ANALYTICAL APPROXIMATIONS FOR ESTIMATING THE FREE ENERGY OF A LATTICE FLUID ON A TWO-LEVEL NON-RECTANGULAR LATTICE

UDC 531.19

  • Groda Yaroslav Gennad’yevich − PhD (Physics and Mathematics), Associate Professor, Assistant Professor, the Department of Mechanics and Engineering. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail:groda@belstu.by

  • Groda Nadezhda Georgievna – Head of the Laboratory of the Department of Physics. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: gng@tut.by

  • Bildanau Eldar Emiravich – Master of Engineering, Assistant, the Department of Mechanics and Engineering. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: eldar.bildanov@gmail.com

DOI: https://doi.org/10.52065/2520-6141-2022-254-1-19-27

Key words: two-level lattice, quasi-chemical approximation, diagram approximation, phase diagram, Monte Carlo simulation.

For citation: Groda Ya. G., Groda N. G., Bildanau E. E. Analytical approximations for estimating the free energy of a lattice fluid on a two-level non-rectangular lattice. Proceedings of BSTU, issue, Physics and Mathematics. Informatics, 2022, no. 1 (254), pp. 19–27 (In Russian). DOI: https://doi.org/10.52065/2520-6141-2022-254-1-19-27.

Abstract

On the basis of the crystal close-packed plane triangular lattice, the model of a two-level lattice system with energetically non-equivalent sites corresponding to potential wells of two types, differing in depth and forming a plane periodic structure, is proposed. For an analytical description of the studied lattice system, it is proposed to divide it into the system of two plane triangular lattices containing energetically equivalent lattice sites and differing both in the distance between the nearest nodes in the sub-lattice and in the total number of sites on it. For the lattice fluid with interaction of the nearest neighbors on the proposed two-level lattice, quasi-chemical and diagram analytical approximations are developed to estimate the free energy of the system. An algorithm for modeling the equilibrium properties of the lattice fluid on the two-level lattice using the Monte Carlo method is proposed, based on the transformation of the original two-level lattice by adding shadow lattice sites to it and transforming it into a square lattice. The phase diagrams of the model with attraction and repulsion of the nearest neighbors are constructed. The results of analytical calculations are compared with simulation data. It has been established that, in contrast to a system with energetically equivalent nodes, a first-order phase transition takes place in a lattice fluid with repulsion of the nearest ones on a two-level lattice.

