The experimental evidence for the distortion of a water molecule when it is condensed to form ice is reviewed. The specific distortions considered are the changes in inter-nuclear distances, energy and its derivatives with respect to nuclear motion, and electrical moments and polarizabilities and their response to nuclear motion. Some of the properties of ice can be expanded as Fourier or Taylor series in the ratio r/R of the O–H to the O—O distances, and these expansions are used to relate various properties of the intermolecular potential energy, of the electrical dipole moments, and of the polarizability. For example, the amplitude of the orientation polarization can be related to the infrared intensity of the fundamental and first overtone infrared bands.

The last five years have seen an increasing interest in clathrate ices as a result of the discovery of extensive deposits of natural gas hydrates in permafrost regions. Twenty-six new clathrate hydrates have been identified, mainly by NMR, including a tetragonal hydrate of dimethyl ether. N-butane and neopentane have been found to be enclathrated in natural gas hydrates, the former as a gauche conformer. As a result of their high symmetries, encaged neopentane, CF4, SF6, and SeF6 exhibit a Resing apparent-phase-change effect in the temperature range of NMR line narrowing. There is increasing evidence that reorientational jumps of water molecules are more frequent than translational jumps in clathrate ices. This is certainly so for ethylene oxide-d4 and tetrahydrofuran-d8 hydrates for which two regions of proton line narrowing and two T1ρ minima have been observed. The reorientational motions of most guest molecules in structure II hydrates only become isotropic on a time scale long enough to permit the cage configurations to be averaged to 43m symmetry by reorientation of the water molecules. The orientations of the water molecules remain disordered to the lowest temperatures.

Ice IV, a wholly metastable ice phase, has a structure based on a framework of tetrahedrally hydrogen-bonded water molecules in a rhombohedral unit cell. The structure involves two non-equivalent types of water molecules and four non-equivalent types of hydrogen bonds. A novel structural feature is a hydrogen bond that passes through the center of a 6-ring of water molecules and links non-adjacent structural layers. The bond network is proton-disordered, even after quenching.

The translational vibrations of hypothetical ordered forms of ice Ic and ice Ih have been predicted and correlated with the known spectra of the actual disordered phases. The TO–LO splittings have been predicted by assuming that the changes of mean refractive indexes across the translational band is the same in all phases, and equal to the known change for ice Ih. Both ordered phases are predicted to have LO components at c. 275 and c. 310 cm-1. These predicted bands are assumed to be related to the bands at the same frequencies in the disordered phases. These bands are therefore LO components corresponding to the TO translational vibrations.

We present the Raman spectra in natural and polarized light of ice Ih monocrystals in the region of the translational frequencies. These spectra are of better quality and higher resolution than previous spectra from monocrystals, and demonstrate the value of the investigation of single crystals by this technique, in spite of the proton disorder. In order to explain the observations we use the model of simultaneous activity of the modes allowed in D6h symmetry and the modes allowed by the proton disorder. By analogy with the interpretation of the phenomena observed in ordered piezoelectric crystals, we suggest that the existence of translation frequencies up to c. 320 cm-1 is due to the splitting between transverse and longitudinal optical modes. On this basis, an initial simple dynamical model using only three parameters permits an interpretation of the Raman spectrum. The probable presence of directional effects in ice Ih argues in favour of the proposed explanation.

Theories of the dielectric constant in ice differ in three fundamentally different ways that are often confused with each other. First, there is the choice of interactions to include in the model, notably whether to try to include long-range dipolar interactions as in the Kirkwood theory or to include only the short-range ice-rule interactions. Second, there is the choice of the kind of statistical quantity calculated, e.g. the Kirkwood correlation factor g or the polarization factor G, which Stillinger and Cotter showed to be different. Finally, there is the choice of the kind of computational tool used, and in original papers this choice often obscures the first two differences. With these distinctions in mind a review is given of current theoretical calculations of the dielectric constant and the residual entropy and how the different theories relate to each other and to experiments.

Positron annihilation techniques (PAT) are briefly discussed, and the information that may be obtained about the positronium (Ps) states is compared to that obtainable about the similar electron states. The behaviour of Ps in monocrystals of pure light and heavy ice was studied at temperatures between — 185°C and the melting point. Ps is very probably trapped in vacancies (i.e. missing water molecules) in ice. A vacancy formation energy of roughly 0.2–0.35 eV was derived in agreement with the value 0.28±0.07 eV obtained previously from studies of the annealing of irradiated ice. The vacancy concentration is at least a few parts per million at the melting point, i.e. roughly 104 times higher than normally assumed in the literature. The fact that the vacancy concentration is comparable to that of the hydrogen-bond defects will probably enforce a pronounced change in the “hydrogen-bond-defects” theory of the electric properties of ice.

