Dielectric constant of ice

Abstract

A series expansion for the dielectric constant of the Bernal‐Fowler‐Pauling model of ice relaxed to allow Bjerrum faults is developed using a renormalization technique which eliminates large numbers of subgraphs. In the no fault limit the dielectric constant has the form ε₀ = ε_∞ + (4πG/3)(N/V)(μ²/kT) where the Bethe type approximation yields G = 3 and the exact result in two dimensions is G = 9/π. In two dimensions the series for G exhibits reasonable convergence to the exact result. For cubic ice the series of Gobush and Hoeve are confirmed and slightly extended. These cases lend support to the series results for the Bernal‐Fowler‐Pauling model of hexagonal ice; namely, that there is very little anisotropy in ε₀ and G is very close to 3. These results are used in discussing whether more refined models of ice are needed. Also, the discussion comparing G with the Kirkwood correlation function g_K, begun by Stillinger and Cotter, is continued.