A method is described for measuring the thermal conductivity of ice in the temperature range from 0.5 to 5.0 K using a 3He apparatus. The results from our first experiments are not too far from the theoretical law for the low-temperature thermal conductivity of ice . Measurements at still lower temperatures are necessary to confirm our results.

100 keV protons with fluxes between 3 × 1015 and 3 × 1016 m-2 s-1 and in doses up to 4 × 1020 m-2 have been used in ice between - 191°C and -87°C to create damage and to analyse it. The Rutherford backscattering minimum yield along the c-axis (about 0.05 in good monocrystals) increases up to unity with the dose, according to a function which can be scaled by a critical dose depending mainly on temperature (Arrhenius law with activation enthalpy of 0.17 ± 0.04 eV above -185°C). Higher flux produces more damage above -180°C, but less below. A beam in a random direction is more efficient below - 180°C, but less at higher temperature than an aligned beam. Beam-induced reordering is observed at definite temperatures and doses. The damage is shown to be due to energy loss by electronic excitations, which decay and produce disordered molecule clusters, mainly by incoherent aggregation of vacancies and interstitials.

The relative permittivity and loss of zone-refined single crystals of hexagonal ice have been measured in the temperature range 200–271 K and frequency range 0.5 HZ–0.2 MHz, using brass, stainless steel, and gold-foil electrodes. The c-axis of the crystal was oriented parallel to the electric field in 14 samples and perpendicular to the field in 8 samples. The equilibrium relative permittivity of orientation polarization ϵ0, parallel and perpendicular to the c-axis, is 96.5±1 and the average relaxation time τay is 36 μs at 265±0.5K; ϵ0 = 124±1.5 and τav = 30 ms, at 210 K. The magnitude of the orientation polarization obeys the Curie-Weiss equation with T0= 15±2 K for both the orientations. These values are in contrast with the c. 17% difference in ϵo for the two orientations reported in the literature. The extrapolated limiting high-frequency relative permittivity ϵ∞, measured for both the orientations, is indistinguishable within 0.5%.

The logarithmic plot of the product of τav and temperature against the reciprocal temperature is linear in the range 210–271 K and gives an activation energy and a pre-exponential factor of 51±2 kJ mol–1 and 0.93±0.22 ps K respectively, for both the orientations of the c-axis with respect to the electric field. The decrease in activation energy which has been reported to occur in polycrystalline ice and in single crystal ice near 230 K is not found until a temperature of 210 K. Single crystals of ice stored in the dielectric cell, after the completion of measurements, for periods ranging from 1–11 weeks at 253±2 K showed no change in their ϵ0, τav, ϵ∞ that could be attributed to the effect of ageing on the orientation polarization.

The influence of plastic deformation on the electrical properties of ice monocrystals has been measured in the frequency range 10-2 to 105 Hz as a function of strain-rate and strain. The crystals have been tested mainly under uniaxial compression, their orientation being for glide in the basal glide system (0001)[1120]. The resolved shear strain-rate ranged from 2 × 10-5 to 1 × 10-3 s-1, the resolved shear strain from 3 to 60%u. Transient as well as bridge methods have been used for the electrical measurements before, during and after the deformation, Plastic deformation reduces the electrical conductivity in the space-charge dispersion range. The decrease depends strongly on the strain-rate; the size of the strain has practically no influence. After the end of the deformation recovery processes have been observed, which restored the original conductivity if the total strain was small. Rapid and large deformations however leave permanent changes. The changes of the d.c. conductivity and of the dispersion strength in the space-charge region are discussed and attributed to the increase of the dislocation density and the change of character of the dislocation network.

Natural ice contains approximately 100 p.p.m. (by weight) of enclosed air. This air is mainly located in bubbles. Carbon dioxide is an exception. We estimate the fraction of CO2 present in bubbles to be only about 20%. The remaining part is dissolved in the ice. Measurements of the CO2 content of ice samples from temperate and cold glacier ice as well as of freshly fallen snow and of a laboratory-grown single crystal are presented. Glaciological implications are discussed.

Radio-echo observations have shown that polar ice in situ is birefringent. The most likely explanation of the birefringence is an anisotropy in the radio-frequency dielectric constant of the ice single crystal, combined with the ordering of the orientations of the ice crystals in polar ice. It is possible to calculate the birefringence of ice which has a distribution of crystal orientations using a technique similar to that used to derive the dielectric properties of heterogeneous media. The experimentally observed birefringence may then be shown to be consistent with the crystal orientation fabric at the site of the observations if the anisotropy of the dielectric constant is slightly less than 1%, that is, slightly less than the accuracy of the laboratory measurements which have failed to detect any anisotropy. Further experimental observations might be used to obtain information on not only the level of anisotropy of the single crystal but also on the crystal orientation fabric of the ice.

