Monocrystals of ice grown from NaCl solutions (concentration 5 X 10–4 to 10–2 mol/l) have been tested in creep at —10°C by basal glide. The maximum resolved shear stress ranged from 0.6 to 2.5 bar. The resulting creep curves show a deceleration, that is, the creep rate decreases with time. At the highest concentration the creep is essentially transient; the strain tends to a fixed value. This is unlike the behaviour of similarly orientated monocrystals of pure ice or of ice grown from solutions of other dopants so far reported in the literature.

The possible causes for this behaviour are discussed and the implications for the mechanical properties of polycrystalline ice, and in particular sea ice and glacier ice, are described.

New experimental and theoretical studies of low-density amorphous solid water (H2O(as)) and of polycrystalline ice lh are reported and integrated with other available data. A variety of evidence is put forward to support the conclusion that low-density H20(as) is derived from ice lh by slightly increasing the dispersion in the O—O separation and by introducing a distribution O—O—O angles (width c. 8°). Our theoretical analysis focusses attention on the consequences of strong intermolecular coupling of OH oscillators. The vibrational modes of both ice lh and H20(as) are found to be complex mixtures of molecular motions, so the identification of regions of the Raman or infrared spectra of these materials with particular isolated molecule modes is not useful. The theory developed gives a good, but not perfect, account of the OH stretching regions of the observed Raman and infrared spectra of ice lh and, to a lesser degree of low-density H20(as).

The dynamics of the freezing process is studied at the surface of growing ice crystal by means of Rayleigh spectroscopy. Light is scattered quasi-elastically at the interface. The line width is proportional to the square of the scattering vector. For a scattering angle of 90° one measure, about 2 krad/s. The line width does not depend on the growth rate or thermal gradients at the interface. Light is scattered isotropically, which indicates that the correlation length is small compared with the wavelength of the scattered light. The intensity depends on the growth rate and shows a hysteresis in that dependence; at a minimum growth rate one observes the onset of fluctuations.

The charge separation of ice particles colliding with metals was investigated in a wind tunnel (air speed 10 m/s) at a temperature of —45°C for different metals as a function of an applied external electric field. The ice particles (to μm radius) collided with the metal target at a rate of 105 per second. The charge separation produced by different metals can be explained by the contact potential difference between the metal and the ice introducing electronic surface states on the ice. A lower limit for their density (1016m–2) is found. The influence of the electric field is explained by an interaction between Bjerrum defects and the electrons of the metal, the transfer probability depending on the charge in the surface states.

Near-infrared absorption spectra of a frozen dilute solution of ytterbium chloride have been obtained at 77 K, 20 K, and 4.2 K. They contain two broad lines revealing a Stark splitting of 60 cm-1 of the excited 2F5/2, level of the Yb3+ ion. Such spectra indicate that in frozen solutions of ytterbium chloride the Yb3+ ions have crystalline or quasi-crystalline surroundings which are similar for most ions; different possibilities are discussed.

Detailed knowledge of the energetics of the interaction of a water monomer with an ice surface is important in understanding the factors which control both the nucleation and the growth of ice. In this work we model this interaction by using a small section of an ice surface and semi-empirical quantum-mechanical calculations of the CNDO/INDO type to investigate the energetics of a gas-phase molecule approaching the surface. In the attempt to simplify the system as much as possible while retaining the essential features of the "real" physical situation, 13 water molecules arranged in the lattice positions for ice Ih were used to represent the surface. Electron-density plots for both basal and prism surfaces were generated. Potential-energy curves were calculated for a monomer approaching a number of different sites on each type of surface. Monomer-surface binding energies varied from approximately 17 to 33 kJ/mol for the surface sites examined. Ion pairs of the H30+-OH- type were included in the surface and their effect on the energy of interaction with an incoming monomer calculated. For these studies no distortion of the ice surface was allowed. The energies found follow the same trends as observed for a free monomer-ion interaction.

Previously the author had suggested that frazil nucleation occurs by a mechanism analogous to spinodal decomposition, aided by turbulence. After further study the following points are made: (1) No critical point exists between solid and liquid; this rules out true spinodal decomposition. (2) Pure water can be supercooled to -40°C; at -40°C the theoretical energy barrier to nucleation is about 10 -19 J. Frazil forms after supercooling less than 0.1 deg; at this temperature the theoretical energy barrier is about 10-14 J. (3) Theory shows that turbulence increases the energy barrier. (4) Turbulence may aid dissipation of heat of solidification, but not sufficiently to account for observed frazil formation at small supercoolings. (5) The author's evidence that frazil can begin to form at supercoolings as small as 0.02 deg suggests that no nucleus except ice itself can account for "heterogeneous" nucleation of frazil.

