Pressure Dependence of the Electrical Properties of Ice

The pressure dependence of the proton conductivity of water ice is studied theoretically. It is shown that the decrease in the hydrogen bond length leads to the decrease in the formation energy of ionic defects and to the increase in the formation energy of bond defects. As a result, the partial conductivity of ionic defects, which determines the static conductivity of ice, increases, while the partial conductivity of bond defects, which determines the high-frequency conductivity of ice, decreases. At a certain pressure, a crossover of majority and minority carriers occurs, and the partial conductivities of ionic and bond defects become equal, while the static conductivity of ice reaches a maximum, and the permittivity of ice reaches a minimum. At the further pressure increase, the static conductivity of ice is determined by the partial conductivity of bond defects and decreases, while the high-frequency conductivity is determined by the partial conductivity of ionic defects and increases. The pressure at which the crossover occurs, as well as the maximum proton conductivity and the minimum permittivity, is estimated, and the comparison with experimental results is discussed.