Third-Order Elastic Constants of Alkali Halide Crystals

Abstract

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 ${a}_{\ensuremath{\alpha}\ensuremath{\beta}\ensuremath{\gamma}}$ 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 ${a}_{\ensuremath{\alpha}\ensuremath{\beta}\ensuremath{\gamma}}$ 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.