractical due to the large error in measuring 51 small pressure differences. Gaseous guest aliquots were first isolated in a 0.1039 liter bulb and then expanded into the 3.853 liter mixing bulb. The numbers of guest mmoles and their pressures in the 2 bulbs are shown below for four clathrate structures. Clathrate mmole X Partial 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 liquid previously isolated and degassed in a side bulb. The system was equilibrated in that state for ten minutes before the liquid H20 was again isolated from the mixing chamber. Since the densities -of the gases in the bulb varied over the range from 17.3 x 10 g/cm3 for H"20 to 13.3 x 10 g/cm for Br2 and 6.30 x 10 g/cm3 for CH^Cl, the mixing was forced by heating the lower hemisphere of ;the chamber with an electric heating tape. Such convection mixing was' main tained for a minimum of 30 minutes before sample deposition. Suitably ; mixed gases were used either directly from the mixing chamber, for deposi tion in the isolated chamber of the metal liquid nitrogen cryostat, or were transferred to a portable 3.0 liter 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 if 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 (107) used for the high pressure ices. Preparation of a suitable spectroscopic sample required approximately 0.5h. A few grams of solid clathrate were placed in. liquid nitrogen in; a mortar at 77°K and ground manually for 10 minutes. A small portion of the sample was placed in the center of a mounted window and enough condensed liquid mulling agent was dropped on the sample to prepare a uniform suspen sion. A second window was placed over the sample and secured in place by a retaining ring. The window assembly was placed in 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 is most likely to occur during cryostat assembly. Blank runs, and runs; with mulling agent only, made it clear that little impurity absorption was found even for the most intense H^O stretching band [see also Whalley (107)]. Recalling that the transmission spectrum of a mulled sample can :be distorted from the idealized absorption spectrum, one can have confidence in the low temperature mull spectra only if distortion is minimized,by • attention to the particle size of the sample and the refractive index of the mulling agent. Whalley (107) found that even for the most intense R^O stretching frequencies, where reflectivity is greatest, the spectra; of5 mulls were in good agreement with those of thin films. 53 B. Isolated Chamber Condensation The sample chamber designed for approximate comparison of absorp tion intensities of clathrate-hydrates was described in detail in section 1.6 ( page 45). A typical run with this isolated 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 10-^ 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 left on but the sample cooling block heater was shut off, while liquid nitrogen coolant was added to the reservoir. Twenty minutes after the collector 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 in short bursts ;down the heated sample tube into the sample chamber which was held at 83°K . after the method of Barrer and Ruzicka (43). With the sample tube ;at . 3^30K and the sample tube heaters on, some heating of the stainless steel 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 sufficient localized heating to permit self-devitrification—diffusion of the guest molecules into clusters or diffusion out of the lattice completely. Subsequently, samples were annealed to temperatures between 160 -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 in the initial 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 in section 2.5. After recooling the sample block to 83°K, the sample tube heaters were shut off and the spectra were observed in the desired range. The specific instrument conditions are listed with the results. •: C. Open Chamber Condensation Deposition of gaseous samples on a cold substrate, which was-., exposed to the cryostat cell 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 directly from liquid H^O, D^O or H^O/D^O mixtures or were water/guest mix tures prepared as described in section 2.3. Cryostats were degassed by evacuation for a minimum of 10 hours before cooling with liquid nitrogen to 83°K. To ensure a minimum collector plate temperature, the source beam was blocked and the cryostat was allowed to equilibrate for 15 to 20 minutes. Typically, samples were deposited as follows. Ten ml of sample (at a pressure at 8.7 Torr), were isolated in the sample deposition tube. Several of these aliquots were passed in bursts onto the collector plate at 83°K. The cryostat vacuum jacket was isolated from the pumping station during sample deposition to minimize distortion of the sample gas stream. The HO v stretching region was monitored briefly after each burst ..to 55 determine the intensity of absorption. We estimated that the sample thicknesses ranged from 0.6u for very thin 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 Devitrification As was discussed in the introduction, deposition of water vapour on. alkali halide substrates held near 80°K has led to doubts of sample crystall-inity and confusion in the interpretation of the various ir results. The situation was clarified by Beaumont, Chihara and Morrison (65) through cor related heat capacity/x-ray diffraction studies. Their work accentuated the differences in sample crystallinity among the ir ice spectra of various authors (105, 106, 95, 97) and clearly demonstrated the processes of devitrification and transition linking the ice I allotropes. ; In order to make comparative ir studies of ice I and clathrate-.; hydrates as a function of temperature in this work, one had to reproducibly form the ice I allotropes. However, no attempt was made to restrict self-annealing by limiting deposition rates to that recommended by Beaumont et  al. — 0.04 g/h-cm^. That the samples did not undergo a high degree of self-annealing was demonstrated by the broad, featureless ir absorption bands observed immediately after deposition. Attention was initially directed to annealing condensed, vitreous samples to the common ice phase, hexagonal ice I, whose transition-tempera ture from cubic ice I lies between 200 and 250°K. The vitreous sample was warmed to the hexagonal transition at 5-0 to 12.5 deg/min from 83°K to 205 - 5°K (with the sample source beam off and no pumping in the sample chamber). It 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 this procedure. In view of the great difficulty with sample stability and the low rate of transition from cubic to hexagonal ice, further attempts to devit-rify at 205 ± 5°K were abandoned. Further extensive tests showed that thin films of H^O could be annealed under vacuum to 185 + 5°K from 83 t 5°K (at between 5 and 12.5 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 little loss of sample as detected by slightly diminished absorption. According to the data of Beaumont e_t_al_. (65) this should give a well developed polycrystalline cubic ice sample, since the transition temperature was well exceeded and the rate of transition is fast, :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 thin 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 is left until Chapter 6. : 2.6 Temperature Variation Methods The purposes of this work are to study the variations of ice and clathrate spectra as a function of temperature and to show that gas con densation and devitrification gives legitimate crystalline samples. The same sample heating and ir observation techniques were used for both vitreous and crystalline sample studies. : 57 All the samples studied.as a function of temperature were formed in either the glass liquid nitrogen cell or the liquid helium cell by the methods of section 2.4(c). The nitrogen cell was mounted only in the P.E. 421 and was used for preliminary observations between 83° and 200°K. The helium cell was mounted either in the P.E. 301 or in 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 cell was allowed to warm from 4? to 83°K by the natural heat influx after evaporation of the liquid helium.' Above 83°K the helium cell was warmed with N,-,(g) (293°K) passing slowly through the reservoir. The nitrogen cell was held at 4 to 8 constant tem peratures (± 3°K) for devitrification studies (at 83°K Ng(liq) was used and at higher temperatures 1-2 ml of N2(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 cell 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 devitrification as a check on the reversibility of absorption maxima shifts. CHAPTER THREE ICE I: EXPERIMENTAL AND RESULTS This chapter is comprised of four main sections. The first section contains the results from temperature variation studies of vitreous ice I— observations of the vitreous-cubic phase transformation. The second section contains the results from temperature variation studies of cubic ice I— observations of Av/AR for crystalline ice. The third section uses the results of sections one and two as an aid in assigning the> ice absorptions. The fourth section is a brief summary of the results. 3.1 The Vitreous-Cubic Ice Phase.Transformation The spectra recorded during vitreous-cubic phase transformations: exhibited diminishing oligomeric peak heights (I) and irreversible peak frequency and half-height width shifts. A. Experimental Two vitreous ice I (HgO) samples were prepared (by the method of section 2.U(c)) and observed in the glass liquid nitrogen cell (section l.h) Sample A was deposited on Csl at 82 - 3°K, warmed from 82° to l69°K in five stages over 105 min and was annealed to a maximum temperature of 185 t 3°K. Sample B was deposited on Csl at 8l ± 3°K, warmed from 8l° to l6l°K in 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 devitrifi 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 cell compensation was used, but the instru ment was purged with dry N^(g). The liquid nitrogen cell and the spectro photometer sample compartment were masked so that the sample compartment was also purged. B. Results of Devitrification Infrared absorption spectra representative of samples A and B are shown in Fig. 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 ilO cm "*") at the intersection of lines along the band sides, while shoulders were determined (to within il4 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 Devitrification on the Peak Maxima The vitreous H^O ice I absorption maxima are plotted in Fig. 3.2 as a function of increasing temperatures. Important parameters derived from these graphs are given in Table III.I. Although devitrifications of D^O ice and HDO bearing ice were not observed in detail, data from such samples, immediately before and after devitrification, are included in Table III.I for comparison to H^O data. In Fig. 3.2, the transformation temperature ranges are indicated for v^, and + v^,. Transformation was assumed to have begun at the onset of peak shift and was assumed to have finished upon reversal of peak shift direction. 4000 3000 2000 Frequency cm-1 i 1000 Fig. 3.1 Representative spectra of vitreous and cubic ices at various temperatures. - Top:.. . A....-, ..cryostat.. background at 83°K.. (compensated),. B - H20 ice Iy at 83°, C - sample B annealed to l85°K and recooled to 83°K (cubic ice), D - sample 'G at T°K, -and E -- cubic ice' CH20(5.9W HDO)) at 83°K; - Bottom: A - cryostat background, B - D20(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 2220 2230 33 30 3350 OA 1590 16IO 1630 1650 1570 32IO 3230 180-140 IOO 800 820 840 3145 FREQUENCY CM 3165 3370 3250 3185 -I Fig. 3.2 Shifts of H^O frequencies during the vitreous-cubic ice phase transformation and. subsequent behaviour of cubic ice. The full circles and triangles are from spectra recorded during warm-up from 83°K to l85°K. The open circles . and -triangles give the behaviour after annealing. OA H 62 Table III.I The frequencies of cubic and vitreous ice I at 82°K, their 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 Ic 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) vl 3191 ± (2372) 7 311*9 ± (2321) 7 -1+2 (-51) 120 - ll*5 0.25 (0.18) 3vR 2220 + (1617) 5 .2235 ± .(1635) 5 +15 (+18) 115 - 130 -0.11 (-0.11) 1660 ± 5 ; l60l+ + 5 -56 115 - 130 0.36 v2 1570 (1212) 1570 (1191*) (-18) (0,11*) V 81*6 1 ( -- ) 7 881 + :(66l) 7 +35 (--) 115 - 130 -0.19 (-0.16) VR 802 ± (600) 5 833 ± (627) .780 + 5 7 +31 (+27) 115 - 130 -0.18 (-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) (2392) •• 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 five important effects to notice: l) between 115° and l45°K the molecular modes shift towards lower frequencies while the lattice modes shift towards higher frequencies, 2) the reversal of peak shift direction, 3) the irreversibility of the devitrification transitions, 4) the large fre quency displacements between the same bands in cubic and vitreous ice I at' 82°K, and 5) the reversibility of peak shifts in cubic ice I. These effects can be seen in Fig. 3.2 for the v^(E^O) data. The fre quency was constant up to 125 i 5°K, and shifted irreversibly by 36 * 2 cm-1 to lower frequency between 125 t 5 and 142 t 5°K. The frequency attained a positive, 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 similarly during devitrification. However, all internal modes exhibited positive, and all librational modes exhibited negative temperature dependences after devitrification. (ii) Oligomeric H2O Absorptions In addition to all the expected vitreous ice I absorptions, weak ab sorptions were observed near the frequencies previously reported (115) for oligomeric HgO and D2O. Weak peaks (0.01 abs units) were found near 3690 cm-1 in H20 and 2720 cm-1 in D20 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 in Table III.II. FREQUENCY CM"1 3900 3700 3500 o.o-0.4-0.5-2900 2800 2700 2600 2500 FREQUENCY CM"1 Fig. 3.3 Oligomeric HgO and D2O absorptions in vitreous ice I at 83°K: l) vitreous H2O ice, 2) cubic H2O ice, 3) vitreous D2O ice, h) cubic D2O ice. The features were more or less accentuated depending on the deposition rate. 65 Table III.II Oligomeric HvpOCDgO) and V3 ir 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 is given in brackets. H20 (D20) Temperatur e of Observation, °K 82 85 94 110 125 140 -1 -1 -1 -1 -1 -1 cm cm cm cm cm cm V3 3692 3687(2724) 3689 3690 3690 — 3677 3658 3674 V 1 — 3637 3650 3647 — — — — 3640 • (iii) The Effect of Devitrification on H2O Half-height Widths A comparison of H2O spectra B and C in Fig. 3.1 (top) shows that the composite bands v3> + VT^' ^V2' ^VFJ an<^ ^VR' VR + VT^ are snarPer in cubic ice I than in vitreous ice I. Half-height widths for these com posite bands from the sets of H2O spectra (samples A and B) were measured as a function of temperature, Figs. 3.4 and 3.5. [The large scatter in the data arises from several sources: l) the choice of baseline (± 2 cm "*"), 2) the error in assessing I and TJ- I f°r intense .peaks (± 5 cm "*"), and 3) atmospheric attenuation or distortion of the V2 band.] The parameters are compiled in Table III.III. LLJ D h < LLJ Q_ LLJ h Az/ 2 150 -100-70 180 A A Az/ A O AAQ O 1,3, H- T AA • «4 o May 29 A May 30 200 220 ~i r 270 300 I ' 1 1 1 1 350 400 HALF-HEIGHT WIDTH CM"1 Fig. 3.H The shifts of H20 half-height widths for the composite H20 bands (vR, vp+vrp.) and (vls V3. VI+VT) during the vitreous-cubic ice transformation' and subsequent" to"'annealing. Solid circles and triangles are for the" uhannealed sample warm-up. Open 'circles and triangles are for the annealed sample warm-up. Az/2 (z/2/2z/R ) - A 50 -A ••..AO A *\o '• A .•j OO -•"" A A • -/ * ^ / O / 4/ / / A / / / -O May 29 A May 30 •• * A / •AAA O TO - 1 I "-T i --T—r 1 —1 1 1 1 280 300 350 HALF-HEIGHT WIDTH CM"1 g. 3.5 The shifts of half-height width for the composite H20 (v2, 2VR) hand during the vitreous-cubic phase transfor mation and subsequently for cubic ice I. Solid points were obtained during vitreous sample warm-up from 83° to l85°K. Open points were obtained from annealed samples. 68 Table III.Ill The half-height widths of the vitreous and cubic R^O ice composite bands at 82°K and their temperature dependences for cubic ice I. Composite Vitreous Cubic Difference Transition Band A J-/2 AvL/2 AvL/2 Temperature 82°K . 82°K 82°K . Range H20 cm -1 -1 cm -1 cm °K (v1, v3, vx + vT) 322 + 7 287 ± 5 -35 115 ± 5 - 130 + 5 (v2, 2vR) .350 10 365 ± 10 +15 115 ± 5 - 140 5 (VR' VR + V 220 + 5 195+3 -25 115 ± 5 - 150 + 5 During warming from 82°K the half-height widths of vitreous ice spectra shifted irreversibly over the transformation temperature range. Subsequent warming-cooling cycles showed that the cubic ice spectra half-widths shifted reversibly and that the vitreous and cubic data agreed above 150°K. There are specific 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 librational band Av35 appeared to increase with increasing temperature. Also, the half-height width initially increased during devitrification, although it was expected to decrease. Annealing effects on v^HgO) were not observed in detail, but the differences between vitreous and cubic ice at 83°K were measured. The data are 62.8 cm and 23.2 cm for vitreous and cubic ice. Also, the 69 absorbance of Vp(cubic), I = 1.285, was almost exactly double that of Vrp(vit.). The vitreous V^(H20) absorption features were: a peak at 212.8 t 0.5 cm"1'and faint 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 in 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 in the liquid helium cell (section 1.5). Samples C(l,2,3) were deposited at 85 1 3°K on Csl, warmed from 85° to l87°K in 9 minutes, annealed at 187 t 3°K for 2 minutes and were recooled to 84°K in 4 minutes. The resulting 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 in H20) were deposited at 83 t 3°K on Csl, warmed to 188 ± 3°K in 8 minutes, annealed at 188 ± 3°K for 4 minutes and rapidly recooled to 83°K. Samples Dl and D2 were then treated as in C above. During warming sets of P.E. 421 spectra were recorded for each sample under identical spectrophotometer conditions. The basic spectrometer con ditions were the same as those for samples A and B (section 3.1 a) with small variations. For example, HDO peaks were recorded at 20 cm "Vin or 2 cm "VdiVj and a 10 cm path gas cell (in the reference beam) was used with the Bodenseewerk unit for effective 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 fre quency reproducibility was only ± 3 cm 1 at l60° or h°K. Typical HDO spectra were shown in Fig. 3.1. (ii) Results of Warming Cubic Ice Containing HDO Frequencies, half-height widths and absorbances were obtained as in section 3.1(b). However, to inhibit 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 VQ^(HDO) frequencies- are slightly low. Baselines for absorbances and half-height widths were drawn from 3391* to 31^0 cm-1 for vQH(HD0) and from 2H80 cm"1 to 23^0 cm-1 for vQr)(HD0). (a) HDO frequencies. The behaviour of vr,TJ(HD0) frequency with in-creasing temperature is shown in Fig. 3.6. The data were derived from one set of spectra during a single warming period. Errors in instrumentation and in the methods of data evaluation limited the precision to t 1 cm 1. Pertinent parameters from Fig. 3.6 are compiled in Table III.IV., The low temperature limiting frequency was obtained by extrapolating the data to 0°K. Although the data are non-linear, they can be approximated by two straight lines—a low and a high temperature line. The low and ..high temperature frequency dependences were evaluated from these lines and the "freeze-in" temperature was chosen as their point of intersection. There is a slight 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 3260 3270 3280 3290 3300 280-60 -40-20 -> CD 200-^: CO 80 -CD CD 6O-CN CD Q 40-CD 20-D O IOO-^_ CD A C 80 -TEN 6O-40-20-O-•4 ^D(HOD) o this work ° Ford and .Falk • this work • Ford and Falk 24IO 2420 2430 2440 2450 CHOD) Frequency cm -1 Fig. 3.6 The shifts 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 VQJJ(HDO) and solid points represent VOD(HDO)- Data of Ford and Falk (100) is included for comparison. —1 H 72 Table III.IV The low temperature behaviour of the HDO stretching modes in the H20 and D20 environments of cubic ice I, vQH(HD0) v0D(HD0) Low Temperature Limit -1 cm 3263.5 - 1 2412.0 + 1 Ratio v0H/vQr) 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 Irregularities °K 45 : - 70 ^60 Behaviour of VQD(HD0) is shown in Fig. 3.6 and some parameters are compiled in Table III.IV. The comments made above concerning VQ^(HDO) apply equally well to v^(HDO). The peak and shoulder near 800 cm in the samples of DgO (4.0% HDO) [tracing C, bottom of Fig. 3.1] were assigned to HDO librations, vR(HD0) and vo(HD0) + vm(Do0) respectively. (For ease of notation v_ + v_ is designated R 1 2 n 1 v '.) Temperature variations of v (HDO) and V '(HDO) are shown in Fig. 3-7 ' R K n and some parameters are compiled in Table III.V. As shoulder positions are z/j Frequency cm-1 220 225 230 180-• 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 • • 40- • 0 0 • • 0 • - 0 • %gog • 20- • ^T (HzO) • a • - z/R (HOD)- i/Rl ( HOD) •• 1 1 O- 1 , , 1 -1 1 1 T • • 1 ui 1 1 1  1 1  1 1 1 1 1 800 8IO 820 830 840 850 86C vR Frequency cm-1 Fig. 3.7 The shifts of vR(HDO), vr'(KD0) and VT(H20) for cubic ice I during, warm-up. The librational shoulder vR'(HDO) is assigned as vR(HDO) + VT(E>2u)' Temperatures are uncorrected for source heating. 74 Table III.V The low temperature behaviour of the HDO librational modes in cubic ice I for dilute solutions of HDO in H2O and D2O. vR(HDO) vR(HDO) + vT(D20) Low Temperature Limit cm 1 823.3 ±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-Irregularities °K. 105 - 120 difficult to determine accurately, v ' data have a higher error than v„—in this case ± 1.5 cm Spectra and data were obtained as in 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 in the preceding section. Details of the plots are compiled in Table III.VI. h -1 Errors in Av.^HDO) (± 0.75 cm ) resulted from l) inaccuracies-in OH assigning baselines (± 0.005 absorbance), 2) errors in estimating 1/2 I for I = 1.0 absorbance (± 0.01 absorbance), and 3) errors in estimating.widths 280 60 1 40 20 > CD en CD Q 200H 80 j 60-40-20 • CD D O IOC-CD Q. 80-E 60H 40-20-o-20 • • i? AZ/o20(HOD) 30 * (HOD) OH 40 M [o] Sublimation • • Ford and Falk • o this work 50 60 Half-height width cm-1 Fig'. 3.8 The shifts 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 in H20 and D20 cubic ice I. vOH(HDO) v0D(HD0) ; Low Temperature Limit -1 cm 35.5 t 0.75 23.5 ± 0.75 Ratio AvQH/Av0D 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 AVQ^(HDO) obtained above 190°K do not extrapolate into those obtained at lower temperatures. h —1 Errors in AvQI)(HD0) (estimated to be ± 1.0 cm ) resulted from l) inaccuracies in assigning baselines due to an underlying 3v^(H,_,0) absorption (t 0.01: absorbance),, 2) errors in estimating 1/2 I for I = 0.70 absorbance (t 0.005 absorbance), and 3) errors in estimating widths (±0.5 cm-1). In both cases above the HDO 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 half-height width. Absorbance data (i) are plotted in Fig. 3.9 and the details are listed in Table III.VII. Normalization of the two sets of intensities was not attempted. Peak heights underwent a relatively smooth, continuous decrease from 28° to l'90°K. Data obtained with the sample above l'90°K indicate a sharp decrease in I as the sample sublimed. No estimate was made of cummu-lative sample loss due to sublimation during the whole experiment. A slight, concave discontinuity centered at 125°K appears in an otherwise convex curve for- -these data. The data appear constant below 35°K indicating I (v^(HDO)) varied by less than -0.24 x 10 absorbance/°K. Table III.VII 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 Irregularities °K 0.945 -O.69 x 10' -2.26 x 10 79 ± 5 130(?) . 0.540. -0.24 x 10' -1.07 x 10 76+5 125 200- [•] [•] o 150-LLI cr D < 100-UJ a. LLI h 50-O o I (z/ (HDO )) OD • I (zv (HDO)) OH ' o o f. o 0.2 0.4 0.6 0.8 I ABSORBANCE Fig. 3.9 The shifts 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 yield information on cubic ice I. (i) Experimental Five sets of spectra from five specimens were recorded on the P.E. 421 or P.E. 301 spectrophotometers in the liquid helium dewar. Details of sample composition and preparation are given in Table III.VIII. General H20 absorptions were: observed in samples E and F and their results were combined with those of cubic samples A and B. General D20 absorptions, were observed in samples H and I and their results were combined with those of sample C. Samples E, F, H and I were observed on Csl in the P.E-. 421. The v^HgO) absorptions were observed in a separate sample (G) with;, poly ethylene windows on the P.E. 301. c P.E. 421 function settings were again identical within one set pf spectra and as consistent as possible between samples. Specific conditions were given in section 3.1. Only small alterations in instrument purging, reference beam attenuation and optical wedge settings were made. The P.E. 301 was used in the I/IQ mode between 666 cm 1 and;l60,: cm 1 with Bodenseewerk purging and no evacuated reference cell. Spectra were scanned at 40 cm "Vmin. and recorded at 4.4 cm "Vdiv. Spectral slit widths varied but were usually less than 4 cm \ 4 Table III.VIII Details of depositing and annealing of H2O, D2O and HDO bearing ice I samples. Sample ;, 1 E H20 F H20(D20) G H20 H D20 I D20(H20) 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) 210 123 Length of warmup run (min.) 243 166 433 920 348 Co o 81 (ii) Results of Warming H20 and :D20 .Cubic :Ice I Frequency data were obtained as in section 3.IB. The sets of spectra were analyzed randomly with respect to temperature as in section 3.2A(ii). Each complete set of spectra was analyzed one band at a time. Because of the breadth of H20 and D20 bands, frequency data were accurate only to t 2.5 -1 cm (a) Fundamental H20 and DgO frequencies. The v-j frequencies are plotted as a function of temperature in Fig. 3.10 and some plot parameters are compiled in Table III.IX. From Fig. 3.10 and Table III.IX it is apparent that liquid nitrogen and liquid helium cell data (samples A - B and E - F) do not concur. - ...-.=_.•.• For v-^LVjO) no data were obtained between 51° and 83°K since a sudden slight rise in cryostat pressure (from traces of condensed residual 02 and N2) caused heat losses between the nitrogen shield 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 in 2 - 3 minutes, the pressure rise was sufficient to rapidly warm the helium dewar and sample block. The frequency variations during sample warming are plotted in Fig. 3.11 and some details of the behaviour are given in Table III.IX. For V1^2^ ^e neHum an<! nitrogen cell data agree reasonably well. For v^(D20) a high scatter of points did not permit evaluation of low temperature depen dence. No data was obtained between 51° and 83°K for the same reasons as with v^, a rapid pressure rise. Helium and nitrogen cell v2 data do not agree (Fig. 3.12). Details of the plots are given in Table III.IX. Data for three helium cell "samples and two nitrogen cell samples are plotted (including unannealed sample data at 200' o 150 UJ cr D <t IOO or uj n UJ 50 h z/ ( H O) 3 2 o o 82 3230 200 0 150 111 or D £ ,0°' or UJ o. UJ h 50-o-^3(D20) 24IO 2420 2430 FREQUENCY CM -i Fig. 3.10 The shifts of cuMc ice I during warm-up. open circles represent data from experiments between 83° For H20 the and l80°K on a Hornig-Wagner all-glass cell, are uncorrected for source beam heating. Temperatures Table III.IX The temperature dependences of cubic ice I H?0 and Dp0 vibrational absorptions. Low temperature Low temperature High temperature Freeze-in limit 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 V3 320*1 (3215 + + 2 5) 0.03 ± 0.03 + 0.17 ± 0.05 (+ 0.19 ± 0.0*0 70 + 10 Vl 3133 + 3 + 0.3k ± 0.03 65 + 5 3VR 2239 + 3 < -0.09 - 0.12 ± 0.03 70 + 10 v2/2vR 1562 (1605 + + h 10) < 0.1k (0.36 ± 0.10) v ' R 881 + 7 — - 0.19 ± 0.08 80 + 20 V R 832 + 5 — - 0.18 ± 0.06 75 + 10 VT 229. £ ! ± 0.75 - 0.102 ± 0.012 95 + 5 CO OO Table III.IX (Continued) Low temperature low temperature High temperature Freeze-in limit dependences dependences temperature D20 -1 " cm cm 1/°K cm 1/°K °K Vl + VT 2464 + 3 — 0.17 ± 0.05 80 + 30 V3 2413 + 4 < 0.06 0.13 ±0.04 100 + 20 Vl 2320 + 5 — 0.19 ± 0.03 70 + 10 3vR 1637 + 3 <-0.07 -0.11 ± 0.03 60 + 5 V2vR 1189 + 2 0.13 ± 0.03 0.08 ± 0.05 50 + 10 V 663 + 6 — -0.10 ± 0.05 100 + 10 VR 630 + 4 — -0.11 ± 0.04 65 + 15 CO Fig. 3.11 The 'shifts of cubic ice I v during warm-up. For R^O typical annealing run data are included for pre-and post-annealing behaviour (open circles and squares). 