An Easy Method for the Determination of Debye Temperature from Thermal Expansion Analyses

A combination of the early approaches of the Debye model for specific heat and the Grüneisen theory of the thermal expansion of solids is used to interpolate the thermal variation of lattice parameters. From this analysis, relevant parameters such as the Debye temperature and the value of lattice parameters extrapolated at 0 K are deduced. This method and its limitations are reported. A program has been developed which can be readily used with any computer. Practical applications are given as an illustration. The method is first applied to an ideal cubic compound Na₂Ca₃Al₂F₁₄, which we propose as a standard for thermal expansion calibrations. Then, magnetoelastic phenomena, which occur at very low temperature, are displayed in cubic rare earth garnets by comparison of experimental and extrapolated data. The model is extended to an anisotropic hexagonal system, where the values of lattice parameters extrapolated at 0 K are determined within 10^-5. Debye temperatures are estimated within a relative error of 10% and are in good agreement with those calculated from specific heat data; they prove the relevance of this easy method.