Mixed mode growth of an ellipsoidal precipitate: Analytical solution for shape preserving growth in the quasi-stationary regime

The growth of an ellipsoidal precipitate has been analysed in the mixed-mode regime for a binary system. Under the assumption that the precipitate grows with constant eccentricities, an analytical solution was developed giving the time evolution of the size of the precipitate and the non-equilibrium concentration of the solute in the matrix. The mathematical analysis revealed that the evolution of the growth is characterized by a constant k called the interface migration coefficient. This coefficient was found to be equal to 12υc/ac, where ac is the critical size of nucleation and υc is the maximum growth velocity attainable with the applied driving force. This velocity, which was found to be proportional to the square root of the interface mobility, was assumed to be constant during the nucleation stage, making ac/υc to be the nucleation time. This finding suggests that there is a close link between the nucleation time and the mobility of the interface separating the nucleus from the matrix.