Thermodynamic Modeling of the Phase Diagram for Cu2SnS_3-Cu_2SnSe3 System

摘要

The phase diagram of the Cu2SnS_3-Cu2SnSe_3 system was plotted by thermodynamic calculations. Experimental data from differential thermal (DTA) and X-ray diffraction (XRD) analyses have used for the calculation. From the fundamental principles of thermodynamics for heterogeneous equilibria, new equations have been obtained for the direct calculation of the coordinates for (Cu_2SnS_3)_(1-x)(Cu_2SnSe_3)_x liquid and solid solutions. The parameters of the analytical dependencies of the Gibbs free energy within the asymmetric version of the model of regular solutions were determined by means the multipurpose genetic algorithm (MGA), whereas the boundaries of solid solutions are determined based on Gibbs function for the internal stability. Analytical dependencies between the variables and formation thermodynamic functions for the compounds allowed us to estimate the sensitivity of the calculated data with the input data. It was established that, the coordinates of the liquidus and solidus curves are insensitive to formation enthalpy of the Cu_2SnS_3 and Cu_2SnSe_3 compounds. At the same time, a high sensitivity of the liquidus and solidus coordinates to the excess free energy values of solutions was observed. A 3D model of the Gibbs energy dependences on compositions and temperatures was visualized.