Modelling of the diffusion of atoms in the presence of the mobile and immobile traps and under the influence of the external stochastic force
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Abstract
The influence of the external stochastic effect on the re-distribution of the diffusing atoms in the cubic lattice at presence of flows had been studied with the use of the Monte – Carlo method. We considered the case in which the mobile and immobile traps are distributed randomly. It was shown that, the mean value of the stochastic component has no influence on the distribution of the diffusing atoms. The existence of traps alters the type of the concentration profiles: we found that the Gauss distribution at the trap concentration C < 10-3 switches to the exponential dependence at C > 10-3. The mobility of traps exerts an influence on the shape of the concentration distributions. The additional local maximums in the concentration distributions of the diffusing atoms emerge due to the action of the external stochastic force. In the case when the traps are mobile the concentration profiles become less distinct than in the case when the traps are immobile at the same duration of random walks of the migrating atoms. The additional maximum of the distribution function of the migrating atoms emerges with the setting up the high values of the mobile trap concentration. The position of this maximum depends on the intensity of the trap displacement.
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References
1. Philibert J. M. Atoms Movements: Diffusion and Mass Transport in Solids / J. M. Philibert // EDP Sciences, – 2012. – P. 577.
2. Murch G. E. Calculation of the diffusion correlation factor by Monte Carlo methods / G. E. Murch, R. J. Thorn // Phil. Mag. A. – 1979. – Vol. 39. – P. 259–265.
3. Pandey R. B. Classical diffusion, drift, and trapping in random percolating systems / R. B. Pandey // Phys. Rev. B. – 1984. – Vol. 30. – P. 486–493.
4. Young W. M. Monte Carlo studies of vacancy migration in binary ordered alloys : I / W. M. Young, E. Elcock // Proc. Phys. Soc. – 1966. – Vol. 89. – P. 735–741.
5. Le Claire A. D. Solute effects in diffusion / A. D. Le Claire // An Advanced Tretiase. – 1970. – Vol. 10. – P. 261.
6. Hatlee M. D. Random walks on finite lattices with traps. II. The case of a partially absorbing trap / M. D. Hatlee, J. J. Kozak // Proc. Phys. Soc. – 1981. – Rev. B. – 23. – P. 1713–1722.
7. Allnatt A. R. Diffusion kinetics in dilute binary alloys with the h.c.p. crystal structure / A. R. Allnatt, I. V. Belova, G. E. Murch // Phil. Mag. A. – 2014. – Vol. 94, № 22. – P. 2487–2504.
8. Divinskiy S. V. Diffusion of atoms at presence of traps under influence of stochastic external force / S. V. Divinskiy, S. M. Zakharov // Proceedings of DIFTRAN’S ; Bulletin of Cherkasy State Universiti. Physics. – 2001. – Vol. 37–38. – P. 213–217.
9. Gertsricken D. S. Mass-transfer in metals at low temperatures under external forces / D. S. Gertsricken, V. F. Mazanko, V. M. Tyshkevich, V. M. Falchenko // Kiev, JMP Publ., – 1989. – P. 89.
10. Захаров С. М. Исследование массопере-носа 63Ni при ударном сжатии никеля и циркония / С. М. Захаров, В. Ф. Мазанко, Р. Л. Межвинский // Металлофизика. – 1993. – Vol. 15, №6. – С. 18–24.
11. Athenes M. Identification of novel diffusion cycles in B2 ordered phases by Monte Carlo simulation / M. Athenes, P. Bellon, G. Martin // Phil. Mag. A. – 1997. – Vol. 76. – P. 565–570.
12. Хеерман Д. В. Методы компьютерного эксперимента в теоретической физике / Д. В. Хеерман // Компьютеры в физике. – М. : Наука, 1990. – 175 с.