Mean field rate equation for diffusion-controlled growth in binary alloys

Abstract

A system of rate equations is developed for modeling the kinetics of diffusional phase transitions in binary alloys. By employing a mean field assumption and the quasi static approximation a novel expression for the growth law of the nuclei is obtained in terms of supersaturation and diffusion length of component in the parent phase. The mean field rate equations are integrated for the model case of a transformation ruled by simultaneous nucleation and the behaviour of both Avrami’s exponent and rate constant investigated as a function of the initial value of the supersaturation. The expression of the activation energy, as extracted by the Arrhenius plot of the rate constant, is determined and is shown to be a function of the activation energies for nucleation and diffusion, and of the initial value of the supersaturation. The limiting case of infinite diffusion length is also analysed and discussed.