Thermoelastic properties of perfect crystals with nonprimitive lattices. I. General theory

Abstract

Following general ideas proposed by C. Feldman et al. and extended by D. C. Wallace in his book on the thermodynamic properties of crystals, we have derived detailed expressions for both external and internal strain derivatives of the Helmholtz free energy of a perfect crystal. The thermodynamic functions are calculated in the quasiharmonic approximation though the present theory can be straightforwardly extended for an arbitrary order of anharmonicity. The formalism developed in this paper is similar, but not equal, to those proposed by previous authors. We have made several important generalizations of the existing theory and, besides, have obtained equations which are much simpler. It makes it possible to consider an arbitrary shell-model crystal with nonprimitive lattice (including piezoelectric crystals) and to pay special attention to the numerical implementation of the formulas obtained. Moreover, by careful consideration, we have corrected a physically doubtful conclusion existing in a particular piece of the literature, namely that microscopic and macroscopic expressions for the crystal energy may not coincide. We prove rigorously that a proper microscopic consideration does lead to the same macroscopic expression. In the second part of this work the theory developed here will be applied to KCl and NaCl crystals.