Third-Order Elastic Constants of Alkali Halide Crystals

Third-order elastic constants of NaCl-type and CsCl-type crystals have been calculated using the Born model of ionic solids. Short-range repulsive interactions have been included up to second-nearest neighbors. Assuming that the temperature variation of these constants is linear, we have calculated the temperature coefficients $a_{\alpha \beta \gamma }$ in the high-temperature limit. In the case of NaCl-type crystals, $C_{111}$, $C_{112}$, and $C_{166}$ are negative and $C_{123}$, $C_{456}$, and $C_{144}$ are positive, whereas all the third-order elastic constants of CsCl-type crystals are negative. The temperature coefficients $a_{\alpha \beta \gamma }$ are all positive for CsCl-type crystals, whereas $a_{111}$, $a_{112}$, and $a_{166}$ are positive and the others are negative for NaCl-type crystals. The computed values of the third-order elastic constants have been used to calculate the pressure derivatives of the second-order elastic constants and a comparison is made with the available experimental data.