0_| , , — , II80 II90. I200 I2IO FREQUENCY CM"' Fig. 3.12 The shifts of in cubic ice I during warm-up. For comparison to the helium cell data, nitrogen cell 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-v2(D20) data were not obtained from the same set of spectra as the more intense and absorption data. Data relating the v frequency temperature dependence are plotted in Fig. 3.13 and important parameters obtained from the figure are listed in Table III.IX. For v (Ho0) , helium and nitrogen cell data are in good K d. agreement. Because the v band is broad the maximum was difficult 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 translational H20 absorptions is shown in Fig. ,3.lH. The peak frequency temperature dependence is given in Fig. 3.15. An irregular shift of 1.5 cm 1 occurs between 55 and 60°K and the frequency is invariant from 155° to 200°K. The details of the graph are listed in Table III.IX. 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 is 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 listed in Table III.X. ' (b) Overtone and combination frequencies. The (v + v^) data are plotted in Fig. 3.l6 and summarized in Table III.IX: One can see that the helium and nitrogen cell data agree. However, the data are too poor to permit an approximation of a linear low temperature dependence. Both the Ho0 and Do0 3v^. frequencies (Fig. 3.17) decrease with in-d d K creasing temperature at rates indicated in Table III.IX. Again the.helium and nitrogen cell data agree near 80°K. 88 280-60-40-20-200-80-60-z 4a "> 20-_l LU 100 80-00 LU 60-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 < rr 4OH; LU Q_ 20 LU 100 h-80-60 40-20 • ~I 8 20 8 30 o A 610 620 630 640 FREQUENCY CM -1 Fig. 3.13 The shifts of vR for cubic ice I during warm-up. For H2O Pimentel and Zimmerman's (97) data and liquid nitrogen cell data are included for comparison. 89 Fig. 3.14 The cubic ice I V^CH^O) band at 83°K and the background spectrum through the blank cell at 83°K. The feature near- 2l8 cm"! arises from a filter change. 200 z/ (HO) T 2 150-100-50 A4 1 A o- -T 1 r 225 220 ~* 1 1 230 FREQUENCY CM'1 3.15 The shifts of v-d^O) for cubic ice I during warm-up. The sample was mounted on a polyethylene window 0.25 cm thick. The cell 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 results. T 2 Description Frequency Feature -1 cm A peak <l6l B minimum 176.5 ± 1 C shoulder edge 193 ± 3 D shoulder edge 21k ± 3 E peak 229.6 ± .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 in Fig. 3.18 and summarized in Table III.IX. This band is a poorly defined shoulder on the intense v_ band and r\ thus could only be estimated to within ± 7 cm 1. Helium and nitrogen cell data are not in good agreement. Low temperature dependences could not be defined. , (c) H20 and DgO half-height widths. Data for cubic ice I (H20) were plotted in Figs. 3.k and 3.5 of section 3.1. The half-height widths of the composite stretching band and the composite librational band increased with increasing temperature. However, the composite (v0, 2vra) 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 50H o 200 (zf + z/T)(HzO) o0 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 FREQUENCY CM"1 Fig. 3.16 The shifts of (v + the nitrogen cell'data are included, uncorrected. v,p) for cubic ice I during.-warm-up. | For " ' . ., „ , Temperatures aire 93 280 .60 40 20 200 80H ~Z_ 60 40 \£ 20 CO 100 UJ 8°-1 LT C9 60 Ld Q 40 UJ 20 cr D a: L±J 60 Q_ •^r 40 O 2210 h- 20-100-80 60 40 20 i o 1610 O 3 v or O * V K A A 2220 o 2230 2240 3vR or 2250 -2+-R(D20) 8o o o I— 1620 1630 1640 1650 FREQUENCY CM Fig 3.IT The shifts of 3vR for cubic ice I during -warm-up. For H20 annealing data and data of Pimentel and Zimmerman (97) are included. Temperatures are uncorrected. 200 0 l5°H LU D h IOO-< Q: LU n ^> 50-LU h o-• O • (z/ + z/T)(H20) oa • o a • ° A Aa 8a ±A£A ii 1 1 : I I I I 1 1 | T 1 1 1 866 876 886 200 o I50-LU cr D h IOO-< LU d LU h 5CH o- —I i 650 A A A A * (z/ + z/)(D20) A A A A ^ I I 660 T T 1 r 670 FREQUENCY CM Fig. 3.18 The shifts of (v^ + v^) for cubic ice I during warm-up. Nitrogen and helium cell data are included for R^O. 95 3.3 The H20, DgO and HDO Ice I Absorptions at 83°K In this section are listed the details of the H2O, D20 and HDO vitreous and cubic ice I"absorptions at 83°K for comparison in Chapter h to the literature values. A. Experimental Typical spectra of vitreous and cubic ice were shown in Fig. 3.1: v,p(H20) was shown in Fig. 3.1*+. The samples, spectra and methods of treat ment were described in sections 3.1 and 3.2. B. Results at 83°K Vitreous and cubic ice I have the same skeletal absorption spectra (Fig. 3.1) but are easily distinguished in details of band structure, frequency and width. Frequencies observed for the H20, HDO and D20 systems at 83°K are, compiled in Tables III.XI, III.XII and III.XIII respectively. Results of previous workers are included for comparison. (i) H20 Absorptions at 83°K Spectra of vitreous and cubic ice I obtained in this work are in sharp contrast and•exhibit features not previously observed. The stretching band of cubic ice I is 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 \ (D20 data are given in brackets.) In contrast, vitreous ice I has very weak absorptions at 3686(2720) cm 1 and 36UO cm-1 in addi tion to a peak at '3253(2*+36) cm 1 and two poorly defined shoulders at Table Ill.Xl(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 v3 olig 3686 vw — v± olig 3640 vw — vl + VT ^3367 sh 3340 ssh 3350 shs (vx)3360 Msh 3321 (2) .3340 v3 3253 vs 3210±5 vs 3220±5 s (v J3210 vs 3260 3210 (4) 3224 (3217±5)* vl ^3191 sh 3149 ssh 3140 shs (2v2)3125 Msh 3088 (10) 3140 2220 w 2235 w 2266±20 vbw .2225 s 2250 2235 v? 1660 m 1570+10 m l650±30 vbw 1585 s 1580 (1604 5)* 1570 sh — — (1130 msh) *# 846 ssh 881 ssh 900 sh VR 802 s 833 s 840 s 850 850 846 — ^780 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. 108. ON Table III.XI(b) The translational lattice mode features of vitreous, cubic and hexagonal ice I. vT(H20) 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 limit 326 +3 33U ± 3 ^328 (330)* shoulder 301 296 295 293 300-310 (305) shoulder 271 267 259 257 ^275 (275) change of slope 2U6 ^2k0 peak 212.8±0.5 227.8±0.5 225 (ms) 223 m 229.2 229 change of slope 211 220 change of slope 197 200 shoulder 191 190 188 190 minimum 173 180.5 peak 162 15U (m) 152 l6h * taken from Fig. 3 of Ref. (97). (a) Ref, 89 (b) Ref. -95 (c) Ref. 97-Table III.XII 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 in D20 3304 m 3266 s 3277 ± 4 s 3275 vs 3270 ± 5 3300 V OD — (2442) wsh 2445 msh 2442 s HDO in H20 2437 m 24l6 s 2421 ± 4 s 24l6 vs 2418 ± 3 2440 (2392) wsh 2395 msh 2393 1975 s w ^2(HDO) 1490 s 1470 V + V R T — 854 wsh HDO in D20 VR HDO in D20 792 w 819 mw 822 ± 6 m 800 620 HDO in H20 515 i 10 m "(a) Ref." '95 (b) Ref. T0'6 '(c) Ref. 100 (d) Ref. 105. MO CO Table III.XIII The frequencies and assignments of D20 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 olig 2720 v olig — — vl + VT 21*99 ssh 21*65 21*85 ± 10 msh (v1,2v2)+2l+95 msh 251*2 (0.5) V3 21*36 s 21*13 21+25 ±5 s (v3) 21*32 vs 21*50 2l*2l* (3) Vl 2372 ssh 2321 2332 ±5 s 221*0 vwsh (vlS2v2)"2336 s 2291 (10) 3\ 1617 w 1635 1650 ± 30 1635 s 1630 v2 1212 m 1191* 1210 ± 10 1210 s 1210 M.2l*0 vR + vT ssh 661 675 sh VR 600 s 627 61*0 s 630 VR ~ VT 1*25 sh "(a)""Ref. 95 '(b) Ref. 106 (c) Ref. 98 (d) Ref. 99. VO 100 3367(21+99) cm-1 and 3191(2372) cm-1. For H~20 cubic ice. I, the liquid helium and liquid nitrogen experimental data do not agree at 83PK (Fig..3.10). •Two distinct values of v^HgO) are indicated among liquid helium /V''' experiments and some liquid nitrogen experiments. All helium runs ,and some nitrogen runs gave v2(83°K) at 1570 cm-1. A few nitrogen runs with thin samples gave v2(83°K) at l6oU cm-1. Atmospheric H20 absorptions may have attenuated the weak v2(H20) absorptions of thin samples. Ice samples annealed with care above 200°K showed two distinctions from those annealed below 200°K. The former gave spectra with a distinct shoulder at 1130 cm 1 (on the side of v2). As well, a deep minimum appeared between the 1130 cm 1 shoulder and the vR band. Pimentel's (97) spectra showed the same features although he offered no explanations for them. Inspection of the cubic ice I H20 vT band (Fig. 3.11+) shows, two peaks and three shoulders. However, Whalley's (87) theory showed that additional vT features yield important information on the densities of phonon states. Accordingly, ten features of v^(E^O) at 93°K were reported in Table III.X. In contrast, the vitreous ice I band had no low fre quency shoulder or peak. As well the 267 cm-1 shoulder was poorly defined. (ii) D20 Absorptions at 83°K DgO ice I has the same sets of spectral features as H20 ice I. Vitreous B^O ice spectra have a weak oligomeric absorption at 2720 cm 1 which has not been reported previously for ice. Oligomeric absorptions are absent in cubic D,_,0 sample spectra. As in E^O ice I, the stretching band shoulders are.better defined in cubic than in vitreous ice. The 101 problems caused by atmospheric H^O attenuations encountered in H^O ice I • were eliminated by more efficient purging. (iii) HDO Absorptions at 83°K Only three HDO absorptions were observed, the OH and 0D stretches and an HDO libration. In vitreous samples the three absorptions were broad, relatively weak and without shoulders. In cubic samples the v_„ band On had no shoulders, the v band had two shoulders and the v band had one OD n shoulder. No v^(HDO) absorption was observed near 600 cm"1 for HDO in H^O. 3.h Summary of Ice I Results A. Vitreous-Cubic Ice I Transformation 1. All HgO absorptions shift irreversibly in the temperature range 115 - lIt5°K; internal modes shift to lower frequencies while lattice modes shift to higher frequencies. 2. Above 150°K, vitreous and cubic frequency data concur and shift reversibly with respect to temperature. 3. Oligomeric H^O absorptions are absent above 125°K. U. Upon sample devitrification the absorptions are shifted, shar pened and better defined. 5. D^O and HDO absorptions appear to have the same behaviour as those of H20. 6. Composite-band half-height widths exhibited unusual behaviour in the case of (vQ, 2vp). 102 B. HDO in Cubic Ice I 1. Dilute concentrations of HDO in H^O and D^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 limits, linear low.and high temperature dependences and indications of irregular behaviour. 3. A new absorption was observed as a shoulder on v (HDO) and is K designated v^HDO) + vm(DJD) or v '(HDO). n Id n h. Internal mode cubic ice I HDO absorptions shift reversibly to higher frequency and lattice mode HDO frequencies shift reversibly 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 in creasing temperature. C. H20 and D20 in Cubic Ice I These results provided measures of eight H^O and seven D^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 ir 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 R20, D2O, and HDO vibrations and potential well. 4.1 The Ice I Vitreous-Cubic Phase Transformation The x-ray and electron diffraction experiments (58) indicated that the structure of the solid formed by condensing H2O 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 irreversible phase transformations indicated varying trans formation temperature ranges and degrees of crystallinity. The confusion with respect to vitreous, cubic and hexagonal sample formation is reflected in the variations among the ir spectra of various authors (95, 97, 98, 105). Bertie and Whalley (88,95) obtained spectra of mulled, crystalline samples (checked by x-ray diffration) and they criticized the use of a "recipe" such as that of Beaumont et_ al. (65). With ir observations Zimmerman and Pimentel (97) pointed out the need to devitrify solids condensed from the vapour. While they were the.first to detect the irreversible shift in the ir spectra between vitreous and cubic ice, they did not study the transformation in detail. 10k The transformation process was observed in this work in every ir absorption except v (H 0), but the results of the transformation for all H2O, HDO and D20 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 in vibrational 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, crystalline samples (95)-A. General Discussion Some general comments apply to all the HgO band maxima in their be haviour before, during and after the vitreous-cubic phase transformation. Between 83 ± 3°K and-120 ± 10°K all H20 band maxima had constant frequencies (Fig. 3.2). The absence.of frequency shifts is indicative of no changes in the degree of hydrogen bonding. Below 120 t 10°K the thermal kinetic energy was insufficient to allow molecular reorientation, softening of the glass, and hydrogen bond formation. The H20 band maxima all shifted irreversibly during the vitreous-cubic transformation. However, the data (page 62) indicated different, transformation temperature ranges for different bands: Ranges from 115 i 5° to 130 + 5°K and 130 ± 5° to IH5 + 5°K were found for vR and v± + vT. 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 in Fig. 3.2 show that vR was constant up to 100°K and was completely shifted to the cubic frequency at 125°K. 105 That indicates, on first 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 is incorrect. Specifically consider the positions of the data indicated by solid triangles ( • ) at 125°K in Fig. 3.2 for all six bands. The data were ob tained from one sample during one run at constant temperature. At 125°K the Vl + VT band- was unshifted from the vitreous frequency, the and bands were only slightly shifted, the 3vR band was shifted approximately one-half the total shift towards 3v cubic, the v band was shifted three-quarters the i\ d total shift and vR was completely shifted. .The amount of shift is propor tional to the time the sample was held at 125°K. In this work, spectra were, scanned from 4000 to 530 cm-1 in 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. If the transforma tion rate is assumed to be linear, then a plot of (v^ - v^^/Cv^ - vc)t _ m (where t is the time at 125°K and t = 00 is maximum annealing shift) against -2 -1 time in minutes gives the transformation rate at 125°K as 5.5 x 10 , min One concludes that the transformation temperature ranges listed;in Table III.I for v + v , v , v , 3v0 and v0 were artificially elevated,by X 1 3 1 K d the recording technique. The transformation temperature range for all bands must be consistent, 120 - 135 - 5°K (corrected for sample window heating). During the transformation the lattice modes v and 3v shifted irre-n R vers'ibly to higher frequency while the molecular modes shifted irreversibly to lower frequency due to large alterations to the intramolecular and inter molecular potentials'which occurred. The shifts of molecular modes, are 106 consistent with the formation of more and/or stronger hydrogen bonds. During the transformation the molecules attained sufficient thermal kinetic 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 libration and translation and increased the frequencies of those bands. After the irreversible shift had occurred, i^.e_. above 150°K, and during all subsequent warming-cooling cycles the spectra had a reversible temperature dependence: the lattice modes decreased in frequency and the molecular modes increased in frequency as temperature increased. The sample devitrification 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 orbital rehybridization) were measured for H20, D20 and HDO. If the frequency shifts between cubic and vitreous ice did rise from hydrogen bond formation, then the relative effects on H20, D20 and HDO frequencies should have been the same provided all the vitreous samples had comparable degrees of microcrystallinity. The frequency shifts would ideally be in the ratio Av^(H20) /Av^(D20) near 1.*+, where Av.^ v^(cubic) - (vitreous) for the i-th vibrational mode. Only the peaks and vR give reasonable agreement with the ideal ratio, i_.e_. 1.6 t 0,> 3 and 1.1 ± 0.30 respectively. All the other bands were poorly defined and the ratios range from 0.79 ± 0.5 to 3.1 ± 0.5 for v.^ + vT and respectively. A modified product rule AvjAv2(H20) /Av^Avg^giO) does not improve the ratio. For 4.00 % HDO in D20 AvR(HD0) = AvR(D20) = +27 cm-1, Av^HgO) ./ AvOTJ(HD0) = 0.94 and Avo(Do0) /Av--(HDO) = 1.1: None of these are ;in agree-On 3 uu ment with the ideal ratio. The ratio for Av (HDO) /Av (HDO) = 1.8 is much 107 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) is too large, Av.^HDO) is On OD too small (compared to pure H2O and D20) or both. However, since samples were not identically deposited, they would have had different degrees of self-annealing, and different frequency displacements from the cubic ice values. Each band will now be considered in turn. B. Fundamental Lattice 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 is understandable from the very different nature of the two solids. For example, since the positions of the atoms in a vitreous solid are ideally completely irregular, then forces acting on the atoms are irregular and the normal vibrations of the solid are also irregular (87). The resulting range of translational energy levels, and range of transitions among the levels, is very broad. Combined' wi£h the collapse of normal phonon selection rules (87), a very broad ir. (vitreous) band is expected and observed. In contrast, cubic ice I has regular, long range ordering of oxygen atoms, but irregular, short range ordering of the protons (orientational disorder). Whalley (87) has shown that the orientational disorder does not have a significant irregular effect on the mechanical vibrations of cubic ice, but that it does affect the; local electric oscillations. Consequently, one obtains a structured (cubic) band whose features are indicative of the crystalline state. It is suf-108 ficient here to compare our vitreous and cubic v^, data (83°K) to those of Whalley (88) and Giguere (89). Consider the v^, data given on pages 89, 90, and 91 of Chapter 3. That v^, (cubic), 227.8 cm \ was 7% higher than (vitreous) is 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 translation. These effects resulted from extension of hydrogen bonding closer to the limit (4 bonds/molecule), reduction of the mean 0 0 distance, and a change in the density in cubic crystals. However, in reality the explanation for the frequency shift may not be so simple. Formation of a well defined Brillouin zone in cubic samples may entail complex changes in the densities of states and selection rules from those of the vitreous sample. The half-height width of 'V (vitreous) was 62.8 an \ in sharp con trast to that of v^, (cubic) which was very nearly one-third of that value, 23.2 cm Increases in the densities of states at the Brillouin zone boun daries probably accounts for this dramatic change. That the peak height of ^ (cubic), 1.285 absorbance, was almost exactly double that of (vitreous) is probably due to two effects. The first effect is again the increased density of states in cubic ice I for ]c_ = 0 transitions. The second effect arises from the increase in oscillating dipole moments in completely hydrogen bonded lattices as compared to weaker dipoles in partially hydrogen bonded glasses. The Vj, (vit.) band of this work compares very well with Whalley's (88) vtj, (vit.) but not with Giguere's (89) v (vit.). The v^, (vit.) 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, 212.8 cm He did not list the positions of other vitreous band features and it is hard to determine if the difference is only due to calibration errors. [On the basis of the two sets of vT (cubic) features, the latter seems unlikely.] In contrast Giguere's (89) vT (vit.) band showed too much structure and suggested a largely crystalline sample. The present work supports Whalley's observations of v^, (vit.). For \> (cubic) the results of this work agree in general features with both Whalley (88) and Giguere (89). However the two peaks in:, the present work are nearly 2 cm 1 lower than Whalley reported, probably due to a calibration error. Whalley found that all cubic samples, either condensed from the vapour or formed under pressure and mulled, gave the same absorp tions. Since v observed in this work agrees with his results, one can conclude that the sample deposition and devitrification techniques used here gave legitimate cubic ice I samples with respect to v^. , (ii) The vR Transformation At 83°K vitreous ice vj^HgO) had two distinct and two faint features: a distinct peak (802 cm "*") and a distinct shoulder (535 cm "*"), and two faint shoulders (846 cm 1 and 675 cm 1). However, vitreous ice VR(HDO) and Vp>(Dg0) each had only a single feature. In contrast, cubic ice vR(H20) had five features (one peak and four shoulders) while VR(HDO) and vR(D2.Q) had two features each (a peak and a high frequency shoulder). The HDO high frequency shoulder, VR(HDO) + vij^DgO) , has not been previously reported. Changes in frequency and half-height width between the vp> bands of vitreous and cubic H2O ice samples were shown in Figs. 3.2 and 3.4 (pages 6l and 66) and the results of devitrification for vR(H20, D20, HDO) were given in 110 Table III.I (page 62). After the vitreous sample was annealed at 185 i 5°K for 2-3 minutes and recooled to 83°K, one found all the vR features had shifted to higher frequency and that three new features appeared. Precisely, vR(Hg0) shifted by +31 cm-1, vR(HD0) by +27 cm-1 and vR(D20) by +27 cm-1. As for vT, the vR shift to higher frequency may be simply understood on the basis of hydrogen bonding. Cubic ice has more and stronger hydrogen bonds than vitreous ice. The results are a deeper hydrogen bond potential, larger hydrogen bond force constants, increased.hinderance to libration and in creased absorption frequency. However, as for v^, complex changes in the crystal entail complex changes in the solid librations, densities of states and selection rules. The final explanation of v_ behaviour must combinevthe K changes in hydrogen bond potential with the lattice vibration theory. The plot of half-height widths (AvR ) of the composite band (vR, vR + vT) was shown in Fig. 3.h (page 66). It also indicated a "de pressed" vR transformation temperature range (115 - 130 ± 5°K). However, the low range may be explained as in section k.lA (page IO5) for v^ffreq.). One also sees that the behaviour of Av0 above 130°K did not conform to n the reversible behaviour of fully annealed cubic samples, i_*e_* the half-height width continued to decrease. Finally, on completing the annealing and recooling of the sample to 83°K, one found that the disorder broadening due to irregular 0 positions was removed but that there remained the orien-tational disorder broadening. The half-height widths at 83°K decreased in the following way: Ill H20 HDO D20 H20/D20 Av (vit.) 220 cm-1 88. cm"1 ^200 cm"1 1.10 Av (cub.) 195 51 140 "1.30 Av^cub.) 0.89 0.58 ^0.70 1.27 Av^vit.) The differences may be due simply to errors in determining baselines, inten sities and widths, or may arise from differences in microcrystallinity among the three vitreous samples formed. C. Fundamental Molecular Mode Transformations (i) The v2/2vR Transformation Absorptions between 1000 and 1800 cm 1 in H20 ice have been variously assigned to 2VR or v2- All previous workers (95,97 ,105 ,106,108) reported only a single feature in this range for both H20 and D20 ices (vitreous or cubic). However, Zimmermann and Pimentel's (97) Fig. 1 for cubic ice has shoulders at 1100 and 1530 cm-1 and a peak at l6l5 cm"1:. They treated the l6l5 cm 1 peak and 1530 cm 1 shoulder as one band centered at 1580 cm"1 (83°K) in cubic H20 ice. Most thick vitreous H20 ice spectra recorded in this work had two features, a peak at 1660 t 10 cm"1 and a shoulder at 1570 ± 20 cm"1. In contrast, cubic samples annealed below 190°K only had a peak at 1570 + 10 cm \ Cubic samples annealed to 205°K had a peak at 1570 t 10 cm-1 a shoulder at 1130 cm and a deep minimum at 1050 cm-1, much like Zimmermann and Pimentel's (97) spectra. While the final assignments of the bands are left 112 until section k.3 (page 175), it seems logical to consider the vitreous 1570 cm 1 shoulder and the 1660 cm 1 peak as being either v_ or 2v . Cor-d K responding features were not observed in vitreous DgO ice I. The reasons for shifts to lower frequencies, Av^CH^O) = .56 Cm 1 and AV^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 shifts for H^O and D^O, observed here, is not understood. In Fig. 