Thermodynamic and dielectric properties of polar lattices

Abstract

Monte Carlo results are presented for the free energy and dielectric constant of systems of permanent dipoles disposed on the sites of simple cubic and face-centred cubic lattices as functions of the parameter ϑ = μ²ρ/kT. Alternative schemes are considered for taking account of the long-range character of the dipolar interaction, based on an Ewald-type sum or a reaction-field approximation; use of such a procedure is essential if the system is to have the correct dielectric properties. Different methods of calculating the dielectric constant are also compared. It is shown that the two methods of treating the long-range contribution to the energy lead to similar results for the dielectric constant, but use of the Ewald method apparently introduces a small but systematic error. The results on both free energy and dielectric constant are discussed in the light of predictions of a number of analytical approaches. In the case of the simple cubic lattice the general trend in the computed dielectric constant as a function of ϑ is in closer accord with the solution of the mean spherical approximation than with a simple Padé approximant to the Clausius-Mossotti function.