Third-Order Elastic Constants of NaCl and KCl Single Crystals

Abstract

Measurements have been made to determine the third-order elastic constants of NaCl and KCl single crystals. The relations between the velocities of ultrasonic waves propagating along the [$1\overline{1}0$] and [$\overline{1}\overline{1}2$] directions under a uniaxial compression applied in the [111] direction and the elastic constants were derived. Six velocities of these ultrasonic waves were then measured at room temperatures as functions of the strain using the pulsed-ultrasonic-interference technique. From the present measurements under the $〈111〉$ compression and those under the hydrostatic pressure by Lazarus, eleven equations were obtained for both NaCl and KCl crystals. From these equations, the following five constants (Brugger's definition for the third-order elastic constants) in units of ${10}^{12}$ dyn/${\mathrm{cm}}^{2}$ were solved by the method of least squares: The Cauchy relation ${C}_{456}={C}_{144}$ is seen to be satisfied to within the probable error in both NaCl and KCl crystals at room temperature. By assuming the validity of the other two Cauchy relations, one can estimate the constants ${C}_{111}$, ${C}_{112}$, and ${C}_{123}$ as follows: