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

Abstract

A combination of the early approaches of the Debye model for specific heat and the Gr0neisen 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 Na2Ca3AI2F14, 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.

Negative thermal expansion materials: technological key for control of thermal expansion

“…It is also useful for estimating the ideal phononic contribution to thermal expansion in a magnetic metal (see section 3.3). Functions approximating the integral in equation (4) for the convenience of analyses are available in the literature [8].…”

Thermal expansion of monogermanides of 3d-metals

“…Unit cell dimensions as a function of temperature have been parametrised with the Debye-Grüneisen equation, see e.g. [26,27]. The derived parameters are the following, a 0 is the unit cell dimension approximated to 0 K, Θ D is the Debye temperature, α is the high temperature asymptote of thermal expansion coefficient.…”

Low-temperature x-ray crystal structure analysis of the cage-structured compounds MBe13(M=La,Sm,and U)

“…To estimate a Debye temperature θ D , the a(T ) curves were analyzed using the Debye-Grüneisen approximation [31] described by…”