Temperature Dependence of the Debye Temperatures for the Thermodynamic Functions of Alkali Halide Crystals

The temperature dependence at constant volume of the experimental Debye temperatures for the entropy, the thermal energy, and the heat capacity at constant volume of potassium chloride, bromide and iodide, and of sodium iodide is analyzed over a wide range of temperature ($30°\mathrm{K}\lesssim T\lesssim 270°\mathrm{K}$) taking into account anharmonic effects. The inclusion of the leading anharmonic contribution into the quasiharmonic expansions of the Debye temperatures for the three thermodynamic functions allows one to reproduce over the entire temperature range the curves for the entropy, which are the most accurate, and also those for the thermal energy. The curves for the heat capacity are reproduced at the lower temperatures, and their proper course is indicated at the higher temperatures, where they are affected by sizeable uncertainties. The different form of the temperature dependence of the Debye temperatures for the three functions in the quasiharmonic temperature range, and the different magnitude of the effect of the anharmonic contributions on the Debye temperatures for the three functions at high temperature, are clearly illustrated. Refined values are obtained in each salt for the geometric mean of the vibrational frequencies and for the first few moments of the vibrational spectrum. The good agreement between the values of the moments derived from the three functions confirms the good validity of the quasiharmonic description of the thermal free energy at the lower temperatures. Values are obtained for the anharmonic contributions to the thermodynamic functions at high temperature.