ИСТИНА

Multiple Einstein functions (MEF) allow standard thermodynamic functions to be approximated with an accuracy corresponding to experimental measurements from 0 K up to the melting point. Critical review of available data for solid and liquid phases of Sn, Si and Ge were performed. Adiabatic calorimetry and enthalpy increment measurements for solids were fitting simultaneously with CpFit program. As a result, a set of self consistent thermodynamic properties of pure solid elements were obtained. One of interesting and useful result of MEF applying is a possibility to estimate the entropy and enthalpy of transition at temperature of reversible phase transformation α-Sn and β-Sn (the transformation from the white tin to grey tin is very difficult). Result of reassessment for α-tin (grey) and β-tin (white) were compared with ab initio calculations of Cp performed within the framework of density functional theory using the Vienna ab-initio simulation package VASP code. The good agreement of ab-initio calculations and estimation carried out based on the Voronin and Kutsenok method (Multiple Einstein functions (MEF)) is obtained. The possibility to describe Cp(T) in premelting area and after melting point with multiple Einstein functions and additional term was investigated. It was shown that in some cases it’s possible to describe available data within the experimental error and to predict a correct limited behavior of thermodynamic functions.