Recent progress in studies of the structure and behaviour of grain boundaries in ice are reviewed. As a lattice geometrical model of the boundary, the coincidence-site lattice (CSL) model is considered for ice crystals. Some evidence of the validity of this model is presented through observations of special shapes of natural snow, results of grain-boundary energy measurements, and direct microscopic observations of boundaries by X-ray diffraction topography. Although methods of measurement of grain-boundary energy have been developed recently, results are still not adequate to be analysed in terms of real energetics for comparison with models of atomic bonding. Modern methods of observing grain boundaries in ice using X-ray diffraction topography are described. Observations of migrating boundaries have revealed that faceting along most closely packed CSL points impede the migration of the CSL boundaries whilst increased numbers of steps among facets with boundaries of other kinds enhance it. The mobility of a fast-moving boundary has been determined to be of the order of 10-10 cm3 dyn-1 s-1 (10-11 m3 N-1 s-1) either in the case when the driving force is the capillary force due to the boundary energy or when it is the stored energy of dislocations.

For several types of polycrystalline ice of different origins, the spatial lattice orientation of each crystal was determined by measurements of both the a- and c-axis orientations. Analyses of the orientations of adjoining crystals showed that a great majority of adjoining crystals may be in a twinning relation. With special reference to the multi-maximum c-axis preferred-orientation fabric (the so-called “diamond pattern”), which is expected to occupy the largest part of a glacier ice mass, the crystal boundary structure was estimated. The preferred c-axis orientations of this fabric were explained as being the result of coincident oxygen-oxygen lines (hydrogen-bond lines) between adjoining crystals being concentrated in the orientations where seven oxygen-oxygen lines of one single crystal of ice are distributed. From the above result, it was concluded that the multi-maximum fabric is of the polycrystalline structure closest to the structure of a single crystal of ice among all the fabrics found in large ice masses.

It is found that the occurrence, in glaciers and ice sheets, of a multi-maximum fabric has a bias to the parts which have undergone a strong shear deformation for a long time. It is thus suggested that plastic deformation of ice with this fabric may be attributed to mechanical twinning due to a strong shear stress.

Torsion creep tests were performed on glacier ice at temperatures above -12°C. The polycrystalline ice, when unloaded, exhibits creep recovery. The time-dependent recoverable component of deformation (or anelastic strain) ϵa was found to be adequately described by a relationship of the form: ϵa = Δτ log(r + αt)/h, where Δτ is the stress decrement, α a constant, and t the time. The anelastic modulus h defined for times t in excess of 3 h is always smaller than the dynamic elastic modulus. The movement of dislocations composing the sub-boundaries or in dislocation pile-ups may produce this important reversible deformation. The time-dependent recovery is explained in a similar way to the transient creep behaviour observed at low temperatures for metals. The small temperature dependence of creep recovery would arise from the existence of a distribution of internal stresses values.

Large-angle tilt grain boundaries in artificially-grown ice bicrystals were observed by the method of X-ray diffraction topography. In bicrystals for which misorientation angles satisfy the conditions of a high-density coincidence site lattice (CSL) at the boundary, the images of fine parallel line defects appear on the topograph taken immediately after a light deformation. Since these images disappear in a time period between several hours and a few days and reappear again at the same sites when the specimen is deformed subsequently, it is concluded that these line defects are not stable like the boundary dislocations but may be steps generated on the boundary to form facets which coincide with the high-density CSL plane. X-ray topographic images of boundaries which do not satisfy the conditions of a high density CSL are complex and difficult to interpret, although some of the images indicate that there may be different types of structures on such boundaries.

The thermodynamics of phase equilibrium control the temperature distribution around the ice particles in wet snow. When the snow is stressed, pressure melting occurs at the inter-particle contacts and the snow densifies. Densification is described by a physical model which simulates the heat flow, meltwater flow, and particle geometry. The effects of ionic impurities, liquid saturation, and particle size are demonstrated. Typical values of the temperature difference, inter-particle film size, and density are calculated as functions of time. The calculated rates of compaction are too large, hence, at some later time, the effects of simultaneous grain growth must be added to the model.

This paper describes the first results from an experiment to measure the fracture toughness of ice. Two experimental techniques have been used; fracture of pre-notched rectangular specimens in three- and four-point bending, and from the observation of the cracks which form underneath an indenter forced into the ice surface. In the latter test the indenter behaves like a wedge. We have observed that for indenters with large interior angles the plastic zone beneath the indenter may itself behave like a wedge. Data obtained over a range of temperatures has been compared with the little other data available. We find a decrease of fracture toughness as the temperature is lowered, which is the reverse of that observed by H. W. Liu and L. W. Loop.

