Efficient Debye Function Interpolation Formulae: Sample Applications to Diamond

Abstract

The well-known classical heat capacity model developed by Debye proposed an approximate description of the temperature-dependence of heat capacities of solids in terms of a characteristic integral, the T-dependent values of which are parameterized by the Debye temperature, Θ D . However, numerous tests of this simple model have shown that within Debye’s original supposition of approximately constant, material-specific Debye temperature, it has little chance to be applicable to a larger variety of non-metals, except for a few wide-band-gap materials such as diamond or cubic boron nitride, which are characterized by an unusually low degree of phonon dispersion. In this study, we present a variety of structurally simple, unprecedented algebraic expressions for the high-temperature behavior of Debye’s conventional heat-capacity integral, which provide fine numerical descriptions of the isochoric (harmonic) heat capacity dependences parameterized by a fixed Debye temperature. The present sample application of an appropriate high-to-low temperature interpolation formula to the isobaric heat capacity data for diamond measured by Desnoyers and Morrison [17], Victor [24], and Dinsdale [25] provided a fine numerical simulation of data within a range of 200 to 600 K, involving a fixed Debye temperature of about 1855 K. Representing the monotonically increasing difference of the isobaric versus isochoric heat capacities by two associated anharmonicity coefficients, we were able to extend the accurate fit of the given heat capacity ( C p ( T ) ) data up to 5000 K. Furthermore, we have performed a high-accuracy fit of the whole C p ( T ) dataset, from approximately 20 K to 5000 K, on the basis of a previously developed hybrid model, which is based on two continuous low-T curve sections in combination with three discrete (Einstein) phonon energy peaks. The two theoretical alternative curves for the C p ( T ) dependence of diamond were found to be almost indistinguishable throughout the interval from 200 K to 5000 K.