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 Av2 had a negative, reversible temperature depen dence, -1.6k cm 1/°K. All other vitreous H^O, HDO and D^O bands were narrower after the transformation and subsequently broadened with increasing temperature in the cubic phase. The anomalous behaviour of Av^ (H^O) may be explained if the vitreous ice band is composed of a medium absorption slightly below 1570 cm 1 and a 2v absorption slightly above 1660 cm \ Although v and 2V,.. both must t\ d K narrow upon devitrification, their frequencies both shift away from 1570 cm 1 yielding a net broader v /2v band. For this explanation it is also neces-d a sary that the peak absorbance of 2v decrease in the cubic phase. The negative temperature dependence of the band results from the shift of a weak underlying 2vR to lower frequency (towards 1600 cm 1) and the shift of Vg to higher frequency (towards 1600 cm 1).with increasing temperature. As the two absorptions further coalesce, the composite band becomes narrower. However, the frequency dependence of the cubic band is determined by the more intense absorption. The Vg frequencies obtained for crystalline ice formed from the vapour 113 (this work, 97, 105, 106) do not agree with Whalley's (95) work. For all phases of ice Whalley found to be higher than 1650 cm-1. The results of this work support Ockman's (108) observations for samples formed from the liquid. Ockman's (108) reflection spectra indicated a weak maximum at 1600 cm 1. It is possible that Whalley's (95) mulling technique gave a different reflection spectrum than occurs for thin films and enhanced the high fre quency portion of his v^. His results showed the mulling agent decreased reflection and scattering compared to powder spectra. On the other hand, reflection and scattering may be severe for thin films. Finally, the weak shoulder and deep minimum (1130 cm 1 and 1050 cm "*") may have arisen from a strong Christiansen filter effect on the high, fre quency side of v . (ii) The v___ Transformations Din In the region from 3000 to 4000 cm 1 one observes the symmetric and asymmetric 0-H stretching frequencies from H^O molecules in various degrees of polymerization and the combinational absorption of with the lattice modes. The corresponding 0-D stretches are found betweeen 2000-2800 cm Data for and of H^O, HDO and D^O in the vitreous and cubic phases, were shown in Figs. 3.2 and 3.4 (pages 6l and 66) and were compiled in Table III.I (page 62). . , (a) The- shoulder. The low frequency shoulder (v-^) was very poorly defined (at 83°K) in vitreous ice (3191 - 15 cm 1) but was better defined in 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 shift of -36 cm-1 (AV^CD^O) = -23 cm ^~) . The explanation for a negative shift follows from above. (c) The HDO modes. The vitreous ice HDO absorptions were listed in Table III.I, v_n = 2437 cm-1 and vnri = 3304 cm-1. The cubic ice HDO fre-UD Un. quencies were shifted -21 and -38 cm 1 respectively from their vitreous values. Reference to Table III.I shows that these shifts correspond very well to the shifts of D^O and H^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 in an H^O or D^O lattice. There appear to be no differences among the couplings of HDO, HgO and D^O molecules for either vitreous or cubic ice I. Finally, the explanation for the direction of shift 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 positional disorder and proton orientational disorder contri buted to the widths. In cubic ice the 0 positions were ordered, but the proton disorder broadening remained. Even in the cubic phase the uncoupled HDO molecules had Av values about twice as large as expected for ordered solids. For example, Whalley (96) found Av (EDO) data of 8 - 13 cm-1 for an ordered high pressure ice. 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 dilute H / D isotopic substitution should be employable in rate studies of other disordered systems. (d) The oligomeric modes. All vitreous HgO and D^O ice samples observed in this work had very weak absorptions between 3600 and 3700 cm 1 in HgO (near 2620 cm 1 in D^O). Typical E^O peaks were shown in Fig. 3-3 (page 6k) and the frequencies were listed in Table III.II (page 65). These absorptions occurred quite close to the vapour phase monomeric frequencies. Shurvell (115) and Van Thiel et_ al. (117) studied the absorptions from dilute concentrations of H^O and D^O in various matrices. Van Thiel et_ al. assigned the (v^s v^) monomeric, dimeric and trimeric H^O (in an N matrix at 20°K) absorptions to (3725 and 3625 cm-1), (3691 and 35^6 cm-1), and(3510 and- 3355 cm ^) respectively. For D^O Shurvell reported (v^s v^) monomer and dimer absorptions for an matrix at (2765 and 2655 cm 1) and (2725 and 2650 cm 1) respectively. Our frequencies appear to rise from dimeric systems.• We observed half-height widths of 15 - 20 cm 1 which were slightly smaller than in matrix isolation, 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 in this work were stable up to the softening temperature of the H^O glassy matrix, 125°K. That corresponds to the temperature of onset of peak shift in other bands, i_.e_. the temperature of molecular reorientation. The high softening temperature is consistent with the increased van der Waals forces in molecular solids compared to1 rare gas solids. For example, Shurvell (115) observed that H^O oligomers were stable up to 80°K in a CCl^ matrix. 116 For this work, one understands that the softening permits short-range molecular diffusion and reorientation resulting in progressively higher polymerization. The monomeric, oligomeric and medium polymers disappear as well as their absorptives. The high frequency side of the vgTR hand was greatly sharpened. One can estimate the fraction of the sample which was in the form of dimers. In this work the ratio of absorbances for dimeric and fully polymerized H^O is 1 to TO. Work by Ikawa and Maeda (ll8) on the crystalline solid (complete polymer) and by Ferriso and Ludwig (119) on the vapour phase (monomeric H^O) showed that the extinction coefficients of monomeric and fully polymeric HgO are in the ratio 1 to 30. Thus one finds 1 part of monomeric-dimeric H^O to 2.3 parts of completely polymerized HgO. There re mains an unknown portion of the sample in intermediate stages of polymeriza tion. However, while this estimate seems to be very high, the point, is-that a considerable amount of oligomeric H^O and DgO sample was formed by our condensation technique. i (e) The Av35 of the band (v^ v^, v1 + vT). 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 ice. The band t sharpened irreversibly between 115 i 5°K and 125 ± 5°K by the specific loss of approximately 20% of the high frequency absorption. Such absorption arises from medium length H^O and D^O polymers with incomplete hydrogen bonding. In addition, the band sharpened by the increase of 0 positional 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 in HgO ice and near 1600 cm-1 in DgO ice has been variously assigned to 3VR andv2 + VR. Specifically, the H20 absorption had a single feature, a peak at 2220 or 2235 cm 1 in vitreous or cubic ice. The shift upon annealing was to higher frequency, and was also found for VR and VIJI. The nature of the shift was given in Fig. 3.2 (page 6l) while data was given in Table III.I (page 62). Cubic ice absorptions, 2235 and 1635 cm"1 for H20 and D20 (at 83°K), agreed very well with the single crystal observations of Ockman (108), Table III.XI. As well, Haas and Hornig's (106) and Giguere and Harvey's (98) re sults were comparable. However, Whalley's (95,96) results were consistently higher. As for v2, the differences in Whalley's results may have arisen from changes in the reflection spectrum caused by the mulling agents. The shift by + 15 cm 1 (for H20) to higher frequency upon devitrifi cation may provide a clue to the origin of this band. If the band is V2 + VR then one would expect the shift A(v2 + VR) to be proportional to Av2 + AVR = (-56 + 31) = -25 cm 1 for H20. If the band is 3VR then one. would expect A(3VR) to be proportional to 3(AVR) = +93 cm-1. The observed shift to higher frequency by +15 cm-1 in H20 and +18 cnT^ in D20 supports the 3VR assignment. Finally, the 3VR results suggest that our cubic sample formation technique is adequate since the results are consistent with results from crystalline samples prepared from the liquid, i_.e_. the results of Ockman (108) and Giguere (98). 118 (ii) The (v + v ) Transformation The high frequency shoulder (v + v ) was very poorly defined in vitreous ice, but was well defined in cubic ice. As for other molecular modes, (v + v^) shifted irreversibly towards lower frequency (-27 cm 1 for HgO and -34 cm 1 for D^O) between 130 and 145 i 5°K. Comments made above with respect to the origin of the molecular mode shifts and the temperatures of transformation also apply to (v + v ). E. Confidence in the Cubic Ice I Samples Does devitrification provide a good cubic sample of icel? Beaumont et al. (65) found that the vitreous-cubic transformation took only a few minutes to finish even at 150°K. As well they found that vitreous ice transformed cleanly to cubic ice. On the other hand, Dowell and Rinfret (74) estimated only a 30 per cent conversion to cubic ice and an average -cubic o crystallite size (embedded in 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 al. In fact they estimated the ,heat of cubic-hexagonal transformation to be less than 1.5 cal/gm. ; If the samples in 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 ice. Only one stretching peak was observed and the bands matched very closely the spectra of hexagonal ice I (95)- These facts support Beaumont's interpretation of the vitreous-cubic transformation. 119 . The evidence suggests samples prepared in this work were transformed fully to cubic ice I. The presence of significant amounts of residual vitreous ice would have broadened the stretching bands asymmetrically, giving a tail on the high frequency side. The half-height widths and band shapes of spectra in Fig. 3.1 compared very favourably with spectra of hexagonal ice I formed from the liquid. Deposition rates in these experiments lie near the maximum set by Beaumont et al. (65) —0.0k gm/cm^/hour. Assuming a v-^HgO) extinction coefficient of lkO for hexagonal ice I (119) the sample thickness was 0.5 --h 3 1.0 microns. The volume of ice I sample was at least 1.4 x 10 cm . At a density of 0.924 gm/cm^ one had a minimum sample of 1.3 x 10 gms.• Such samples were applied in two bursts, of two seconds duration each, onto a window initially at 83°K. By assuming a 1.0 crn^ image, the rate of- deposi tion was at least 0.04 gm/cm2/hour. -k During the deposition, 1.3 x 10 gms of H^O vapour release 0-09 cal (assuming the heats of sublimation of amorphous and hexagonal ice Ir are the same). There was sufficient heat of condensation to induce localized heating and to permit diffusion of individual molecules. The extent of heating and diffusion, or the amount of self-annealing, depended on the rate of; dissi pation of heat at the window-sample surface. Several attempts, under various conditions, were made to form hexagonal ice. However, all attempts to anneal samples above 210°K led to almost instantaneous sublimation since the samples were uncovered. Such sublimation has also been the experience of other workers (120). The extensive sharpening and alteration of the bands between vitreous and cubic ice I was due to two effects. The first was the diffusion and 120 reorientation of individual molecules into lattice sites in the cubic unit cell. The cubic unit cells put all molecules in the same electrical en vironment, but where the mechanical vibrations were broadened by asymmetries in proton orientation at equivalent unit cell sites. The second effect was the extension of low, medium, and high;polymer H2O clusters of the vitreous phase into fully hydrogen bonded networks of the cubic phase. During the process of crystallization the clusters amal gamated into larger units where the deformed or absent hydrogen bonds at the contact surfaces between clusters (or crystallites) represented only a small fraction of the total number of hydrogen bonds. • h.2 Temperature Dependence of Cubic Ice I Absorptions 1 Accurate measurements of shifts in frequencies and half-height widths in H>>0, D20 and HDO spectra between h°K and 200°K permit accurate correla tions of the shifts to changes in R(0*••-0) and changes in hydrogen bond strength. In this section values of R(0,-,*0) for cubic ice I are calculated over the range 10° - 200°K and plotted against v.TJ(HD0) and v.^(HDO') . , That On OD plot is compared to the predictions of an empirical equation which relates v^(HDO) to R(0 0). In addition, values of <TT(HD0) and X^TT(HD0) 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 limits and temperature dependences of all the absorption bands. The low temperature limiting frequencies were obtained by extrapolation to Q°K simply as a matter of convenience. The individual frequencies had virtually the same values when extrapolated to 5° or 0°K. There is 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 limiting frequencies, half-height widths and peak heights are for E^O molecules at the distance of minimum approach. The' 0-,,,H potential is deepest and the 0-H potential is shallowest. The conditions at minimum approach permit the largest orbital overlap and degree of hydrogen bond covalency, the largest electrostatic effects, and the largest contri bution of CT. As well, the low temperature limiting frequency gives the 0 -> 1 energy level spacing for minimum root-mean-squared (RMS) amplitudes of HgO translation and 0-H vibration. Finally, the contours of the;bands are least distorted by hot bands and vibrational perturbations of the , potential. :.< As the temperature was raised the ice I sample expanded, giving; increasing R(0-,,-0) and resulted in the weakening of the 0-*-,H bonds and a strengthening of the 0-H bonds. Hence the lattice 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 lines. The, lines 122 corresponded to regions of slow and fast crystal expansions. Below 50°K the effects of AR(O'--'O), changes in RMS amplitude of translation and hot hands (v = 1 -> 2) were small. Finally, some irregularities or discontinuities in the temperature dependences indicate possible changes in the solid phase or changes in energy level populations. (ii) Dependence of HDO Frequencies on Temperature (a) v (HDO) and v '(HDO). A full discussion of the origin and nature n K of the librational modes is given in 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 vm hot bands should have been negligible. Above 55°K, however, v and v hot bands, may have contributed significantly to the changes in band frequency, width and height. For v (HDO) (Fig. 3.7) one saw an apparent discontinuity between 105° n and 120°K. The change in slope may have arisen from significant population of molecular mode hot bands. The "hot" molecules would be decoupled from the remaining lattice molecules, and would have weaker hydrogen bonds. Consequently, smaller librational frequencies would be seen. (b) vrtTI(HD0) from h.00% HDO in Do0. The shallow molecular potential On d is demonstrated by the low temperature limiting v (HDO) frequency, i.e. On 3263.5 cm-1 at 0°K compared to 3268 cm-1 and 3288 cm-1 at 80° and l80°K respectively. The HDO frequency-temperature plot (.Fig. 3.6) showed unambiguously that the frequency shift was continuous and non-linear in the high and 123 low temperature approximations. Since there is little point in doing a least-mean-squares fit to some arbitrary function, the data were approximated on a bilinear basis. Up to 45 * 5°K v (HDO) was constant within the random On point scatter, + 0.T5 cm Within the sensitivity of the experimental technique and the spectrophotometer, changes in v (HDO) due to changes in un R(0"*'*0) and the effects of v combination bands with translational hot On bands are insignificant 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 definite effect due.to.in creasing R(0---"0), the shift of frequency exceeds the point scatter. .Thus the thermal expansion data of Brille and Tippe (60) suggest that when o AR(0 0)> ±0.0001 A/°K significant changes in v.^HDO) occur. On Linear high temperature dependence was assumed for v (HDO) between On 80° and 190°K, i_.e_. +0.200 t 0.005 cm-1/°K. Data of this work are in good agreement with the data of Ford and Falk (100). Their data were shown in Fig. 3.6 and were obtained from the best straight line through their Fig. 2. One sees that the steadily increasing R(0*--,0) in a cubic ice lattice yields a steadily increasing v (HDO) frequency. The specific dependence On of vQH on R(0--'-0) is given in the following section•(page 1371. ; • There was a slightly irregular shift of vOTI(HD0) between *t5°K and On , /' 70 K in Fig. 3.6. The irregularity may Have been due to a partial order-disorder phase transformation predicted ib be near 60°K by Pitzer and , Polissar (70). However, they pointed out probably greater than 2h hours. That peiiod is far in excess of our very that the period of transition was rapid cooling time of 15 - 20 minutes. P. a order-disorder phase transfor mation is also unsupported by any compara'lle shift in half-height width. 121* Alternately, the irregularity 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 in ice 1^ was not indicated by heat capacity experiments (82), although C„ had a slight irre-gularity near 80°K. The ir irregularity represents only 1 - 2% of the total frequency and is probably undetectable in Cp experiments since molecular modes contribute little to Cp. (c) VQp(HDO) from 5-9^% HDO in H^O. The general comments made above with respect to VQJJ(HDO) apply as well to VQ^HDO) : However, there are differences in details. Specific differences can be seen in Fig. 3.6 and Table III.IV (pages 71 and 72). The low temperature limiting vQD(HDO) fre quency was 2412.0 - 1 cm The ratio of HDO frequencies, v^/v', is Un UD 1.35^ - 0.001. That ratio is the same as reported by Whalley (96) for ices I, II and III and is very close to the vapour phase ratio of 1.360. From the ratios 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 it is 23% larger than in the vapour phase. This does not mean the anharmonicity is independent of temperature as is shown in the next section. . The temperature dependence of VQ^(HDO) was different from that of v^^XHDO) in several ways. The v__(HD0) data were constant within the point Un UD scatter up to 30 t 5°K in contrast to 45 ± 5°K for v_„(HD0). The low Un 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 UD Un I.626 times higher, 0.200 cm~'1"/0K). The differences in the high temperature dependences probably arose from differences in the physical properties of 125 the two mediums. The v data are from HDO in DO while the u „ data are On d OD from HDO in HgO. Consider the percentage shift from the low temperature limiting fre quencies for the asymmetric stretches in HDO, D^O and H^O, T _ 0 percentage shift = VSTR VSTR x 100 v STR T where v is the stretching frequency at temperature T, bin and v^mT3 is the low temperature limiting frequency, bin One might have expected in H^O and D^O to shift by the same percentage of the low temperature frequencies. However, between 10° and l60°K the —2 -2 shifts of H20 and DG0 increased from 0.6 x 10 % to 82 x 10 % and 0.0$ to _;2 36 x 10 % respectively. The stretching frequencies do not shift propor tionally. The shifts of v.^CHDO) and v (HDO) are not proportionally the un uv same, nor do they compare to the percentage shifts of in H^O and D^O. The VQ^(HDO) shift was faster than for v^D^O) at all temperatures,, while the vOIJ(HD0) shifted proportionally faster than v_(HO0) only below 100°K. On 3 d The percentage shift from the low temperature limiting frequencies were: Temperature °K Percentage Shift x 102 VOH' (HDO) vQD(HD0) v3(H20) v3(D2( 20 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 .0 100 23 .6 26 .1 21. .2 11 .6 20 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 .9 200 89 .2 81+ .2 — — 126 Dantl (6h) found the thermal expansion coefficients for H20 and D20 lattices were the same above 120°K. Hence, differences in AR/AT seem to be an unlikely source of the dispersion. The difference in temperature depen dences may arise from differences in HDO coupling to H20 and D20 lattices.. If HDO coupling to D20 decreases faster than to H20 then the OH (HDO.) hydrogen bond to DpO must weaken faster and the vOTI(HDO) frequency must shift faster On than vQD(HDO). The v (HDO) data are not in as good agreement with the data; of^ Ford and Falk (100) as for v_„(nT)0). Again their data are from the best Un straight line through their Fig. 2. The v slopes agree but their.data are displaced 2 cm 1 to lower frequency. This is probably due to differ ences in instrument calibration. (ii) 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 rela tionships were proposed (28,29,32) by neglecting specific differences in molecular properties. The empirical relationships give only an average v /R(O--'-O) behaviour. The HDO frequencies observed in this 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 directly as a function of R(0*,-*0). One requires the variation of R(O----O) in cubic ice I as a function of temperature. A detailed study of the temperature dependence of the lattice para meters of cubic ice I has not been reported in the literature. However, the 127 cubic ice I lattice parameter was given by Wyckoff (62) for lU3°K, o o ao(H20) = 6.350 ± 0.008 A and ao(D20) = 6.351 - 0.008 A. For hexagonal ice I, Brille and Tippe (60) made a detailed study of the lattice parameters between 13° and 193°K: aQ, cQ and the linear thermal expansion coefficients were evaluated every 20° from 13° to 193°K. In addition, x-ray diffraction (58) and ir (95) studies indicated that the nature of the hydrogen bonding and the nearest-neighbour configurations are the same in hexagonal and cubic ice I. On that basis we assumed the linear thermal expansion coefficient of cubic ice I (aa,o^' ) "to be the average of the expansion coefficients of hexa-, hex hex gonal ice I (ctao (T) + cxcQ (T)), _i.e. cub/ x 1 / hex, , hex aa (T) = 2-(cxa0 (T) + ac0 (T)) at temperature T.. cub Values of aaQ (T) were determined every 10°K in the interval 10° to 200°K by the following method. Brille and Tippe's (60) ten aQ and cQ para-hex meters were plotted as a function of temperature. Twenty values of aaQ (T) hex no and a.c0 (T) were determined at ten temperatures between 20 and 200 K, two values at each temperature. The pairs of coefficients at each temperature were obtained from intervals of 2° above and below that temperature, JL.e_. aheX(l50°K) = I[aheX(l48°-150°) + aheX(150°-152°)] a0 2 aQ aQ In the same way ac^X(T) was evaluated. From the ten values of ^ao^T1) and CCQX(T) , ten values of were obtained, Fig. h.l. Using Wyckoffs (62) aoUb(H"20) at l43°K (6.350 A) and the linear thermal expansion coefficients in Fig. U.l, the cubic ice I lattice para meter aQUb(T) was calculated every 2°K down from lh3° to 10°K and every 2°K up from lh3° to 200°K, aQUb(T) is shown in Fig. h.2. [Since the a^tn^O) and a^ub(DQ0) lattice parameters were the same within experimental error, 60 -1 50 -40 -30 -20 -10 -O i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1——i 1 1 O 50 100 T50 200 TEMPERATURE°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 Brille and Tippe (60). ^ CO 200H 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 CUBIC ICE i ! Fig. k.2 The cuhic ice I lattice parameter as a function of temperature. The values were calculated from the experimental aQ at l43°K and the calculated thermal expansion coefficients. 130 only the a^^CHgO) parameter vas evaluated.] For the cubic ice I unit cell the distance R(0 0) = ( J$~t'/k)a^°{T). The resulting cubic ice I 0 0 distances are plotted in Fig. U.3 as a function of temperature. HDO stretching frequencies from section 3.2A are plotted as a function of R(0**'-0) in Fig. 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 linear function of tem peratures. Both the v^„(HD0) and v^(HDO) plots were linear from 150° to 200°K: Un 01) Av (HDO) — — = 1.921 x 10J cm AR(0 0) I and AV0D(HD0) 1 pfll in3 -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 in Dg,0. There is no experimental evidence to suggest that the linear thermal expansion coefficients of the HgO and D20 ices are different. However, it may be incorrect to assume the same behaviour since the amplitudes of trans lation, libration and vibration are different. From Fig. h.k one sees that the frequency—R(0,,,*0) dependence is also linear between 30° and 100°K: 250 200H 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 Fig. 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 ro o 00 C\J ro O CM ro O CO CM ro oo CvJ OJ 30i oiano (o --o) d Fig. h.k The HDO stretching frequencies in cubic ice I as a function of R(O--'-O). 'Frequency and R(0-••*0) were correlated at common temperature. 133 • ^ = 8.202 x 103 cm"1/! AR(0 0) Av0D(HD0) 0 = 6.629 x 10 cm /A AR(0 0) Below 30°K the frequency shift was negligible. Between 100° and 150°K the frequency—R(0'*'*0) dependences were non-linear. The points of inter section of the low and high temperature linear 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 arising from orientational disorder was only a few hundreths of an angstrom. The tangent to v.u(HD0) vs. R(0""0) at 100°K in Fig. 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 well, Whalley (96) found that the most intense v (HDO) bands for OH ices II, III 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 ice I vriu(HD0) Un (3272 cm were caused by larger 0''*'0 distances. Specifically, the most intense v (HDO) absorptions in ices II, III and V had R(0'"*0)'s larger Un o than cubic ice I (100°K) by 0.008, 0.007 and 0.012 A. Ice II also had two other v„u(HD0) absorptions (3357 and 3373 cm ^) which suggest two other Un 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 II appears to have three dis tinct O 0 bond lengths, 2.756, 2.761 and 2.763 A. 13h Ice III had one additional peak at 100°K, 3326 cm 1. That could be due to a second distinct '0*••*0 distance, which is longer than R(0 0) o cubic by 0.008 A. Thus ice III 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 is not certain. The estimates of RCO-'-'O) above are only approximate. At 0°K the half-height width for v.^CHDO) in Do0 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 in 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 for an ordered phase (96), then the deviations in R(0-••-0) arising from orientational disorder were less than 1/2 the above values, o ± 0.002 and ± 0.011 A for 0° and l80°K respectively. Similarly by using Av0r>(HD0) and. AvQD/AR one finds dispersions in 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) in H^O and D^O are equal but the changes in force constants are related by approximately 1 y~2. Clearly one does not expect the HDO frequencies to be a linear func tion of R(0*•••()) over all values of RCO'-'-O). If the hydrogen bond is truly partially electrostatic and partially covalent in nature then the strength of the hydrogen bond should increase as (l/R(0'••*0)1^as temper ature is increased. Correspondingly the covalent nature of the bond will 135 change non-linearly. The effects of such changes in hydrogen bond strength are seen in the observed non-linear behaviour and in the four-fold in crease in Av/AR. (b) Comparison of observed and empirical Av/AR relations. The detailed study of vr.tI(HDO) absorption as a function of temperature and its On correlation to R(O----O) permitted detailed checks of empirical relations between stretching frequencies and hydrogen bond lengths in ice I. Many workers (27,28,33) have made correlations from data of large numbers of compounds in different hydrogen bonding families. The linear relationship of Pimentel and Sederholm (28), satisfies neither the behaviour of Av/AR in a family of O-H'-'-O compounds as Nakamoto et al. (27) found, nor the behaviour of ice I as was shown in Fig. k.k. Recently Bellamy and Owen (33) gave a formula relating the frequency shift (from the monomeric frequency) to a maximum effective hydrogen bond length and the measured 0,*'-0 distance: = k.h3 (103) (2.8U-R) cm' -1 Av str = c [(f)12- (|)6 ] where Av str shift of the stretching frequency from the gas phase value, d the sum of the collision radii of two oxygen atoms o in Angstroms (d = 3.35 A), R the 0*-,'0 distance in Angstroms, and C the constant of proportionality between the potential and the frequency shift. 