Fourth-order elastic constants and the temperature dependence of second-order elastic constants in cubic materials

Abstract

A theory analyzing the temperature dependence of second-order elastic constants on the basis of a quasiharmonic-anisotropic-continuum model is applied to LiBr, KCl, RbF, $\beta$-brass, Cu, Ag, and Au. The number of fourth-order elastic constants is reduced from 11 to 2 by assuming that nearest-neighbor (nn) and next-nearest-neighbor (nnn) central-force interactions predominate in fourth order. The fourth-order elastic constants found from the experimental results show that nn interactions are dominant for the NaCl structure and that nnn interactions are dominant for the CsCl structure, as would be expected for a potential containing a term describing a rapidly varying central-core repulsion. Using recent measurements for Cu in the low-temperature $T^4$ regime where the anisotropic-continuum theory should be exact, a potential is derived which is in close agreement with one used extensively in point-defect calculations.