Lattice Dynamics of Calcium Fluoride: Part Ii. Thermal Expansion of Calcium Fluoride

With the model which explained the specific heat, the thermal expansion of calcium fluoride is calculated. Using the data on the temperature variation of the Raman line and the elastic constant C 44 , the Gruneisen parameter γ i = −∂log ω j /∂log V is calculated as a function of ω for the optical and acoustic branches along [100], [111], and [110] directions. The thermal expansion coefficient is evaluated using Houston's method. The calculated values are in good agreement with the measured values of Valentiner and Wallott. Calculations reveal that γ 0 = βV/χC v will increase with decreasing temperature, the rise starting in the liquid hydrogen region of temperature. The thermal expansion of this crystal can be measured up to liquid helium temperature to verify the result of these calculations.