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/± VQH(HD0) of the vapour phase (3757.5 cm "*") and the cubic ice I values (10°K 3263.8 cm-1 and 130°K 3276.8 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 = 2,263 cm /A. Experimentally Av/AR = 7,360 cm /A from 2.7^70 A O n O O to 2.7U80 A (10° 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 fails. Bellamy and Owen (33) started from the Lippincott-Schroeder potential and made certain assumptions about the intermolecular interaction. The Lippincott-Schroeder potential (25) consists of four terms, one term being 137 0< 2.755-o 6 *—* o LU 5^ 2.750 2.746-• — 200°K 150 °K mu* IOO°K ^500K A '-IO°K 3260 70 80 90 FREQUENCY CM Fig. 4.5 The stretching frequency—R(O----O) dependence. The observed frequencies are plotted against the' R(O-'--O) distances esti mated for cubic ice I from hexagonal ice I linear thermal expansion coefficients and are indicated by solid squares (•). The predicted Av/AR behaviour based on Bellamy and Owen's formula are shown as circles 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 filled orbitals was similar to that of non-polar spherical atoms. Bellamy and Pace (32) suggested that if the van der Waal's repulsion originates largely in the lone-pair/lone-pair repulsions of the two oxygen atoms then the 6-12 provides a good distance/ energy relation. The relation between the potential energy and the frequency 138 shift was assumed to be linear. From our results 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 in the lone-pair/lone—pair repulsions below 130°K, or that some complex change occurred in the system. The depopulation of Av . hot bands below 130°K is an unlikely source of the discrepancy since that would have resulted in a shift to higher frequency as temperature was lowered, in opposition to the observed increase in shift to lower frequency. It is possible that the 0-H stretching amplitude affects the strength of an individual hydrogen bond (and hence the frequency shift) by increased modulation of the potential energy as temperature increases reaching a limiting value at 130°K. However, the experimental amplitudes (5) continued to increase above 130°K and did not reach a limiting 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 it increased by 0.028 A. On the other hand, that does not . mean that the modulation of the potential energy did not approach a limiting value. The Bellamy and Owen (33) formula reproduced the Av/AR results for a large number of molecules observed near 300°K, while our results were ob tained below 200°K. One is tempted to look for a property common to all samples above 130°K. Such properties may be the population of translational 139 hot bands and large amplitudes of translation. Molecular translation would modulate the 0-**-0 distance and hence the hydrogen bond energy. Larger amplitudes of translation would result in increased modulation of the poten tial, weaker hydrogen bonds and smaller shifts. If the translational ampli tude modulation increases from 0°K to a limiting 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 in all molecules.-(c) The HDO anharmonicity (X ) and the HDO harmonic frequency (.<*>_.„) OH. On and their dependences on temperature and R(0*'"*0). According to Kibler and Pimentel (l2l) the anharmonicity XOTI of HDO in the vapour phase, is . On 91.2 cm \ For cubic ice I Haas and Hornig (106) predicted X (from On overtone data) to be 125 cm 1 while Bertie and Whalley (96) estimated it to be 100 cm 1 (by a modified product rule). While Bertie and Whalley.'s (96) estimate was very approximate, the point is that the anharmonicity increases only a little from the vapour phase. Since we did not observe the first overtone of v-^HDO) (near 6200 Un cm ^) the HDO anharmonicity must be estimated by the method of Bertie and Whalley (96). •, Application of free molecule theory to solids, particularly hydrogen bonded solids, is suspect but the method yields useful qualitative infor mation. For a free, bent XY2 molecule one finds that ; vl = ul ~ 2X11 ~ X12 " X13 v2 = u2 - 2X22 - X21 " x23 v3 = o>3 - 2X33 - X31 - X32 . iko If X. . (i ~f j} are assumed to be small and are neglected then Vl = <°1 - 2X11 ' v2 = co2 - 2X22 V3 = "3 ~ 2X33 -For isotopic substitution one can employ the Teller-Redlich product rule i i i p = a i> e . over 1 symmetry representation . wa u>b we and by analogy to the diatomic case one also knows that x1 11 Ai i lilt Id For of H20 and D^O the application is straightforward since v^ and v2 are of a^ symmetry while v^ is of bj symmetry (assuming the C2v point group) Then ' • » ' ^- and p. - \ ±f - > . Hence, one can write for HgO V3 = W3 " 2X33 " x " 2 and for DgO v3 = ^3 ~ 2X33 = p(°3 ~ 2p X33 By assuming that p of the vapour phase (say from Nibler and Pimentel's harmonic data) applies also to the solid and by using the observed H20 and D20 frequencies, then the two equations can be solved for w? and X-^ of ice I. lUl For HDO the prohlem is more complex. The strict product rule would he VOD^HODV^X hdo P = • U1U3M2VTZ\ H2° Even by assuming that the librational and translational force constants approach zero and the frequencies approach zero (which they obviously do not), the product rule is still complex "OHWHOD W1W3W2 As an approximation we can treat the problem as a diatomic molecule H -(0D) with the isotopic analogue D-(OH). Then the product rule is W0D P = "OH The expected value of p is given by 1 W0H IG _ - r MD + tm0 + MH' 1 "OH II mH + (mQ + mD) = 0.T2T8 . From the vapour data of Nibler and Pimentel (121) one finds p= 0.'726l. Briefly the method of Bertie and Whalley (96) involved assuming such a modified product rule for HDO, where P W0D(ice) uQD(vapour) cjjQH(ice) <u (vapour) and OD 2 X— = p X0H 1U2 Then v OH OH - 2X. OH and ' v OD OH - 2p2X, OH where p = O.72608 of the vapour phase. The anharmonicity of the HDO stret ching vibrations in ice I was then given by Hence the anharmonicity can be determined as a function of temperature between 10° and 200°K. The harmonic HDO frequency and the HDO anharmonicities cal culated in this way are shown in Figs, 4.6 and 4.7 respectively. While the magnitude of the calculated anharmonicity is not accurate, the trend in Xou(T) indicates some fundamental changes in the hydrogen bonded system. Be-On tween 10° and 80°K X.„ underwent a regular increase of k% and from 80° to On 200°K X_„ underwent a regular decrease of 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 -3.75 x 10 cm /°K:. The anharmonicity reached a maximum at 80°K. The temperature dependence of to was 0.138 cm "V°K if it was assumed to be linear. The maximum in the ; anharmonicity is also seen in the harmonic frequency. The anharmonicity was also plotted as a function of R(0,,,-0), Fig. 4.8. That plot looks surpris ingly like 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 all sources present in the cubic ice I crystals. There appear to be two major sources of changes in the anharmonicity as a function of temperature. As the crystal is cooled from 200°K to;5°K it 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) cm-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 in the contribution of increasing hydrogen bond energy to the total anharmonicity down to about 80°K (the 1U6 R(O-'--O) freeze-in temperature).. Changes in R(0,,-,0) and the hydrogen bond energy are very small below 80°K. The other source of anharmonicity is probably due to changes in the amplitudes of 0-H stretch and HDO translation. The 0-H stretching amplitude must be discussed in terms of the total population distribution among all the energy levels. Below 200°K virtually all of the molecules must be in the ground vibrational 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 in H20 ice Ih. Corresponding 0-D, ampli-o o tudes for D20 were 0.129 A at 1°K and 0.217 A at 223°K. Thus the anharmon icity experienced by the molecules can be expected to decrease below 200°K. .As well, the RMS amplitude of translation decreases from 200°K to 1°K. Since v , X , and oi are all strongly coupled to the instantaneous On OH On R(O----O), then decreases in the range of R(0,,-,0) through decreased ampli tudes of translation will give a smaller range of X_.„ and a net. smaller: Un X0H' We suggest that: l) below 80°K AXnTJ from changes in amplitudes is On greater than AX due to changes in 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) is greater than AX.^ (amplitude.). On (d) Correlation of the HDO stretching frequencies to the RMS.ampli tudes of translation. 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 translation, then it is interesting to consider the relationship between v and<Ar^> 2 as a function of temperature. lVf Decius (122).gave the mean-square displacement from the equilibrium distance between two atoms resulting from all modes of vibration as: <fir2> = 2 L2k<o2> [l] k where o Ar^. = the displacement distance of internal coordinate t due to all normal coordinates, k, = the element of the matrix transforming normal coordinate k into internal coordinate t, and 0^. = "the k-th normal coordinate. The mean-square amplitude of the k-th normal coordinate C^Q^^) was given by Morino et al. (123) as: h hcvk <Qv > = o 2 coth ±L rol K OTT^CV^ 2kT L 2 J where v, = the vibrational frequency of the.k-th normal mode in cm \ . k = Boltzman's constant, T = the temperature in degrees Kelvin, c = the velocity of light, and h = Planck's constant. The formulas [l] and [2] were derived for the'isolated, free molecule case. In a rigorous treatment of ice it would be necessary to consider all internal and lattice modes in the sum over k. Cubic ice I has two HgO molecules per primitive unit cell and there are three non-zero translational, six librational and six internal vibrational modes. If the pair of HgO molecules is considered as a weakly bonded diatomic molecule, (HgO)••'*(H20), then there is one normal mode of vibration, the IkQ R(0-•••(}) stretch. The mean-square amplitude of translation between two molecules can then be estimated. Equations [l] and [2] give h <AR^> = <Ar^> = LL'T^ coth he 71 CVT 2kT and for the (H^cOg "diatom" LL' = G, which is easily evaluated for HgO or DgO. The RMS amplitude of displacement is then given by h <Ar2> = hcvm coth i-mi UTT2CVT 2kT 2^ .3] where m^ is the mass of H^O or D20, and the variation 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 10° and 200°K. In both cases the v^HgO) frequencies used were from the best smooth curve through the experimental points (Fig. 3.15). Since the v^H^O) frequency varied by less than 5% between 10°K and 200°K, one set of <Ar2>'5 was calculated at constant v t L-OL' VIJ = 227.0 cm 1 at 80°K. That is reasonable since l/T dominates the function. A corresponding set of (Ar2) for E>20 were calcu lated using the H20 frequencies and D20 masses. These data are compiled in Table IV.I and are plotted in Fig. k.9. For comparison, a set of HgO (Ar2}3"2 were calculated using the full range of observed frequencies..' Those data'are also compiled in Table IV.I. The only significant change was a slight decrease in the low temperature values and a slight increase,- in the high temperature values. Plots of RC0---"0) against (Ar2) at equal temperatures and of v0H(HD0) and VQ^HDO) against (Ar2)35 are given in Figs, k.10 and U..11 res pectively. TABLE IV. I The RMS amplitudes' of translation calculated from H20 vT and compared to results of-thermodynamic calculations. <Ar2>15 <Ar2> h <Ar2> 35 <Ar2> Temperature H20 • v\ D20 H20 const. Vrp vTtT) COnSt . Vrp (a) (a) o o 0 0 9 0 _ 0 °K xlO2 A xlO^ A xlO2 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+. DO <Ar2>2 AxlO2 8.6 9.0 95 IO.O 200H 5CH IOO-1 50 10.5 9.0 9.5 IO.O H O Wzf A x IO: ;. U.9 The RMS amplitudes of H20 and DpO translation calculated with a constant vT(H20) assuming an (H20)2 diatomic unit cell model. i—1 O 2000K t O 0<[ 2.755-1 jo X 2.750-2.746 I50°K IOO°K 50°K 1 O loo o o ° IO°K "i r 9.0 9.5 IO.O L o "i i | i r I0.5 H 0<Ar2)2 AxlO' i—i I.O Fig. U.10 The correlation of RMS amplitude of translation to the calculated 0f,,,0 distance in cubic ice I. " ' R(0-• •'i0)" and ^Ar2) !s were correlated as a'function of common temperature. H 3290-O o Q I 3280-3270-3260-2000K i • I500KA I A I500K I • • • IOO°K A I • IOO°K-A-50°K I |00K -40 °K O >—50 °K O °K 200 °K I - 2440 2430 Q ys (Ar2)2DO IO°K .Z/ VS (Ar2)2 H O OD — X 2 2420 24IO 8.6 9.0 9.5 IO.O 10.5 II.O 0 O Hp<Ar2>" Ax lO2 Fig. h.ll The dependence of the observed HDO stretching frequencies' on the RMS amplitudes of translation w of HgO and D20. The frequencies continued to decrease although the ^Ar2^3s became constant at low temperatures. 153 From Table TV.I one sees that the RMS amplitudes of translation for HgO and D20 agree at low temperatures, i_.e. below- 10°K, quite well with those calculated by Leadbetter (8U) from thermodynamic data. His data appears to be linear in 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 his. Between 100° 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 esti mate, among which are neglect of translational hot bands above 50°K, neglect of two other translational modes, and the inadequacy of the free molecule theory. The contributions of the larger amplitudes of molecules in excited translational states must certainly increase drastically as the temperature approaches 200°K, with as much as 15% of the sample in excited states. The contribution of the lattice fundamental at l60 cm 1 to the individual molecular amplitude must be even larger than for the 229 cm 1 fundamental chosen above, although the apparent density of states is less. The plot of <Ar2)^ against R(0 0) in Fig. k.10 showed that below 50°K our calculated RMS amplitude was constant although our calculated 0'"''0 distance was still decreasing. As well, 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 *»• (iii) HDO Stretch Half -^Height Widths As can be seen from Fig. 3.8, the low temperature, limiting half-height widths for v (HDO) and vw(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 dilute samples of HDO in HgO and D20 used in this work, care was taken to prevent accumulative exchange between atmospheric H20 and D20 liquid during handling. In our HDO in D20 samples, exchange of D2.0 with unwanted H20 absorbed on preparative surfaces or H20 vapour in 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 still much h ; -1 narrower than those observed by Whalley (96), i.e. Av (HDO) = 50 cm . and — — OH h -1 Av (HDO) = 30 cm . It is important to recognize that the coupling-broadening does not necessarily originate from HDO-HDO pairs. Since at least one HDO stretching frequency is always coupled to the host, even at low concentration, and since the (H20 or D20) bands are both very broad distributions of frequencies, then HDO may have a quite broad range of interaction energies with H20.and D20 neighbouring molecules.. The consequent range of perturbations inflicted on the isolated HDO frequency also may be broad. Hence, as the concentration of HDO molecules increases, the group of HDO molecules will be exposed to 155 a -wider range of perturbations giving increased AA> even in the absence of HDO-HDO pairs. Clearly, the number of HDO molecules coupled to the fewer lattice molecules with stretching frequencies far down the sides of the band (fewer than the number oscillating at the central frequency) increases as the concentration of HDO increases. The absorption by such molecules increases in importance in the total HDO absorption. Our data for VQD(HDO) from 5.9W D2O in H2O showed good agreement since exchange with atmospheric HgO was only very slow and tended to deplete HDO rather than increase it. Half-height widths of stretching modes in the high pressure ices, were . . L \ n —1 indicated by Whalley (96) to be: AvSL = 5 cm and Av^ = lo cm for ices II and III. There was obviously a dramatic change in the ice crystal in transforming between ice I and ices II or III. Whalley (96) and others (100, 105, 106) suggested a number of reasons for the observed ice band widths. The postulates can be condensed into four main mechanisms. The first mechanism was first mentioned by Hornig (106), but Bertie and Whalley (96) have described it in more detail. The mechanism suggested the band width arose from closely spaced transitions between a range of closely spaced ground state energies and corresponding, closely spaced first excited states found over a mole of crystal. It was understood that any individual molecule had only one narrow ground state and first excited state, but that over the whole crystal the sets of equivalent molecules sat in sites of varying 0-H-*-*0 energies. The variation of 0-H*••'0 energies arose from the variation in 0----0 distances prescribed at equivalent oxygen sites by disorder allowed in the proton orientations. A result of the proton orien-tational disorder at.equivalent oxygen positions in the set of unit cells 156 was the loss of site symmetry. Consequently, all vibrations became a or a' and the selection rules collapsed to one general selection rule allowing transitions between all forms of combination and overtone levels. The second mechanism of stretching region broadening was.through Fermi resonance of any fundamental (or the fundamental sum and difference bands with low frequency lattice modes) with other overtone and combination bands such, as 2Vg» ^VR' AN^ v2 + 2VR' Notice that because of the lack of site symmetry through proton orientational disorder, Fermi resonance between any two near-degenerate levels was possible, not just between 2v^ and as was expected from crystal site symmetry. The third mechanism invoked Heisenberg's un certainty principle. Specifically, the energy level uncertainty, AE,, was J, increased by a shortened half-life, 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 lattice modes giving the ground state, fundamental internal mode and excited lattice vibrations.. Both proton tunnelling and ejection from the excited vibration to nearby upper lattice modes constituted radiationless transitions. The fourth mechanism of broadening was through the occurrence about the fundamental of sum and difference bands of the fundamental with low frequency translational lattice modes and the occurrence of nearby hot lattice 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 signifi cant. If the observed stretching modes were broadened by difference and hot bands involving lattice modes, then the stretching modes should have,; under gone significant sharpening once the higher lattice energy levels were 157 depopulated at low temperatures: The.stretching modes were not signifi cantly sharpened as far down as 10°K. A simple calculation of the ratios of numbers of molecules in the ground, 1st, 2nd and 3rd excited states for —1 —1 vT( = 229 cm ) and vR C = 832 cm ] showed that at 10°K all upper levels were effectively 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 lattice contracted, the mean deviation from the ideal symmetry site 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 ^Ar2)35 decreased so should the stretching band width. Once the 0'*'*0 dis tances were invariant, so was the half-height width. A further modification to the stretching mode of dilute HDO molecules in a parent lattice was in lattice coupling. Ideally one wanted to.compare the uncoupled OH stretch to the coupled OH stretch in identical crystal fields or lattice environments. At best one compared uncoupled, but per turbed OH stretch to coupled OH stretch in identical electron distributions. However, the periodic modulation of the electrons by lattice modes was, different for the two cases. The conclusion is that if the stretching.modes were broadened by lattice modes then the effect of broadening of OH(HDO) stretch by the D^O lattice was different than the broadening of OHvHgO) stretch by the HgO lattice since H2O and DgO have different lattice, funda mental frequencies and amplitudes. i 158 The half-height widths had a near-linear temperature dependence of 13.5 x l(f2 cm-1/°K for v„„(HDO) and 7.0 x 10~2 cm_1/°K for v._(HD0) in the Un UD high temperature range from 100° to 190°K. Those data compare well with our interpretation of the data of Ford and Falk (100) in 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 10_2 cm"1/^ and o£Wn(HD0)« 10.7 (10_2) cm_1/°K. Un. UlJ Our experimental data lie within their results, and our scatter of data is significantly lower than theirs. (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 Un triangles were constructed which had heights equal to the peak height on a linear absorbance scale and a base at 1/2 of %(A.v 2) . The area of two such triangles, extended to the baseline, was assumed to represent the integrated intensity (A) approximately. Typical results 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 in v (HDO) peak height seems to predominate in Un the decreased band area and is consistent with the concept of a weakening hydrogen bond and a decrease in molecular dipole with increasing R(0....)) as temperature increases. Above 190°K the samples sublimed rapidly and presumably a small amount of the original decrease was due to cumulative sample loss by sublimation. A slightly concave portion of the I (VQ^(HDO)) betx<reen 110° and 140°K indicated first a more rapid and then a less rapid decrease in hydrogen bond energy. Some unusual heat capacity effects were noticed near 110°K (82), but it is not certain that the effects are related. 159 B. Dependence of HgO and DgO Bands on Temperature (i) Fundamental Lattice Mode Temperature Dependences (a) The Rr>0 translational mode. Cubic ice I (Fd3m) has two mole cules per unit cell which provide six translational modes, of which three are zero frequency translations of the whole finite crystal. Whalley and Bertie (87, 88) developed a theory for hexagonal and cubic ice I which incorporates proton orientational disorder in the description of v^. They deduced from an approximate density of states relation that points of inflection,minima and shoulders, as well as peaks, are associated with specific branches of the optical and acoustical modes. The lattice modes of hexagonal ice I were also observed by neutron inelastic scattering (92, 93). Our observed v (H 0) structural absorption features were given in Table Ill.IXb along with some previous results (88,92,93). The poor definition of the absorption features (other than the 229 cm 1 peak maxi mum) made it impossible to follow their temperature dependences. The features recorded here at 83°K agreed with the mull results of Bertie and Whalley (88) and the condensation results of Giguere and Arraudeau (89). The lowest temperature indicated by the (Au-Co) / (Ag-Au) thermocouple for this experiment was 25°K, probably due to some solidified N2 (gj used to precool the helium dewar. The low temperature (25°K) limiting values of the features ex hibited no special behaviour. From 25° to 70°K the maximum underwent a stage of invariant frequency up to 55 t 5°K, and an apparent shift by 2 cm-1 to lower frequency between 55 + 5° and 70 + 5°K. From 70° to 90°K v,p was relatively constant in frequency, while above 90°K v had a con-i6o tinuous, near linear shift towards lower frequency of -0.093 cm- /°K. Above l60°K (max.) remained constant at 221 i 0.5 cm \ In comparison, Zimmermann and Pimentel's (97) data indicated a slope of -0.081 cm~^~/°K from 90°K to 250°K. The dependence(rate of change) of vT on the hydrogen bond energy was less than for the molecular modes, i_.e_. a given change in hydrogen bond energy had 0.5 to 0.3 times the effect on vT as it did on vR or the molecular modes. The sensitivity (minimum- detectable change) of v to hydrogen bond energy changes.was the same as for v , vn , v_ and v , o i_.e_. sensitive to changes of ± 0.0001 A/°K in R(0-\--0). The origin of the sharp shift near 55°K is unknown, but it may have arisen from a change in the crystal structure (and hence the unit cell and Brillouin zone), or a change in proton ordering. A similar effect was observed for HDO stretching modes and it was correlated to the predicted (70) ordering near 70°K. (b) The HgO and DgO librations. The low temperature limiting v^CHgO) frequency (832 cm 1) and v^DgO) frequency (630 cm-"*") exhibited no special 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^(D20) (Fig.' 3.13). Within these frequency limits the absorption maximum was constant. The freeze-in temperature for ^(H^O) and v^(D20) was 70' ± 10°K and agreed with other H2O and D2O bands but did not conform to our more precise measurements on HDO peaks. The sensitivity of v^(H20 and D2O) to changed hydrogen bond energy through AR(0,,'"0) was larger than HDO, i_.e_. l6l o > 0.0001 A/°K. Between 70°K and l80°K vR(H20 and D20) exhibited linear -1 -1 temperature dependences of -0.18 cm /°K and -0.11 cm /°K respectively. Again the frequency scatter of points was large and a curvilinear depen dence may be true, as was indicated for v^HDO) (Fig. 3.7). Liquid nitrogen and liquid helium cell data agreed in their overlap region for vR(H20). Zimmermann and Pimentel's (97) data for vR(H20) indicated a slightly curvilinear temperature dependence of about -0.22 cm-1/°K. Their points, were approximately 10 cm 1 higher in frequency than ours: They chose the band center and ignored any vD band structure (indicated in their spectra). Details of the origins, possible theoretical treatments, and the nature of the modes will be given in section h.h. (ii) Fundamental Molecular Mode Temperature Dependences (a) The v-j_ and stretching modes. The low temperature limiting frequencies for v± and v3 of H20 and D20 were 3133 (2320) cm-1 and 320U (2413) cm 1 respectively. As for HDO that extrapolation to 0°K may not have been valid, 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 is very long below 60°K (70). As well, translational, librational and vibrational excited levels are all depopulated at 5°K: Further effects from depopulation should-have been negligible. Also, nuclear spin and electron spin perturbations (i_.e_. as in ortho-para hydrogen) were expected to be very small. No changes in hydrogen bonding were expected since the lattice was no longer contracting. From 4.2°K to 60°K, v-^ and v3 (H20 and D20) absorptions were invariant within the errors of measurement. Over that temperature range the crystal 162 o expanded very slowly, less than 0.0001 A/°K. Accompanying changes in R{0''•'0) and or were too small to "be detected by this ir absorption technique. The large frequency scatter in points was pre-determined by the uncertainty in peak and shoulder positions. The v^HgO) data from liquid helium and nitrogen cells did not completely agree (Fig. 3.10). Liquid nitrogen cell data indicated a "freeze-in" frequency near 3215 cm 1. Liquid helium cell 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 if the absorption peak underwent a type of "hysteresis" during cooling from 77°K to U.2°K, frequency shift lagged behind temperature decrease. Since the samples were always held at h:2°K for three hours, sufficient time may have been given for completion of the hysteresis loop before warm-up observations began: Observations of frequency shift during a cooling cycle are required to test that; possi bility. Data from the same two cells for v (R\p0) (Fig. 3.11) also suggested hysteresis although the separation of points was not as well defined. ;Only the results from the liquid helium cell were obtained for v^ and v^ of DgO. Above 60°K the and v^ modes underwent regular shifts to the ; progressively higher frequencies associated with progressively decreased hydrogen bond strengths. The explanation follows that of v (HDO)., On The ir 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 ir (H^O and DgO) observations concurred directly. However, the v^HgO and D^O) Raman observations were all shifted (by 55 and 32 cm 1 respectively) to lower frequency than the ir 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 all temperatures, then the Raman and ir data agreed. The following temperature dependences were observed by Val'kov and Maslenkova (90): H20 AT Av0 Raman IR cm-l/°K cm-l/°K 0.25U 0.26 0.2U6 0.24 AT A(vx + vT) AT Av. AT Av, 0.222 0.20 D20 —- 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 is a potentially interesting extension of these cubic ice I temperature dependences to hexagonal ice I. It is known that the linear thermal expansion coefficients of hexagonal ice I are not equal (60) and that the 0--,*0 distances parallel and non-parallel to the c-axis are not equal, Fig. 4.3. Hence, the temperature dependences of R(0* • • *0) ,. i^.e_. parallel 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 parallel and perpen-164 dicular to the c-axis, should be distinguishable. For example, consider the six possible arrangements of the four protons about any one oxygen atom in hexagonal ice, H H H 4. H H H H H 'I c- axis Then the three arrangements 4,5 and 6 have both protons along the shorter 0****0 distances and will 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 distinct from cases 4,5 and 6. The frequencies observed parallel to the c-axis should be intermediate between those observed perpendicular to c and those expected if 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 parallel 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) in cubic ice I(Fig. 4.3), one can determine the R(0*'"0) - v3 correlations for H20 and D20, Fig. 