Values of relative permittivity measured by the wide-angle reflection technique on the Ross ice Shelf show substantial variations between sites, from 3.09 to 2.89, with estimated errors of ±0.03. The largest values, closest to those normally measured in the laboratory, are found nearest to the grounded ice sheet; values decrease generally in the direction of thinner ice that has been longer on the ice shelf. We believe the variation reflects some real physical phenomenon in the ice shelf, either a true variation in the permittivity of the ice or a complication of the ray-path geometry, but are not able to offer a satisfactory model at present. We hope an explanation will be forthcoming when actual ice core samples from the deep shelf ice are available for examination.

The temperature dependence of the high-frequency conductivity of snow was studied for eight samples in the range — 10°C to — 80°C. The activation energies for granular snow varied from 0.60 eV at temperatures down to — 25°C to 0.24 eV at temperatures below — 25°C, and for dry snow from 0.42 eV to 0.18 eV in the same temperature ranges. Dry snow samples had higher conductivities and lower activation energies than granular icy samples throughout the complete temperature range.

Volume and surface conduction processes were operative. At the higher temperatures above — 25°C volume conduction was attributed to Bjerrum defect migration, while at lower temperatures Bjerrum conduction was replaced by ionic-defect conduction. Granular samples which had experienced melting and reflecting on the surface of the crystals have a structural change which decreased the ionic-defect density at the surface and lowered the sample conductivity.

Above — 25°C, the activation energies for granular icy snow were consistent with those for temperate glacier ice and for laboratory single and polycrystalline ice samples, but was not in agreement with those of either polar snow or ice. Below — 25°C, the activation energies for granular snow were consistent with those for temperate glacier ice, containing impurities, and for polar snow and ice. Fresh dry temperate snow-samples had lower activation energies than in situ polar snow.

The evidence concerning the velocity of glide of dislocations on the (0001) plane of ice Ih is reviewed and related to atomic processes occurring within or near the dislocation core. The velocity is directly proportional to stress at low stress, with a value of the order of 500 Burgers vectors per second at — 18°C and a stress of 105 N m-2. The usual idea of a dislocation core is that it is “crystalline” in the sense that the linkages between molecules are as far as possible the same as those in the normal lattice. For such a model the disorder of protons presents an obstacle to dislocation movement, and recent theories predict that dislocations should not be able to glide as fast as they are observed to do. Various ways of avoiding this difficulty within the context of a crystalline core are discussed, but none seems likely to be successful. An alternative model is that the core is “non-crystalline”, with a disordered arrangement of mobile molecules within it. The movement of such dislocations should not be seriously impeded by proton disorder. Dislocation mobility would then be limited at least in part by anelastic loss due to the stress-induced order of protons in the surrounding lattice.

A new model of dislocations glide in ire Ih is proposed. In developing this model certain assumptions are made: (i) dislocations have a non-crystalline extended core, and (ii) transitions occur through cooperative movements of ?2? molecules in the core of dislocations. A relation between the velocity νd of linear defects and shear stress τ or temperature T is obtained. This relation shows that νd varies linearly with τ at low values of τ and (or) T but varies more rapidly at higher stresses; this non-linearity is more pronounced the higher the temperature. Such results are in agreement with experimental data.

The inelastic behaviour of ice Ih single crystals has been investigated by an inverted torsional pendulum in the low-frequency range. Three features are distinguished:

(i) a relaxation peak previously observed by several authors in the higher-frequency range,

(ii) an internal friction increasing with temperature in the high-temperature range (230–273 K),

(iii) within this high-temperature range, internal friction becomes amplitude dependent, and this dependence becomes greater the greater the temperature.

In this case, the internal friction has been interpreted in terms of movements of dislocations. Hence, the experimental results are interpreted with a model of internal friction based on an empirical relation for the velocity of dislocations. This model of internal friction is in fair agreement with experimental data . It is possible then to get an estimate of dislocation density. Hence it is shown that internal friction experiments can be useful in the study of the plastic behaviour of ice single crystals.

A method is described for preparing the surface of ice and for forming etch pits on the prismatic surfaces with whisker replicas that correspond to basal dislocations. The technique removes the ambiguity sometimes associated with etch pits and dislocations, and allows direct observation of dislocation glide, pile-up against barriers, and other features in deformed ice.

Ice crystals grown from the vapor under controlled conditions have been examined by X-ray topography. Plates grown in the region — 1.5°C to —3°C and at — 15°C near water saturation were often free of defects, as were plates grown at smaller supersaturations (1.5% at — 3°C, 6% at — 15°C). It is inferred from these observations that growth was occurring by two-dimensional nucleation on the prism plane. It is suggested that multilayer adsorption on the crystal surface was responsible for growth at the low values of supersaturation, compared with higher values predicted by the Burton—Cabrera—Frank theory. Ice crystals dependent on dislocations for growth could only occur at supersaturations lower than these values. The crystal habit is interpreted as being dependent on differential two-dimensional nucleation on prism or basal faces. Rib structure is often associated with dislocation loops; stacking faults were evident in some crystals.

