Fourth‐Order Adiabatic Linear Compressibilities for Non‐Cubic Solids

Abstract

AbstractExpressions for the linear adiabatic compressibilities of an at least orthorhombic crystal and their pressure derivatives are derived in terms of the second‐, third‐, and fourth‐order elastic constants within a finite‐strain theory which includes thermal effects according to the quasi‐harmonic approximation of lattice dynamics. The expressions are derived in terms of the Lagrangian strain tensor and the frame‐indifferent analogue of the Eulerian strain tensor. Numerical applications are given for three hexagonal metals: cadmium, magnesium, and zinc, namely the temperature variations of the linear adiabatic compressibilities and their pressure derivatives, including recent estimations of the combinations of fourth‐order elastic constants appearing in the present work. When possible, the comparison with experimental data shows a rather good agreement with the compressibilities calculated within the present theory using the Green‐Lagrange strain measure of the deformation. About the variations of the first pressure derivatives of the adiabatic compressibilities with temperature, the present work provides us with theoretical values in the lack of experimental data.