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Quantitative description of phase transitions in binary mixtures via Mayer’s cluster expansion

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  • Ushcats, M.V.
  • Ushcats, S.Yu.
  • Kondratieva, A.A.
  • Koval, S.S.

Abstract

For lattice models of binary mixtures (alloys, solutions) on the one side and models of lattice gases on the other side, the formal relationship among their basic thermodynamic parameters is derived without the simplification of nearest-neighbor interactions: in fact, the models may include arbitrary pair-wise interaction potentials (even anisotropic ones) independent for all pair combinations of the mixture components. With regard for the previously established similar relationship between the Ising problem and lattice-gas models, the long-standing conventional term “Nearest-neighbor Lattice Statistics” may now be essentially generalized to the “Lattice Statistics” one. Based on the mentioned relationship, Mayer’s cluster expansion is reformulated as an approach to describe quantitatively the behavior of binary mixtures in general and possible phase-transitions (spinodal decomposition) in particular. The computations by using a modern technique of approximating the high-order cluster integrals demonstrate the high accuracy of such cluster-based approach for a wide range of mixture models (including the “long-range interaction” model, where each particle can interact to others in two coordination spheres with various intensity) especially at values of temperature below 0.9 of critical one. In addition, some quantitative universality of the subcritical behavior is established for all the considered models at the same values of “reduced temperature”.

Suggested Citation

  • Ushcats, M.V. & Ushcats, S.Yu. & Kondratieva, A.A. & Koval, S.S., 2024. "Quantitative description of phase transitions in binary mixtures via Mayer’s cluster expansion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 649(C).
    • Handle: RePEc:eee:phsmap:v:649:y:2024:i:c:s0378437124004667
    DOI: 10.1016/j.physa.2024.129957
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    References listed on IDEAS

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    1. Bannur, Vishnu M., 2015. "Virial expansion and condensation with a new generating function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 675-680.
    2. Nightingale, M.P. & Blöte, H.W.J., 1998. "Universal Ising dynamics in two dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 251(1), pages 211-223.
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