Specific Heat and Elastic Constants of Calcium Fluoride at Low Temperatures

Measurements of specific heat from 3.5°K and of elastic constants from 4°K to 300°K have been made on single crystals of calcium fluoride. The Debye theta at 0°K, ${\theta }_0$, as calculated from the specific heat data is 508±5°K. Values of the elastic constants at 4.2°K are $c_{11}=17.4\mathrm{}$, $c_{12}=5.6\mathrm{}$, and $c_{44}=3.593\mathrm{}$ in units of ${10}^{11}$ dynes/${\mathrm{cm}}^2$. ${\theta }_0$ calculated from elastic constants is 513.6±2.5°K. The two ${\theta }_0\text{'}\mathrm{s}$ are now in good agreement and are significantly greater than the value calculated from previous specific heat work.