Heat capacities of non-cubic solids

Abstract

For non-cubic solids there is no unique heat capacity at constant volume, although the symbol C_v has often been used to denote the quantity C_p -β²VT/X^T. This quantity is sometimes wrongly identified with C_η, the heat capacity at constant strain. In this paper it is pointed out that C_p -β²VT/X^T is actually the heat capacity defined under the double restraint of constant volume and isotropic stress, here denoted by C_v. The relation of C_v to C_p and C_η is examined, and it is shown that C_p >or= C_v>or= C_η. C_v and C_η are equal if and only if γ₁ = γ₂ = γ₃, γ₄ = γ₅ = γ₆ = 0, where the γ_λ are the generalized Grüneisen functions. Explicit expressions for C_v - C_η 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 C_v - C_η at zero pressure are calculated from experimental data for a variety of non-cubic crystals. For all these crystals the differences between C_v and C_η are of the order of 1% of the heat capacity or less; they are largest for highly anisotropic solids at high temperature.