Thermodynamics of polar lattices

Abstract

The high-temperature series expansion for the free energy of a lattice of classical permanent dipoles is obtained to order (μ²/T)⁵, where μ is the dipole moment and T the temperature. Numerical values of the coefficients in the series are presented for three cubic lattices. Two Padé approximants to the expansion are constructed which exhibit the appropriate low-temperature behaviour of the free energy. These approximants are compared with results of the spherical model for this system, and it is found that the simplest of these gives an accurate assessment of the exact low-temperature behaviour. The Padé approximant results for the free energy also agree quite well with the spherical model results. The implications of these observations for polar fluids are noted. A connection is presented between the free energy and the Clausius-Mossotti function for dipolar lattices. A Padé approximant to the Clausius-Mossotti function which is constructed to satisfy known bounds is found to agree with the spherical model results for this quantity.