Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials
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Surface layer thickness and anisotropy of the surface energy of cubic ruthenium crystals

V.M. Yurov1, V.I. Goncharenko2, V.S. Oleshko2, S.A. Guchenko1

1 Research Center of the Karaganda University named after E.A. Buketov
2 Moscow Aviation Institute (National Research University)

DOI: 10.26456/pcascnn/2021.13.522

Original article

Abstract: The paper deals with the anisotropy of the surface layer and the anisotropy of the free surface energy of cubic ruthenium crystals. This consideration is based on an empirical model of atomically smooth crystals, the thickness of the surface layer of which depends on single fundamental parameter – the atomic volume of an element. Calculations of ruthenium crystals showed that the thickness of the surface layer of ruthenium crystals in all directions does not exceed  d(I)<10 nm and they represent a nanostructure. Crystals of ruthenium aluminum, ruthenium hafnium, ruthenium titanium, ruthenium zirconium have  σ>3  J/m2 in the (100) direction. We have considered the problem of gas diffusion in a nanometer ruthenium plate. In contrast to the classical problem, a logarithmic term appears in the resulting equation. This leads to divergence at the origin. Therefore, the boundary conditions must be specified not at x=0, but at x=d(0) – the de Broglie wavelength of electrons. Only in this case the classical diffusion equations are meaningful. It is also important that, according to the obtained equation, the diffusion of the nanoplate depends both on the material of the plate through the diffusion coefficient of the bulk sample and on the size factor. In the classical case, there is no such dependence. Various models have been proposed to describe phase transitions in nanostructures, among which we can mention the Landau mean field method, in which the order parameter is used. We will use Landau’s theory, replacing the temperature T with the coordinate h .

Keywords: surface layer, nanostructure, surface energy, atomic volume, size effect, ruthenium

  • Viktor M. Yurov – Ph. D., Docent, Director of the Research Center «Ion-plasma Technologies and Modern Instrument-making», Karaganda University named after Е.A. Buketov
  • Vladimir I. Goncharenko – Dr. Sc., Professor, Director of the Military Institute, Moscow Aviation Institute (National Research University)
  • Vladimir S. Oleshko – Ph. D., Professor of the Department of Aircraft, Moscow Aviation Institute (National Research University)
  • Sergey A. Guchenko – 3rd year postgraduate student, Research Center of the Karaganda University named after E.A. Buketov


Yurov, V.M. Surface layer thickness and anisotropy of the surface energy of cubic ruthenium crystals / V.M. Yurov, V.I. Goncharenko, V.S. Oleshko, S.A. Guchenko // Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials. – Tver: TSU, 2021. — I. 13. — P. 522-533. DOI: 10.26456/pcascnn/2021.13.522. (In Russian).

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