Thermoelastic properties of perfect crystals with nonprimitive lattices. II. Application to KCl and NaCl.

Abstract

In Part I, the theory for external and internal strain derivatives of the Helmholtz free energy of a perfect crystal was developed in the quasiharmonic approximation. The theory allows us to consider arbitrary piezoelectric shell-model-like crystals at any temperature and under general external stress conditions. In the present part of this work we show how these derivatives can be utilized in the simplest way in order to calculate a wide range of macroscopic thermoelastic properties of the crystals. The method was realized in a computer code written without additional artificial constraints concerning crystal symmetry and structure. Special attention is paid to the numerical implementation of the formulas obtained. Using different types of pair potentials including ab initio ones, various elastic, dielectric, and general thermodynamic properties of KCl and NaCl crystals are calculated here for a wide range of temperatures and pressures (only for NaCl). Our calculations in the vicinity of the melting point demonstrate that the free energy has a minimum which disappears at some critical temperature, and the transition is controlled only by the isothermal elastic constant ${\mathit{C}}_{11}^{\mathit{T}}$. It decreases so catastrophically rapidly with increase of temperature that it leads to an immediate violation of the stability condition ${\mathit{C}}_{11}^{\mathit{T}}$>${\mathit{C}}_{12}^{\mathit{T}}$ before the isothermal bulk modulus reaches zero. The calculations also clearly show that the empirical pair potentials of Catlow et al. are in reasonably good agreement with most of the experimental data. In addition, we show, in accord with other authors, that the quasiharmonic approximation can be successfully used almost up to half of the crystal melting temperature, although physically correct qualitative results could be expected even near the melting point.