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Nanosize Dependence of the Mutual Solubility in the Solid State in a Mo–Ru Metal System

  • STRUCTURE, PHASE TRANSFORMATIONS, AND DIFFUSION
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Abstract

The present study is devoted to constructing a method for calculating the solubility curves for molybdenum and ruthenium in the solid state in the binary Mo–Ru system with consideration for nanoscale effects. The approach is based on the thermodynamics of phase equilibria, taking into account the surface phenomena within the framework of the Gibbs thermodynamic method of separating surfaces. The tension surface is chosen as such a separating surface. Calculations of the solubility were performed considering the size dependences of the individual characteristics of metals and the parameters of interparticle interaction in the phases. A good agreement of the obtained results with the available experimental data is observed for the macroscopic case.

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REFERENCES

  1. E. Roduner, Nanoscopic Materials: Size-Dependent Phenomena (RSC Publishing, Cambridge, 2006).

    Book  Google Scholar 

  2. R. A. Andrievskii, Foundations of Nanostructured Materials Science: Capabilities and Problems (Laboratoriya Znanii, Moscow, 2020).

    Google Scholar 

  3. M. G. Zemlyanov, G. Kh. Panova, G. F. Syrykh, and A. A. Shikov, “Size effects in the vibrational and electronic properties of Cu–Pb nanocomposites,” Phys. Solid State 48, 139–143 (2006). https://doi.org/10.1134/s1063783406010264

    Article  CAS  Google Scholar 

  4. I. Kosacki, Ch. M. Rouleau, P. F. Becher, J. Bentley, and D. Lowndes, “Nanoscale effects on the ionic conductivity in highly textured YSZ thin films,” Solid State Ionics 176, 1319–1326 (2005). https://doi.org/10.1016/j.ssi.2005.02.021

    Article  CAS  Google Scholar 

  5. R. A. Andrievski, Z. M. Dashevsky, and G. V. Kalinnikov, “Conductivity and the Hall coefficient of nanostructured titanium nitride films,” Tech. Phys. Lett. 30, 930–932 (2004). https://doi.org/10.1134/1.1829346

    Article  CAS  Google Scholar 

  6. W. H. Zhong, Ch. Q. Sun, and S. Li, “Size effect on the magnetism of nanocrystalline Ni films at ambient temperature,” Solid State Commun. 130, 603–606 (2004). https://doi.org/10.1016/j.ssc.2004.03.025

    Article  CAS  Google Scholar 

  7. D. Rafaja, L. Havela, R. Kužel, F. Wastin, E. Colineau, and T. Gouder, “Real structure and magnetic properties of UN thin films,” J. Alloys Compd. 386, 87–95 (2005). https://doi.org/10.1016/j.jallcom.2004.06.020

    Article  CAS  Google Scholar 

  8. A. I. Rusanov, “The condition of the phase equilibrium of a soluble nanoparticle,” Colloid J. 68, 334–340 (2006). https://doi.org/10.1134/S1061933X06030112

    Article  CAS  Google Scholar 

  9. V. M. Samsonov, “Problem of phase state of nanoparticles,” Bull. Russ. Acad. Sci.: Phys. 69, 1161–1164 (2005).

    Google Scholar 

  10. A. G. Kuzamishev, M. A. Shebzukhova, and A. A. Shebzukhov, “Effect of the size of nanoparticles on temperatures of melting,” Bull. Russ. Acad. Sci.: Phys. 85, 970–973 (2021). https://doi.org/10.3103/s1062873821090215

    Article  CAS  Google Scholar 

  11. Y. D. Qu, X. L. Liang, X. Q. Kong, and W. J. Zhang, “Size-dependent cohesive energy, melting temperature, and Debye temperature of spherical metallic nanoparticles,” Phys. Metals Metallography 118, 528–534 (2017). https://doi.org/10.1134/S0031918X17060102

  12. Ya. Qu, W. Liu, W. Zhang, and C. Zhai, “Theoretical study of size effect on melting entropy and enthalpy of Sn, Ag, Cu, and In nanoparticles,” Phys. Met. Metallogr. 120, 417–421 (2019). https://doi.org/10.1134/S0031918X19050181

    Article  Google Scholar 

  13. A. G. Kuzamishev, M. A. Shebzukhova, K. Ch. Bzhikhatlov, and A. A. Shebzukhov, “The dimensional dependences of the thermophysical properties of nanoparticles: Surface tension,” High Temp. 60, 304–310 (2022). https://doi.org/10.1134/s0018151x22030105

    Article  CAS  Google Scholar 

  14. A. A. Afashagov, M. A. Shebzukhova, and A. A. Shebzukhov, “Thermodynamic characteristics of the interface between condensed phases in binary metal alloys,” Phys. Solid State 64, 293–299 (2022). https://doi.org/10.1134/s1063783422070010

    Article  CAS  Google Scholar 

  15. N. T. Gladkikh, S. V. Dukarov, A. P. Krishtal’, V. I. Larin, and V. N. Sukhov, Capillary Properties of Island Films and Small Particles (Kharkov. Nats. Univ. im. V.N. Karazina, Kharkov, 2015).

