Theory of the nucleation of multicomponent precipitates

Abstract

The nucleation kinetics of multicomponent precipitates is studied. For this, asymptotic solutions of the corresponding stationary Fokker-Planck equation are derived and analyzed. The nucleation flux in composition space ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{n}}}$ is determined by the reaction rates $R$ of the constituent components (kinetic barrier) and the formation free enthalpy $G(\stackrel{\ensuremath{\rightarrow}}{\mathrm{n}})$ of the precipitates (energetic barrier). If the kinetic barrier is small compared with the energetic one, the nucleation flux goes across the saddle point of $G(\stackrel{\ensuremath{\rightarrow}}{\mathrm{n}})$. For significantly different reaction rates the nucleation flux is bent into the directions of the rapidly reacting components, and the kinetic barrier is controlled by the fastest component $i$ for which $\frac{{\ensuremath{\partial}}^{2}G}{\ensuremath{\partial}{{n}_{i}}^{2}}l0$. If the kinetic and energetic barriers are comparable, the nucleation flux can go across a ridge in the direction of a rapidly reacting component. In this case the nucleation barrier is governed by a balance of the kinetic and the energetic barriers. The condition for this is in approximate agreement with the one suggested by Stauffer and Kiang. As the simplest example for binary nucleation the formation of ideal gas bubbles under gas and vacancy supersaturation is considered to illustrate and test the most important results of the theory.