Determination of Activation Energy of Surface Diffusion Based on Thermal Oscillations of Atoms

  • Yu.V. Syrovatko Dnipropetrovsk Branch of the State Institution “Soil Protection Institute of Ukraine”
  • Ye.P. Shtapenko Dnipro National University of Railway Transport named after Academician V. Lazaryan
Keywords: activation energy, ad-atom, thermal oscillations of atoms, geometric mean oscillation frequency, amplitude of oscillations, heat energy, potential barrier

Abstract

This paper covers calculations of the activation energy of surface diffusion of ad-atoms on the substrate surface from the point of view of thermal oscillations of substrate atoms and ad-atoms. The main characteristic of oscillations of atoms and geometric mean frequency was calculated based on statistical approximation of the Debye model using the reference values of entropy and heat capacity of metals. The basic principle of the model of activation energy calculation presented in the paper is the formation of potential wells and barriers during oscillations of atoms localized in the sites of the lattice. Oscillations of atoms were considered in the framework of quasiclassical quantum approximation as the oscillations of harmonic oscillators in the potential parabolic wells. Dimensions of the negative part of values of the potential well energy were determined by the amplitude of thermal oscillations of atoms. Positive values constituted a significant part of the potential well energy values. Barriers were formed owing to interaction of positive values of the energy of parabolic wells of adjacent atoms. Therefore, in order to make the ad-atom jump, it is necessary to get out of the potential well having the negative values, and to overcome the potential barrier. The energy required for the ad-atom jump on the substrate surface was the activation energy of surface diffusion. The results obtained in this paper agree satisfactorily with the results of another method, which is based on determining the energy of ad-atom binding with the substrate atoms.

References

Ya.Ye. Geguzin, Yu.S. Kaganovskyi, Diffusion processes on the crystal surface (Energoatomizdat, Moscow, 1984).

S. Almeida, E. Ochoa, J.J. Chavez, X.W. Zhou, D. Zubia, Journal of Crystal Growth 423, 55 (2015); http://dx.doi.org/10.1016/j.jcrysgro.2015.04.036.

A.G. Naumovets, Yu.S. Vedula, Surface Sci. Rep. 4, 365 (1984).

Ya.Ye. Geguzin, Surface diffusion and spreading (Nauka, Moscow, 1969).

E. Muller, Т. Cong, Field ion microscopy, field ionization and field evaporation, (Nauka, Moscow, 1980).

Yu.V. Popik, V.N. Zhykharev, Scientific Bulletin of Uzhhorod University. Physics Series 7, 109(2000).

C.M. Chans, C.M. Wei, S.P. Chen. Phys. Rev. B 54(23), 17083 (1996); https://doi.org/10.1103/PhysRevB.54.17083.

C.L. Liu, J.M. Cohen, J.B. Adams, A.F. Voter, Surf. Sci. 253, 3, 334 (1991); https://doi.org/10.1016/0039-6028(91)90604-Q.

P.J. Feibelman, J.S. Nelson, G.L. Kellogg, Phys. Rev. B 49, 15, 10548 (1994); https://doi.org/10.1103/PhysRevB.49.10548.

S.Yu. Davydov, Solid-state physics 41(1), 11 (1999).

S.Yu. Davydov, S.K. Tikhonov. Surf. Sci. 371(1), 157 (1997).

E.P. Shtapenko, V.V. Titarenko, V.А. Zabludovskyi, Ye.О. Voronkov, Solid-state physics 62(11), 1943 (2020); https://doi.org/10.21883/FTT.2020.11.50074.129.

W. Koch, M.C. Holthausen. Chemists Guide to Density Functional Theory. (2nd Ed. Wiley–VCH, N. Y, 2001); https://doi.org/10.1002/3527600043.

L.D. Landau, E.M. Lifshitz, Statistical physics (Nauka, Moscow, 1976).

V.P. Glushko et al., Thermodynamic properties of individual substances: Handbook, Vol. 3 (Nauka, Moscow, 1981).

М.Е. Kompan, Solid-state physics 34(6), 1779 (1992).

L.D. Landau, E.M. Lifshitz, Quantum mechanics (Nauka, Moscow, 1974).

Ye.V. Vybornyi, М.V. Karasev, Nanostructures. Mathematical physics and modeling 11(1), 27 (2014).

Ye.V. Vybornyi, Mathematical physics and modeling 178(1), 108 (2014).

S.G. Simonian, Differential equations 6, 1265 (1970).

V.G. Levich, Theoretical Physics Course. Volume 1 (State Publ. House of Phys.-Math. Literature, Moscow, 1962).

Published
2021-09-07
How to Cite
[1]
SyrovatkoY. and ShtapenkoY. 2021. Determination of Activation Energy of Surface Diffusion Based on Thermal Oscillations of Atoms. Physics and Chemistry of Solid State. 22, 3 (Sep. 2021), 522-528. DOI:https://doi.org/10.15330/pcss.22.3.522-528.
Section
Scientific articles (Physics)