COMPREHENSIVE STATISTICAL-VARIATIONAL CALCULATION OF THERMODYNAMIC AND STRUCTURAL CHARACTERISTICS OF HETEROGENEOUS SYSTEM «CRYSTALLINE NANOPARTICLE – HOMOGENEOUS GASEOUS ENVIPONMENT»

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

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

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

DOI: https://doi.org/10.52065/2520-6141-2021-248-2-33-40

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., Kulesh A. A., Rogach A. A. Comprehensive statisticalvariational calculation of thermodynamic and structural characteristics of heterogeneous system «crystalline nanoparticle – homogeneous gaseous enviponment». Proceedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2021, no. 2 (248), pp. 33–40 (In Russian). DOI: https://doi.org/10.52065/2520-6141-2021-248-2-33-40.

Abstract

In this paper we used the procedure developed before for solution of system of statistical equations, and formula, determining structural and thermodynamic characteristics of inhomogeneous molecular systems. These equations were derived within two-level statistical approach, based on Bogolubov – Born – Green – Kirkwood – Ivon correlation function method (BBGKI), Rott condition correlative function method and thermodynamic density functionals method.

The used closed system of integral establishes connection between microscopic system parameters of interacting particles (atoms or molecules) and macroscopic characteristics of crystalline nanoparticles in equilibrium with a gaseous environment, i.e., in a heterogeneous crystal – gas system at a temperature below the triple temperature point. When solving this system, the radial density profile in the interphase region is approximated using a function containing three parameters and a hyperbolic tangent. One of the parameters is found from the condition of equilibrium of a liquid or gaseous medium with the investigated crystalline spherical nanoparticle, and the other two are variation parameters while solving the variational problem of finding the minimum of the large thermodynamic potential of a heterogeneous system.

The article implements a method for the variational calculation of the density profile in the vicinity of a spherical crystalline nanoparticle in equilibrium with a gaseous medium at a temperature below the triple point, and also establishes a correlation between the structure and thermodynamic characteristics of crystalline nanoparticles, taking into account the spatial relaxation of the lattice at their boundary with the

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14.04.2021