A model kinetics for nucleation and diffusion-controlled growth of immiscible alloys

A system of mean field rate equations is employed for describing the kinetics of solid-solid phase separation within the immiscibility gap of binary alloys. The system allows us to study the time evolution of both supersaturation and diffusion length of the components in the metastable phase. It is shown that in the case of simultaneous nucleation the system of differential equations leads to a simple formula for the characteristic time of the transformation in terms of material parameters and initial supersaturation. The nucleation rate is computed on the basis of the classical nucleation theory and the alloy is assumed to behave as a regular solution. It turns out that for low values of the initial supersaturation the nucleation process can be considered as simultaneous. It is also found that thermally activated nucleation takes place for supersaturation values lower than about 0.21. The assumption of a concentration-independent diffusion coefficient and the effect of nucleus curvature on interface composition have been analyzed and discussed.