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 parallel and non-parallel to the c-axis, Fig. 4.13. For v^O^O) of hexagonal ice one sees that at 150°K the asymmetric stretching frequencies would be 3214 and 3229 cm 1 parallel and non-parallel to the c-axis, while at 100°K the values would be 3202 and 3225 cm 1. Similarly for v3(D20) 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^ is probably greater than 100 cm and because of the relatively small split between the bands. In contrast the bands due to dilute concentrations of HDO in H^O or J)^0 are narrower and absorptions parallel and non-parallel to the hexagonal c-axis should be separable. Sets or predicted vQH(HD0) and v^(HDO) fre quencies in the two directions were determined as above (i..e_. from Figs. 3.6 and 4.3) and are plotted in Fig. 4.14. Thus at 150°K vQH(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 in the a and c temperature, dependences 165 ICE I tj (DO) cm-1 Co 2 2410 20 30 -I 1 1 2.746 H 1 , — , 3200 10 20 30 ICE Ic ^3(H20) cm-1 Fig. U.12 The correlations of V3 of, H2O and DpO to the 0-• •-0 distances as a function of common temperature. The frequency data were un corrected for source beam heating. 166 ICE Ih z,3(D20) cm-1 2410 20 30 ICE Ih z/3(H2Q) cm-1 Fig. 4.13 The calculated frequencies of H2O and D20. in hexagonal ice I along the c and a axis as a function of temperature. 167 ICE I is (HDO) cm-1 h OD 2410 20 30 ICE Ih v (HDO) cm-1 g. k.lk The calculated vOH(HDOl and vODCHDO) frequencies for HDO in hexagonal ice I and along the c and a axis as a function of temperature. 168 should yield valuable information on the anisotropic deformation of the hydrogen bond in hexagonal ice I. —1 —1 (b) The v2 bending mode. Absorptions near l600 cm and 1200 cm in cubic ice I (HgO and D2O) were very near the corresponding vapour phase v2 fundamental absorptions of 1595 cm ^ and 1179 cm ^ respectively. Doubts arose in the previous literature assignments (Tables III.XI and III.XIII) of these ice frequencies to either V2 or 2vp, which should nearly coincide. In fact, these absorptions in ice appear to be composite overlapping V2 and 2vj; peaks as was previously described (page 112). The inconsistency between the liquid helium and liquid nitrogen cell V2 data (Fig. 3.12) may have arisen from a temperature hysteresis , i^.e_. the lagging of frequency shift behind the temperature drop during cooling. Zimmermann and Pimentel' (97) results (Fig. 3.12) tend to discount that possibility for V2(H20). Their results from liquid nitrogen experiments agree with the present results from liquid helium experiments. Much of the disparity in the pre sent results probably arose from reference beam uncompensation for the liquid nitrogen cell data. The strong atmospheric water vapour absorption below 1595 cm and above l6l5 cm ^ may have distorted the V2(H"20) ice band severely, while a gap in the vapour spectrum between 1595 and l6l5 cm may have presented an artificial V2(H2U) ice maximum. However, such a maximum would be independent of the ice sample temperature. .- •;-For V2(H20) the liquid nitrogen cell data indicated a low temperatur limiting frequency of l605 cm , while the liquid helium cell data indi cated a low temperature limiting v2 frequency of 1560 cm ^: Zimmermann and Pimentel's data were extrapolated to near 1570 cm \ Whalley (96) found the Vp maxima in high pressure H2O ices were above 1680 cm ^ /and 169 argued that V2(ice) > V2(vapour). However, 2vp may be more intense than V2 in these cases. Whalley's (96) frequency for cubic and hexagonal ice I at 110°K in an isopentane mull was more than 25 cm 1 higher than observed here, or by Ockman (108) (V2 = 1580 cm-1) and Hornig (106) (v2 = 1585 cm 1). The reflectivities of Whalley's (95,96) mulled samples may have been significantly different than for our condensed samples leading to his higher apparent maxima. However, Ockman found only a small (0.5%) increase in the one percent general reflectivity of crystalline ice -1 -1 over the range 1500 cm to 1700 cm , the maximum reflectivity was at 1575 cm 1 at 110°K. It is also possible that sample formation by vapour condensation accentuated the reflectivity, creating an artificial low frequency maximum in our results. For D2O the liquid helium cell data indicated a low temperature limiting Vg frequency of 1189 cm ^, however the B^O liquid nitrogen ,-cell experiments were not attempted. The region near 1200 cm 1 was free *from atmospheric HgO vapour attenuations and the recorded D2O spectrum was free of atmospheric absorption distortions. The D2O observation of II89 cm 1 is greater than the D2O vapour frequency, 1179 cm In contrast, Hornig (106) and Ockman (108) observed v2(D20) to be even higher, i_.e_. near 1210 cm-1 at 100 t 10°K. These D20 results were contrary to our v2(H20) helium data as well as the nitrogen data of others, as noted above. Possibly in DgO the relative positions of 2v^ and are altered from that of H2O, giving a different peak maximum relative to the vapour. Maximum V2/2v-^(H20) absorption was constant over the temperature range 5°K to 70 - 10°K, while maximum V2/2vp(D20) absorption was constant 170 over the temperature range 5°K to 50 t 10°K. The low D20 "freeze-in" temperature of 50°K was probably due to insufficient data. The cubic ice I v2/2vp band exhibited the same dependence as the stretching modes in this low temperature range, constancy within ± 8 cm-"*". As a check on hysteresis in this temperature range, detailed observations should be made during fast and slow cooling, i_.e_. cooling in 10 - 20 min. and 150 - 200 min. respectively. The V2/2VR absorption also exhibited the same sensi tivity to changes in hydrogen bond length (energy) as did the stretching modes, i_.e_. it was sensitive to changes in R(O----O) greater than 0.0001 A/°K. The question of whether v2(ice) is less than or greater than v2 (vapour) is still unanswered. If the V2/2VR(D20) absorption maximum was due to more intense v2 transitions then v2 ice > v2 vapour. If 2v^(D20) was the more intense transition then 2VR(E20) ice >v2(D20) vapour and v2(D20) ice may be less than v2 vapour. Positive high temperature depen dence indicated the peak maximum was v2 and not 2VR, since (and pre sumably 2VR) had a negative frequency temperature dependence. The tempera ture dependence of the v2/2vpj H20 absorption was also positive for either liquid helium or liquid nitrogen data. The maximum of absorption must then be v2(H20) and 2VR must be masked. Whether v2(H20) ice was greater than or less than v2(H20) vapour could not be unambiguously determined. Maximum V2/2VR(H20 and D20) absorptions had approximately linear, positive temperature dependences of 0.37 cm "V°K and 0.15 cm~"'"/0K respec tively over the temperature range from 60° to l80°K. In contrast the H20 data of Zimmermann and Pimentel (97) indicated a slope of 0.28l cm •^/°K 171 in the range from 90°K to 253°K. The relatively small temperature depen dence of V2/2VR(D20) may have resulted from the closer coincidence of V2(D2°) and- 2vR(D20) than in HgO. If the H2O and D20 bands had the same structure then their temperature dependences should have been simply related since their changes in R(O----O) were nearly the same. (iii) The Combination and Overtone Mode Temperature Dependences (a) The 3vR or (v2 + vR) mode. Broad weak absorptions near 2235 cm 1 and 1635 cm 1 in 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 v2/2vR bands. First consider the. R"20 ice absorption at 2238 cm ^. If the absorption arose from a v2 + \)R transi tion then the temperature dependence should have been positive, i_.e^. AvR/AT = -0.17 cm-1/°K and Av2/AT = +0.36 cm_1/°K, therefore (Av2 + AvR)/ T = +0.19 cm /°K. However, the temperature dependence was observed to be negative. If the absorption arose from a 3vR transition then the tempera ture dependence should have been negative, i_.e_. A(3vR)/AT = -0.51 cm "V°K. As was seen in Fig. 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(3vR)/ 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 this result. Either the 2235 cm 1 H20 absorption was a vR fundamental, or the 3VR anharmonicity was decreasing with increased temperature, or energy level population redistribution was affecting the results. Such a.high 172 frequency fundamental lattice mode seems unlikely, as do such large effects from populational redistribution. Alternately decreased anharmonicity of 3vR and vR from decreased hydrogen bond energy may be larger than the in creased anharmonicity arising from increased amplitude of libration at higher temperatures. Consider the absorption at 1637 cm where the same considerations apply as for H2O. Absorption arising from D20(v2 + vR) transitions- would obs. obs. exhibit zero temperature dependence; A(v2 + vR)/AT = (AV2/AT) + (Av^/AT) = +0.15 cm ^/°K - 0.15 cm "V°K = 0. The temperature dependence was observed to be distinctly negative, -0.15 cm "V°K. In fact VR(D20) and the 1637 cm ^ D2O band had the same observed temperature dependences. Low temperature limiting 3VR absorption was 2235 cm for H20 and 1635 cm ^ for DgO. That implied an approximate H20 low temperature limiting anharmonicity for 3VR(H20) (from = 833 cm of -258 cm and for 3yR (D20) (from vR = 627 cm-1) of -253 cm-1. The apparent HgO and D20 3vR anharmonicities were nearly equal. Now the parent transitions underwent considerable isotopic shift: vp(H20) = 833 cm 1 and vR(D20) = 627 cm "L. The H20 anharmonicity of -258 cm ^ represented 11.5 percent of the observed absorption band frequency, 2235 cm ^~. The increased DgO percent anharmon icity was unexpected for the mass substitution made. For example, in the -1 -1 vapour phase the anharmonicity of H20 (x-^ = -43.8 cm , x22 = -19-5 cm , x33 = -^6.4 cm is almost halved in D20 = -22.8 cm , x22 = -10...hk cm \ x33 = -24.9 cm for v^, v^, and (l2h)9 since the amplitudes of D20 motion are smaller. Similar behaviour was expected for the solid, but the observed 3vR(.D20) anharmonicity was not one- half that of 3vR(H20)., Thus the large shifts of 3vR below the expected frequencies cannot /be simply 173 explained as anharmonicities. The large shifts of 3vR(H20, D20) below the expected frequencies (3vR observed = 2235 cm-1, 3(vR) = 3(833) = 21+99 cm-1) may arise from dif ferent maximum transition moments for the band of ground state librational energies for the v^ and 3vR transitions. The extreme case is: molecules occupying the higher energies of the band have maximum transition moments for (0 -> l) transitions and minimum transition moments for (0 -* 3) trans itions , while molecules occupying the lower energies of the band have minimum transition moments for (0 -»- l) transitions and maximum transition moments for (0 3) transitions. The maximum of the (0 -> 1.) vR transition would occur above the center of the energy band and the maximum of the (0 3) vR transition would occur below the center of the energy band. In support of this recall that the vR absorption had a AvR 2 of about ; 125 cm ^, indicating a very large librational energy range. Data on 3vR from spectra recorded during warm-up from 5°K to 60°K showed that the 3vR energy level had the same sensitivity to hydrogen-bond changes as the internal modes, i_.e_. it was insensitive to changes in hydrogen-bond energy from changes in R(0--**0) that were less than 0.0001 o : A/°K. Data from the liquid nitrogen and liquid helium cells agreed satis factorily. The 3vR freeze-in temperatures for H20 and D20, 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 limits of 333U and 2h6k cm 1 for H20 and DgO respectively (Table III.IX). Those frequencies are 201 and ikh cm 1 higher than the low temperature limiting 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 III.IX). If the high frequency shoulders are in fact due to (v^ + v ) transitions then the v^ to (v + v ) displacement should have been 229 cm ^ (observed 201 cm ^) for H^O and the temperature dependence of (v^ + v ) of H^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 well with the observed v^ + v^ value of 0.20 cm "*"/°K. For D20 the high frequency shoulder appears to be composed of v^(D20) and the LA translational mode near 160 cm-"'". The tem perature dependence of v^(D20) is 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 all the modes was the increase in the amplitudes of vibration. 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 transitions. Above l60°K (Fig. 3.k) the A(V-^, V^? V-^ + Vrp) ^ data are not reliable since sample sublimation had a pronounced effect. The observed temperature dependence of A(vR, VR + 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 limits of the low temperature data. As well, the temperature dependence of A(VR, Vr + vip) seems to be too small. ; It would be interesting to study the origin of vR in the solid, liquid and 175 vapour phases about the triple point as well as the origin of \^ as the critical point is approached from the vapour phase. i. The temperature of A(Vg, 2vR) 2 (Fig. 3.5) was opposite to that, of A(vp, vR + Vrp)3"5 and A(v^, V^, + v^)^ in the amorphous and cubic ice I phases. An explanation was given in section U.lC(i) (page HI). k.3 Assignments of the Cubic Ice I Absorption Bands A. The Fundamental Lattice Modes (i) The Translational Modes Two peaks (l62 and 227.8 cm-1) and three shoulders (191, 267 and 296 cm 1) were observed at 93°K for H"20 cubic ice I. The features of the band differed only slightly from those of Bertie and Whalley (88). In this work no calculations were made which disagreed with the assignments of Bertie and Whalley. (ii) The Librational Modes The low temperature limiting frequencies- of the observed librations are in the ratio, vR/(vR + v^) = O.963. That compares to the same ratios in H20 and D20 of:0.9lAU and 0.953 respectively. The peak to shoulder separations at 10°K were: [(vR + vT) - vR]H20 = 50 ± 5 cm"1 I(vR + vT) _ vR]HD0 = 33+1.5 cm"1 I(vR + vT) _ vR]D20 = 31 ± 5 cm"1 ' I - 176 • If the shoulder did arise by a combination transition of vR(HDO) and v,p(host), then the value of to apply to HDO is that of the host DgO since at a concentration of k.0% HDO in D20 the lattice dynamics must surely be domin ated by the D20 molecules for any reasonable model. The fact that the D20 peak to shoulder separation is 31 cm 1 supports this conclusion. As well, the peak to shoulder separations of pure D20 and of HDO in D20 agree well. Presumably HDO in H20 should have a v-p peak to (vR + \Jt) shoulder separation of about 50 cm 1. However, that has not been observed yet by any workers. Recent work by Trevino (93) quoted experimental data of neutron inelastic 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 ir observations from 50 to 3500 cm 1 are the same for cubic and hexagonal ice I, and assumed that the basic dynamical lattice unit of cubic ice (one 0 atom surrounded tetrahedrally by k others) was a suitable model for hexagonal ice. That is supported by the fact that the nearest-neighbour configurations'are the same. Trevino's (93) theory also assumed that the protons are in ordered positions, which they are not. However, the basic translational unit in ice is the 0 atom and the orien tation of protons is relatively insignificant in this case. } For hexagonal ice I at 150°K the neutron inelastic scattering ex periments (93) demonstrated lattice maxima at 63 cm-1 (TA) depending on the assignment of peaks. Other workers (92) found (for H20 hexagonal'ice I at 26l°K) lattice modes at 60 and 70 cm \ Clearly there exists a high density of H20 translational states near 50 - 10 cm 1 at 150°K for hexa- . gonal H20 ice I. The corresponding modes for D2O cubic ice I at 10°K may be lower than 50 cm 1 since the mass difference would shift the frequency 177 to O.9484 x 50 cm-1 =47.5 cm-1. The observed neutron hand width in H20 was 50 cm-"*". Of the broad band of real translational frequencies, the maximum transition moments do not have to occur over the same sections of the band for ir absorption and neutron inelastic scattering. The ir transition moment maximum may lie at lower frequencies than the neutron scattering transition moment maximum. Further, the overlap in the ir of vR and (vR + Vrp) brings the instrumentally traced, summed absorptions closer together, i_.e_. if vR and (vR + VIJ) could be resolved completely their peak positions would be separated by more^ than 50, 33 and 31 cm 1 for H20, HDO and D20 respectively. One may conclude that a single librational mode and a combination librational-translational mode were observed for HDO. Since vRx and vRy. are expected to be about equally intense, and since only one band was observed, then vRx and. vRy 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 conflicting assignments of the three main ir absorp tion 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 v3, and the high frequency shoulder to (v3 + vT), while Hornig et_ al. (105) assigned the three bands as 2v2, v3, 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 - v3 vibrations, and they eliminated the distinction 1 178 between v-j_ and absorption bands of H20 and D2O. We propose that the low frequency shoulder is v-^, the main peak is and the high frequency shoulder is (v-^ + vT) in agreement with the Raman results of Val'kov and Maslenkova (99) and as Ockman (108) interpreted them. The stretching frequencies of HDO do not lie at the positions ex pected on the basis of H20 and D20 shifts in cubic ice I. This result will be discussed in terms of a theory proposed by Pimentel and Hrostowski (lOl) and Hornig and Hiebert (102) in the early 1950's: They suggested that the two major effects on molecular vibrations in solids, crystal-field per turbations and inter-molecular coupling, were separable by dilute 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 relative intensities 10:4:2. The 3088 cm peak had a, polari zation, ratio 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 (95,96) that v-j_ and vg are coupled and indistinguishable cannot be entirely correct. If 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 ir transitions, 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 ratio. Hence the v-^ and V3 energy levels appear to be separated (lack of 179 non-resonant coupling) while - and - resonance coupling of neighbours may still be effective. There remains the problem of the disparity between the v-^ ir 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. Similarly in D20 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 levels, the same portions of the band need not be both Raman and ir active nor with the same intensity factor. Thus for the Raman scattering only a narrow band in the lower one-half of the v-^ band was active while for the ir a large range of frequencies was observed and the maximum intensity occurred at a higher frequency. For the asymmetric mode the same portions of the band of frequencies was ir and Raman active. This may indicate a fundamental dif ference in - v^ and - resonance coupling. Thus the Raman scattering from hexagonal ice I indicated that in the ir absorption spectra the low frequency shoulder was and the main peak was v^, .i.e.. v-^HgO) = 3210 cm 1 and v-^d^O) = 2U13 cm-1. By, assuming that the two assignments are correct, then the ratio of v^Cice^v^Cvapour) is O.85U6 for H2O and 0.8655 for D20. If the effects of hydrogen bonding are the same on all 0-H bonds, then and are expected to be in the same order as in the vapour phase and should have the same relative dis placements from the vapour phase frequencies, Fig. U.15. The \>3(H20) cubic ice I absorption (3210 cm-1) is O.85U6 times the V3(.H20) vapour frequency (3756 cm-1). In order to preserve the displacement due to hydrogen bonding 4000-3756 3500-3000-2500-2000 3 2727 2788 . 2672 H20 HDO DzO J 180 : 3340 3266 \32l6*x ,3,49^ l (31681 (3125 ) *•. * 2465 •..2416 7, \24I3 3 (2360)' ...2321 ^ (2313) 1 HDO D O 2 ; VAPOUR SOLID ICE Fig. 4.15 The ohserved vapour phase and cubic ice I phase. H2O, HDO and D20 frequencies are shown as solid horizontal lines. The ratios of V3(ice)/v3(vapour) are shown on the diagonal solid lines. The H20, HDO and D2O ice frequencies predicted with those ratios are shown as dotted horizontal lines. 181 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) fre-quency of 31^9 cm . By similar arguments v^p(l>20) = O.8655 x 2671 cm" = 2313 cm compared to the observed value of 2321 cm-1. The predicted v-^ frequencies, which preserved the relative effects of hydrogen bonding on and vj, agree very well with the observed ir results. The agreement is probably better than indicated since the observed ir Vj 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 is v-^ = 3210 cm-1 and = 33^0 cm-1. The ratio < of vg(ice)/^(vapour) is then O.8858 and the predicted v-^ frequency is 3253 cm \ compared to the ir result, v-^ = 3210 cm-1. Neither the v-^HgO) nor the v-^(D20) frequency was a good approximation to an observed ir 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 in 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 dilute isotopic substitution to separate the crystal field and resonance coupling perturbations (101,102) was originally suggested for studying the molecular vibrations of DC1 under' the influence of an HC1 crystal field, but in 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 results, i_.e_. as in H2O in D2O •.( 106,95) • Because of the rapid isotopic exchange it 182 is impossible to isolate D20 in H20 or H20 in D20 at low concentrations. One obtains a dilute solution of HDO and very, very dilute residues of H20 or D20. Now HDO has Cg molecular symmetry and three internal coordin ates, an OH stretch, an 0-D stretch and an HOD bend. It is unreasonable to expect both of the HDO stretching modes to be completely uncoupled from the stretching modes of the H20 or D20 lattice. Just such an assumption by Hornig et al. (106) and by Bertie and Whalley (95) has resulted in mis interpretation of the ice I HDO ir results. As a first approximation to ice I, consider the ir observations for HDO, H2O and D2O in the vapour phase, Fig. H.15. One HDO stretching mode lies almost exactly midway between V3 and v-j_ of H2O, while the other HDO stretch is observed nearly midway between V3 and of D20. That is entirely understandable since the symmetric and asymmetric H20 modes may be considered as constructed from a basis of two isolated 0-H (HDO) stretches which interact weakly. Hornig ejt al. (105,106) claimed that such a picture of the H20 and D2O potentials should extend to the solid as well, i_.e_. in ice I they expected the HDO modes to lie between the v-^/vj modes of H2O and D20. For ice I (Fig. U.15) VQ^HDO) was observed between two ir H20 features, while VQ^(HDO) was almost coincident with a central ir D20 fea ture. Ignoring the weight of Raman data to the contrary, Hornig et al. assigned V3(H20) to 3210 cm 1 and v^(HgO) to 3360 cm 1 with v^H(HD0) between them at 3275 cm +. Their central aim appears to have been the preservation of the VQ^(HDO) observed position between V3 and v-j_ of H20. Bertie and Whalley's (95) discussion of the relationships between HDO, H20 and D20 stretches was confusing. They also assumed the nature of the H-OD (in D20) stretch was the same as the H-0H(in H2O) stretch. 183 The above ratios of v^(ice)/v^(vapour) for and D20 (Fig. h. 15) yield interesting results when applied to HDO (vapour) frequencies. The observed vapour phase frequencies of HDO stretching are 3707 and 2727 cm \ The predicted HDO frequencies using the HpO and D20 ratios (0.85^6 and 0.8655) are vQHP(HD0) = 3l68 cm-1 and vQr)P(HD0) = 2360 cm-1 compared to the observed HDO frequencies of 3263 cm 1 and 2Ul3 cm-1 respectively. .Thus the predicted frequencies lie close to the - mid-points, in agreement with the concept of Hornig et_ al. (105,106), 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 - interval of pure H20. Cor respondingly, the VQ^(HDO) stretch was just above v^(D20), Fig. k.l6. A clear explanation of the mispositioning of the HDO stretches can be found by considering the coupling of HDO to H20 and D20 lattices. Consider the case of k.0% HDO in a D20 cubic ice I lattice.,. Of the two HDO stretches only VQ^(HDO) can undergo reasonably strong near-resonance coupling to vo(Do0): v~„(HD0) is "uncoupled" from the lattice vibrations. 3 . OH One then compares the observed v„„(HD0) to v. and v„ of Ho0 on the assump-Un X 3 d. tion of equal hydrogen bond effects, Fig. h.l6. However, vOTJ(HD0) lies On 86 cm 1 above the - v^(H20) midpoint. A possible explanation is a lengthened D0-H-'--0H2 distance due to the very process of uncoupling. For example the covalent character of the hydrogen bond is dependent upon an equal sharing of e~ among the overlapped orbitals. If the orbital following of e~ about vibrating nuclei is not at the same rate then the hydrogen bond may .be weakened. 18U 3250-+ 86 32CO - "Ms 3150 ,Z/1 -73 O 3100 -o c CD CT 2450 • LL 24 OO 2350 -2300--58 OD +49 H2Q HDO in Dp HDO in H20 D2Q 1+.16 The. relative positions of the observed H2O, HDO and D20 stretching vibrations are shown as horizontal solid, lines. The expected positions of the. HDO absorptions before and after the effects of uncoupling, are shown as dotted horizontal lines 185 -1 ° From section 4.2A(ii) we found that AV.^/ARCO 0) = 1,921 cm /A. On Hence, a AvQH 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) dis ci tance should have been shorter than expected by O.OH5 A and vQI)(HDO in D20) would have been 58 cm 1 lower than expected (but it was unobservable lying under v1(D20)), at 2311 cm-1. (The - midpoints are 3180 and 2367 cm 1 for H20 and D20 respectively.) For 5.9W HDO in 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. Similarly o R(0 0) for DO-H H20 must have been shorter by 0.038 A and vQH(HD0) would have been lower than normal by 73 cm \ at 3107 near v^(H20).. For HDO in H20 and D20 the point is that one HDO mode was coupled to the lattice 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 in relation to the H20 and D20 frequencies cannot be readily confirmed by any meaningful calculation or conceived experiment. However it serves to. point out an important fact in dilute isotopic substitution studies in solids: The molecules of mixed analogues are not all uncoupled from the lattice. The method is not generally useful nor applicable to molecules with mixed isotopes unless one recognizes that unusual effects can occur. 