  16. S. P. Chizhik, N. T. Gladkikh, L. K. Grigor’eva, R. N. Kuklin, S. V. Stepanova, and S. V. Chmel’, “Displacements of solubility boundaries in highly disperse systems,” Izv. Akad. Nauk SSSR. Met., No. 2, 175–181 (1985).

  17. A. A. Minenkov and A. P. Kryshtal’, “Effect of characteristic size on the solid-state solubility in the Ag–Ge film system,” Fiz. Inzh. Poverkhn. 13, 259–263 (2015). http://dspace.nbuv.gov.ua/handle/123456789/108725.

  18. L. S. Palatnik and B. T. Boiko, “On the state diagram of aluminum–copper alloys in thin films,” Phys. Met. Metallogr. 11, 119–122 (1961).

    Google Scholar 

  19. V. M. Koshkin and V. V. Slezov, “Do** nanoparticles,” Tech. Phys. Lett. 30, 367–369 (2004). https://doi.org/10.1134/1.1760857

    Article  CAS  Google Scholar 

  20. P. E. L’vov and V. V. Svetukhin, “Nanodimensional effects in the phase composition of binary alloys,” Tech. Phys. Lett. 35, 1040–1043 (2009). https://doi.org/10.1134/S1063785009110200

    Article  CAS  Google Scholar 

  21. P. E. L’vov, V. V. Svetukhin, and A. V. Obukhov, “Thermodynamics of phase equilibrium of binary alloys containing nanprecipitates,” Phys. Solid State 53, 421–427 (2011). https://doi.org/10.1134/S1063783411020156

    Article  CAS  Google Scholar 

  22. P. E. L’vov and V. V. Svetukhin, “Thermodynamics of the phase equilibrium of multicomponent solid solutions containing nano-sized precipitates of the second phase,” Phys. Solid State 55, 2374–2380 (2013). https://doi.org/10.1134/S1063783413110140

    Article  CAS  Google Scholar 

  23. S. Novy, P. Pareige, and C. Pareige, “Atomic scale analysis and phase separation understanding in a thermally aged Fe–20 at % Cr alloy,” J. Nucl. Mater. 384, 96–102 (2009). https://doi.org/10.1016/j.jnucmat.2008.10.008

    Article  CAS  Google Scholar 

  24. M. A. Shebzukhova and A. A. Shebzukhov, “Interface tension in a binary system with curved boundary,” Bull. Russ. Acad. Sci.: Phys. 71, 732–734 (2007). https://doi.org/10.3103/s1062873807050395

    Article  Google Scholar 

  25. M. A. Shebzukhova and A. A. Shebzukhov, “Interface tension at the boundary of two condensed phases in a binary system with allowance for nanodimensional effects,” Bull. Russ. Acad. Sci.: Phys. 80, 718–721 (2016). https://doi.org/10.3103/S1062873816060319

    Article  CAS  Google Scholar 

  26. M. A. Shebzukhova and A. A. Shebzukhov, “Influence of the nanodimensional effects on the composition of coexisting phases in a binary system with curved boundaries,” Phys. Solid State 59, 1395–1405 (2017). https://doi.org/10.1134/s1063783417070253

    Article  CAS  Google Scholar 

  27. M. A. Shebzukhova and A. A. Shebzukhov, “Phase diagram and interfacial characteristics in a binary system,” Phys. Solid State 60, 183–190 (2018). https://doi.org/10.1134/s1063783418010225

    Article  CAS  Google Scholar 

  28. M. A. Shebzukhova and A. A. Shebzukhov, “Phase equilibrium and surface properties of a binary system containing nanoparticles,” Phys. Solid State 60, 397–403 (2018). https://doi.org/10.1134/S1063783418020245

    Article  CAS  Google Scholar 

  29. A. I. Rusanov, Phase Equilibria and Surface Phenomena (Khimiya, Leningrad, 1967).

    Google Scholar 

  30. M. A. Shebzukhova and A. A. Shebzukhov, “Dimensional dependences of the interfacial tension at a solid–liquid interface and the melting temperature of metal nanoparticles,” Bull. Russ. Acad. Sci.: Phys. 76, 773–777 (2012). https://doi.org/10.3103/s1062873812070313

    Article  CAS  Google Scholar 

  31. V. B. Kogan, Heterogenic Equilibria (Khimiya, Leningrad, 1968).

    Google Scholar 

  32. T. Tanaka, “Prediction of phase diagrams in nano-sized binary alloys,” Mater. Sci. Forum 653, 55–75 (2010). https://doi.org/10.4028/www.scientific.net/msf.653.55

  33. A. A. Smirnov, Molecular-Kinetic Theory of Metals (Nauka, Moscow, 1966).

    Google Scholar 

  34. L. Kaufman and H. Bernstein, Computer Calculation of Phase Diagrams: With Special Reference to Refractory Metals, Refractory Materials. A Series of Monographs, Vol. 4 (Academic, New York, 1970).