Positron annihilation techniques, which are specifically sensitive to vacancy-type defects have been used to study the effect on ice of irradiation and HF doping. Main conclusions are that immobile water-molecule vacancies can be created at low temperatures by either irradiation or HF doping. Upon heating, the vacancies become mobile at about 100 K. Some of them cluster into di- and multi-vacancies which grow in size with temperature up to at least 145 K. A vacancy migration energy of 0.34 ± 0.07 eV is deduced, about three times higher than previously assumed. Possible mechanisms for vacancy formation by HF doping are discussed. Out-diffusion of HF is followed at –26°C over several weeks. The diffusion constant derived agrees within uncertainty (a factor of two) with the large value obtained by Haltenorth and Klinger. In particular two results seem important for other parts of ice physics. One is that HF doping creates an appreciable increase in the vacancy concentration, the influence of which should be considered in models for other defects in ice. The other is that vacancies migrate at about 100 K, a fact which might be important for the interpretation of some of the many “anomalous” effects observed in ice at about that temperature.

The interaction of point detects in ice has been neglected for a long time. Experimental data obtained from dielectric measurements on HF-doped crystals stimulated a new evaluation of the possibility of an interaction between Bjerrum defects and ions. In a previous paper it has been shown that this leads us to assume the existence of aggregates of Bjerrum defects and ions. In this paper these aggregates and Bjerrum defects are used to explain the dielectric properties of ice, especially the temperature dependence of the product of the high and low frequency conductivity σ0σ∞.

The interaction of Bjerrum defects and impurity molecules leads to a dependence of the concentration of frenkel pairs on Bjerrum-defect concentration. At HF concentrations above the native Bjerrum-defect concentration the formation of a Frenkel pair is enhanced. This leads to the fast out-diffusion which has been studied in highly doped crystals by means of NMR techniques.

To understand the recent dielectric measurements made on HF-doped ice single crystals requires a full knowledge of the concentration of electrical defects present in ice and their subsequent interactions. Previous interpretations of the behaviour of HF-doped ice have concentrated upon specific features in isolation, whereas this paper presents analyses of a data set of 139 temperature and impurity combinations from 17 HF-doped ice single crystals. The interpretation of the behaviour of these crystals is in terms of several possible theoretical models. All models are based upon the common assumptions that HF molecules enter the ice lattice substitutionally and that excess Bjerrum and ionic defects can be formed at the HF sites. They also use the theory of electrical conduction in ice by Jaccard (1959) and the defect equilibria analysis in ice by Kroger (1974).

All models yield values for the concentration, mobility, energy of formation and charges for the different types of electrical defect considered to be generated.

From the model which assumes that only three fluorine centres exist, the approximate derived values of the mobility and charge for the L-defect and positive ionic defect are as follows: μL = 5 × 10-8 m2 V-1 s-1 at 273 K, eDL = 0.44e; μ+ = 2.7 × 10-8 m2 V-1 s-1 at 273 K, e± 0.73e.

Finally, using the derived defect conductivities and the Jaccard theory of electrical conduction, the relaxation tune of HF-doped ice has been successfully predicted over a wide range of temperature and fluoride concentration.

Three-terminal dielectric bridge measurements (in the range 20 Hz to 100 kHz between — 5°C and —90 to — 120°C) have been made of ice doped with (a) conductivity-enhancing ionic impurities (HCl, HF, NaCl, KF, NH4F) and (b) conductivity-depressing solutes (NH4OH, NH4Cl, NH5CO3, NaHCO3). Blocking electrodes were used for the first group. The true ice parameters were extracted from linearized plots of the Debye equations. Chlorides and fluorides showed very similar characteristics in their spectra and static conductivity. The results suggest that static conductivity is controlled by extrinsic protons. On the other hand, bases, or solutes that impart a positive freezing potential to the ice, suppress extrinsic protons. In this case, the static conductivity was not, or only weakly, temperature dependent and lower than in the first group. A conductivity cross-over was observed in neither case. The dielectric conductivity contribution is strongly dependent on impurity concentration but apparently less affected than the static conductivity by the nature of the solute. The principal relaxation time is reduced by most solutes, exceptions are pure (bicarbonate-free) bases, sodium bicarbonate, and carbon dioxide.

