Many-body effects on the third-order elastic constants and pressure derivatives of the second-order-elastic constants of NaCl-structure alkali halides

Expressions for the third-order elastic (TOE) constants have been derived from the Lundqvist potential for ionic solids. It has been observed that the Cauchy relations among these constants are broken owing to the presence of the many-body term in the crystal potential. All the parameters, except one, appearing in the expressions for the TOE constants, can be determined from the values of the second-order elastic (SOE) constants, the equilibrium condition and a plausible assumption concerning the overlap repulsion. Determining the remaining parameter from the expression for $\frac{d{S}^{\prime }}{dp}$, we can evaluate all the six TOE constants ($C_{111}$, $C_{112}$, $C_{166}$, $C_{123}$, $C_{144}$, $C_{456}$) and the remaining two independent pressure derivatives of the SOE constants. The values, so calculated, compare very well with the corresponding experimental results.