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Simulation of Nucleation of Multiple Component 2D GaSxSe1 – x Using an Evolutionary Equation

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Abstract

Nucleation and crystallization processes of multicomponent particles are simulated using the example of the formation of two-dimensional (2D) GaSxSe1 – x (0 ≤ x ≤ 1) solid solutions in thermodynamically closed systems. A nonlinear physicochemical model of the formation of 2D thermodynamic phases is developed using an evolutionary equation of the Fokker–Planck (F–P) type in dimensional space. The evolution of the particle size distribution function is approximated in time. A model of phase formation processes containing a system of nonlinear differential F–P equations is investigated taking into account the theories of homogeneous and heterogeneous crystallization, and the model equations are solved by the finite difference method. Numerical approximations are carried out for the formation of 2D nanocrystals of the GaSxSe1 – x systems. In the description of the model of the chosen distribution function, the influence of the chemical potential of the components, temperature, and also impurities on the formation of a new phase is taken into account. The influence of the activity coefficient, the distribution of impurities, temperature-dependent factors, and the diffusion effect on the formation of 2D phases are also considered.

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REFERENCES

  1. Lukichev, V.F. and Amirov, I.I., Research and development in the field of micro and nanosystems, Istor. Nauki Tekh., 2018, no. 8, pp. 92–99.

  2. Wang, T., Li, J., Zhao, Q., Yin, Z., Zhang, Y., Chen, B., Xie, Y., and Jie, W., High-quality GaSe single crystal grown by the Bridgman method, Materials, 2018, vol. 11, no. 2, pp. 2–9. https://doi.org/10.3390/ma11020186

    Article  Google Scholar 

  3. Ho, C.H., Wang, S.T., Huang, Y.S., and Tiong, K.K., Structural and luminescent property of gallium chalcogenides GaSe1–xSx layer compounds, J. Mater. Sci.: Mater. Electron., 2009, vol. 20, pp. S207–S210. https://doi.org/10.1007/s10854-007-9539-3

    Article  Google Scholar 

  4. Bereznaya, S., Korotchenko, Z., Redkin, R., Sarkisov, S., Tolbanov, O., Trukhin, V., Gorlenko, N., Sarkisov, Y., and Atuchin, V., Broadband and narrowband terahertz generation and detection in GaSe1–xSx crystals, J. Opt., 2017, vol. 19, no. 11, p. 115503. https://doi.org/10.1088/2040-8986/aa8e5a

    Article  Google Scholar 

  5. Kolesnikov, N.N., Borisenko, E.B., Borisenko, D.N., Tereshchenko, A.N., and Timonina, A.V., Synthesis and growth of GaSe1–xSx (x = 0–1) crystals from melt. Phase composition and properties, Inorg. Mater.: Appl. Res., 2018, vol. 9, no. 1, pp. 66–69. https://doi.org/10.1134/S2075113318010173

    Article  Google Scholar 

  6. Asadov, S.M., Mustafaeva, S.N., and Lukichev, V.F., Charge transport in layer gallium monosulfide in direct and alternate electric fields, Russ. Microelectron., 2019, vol. 48, no. 6, pp. 422–427. https://doi.org/10.1134/S1063739719660016

    Article  Google Scholar 

  7. Mustafaeva, S.N. and Asadov, M.M., Currents of isothermal relaxation in GaS〈Yb〉 single crystals, Solid State Commun., 1983, vol. 45, no. 6, pp. 491–494. https://doi.org/10.1016/0038-1098(83)90159-X

    Article  Google Scholar 

  8. Asadov, S.M., Mustafaeva, S.N., Lukichev, V.F., and Guseinov, D.T., Effect of the composition on the dielectric properties and charge transfer in 2D GaS1–xSex materials, Russ. Microelectron., 2019, vol. 48, no. 4, pp. 203–207. https://doi.org/10.1134/S1063739719040024

    Article  Google Scholar 

  9. Mustafaeva, S.N., Asadov, M.M., and Ismailov, A.A., Charge transfer over localized states in a TlS single crystal, Phys. Solid State, 2008, vol. 50, no. 11, pp. 2040–2043. https://doi.org/10.1134/S1063783408110073

