ALBERT

Description: 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.

Description: 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, g I is 10%, or more, greater than g II 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.

Description: The relative permittivity ∊’ and attenuation ∊ in laboratory-grown, polycrystalline and single-crystal ice Ih are reported at 35 and 60 MHz in the temperature range —25ΰC to — 0.2 ΰ C.The∊’ and α at 35 MHz and — I°C are 3.208±;0.010 and 6.2 ± 0.1 dB/100 m, respectively. From a comparison between the respective ∊’ andαof the polycrystalline and single-crystal ice measured perpendicular to thec-axis, it is concluded that any anisotropy of polarization at these frequencies is so small as to be undetectable. Amongst several factors that may contribute to anisotropy in ice, electronic polarization contributes 0.0037 to the difference between the relative permittivity measured parallel and perpendicular to thecaxis at — Iΰ C and at frequencies less than 500 THz.Experiments have shown that the plastic deformation resulting from a uniaxial compressive stress of up to 100 bar does not influence the ∊’ and α of ice at 35 and 60 MHz.

Description: The relative permittivity ∊’ and attenuation α in laboratory-grown, polycrystalline and single-crystal ice Ih are reported at 35 and 60 MHz in the temperature range —25°C to — 0.2 ° C. The ∊’ and α at 35 MHz and — 1° C are 3.208±0.010 and 6.2±0.1 dB/100 m, respectively. From a comparison between the respective ∊’ and α of the polycrystalline and single-crystal ice measured perpendicular to the c-axis, it is concluded that any anisotropy of polarization at these frequencies is so small as to be undetectable. Amongst several factors that may contribute to anisotropy in ice, electronic polarization contributes 0.0037 to the difference between the relative permittivity measured parallel and perpendicular to the c-axis at — 1° C and at frequencies less than 500 THz.Experiments have shown that the plastic deformation resulting from a uniaxial compressive stress of up to 100 bar does not influence the ∊’ and α of ice at 35 and 60 MHz.

Description: 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.

Description: 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,1where 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,2where 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.

Description: 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.

Description: 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 T 0 = 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.