Dispersions of ice microcrystals were obtained from the breakdown of super-cooling of water-in-oil type emulsions whose disperse phase was either resin-exchanged water or aqueous solutions of NH4C1. Their complex permittivity ϵ* = ϵ′ - ϵ″ was studied versus their temperature T, up to the melting point of the ice microcrystals, by means of an automatically balancing admittance bridge (General Radio 1680A) working at 400 Hz and 1 kHz. The plots ϵ′(T), ϵ″(T), and ϵ″(ϵ′) reveal that these systems exhibit two distinct dielectric relaxations located on both sides of a temperature Tm which was found to be equal to about —20°C in the case of water and lower than —20°C in the case of aqueous solutions of NH4C1. The relaxation located in the lower temperature range arises from the Debye dipolar absorption of ice while the other one could be related to structural changes occurring within the lattice of ice as T approaches its melting point. These results are consistent with those obtained by investigating versus frequency the dielectric behaviour of ice microcrystals, at discrete sub-zero temperatures close to their melting point.

This paper has been accepted for publication in full in a forthcoming issue of the Journal of Glaciology.

During the 1976-77 Antarctic field season, electrical resistivity profiling was carried out in the south-eastern quadrant of the Ross Ice Shelf. Drilling to a depth slightly greater than 300 m at the same site, where the total ice thickness is 425 m, permitted tem-perature determinations (personal communication from B. L. Hanson and J. H. Rand) that can be extrapolated to the ice-water boundary. Numerical modelling of the apparent resistivity, allowing for a continuous variation of temperature and density, and hence con-ductivity, with depth, was done in the same manner as has been described previously (Bentley, 1977). Temperatures calculated by assuming no basal melting or freezing show excellent agreement with those measured. Two models of apparent resistivity, taking the activation energy in the solid ice to be 0.15 eV and 0.25 eV, respectively, bracket the observed data, with the points tending to favor the lower value. This is in satisfactory agreement with (although perhaps slightly lower than) other measurements on polar ice. Assuming that the same temperature model applies at the site of the earlier measurements (Bentley, 1977), only 30 km away and approximately "up-stream", leads to apparent resistivity models, with activation energies of 0.15 eV and 0.25 eV, that again bracket the observations. The effect of other possible causes for the change of conductivity with depth besides temperature, such as varying grain size, crystal orientation, CO2 content, etc., is unknown but believed to be small because of the similar history of all the ice in the relevant depth range, about 100-350 In, over which the conductivity increases by a factor of 2. The conductivity in the ice at 100 m depth (temperature —23°C) at both sites is within ± 10% of 1.4 × 10-5 Ω-1. We conclude that an activation energy of 0.20 ± 0.05 eV not only can be used for modelling, but also closely represents the true value for ice-shelf ice.

Relaxations around a shear dislocation loop on a basal plane in ice have been studied by molecular dynamics. The model intermolecular potential included directional components which stabilized the open ice structure. A random phase approximation was introduced to simulate the disordered arrangement of hydrogen bonds. The dislocation formation volume was found to be zero within the limits of computational error. This paper is published in full in Nuclear Metallurgy, Vol. 20, Pt. 1, 1976, p. 572-81.

Conventional studies of plastic deformation have been complicated by the simultaneous variation of dislocation velocity and dislocation density during the tests. In the present study this difficulty was avoided by carrying out deformation tests at low stress levels on samples which had been predeformed to relatively higher stresses prior to the measurements. Creep, mechanical after effect, constant strain-rate, and stress relaxation tests were carried out as a function of measurement stress or strain-rate, temperature, and predeformation level. The results were analysed in terms of a linear stress-dependent dislocation velocity in order to determine whether that simple behavior is able to account for the macroscopic deformation behavior of ice crystals. This report is a brief summary of the results; a complete discussion is to be published elsewhere. The principal results of the study are as follows:

1. 1. The observed behavior was particularly simple for predeformed samples. The creep strain showed a nearly linear increase with time, without the large positive curvature characteristic of conventional tests. No stress maxima were observed in the constant strain-rate tests as have been found in previous studies of non-predeformed samples. The (complete) stress relaxation curve was virtually identical in shape to the inverted constant strain-rate curve.

2. 2. The steady-state creep and constant strain-rate behavior could be described to good approximation in terms of the motion of a constant density of dislocations moving with the same linear stress-dependent velocities as have been observed directly by others. The strain-rates were linear in stress and the estimated dislocation densities (4 to 16 × 10 cm-2) varied with the magnitude of the predeformation level in a manner consistent with previous observa-tions. The strain-rates or stress levels are exponential in 1/T with an activation energy of 0.6 eV, which is approximately equal to the activation energy reported for the motion of dislocations and for the mechanical relaxation time in internal friction studies.