    Article  Google Scholar 

  10. Mustafaeva, S.N., Asadov, M.M., and Ismailov, A.A., Dielectric and baric characteristics of TlS single crystal, Phys. B (Amsterdam, Neth.), 2014, vol. 453, pp. 158–160.https://doi.org/10.1016/j.physb.2014.03.095

    Book  Google Scholar 

  11. Mustafaeva, S.N. and Asadov, M.M., High field kinetics of photocurrent in GaSe amorphous films, Mater. Chem. Phys., 1986, vol. 15, pp. 185–189. https://doi.org/10.1016/0254-0584(86)90123-9

    Article  Google Scholar 

  12. Asadov, S.M., Mustafaeva, S.N., and Mammadov, A.N., Thermodynamic assessment of phase diagram and concentration-temperature dependences of properties of solid solutions of the GaS–GaSe system, J. Therm. Anal. Calorim., 2018, vol. 133, no. 2, pp. 1135–1141. https://doi.org/10.1007/s10973-018-6967-7

    Article  Google Scholar 

  13. Mustafaeva, S.N., Asadov, M.M., and Ismailov, A.A., Charge transfer along localized states in InSe and InSe〈Sn〉 single crystals, Low Temp. Phys., 2010, vol. 36, no. 4, pp. 310–312. https://doi.org/10.1063/1.3388822

    Article  Google Scholar 

  14. Mustafaeva, S.N., Asadov, M.M., and Ismailov, A.A., Effect of γ irradiation on the parameters of localized states in p-InSe and n-InSe(Sn) single crystals, Low Temp. Phys., 2010, vol. 36, no. 7, pp. 642–644. https://doi.org/10.1063/1.3479690

    Article  Google Scholar 

  15. Tan, L., Liu, Q., Ding, Y., Lin, X., Hu, W., Cai, M.-Q., and Zhou, H., Effective shape-controlled synthesis of gallium selenide nanosheets by vapor phase deposition, Nano Res., 2020, CN 11-5974/O4. https://doi.org/10.1007/s12274-020-2653-8

  16. Jung, C.S., Shojaei, F., Park, K., Oh, J.Y., Im, H.S., Jang, D.M., Park, J., and Kang, H.S., Red-to-ultraviolet emission tuning of two-dimensional gallium sulfide/selenide, ACS Nano, 2015, vol. 9, no. 10, pp. 9585–9593. https://doi.org/10.1021/acsnano.5b04876

    Article  Google Scholar 

  17. Li, X.F., Lin, M.W., Puretzky, A.A., Idrobo, J.C., Ma, C., Chi, M.F., Yoon, M., Rouleau, C.M., Kravchenko, I.I., Geohegan, D.B., and Xiao, K., Controlled vapor phase growth of single crystalline, two-dimensional GaSe crystals with high photoresponse, Sci. Rep., 2015, vol. 4, pp. 1–9. https://doi.org/10.1038/srep05497

    Article  Google Scholar 

  18. Hu, P.A., Wen, Z.Z., Wang, L.F., Tan, P.H., and Xiao, K., Synthesis of few-layer GaSe nanosheets for high performance photodetectors, ACS Nano, 2012, vol. 6, no. 7, pp. 5988–5994. https://doi.org/10.1021/nn300889c

    Article  Google Scholar 

  19. Becker, R. and Doring, W., Kinetischebehandlung der Keimbildung in Ubersattigtendampfen, Ann. Phys., 1935, vol. 416, no. 8, pp. 719–752. https://doi.org/10.1002/andp.19354160806

    Article  MATH  Google Scholar 

  20. Zel’dovich, Ya.B., Towards the theory of the formation of a new phase. Cavitation, Zh. Eksp. Teor. Fiz., 1942, vol. 12, nos. 11–12, pp. 525–538.

    Google Scholar 

  21. Kashchiev, D., Nucleation. Basic Theory with Applications, 1st ed., Oxford: Butterworth-Heinemann, 2003.

    Google Scholar 

  22. Saito, Y., Honjo, M., Konishi, T., and Kitada, A., Time-dependent nucleation rate, J. Phys. Soc. Jpn., 2000, vol. 69, no. 10, pp. 3304–3307. https://doi.org/10.1143/jpsj.69.3304

    Article  Google Scholar 

  23. Anisimov, M.P., Nucleation: Theory and experiment, Russ. Chem. Rev., 2003, vol. 72, no. 7, pp. 591–628. https://doi.org/110.1070/rc2003v072n07abeh000761

    Article  Google Scholar 

  24. Nucleation in Condensed Matter: Applications in Materials and Biology, Kelton, K.F. and Greer, A.L., Eds., Amsterdam: Elsevier, 2010.

