Generalization of Fisher Model for Periodically Non-Uniform Grain Boundary
The problem of grain boundary diffusion for a case of boundary grain with periodic heterogeneity diffusion properties is considered. Dependence of Laplace transform images of impurity concentration on various diffusion conductivity places is built. The dimensionless parameters, forming the system of grain boundary diffusion regimes are determined. The space (ln x,lnt,1/T) is divided into areas in which the ratio ln ln ~ ln ln ( / ) ln eff o C r x−k t− Q RT − A is maintained, when the parameters of diffusion regime are constant. The values of parameters , , , eff o r k Q A fully specify the diffusion regimes. On this base the new concept for the definition of grain boundary diffusion regimes is carried out and the method for construction of simplified tracer concentration profile is proposed.
D.Beke, A.Gusak, G.Murch, J.Philibert
V.L. Gapontsev et al., "Generalization of Fisher Model for Periodically Non-Uniform Grain Boundary ", Defect and Diffusion Forum, Vol. 277, pp. 213-220, 2008