Diffusion-Controlled Phase Transformations in Finite Regions. An Exact Time-Dependent Analytic Solution
O. Simmich · physica status solidi (a) · 1986
An exact solution of the diffusion equation (DE) for the one-dimensional diffusion-controlled growth is presented applying the method of reflection and superposition of partial solutions of the DE. The solution for the finite matrix (FMS) shows that no anomalous course of concentration at the far-side boundary of the matrix with time occurs, contrary to the approximative solution of this problem [1]. It can be shown that the FMS is well approximated by the IMS (solution for the infinite matrix) in a considerable time interval.