Elastic Constants of the Alkali Halides at 4.2°K

Adiabatic elastic constants of LiCl, NaF, NaCl, NaBr, KF, RbCl, RbBr, and RbI were measured at 4.2 and 300°K, using the ultrasonic pulse-echo technique. Data are also given for several of these materials, for the temperature interval 4.2 to 300°K. It is observed that the elastic anisotropy factor, $A=\frac{2c_{44}}{(c_{11}-c_{12})}$, 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 $T=0\mathrm{}°$K. The Cauchy relation ($c_{12}=c_{44}$) is not satisfied at 4.2°K for any of the materials studied. The degree of failure of the Cauchy relation ($\Delta =c_{12}-c_{44}$) is larger at 4.2°K than at room temperature for the Li and Na halides but is smaller for the K and Rb halides. Also calculated was the $T=0\mathrm{}°$K value ${{\Theta }_0}^{\mathrm{el}}$ of the Debye characteristic temperature from the 4.2°K elastic-constant data, using the tables given by de Launay. The values of ${{\Theta }_0}^{\mathrm{el}}$ in °K are: LiCl (429±2.2), NaF(491.5±2.4), NaCl(321.2±1.6), NaBr(224.6±1.2), KF(335.9±1.7), RbCl(168.9±0.85), RbBr(136.5±0.7), and RbI(108.0±0.55). Comparison with ${{\Theta }_0}^c$ 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 ${{\Theta }_0}^{\mathrm{el}}$ being larger than ${{\Theta }_0}^c$ 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.