Formation of Ordered Structure from Vacancies at Two-Dimensional Rectangular Plate

E. E. Zasimchuk, V. I. Zasimchuk, O. S. Gatsenko

G. V. Kurdyumov Institute for Metal Physics, NAS of Ukraine, 36 Academician Vernadsky Blvd., UA-03142 Kyiv, Ukraine

Received: 08.05.2022; final version - 19.07.2022. Download: PDF

The conditions of vacancies’-concentration ordered-distribution formation inside the two-dimensional rectangular plate are considered. Corresponding equation for the stationary case is analysed. The interaction between vacancies is described by the function $S(x, y)$; in the work, evident expression for $S(x, y)$ is found. As shown, for the constant temperature on a surface plate, self-organization (ordered-distribution formation) can take place only inside the very little plate. It is possible the onset of complicated dependence of vacancies’ density on the co-ordinates within the big plate, if there is a functional dependence of temperature on the plate co-ordinates.

Key words: self-organization, vacancies, ordered solutions, boundary conditions, eigenvalues, eigenfunctions.



PACS: 02.30.Jr, 05.65.+b, 61.72.Bb, 61.72.Cc, 61.72.jd

Citation: E. E. Zasimchuk, V. I. Zasimchuk, and O. S. Gatsenko, Formation of Ordered Structure from Vacancies at Two-Dimensional Rectangular Plate, Metallofiz. Noveishie Tekhnol., 44, No. 10: 1335—1346 (2022) (in Ukrainian)

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