Heat capacities of non-cubic solids

Abstract

For non-cubic solids there is no unique heat capacity at constant volume, although the symbol Cv has often been used to denote the quantity Cp -β2VT/XT. This quantity is sometimes wrongly identified with Cη, the heat capacity at constant strain. In this paper it is pointed out that Cp -β2VT/XT is actually the heat capacity defined under the double restraint of constant volume and isotropic stress, here denoted by Cv. The relation of Cv to Cp and Cη is examined, and it is shown that Cp >or= Cv>or= Cη. Cv and Cη are equal if and only if γ1 = γ2 = γ3, γ4 = γ5 = γ6 = 0, where the γλ are the generalized Gruneisen functions. Explicit expressions for Cv - Cη are obtained in terms of experimental thermodynamic properties. With suitable definitions for strain coordinates and elastic constants these expressions are valid at all pressures. Values for Cv - Cη at zero pressure are calculated from experimental data for a variety of non-cubic crystals. For all these crystals the differences between Cv and Cη are of the order of 1% of the heat capacity or less; they are largest for highly anisotropic solids at high temperature.