Issues »  Volume 45, Issue 9

Formation of Ordering Temperature and Vacancies’ Distributions During Deformation of Metal Crystals

O. Eh. Zasymchuk, V. I. Zasymchuk, T. V. Turchak, O. I. Baskova, O. S. Gatsenko

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

Received: 08.09.2020; final version - 10.01.2023. Download: PDF

Three-dimensional equations of heat conduction and diffusion are considered in the article: a) with a small, but well-ordered function for thermal sources $f(r,t)$; b) for $f(r,t) \equiv 0$. Stationary and non-stationary cases are discussed, and the formation of arbitrary complex distributions of temperature and concentrations of vacancies along co-ordinates is established. As shown, new two-dimensional structures not specified by the boundary conditions arise within the sample.

Key words: thermal-conduction equation, diffusion, heat-source function, vacancies, ordered distribution, stationary solution, Fourier series, self-organization, hydrodynamic channels.

URL: https://mfint.imp.kiev.ua/en/abstract/v45/i09/1099.html

DOI: https://doi.org/10.15407/mfint.45.09.1099

PACS: 02.30.Jr, 02.30.Nw, 05.65.+b, 61.72.Bb, 61.72.jd, 82.40.Ck, 82.40.Np

Citation: O. Eh. Zasymchuk, V. I. Zasymchuk, T. V. Turchak, O. I. Baskova, and O. S. Gatsenko, Formation of Ordering Temperature and Vacancies’ Distributions During Deformation of Metal Crystals, Metallofiz. Noveishie Tekhnol., 45, No. 9: 1099—1107 (2023) (in Ukrainian)

REFERENCES
  1. E. Zasimchuk, T. Turchak, and N. Chausov, Results Mater., 6: 100090 (2020). Crossref
  2. E. Zasimchuk, L. Markashova, O. Baskova, T. Turchak, N. Chausov, V. Hutsaylyuk, and V. Berezin, J. Mater. Eng. Perform., 22, No. 7: 3421 (2013). Crossref
  3. E. Zasimchuk, O. Baskova, O. Gatsenko, and T. Turchak, J. Mater. Eng. Perform., 26, No. 3: 1293 (2017). Crossref
  4. E. E. Zasimchuk, V. I. Zasimchuk, and T. V. Turchak, Uspehi Fiz. Met., 14, No. 3: 275 (2013) (in Russian). Crossref
  5. Yu. G. Gordienko and E. E. Zasimchuk, Philos. Mag. A, 70, No. 1: 99 (1994). Crossref
  6. N. D. Bega, E. Eh. Zasimchuk, S. N. Kaverina, and S. A. Firstov, Metallofizika, 2, No. 1: 71 (1980) (in Russian).
  7. V. T. Troshchenko, E. E. Zasimchuk, and N. D. Bega, Fiz. Met. Metalloved., 45, No. 4: 850 (1978) (in Russian).
  8. B. M. Yavorsky and A. A. Detlaf, Spravochnik po Fizike dlya Inzhenerov i Studentov Vuzov [Handbook of Physics for Engineers and University Students] (Moskva: Gos. Izd. Fiz.-Mat. Lit.: 1963).
  9. T. Blomberg, Byggnadsfysik LTH (Lunds Tekniska Högskola: 1996).
  10. S. Ahmed, P. Singh, and S. Ekkad, ASME. J. Heat Transfer, 142, Iss. 5: 051302 (2020). Crossref
  11. G. S. Carslaw and J. C. Jaeger, Teploprovodnost Tverdykh Tel [Conduction of Heat in Solids] (Moskva: Nauka: 1964) (Russian translation).
  12. G. Korn and T. Korn, Spravochnik po Matematike dlya Nauchnykh Rabotnikov i Inzhenerov [Handbook of Mathematics for Scientists and Engineers] (Moskva: Nauka: 1978) (Russian translation).
  13. V. I. Zasimchuk and E. Eh. Zasimchuk, Metallofiz. Noveishie Tekhnol., 41, No. 6: 765(2019) (in Russian). Crossref
  14. V. T. Troshchenko, Deformirovanie i Razrushenie Metallov pri Mnogotsiklovom Nagruzhenii [Deformation and Destruction of Metals under High-Cycle Loading] (Kiev: Naukova Dumka: 1981) (in Russian).
  15. O. V. Oliinyk and V. A. Tatarenko, Dopov. Nac. acad. Nauk Ukr., No. 3: 55 (2019) (in Ukrainian). Crossref
  16. O. V. Oliinyk and V. A. Tatarenko, Radiation Effects and Defects in Solids, 174, Iss. 5-6: 519 (2019). Crossref

Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License
© 2000–2023 “G. V. Kurdyumov Institute for Metal Physics of the N.A.S. of Ukraine”