Thermodynamic Modeling of the Phase Diagram for Cu2SnS3-Cu2SnSe3 System

  • A. N. Mammadov
  • I. Dz. Alverdiev
  • Z. S. AlievEmail author
  • D. B. Tagiev
  • M. B. Babanly
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1095)


The phase diagram of the Cu2SnS3-Cu2SnSe3 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 (Cu2SnS3)1-x(Cu2SnSe3)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 Cu2SnS3 and Cu2SnSe3 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.


Phase diagrams Cu2SnS3-Cu2SnSe3 system Thermodynamic modeling Multipurpose genetic algorithm 



This work was performed in the frame of a scientific program of the international laboratory between the Institute of Catalysis and Inorganic Chemistry of the National Academy of Sciences of Azerbaijan (Azerbaijan) and Centro de Fısica de Materials at Donostia (Spain).


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • A. N. Mammadov
    • 1
    • 2
  • I. Dz. Alverdiev
    • 3
  • Z. S. Aliev
    • 4
    Email author
  • D. B. Tagiev
    • 1
  • M. B. Babanly
    • 1
  1. 1.Nagiyev Institute of Catalysis and Inorganic Chemistry of ANASBakuAzerbaijan
  2. 2.Azerbaijan Technical UniversityBakuAzerbaijan
  3. 3.Ganja State UniversityGanjaAzerbaijan
  4. 4.Azerbaijan State Oil and Industrial UniversityBakuAzerbaijan

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