Open AccessMATHEMATICAL MODELLING OF IMPURITY DIFFUSION IN GRAIN BOUNDARY NEIGHBORHOOD IN A DISLOCATION WALL FORCE FIELD (MODIFIED FISHER MODEL)
Author(s) -
M. M. Chuiko,
А. К. Федотов,
V. G. Rychagov
Publication year - 1998
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.1998.9637086
Subject(s) - impurity , dislocation , monotone polygon , grain boundary , mathematics , norm (philosophy) , diffusion , computation , work (physics) , grain boundary diffusion coefficient , boundary value problem , boundary (topology) , mathematical analysis , statistical physics , materials science , geometry , condensed matter physics , physics , thermodynamics , metallurgy , microstructure , algorithm , quantum mechanics , political science , law
In this work a computer simulation of impurity diffusion in the vicinity of individual bicrystalline grain boundary has been carried out with the use of a modified Fisher model in which the grain's boundary influence (in the form of internal mechanical stresses) onto impurity atoms is taken into account. In computations the monotone difference schemes of the second order of accuracy on irregular grids were used. For such schemes under intrinsic restrictions on the grid steps the stability in the uniform norm has been proved.