Download

References

  1. Stromme M. Li insertion into WO3: introduction of a new electrochemical analysis method and comparison with impedance spectroscopy and the galvanostatic intermittent titration technique. Solid State Ionics, 2000, vol. 131, pp. 261–273.
  2. Vakarin E. V., Holovko M. F. Adsorption of HCl on ice. Effects of the surface heterogeneity. Chem. Phys. Lett., 2001, vol. 349, pp. 13–18.
  3. Bisquert J., Vikhrenko V.S. Analysis of the kinetics of ion intercalation. Two state model describing the coupling of solid state ion diffusion and ion binding processes. Electrochim. Acta, 2002, vol. 47, pp. 3977–3988.
  4. Levi M. D., Wang C., Aurbach D., Chvoj Z. Effect of temperature on the kinetics and thermodynamics of electrochemical insertion of Li-ions into a graphite electrode. J. Electroanal. Chem, 2004, vol. 562, pp. 187–203.
  5. Garcia-Belmonte G., Vikhrenko V., Garcia-Canadas J. Bisquert Interpretation of variations of jump diffusion coefficient of lithium intercalated into amorphous WO3 electrochromic films. Solid State Ionics, 2004, vol. 170, pp. 123–127.
  6. Vorotyntsev M. A., Badiali J. P. Short-range electron-ion interaction effects in charging the electroactive polymer films. Electrochim. Acta, 1994, vol. 39, pp. 289–306.
  7. Chvoj Z., Conrad H., Chab V. Thermodynamics of adatoms diffusing on a surface with two different sites: a new type of phase transition. Surf. Sci., 1997, vol. 376, pp. 205–218.
  8. Chvoj Z., Conrad H., Chab V. Analysis of the Arrhenius shape of adatom diffusion coefficient in surface model with two energy barriers. Surf. Sci., 1999, vol. 442, pp. 455–462.
  9. Masin M., Chvoj Z., Conrad H. Diffusion on a face-centered cubic (111) surface in the presence of two non-equivalent adsorption sites. Surf. Sci., 2000, vol. 457, pp. 185–198.
  10. Tarasenko A. A., Chvoj Z., Jastrabik L., Nieto F., Uebing C. Thermodynamic properties of a system of interacting particles adsorbed on a lattice with two nonequivalent sites. Phys. Rev. B, 2001, vol. 63, art. no. 165423 (11 p.).
  11. Tarasenko A. A., Chvoj Z., Jastrabik L., Nieto F., Uebing C. Phase diagram of a system of particles adsorbed on a lattice with two non-equivalent sites: repulsive interaction. Surf. Sci., 2001, vol. 482–485, pp. 396–401.
  12. Tarasenko A. A., Jastrabik L. Surface diffusion of particles adsorbed on a lattice with two non-equivalent sites. Surf. Sci., 2002, vol. 507–510, pp. 108–113.
  13. Nieto F., Tarasenko A. A., Uebing C. Criticality effects on diffusion on heterogeneous surfaces. Appl. Surf. Sci., 2002, vol. 196, pp. 181–190.
  14. Tarasenko A. A., Jastrabik L., Muller T. Surface diffusion of particles adsorbed on an inhomogeneous lattice with two non-equivalent sites. Surf. Sci., 2007, vol. 601, pp. 4001–4004.
  15. Tarasenko A. A., Jastrabik L. Diffusion of particles on an inhomogeneous disordered square lattice with two non-equivalent sites. Surf. Sci., 2008, vol. 602 pp. 2975–2982.
  16. Tarasenko A. A., Jastrabik L. Diffusion of particles over triangular inhomogeneous lattice with two non-equivalent sites. Physica A, 2009, vol. 388, pp. 2109–2121.
  17. Tarasenko A. A., Jastrabik L. Diffusion in heterogeneous lattices. Appl. Surf. Sci., 2010, vol. 256, pp. 5137–5144.
  18. Tarasenko A. A., Jastrabik L. The studies of particle diffusion on a heterogeneous one-dimensional lattice. Surf. Sci., 2015, vol. 641, pp. 266–268.
  19. Tarasenko A. A., Bohac P., Jastrabik L. Migration of particles on heterogeneous bivariate lattices: The universal analytical expressions for the diffusion coefficients. Physica E, 2015, vol. 74, pp. 556–560.
  20. Groda Y. G., Lasovsky R. N., Vikhrenko V. S. Equilibrium and diffusion properties of two-level lattice systems: Quasi-chemical and diagrammatic approximation versus Monte Carlo simulation results. Solid State Ionics, 2005, vol. 176, pp. 1675–1680.
  21. Vikhrenko V. S., Groda Ya. G., Bokun G. S. Ravnovesnyye i diffuzionnyye kharakteristiki interkalyatsionnykh sistem na osnove reshetochnykh modeley [Equilibrium and diffusion characteristics of the intercalation systems on the basic of the lattice models]. Minsk, BGTU Publ., 2008. 326 p. (In Russian).
  22. Metropolis N., Rosenbluth A. W., Rosenbluth M. N., Teller A. H. Equation of state calculation by fast computing machines. J. Chem. Phys., 1953, vol. 21, no. 6, pp. 1087–1092.
  23. Bokun G. S., Groda Ya. G., Belov V. V., Uebing C., Vikhrenko V. S. The self-consistent diagram approximation for lattice systems. EPJ B, 2000, vol. 15, pp. 297–304.
  24. Groda Ya. G., Argyrakis P., Bokun G. S., Vikhrenko V. S. SCDA for 3D lattice gases with repulsive interaction. EPJ B, 2003, vol. 32, pp. 527–535.
  25. Vikhrenko V. S., Groda Ya. G., Bokun G. S. The diagram approximation for lattice systems. Phys. Lett. A, 2001, vol. 286, pp. 127–133.
21.01.2022