The Temperature Variation of the Elastic Moduli of NaCl, KCl and MgO

Abstract

The principal adiabatic and isothermal elastic moduli and elastic constants of NaCl, KCl and MgO have been measured over the temperature ranges 80\ifmmode^\circ\else\textdegree\fi{}K to 270\ifmmode^\circ\else\textdegree\fi{}K (Balamuth and Rose) and 270\ifmmode^\circ\else\textdegree\fi{}K to 480\ifmmode^\circ\else\textdegree\fi{}K for NaCl; 80\ifmmode^\circ\else\textdegree\fi{}K to 280\ifmmode^\circ\else\textdegree\fi{}K for KCl; and 80\ifmmode^\circ\else\textdegree\fi{}K to 560\ifmmode^\circ\else\textdegree\fi{}K for MgO. The Debye characteristic temperatures of these substances at 80\ifmmode^\circ\else\textdegree\fi{}K, calculated from the adiabatic elastic constants, are 320\ifmmode^\circ\else\textdegree\fi{}K, 246\ifmmode^\circ\else\textdegree\fi{}K and 946\ifmmode^\circ\else\textdegree\fi{}K, respectively. The variation of the isothermal ${c}_{11}$ and ${c}_{44}$ with temperature is described very accurately by the formula: ${({c}_{\mathrm{ii}})}_{u}={({c}_{\mathrm{ii}})}_{0}\mathrm{exp}(\ensuremath{-}{A}_{\mathrm{ii}}{F}_{\mathrm{ii}}(u))$, where $u=(\frac{T}{\ensuremath{\theta}})$, $T$ is the absolute temperature and $\ensuremath{\theta}$ the characteristic temperature, ${({c}_{\mathrm{ii}})}_{0}$ denotes the value at absolute zero, ${A}_{\mathrm{ii}}$ is a constant of the material, and ${F}_{\mathrm{ii}}(u)$ is a function of $u$ which assumes the value unity when $u=1$, and which is the same for all three substances. Experimental values of ${F}_{11}(u)$ and ${F}_{44}(u)$ are given for values of $u$ between 0.1 and 1.5. The isothermal ${c}_{12}$ does not vary with temperature, over the specified ranges, by more than the error of measurement.