186 (ii) The Bending Mode The position of the 1570 (l60H) cm-1 H20 cubic ice I absorption (Table III.XI) indicates it could be either v2 or 2vR and possibly over lapping v2/2vR absorptions. The vapour phase v2(H20) frequency is 1595 cm 1. The frequency shift upon annealing was to lower frequency (Fig. 3.2) a characteristic of molecular modes and thus favours the v2 assignment. As well, the cubic ice I frequency shift was to higher frequency and simi larly favoured \Jg. However the half-height width increased upon annealing and for cubic ice I it decreased with increasing temperature (Figs. 3.12 and 3.5 and page 67). That data favours a combined v2/2vR absorption. The v2 absorption was more intense than the underlying 2vR and was pro--1 -1 bably centered below 1595 cm , i_.e_. near 1570 cm . Similarly for D20 the v2/2vR band was found at 119k cm-1. C. The Overtone and Combination Modes (i) The 3vR Modes The 2235 cm 1 H20 and 1635 cm 1 D20 absorptions have been inter preted as both 3vR and v2 + vR (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 lattice mode and we assign the absorption to 3vR. However, there is at least one disconcerting factor, the relative intensities of vR, 2vR and 3vR that were observed. One expects the overtone intensities to fall very rapidly and thus the intensity of 3vR should be much less than 2vR. However the 3vR absorption is only about 1/k less intense than the combined v2/2vR absorption, and 187 that indicates that 2vR is less intense than 3vR. However, the interpre tation in terms of individual molecular librations is weak and a complete solid state treatment is necessary. (ii) The (v + vT) Mode ••' • The shoulder at 33h0 cm in H20 and 2I+65 cm-1 in D20 cubic ice I has been variously assigned as v-^, + and v-^ + Vrj-i (Table 0.5). Our previous discussion on the stretching modes of H20, D20 and HDO (page 181) eliminated the assignment. The peak to high-shoulder separation (v^ to "v^ + Vrp") is 130 cm 1 while the low to high frequency shoulder separation (V-L to "v± + vT") is 191 cm . The latter separation lies closer to our observed vrp(H20) band maximum and favours the v-j_ + Vrp assignment. In addi tion, the Raman data (99) favours a + Vrp assignment on the basis of frequency separation and relative intensities, i_. e_. the relative , to vl + VT in"tensities are 10:it: 2. k.h The Librations of HDO, H20 and D20 A. The Moments-of-Iriertia Models Past treatments of the librational lattice modes of the ices have dwelt upon the association of the librations to free rotation of oriented-gas or gas phase molecules (85,89). Implicit in such treatments have been comparisons of the moments-of-inertia (i) about the three principal axes of H20, HDO and D20. Blue (85) was the first to evaluate the librational frequencies through moments-of-inertia. We have extended the calculations 188 to include weighted lone-pair orbital contributions to the moments. (i) The Non-Interacting Molecules Model The molecular parameters and the positions of the principal axes are shown in Fig. U.17- The moments-of-inertia are given in Table IV.II as well as the differences between the HDO, H2O and D2O moments. Under the molecular symmetries, librations about the H2O and D2O z-axes are ir inactive, while libration of HDO about z is ir active due to the loss of C2v symmetry and the orientation of the molecular dipole at 17°51+' to the z-axis. However, VRZ(HD0) is expected to be weak compared to vRy and vRx 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 0.012 A/deg arc in a classical approach. The HDO moments are split between the H2O and D2O moments-of-inerti Table IV.II. Hornig et_ al. (105) pointed out that on the basis of• moments of-inertia the observed HDO librations would be expected to split between the H2O and D2O librational frequencies. From the differences in the moments one sees that IX(HD0) is nearer T^^O, IZ(HD0) is nearer I^(D20), and Iy(HDO) is midway between Iy(H20) and Iy(D20). It does not necessaril follow that the HDO librational frequencies will be observed in a corres ponding manner. HDO librational absorption was observed here only for HDO in a D2O matrix: One peak and one shoulder were observed at 823 cm 1 and 856 cm 1 respectively (page 7^). Assuming that the librational frequencies for HDO, H2O and D2O can be defined by a single function such as Blue's Z H20 z z HDO Fig- 1+'r'' 71:16 Principal axes of H20, HDO and D20 and their molecular parameters. The angles were assumed to be tetrahedral. X H Cpage 27) then vRx(HD0) should be relatively weakly coupled to any libra tion of the D20 lattice since the HDO and D20 librational.frequencies observed were about 90% separated. One of the absorptions at 856 and 823 cm 1 must contain at least Vnx(HD0) si-nce it nas "the lowest moment-of-inertia and is expected to be closest to the H20 values. The other feature above cannot be due to VR (HDO) nor vpz(HD0) since the peak-shoulder separation was too small, 190 Table IV.II The moments-of-inertia of H20, HDO and D20 and a comparison of HDO to H20 and D20. The parameters used to calculate the principal moments-of-inertia are given in the text. H20 D20 HDO 0.89 x io-ho • 1.61 x io'ho 1, .08 x 1040 2.91 5.63 h. .23' 2.01 1+.02 3. .15 units gms-cm2 / molecule Comparison of moments Ix(HD0) - Ix(H20) = = 0.19 x 10~h° Ix(D20) - Ix(HD0) = -1+0 0.53 x 10 Iy(HDO) - Iy(H20) = = 1.32 Iy(D20) - Iy(HDO) = 1.1+0 Iz(HD0) - Iz(H20) = = 1.1k Iz(D20) - Iz(HD0) = 0.87 I 33 cm" . As mentioned earlier, the shoulder appears to be due to (.vR + v^) absorption. Alternately the peak and shoulder may have resulted from nearly de generate VRx(HD0) and v-py(HDO) absorptions. Such an event implies that either Ix and Iy of HDO are degenerate through coupling, or that the li brations cannot be treated on the basis of moments-of-inertia. Both of these possibilities will be treated in detail. : 191 Assume that the librations of HDO, H20 and D20 can be simply re lated to the principal moments-of-inertia by Blue's (85) formula (page 27). Since the oxygen atoms lie close to each of the principal axes then the 2 r are all small and since the restoring forces on the oxygen atoms are °n all small then Blue's equation reduces to: —1 11 2 2 1/2 VRn(cm" ) = 2^l7T C2 (kHlnrHm + kH2nrH2n)] . [k] where: is the librational frequency about axis n kjj^n = kn2n = ^Hn on *ne tiasis of symmetry and r2 is the distance of atom Hn normal to axis n. ' Hln 1 Using the calculated moments-of-inertia from Table IV.II one obtains the librational frequencies in terms of the kgn force constants: H20 HDO . D20 vRx = 2.1*5 kH 2.60 kH' 1.83 kD VRy = 2.77 kH 2.33 kH' 1.99 kD ^2 = 2.90 kH 2.23 kH' 2.05 kD It is implicit in this treatment that the three librations of each molecule are non-degenerate. On the basis of the above equations the lowest observed frequencies of H20 and D20 must be associated with the Vpx's since they have the lowest force constant coefficients: Thus Vgx(H20) = 833 cm-1, and v]Rx(D20) = 627 cm-1. Using those frequencies the force constants are : kH(H20) = (1.15 t 0.03) 105 dynes/cm kD(D20) = (1.17 t 0.03) 105 dynes/cm For HDO, vR (HDO) has the smallest force constant coefficient and we assign that (on a trial basis) to the 819 cm 1 peak. Then the HDO force constant, 192 kg' , is (l.2k 1 0.03)10^ dynes/cm, in 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: H20 ' HDO D20 vRx 833 cm-1 916 cm-1 627 cm-1 % 9h0 819 682 VRZ 98U 785 702 where the observed frequencies which were used to define the force con stants are underlined. Since libration about the y principal axis entails a greater distortion of one HDO hydrogen bond than for vRx of H20 and D20 then the slightly larger HDO force constant is understandable. Of the nine frequencies listed above three were assigned from ex perimental observation. From the remaining six frequencies, two were ex pected to be ir inactive (i_.e_. vRz(H20) and vRz(D20)) while a third one (VR2(HD0)) is expected to be very weak. That leaves three predicted fre quencies to compare with experiment: vR (H20) , vR (HDO) and vR (D20). y y Only the prediction of (D20) at 682 cm 1 lies near an observed band, the D20 cubic ice I band at 66l cm-1. However, even that prediction is out by more than 20 cm As well, there were no observed absorptions . near the 9^0 cm 1 or 9l6 cm 1 predicted frequencies. Therefore, VR (H20) , y VRx(HD0) and VR (D20) are either weak or inactive ir absorptions. Alter-y nately those modes may be ir active and strong but degenerate with the other librational modes. 193 The conclusion must he that Ix and Iy are degenerate or Blue's for mula is invalid. 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 orbitals. As well, Blue's formula (85) over simplifies the problem since it ignores the motion of the four adjacent molecules through the hydrogen bonds. (ii) The Weighted Lone-Pairs Model Consider one R2O molecule as being suspended with neutral density in a cubic ice I lattice. The supporting lattice can be considered as having two principal effects. First, the principal moments of the two protons attached to the central molecule (0-H* •••()) are decreased through reduction of their :real masses to an effective mass by the "buoyancy" of the surrounding lattice through the hydrogen bonds. The mass "lost" by the two central protons is gained in the lone-pair orbitals of two neigh boring molecules. ' Similarly, the two lone-pair orbitals 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 their initial values. The second effect on the moments-of-inertia which arises from hy drogen bonding is 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. If 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, Ix = lv = lz. 19h A pseudo-symmetric top is 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 is that if the moments-of-inertia Ix and Iy are equal for H20 and DgO then by Blue's (85) formula vRx and vRy should be degener ate . . Consider the effect of reduced protonic masses and effective lone-pair masses where the molecular parameters will be assumed to be: r0H = r0D = °-950^ 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 H2 = 0.75(1.008) gms/mole =0.756 gms/mole the masses of H3 and H^ = 0.25 (1.008) gms/mole = 0.252 gms/mole (This is called the (3/h, 1/h) effective mass option.) The moments-of-inertia of H20#*-*H2 are: Ix' = 3.1+3 x 10 gm-cm2/molecule Iy' = 3.15 x 10 -1+0 -ho Iz = 3.30 x 10 Substituting those'values of the moments into Blue's (85) formula, [h], where the contributions of the oxygen force constants are still small, then: 195 X(H20, 3A,lA) = 2.87(0.282 kH + 3.20 ki) Se° VRy(H20,3/l+,l/4) = 2.99(0.602 kH + 2.14 k^) VRZ(H20,3/1+,1/1+) = 2.92(0.902 kH + 1.10 kg) where k^ is the 0-H----0 bending force constant and kjj is the 0'-**H-0 bending force constant. Our model supposes that vR and vR of H20 are degenerate at 833 x y cm \ By solving the first two expressions above one finds \-Yi ~ 0.60 x 10^ dynes/cm .and kg = 0.21 x 10^ dynes/cm. Using those values of k^ and kjj in the third expression above, then VRz (H20,3/1+,1/1+) is 831 cm which is degenerate with vRx and VR_^_ within error. How well do kH(H20) and k^(H20) apply to D20 D2? Using the above molecular parameters and deuterium effective masses of 0.75(2.011+) gms/mole for the attached pair (Dj and D2) and masses of 0.25(2.011+) gms/ mole for the detached pair (D^ and D^) then the D20--''D2 moments-of-inertia are: Ix = 6.8H(l0-^) gm-cm2/molecule Iy = 6.28(10"^°) and lz = 6.59(l0-1+0). The corresponding set of expressions from Blue's formula are: 196 :(D20,3A.1/U) = 2.03(0.268 kH + 3.20 k^} = 586 ?calc(D20,3A,l/U) = 2.12(0.902 kH + 1.13 kg) = 588 cm" v -MX — .i, ^oo -1 s'r v calc(D?0,3/U,lA) = 2.07(0.602 kH + 2.lk k') = 591 cm"1 Rz H where k^ and kjj of R^O were used. The three DpO librational frequencies are reasonably degenerate and lie 6% below the main observed band at 627 cm 1. This is as much accuracy as can be expected from so simple a model. By invariance of the potential energy to symmetry operations kj^O^-H-^-• • *02) = kj^Oj-Hg 03) and kj^O^Hg" - • *0^) = kntO-j-H^ O5). However, it does not follow that kH(0-Hj 2*'"'u) = kjj(0* ' "'H3 ^-0) , since they are not interchangeable by site or point symmetry. 1 That kjj is 0.309 times kg may be rationalized on the following basis. The potential for libration is the same in all 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 is 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-j^ g and O-'-'H^ ^ distances are 0.9^ and 1.79 A respectively, then! the 2 2 ratio (r^) /R(0',,-H) = 0.3^5. The moment' of the force acting at H and OH i 2 -11 H2 is kjjr = 0.53 x 10 dyne-cm compared to the moment acting at. H^ and H4, k^O H)2 = 0.67 x 10-11 dyne-cm. There is at least one disconcerting fact about this model that is seen for the case of h.0% HDO in D2O. The effective masses added to the HDO lone-pairs are 0.25 times the deuterium mass not the protonic•mass. Thus HDO librational frequencies would be calculated nearer to the D^O values than the H2O values, contrary to our observations. 197 Another weighted lone-pairs option was investigated, the (H20, 1, l/U) option. In this model the two attached protons were assigned full protonic masses, while the two detached protons were assigned masses of 0.25 times the full mass. Such a model seems unreasonable since the mass' sums are not conserved. By the same treatment as above one finds: kH(H20,l,lA) = 0.783 x 105 dynes/cm kfl(H20,1,1/1+) = 0.213 x 105 dynes/cm. The predicted vRz(H20) frequency is 829 cm 1 for this model and the pre dicted D20 frequencies are 582, 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 ^ —11 —11 are now nearly equal, O.69 x 10 dyne-cm and O.67 x 10 dyne-cm res pectively, x In summary let us consider the results of the two models considered First, Blue's (85) formula for non-interacting molecules gave three non-degenerate, widely separated frequencies for the three librations. That is contrary to the observed spectra and must be rejected. Secondly, for degenerate vR and vR the moments-of-inertia must be equal. Using a weighted lone-pairs model it was necessary to consider two kinds of hy drogen bond bending force constants, which were not accurately transfer able between H20 and D20 molecules. As well, the hydrogen bond bending force constants calculated were about as large as the molecular H0H bendin force constant, i_.e_. Zimmermann and Pimentel (97) found the H0H bending force constant in ice to be 0.1+9 x 10^ dynes/cm. The value of 0.60 x 10^ dynes/cm seems to be an unsatisfactorily high 0-H*••*0 bending force con stant . 198 B. The H203 Model.of Ice An alternate approach to the librations of H20, HDO and D20 molecules in ice is the normal coordinate analysis of an extended molecule HgO-j. The structure and parameters of the H203 molecule are shown in Fig. U.l8. For a freely rotating and translating H203 molecule there are nine degrees of freedom and nine internal coordinates (R) are defined as: R-L = Ar]_ R5 = A<(> R2 = Ar2 R6 = A6i R3 = Ar3 R7 = A62 = R8 = A61 \.- ^ A similar model was studied by Zimmermann and Pimentel (97) in order to calculate the hydrogen bond bending and stretching force constants asso ciated with molecular libration and translation. With Cp^. point symmetry the H^O^ molecule has the reducible repre sentation composed of 5^ 2a2 5b^_ and 3b2 irreducible representations. The representations of vibration, translation and rotation of the H203 molecule, as well as the representations of the.sets of symmetry coordin ates, are shown below: 199 Fig. k.18 The H203 model of H20 in ice I. The 000 and HOH angles were assumed to be tetrahedral. The hydrogen bond bending coor dinates 6-j_ and 02 are in the HOH plane and 8-|_ and 6^ are perpendicular to them. C2v E c2 °xz a yz al 1 1 .1 1 axx' ayy azz 1 1 -1 -1 Rz axy °i 1 -1 1 -1 TX Ry axz b2 1 -1 -1 1 Ty * RX "y? , r(H2o3) 15 -1 5 1 5ai + 2a2 + 5bx + 3b2 r(Rot.) • 3 -1 -1 -1 a2 + \ + D2 r(Trans.) 3 -1 1 1 a-|_ + bx + b2 r(vib.) 9 1 7 -1 l+a1 + a2 + 3b]_ + b2 ri(R1,R2) 2 0 2 0 a-^ + bl 2 0 2 0 aj + *1 r3(R5) 1 1 1 1 al ru(R6,R7) 2 0 2 0 a-^ + bl T5(R8,RQ) 2 0 -2 0 a2 + b2 200 The symmetry coordinates of HgO^ are S1 = 1//2 (R^ + Rg) S2 = 1//2 (R3 + R^) = R. Sh = 1//2 (R6 + R?) a. 1//2 (R1 -V ] S6 = 1//2 "(R3 - V \ S7 = 1//2 (R5 -V J S8 = 1//2 (Rg -v a2 S9 = 1//2 (RQ + v b2 In matrix notation the transformation from internal to symmetry coordinates is S = p where S_ and R_ are column matricies of symmetry and internal coordinates , and U is an orthogonal matrix. The solution of the secular equation is simpler in symmetry coordinates and the F_ and G 'matrices must also he transformed from internal coordinates (F_(R) and G_(R)) to symmetry coordinates (F_(S) and (J(S)) by the transformations F(S) = U F(R) UT G(S) = U G(R) UT The F(S) and G_(S) matricies each are diagonalized into block form contain ing a (k x lOaj, a(3 x 3)b^, a(l x l)a2 and a(l x l)b2 block. The form of G_(S) in terms of G_(R) elements and the numerical values of the G_(s) blocks are given in Table IV.III. The form of the F_(S) elements in terms of F(R) elements is the same as shown in Table IV.Ill for G_(S). Before proceeding further with the normal coordinate analysis, the normal modes of vibration, rotation and translation of H20 in ice I must be assigned to the internal vibrations of the H203 molecule as represented 201 Table XV.III. The symmetric G matrix elements in terms of the internal coordinates and their numerical values for the HgO^ model in units of (gm~^- A2 moles). ai G(S) G(S) = gll+ S12 S13+ slU 2g15 sl6+ gl7 1.03^ 0 992 0 088 0.062 E13+ g33+ 83h 2g35 S36+ s37 0.992 1 055 0 D 2g15 2g35 S55 2g 56 0.088 0 2 393 2. 511 s17+ gl6 g36+ S37 2g56 g66+ g76 0.062 0 2 511 2.733 sll- S12 S13 gl6" 'g17 1.076 0 992 0.062 S13 S33" g3U g36 = 0.992 1 055 0 gl6" s17 g36 g66" • g76 0.062 0 2.595 G(S) = [g88 -,g89] = 2.595 b2 G(S) = [g88 + g89] = 2.733 by the symmetry coordinates above. The displacement vectors of each kind of internal HgO^ coordinate are shown in Fig. h.19. The corresponding displacement vectors of the symmetry coordinates constructed from those internal coordinates are shown in Fig. h.20. The RgO ice I normal mode associated with each HgOg internal vibration is listed in Fig. k.20. The symmetry coordinates , Sg and , which correspond to vRxt> vRz, and respectively, are of particular interest for this discussion. / / R5=A<£ 6 Fig. 4.19 The internal 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 linear combinations of the internal 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. in Table IV.Ill shows that the two librations ("vRx and vRz) are "kinetically" degenerate and that vpv is very nearly degenerate with them: 20k G77 = %6 - S6T VRX  G88 53 §66 ~ 667 VRZ  G99 = §66 + g67 vRy If the forces restraining libration about x and y are equal (which they are for HyjCU by symmetry) then vR is degenerate with VR . -J x y The secular equation can be solved for the diagonal symmetry force constants by an iteration formula given by Green (.125): k*?1 = A.{ G. . + £ (GiJ)2kiJ } _1 [5]. 1 " j 5 The b2 block is trivial and gave the solution of kQQ = O.IH9 x 10 dyne-cm when was assigned to the peak at 833 cm ^. The a2 block is also trivial and gave the solution kgg = 0.157 x 10^ dyne-cm, in good agreement with knq(vT? and VR were assumed to be degenerate at 833 cm-"1"). For the (3 x 3)b^ block the S^, Sg and symmetry coordinates were associated with ^2^2°^' VTX^H2G^ &T1^ VRy^H2u^> respectively. Applying the iteration formula: 4 = \ (G„ + (0-992)2k661 + ^•062)2k771 }_1 55 5 55 —5; r 5; 7 •5-6 A5 " 7 A6 - X5 A7-S where A. = (v./1303-l) . Initial force constants k?. = 1.000 were assumed 11 11 and the formulas converged to t 0.001 in eleven iterations. The force constants determined were: 205 k,.,. = 5.U81 x 10^ dynes/cm kgg = 0.192 x 105 dynes/cm k = 0.15U x 10^ dyne-cm Notice that the symmetry force constant associated with vn , k„„ = 0.15^ Ky 77 x 10^ dynes/cm, does not agree with those of vR and VR . x z Finally 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 it was a genuine mode of HgO^. As a redundant coordinate terms due to in 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 initial force constants of k.. = 1.000, then the three iteration 11 formulas converged in fifteen steps to: k^ = 5-369 x 10^ dynes/cm k22 = 0.231 x 105 dynes/cm k ^ = 0.601 x 105 dyne-cm With better choices of initial force constants, the formulas converged in four to five steps to ± 0.001 x 10 ^ dynes/cm. To convert k^5 kyy' k88 and k units from dyne-cm to dynes/cm it is 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 kll(V = 5'369 k55(v3) = 5.H82 k33(v2) = 0.666 x 105 dynes/cm Of the three possible H20 translations only two force constants were estimated: k22(Tz) = 0.231 kgg(Ty) = 0.192 x 105 dynes/cm. Finally, three force constants associated with the three possible librations were estimated: k99(Rx) = 0.088 k77(Ry) = , 0.091 k88^Rz^ = °-°92 x lo5 dynes/cm. The above symmetry force constants were transformed back to internal coordinates force constants for comparison to those of other workers. For example, the symmetry force constants in terms of internal force constants are: kll^Vl^ = k^rlrl^ + k(r]_r2) k^(v3) = k(rir-]_) - kCr-ji^) k33(v3) = k Co)*) k99(Rx^ = k(eie'i)+ k(e|e2) kTT(Ry) = k(.e1e1)- kCe^g) k22(Tz) = k(r3r3) + k(r3r1+)k88(Rz) = kCe^e^)- k(e{e2) k66(V = k(r3r3) - k(r3*V 207 Thus one found that the internal coordinates force constants for H20 are (in 10^ dynes/cm): internal translational lie-rational (0 0 stretch) (0-H 0 bend) k(r1r1) = 5-425 k^r3r3^ = °-212 kCe^) = 0.090 k(r-Lr2) = -O.O56 H^r^) = 0.019 k(0-[02) = -0.002 kU<j>) = 0.666 *k(e1e1) = 0.093 *k(e1e2) = -0.002 Since the other symmetry coordinate involving 0^ and 0^ was assumed redun dant and eliminated, then k(9^0^) could only be evaluated by assuming that k(0102) = k(6J02) = -0.002 x 105 dynes/cm. A set of D20 force constants was estimated in the same way (from LV>03) as for H20. The results of the H20 and D20 ice I force constant : models are listed in Table IV.IV along with the results of Zimmermann and Pimentel (97) and Trevino (93). Our k(0^9-^) is an in-plane hydrogen bond . I ! . bend while k(0^0^) is the out-of-plane bend. Our in-plane hydrogen bond bend is approximately 1.5 times Trevino's value: Part of the difference is probably due to differences in the models, Trevino's (93) was extended further and in a three-dimensional lattice while ours was planar. The following comments can be made about the H20 force constants estimated using the HgO^ model and equation [5]: • • - the OH stretching force constant (k(r-j_r^) = 5.^25 x 10^ dynes/cm) is less than the gas phase value and is in the region predicted from the ratio of frequencies for harmonic oscillators, 208 Table 17.IT The force constants of ice I from the HgO^ and D20 models as well as the results of Pimentel and Zimmerman and Trevino. Force Constant Associated Motion D20 Pimentel This Work ' (a) (f) i.r. i.r. H20 This Work (f) i.r.. Trevino (e) neutron k(r1r1 kCr^ k(r3r3 k( r3ru k(e1e1 k(e1e2 *(9W k(0^02 0-H str. 0-H, 0-H interaction H- •0 str, 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) 5.7H -0.0U9 0.225 0.023 0.099 -0.002 (d) 5.U25 -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 0.730 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) all force constants are lO^ dynes/cm. (e) Trevino, Ref. 93. (f) This work, Green's formula, H203 model. 209 - the'hydrogen-bond stretching force constant (klr^r^l- = 0.212 . x 10^ dynes/cm) is of the order of magnitude expected on the basis that the hydrogen bond strength (5-10 Kcal/mole) is about l/25th of the 0-H bond strength, - the H-O-H bending force constant (k^^ = k(<j><j>) = 0.666 x 10^ dynes/cm) is slightly decreased from the gas phase value (0.69 x 10^ dynes/cm) as expected from the shift .in frequency, and - the out-of-plane hydrogen bond bending (O'-'-H-O) force constant (kfe^Gj) = 0.090 x 10^ dynes/cm) is very small, this may be interpreted as indicating the hydrogen bond is relatively insen sitive to bending through small angles. It is interesting to notice that for every diagonal, internal coor dinate force constant the DgO values are'larger than the H2O values by 5 to 10$. The source of this effect is in the nature of the force constant model. Green's (125) formula [5] assumes a diagonal force field and a harmonic oscillator approach. Since D20 energy levels are lower, and since D20 internal coordinates displacements are smaller than H20 displacements, then our D20 "sees" a lower, more symmetric portion of the "true" poten tial curve. The simulated D20 parabola is thus narrower and steeper than the simulated H20 parabola and consequently the D20 force constants are larger than the H20 force constants. It is obvious that such diagonal H202 and D203 models assumed no anharmonicity in ice. Such a case seems highly unlikely in view of the strong neighbour-neighbour interaction through strong hydrogen bonds. In spite of this oversimplification, the force constants appear to give a faithful representation of the spectrum. 210 The test of any set of. force constants, however, ll.es. in its ability to reproduce the observed frequencies of isotopic analogues. To check the force constants derived from RVjO-g for the H20 internal, translational and librational vibrations in ice, the frequencies of D2Q ice frequencies were calculated. Formula 15] was inverted and solved:-2 , [G„ + ,1 Gijkjj] [6] A. = k. . LG.. + . j. ij ,1,1 1 11 11 lyCJ . . where k.., k are taken from HgOCHgO^) 'Ai~ h A. is taken to be the observed value, and J A. is to be calculated. I The a2 and b2 blocks are easily solved of course since they reduce to the form - A. = k..G.. l n n in 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) yield 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: vcalc. vobs. Vcalc. Vobs. v3 vl v2 -1 -1 -1 cm cm cm 2325 2^13 -88 2258 2321 -63 1138 119k -56 595 -32 HX nn), £o-Aai vR~ 59^ 627 r -33 vj 601 627L&1 -26 (b) 232 220^' +12 Tx 229 220£bj +9 (a) VRXJ vp and VRz are assumed to be degenerate (b) Reference 96. 211 The D20 ice internal mode frequencies CyijVgj'V^l- calculated from formula [6] using H2OC.H2O3} force constants were all too low- C-6"3 cm-1, -56 cm/*'", -88 cm "*") by 3 to 5%. The D20 translational lattice frequencies calculated in the same way were too high by 5%. The modes of interest, for which the HpO^ model was constructed, are the librational lattice modes. Their cal culated frequencies were also too low by 5 - 6%. It is interesting that the librational D20 frequencies from the H203 model are nearly the.same as those predicted for HgO and D20 in the weighted-lone-pair, moment-of-inertia model previously discussed. There the frequencies calculated were 586 cm "*", 588 cm 1 and 591 cm "*" for vpx, Vp and vpz respectively. y ; One can conclude that the H2O3 normal coordinate analysis, as a basis for H2O/D2O ice librations offers no improvement over a weighted lone-pairs moment-of-inertia model. The HgO^ model does give reasonable internal and lattice, mode frequencies and reasonable ice force constants. C. A Summary of H2O, HDO and D2O Librations Three models, of ice libration were presented: Blue's (85) harmonic, hindered oscillator model using moments-of-inertia, a weighted lone-pairs moments-of-inertia model, and a normal coordinate analysis of the H2O3 ex tended molecule. Blue's formula [k] gave widely dispersed Vpx and Vp^. frequencies in H2O: and D2O, jL.e_. separation of about 100 cm \ This did not conform to the observed ir absorption. The last two models were discussed on the assumptions that the librational modes were degenerate or nearly degenerate and that VRx and vp^. are of equal intensity while vpz was weak or inactive. 