Many‐Body Effects on the Fourth‐Order Elastic Constants of Ionic Solids

Abstract

AbstractExpressions for the fourth‐order elastic (FOE) constants are derived from the Lundqvist potential for ionic solids along the line adopted in the derivation of the expression for the second‐order elastic (SOE) and third‐order elastic (TOE) constants. As in the case of the SOE and the TOE constants it is observed that the Cauchy relations among the FOE constants are broken even at O K and discrepancies in these relations are directly expressible as functions of the many‐body term in the crystal potential. The expressions for the FOE constants suggest that they must satisfy four identities so that the number of independent constants is only seven. It is suggested that measurements of fourth‐order elastic constants at O K in conjunction with these identities can provide an useful test for the validity of the Lundqvist potential in ionic solids.