Measurements were made of the kinetic friction which occurs when a tungsten carbide ball slides in various directions on the surface of a single crystal of ice, the track width produced on the surface was also measured. Anisotropies were detected in both the friction coefficient and the track width. The track width φ was at a maximum when the ball was slid normal to the basal plane and a minimum when it was moving parallel to (0001) in the temperature range —5 to —30°C. Although the friction coefficient was at a minimum when slid normal to (0001) and maximum in parallel to (0001) at temperatures of —19°C and below, this relation was found to be reversed at temperatures of —10°C and above. Anisotropy in track width can be explained in terms of the amount by which a slip system contributes to deformation in a specimen. However, our understanding of frictional anisotropy calls for knowledge of the ploughing strength p defined by the adhesion theory of friction. It was found that p reached a maximum in parallel to (0001) and a minimum normal to (0001) and that the frictional anisotropy on (0001) was influenced by the value . A remarkable frictional anisotropy was also observed on the surface inclined to the basal plane at 30°; the maximum friction coefficient was twice the minimum, whereas the maximum track width was only 1.3 times the minimum.

An analysis of the thermal properties of vitreous ice shows that both its heat capacity Cp and its entropy above 100 K are partly configurational in origin. The configurational contribution increases with temperature, and the excess Cp and entropy near the solid-liquid transformation temperature are 36.7 and 2.1 J K-1 mo1-1, respectively. The increase is interpreted as indicating the onset of molecular mobility in vitreous ice. The configurational Cp, of the melt of vitreous ice at 133.6 K, of ≈ 36.7 J K-1 mo1-1, is the same as the configurational Cp, of water at 273 K. Thus, the short-range order in the melt differs little from that in water at 273 K. The maximum calorimetric residual entropy of vitreous ice is 13.4 J K-1 mol-1, which is in fair agreement with the maximum value of 9.2 J K-1 mol-1 anticipated for a tetrahedral random-network model with fully disordered positions of H atoms. Thermodynamic consideration of a glass transition in supercooled liquid water indicates that there is no continuity of state between supercooled water and vitreous ice and, therefore, the structure and thermodynamic properties of a possible glassy state of water should be different from that of vapour-deposited vitreous ice. This paper is published in full in Philosophical Magazine, Eighth Ser., Vol. 35, No. 4, 1977, p. 1077-90.

The dipole moment μ of an H2O molecule in the orientationally disordered ices is greater than the moment of an isolated molecule, 1.84 D, due to two factors: (i) the mutual polarization of molecules, and (ii) the short-range average correlation of the dipole vectors, if the molecules are able to reorient. The magnitude of the average enhancement is given by Kirkwood's equation,

1

where ϵ0 and ϵ∞ are respectively the limiting low- and high-frequency relative permittivity of orientational polarization, N is the number density of dipoles, k is the Boltzmann constant and T is the temperature. The dipolar correlation factor g is defined by,

2

where μi and μj are the dipole moments of molecules i and j in a spherical region of radius r immersed in a larger spherical region of radius R and the angular brackets indicate average over all molecules i and all their orientations. In view of the defects, vacancies, imperfections, etc., in ice, it is not certain if the limits in Equation (2) have any experimental significance. However, an approximate value of g can be calculated by taking molecules up to the second co-ordination shell.

The theoretical value of g for polycrystalline ice VI which is fully disordered (within the restrictions of ice rules) has been calculated by taking molecules up to the second nearest neighbours, in both the dendritic and non-dendritic models. The calculations were done for two kinds of molecules, I and II, having multiplicities 2 and 8 respectively, in the tetragonal unit cell in space group P42/nmc, and, through the use of symmetry, keeping to a minimum the number of scalar products.

In both the dendritic and non-dendritic, models, gI is 10%, or more, greater than gII and the appropriately weighted values of g are 2.342 in the former and 2.065 in the latter model. The effect of ring closure is, therefore, to reduce the value of g by 13%. The limiting high temperature experimental value of g from Equation (1), using Onsager's theory for the enhancement of the dipole moment by its own reaction field, is 2.42 (Johari and Whalley, 1976). By analogy with the 10% discrepancy between the theoretical and experimental values of g of ice I, a better estimate of the experimental g of ice VI (using a reaction field other than that given by the Onsager theory) would be about 10% less than this value. Thus the suggested experimental g of ice VI (2.18) is close to the theoretical values obtained from either of the two models and there is little contribution to g from neighbours beyond the second co-ordination shell.