  25. Flemings, M.C., Solidification Processing, New York: McGraw-Hill College, 1974.

    Book  Google Scholar 

  26. Chernov, A.A., Modern Crystallography III, Berlin: Springer, 1984.

    Book  Google Scholar 

  27. Perepezko, J.H., Hoffmeyer, M.K., and de Cicco, M.P., Analysis of melt undercooling and crystallization kinetics, Metall. Mater. Trans. A, 2015, vol. 46, no. 11, pp. 4898–4907. https://doi.org/10.1007/s11661-015-2970-9

    Article  Google Scholar 

  28. Ivanov, A.O. and Zubarev, A.Yu., Non-linear evolution of a system of elongated droplike aggregates in a metastable magnetic fluid, Phys. A (Amsterdam, Neth.), 1998, vol. 251, pp. 348–367. https://doi.org/10.1016/S0378-4371(97)00561-X

  29. Mullin, J.W., Crystallization, London: Butterworth-Heinemann, 2001, 4th ed.

    Google Scholar 

  30. Phase Transformations in Multicomponent Melts, Herlach, D.M., Ed., Weinheim: Wiley-VCH, 2008.

    Google Scholar 

  31. Aaronson, H.I., Enomoto, M., and Lee, J.K., Mechanisms of Diffusional Phase Transformations in Metals and Alloys, Boca Raton: CRC, Taylor and Francis, 2010.

    Google Scholar 

  32. Rachah, A., Noll, D., Espitalier, F., and Baillon, F., A mathematical model for continuous crystallization, Math. Methods Appl. Sci., 2016, vol. 39, pp. 1101–1120. https://doi.org/10.1002/mma.3553

    Article  MathSciNet  MATH  Google Scholar 

  33. Risken, H., The Fokker–Planck Equation. Methods of Solutions and Applications, Berlin: Springer, 1996, 2nd ed.

    MATH  Google Scholar 

  34. Gorbachevskii, A.Ya., Numerical study of nonlinear crystallization models, Mat. Model., 1999, vol. 11, no. 8, pp. 23–31.

    Google Scholar 

  35. Frank, T.D., Nonlinear Fokker-Planck Equations. Fundamentals and Applications, Berlin, Springer, 2005.

    MATH  Google Scholar 

  36. Makoveeva, E.V. and Alexandrov, D.V., A complete analytical solution of the Fokker–Planck and balance equations for nucleation and growth of crystals, Phil. Trans. R. Soc. London, Ser. A, 2018, vol. 376, p. 20170327. https://doi.org/10.1098/rsta.2017.0327

    Article  MathSciNet  MATH  Google Scholar 

  37. Kukushkin, S.A. and Slezov, V.V., Dispersnye sistemy na poverkhnosti tverdykh tel (evolyutsionnyi podkhod): mekhanizmy obrazovaniya tonkikh plenok (Disperse Systems on the Surface of Solids (Evolutionary Approach): Mechanisms of the Formation of Thin Films), St. Petersburg: Nauka, 1996.

  38. Godunov, S.K. and Ryaben’kii, V.S., Raznostnye skhemy. Vvedenie v teoriyu (Difference Schemes. Introduction to Theory), Moscow: Nauka, 1977, 2nd ed.

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Funding

This study was supported by the Science Development Fund under the President of the Republic of Azerbaijan (grant no. EİF-BGM-3-BRFTF-2+/2017-15/05/1-M-13).

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  1. Institute of Catalysis and Inorganic Chemistry, National Academy of Sciences of Azerbaijan, AZ-1143, Baku, Azerbaijan

    S. M. Asadov

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Asadov, S.M. Simulation of Nucleation of Multiple Component 2D GaSxSe1 – x Using an Evolutionary Equation. Russ Microelectron 50, 264–277 (2021). https://doi.org/10.1134/S1063739721030021

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