  35. H. Okamoto, “Mo–Ru (molybdenum–ruthenium),” J. Phase Equilib. 21, 572–572 (2000). https://doi.org/10.1007/s11669-000-0030-6

    Article  CAS  Google Scholar 

  36. N. P. Lyakishev, Phase Diagrams of Binary Metallic Systems (Mashinostroenie, Moscow, 2001).

    Google Scholar 

  37. S. I. Popel’, Surface Phenomena in Melts (Metallurgiya, Moscow, 1994).

    Google Scholar 

  38. A. I. Frenkel, A. Yevick, Ch. Cooper, and R. Vasic, “Modeling the structure and composition of nanoparticles by extended x-ray absorption fine-structure spectroscopy,” Annu. Rev. Anal. Chem. 4, 23–39 (2011). https://doi.org/10.1146/annurev-anchem-061010-113906

    Article  CAS  Google Scholar 

  39. M. A. Shebzukhova, Z. A. Shebzukhov, and A. A. Shebzukhov, “The Tolman parameter, self-absorption, and surface tension on flat and curved surfaces of liquid metals,” Bull. Russ. Acad. Sci.: Phys. 74, 697–704 (2010). https://doi.org/10.3103/s1062873810050333

    Article  Google Scholar 

  40. A. I. Rusanov, Lectures on Thermodynamics (Lan’, St. Petersburg, 2013).

  41. V. V. Baidov and L. L. Kunin, “To the question about relation between the speed of sound and surface tension in metals,” in Surface Phenomena in Metals and Solid Phases Arising from Them, Ed. by S. N. Zadumkin (Kabardino-Balkarskoe Knizhnoe Izd-vo, Nal’chik, 1965), pp. 89–93.

    Google Scholar 

  42. Z. A. Shebzukhova, M. A. Shebzukhov, and A. A. Shebzukhov, “Surface tension and surface energy of metallic nanoparticles,” Izv. Kabardino-Balkarskogo Gos. Univ., No. 1, 17–58 (2010).

  43. Q. Jiang and H. M. Lu, “Size dependent interface energy and its applications,” Surf. Sci. Rep. 63, 427–464 (2008). https://doi.org/10.1016/j.surfrep.2008.07.001

    Article  CAS  Google Scholar 

  44. M. M. Magomedov, Studying the Interatomic Interaction, Formation of Vacancies, and Self-Diffusion in Crystals (Fizmatlit, Moscow, 2010).

    Google Scholar 

  45. A. A. Shebzukhov, T. P. Osiko, F. M. Kozhokova, and A. G. Mozgovoi, “Surface tension of liquid alkali metals and their alloys,” in Surveys on Thermophysical Properties of Substances (IVTAN, Moscow, 1981), p. 142.

    Google Scholar 

  46. M. A. Shebzukhova, Z. A. Shebzukhov, and A. A. Shebzukhov, “Interfacial tension of a crystalline nanoparticle in the liquid mother phase in a one-component metallic system,” Phys. Solid State 54, 185–193 (2012). https://doi.org/10.1134/s1063783412010295

    Article  CAS  Google Scholar 

  47. S. I. Novikova, Thermal Expansion of Solids (Nauka, Moscow, 1974).

    Google Scholar 

  48. V. P. Skripov and M. Z. Faizullin, Crystal–Liquid–Vapor Phase Transitions and Thermodynamic Similarity (Fizmatlit, Moscow, 2003).

    Google Scholar 

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Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Berbekov Kabardino-Balkarian State University, 360004, Nalchik, Russia

    A. A. Afashagov, M. A. Shebzukhova, K. Ch. Bzhikhatlov & A. Kh. Tsipinova

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  1. A. A. Afashagov
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  2. M. A. Shebzukhova
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  3. K. Ch. Bzhikhatlov
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Correspondence to A. A. Afashagov.

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Translated by A. Seferov

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Afashagov, A.A., Shebzukhova, M.A., Bzhikhatlov, K.C. et al. Nanosize Dependence of the Mutual Solubility in the Solid State in a Mo–Ru Metal System. Phys. Metals Metallogr. 124, 995–1004 (2023). https://doi.org/10.1134/S0031918X23601609

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