212 Transfering effective mass from a nearest-neighbour proton to the central molecule's lone-pair orbitals produced a nearly spherical top. The three principal moments-of-inertia differed by only ± 5 percent for the (H20, 3/4,1/4) option. The force constants for molecular libration were k = 0.60 x 10^ 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 vpx = = 832 cm \ Application of k^ and k^' to formula [h] in D20 parameters predicted D20 frequencies of: 586 -1 cm vRy = 588 -1 cm 591 -1 cm The D20 frequencies' are reasonably degenerate, but lie six percent below the observed band maximum. Analogous results were obtained for an (H20, 1,1/U) effective mass option. Transferability of force constants among isotopic analogues was violated in 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 H20 force constants did not duplicate the D20 frequencies.. The dispersion was explained by considering the difference in shape of harmonic potential simulated by formula 15]. Degeneracy of the librational modes was acceptable in this model with respect to force constant evalua tion. 213 Further improvements in the analysis of ice may be found by treat ing it 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 traditional Wilson FG method, and lists 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 ir absorptions of vitreous, condensed mix tures of H20 and guest species were completed in the liquid nitrogen cell (page k2). Stoichiometric gaseous mixtures corresponding to the three classes of clathrate-hydrate were prepared and condensed in the same manner as the ice samples (page 58). Samples studied in the first clathrate class (page 13) 6G-1+6H20 were G = CH3CI, CH3Br and Cl2, 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 third class,. 20G*1T2H20 (page 15), was studied, i_.e_. G = Br2. The conditions of sample formation and annealing are listed in Table V.I. In order to • avoid separation of the clathrate mixture, all these samples were depo sited through the heated metal deposition tube (page kh). As with the H20, HDO and D20 samples, the source beam was blocked when the clathrate mixture samples were warmed above l80°K, in order to prevent sublimation. As well, the cell 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 in that way since the source beam was off then. Table V.I. The clathrate mixture sample histories for the deposition and annealing procedures, temperature refers to the.sample block temperature.with the source off. The deposition Molar gas ratio Deposition Rate Sample Substrate Deposition Temperature °K Annealing Time Min Maximum Annealing Temperature °K Time at Maximum Temperature Min B2 ICH3CI: lCH^Br: CI (CU) ICH3I: 10 sec 1.5 min Csl 83 139 200 12 Csl 81* 265 199 U5 5 sec ( -- ) Csl 83 (83) 98 (105) • 188 (189) 16 (18) D 1CHC1-: 7 H20 7 H20 17H20 17H20 2 sec Csl 83 172 189 15 E lC2H5Br: 17H20 3 sec Csl 81 170 189 16 Fl (F6) 1C12: 7 H20 3 sec ' (2 min) Csl 81 (82) 103 (25) 189 (190) 12 (15) G3 1C12: 7 H20 3 sec AgCl 83 . 15 190 11 lBr2: 8. 6H~20 3 sec AgCl 83 2k0 200 25 ro H 216 All 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 850 and l80°K. Peaks and shoulders were assigned as for ice I (page 59). B. Results of Devitrification While the degree of crystallinity of the samples condensed from the vapour phase depended upon the sample history, the basic results for all the unannealed, vitreous.samples were the same. Consequently, only one set of normal annealing results will be discussed in detail. Some irregularities were observed for 6Cl2'46R"20 condensed and annealed on a Csl window.: Those results will be discussed separately. Each of the H^O skeletal bands (v]_ + vp), v3» vl» 3yR» V2/2.Vp and vR was analyzed, as were those guest absorptions which were observed. No distinction between the classes^ of. clathrates was noticed in this work. (i) The Effect of Devitrification on the Lattice Peak Maxima For the seven samples listed previously (page 215) only the results of the chloromethane clathrate mixture will be given. The six other samples (including Cl2 on Csl) had the same behaviour within the limits of error. The frequency-temperature dependences of the main H20 skeletal features are shown in Fig. 5-1. The absorption spectra of some unannealed and annealed samples (all at 83 ± 3°K) are shown in Figs. 5.2, 5-3 and 5-4. Some details of the CHjCl'T^THgO clathrate mixture annealing (Fig. 5-l) are 0 UJ D h < Q: UJ Q_ LU 200 -o LU D h < LU Q. LU h o LU DC D h < LU CL LU h 150-IOO -70 200 150 -IOO 70 200-I5Q-IOO-70 • 8 ^3 • 7 •7 •5 • 4 • 3 • 2 •5 • 4 • 3 • 2 • 6 • 1 • 6 • 1 I'll 1 3150 3170 1 1 i 1 3220 3240 • 8 •8 • 7 • 5 • 4 •3 • 2 • 7 • 4 •3 •2 • 5 • 6 • 1 • 1 • 6 i i 3360 i i i i 3370 • i i I 2220 i 2230 • 8 • 8 •7 •5 • 4 •3 • 2 •5 • 4-• 3 •2 • 6 •f •1 • 6 i i i i i i 1610 1630 1650 i i i 1 790 810 i i 830 217 FREQUENCY CM -1 Fig. 5.1 The shifts of the unannealed clathrate mixture (CB^Cl^^R^O) H20 peaks during warming from 83 ± 3°K to 200 ± 5°K. The data are typical of all the clathrate mixtures and appear to be the same as for ice Iv. The data are numbered in the order of observation. A.B A.B •4000 3000 1000 A.B 4COO 3000 2000 FREQUENCY CM" IOOO 500 A.B 500 Fig. 5.2 The infrared absorption spectra of some clathrate mixtures. In. all cases spectra numbered "A" are backgrounds through the low temper ature cell, (a) CH3CI•7.67H20 unannealed at 83 ± 3°K (B), at 83 ± 3°K but annealed to l60 ± 3°K (C), and at 200°K (D). (b) CH^Br• 7.67H20. unannealed at 83 ± 3°K (B), at 83 ± 3°K but annealed to 158 + 3°K (C) and at 189 + 3°K (D). (c) CH3I-17H20 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 all of the spectra, i.e. for each absorbance scale. Fig. 5-3 The effects of annealing clathrate mixtures of CHCI3 and C^^Br" 17H20. (a) CHC13-17H20 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) C2H5Br•17H20 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 is shown for D than for E. A.B A,B 4000 3000 2000 1000 FREQUENCY CM" 500 Fig. 5.U Ca) Br2'8.6 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 six hours apart while spectra D and E were recorded thirty minutes apart. (b) C12-7.67H20 on AgCl unannealed at 83 ± 3°K (B) and at 83 ± 3°K but annealed to 190 + 5°K Cc). (c) C12-7.6T H20 on Csl unannealed at 83 + 3°K (.B) and at 83 ± 3°K but annealed to 190 ± 5°K for 15 minutes (C). 221 in Table V.II. As for ice I, the frequency shifts of the vitreous sample peaks were irreversible. The points in Fig. 5.1 are numbered in the sequence in which they were obtained for each band. The sixth point was obtained by cooling the sample to 83 - 3°K after annealing it at 160 ± 3°K for 20 minutes and before warming to higher temperatures. Table.V.II The R"20 frequencies of the CH3C1*7.67H20 clathrate mixture before (vu) and after (va) 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 vu • • va va - vu Range AT cm cm cm 1 °K cm ""V°K v + vT 3382±5 3361+ _i8 (lUO-170) ±10 0.10 V3 vl v2 VR 3258±3 3219 -39 (lHO-l6o)±10 0.12 3195±5 311+6 -1+9 (130-155) ±10 0.25 3vD 2209±5 2227 +18 (125-155)±10 -0.09 R l65l+'±3 1610 -1+1+ (125-Il+0)±10 0.18 792±1+ 823 +31 (I15-ll+0)±10 -0.l6 222 The five conclusions made with respect to the ice I devitrification (page 63) apply to RgO in these clathrate mixtures also. • Typical visual observations of the annealing process are illustrated by those for CH3CI'7.67^0: - at 83 i 3°K (before' annealing) a transparent film around a translucent, milky-white mass about 0.25 inches in diameter, - at 168 i 3°K an opaque white mass opposite the nozzle surrounded by a thin transparent film, and - at 188 t 3°K the sample appeared to be totally white and opaque. In general, the source image was centered on the thinner portion of the sample. The Br2'8.6H20 mixtures were not white, but were orange and yellow-orange depending on the thickness. (ii) The Effects of Devitrification on the Oligomeric HpO Bands Weak peaks and shoulders on the high frequency side of the skeletal unannealed HgO stretching band had the same appearance as for vitreous ice I (Fig. 3.3) and can be seen in 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 in Table V.III: 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 results were obtained from mixtures deposited through a needle valve in ^.5> 1.5 and 11 minutes respectively. The temperature dependences of the H2O oligomeric absorptions from a number of clathrate mixtures are given in Table V.IV. With a single exception the oligomeric HgO "absorptions began to diminish in peak height between 120 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 in several unannealed clathrate mixtures. Csl AgCl CR£1 CH3Br CH3I CHCI3 C2H^Br Br2 C12 ci2 H20 '7.67H20 7-67H20 "17H20 •17H20 •17H20 *8.6H20 *7.67H20 •7.67H20 ice Iv 1"5 cm """ ±5 -1 cm ±5 cm ±5 cm """ ±5 cm *"" +5 cm """ ±5 -1 cm ±5 cm """ ±5 cm 1 36U5 (vw) 3580 (w) 3689 (ww) 36k3 (vw) 3691 (ww) 3689 (ww) 3635 (vw) 3687 365h (vw) 3605 (vw) 3639 (vw) 3565 (w) 3612 (vw) 3672 (vw) 3658 3583 (w) 3635 (w) 3637 3687 (ww) 3670 (vw) 3617 (w) 3687 (vw) 3668 (ww) 3673 (w) 3623 (vw) 36U8 (ww) 3636 (vw) 3620 (v) 3625 (ww) 3638 (vw) 3689 (ww) 36k2 (w) 3620 (w) 3690 (vw) 3690 (ww) 362k (vw)-3671 (vw) 36lU (w) ro ro 22h Table V.IV The temperature dependences of the oligomeric H2O absorption frequencies of some clathrate mixtures and unannealed ice I. 85±3°K 9i+±3°K 110±3°K 125±3°K , H20 Ice Iv -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 H20 cm ^ 3689 (sh) 3639(0.11) 3687 (sh) 361+0 (0.10) 3673 (sh) 361+0(0.06) 3672 (sh) 3652 (sh) 363l+(0.0U) 83±3°K 110±3°K 129±3°K 150±3°K C2H5Br'17 H20 -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 Cl2-7.67 H20 -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 170±3 +0.5 hours °K 83±3°K Br2-8.6 H20 -1 cm 3691(0.02) 3612(0.10) 3693(0.02) 3616(0.08) 3609(0.06) 3563 (sh) 3528 (sh 225 Table V.V The temperatures at which the oligomeric peak heights began to decrease (T-.) and the maximum temperature at which they were observed (T2) Guest Tl T2 CH3CI ±5°K 120 ±5°K 120 CH3Br 120 < 138 CH3I 120 < iho CHC13 ikg < 169 C2H5Br 125 < 150 Br2 — > 185 Cl2(Csl) 129 < lh9 H20 ice Iv 110 125 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 visual appearance of the Br2'8.6H20 sample changed markedly during annealing above 185 t 3°K (with the source beam off): 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 off. 226 (iii) The Effects of Devitrification on Gl2-7.6THpO Mixtures Gaseous mixtures of Cl2"7-67 H2O condensed on Csl and annealed for long periods appeared to react with the Csl. Consequently the Cl2'7-67 H20 mixture was studied on two substrates, i_.e_. Csl and AgCl, samples F and G respectively. In all six samples were studied on Csl and three on AgCl. (a) C12'7.67H20 on Csl (sample F). The ir absorption spectra of Cl2*7.67H20 at 83 ± 3°K before and after annealing to l89°K were shown in Fig. 5.*+ (sample Fj), while the temperature-frequency dependences of the H20 skeletal absorptions were the same as for CH3CI•7•67H20 (Fig.5-1). The effect of annealing Cl2"7.67H20 to progressively higher temperatures is shown in Fig. 5-5 (sample Fg). The visual 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 in diameter, and - (at 83 ± 3°K after annealing) a uniformly white opaque sample. The visual appearance of sample Fg before and during annealing was the same as for sample F]_. By visual observation no distinction could be drawn between the samples annealed to 170 ± 3, 180 ± 3 and 190 ± 3°K although their 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 4000 3000 2000 IOOO FREQUENCY CM Fig. 5.5 Spectra of one sample of Cl2,T.67H20 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 cell at 83°K. ro ro —] 228 190 ± 2°K, i_-e_. the intensity of the low frequency shoulder increased and a new high frequency shoulder appeared. Annealing to 170 + 2°K or 180 t 2°K gave only the characteristic sharpening into 1 peak and 2 shoulders. As well, the nature of the v2 absorption changed. (b) C12*7.67H20 on AgCl (sample G). Detailed studies of the annealing process of amorphous solid Cl2-7 HgO on an AgCl substrate were not made. Spectra were recorded at 83 ± 3°K before and after annealing to various temperatures. The visual 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. Cl2 guest absorption as might be expected was not observed and the H20 skeletal absorption was shown in Fig. 5.^. None of our attempts to split the C12'7-67H20 stretching band into 1 peak and 3 shoulders succeeded for samples on an AgCl window. Nor was the nature of the v2 band changed. As well, no increased absorption between 3000 cm-1 and 2^00 cm-1 was observed. The positions of the C12'7.67H20 bands on Csl and AgCl will be discussed in section 5-3 (page 23*0. 5-2 Clathrate Mixture Guest Absorptions , • The ir absorptions due to the guest molecules which were expected to be trapped in the cages of the- H20 host lattice were formed and observed by three techniques. In the first method (section 5-l) the stoichiometric gaseous mixtures were condensed rapidly onto a substrate held at 83 i 3°K in an open chamber (section 2.kc). To ensure that the guest molecules were not diffusing out of the host lattice, a second and a third method 229 were investigated. The second method was condensation of the mixtures in an isolated chamber (section 2.4B), and the third method was the prepara tion and observation of low temperature mulls (section 2.kA) of solid clathrate mixtures (section 2.3A). Of the seven clathrate mixtures studi< Clg'T-STHpO and Brp'S^RgO should have no guest ir absorptions. A. Condensation in an Open Chamber During devitrification 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 will be described in detail. For example, the CH3CI'7.67^0 guest absorptions were observed at 2957 (m), lkk3 (m), 1U37 (sh), 1347 (w) 1338 (vw), 1021 (vw) and 700 (ms) cm 1 (Fig. 5.2(a)) near the solid CH3CI absorptions. They were observed up to 100 ± 3°K with undiminished intensity and up to l60 ± 3°K with diminishing intensity. In contrast CH^I'^^O guest absorptions"were undiminished up to 138 +2°K and nil at 168 + 2°K for one specimen, while for a second specimen the CH3Br absorptions were slightly diminished at 110 + 3°K and slowly diminishing up to 189 ± 3°K (the 1235 cm-1 peak was still present). The guest absorptions from a number of unannealed clathrate mixtures at 83 t 3°K, immediately after deposition, are listed in Table V.VI. The variations of those guest absorptions as a function of temperature are given in Table V.VII and the temperatures of the onset of alteration, in guest absorptions and the maximum temperature at which they were observed are given in Table V.VIII. Table V.VI The alkyl halide guest absorptions at 83 t 3°K in a number of alkyl halide clathrate mixtures before annealing began CH3CI CH^Br CH3I CgH^Br •T.67H20 -7.67H20 -17H20 CHC13 ' 1TH2° -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) 2950 (w) 2936 (ww) 2985 (vw) lhk3 (m) 2915 (ww) 1^37 (sh) 1292 (vvw) 13^7 (w) 1218 (ww) 1238 (w) 12kk (sh) 1238 (sh) 12U1 (ww) 1238 (ww) 125^ (vw) 1338 (vw) 1200 (sh) 1233 (sh) 123U (w) 121U (w) 1216 (vw) 12ll| (vw) 12k2 (vw) 1021 (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 typical of all samples. . 83±3°K 110±3°K CH.3I • 17H20 2950 Cw) 1238 Cw) 1233 (sh) 2960 Csh) 1247 (w) 1240 (vw) 83±3°K 139±3°K 2936 (ww) 2915 (ww) 12kh (sh) 123-4 (w) 2939 (ww) 2917 (ww) 1244 (sh) 1236 (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 C2H5Br'lTH20 2985 (vw) 1254 (vw) 12U2 (vw) ' 955 (w) 760 (sh) 2983 (vw) 1255 (vw) 1245 (w) 956 (w) 760 (sh) 2981 (vw) 1252 (sh) 12U5 (vw) 952 (vw) 763 (sh) 1258 (sh) 1245 (ww 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 (T2). Guest Tl T2 G-7.6TH20 ±3°K ±3°K CH3C1 100 160 CH3Br 138 < 170 G'1TH20 CH3I 138 < 168 110 > 189 CHC13 129 < 189 > 169 C2H5Br 110 < 170 The guest frequencies shifted very little, if at all, upon warming for devitrification, however the peaks did sharpen near 125 1 5°K. For example, in annealing CHC13'17H20 (Fig.5.3(a)) the absorptions near 1200 cm sharpened at 129 - 3°K. In fact it split into two distinct peaks at 1223 and 1203 cm-1 and a shoulder at 12lU 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 is that they were unobserved after annealing. 233 B. Condensation in'an'Isolated'Chamber The condensation apparatus and the technique were described in sec tions 1.6 and 2.UB respectively. Stoichiometric mixtures of Cl2 "7.67^0, S02-7.67H20, CH3C1-7.67D20, CH3C1-7.67H20, CH3Br•7•67H20, CC13F'17H20, and CH3I'17H20 were condensed rapidly in a precooled chamber and annealed to I85 i 5°K for 2-5 minutes. Spectra were subsequently recorded at 83 i 3°K on the P.E. 112-G- spectrophotometer. The results of this method were the same as for condensation and devitrification in an open chamber. No guest absorptions were observed in the annealed samples, while the H20 "host" absorptions were the same as for section 5.1 but with considerably more scattering. As well these samples had spectra much like C12'7.67H20 (on Csl) between 3000 and 2200 cm-1 (Fig. 5.4(c)). C. Low Temperature Mulls The technique was described in section 2.kA and spectra were recorded on the P.E. 421 spectrophotometer. The present samples were mulled from ground solids prepared by freezing-warming cycles on stoichiometric liquid mixtures. At 83 + 3°K CH3I'17H20 and CC13F-17H20 had no guest absorptions and the R"20 skeletal absorptions were like those reported in section 5.1 for annealed samples. However, the scattering was greater than in methods 5.2A or 5.2B. Some guest absorptions may have been masked by the C3Hg and CC1F3 mulling agent absorptions, but it seems unlikely that all the CH3I peaks would be masked by both agents. Several thicknesses of samples and amounts of mulling agent, were tried, all with the same results. 23h 5.3 Temperature Dependence of the Crystalline Clathrate Mixture Absorptions The results of warming annealed samples of clathrate mixtures from k.2°K or TT°K to 200°K are in general the same as for cubic ice I, .i.e.. only the H20 ir absorptions were observed. Thus only a few typical clath rate mixture results will be quoted and the remaining clathrate mixture results will be given in tabular form or as an average over all samples.. A. Temperature Dependence of the HDO Absorptions (i) Experimental The data reported here for v^HDO) in CH3C1-7.67D20, CHgBr • 7 • 67D20 and CH3I-1TD20, for V (HDO) in CH3Br•7.6TH20, and for vR(HDO) in CH3Br•7•6TD20 were obtained from gaseous samples condensed in an open chamber followed by devitrification (section 5-l). The observations were made with the liquid.helium dewar and the P.E. h21 spectrophotometer. Details of the sample histories were typical of those for ice I (page 69) as were details of spectrophotometer operating conditions. The HDO peak maxima were determined as before (page 69) and: were estimated to within ±0.5 cm-1. (ii) Results of Warming Clathrate Mixtures Containing HDO (a) The HDO.stretching bands. These bands appeared to be the same as in cubic ice I (Fig. 3.l) and typical spectra will not be reproduced. The temperature dependences of ^(HDO) and v (HDO) for CHoBr•7.67H?0 On , OD J are shown in Figs.. 5-6 and 5.7: They are typical of the other clathrate i-I 1 200 235 150 X. o <D D o ioo-a E' 50-A i • A O A • • A • A e A 6 A • A # • AA| A Z/ (HDO) OH o-3262 70 80 3290 Frequency cm -1 Fig. 5-6 The temperature dependence of v (HDO) for CH3Br-7D20 (k.0Q% HDO) after annealing. This was typical of all the annealed clathrate mixtures of the alkyl halides. 200 I5CH o CD D O Cl E IOOH 50 236 (HDO) OD o 2412 20 2430 Frequency cm -1 Fig. 5.7 The temperature dependence of v CHDO) for CH^Br•7•67H20 (5.9W ' HDO) after annealing. This behaviour was typical of other alkyl halide clathrate mixtures. mixtures and are very similar to cubic ice I. The details of the frequency-temperature dependences for all clathrate mixtures containing HDO are given in 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 in these clathrate mixtures behaved h in ,the same way as for HDO in cubic ice I. Some Av data are given m Fig. 5.8. Table V.IX Some parameters derived from the. plots of vOH(HDO) and. vQD(HD0) against temperature for four annealed clathrate mixtures. Clathrate Guest G CH3C1 CH3Br CH3I CH3Br Mode Observed vQH(HDO) vQH(HD0) v0H(HD0) v0D(HD0) Low Temperature Limit -1 cm V Av55 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 Av13 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 Av32 100±20 10015 0.1+±5 9515 8515 Irregularities in Frequency Shift, °K V 1+2-48 1+2-65 1+5-67 63-75 52-57 1 200 i o = Azy^ (HDO) CH CI - 7.67 HO OH 3 2 A--A^2(HDO) CH I - 17 H O OH 3 2 ^ ISP-CD -t— o ioo-CD a £ ^ 50-• • A • AA • A i=Az/ (HDO) OD CH Br - 7.67H O 3 2 O AA Aa eo 9 •• •< • M 40 50 60 70 Half-height widths Az/2cm_1 Fig. 5.8 The half-height widths for VQ^CHDO) and v (HDO) in several clathrate mixtures after annealing These data were almost twice as large as for the cubic ice I data. IV) CO 239 Cb) HDO librations. Data for vR(HDO) of CH^Br•7.67D20 (k.0% HDO) are given as a function of temperature in Fig. 5.9- This data is typical of other clathrate mixtures as well. The details of the temperature dependences are given in Table V.X. B. Temperature Dependence of the H20 and D2O Absorptions (i) Experimental The H20 and D20 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 Do0 clathrate mix-llol.K^KK r( d tures the stretching band was studied in detail for CH^I • ITD^O, 0^01*7.67 DpO and CH0Br'7.67Do0, and the (v ' v V band was studied only in CH_Br-7-67 D^O.. All mixtures except Cl^ and Br^ were studied between U.2°K and 200°K, while Cl^ and Br,, were observed only above 77°K. Sample histories and spectrometer conditions were typical of the ice experiments. (ii) Results of Warming Clathrate Mixtures Containing H20 and D20 The temperature dependences of the H20 and D20 absorptions in the annealed clathrate mixtures were the same as for cubic ice I. Typical spectra for v^ and v^. of CH^Br•7.67D.20 are given in 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 in Table V.XI. The details of several C12'7.67H20 and Br2'8.6H20 mixtures above 83 ± 3°K are given in Table V.XII. The spectra and plots were treated in the same manner as for 2h0 180 i • 150 -Y. o CD -4— CD a 100-50-o-795 o e 1/ (HDO) R •• • ^ # A 800 810 Frequency cm-1 820 Fig. 5.9 The temperature dependence of VRCHD0) for annealed CHgBr*7•6TD20 (k.00% EDO) clathrate mixture.. This data is typical of other alkyl halide clathrate mixtures. Table V.X The parameters for the HDO librations of three annealed clathrate mixtures. CH3Br-7.6TD20 CH Br-7.67D 0 CH I-17D20 CH Br'7.67I>20 ( k.00% HDO) 3(k.00% HDO) {k.00% HDO) (k.00% HDO) v (HDO) v (HDO) v (HDO) v (HDO) + v Low Temperature Limit cm1 8lU.0±2.0 '817.8+1.0 8l6.3±1.3 853.3±2.8 Low Temperature Dependence cm" < -0.03 < -0.03 — < -0.09 °K High Temperature cm-l _0.061|±0.031 -0.135±0.055 -0.l6U±0.045 -0.125±0.028 Dependence °K "Freeze-in" Temperature °K 75±10 70±5 62±5 80±5 Irregularities in Frequency shifts °K H8-58 Vf-57 56-72 ro H 2h2 I8O-1 150 -X. o 0) >_ D -t— 2 cu a E lOO-O-z,(D20) B H B B° A B a A A A a • a A B ' " * 2410 2420 2430 Frequency cm-1 2440 Fig. 5.10 The temperature dependence of v^DgO) for annealed CH^Br*7.cJD^O. Data from two specimens which had similar sample histories are given. ice I to determine the details of tine samples behaviours. The liquid helium and liquid nitrogen cell frequency data did not always coincide within the errors of the two experiments. In general, the liquid helium cell data have been quoted in 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 resulting instrument imbalance near 2300 cm 1, 2k3 \80-{ WDO) 12 o CD =5 100H o CD a o o o, o o o 0 o ° • • o o o 2310 O o o I 1 1 1— 20 30 40 2350 -1 60 Frequency cm Fig. 5.11 The temperature dependence of v (D 0) for annealed CH3Br-T.6TD20. Data from the same two experiments as in Fig. 5.10 are shown. The best study of 3VRCH"201 was ma(ie for a thick sample of Br2*8.6H20. The frequency-temperature dependence was distinctly negative. Samples of Gl2*7.67H20 on Csl support windows gave anomalous behaviour after annealing to 190 ± 5°K. The stretching band split 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 V2 absorption:' A peak at 1628 cm-1 and a shoulder near 1620 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 in brackets) modes averaged over the five alkyl halide annealed clathrate mixtures. v Vl Low Temperature Low Temperature High Temperature Freeze-in Limit Dependence Dependence Temperature H2° cm"1 ' cm-1/°K * cm_1/°K (D20) v + v 3331±5 (sh) <0.06 0.17±0.05 82±10 (2l+40±5) (0.06±0.O3) (0.lU±0'.06) (93±15) 3K 3208±3 (vs) <0.06 0.19±0.05 8l±15 J (2l+l6±2) (0.05±0.03) (0..12±0.0U) (88±10) 312T±5 (sh) <0.15 0.24±0.05 85±20 (23l6±2) (<0.08) (0.2U±0.05) (86±10) v0/2v„ 1588±6 (m) <0.2 0.36±0.15 80±15 c. K R R 896±5 (6T7±3) 831±5 (6U6±3) (sh) (s) -0.07±0.01 (<0.03) -0.05 ±0.01 (<-0.02) -0.l8±0.05 (-0.15±0.07) -0.l4±0.06 (-0.15±0.07) 83±15 (80±10) 85±17 (90±10) ro -p-p-Table-V,XII The frequencies at. 80°K-and the hi^ and of Br2-8.6H20 on Csl.' *h temperature dependences of Cl2' •T.67H20 on AgCl and Csl Host Lattice H20 Guest Species Clg ci2 ci2 Br2 Br2 Sample Support Window Csl Csl AgCl AgCl Csl Frequency at 80°K from Extrapolated Linear Dependence cm -1 + VT 3368 3365 3338 3333 3332 1 V-5 3218 3215 3221 3222 3216 3 311+5 3119 311+7 31 vr 311+7 3vR 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 8^2 831 Frequency Vl + VT -0.12 -0.20 0.32 0.26 0, .28 J. 1 0.13 0.12 0.22 0.16 0, .17 Dependence on 0.19 0.21+ 0.18 0, .21 -1 — — -0.18 -0.12 -0. .01+ Temperature q-z— -0.06 <±o.o6 0.1+6 0.19 0, .1+0 4' VR -0.09 -0.18 -0.10 -0.20 -0, .05 -0.17 -0.15 -0.20 -0.16 -0, .13 -p-V71 2h6 tion attributed'to. C^i + vTl was a.peak near 336.5 cm*" for C12"7.67H20 on Csl. That was about 30 cm higher than the shoulder observed in other samples and for C12,7.67H20 on AgCl. Also, the frequency-temperature dependence of (v^ + v^l (JH^Ol from samples of Clg^^H^O on Csl was nega tive. 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) 3338 Csh) cm' 3285 Csh) — 3218 Cvs) 3221 Cvs) 31U5 (sh) . 31U? (sh) 2220 (w) 2225 (w) . 