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Abstract

An accurate non-integral approximation of the Debye model of heat capacity has been developed. The approximation is based on segmentation in temperature and the linear combination of the Einstein function [1]. The method gives an accurate description of the Debye function and has been validated from a mathematical and physical point of view. The method is applied to the experimentally determined heat capacity data of pure Al, Cr, Fe, Ge, Ir, Mo, Nb, Ta, W and Ni. The proposed non-integral solution is accurate for the entire temperature range and can be easily integrated into the TDB format of thermodynamic databases. An example of thermodynamic calculation performed in the pycalphad open-source software [2] using the newly proposed approximation of the Debye model will be demonstrated. [1] I. Roslyakova, B. Sundman, H. Dette, L. Zhang, and I. Steinbach. Modeling of Gibbs energies of pure elements down to 0K using segmented regression. Calphad, 55, Part 2:165- 180, 2016 [2] R. Otis, Z.-K. Liu, pycalphad: Calphad-based computational thermodynamics in python, Journal of Open Research Software 5 (1).