Spatially varying polarization in ice

Abstract

We calculate the response of an ice crystal to a spatially varying applied electric field. The dielectric polarization of the ice is not assumed to be proportional to the local macroscopic electric field. Instead, we formulate an expression for the free-energy density of an ice crystal with non-uniform polarization and derive the functional forms of the electric and polarization fields which minimize the free energy of the whole system. In general, the two fields have different spatial variation. Their behaviour is governed by two characteristic lengths: the Debye length and a polarization decay length, determined, respectively, by the concentration of ions and Bjerrum defects in bulk ice. The model is a generalized Poisson–Boltzmann theory which includes the effects of the microscopic structure of the medium in a description of electrostatic screening of external charges.