Fractal properties of the Nd100–xFex alloys surface in the fractal thermodynamics model

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Abstract

The study of the fractal properties of the surface of Nd100–xFex alloys in a wide range of concentrations х (х = 20–90) was carried out in the framework of the fractal thermodynamics model. To this end, we performed an analysis of images obtained by (scanning electron?) microscopy of the surfaces of a series of Nd100–xFex alloys synthesized by induction melting. A high degree of proximity of the surface structure of all the studied samples, both before and after etching, to fractals is shown. The values of the parameter δ characterizing the relative deviation of the studied samples from the fractal are in the range of 0.017–0.029. Three-dimensional diagrams of the fractal parameters Sf , Tf , Ef , x and two-dimensional diagrams of the same parameters: Sf , Tf , Ef , x, reflecting the nature of the state of the surfaces of Nd100–xFex alloy samples before and after etching, are constructed. For all investigated samples of alloys, the values of the parameters of the fractal equations of state arecalculated. The correlation of the maximum value of the coercive force Hc = 4.8 kE with the values of fractal entropy Sf = 39.86, fractal temperature Tf = 529, and fractal dimension D = 2.6530 of the Nd100–xFex alloys at x = 20 has been established.

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About the authors

S. A. Mikheev

Tver State University

Email: mancu@mail.ru
Russian Federation, 170100, Tver

E. M. Semenova

Tver State University

Email: mancu@mail.ru
Russian Federation, 170100, Tver

Yu. G. Pastushenkov

Tver State University

Email: mancu@mail.ru
Russian Federation, 170100, Tver

V. P. Tsvetkov

Tver State University

Email: mancu@mail.ru
Russian Federation, 170100, Tver

I. V. Tsvetkov

Tver State University

Author for correspondence.
Email: mancu@mail.ru
Russian Federation, 170100, Tver

References

  1. Llamazares S., Calderon F., Bolzoni F., Leccabue F., Hua X.R., Nozieres J.P. // J. Magn. Magn. Mat. 1990. V. 86. P. 307.
  2. Karpenkov A.Y., Skokov K.P., Dunaeva G.G., Semeno-va E.M., Lyakhova M.B., Pastushenkov Yu.G. // J. Phys. D: Appl. Phys. 2022. V. 55. Iss. 45. P. 455002. https://doi.org/10.1088/1361-6463/ac90d2
  3. Zhdanova O.V., Lyakhova M.B., Pastushenkov Yu.G. // Phys. Metals Metallography. 2011. V. 112. Iss. 3. P. 224. https://doi.org/10.1134/S0031918X11030306
  4. Van Ende M.A., Jung I.H. // J. Alloys Compd. 2013. V. 548. P. 133. https://doi.org/10.1016/j.jallcom.2012.08.127
  5. Menushenkov V.P., Andersen S.J., Hoeier R. Electron-microscopy investigations of microstructure in Fe-Nd alloys // Magnetic Anisotropy and Coercivity in Rare-Earth Transition Metal Alloys. Proceedings. P. 97.
  6. Landgraf F.J.G., Schneider G.S., Villas-Boas V., Missell F.P. // J. Less Common Metals. 1990. V. 163. Iss. 1. P. 209. https://doi.org/10.1016/0022-5088(90)90101-O
  7. Kim D.-H., Cho Y.-Ch., Choe S.-B., Shin S.-Ch. // Appl. Phys. Lett. 2003. V. 82. P. 3698.
  8. Bathany C., Romancer M.L., Armstrong J.N., Chop- ra H.D. // Phys. Rev. B. 2010. V. 82. P. 184411. https://doi.org/10.1103/PhysRevB.82.184411
  9. Catalan G., Béa H., Fusil S., Bibes M., Paruch P., Barthélémy A., Scott J.F. // Phys. Rev. Lett. 2008. V. 100. P. 027602. https://doi.org/10.1103/PhysRevLett.100.027602
  10. Картузов В.В., Дмитришина Я.Ю. // Электронная обработка материалов. 2015. Т. 51. № 2. С. 31.
  11. Bucher J.P. // European J. Phys. 1991. V. 12. № 3.
  12. Lisovskii F.V., Lukashenko L.I., Mansvetova E.G. // JETP Lett. 2004. V. 79. P. 352. https://doi.org/10.1134/1.1765181
  13. Семенова Е.М., Иванов Д.В., Ляхова М.Б. и др. // Известия РАН: Сер. Физ. 2021. Т. 85. № 9. С. 1245.
  14. Mikheev S.A., Paramonova E.K., Tsvetkov V.P., Tsvet kov I.V. // Russ. J. Mathematical Phys. 2021. V. 28. P. 251.
  15. Tsvetkov V.P., Mikheyev S.A., Tsvetkov I.V. // Chaos, Solitons & Fractals. 2018. V.108. P. 71.
  16. Paramonova E., Kudinov A., Mikheev S., Tsvetkov V., Tsvetkov I. Fractal thermodynamics, big data and its 3D visualization // CEUR Workshop Proc. 2021. V. 3041. P. 38.
  17. Tsvetkov V.P., Mikheev S.A., Tsvetkov I.V., Derbov V.L., Gusev A.A., Vinitsky S.I. // Chaos, Solitons & Fractals. 2022. V. 161. P. 112301.
  18. Мейсурова А.Ф., Цветков В.П., Цветков И.В., Нотов А.А. // Вестник Тверского государственного университета. Серия: Биология и экология. 2022. № 1. Вып. 65. С. 180.
  19. Maslov V.P. // J. Math. Phys. 2016. V. 23. Iss. 2. P. 278.
  20. Gwyddion – Free SPM (AFM, SNOM/NSOM, STM, MFM) data analysis software (2021) Department of Nanometrology, Czech Metrology Institute. http://gwyddion.net
  21. Maple: эффективный инструмент для решения математических задач (2023) Waterloo Maple Inc., Canada. https://www.maplesoft.com/demo/streaming/Maple 15Russian.aspx

Supplementary files

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2. Fig. 1. Sample Nd10Fe90 before (a) and after (b) etching.

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3. Fig. 2. Sample Nd30Fe70 before (a) and after (b) etching.

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4. Fig. 3. Sample Nd70Fe30 before (a) and after (b) etching.

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5. Fig. 4. The function N(h) in doubly logarithmic coordinates for the image of the Nd70Fe30 sample after etching.

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6. Fig. 5. Graph of the dependence of δ(x) samples before (1) and after (2) etching.

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7. Fig. 6. Three-dimensional diagram of the state of Sf , Tf , x samples before (1) and after (2) etching.

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8. Fig. 7. Diagrams of the state of Sf, Tf samples before (1) and after (2) etching at different scales.

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9. Fig. 8. Tf (a) Sf (b) state diagrams, three-dimensional diagram of the state of Ef , Tf , x (c) samples before (1) and after (2) etching.

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10. Fig. 9. Diagrams of the Ef (Tf) state of the samples before (1) and after (2) etching.

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11. Fig. 10. Concentration dependence of the coercive force of fast-quenched Nd100-xfex alloys obtained by pouring the melt onto a copper plate

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