1883 (w) — 1628 (sharp, weak) — c.a. 1600 (broad, m.) 1609 (broad, " 89^ (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 crystallization, the effects on the ir spectra and the processes involved in reorientation. As before the H20 lattice 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 irreversibly below 150°K and reversibly once warmed above 150°K. It was not clear that annealing vitreous clathrate mixtures o o produced the desired cubic 12 A or 17 A unit cell structures. We suspect that not a clathrate structure, but cubic ice I was probably formed. The longer transition 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 shift was the same as in ice I (the formation of a fully hydrogen bonded network of each oxygen to four nearest-neighbour oxygen atoms at about the same distance as in ice I) there should be a fundamental difference for the ir spectra of clathrate-hydrates. X-ray crystallography had shown that the alkyl 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 cell size. The annealing results did not support this concept, but results on H20 and D2O were subject to large errors. HDO results were better and are discussed in section 6.3A. B. Annealing Cl2-7.6TH20 on Csl • Samples of C12*7.67H20 which were deposited on Csl and annealed to 190 or 200°K for 10 to 15 minutes gave unique H20 spectra (Figs. 5-^(c) and 5.5), while the same samples annealed to only 180 ± 3°K gave typical H20 spectra (Fig. 5-5) • As well, the spectra from samples of C12*7-67H20 annealed on AgCl windows to 190 or 200°K for long times were typical of ice, as were the spectra of CH3CI, CH^Br, CHCI3 and C2H^Br clathrate mixtures annealed on Csl at 195°K for more than 10 minutes. The Cl2'7.67H20 on Csl samples had five 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 in 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 well 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 distinct shoulder at 1100 cm and pronounced absorption between 2300 cm and 3000 cm-1 (Fig. 5-^Cc)). The last effect may have been due to increased scattering losses if the substrate surface became pitted by the sample, while 2h9 the shoulder at 11Q0. cm~ may- have heen due to a Christiansen filter effect. Me eke et al. (103) observed four well defined bands in their "ice 1^" spectra on NaCl windows (Table VI.I). However, Schiffer (.104) studied a number of dihydrated sodium halides and showed that Mecke's "ice" was NaCl-2H20. The data of Table VI.I suggest that the C12'7.67H20 condensed and annealed on Csl may have formed a hydrated cesium halide layer on the substrate, i_.e_. CsI'xH20, CsCl-xH20 or CsICl2'xH20. The presence of hydrated cesium halide substrate was supported by the appearance of the sharp, weak peak at 1628 cm" and a shoulder at 1607 cm 1 in the spectra of C12'7.6"7H20 on Csl. These were similar to peaks observed by Mecke et_ al. (103) and Schiffer (.104) , Table VI.I. That substrate hydration did not occur for C12"7.67H20 on AgCl nor for CH3CI, CH^Br, CH-^I, CHCI3 and C2H^Br clathrate mixtures is not sur prising. For AgCl and C12'7.67H20 it is probable that the Cl2 does not oxidize AgCl, whereas it may oxidize Csl. As well, AgCl is chemically more resistant to hydration. It is possible that Cl2 reacted with Csl to form CsCl and IC1 or else CsICl2. Intermediate steps may have allowed the formation of hydrated halide salts. Although hydrates of CsCl, Csl and CsICl2 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 ly (10,000 A) thick. From the relative intensities of the ice I and hydrated salt absorptions one might expect 10% or more of the H20 in the original sample to be attached as water of hydration. Thus the formation of several hun dred monolayers of CsICl2 is unlikely since IC12 is too long to fit 250 Table VI.I The ir absorptions due to RgO stretches in dihydrated salts, "Mecke's ice", and annealed Cl0"7.67K20 on Csl(all at 83 i 3°K. C12*7.67H20 on Csl Ice on NaCl(a) NaCl•2R20 (b) NaBr•2H2O Cb) , NaI-2H20 Cb) CaSOi,-2H20 Cc) -1 -1 cm cm • 31*12 (sh) 3555 (m) 3538 (s) 3539 (s) 3568 (sh) 35^9 (vs) 3368 (ms) 3^71 (s) 3U68 (vs) 31+69 (vs) 3506 (s) 31+96 (s) 3285 (sh) 3^07 (s) 31+05 (vs) 3I+06 (vs) 31+61 (s) 31+01+ (vs) 3218 (s) 321+5 (w) 3310 (ww) 3360 (sh) 31+37 (sh) 321+2 (m) 311+5 (sh) 3265 (mw) 31+21 (vs) 321+2 (mw) 1628 (vw) 161+5 (m) ' 161+3 (s) 1635 (s) 1626 (sh) 1607 (sh) I6l6 (m) 1615 (s) 16H+ (s) I6l3 (s) (a) Ref. 103 (b) Ref. 101+ (c) Ref. 127 into an.interior I- lattice site: It may however occupy an I- surface lattice site. As well it seems unlikely that a solid-solid reaction would lead to deep penetration of Cl2 or Cl~ into Csl since Harrison et al. (128) found some alkali halide single crystals were'very resistive to exchange with Cl2 even at room temperature. The origin of the new absorption at 1883 cm 1 is not known. It lies well above the calculated v^HgO) position of Hornig ejfc_ al_. (105) , 1780 cm-1. It may be due to Cv2 + vT) for the hydrated salt v2(H20) and the H20 lattice 251 C. Oligomeric K2Q Absorptions All the'"unannealed clathrate mixtures exhibited very weak peaks or shoulders in the region 3500-3700 cm"1, Table VI.II. Similar absorptions were found for H20 and D20 ice Iv and the clathrate mixture peaks were also assigned to oligomeric H20 and D20 units. As was shown for CH^Br•7•67H20 (Table V.IIl) in three different specimens the positions, intensity and number of oligomeric features were dependent on the rate of sample deposi tion. The 3690 cm 1 peak was obtained from a CH^Br•7•67H20 sample deposited in 11 minutes, while the 3620 cm 1 peak was obtained from a sample deposited in 1.5 minutes and the peaks at 36h5 and 3605 cm-1 were obtained from samples deposited in 4.5 minutes. Fast deposition produced more localized heating and H20 polymerization than slow deposition. Van Thiel et_ al_. (117) suggested monomeric, dimeric and trimeric H20 absorbed at (.3725 and 3625), (3691 and 35^+6), and (3510 and 3355) cm 1 respectively. On that basis we appear to have formed residual dimeric H20 in the unannealed clathrate mixtures. The presence of oligomeric H20 and D20 suggests a low mobility of molecules during condensation. However, low mobility of guest molecules does not necessarily follow. Finally, it may be possible to follow the rate of crystallization in ice I and clathrate mixtures by following the peak heights of oligomeric H20. D. Unannealed Sample Guest Absorptions Guest absorptions in unannealed clathrate mixtures due to alkylhalides were observed for all 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 in some clathrate mixtures and in some inert matricies. M CH3CI CH3Br CH3I CHC13 C2H5Br Cl2 Br2 Ar(a) Kr(a) N2(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 is H20 -1 cm 3690* 3687 3689 3690 3691 3708 3700 3725 365h 3683 361+5 3620X 3605 3668 361+8 3625 3580 3639 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 is D20 26U8 261+1+ 26U7 2626 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 in different clathrate types decreased at different 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 in guest peak heights began at the same temperature as the oligomeric H^O disappeared (near 130 + 10°K). Frequencies of guest absorptions in the unannealed clathrate-hydrates and of pure, solid guest molecules (all at 83 ± 3°K) are listed in Table VI.III. For unannealed clathrate mixtures of CH3C1, CHCl^ and C^Br all strong and medium intensity absorptions of the pure solid were observed. In contrast, for CH^Br and CH^I unannealed clathrate mixtures, only some of the pure solid absorptions were observed. Strong unannealed clathrate guest absorptions expected near 3050, 1420, 895 or 964, and 596 cm 1 were unob served. Also in the CH^Br *7.67^0 sample, peaks were observed in the clathrate (1218, 1200, and 750 cm 1) which were unobserved in the pure solid. The clathrate guest peaks were shifted only slightly from the pure solid peaks. However, where the pure solid had multiplets of peaks the clathrate peaks were singlets. We can offer 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 splitting between the pure solid and clathrate was not unexpected, the splitting of degeneracies in pure crystals being lost due to the range of absorption frequencies arising from the inhomogeneity among the guest sites in the vitreous mixtures. There are at least three explanations of the loss of the clathrate guest absorptions in the annealed samples. First, there was too much guest in Table VI.Ill Alkyl halide ir absorptions in the pure solid state and in some unannealed clathrate mixtures at 83 ± 3°K. CH3CI . CH3Br CH3I CHCI3 C2H5Br 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 2957 m 2950 Ikkk lkk3 w sh s 2965 sh 295H 2846 2830 s m m 2936 2915 WW WW 2935 2803 1436 1426 s m m ms 2963 w 2921 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 1396 ms s 1433 sh 1376 m 13^7 W 13^5 m 1293 sh 1244 sh 12 kl vs 1238 WW 1235 1371 m 1338 vw 1336 m 1292 1218 1200 vvw WW sh 1291 vs 123k w 1236 vs 1214 vw 1220 1218 1254 1242 vw vw 1255 m 1242 s 1232 m 1021 vw 1020 m 962 955 vw vs 895 888 vs vs 752 m 767 748 955 w 960 s 961 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 off the'-window; during annealing, while .the remainder. was, too small to detect. Secondly, all of the guest molecules may have diffused out .of the H2O lattice and sublimed off the window. Thirdly, the guest molecules may have been present but ir inactive due to some cage effect. The third possibility is unlikely since cage perturbations are more likely to induce anharmonicities, peak shifts or even enhance the intensities. The first explanation also seems unlikely since H2O condenses at a much higher tempera ture than most of the guests, if anything the samples may have been defi cient in guest. The expulsion of all guest molecules from the H20 lattice seems most probable. , Further work, to be described later, was done to check which of the above reasons was most probable. One further logical method to use (which we did not) is observing clathrate-hydrates in Raman spectroscopy. There the H2O bands are sharp, while most alkyl halide bands are ir and Raman active and thus the bulk samples may be prepared and observed, in contrast to the thin films of our ir technique. 6.2 Guest Species Absorptions It was suggested in section 6.1 that sample condensation and annealing in an open cell chamber leads to expulsion of the foreign guest molecules from the H20 or D20 lattice in the absence of the equilibrium dissociation pres sure of the clathrate. Two further experiments tested the possibilities of sample fractionation between the sample deposition tube and the substrate surface, and simple sample dissociation. 256 A. Isolated Chamber Condensation Gaseous clathrate mixtures condensed in an isolated chamber (Fig. 1.2) and unannealed exhibited guest absorptions with approximately the same intensities relative to H2O bands as open chamber samples. Therefore we concluded that the open chamber samples did not fractionate during deposition. The design of the closed chamber cell ensured that all of the gaseous sample condensed on one window while for open chamber condensation the heated deposition tube ensured that no H2O or guest molecules condensed on the deposition tube tip. Clathrate mixtures condensed in 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 (57) results and probably arose from the differences in maximum annealing temperature: He annealed only to 1^5 ± 5°K. The annealing process was not followed in detail (spectroscopically) for closed chamber samples, but the annealed sample spectra for 83°K appeared the same as those in section 6.1 and in ice I. : -The same spectroscopic results were obtained for unannealed or annealed samples whether they were observed in open or closed sample chambers. The guest molecules must have been expelled from the H2O or D2O lattice in the closed chamber, due to the absence of a positive clathrate stabilizing pressure of guest vapour at 185 ± 5°K. 257 B. Low Temperature Mulls The obvious alternative was to form clathrate-hydrate samples in bulk and observe their spectra by- low temperature mulling. It was diffi cult to grind the samples at 77°K to a very fine powder and considerable scattering was observed from the large particle size.. Whalley C95) obtained much better spectra (of ice) apparently with finer powders. The indices of refraction of the mulling agents and ice agreed fairly well in the visible region, but the indices change very rapidly over absorption bands and this seems to induce considerable scattering between 1700 to 2000'cm-"1" and 2300 . to 3000 cm-1. It was of course unnecessary to anneal mulled samples since the crystalline samples were initially cooled from 273°K to 83°K at 1 atmosphere of N2(g). However, no guest absorptions were observed for either the mull of CH3I-17H20 or CC13F-17H20. Most of the CH3I or CCI3F guest absorptions should have been observed in either the C3H8 or CC1F3 mulling agent. Two explanations are possible. First, during transferal of sample from the preparation tube to the mortar and pestle the sample was warmed to 2T3°K momentarily and it may have dissociated. However, the CH3I and CC13F clathrates were chosen specifically for their guests liquid states and low vapour pressures at 273°K and their clathrates low dissociation pressures. Secondly, the CH3I and CCI3F molecules may have been very soluble in liquid C3H8 and liquid CCIF^ even at low temperature. However, the clathrate samples were not observed to dissolve in the'mulling agents. If the guests did dissolve in the mulling agent then they should still have been observed in the spectra as a solid 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 cell to room temperature. The H2O skeletal absorptions observed in mulls were much like previous cases: Scattering distorted the bands considerably. One difference did occur, however, the v2 absorption was well defined at 1570 cm-"1" at 83°K. In most spectra the region from 1600 to 3000 cm 1 was just one broad band which steadily increased in intensity. C. Summary Infrared observations by Hexter and Goldfarb (53) on HC1, H2S, C02 and S02 clathrated in hydroquinone demonstrated that for weakly absorbing guests the guest absorption was unobserved in the clathrate, but strong absorbers like C02 and S02 were easily observed. They pointed out that in the amount of HCl-quinone clathrate used for the ir observations, only about 5% of the HC1 needed for a reasonable HCl(g) spectrum was present. Davies and Child (55) also observed ir absorption by guests in quinone clathrates. They suggested that the shifts in guest frequencies were no larger than for solutions of guests in CCl^. Their conclusion was that the cage had pertur bing influences no larger than a non-polar solvent. We deduce that in our annealed clathrate-hydrate mixtures the guests all could not have been present and ir 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. If the binding in the unannealed samples was not physical, but chemical, then we expected new guest functional group frequen cies. The evidence indicates our methods were insufficient to form clathrate-hydrates . 6.3 The Temperature Dependences of Crystalline Clathrate Mixture Absorptions A. HDO in Clathrate Mixtures Discussion of the results from annealed clathrate-hydrate mixtures collapses to a discussion of cubic ice I: We assume the guest was all dis persed and a cubic ice I lattice formed at 185 ± 5°K. The clathrate studies became independent checks of the reproducibility 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 results, the clathrate-mixture low temperature limits, low temperature dependences, high tempera ture, dependences, "freeze-in" temperatures and irregularities in frequency-temperature shifts agreed, within error, with HDO cubic ice I data. Clathrate mixture M^CHDO) frequency limit, temperature dependences, "freeze-in" 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 in 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, in spite of precautions. One cannot rationalize increased AvQp in that way. Notice that if 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•7.67H20 ideal stoichiometry) with a 12.09 A cell 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 in cubic ice I we found v (HDO) = 3290 cm (Fig. 5-12) UrL _n O O and Av/AR = 1921 cm /A. Since the 0 0 distances differed 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 339^ cm 1(273°K). Assuming the same frequency-OH temperature dependence as in ice then at 83°K v (HDO) should have absorbed at 339^ 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 CH3I-17D20(HD0) and CH3Br•7.67H2O(HDO) mixtures. The distribution of 0*---0 distances is much greater in clathrates than in ice I due to four unique distances, each of which must have an ice-like distribution. One would expect considerably broader HDO bands in clathrates. Librations of HDO in clathrate mixtures and cubic ice I also agreed within error with respect to high temperature frequency dependence, "freeze-in" temperature and frequency shift irregularities. The low temperature limits did not agree within our stated errors. The disagreement was not 26l sufficient to suggest clathrate had formed, i_.e_. increased R(0**"'0) in clathrates suggested a shift of'(15 - 20) cm 1 from cubic ice I. The irregularities observed in frequency shifts with increasing tem perature were discontinuous shifts by 2 - 3 cm 1, generally to higher fre quency in the case of stretches and to lower frequency in the case of librations. Another break in the curves appeared near 80°K. These breaks may have been related to partial ordering, as was suggested before. B. H2O and D20 in Clathrate Mixtures Discussion of H20 and D20 absorptions in annealed clathrate-hydrate mixtures also reduces to a discussion of cubic ice I. The behaviour of H20 and D20 clathrate mixture absorption frequencies, half-height widths and temperature dependences were the same as in cubic ice I. If true clathrate hydrates had formed.on annealing then low tempera ture limits and half-height widths should have been significantly different from ice: They were not. The low temperature limits of each individual H20 or D20 absorption agreed within error, Table V.XI, for the set of clathrate mixture data. The average for each band, over all clathrate mixtures, agreed with the observed H20 and D20 ice I data. The only ex ceptions were for + vT (D20), vp'(D20) and vR(D20). Those three sets of data were obtained from broad shoulders or ill-defined 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 1628 cm 1 (CsI^R^O ?) band. Negative temperature dependence was characteristic of lattice modes. Since such an intense lattice overtone was unlikely, the 3368 cm band may have been a combination of with an overtone of a low frequency lattice" mode (say 2vT'). The shift of + vT to higher frequency by 30 cm 1 was understood in terms of the smaller overlap with than in ice I. Insensitivity of the weak, sharp 1628 cm-1 absorption to temperature is characteristic of non-hydrogen-bonded-lattice IL^O: That supports its assignment to of,say, CsT^^O. Results of section 5.3 on H2O and D2O in annealed clathrate mixtures differed from those of McCourt (56) and Shurvell (57). We failed to detect their additional 3VR absorption near 2^00 cm \ However, we experienced problems from instrument imbalance through atmospheric C02 between 2280 and' 2360 cm As well, attempts to duplicate their (56,57) SO2 results failed. 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 (56) and Shurvell's (57) original background spectra revealed slight, 0.02 abs. units, negative CO2 absorptions from 2280 to 2360' cm For thick samples, requiring extensive reference beam attenuation and very small instrument source signals, the negative CO2 absorption would be proportionaly greater and could give the appearance of 2 (3VR) bands instead of one. The position of the minimum between their 2 (3VR) peaks corresponds closely to the CO2 (gas) maximum. There was also evidence of oligomeric H2O absorption in 263 their original spectra. We concluded their samples were unannealed and vitreous and that no extra 3vR (H2O) absorption appeared. Finally, the nearly identical spectra of the various ices suggests that similar spectra should be expected for the clathrates. CHAPTER SEVEN SUMMARY 7.1 Suggestions for Further Work Extensions and new applications of this work are proposed under three headings: further work in 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 in 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. It is important to choose guest species which are strong Raman scatterers and whose frequencies are widely separated from the H2O frequencies. In that case the guest frequencies would be perturbed the least by coupling to the H20 lattice. As an extension of the effect of the lattice, one could study clathrates whose guests frequencies are close to H20 frequencies and would be expected to couple (to ^(^0) say, which is weak in the Raman effect). One could also study the perturbing effect of the lattice on the guest by observing the D2O clathrate analogues. 265 Finally, careful technique should permit one to grow clathrate-hydrate single crystals in 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 diffraction. Use of clathrate-hydrates which are more stable under am bient conditions (i_.e_. tetrahydrofuran hydrate) should facilitate mull preparation, but may make the spectroscopy more complicated. B. Ice Systems Some extentions of this work which should be completed are listed below. 1. Use dilute HDO frequencies to follow the annealing or vitreous-cubic ice I transformation in detail. 2. Determine the rates of transformation at various constant temperatures by following the shifts in HDO frequencies as a function of time. 3. Study v2 and Av2 in detail for liquid helium and liquid nitrogen experiments to resolve the v2 - 2vp 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 Cl2,and H20. Some other projects related to this work are included below. 266 1. Carefully check the properties of cubic ice I in the temperature range ko - 70°K by Raman scattering, infrared absorption and n.m.r. of HDO in D20 considering the shift in stretching frequency in that range. 2. Investigate the behaviour of HDO frequencies below 10°K to check the extrapolation of our data. 3. Study HDO absorptions in the family of high pressure ices as a function of temperature over their stable ranges. This will permit the extension of hydrogen-bond force constants over a wider range of R(O--'-O) in similar electronic environments. k. Obtain detailed linear expansion coefficients of cubic ice I down to lt°K. 5. Study the origin of as the H20 triple point is 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 in the covalent and electro static nature of the hydrogen-bond. 7. Study the anisotropy of hexagonal ice I single-crystals by observing differences in HDO frequencies and Av/AR (as a function of temperature) along the aD and cQ axes. 8. Determine the proton jump energy by observing at what tem perature during warm-up a thin layer of D20 embedded between thick layers of vitreous H20 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 isolation of a few mono-layers of D20 on H20. C. Other Chemical Systems Several possible applications of the dilute isotopic substitution and temperature variation technique are listed below. 1. Study single-crystals of organic acids, whose crystal structures and linear expansion coefficients are known, as a function of temperature and relate VQ^CHDO) 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 variation of 0-H*••*0 hydrogen bonding. 3. Use dilute isotopic substitution in biological systems generally since the H20 medium masks spectroscopic obser vations of H20. h. Use dilute HDO and temperature variation to study the nature of hydrogen bonding in poly-water. 268 7.2 Conclusions A. Annealing Ice Iv 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_ al. (6). However, these ir results do not support Dowell's (7^) conclusion that only 30% of the vitreous ice I was transformed to cubic ice I. However, their results may indicate that only 30% of their original sample was vitreous. The irreversible transformation frequency shifts (at ll+5°K) were: Avj_ = -h2, Av^ = -36, Av2 = -56, AvR = +31 and AVIJ = +12 cm 1. The transformation temperature range was independent of deposition rate, but transformation frequency shifts were not, faster depositions gave smaller shifts. Oligomeric (probably dimeric and trimeric) H20 and D20 were present in considerable concentration in 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 in the form of oligomers. B. HDO Studies The assumption that dilute concentrations of HDO in H2O or D2O gave completely uncoupled HDO vibrators is invalid. At least one HDO frequency is coupled to a parent H20 or D20 frequency. 269 The low temperature limits of vOTI(HDO) and v._(HDO) were 3263.5 cm 1 On OD and 2412.0 cm 1 respectively. The low temperature dependences of v and On vQD were both 0.0^7 cm_1/°K between 10°K and 80°K. The high temperature dependences of v.„ and vOT^ 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 potential of HDO molecules in H2O/D2O lattices changed its shape irregularly with temperature, i_.e_. the changes in to were not linear as temperature increased. On Hot bands and difference bands did not contribute significantly to the breadth of v and v^(HDO) and, by extension, not to stretches in H2O or D2O. Half-height width data supported the orientationally disordered proton theory of Whalley (88). 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 limits of the infrared technique, v (HDO) and v (HDO) peak frequencies were sensitive to changes On OD o in R(0'••'0) greater than 0.0001 A. HDO stretching absorptions were not linear 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 limit of RC0,,,,0) for cubic ice I o o was 2.753 A assuming aQ = 6.350 A exactly at l43°K. The calculated changes 6 0 in 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 (33) formula gave a good approximation to the relation between R(0--*-0) and v (HDO) in 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 limit of 105.6 On cm-1, a low temperature (0 - 60°K) dependence of +0.032 cm-1/°K, a high temperature dependence (100° - 200°K) of -0.038 cm"1/0!^, and a maximum value of 108.7 cm-1 at 80°K. The HDO harmonic stretching frequency had a low temperature limit 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 linearity at 80°K. Vp''(HD0) had a low temperature limit of 823 cm-1 and the shoulder (assigned to (vR,T + Vrp)) had a low temperature limit of 856 cm-1. Various calculations indicated vRx,. VRv and vRz were degenerate for H2O and D20 and non-degenerate for HDO. The negative temperature dependence of lattice modes was understood in terms of a shallower potential and increasing excited state populations as temperature increased. C. The H20 and.D20 Studies The order of v-j_ and in the gas and cubic ice I phases was the same: Hydrogen bonding affected v-|_ and of the gas phase equally, shifting them down proportionally. We conclude that the molecule-molecule coupling of v-j_ tov^ and to V3 were similar in nature and that in cubic ice I, \) and were distinct transitions. The assignments of major H20 and D20 absorptions at 0°K were v-j_ + Vrp = 333^, = 320U, v-j_ = 3133, 3vR = 2239, v2 = 1562, vR + vT = 881, vR = 832, and vT = 229-2 cm"1 for 271 H20 and v + vT = 2k6h, v3 = 2Ul3, v = 2320, 3vR = 1637, v2 = II89, VR + Vrp = 663, and vR = 630 cm 1 for D20, in basic agreement with previous authors. The absorption near 1600 cm 1 in R~20 definitely had a 2vR under lying absorption. Temperature dependence of v3 and v-j_ in absorptions for H20 (above 100°K) confirmed the Raman temperature dependence of Val'kov (99). The data of HDO applied to H20 and D20 as well. Blue's (85) formula led to anomalous results when applied to simple H20 and D20 molecules in ice. Assuming effective masses for two attached and two detached protons and also assuming that the three librations 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 105 dynes/cm and k '(0 H-0) = 0.21 x 105 H dynes/cm. These force constants predicted nearly degenerate D20 librations (586, 588 and 591 cm-1) about 6% below the observed value. The effective mass concept did not apply well to HDO. An H203 model of ice gave a set of H20 internal and lattice force constants in good agreement with those deduced by Trevino (93) and poorer agreement with Pimentel's results (97). That k^(v0) (0.66 x 10^ dynes/cm) Cj)<j> d was smaller than the gas phase value was consistent with the lower ice frequency. 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