3. 3. A small transient creep behavior, and a small but measurable mechanical after-effect with the same (≈ 3 min) time constant were present. These effects, as well as the non-exponential behavior of the constant strain-rate and stress-relaxation stress—strain results, could be accounted for by including a second, anelastic, component in a deformation model corresponding to a restoring force in addition to the linear viscous drag force on dislocations. This leads to a differential equation which is linear in stress and strain, but involves both first-and second-order time derivatives.

4. 4. The solutions of this differential equation describe the observed mechanical response well, and provide a general internal consistency check for the model.

5. 5. A quantitative fit of the experimental test results to the dislocation model gives values of 3-4 for the ratios of total dislocation density to the recoverable component and values of 7-8 dyn/cm2 for the restoring force constant for the recoverable dislocations. The restoring force constants and recoverable dislocation densities were, within experimental error, found to be independent of temperature, measurement stress and strain-rate, and predeformation level. Values found for the parameters for creep and mechanical after-effect tests were equal within experimental error to the values found from constant strain-rate and stress-relaxation tests carried out on the same sample. If the recoverable dislocation component is identified as bowed-out dislocation segments whose ends are fixed, the restoring force could be accounted for by the elastic line tension of dislocation segments of lengths of about 8 × 10-3 cm.

   No feature of the experimental results was inconsistent with this dislocation model, and the results of the study are all in agreement with the theory proposed by Weertman in which the dislocation drag force is very large because of the stress-induced ordering of water molecules in the stress field of the moving dislocation.

Uniaxial compressive creep tests on single crystals and polycrystals of ice at about -10°C under different hydrostatic pressures are described . After creeping under a constant load at atmospheric pressure for some hours, a hydrostatic pressure of the order of 35 MN m-2 was applied and the change in strain-rate was noted. Some hours later the hydrostatic pressure was removed and the test continued at atmospheric pressure. From these changes in strain-rate , an activation volume V was determined from the equation

where R is the gas constant, T is the absolute temperature, P is the hydrostatic pressure and τ is the superimposed uniaxial creep stress. V is negative if E increases with P.

For single crystals, which show an accelerating creep curve, that is the strain-rate increases continuously with time, no sensible activation volume was determined because the strain-rate increased both on the application of the hydrostatic pressure, and on its removal. For polycrystals, application of a hydrostatic pressure caused an increase in strain-rate which gave an activation volume of about - 10 cm3 mol-1. However, on removal of the pressure the strain-rate did not return to its original atmospheric-pressure value implying that steady-state creep had not been reached.

This value of activation volume is in general agreement with two previously published values for creep deformation, but is of opposite sign to the activation volume for dielectric relaxation. Further tests are in progress.

The breaking strengths of snow were measured by a new tester which had been made by the author, and were expressed as functions of density or hardness. One special merit of the apparatus is that they are useable even for new snow, and the strengths were easily measured to several grammes per cm2. The creep expansion of snow was measured by using an optical level, and was expressed as a function of snow density, temperature, internal stress, and lapsed time. One point of the measurement is that the creep expansion rate did not become constant, hut was decreasing with time even several hours from the beginning of the test.

Two different types of experiment were reported. Both used a pure single crystal of ice freshly grown in the laboratory at 2 mm per hour.

Direct volumetric measurements were made by submerging an ice crystal (volume 143 cm3) in mercury in a sealed steel container and electronically monitoring the height of the mercury in a manometer tube connected to it. Measurements over a 60 d period at —4.0°C showed a small gradual decrease in apparent volume. This could be due to the adsorption of perhaps 10-2 cm3 of air trapped by the mercury at the surface of the ice. The total un-certainties of the experiment are such that we believe we would have observed a volume dilation of as little as 2.5 × 10-6 per day.

Direct measurements were also made of the change in length of ice samples from the same crystal. One was cut with length parallel to c and the other perpendicular to c. Over a 28 d period, the fractional change in length at —13.7°C was less than 2 × 10-7 per day and less than 7 × 10-8 per day ║c, leading to an upper bound on volume change of 7 × 10-7 per day.

We conclude that if dilation of ice occurs with time, it is less than 10-6 per day and therefore probably not a factor which needs consideration in ordinary experiments.

