Residual Entropy of Ice

Abstract

We examine the problem of evaluation of residual hydrogen‐bond entropy in ice, first noting by way of introduction the results of applying certain well‐known approximate lattice theory combinatorial techniques (mean field, Bethe, Kikuchi approximations). Subsequently, a general matrix method is introduced for evaluation of the residual entropy in the square planar lattice analog of ice, in terms of a series of contributions, each of which corresponds to a connected cluster diagram. The leading term in this latter method is the Pauling estimate, and two successive orders of terms are evaluated explicitly to indicate rate of convergence. In the real three‐dimensional case the generalization of the matrix method indicates that the Pauling estimate is roughly 1% low.