This paper describes measurements of the dielectric constant and of the conductivity on pure and doped ice single crystals subjected to hydrostatic pressure. The dopants used were NH3 (cNH3 ≈ 5 × 10-5 to 1.2 × 10-4 mol/1) or HF (cHF = 5 × 10-6 and 5 × 10-4 mol/1). The pressure and temperature ranges covered were 1 to 1 500 bar and — 15 to 60°C. The activation volumes for the orientational and the ionic contribution to the conductivity could be determined. A definitive interpretation is not possible because many questions concerning the formation of the defects are still open, hi addition to the main subject, some new data from conductivity measurements on NH3-doped single crystals at atmospheric pressure are presented.

The electrical behaviour of ice which has been finely ground and compressed was investigated during ageing in air and over a range of temperatures. The dielectric behaviour may be accurately represented as the sum of two elliptical relaxation spectra. The behaviour eventually stabilizes with similar activation energies for the mean relaxation time of each spectrum c. 0.25 eV, and the ratio of the relaxation times is ten in samples of density c. 0.42 Mg m-3. Arguments are presented on whether the higher-frequency dispersion is a consequence of the heterogeneous nature of the samples or is a bulk relaxation process. The similarities between the behaviour of such finely ground ice and of deposited snow and polar glacier ice are discussed. The extent to which the results may be attributed to surface adsorption of CO2 are examined by reference to measurements of the CO2 content of finely divided ice and ice from polar regions.

The surface conductivity of monocrystalline ice was measured as a function of temperature impurity concentration, field-strength, and other variables. At temperature, below about –6°C the surface conductivity was found to follow the Arrhenius equation with an activation energy of 33±2 kcal mol−1 (1.43±0.09 eV). Small amounts of impurities contained within the ice increased the surface conductivity and decreased the actuation energy: for HF-doped ice the activation energy was reduced to 10.0 kcal mol−1 (0.44 eV). Mechanical treatment of the ice surface increased the surface conduction. At temperatures above about —6°C the surface conductivity increased more rapidly with the rise in temperature; this is explained in terms of the appearance and development of a quasi-liquid layer on the ice surface. The electrical behaviour of sublimed ice surfaces was found to vary at a temperature around —9°C. At higher temperature a sharp, instantaneous current increase was observed as evacuation began; this was considered to be caused by the formation of ionic states due to the rapid evaporation of quasi-liquid layers. It was concluded that the temperature above which the ice surface was covered with a quasi-liquid layer lay in the range — 6 to — 9°C.

Dielectric properties of dislocation-free hoar-frost ice crystals were measured in the audio-frequency range. Anomalously small relaxation strength was found in the dislocation-free area of the crystal samples while dislocations deliberately introduced by scratching the samples drastically modified the relaxation strength. Since measurements made in the area of high dislocation density indicated normal behavior, electrically charged dislocations are considered to be the source of the normally observed dielectric relaxation.

Ice Ih single crystals were investigated by complex admittance and thermally stimulated depolarization (TSD) techniques, in the relaxation-time ranges 10–5–10 s and 10–104 s respectively.

The relaxation spectrum was resolved and three components of it were studied. Second-order kinetics had to be assumed for two of the TSD spectra to obtain Arrhenius-type relaxation times. The “Debye spectrum” had an activation energy for the relaxation time of 0.64 eV at the high temperatures and its dielectric strength revealed a possible defect cross-over at Tc = 190 K. Far below this temperature the activation energy was 0.38 eV, that is about half of that necessary for a pair of ion defects to form. In comparison with the results of other authors, a lower concentration of ionic defects, or possibly of Bjerrum–ion aggregates, was deduced to occur in our crystals.

Inert-gas host molecules were proposed as a possible origin of the two other spectra, having relaxation times shorter than the “Debye spectrum” and energies of 0.33 eV and 0.37 eV. Moreover the 0.33 eV spectrum, whose dielectric strength appears at a temperature below Tc, might alternatively be related to the cross-over of the “Debye spectrum”.

A brief introduction to neutron scattering is given with special emphasis on the difference between coherent and incoherent contributions. The following report of recent work on ice contains the determination and verification of some phonon dispersion curves, and outlines the state of the art on diffuse scattering due to the proton disorder. Results on “two-dimensional ice” in copper formate tetrahydrate are of great interest as this system exhibits a phase transformation below which the protons are ordered. The study of rotational diffusion and of the tunnel splitting of the rotational ground state of molecules which contain protons is discussed in some detail. These investigations are now possible with very high energy resolution ΔE ≈ 5 × 10-8 eV (4 • 10-4 cm- 1 or 12 MHz).