Complex dielectric constants have been measured for ice from the melting point to −65°C, and for solid D2O to −35°C, by a combination of bridge and transient methods. For both, the dispersion is described by the simple Debye formula, and the relaxation times τ by the simple rate expression τ = A exp(B/RT). For ice, A = 5.3×10−16 sec, B = 13.2 kcal/mole; and for solid D2O, A = 7.7×10−16 sec, B = 13.4 kcal/mole. The equilibrium dielectric constant for ice is 91.5 at 0°C and increases at lower temperatures; the values for solid D2O are only slightly smaller. Measures taken to minimize errors from voids in the sample and direct current conductance are discussed.

Dielectric Properties of Ice and Solid D2O

The permittivity and loss tangent of naturally occurring ice and snow are considered. The direct-current conductivity is considered only when it is of importance to the alternating-current and radio-frequency properties. Laboratory measurements on pure ice, and deliberately contaminated ice, are included to help in explaining and extrapolating the behaviour of natural ice and snow. The lower band of frequencies from 10 c./sec. to 1 Mc./sec. is occupied by a relaxation spectrum in which the relative permittivity falls from approximately 100 to 3. The loss tangent reaches a maximum at a frequency which varies from 50 c./sec. to 50 kc./sec. as the temperature increases from −60°C. to 0°C. We are interested in the effect of snow density, impurities, stress, crystal size, and orientation. For frequencies much greater than 1 Mc./sec., the relative permittivity is 3.17±0.07. The loss tangent reaches a minimum value at approximately 1,000 Mc./sec. beyond which the dominant influence is infrared absorption. The minimum is 10−3 at 0°C or 2×10−5 at −60°C. These values are greatly increased by impurities or free water. Some possible applications to glaciological field measurements are mentioned.

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Dielectric properties of ice and snow-A review

4096 molecules of water forming an ice Ic structure and 2048 molecules forming an ice Ih structure, with standard periodic boundary conditions in each case, have been used to calculate the dipole correlations which arise from proton allocation to the oxygen nuclei according to the Bernal‐Fowler ice rules. The calculations reveal a substantial antiparallel correlation in the coordination shells at about twice the distance of the nearest neighbors in the lattice. The value of gK, the Kirkwood correlation factor, is found to be 2.07±0.02 for ice Ih. For ice Ic the value, determined with less precision, is 2.11±0.10. In connection with Kirkwood's dielectric formula the value of gK implies an effective dipole moment, μs, of the molecule in the solid ice Ih phase equal to 2.92 D.

Proton Distribution in Ice and the Kirkwood Correlation Factor

A statistical mechanical theory of the static dielectric constant of polar substances is presented which differs from the previous theories of Kirkwood and Frohlich in that a precise evaluation of the distortion polarization term is made. The theory is applied to the dielectric constant of ordinary and heavy water and yields 2 percent agreement with experiment over the entire temperature range. Furthermore, the difference between the dielectric constant of water measured at visible and microwave frequencies can be ascribed to vibrations, such as the bending of the O–H–O bond. The calculated dielectric constant of ice agrees with experimental values within a mean deviation of 3 percent over a considerable temperature range using an approximate evaluation of the Pauling model for that substance. Various other liquids are also compared with experiment.

Dielectric Polarization in Polar Substances

The dielectric properties of H2O ice VII have been measured in a piston‐cylinder cell. The limiting low‐frequency permittivity implies a value of the orientational correlation parameter g that increases from 1.41 at 0°C to 1.54 at 70°C. This is about a half the corresponding value for ice I and suggests that the molecular axes are on the average more antiparallel to one another than required by the ice rules, and are consequently not fully disordered. The VI‐VII and VI‐VIII phase boundaries for both H2O and D2O have been measured. The entropy of the transition VII‐VIII is 0.66 cal K−1 · mole−1 for H2O and 0.64 cal K−1 · mol−1 for D2O, which are 0.15 and 0.17 cal K−1 · mole−1 less than expected if ice VIII were fully ordered and ice VII were fully disordered within the limits of the ice rules. Both dielectric and phase boundary measurements therefore indicate incomplete disorder in ice VII.

Dielectric properties of ice VII and VIII and the phase boundary between ice VI and VII

A calculation is made of the static dielectric constant of ice using only simple molecular data and with well‐defined assumptions as to the possibilities of molecular movement in the crystal. The paper serves as an illustration of the procedure for calculating static dielectric constants, and it results in a numerical value of this quantity for ice which is in reasonable agreement with experiment.

A Calculation of the Static Dielectric Constant of Ice

The paper gives a calculation of the static dielectric constant of ice using Frőhlich's general theory of the static dielectric constant and a recent generalization of it for anisotropic materials2. The calculation is made with the principal assumption that an ice crystal containing N molecules can take up any of (3/2)N configurations, each with equal probability, in the manner proposed by Pauling.3 The calculation includes the effect of interactions up to and including the third nearest neighbors of a given molecule. The dielectric constant thus calculated is in good agreement with the experimental values at present available. It seems, therefore, that Pauling's hypothesis although difficult to justify leads to the correct value for the dielectric constant of ice. The anisotropy of the static dielectric constant is probably small but no exact calculation has been possible.

J. G. Powles

Papers

A Calculation of the Static Dielectric Constant of Ice

A calculation of the static dielectric constant of ice