On the n-dimensional diffusion-controlled growth of precipitates in a finite matrix

Abstract

The diffusion-controlled n-dimensional growth (n = 1; 2; 3) in a finite matrix is considered solving the diffusion equation (DE) in the approximation of the stationary solution and having regard to the mass balance of the alloyed atoms. The results are compared with those obtained for the infinite matrix as well as for the non-stationary solutions of the DE. The derived results show that the method applied in this work is a useful approach to gaining information on the diffusion-controlled growth of precipitates.Das diffusionskontrollierte n-dimensionale Wachstum (n = 1 ;, 2; 3) von Ausscheidungen in einer begrenzten Matrix wird untersucht in der Naherung der stationaren Losung der Diffusionsgleichung (DE) und des Massengleichgewichts der zulegierten Atome. Die Resultate werden mit denjenigen verglichen, die sowohl fur eine unendliche Matrix als auch aus den nichtstationaren Losungen der DE abgeleitet werden. Die gewonnenen Ergebnisse zeigen, daI3 die in dieser Arbeit verwendete Methode ein zweckmlI3iger Schritt fur die Gewinnung von Aussagen uber das diffusionskontrollierte Wachstum von Ausscheidungen ist.

Description of Particle Growth by Means of a Difference Approximation

“…The indices i = 1, ... ,4 belong to the following methods. i = 1 : stationary solution of the diffusion equation by Wert and Zener[2], claiming the BC (5), but disregarding the mass balance; i = 2: stationary solution with regard to the mass balance according to Simmich and Loffler[7], but disregarding the RC (5) ; i = 3: non-stationary solution according to Zener [ 13 ; i = 4 : difference approximation according to the results 0. SIainircH Growth coefficients in dependence on the initial supersaturation Ac.…”