Specific Heat and Elastic Constants of Calcium Fluoride at Low Temperatures

Abstract

Measurements of specific heat from 3.5\ifmmode^\circ\else\textdegree\fi{}K and of elastic constants from 4\ifmmode^\circ\else\textdegree\fi{}K to 300\ifmmode^\circ\else\textdegree\fi{}K have been made on single crystals of calcium fluoride. The Debye theta at 0\ifmmode^\circ\else\textdegree\fi{}K, ${\ensuremath{\theta}}_{0}$, as calculated from the specific heat data is 508\ifmmode\pm\else\textpm\fi{}5\ifmmode^\circ\else\textdegree\fi{}K. Values of the elastic constants at 4.2\ifmmode^\circ\else\textdegree\fi{}K are ${c}_{11}=17.4$, ${c}_{12}=5.6$, and ${c}_{44}=3.593$ in units of ${10}^{11}$ dynes/${\mathrm{cm}}^{2}$. ${\ensuremath{\theta}}_{0}$ calculated from elastic constants is 513.6\ifmmode\pm\else\textpm\fi{}2.5\ifmmode^\circ\else\textdegree\fi{}K. The two ${\ensuremath{\theta}}_{0}'\mathrm{s}$ are now in good agreement and are significantly greater than the value calculated from previous specific heat work.