Elastic Constants of Barium Fluoride Between 4.2 and 300°K

Abstract

The elastic constants of single-crystal barium fluoride have been determined in the 4.2-300\ifmmode^\circ\else\textdegree\fi{}K temperature range, by an ultrasonic pulse-echo technique. The values of the elastic constants, extrapolated to 0\ifmmode^\circ\else\textdegree\fi{}K, in units of ${10}^{11}$ dyn/${\mathrm{cm}}^{2}$, are: ${c}_{11}=9.810$, ${c}_{12}=4.481$, and ${c}_{44}=2.544$. The constants ${c}_{11}$, and ${c}_{12}$ change by about 10%, while ${c}_{44}$ hardly changes over the above temperature range. Barium fluoride is found to be mechanically isotropic, the value of the anisotropy factor $2{c}_{44}{({c}_{11}\ensuremath{-}{c}_{12})}^{\ensuremath{-}1}$ being close to unity between 4.2 and 300\ifmmode^\circ\else\textdegree\fi{}K. A value of 282\ifmmode^\circ\else\textdegree\fi{}K for the Debye temperature at 0\ifmmode^\circ\else\textdegree\fi{}K is computed from the elastic constants. The values of the elastic constants are deduced theoretically from a rigid-ion model, and the results compared with the experimental data.