Effective Characteristics of Solute Atoms in a Multicomponent Alloy

M. I. Lugovy$^{1}$, D. G. Verbylo$^{1}$, М. P. Brodnikovskyy$^{1}$, T. I. Verbytska$^{2}$, D. S. Leonov$^{3}$, M. Yu. Barabash$^{2,3,4}$

$^{1}$I. M. Frantsevych Institute for Problems in Materials Science, N.A.S. of Ukraine, 3 Omeljan Pritsak Str., UA-03142 Kyiv, Ukraine
$^{2}$National Technical University of Ukraine ‘Igor Sikorsky Kyiv Polytechnic Institute’, 37 Beresteiskyi Ave., UA-03056 Kyiv, Ukraine
$^{3}$Technical Centre, N.A.S. of Ukraine, 13 Pokrovs’ka Str., UA-04070 Kyiv, Ukraine
$^{4}$Institute for Applied Control Systems, N.A.S. of Ukraine, 42 Academician Hlushkov Ave., UA-03187 Kyiv, Ukraine

Received: 01.08.2025; final version - 08.08.2025. Download: PDF

Modified model of ‘inclusion in the matrix’ is proposed to determine the solute-atoms’ characteristics in a multicomponent alloy at different temperatures. The model allows calculating the effective diameter of dissolved atom and the effective shear modulus attributed to it for each component. This becomes possible with the correct interpretation of the input parameters for modelling, in particular, with the correct determination of the correction factors for atomic sizes, shear moduli, and Poisson’s ratios for alloy components in a certain temperature range. It depends on the type of crystal lattices of the pure components and the alloy. The same atom in crystal lattices with a different coordination numbers will exhibit a different size, and the lattice of a pure component may differ from that of an alloy. Statements about different shear moduli and Poisson’s ratios, which can be attributed to atoms in pure components and dissolved atoms in an alloy, if their crystal lattices are different, are also valid. The effective diameters and shear moduli for the dissolved atoms make it possible to determine the temperature dependence of atomic-sizes’ misfits and elastic-moduli misfits. This is enough to calculate the temperature dependence of the lattice distortion of the alloy. Using the example of CrCoNiFeMn alloy, it is shown that the distortion determined using the proposed model increases with temperature.

Key words: lattice distortion, solid solution, solute atom, inclusion, matrix, multicomponent alloy.

URL: https://mfint.imp.kiev.ua/en/abstract/v47/i08/0783.html

DOI: https://doi.org/10.15407/mfint.47.08.0783

PACS: 61.72.Bb, 61.72.J-, 62.20.de, 62.20.dj, 81.05.Zx, 81.40.Cd

Citation: M. I. Lugovy, D. G. Verbylo, М. P. Brodnikovskyy, T. I. Verbytska, D. S. Leonov, and M. Yu. Barabash, Effective Characteristics of Solute Atoms in a Multicomponent Alloy, Metallofiz. Noveishie Tekhnol., 47, No. 8: 783–798 (2025)


