Local orientational order in ice

Abstract

A cluster expansion approach for the Kirkwood orientational correlation factor g_k in ice has been examined. The expansion parameter measures the extent to which neighboring molecules obey bonding requirements of the ``ice rules.'' For cubic ice, leading terms have been evaluated in the series for the separate contributions to g_k from the first three shells of neighbors. These series tend to confirm the validity of a recent Monte Carlo estimate of g_k, but they also suggest that orientational order in cubic and hexagonal ices has long range and is analogous to local order of critical point pair correlations in Ising models. As a result, the cluster expansion for g_k itself likely converges very slowly, if at all.