Determination of heat capacity of pure metals, compounds and alloys by analytical and numerical methods

Abstract

Phase diagrams are normally calculated from a combination of physical equations and experimental parameters. Gibbs free energy of mixing; thermodynamics activity and enthalpy of mixing; transformation temperatures and the concentration range of the alloys components are calculated to permit an alloy system database to be constructed. The molar specific heat capacity (cv) is normally obtained by numerical derivative of the enthalpy equation with respect to temperature and concentration. The experimental determinations of the topological parameters as a function of concentration and temperature is an enormous task. On the other hand, physical formulations such as Einstein’s and Debye’s equations are physically consistent models for the molar specific heat capacity of the solid, and they depend only on a set of basic physical parameters. Einstein’s formulation works very well for temperatures T > 102 K, however, as it varies in the form of 1/T2, it fails to conform to lower temperature experimental data. Debye assumed only three branches of the vibrational spectrum with the same linear dispersion relation, and derived an equation also consistent for lower temperatures, and as the temperature decreases to absolute zero, it varies as a function of 1/T3 thus permitting experimental scatters to be fitted. Another way for calculating cv is by carrying out polynomial functions [1], which are only recommended for temperatures above 298.15 K, because bellow this temperature, cv is strongly dependent on the quantization of thermal energy, which can be stored in different forms in the material, such as electronic, magnetic, vibrational, rotational and translational energies. In this paper corrections for Debye’s and Einstein’s equations for cv are derived to encompass its thermal history dependence, electronic and rotational energies for both lower and higher temperatures in order to permit the calculation of the molar specific heat capacity of pure metals, phases and single-phase alloys.