REFERENCES
  1. D. B. Miracle and O. N. Senkov, Acta Mater., 122: 448 (2017).
  2. E. P. George, W. A. Curtin, and C. C. Tasan, Acta Mater., 188: 435 (2020).
  3. F. R. N. Nabarro, The Physics of Metals (Ed. P. B. Hirsch) (Cambridge: Cambridge University Press: 1976), p. 152.
  4. R. Labusch, Czech. J. Phys. B, 31: 165 (1981).
  5. G. Leyson, W. Curtin, L. Hector, and C. F. Woodward, Nature Mater., 9: 750 (2010).
  6. G. P. M. Leyson, L. G. Hector, and W. A. Curtin, Acta Mater., 60: 3873 (2012).
  7. G. P. M. Leyson and W. A. Curtin, Modelling Simulation Mater. Sci. Eng., 24: 065005 (2016).
  8. C. Varvenne, A. Luque, and W. A. Curtin, Acta Mater., 118: 164 (2016).
  9. C. Varvenne, G. P. M. Leyson, M. Ghazisaeidi, and W. A Curtin, Acta Mater., 124: 660 (2017).
  10. M. Zaiser, Phil. Mag. A, 82, Iss. 15: 2869 (2002).
  11. J.-H. Zhai and M. Zaiser, Mater. Sci. Eng. A, 740–741: 285 (2019).
  12. A. V. Podolskiy, E. D. Tabachnikova, V. V. Voloschuk, V. F. Gorban, N. A. Krapivka, and S. A. Firstov, Mater. Sci. Eng. A, 710: 136 (2018).
  13. S. O. Firstov, T. G. Rogul, N. A. Krapivka, and S. I. Chugunova, Metallofiz. Noveishie Tekhnol., 40, No. 2: 219 (2018) (in Russian).
  14. S. O. Firstov and T. G. Rogul, Metallofiz. Noveishie Tekhnol., 39, No. 1: 33 (2017) (in Russian).
  15. L. A. Gypen and A. Deruyttere, J. Mater. Sci., 12: 1028 (1977).
  16. A. S. Argon, Strengthening Mechanisms in Crystal Plasticity (Oxford: Oxford University Press: 2008).
  17. U. F. Kocks, A. S. Argon, and M. F. Ashby, Prog. Mater. Sci., 19: 110 (1975).
  18. F. Otto, A. Dlouhy, C. Somsen, H. Bei, G. Eggeler, and E. P. George, Acta Mater., 61: 5743 (2013).
  19. A. Gali and E. P. George, Intermetallics, 39: 74 (2013).
  20. S. J. Sun, Y. Z. Tian, H. R. Lin, X. G. Dong, Y. H. Wang, Z. J. Wang, and Z. F. Zhang, J. Alloys Compd., 806: 992 (2019).
  21. G. Laplanche, J. Bonneville, C. Varvenne, W. A. Curtin, and E. P. George, Acta Mater., 143: 257 (2018).
  22. M. Lugovy, V. Slyunyayev, and M. Brodnikovskyy, Prog. Natural Sci.: Mater. Int., 31: 95 (2021).
  23. M. I. Lugovy, V. M. Slyunyayev, M. P. Brodnikovskyy, and S. O. Firstov, Ehlektronna Mikroskopiya i Mitsnist’ Materialiv, 23: 3 (2017) (in Ukrainian).
  24. M. I. Lugovy, V. M. Slyunyayev, and M. P. Brodnikovskyy, Ehlektronna Mikroskopiya i Mitsnist’ Materialiv, 25: 26 (2019) (in Ukrainian).
  25. M. Lugovy, D. Verbylo, and M. Brodnikovskyy, Uspikhy Materialoznavstva, No. 6: 15 (2023) (in Ukrainian).
  26. M. Lugovy, D. Verbylo, and M. Brodnikovskyy, Metallofiz. Noveishie Tekhnol., 47, No. 3: 303 (2025).
  27. M. Lugovy, D. Verbylo, and M. Brodnikovskyy, Uspikhy Materialoznavstva, No. 3: 24 (2021) (in Ukrainian).
  28. M. Lugovy, D. Verbylo, and M. Brodnikovskyy, Uspikhy Materialoznavstva, No. 4/5: 12 (2022) (in Ukrainian).
  29. M. Lugovy, D. Verbylo, and M. Brodnikovskyy, Uspikhy Materialoznavstva, No. 7: 3 (2023) (in Ukrainian).
  30. M. Lugovy, D. Verbylo, and M. Brodnikovskyy, Uspikhy Materialoznavstva, No. 2: 19 (2021) (in Ukrainian).
  31. M. Lugovy, D. Verbylo, and M. Brodnikovskyy, Uspikhy Materialoznavstva, No. 4/5: 36 (2022) (in Ukrainian).
  32. S. O. Firstov and T. G. Rogul, Metallofiz. Noveishie Tekhnol., 44, No. 1: 127 (2022) (in Ukrainian).
  33. J. D. Eshelby, Solid State Physics, 3: 79 (1956).
  34. R. L. Fleischer, Acta Metallurgica, 11: 203 (1963).
  35. I. Toda-Caraballo, Scripta Mater., 127: 113 (2017).
  36. M. Lugovy, D. Verbylo, and M. Brodnikovskyy, Uspikhy Materialoznavstva, Nos. 8/9: 13 (2024) (in Ukrainian).