Effective second-order elastic constants of a strained cubic crystal in the finite strain theory

Expressions for the effective second-order elastic constants of a strained cubic crystal have been obtained using the finite strain theory of Murnaghan, in terms of the higher-order elastic constants of its natural state. These formulae are found to be different from those obtained by the earlier workers. These expressions are used to obtain the pressure derivatives of the effective second-order elastic constants of some cubic crystals for which experimental second- and third-order elastic constants are available. The second-order anharmonic contribution to the pressure derivatives of C111 and C112 of copper, silver, and gold is calculated from a knowledge of the estimated values of the fourth-order elastic constants of these metals.