This paper presents studies on crystal imperfections including basal and non-basal dislocations, small-angle grain boundaries, stacking faults, and dislocation networks in ice using both X-ray diffraction and Laue techniques; these studies examined the growth process or origin of the ice, i.e. ice from glaciers, ice grown from the melt, or ice formed by sublimation. Several hoar crystals were found to be perfect, dislocation-free crystals, this may be due to their very slow growth rate. Dislocations and Shockley-type stacking faults were observed in some crystals. Dislocation density of a hoar crystal is very large at the point at which it started to grow, but away from this region the density becomes so small that no dislocation can be seen. The arrangement and structure of dislocations around vapour figures were also studied by means of X-ray diffraction topography. It was found that the dislocation density is high along the periphery of the vapour hexagon and that the great majority of dislocations within the hexagon are running from its centre towards the vertices or sides of the hexagon. Long screw dislocations with Burgers vector c <0001> were observed in a tabular ice which was formed artificially at a very slight degree of supercooling. The behaviour of dislocations in ice subjected to a tensile stress was studied by the use of the divergent X-ray technique which gives both enlarged Laue spots and a transmission pattern in the same photograph.

A deformation mechanism map for pure polycrystalline ice of 2 mm grain diameter is constructed, New sub-regions in the dislocation glide region are proposed: dislocation glide with crack formation, dislocation creep, and fracture at high stresses above about 1 MPa. The boundary between the dislocation creep and DGC regions is determined by the onset of cleavage cracks due to piled-up dislocations near grain boundaries. The fracture region is that area of the map where fracture occurs readily when the ice is subjected to a rapid deformation rate exceeding 10-3 s-1. Experimental results of the stress dependence of the compressive deformation rate of polycrystalline ice are compared with the map. The effect of changes in the creep activation energy near the melting point is discussed together with those of other factors.

Monocrystals and bicrystals of ice have been creep tested at temperatures between 4 and — 30°C. The bicrystals had a single grain boundary running parallel to the tensile axis; this configuration inhibited grain-boundary slip between the two grains. The creep tests, which were carried out at constant stress σ and temperature T, yielded data of strain ϵ for time elapsed since the start of the test. These data showed accelerating creep for both monocrystals and bicrystals at all strain levels. Strain-rates were derived at strains of 0.01, 0.05. and 0.10, and these rates were fitted to the expression

k is Boltzmann’s constant and E is the creep activation energy. Derived values of n were 1.9 for monocrystals and 2.9 for bicrystals. The creep activation energy was found to be 78 kJ/mol for monocrystals and 75 kJ/mol for bicrystals. The processes of creep deformation in mono-, bi- and polycrystals are discussed.

Constant strain-rate compression tests on ice single crystals at temperatures between –20°C and -0.2°C are described. The power-law dependence of yield stress on strain-rate gives a value of n which varies from 1.95±0.04 at –0.2°C to 2.07±0.08 at –20°C. The activation energy of deformation varies with strain-rate, but a mean value of 70±2 kJ mol–1 is obtained, with no indication of any increase close to maleting point,as has been found polycrystalline ice. An apparent work-hardening effect, at strains greater than 15%, is explained as being due to bending of the crystal changing the orientation of the basal planes.

Deformation characteristics of polycrystalline ice and their dependence on time, temperature, and stress have been analysed on the basis of a phenomenological relation which describes creep in terms of initial elastic, delayed elastic, and permanent strain. It is shown that the effective modulus of ice observed in the laboratory or in the field can be examined on the basis of this model. The model also provides a basis on which the observed flow law of ice can be examined conveniently. Some apparent inconsistencies in the results of earlier investigations of the mechanical property of ice appear of be reconciled by the model.

Quantitative effects of crystallographic orientation fabrics are incorporated into the flow law for isotropic polycrystalline ice by the introduction of an enhancement factor applied to the isotropic fluidity. An aggregate is viewed to a first approximation as a collection of grains deforming independently by basal glide. The influence of preferred orientations on the mean intragranular rate of strain is treated in terms of a redistribution of the magnitude and orientation of resolved basal shear stress. A quantitative measure of this effect on the fluidity of the aggregate is provided through the development of a geometric tensor and a stress configuration parameter. Intergranular interference is then considered as a dissipative process modifying the fluidity of the aggregate.

Empirical justification for the model at low octahedral shear stresses is provided by several laboratory creep tests on naturally anisotropic bore-hole specimens under both in situ and anomalous stress situations. Predicted enhancement factors ranged from approximately 0.2 to 2.8 and agree well with measured values. The tests were carried out in uniaxial compression and simple shear.

Uniaxial compression tests were conducted on polycrystalline-ice samples with random c-axis orientation and steady-state creep rates were determined. Experiments were conducted on both inclusion-bearing and inclusion-free ice and were run at constant stress and constant temperature. During freezing, the presence of inclusions in low concentrations inhibits crystal growth; variations in the volume-fraction of inclusions thus result in variations in ice-crystal size. The creep rate of polycrystalline ice at high temperatures and moderate stresses is extremely sensitive to variations in ice-crystal size. Due to an apparent inversion between dislocation-controlled creep and diffusion-controlled creep, the optimum grain size for creep resistance is about 1.0 mm. Increasing or decreasing the average crystal size from this critical value results in an increase in secondary-creep rate.