We have studied the infrared absorption by the OD stretching, vOD(D2O), and D2O rotational, vR(D2O), vibrations of fully deuterated ice II and ice IX at lo K, and the absorption by OD stretching vibrations, vOD (HDO), of HDO molecules isolated in ices Ih, II, and IX at 10 K. Calculations of the frequencies and relative intensities of the zero-wave-vector normal vOD(D2O) vibrations of ices II and IX have allowed the vOD(D2O) absorption to be assigned. Each component of the band is broad, even at 10 K, most probably because of Fermi resonance between the fundamental OD stretching vibrational states and the isoenergetic continuum of high-order overtone and combination states of the lattice modes. This work has yielded the most complete interpretation yet achieved of an infrared band due to the OH or OD stretching vibrations of a phase of ice.

The far-infrared absorption by the translational vibrations of H2O and D2O ices Ih and Ic at 4.3 K has been measured, and has revealed differences between the spectra of ices III and Ic for the first time.

Papers describing this work in full have been published in Journal of Chemical Physics, Vol. 67, No. 4, 1977, p. 1311-18, and Vol. 67, No. 6, 1977, p. 2445-48.

Detailed mid- and far-infrared spectra have been recorded for authenticated samples of several clathrate hydrates with the two main structures, I and II, at temperatures between 150 and 4 K. The systems are complicated, yet a detailed analysis of the many interesting spectral features is required before reliable, detailed information can be obtained. Consequently only rather general conclusions can be drawn at present.

The mid-infrared spectra have been recorded for the structure I hydrates and deuterates of ethylene oxide, trimethylene oxide, and cyclopropane, and the structure II hydrate and deuterate of trimethylene oxide, all at 100 K. The OD stretching vibrations of isolated HDO molecules, vOD (HDO), and of the fully deuterated forms, vOD(D2O), have also been recorded for cyclopropane and trimethylene oxide structure I hydrates at 40 K, and the absorption by the guest molecules has been studied for all of the structure I hydrates at temperatures down to 40 K.

The absorption by the water molecules at 100 K is similar to that in ice, with frequencies that vary in the expected way with the lattice parameter and, hence, the hydrogen bond lengths. The shapes of the vOH(H2O)vOD(D2O), and vR(D2O) bands are essentially the same for structures I and II, while the vOD(D2O) band varies only slightly and depends more on the guest molecule than on the structure. The water absorption changed only slightly when the samples were cooled from 100 to 40 K.

The vOD(HDO) bands provide clear evidence that the distribution of hydrogen bond lengths in cyclopropane hydrate differs from those in ethylene oxide and trimethylene oxide structure I hydrates, even though powder X-ray methods indicate that the three hydrates are isostructural. The difference is attributed to an interaction between the hydrogen bonds and the dipole moment of the guest which is too irregular to be sensed by powder X-ray methods.

Some absorption bands of the guest molecules are visible in the spectra of structure I hydrates and, as expected, fewer are visible in the spectra of structure II hydrates, which have a higher water-to-guest ratio. For both structures more guest bands are visible in the spectra of deuterates since the D2O absorption is weaker than that of H2O. The guest bands are single in most cases, with half-widths of 1 to 5 cm-1 for ethylene oxide and cyclopropane and 5 to 15 cm-1 for trimethylene oxide in its deuterates of both structures. One band of ethylene oxide at 100 K and below is a doublet, and one degenerate and one non-degenerate vibration of cyclopropane yields a doublet at 40 K. This must mean that there are two non-equivalent positions for the guest molecule in the tetrakaidecahedral cage of the structure I hydrate at these temperatures.

Far infrared spectra have been recorded of the structure I hydrates of ethylene oxide, cyclopropane, trimethylene oxide, and xenon, and of the structure II hydrates of trimethylene oxide, cyclopropane, tetrahydrofuran, cyclobutanone, and 1,3-dioxolane, all at 4.3 K. The spectra of the hydrates and corresponding deuterates have enabled the absorption by the rotational vibrations of the guest molecules in the cage to be identified. The absorption above 100 cm-1 by the translational vibrations of the water molecules is significantly different for the two structures, but is rather insensitive to the guest molecule within one structure.

A careful search was made for evidence of the transition in trimethylene oxide structure I hydrate at which the guest molecules partly order, that was detected by Davidson from dielectric studies. No spectral changes due to the transition were detected.

Papers describing this work have been published in Canadian. Journal of Chemistry, Vol. 51, No. 8, 1973, p. 1159-68; Vol. 53, No. 1, 1975, p. 71-75; Vol. 55, No. 10, 1977, p. 1777-85. A further paper is accepted for publication in Journal of Chemical Physics and others arc in preparation.