Pressure Derivatives of Second-Order Elastic Constants of MgO

Abstract

The deviations of the second-order elastic constants from the Cauchy relation for some representative alkali halides were successfully accounted for by Löwdin's theory of many-body forces of quantum-mechanical origin. In the present paper, this theory is extended to include second-nearest-neighbor (nearest anion-anion) interaction in MgO for the calculation of the pressure derivatives of the second-order elastic constants. The calculated values, $\frac{\partial {c_{12}}^{*}}{\partial p}=1.4\mathrm{}$ and $\frac{\partial {c_{44}}^{*}}{\partial p}=0.5\mathrm{}$, are compared with the empirical results. While the qualitative agreement tends to support the theory that the many-body character of interionic interactions is indeed responsible for the particularly large deviations observed in MgO, better quantitative agreement would require a more elaborate calculation.