VERIFICATION OF THE CONVERGENCE OF THE ITERATIVE SOLUTION PROCEDURE OF SYSTEM OF INTEGRAL EQUATIONS FOR HETEROGENEOUS SYSTEM «CRYSTALLINE NANOPARTICLE – GASEOUS ENVIRONMENT»

UDC 531.19; 538.911

  • Narkevich Ivan Ivanovich – DSc (Physics and Mathematics), Professor, Professor, the Department of Physics. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: narkevich@belstu.by

  • Farafontova Elena Valer’yevna – PhD (Physics and Mathematics), Assistant Professor, the Department of Physics. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: farafontova@belstu.by

  • Rogach Alesya Aleksandrovna – student. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus).

  • Kulesh Aleksey Aleksandrovich – student. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus).

DOI: https://doi.org/10.52065/2520-6141-2021-248-2-41-46

Key words: two-level statistical method, variation method, potential of average forces, heterogeneous system, nanoparticle, density field.

For citation: Narkevich I. I., Farafontova E. V., Rogach A. A., Kulesh A. A. Verification of the convergence of the iterative solution procedure of system of integral equations for heterogeneous system «crystalline nanoparticle – gaseous environment». Proceedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2021, no. 2 (248), pp. 41–46 (In Russian). DOI: https://doi.org/10.52065/2520-6141-2021-248-2-41-46.

Abstract

The paper uses a closed system of statistical equations and formulas that determines the structural and thermodynamic characteristics of ununiform (heterogeneous) molecular systems. It has been obtained using the two-level statistical method, which is a symbiosis of the Bogolyubov – Born – Green – Kirkwood – Ivon (BBGKI) method of correlation, the Rott conditional distribution method, and the density thermodynamic functionals method.

The density field in heterogeneous system with nanoparticles is defined with field of filling numbers, belonging to coordination spheres of FCC-lattice being used for characterization the structure of nanoparticle and its surrounding gaseous environment. For numerical derivation of nanoparticle density field profile taking into account the relaxation of FCC-lattice parameters of its boundary, the computer program, developed before on base of MathCad computer-aided design system, has been modified. Using variationstatistical method, with this program was calculated the density field profile at temperature θ = 0,6, which is the equilibrium point with gaseous environment below triple point. The convergence of the numerical process of solving a complete closed-loop system of integral equations by the iterative method was investigated.

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References

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14.04.2021