The elastic constants of a cubic crystal subjected to moderately high hydrostatic pressure

Abstract

This paper presents the results of an analysis of the finite strain theory that goes to the next higher-order term than third-order in the strains for cubic crystals. Theoretical expressions for the effective second-order elastic constants are presented here in terms of the second-, third-, and fourth-order elastic constants and the Lagrangian strain; these have been derived from the rigorous stress-strain relationship set by the Murnaghan theory of finite deformation. Since typical ultrasonic experiments with pressure result in thermodynamically mixed elastic constants, the practical ultrasonic expressions of the effective elastic constants are presented for a cubic crystal subjected to moderately high hydrostatic compression. The rigorous relationships between the pressure derivatives of the effective elastic constants and partial contractions of the higher-order elastic constants are presented also, and then the primary experimental quantities that are resulting from the usual ultrasonic-pressure experiments have been identified in terms of the thermodynamically mixed second-, third-, and fourth-order elastic constants of the crystal.