Elastic Constants of the Alkali Halides at 4.2°K

Abstract

Adiabatic elastic constants of LiCl, NaF, NaCl, NaBr, KF, RbCl, RbBr, and RbI were measured at 4.2 and 300\ifmmode^\circ\else\textdegree\fi{}K, using the ultrasonic pulse-echo technique. Data are also given for several of these materials, for the temperature interval 4.2 to 300\ifmmode^\circ\else\textdegree\fi{}K. It is observed that the elastic anisotropy factor, $A=\frac{2{c}_{44}}{({c}_{11}\ensuremath{-}{c}_{12})}$, increases with temperature. This results in the Li halides becoming less anisotropic and the Na, K, and Rb halides becoming more anisotropic as the temperature decreases toward $T=0\ifmmode^\circ\else\textdegree\fi{}$K. The Cauchy relation (${c}_{12}={c}_{44}$) is not satisfied at 4.2\ifmmode^\circ\else\textdegree\fi{}K for any of the materials studied. The degree of failure of the Cauchy relation ($\ensuremath{\Delta}={c}_{12}\ensuremath{-}{c}_{44}$) is larger at 4.2\ifmmode^\circ\else\textdegree\fi{}K than at room temperature for the Li and Na halides but is smaller for the K and Rb halides. Also calculated was the $T=0\ifmmode^\circ\else\textdegree\fi{}$K value ${{\ensuremath{\Theta}}_{0}}^{\mathrm{el}}$ of the Debye characteristic temperature from the 4.2\ifmmode^\circ\else\textdegree\fi{}K elastic-constant data, using the tables given by de Launay. The values of ${{\ensuremath{\Theta}}_{0}}^{\mathrm{el}}$ in \ifmmode^\circ\else\textdegree\fi{}K are: LiCl (429\ifmmode\pm\else\textpm\fi{}2.2), NaF(491.5\ifmmode\pm\else\textpm\fi{}2.4), NaCl(321.2\ifmmode\pm\else\textpm\fi{}1.6), NaBr(224.6\ifmmode\pm\else\textpm\fi{}1.2), KF(335.9\ifmmode\pm\else\textpm\fi{}1.7), RbCl(168.9\ifmmode\pm\else\textpm\fi{}0.85), RbBr(136.5\ifmmode\pm\else\textpm\fi{}0.7), and RbI(108.0\ifmmode\pm\else\textpm\fi{}0.55). Comparison with ${{\ensuremath{\Theta}}_{0}}^{c}$ the Debye characteristic temperature derived from low-temperature specific-heat data, shows the two to be equal within experimental error in almost all cases. However, there is some indication of a trend toward ${{\ensuremath{\Theta}}_{0}}^{\mathrm{el}}$ being larger than ${{\ensuremath{\Theta}}_{0}}^{c}$ by an amount on the order of 1 to 3%. Whether this trend is real or the result of some systematic error in the experiments or analysis is not known at this time.