Effects of solid-state diffusion on the incubation time for nucleation in solids

Abstract

Most nucleation in solids is predicated on the aggregation of single atoms into a critical nucleus, which typically contains from tens to thousands of atoms. Clearly solid state diffusion is required for this accumulation. In addition, regardless of how rapid steady state nucleation might be, a characteristic time, known as an incubation time, is required for the formation of even a single critical nucleus. Clearly, the length of this incubation time depends strongly on the diffusional process which is operative in nucleus formation. In some cases, the operative diffusive process is not at all self evident. This paper demonstrates how the quantum mechanical principle of time reversal symmetry may be utilized to identify the path of activation for nucleation, and therefrom the operative diffusive process and the incubation time. Time reversal symmetry will be utilized to obtain the incubation times for homogeneous and heterogeneous nucleation in solids. By contrast, mathematical derivations of the incubation time are cumbersome at best, have been performed only for extremely simple cases, and are often non-physical.