The central-force effective pair potential of Rahman and others (1975) is used to generate minimal binding-energy surfaces and configurations of a water monomer adsorbed on the unrelaxed basal plane surface of ice Ih. In the initial study H2O molecules arc placed with oxygen atoms fixed at the ice Ih lattice positions and associated hydrogens along the tetrahedral bond directions—restricting the H-O-H bond angles to 109.5°. A rigid-body water monomer adsorbed on the surface interacts with all the H2D molecules in the bulk ice model via the central-force effective pair potential. The center-of-mass height, z, and the dipole orientation of the adsorbed H2O molecule are varied to minimize the total binding energy of the monomer over a particular (x,y) point of the surface. Preliminary results showed that a rigid adsorbed monomer with an H-O-H angle fixed at 104.5° produced only minor deviations in the binding-energy surfaces and that a large bulk-ice model (486 molecules) gave effectively the same results as a smaller ice model (50 molecules). Studies on an infinite ice surface using periodic boundary conditions are in progress and will be used to study surface relaxation and long-range effects on the minimal energy surfaces. Three types of sites on the basal plane were considered: (1) a site with all surface molecule protons pointing out of the surface; (2) a site with all surface molecule protons pointing into the surface; and (3) a site with all rows of surface molecule protons pointing alternately into and out of the surface. A "site" generally refers to a region (about 90 Å2) on the surface over which the minimal binding-energy surface is to be determined.

Minimal binding-energy surfaces for the sites have been obtained together with plots showing the surface of the position of the center of mass as a function of x and y. This is a model calculation and is limited by the validity of the potential under close scrutiny. However it gives a qualitative picture of how complex a terrain the real ice Ih surface might present to an adsorbed water molecule and how the water molecule might diffuse from site to site. From these calculations (and in the spirit of this model potential) a value for the mean path length and the mean residence time of the adsorbed water monomer can be estimated.

The probability P that ice embryos, nucleated inside droplets colliding with an ice surface, have crystallographic orientations different from that of the substrate, is correlated with the mean number of droplets which form each crystal in accretions grown in dry regime (substrate temperature Ts < 0°C). The theory of heterogeneous nucleation is applied to represent the ice embryo nucleation rate and the approximate expression is obtained, where ΔGy* is the nucleation energy for randomly oriented critical embryos. Assuming cap-shaped embryos and taking into account the crystal size in accretions grown at Ts = —15°C and air temperatures , it is found that erg

The relationship between the value of ΔGy* and those of the crystal-embryo and crystal-melt interfacial free energies is discussed. Finally the dependence of P0 on the growth conditions and on the ice substrate orientation is analysed, considering the effect of embryo breeding by collision and that of orientation selection, which is responsible for the establishment of preferential orientations in the accretions.

The heat capacities of quenched and annealed heavy ice Ih were measured in the temperature range 14 to 300 K by an adiabatic calorimeter. A relaxational thermal anomaly was found at around 115 K and this phenomenon was ascribed to the onset of deuteron ordering in the crystal. The average activation enthalpy of the relaxational process was determined to be (26±5) kJ mol-1. Residual entropies of the crystal were recalculated on the basis of the present heat-capacity data combined with the revised values for enthalpy of vaporization, saturated vapour pressure, and spectroscopic entropy. They are (3.47±0.41 J K-1 mol-1 for the quenched crystal and (3.44±0.41) J K-1 mol-1 for a crystal annealed at 102-106 K for 264 h. The characteristics and the origin of the anomaly are discussed in comparison with that of ordinary ice.

This paper has been accepted for publication in full in a forthcoming issue of the Journal of Glaciology.

We give a simple explanation of recent experimental evidence that ice crystals may grow in water vapor at low supersaturation (i.e. under atmospheric conditions) without screw dislocations. Examination of the intermolecular potential shows that by assuming non-bulk-like orientations, dangling molecules at surface-cluster edges may form strong hydrogen bonds with substrate molecules. This leads to a study of ice surfaces within the framework of an Ising-like model in which molecules with nearest neighbor vacancies which can provide vertical bonding are allowed two distinct states, yielding bulk-like as well as reconstructed monolayer ledges. The surface roughening transition is examined for this model by means of (i) a Monte Carlo determination of critical points and (ii) an analytical treatment of nucleation clusters. It is found that rough surfaces and, correspondingly, (dislocation-less) surface nucleation growth, prevail at temperatures below the bulk melting point over a wide range of feasible binding energies.

Wavy perturbations formed on disc-shaped internal melting figures in ice were observed. It was found that a minimum wavelength of the perturbations was approximately 100 μm and a critical thickness of the figures for the formation of the perturbations was 10 μ.m. The critical thickness did not depend on the radius and growth rate of the figures. A minimum wave number of the perturbation was 6 and the axis of its sixfold symmetry was parallel to the <1120> direction, The perturbations with large wave number were formed on the inclined side faces of internal melting figures of which the shape was like a truncated cone. Therefore, it was concluded that the perturbations were nucleated at the sharp edge where the side face and the larger plane of the figures intersected. This conclusion was supported by the observation of internal melting figures at grain boundaries where their periphery was always sharp.