Description of the heat capacity of solid phases by a multiparameter family of functions

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The functions Cp and Cv using both the Debye model and the Maier-Kelley equation are proposed to describe the heat capacity of substance in solid state for the first time. They give the possibility to calculate the heat capacity values equal to the experimental data within the range of the deviation. The solution to the problem was reduced to finding the minimum of the objective function of 8 independent adjustable parameters of the form:σ2(T0, a, b,A1,Θ1,A2,Θ2, A3,Θ3)=∑i=1n(Cp,calc−Cp,exp)2/nThe search for the minimum of σ2 was found by three methods: the golden ratio, conjugate gradient and coordinate descent. The literature data on the heat capacities of the АIIIВV, АIIВVI, and IV group of elements (C, Si, Ge, Sn) were used as the object of testing the model. It was found that the phases with the same sum of the atomic number of elements (Z), such as diamond and B0.5 N0.5 (cub) (Z = 6); pure silicon (Si) and Al0.5 P0.5 (Z = 14); pure germanium (Ge) and Ga0.5 As0.5 (Z = 32)); pure grey tin (α-Sn) and In0.5 Sb0.5, and Cd0.5 Te0.5 (Z = 50) have the same heat capacity experimental values in the solid state. The proposed models can be used in both different binary and multicomponent phases. The method helps standardize the physicochemical constants and can be used for different applied purposes.