ON A NUMERICAL-MODEL FOR DIFFUSION-CONTROLLED GROWTH AND DISSOLUTION OF SPHERICAL PRECIPITATES

This paper deals with a numerical model for the kinetics of some diffu sion-limited phase transformations. For the growth and dissolution pro cesses in 3D we consider a single spherical precipitate at a constant and uniform concentration, centered in a finite spherical cell of a ma trix, at the boundary of which there is no mass transfer, see also Ast hana and Pabi [1] and Caers [2]. The governing equations are the diffu sion equation (2nd Fick's law) for the concentration of dissolved elem ent in the matrix, with a known value at the precipitate-matrix interf ace, and the flux balans (1st Fick's law) at this interface. The numer ical method, outlined for this free boundary value problem (FBP), is b ased upon a fixed domain transformation and a suitably adapted nonconf orming finite element technique for the space discretization. The algo rithm can be implemented on a PC. By numerous experiments the method i s shown to give accurate numerical results.