Scale Invariant Fractal and Slow Dynamics in Nucleation and Growth Processes

Original · EN

We propose a stochastic counterpart of the classical Kolmogorov-Johnson-Mehl-Avrami (KJMA) model to describe the nucleation-and-growth phenomena of a stable phase (S-phase). We report that for growth velocity of S-phase v=s(t)/t where s(t) is the mean value of the interval size x of metastable phase (M-phase) and for v=x/τ(x) where τ(x) is the mean nucleation time, the system exhibits a power law decay of M-phase. We also find that the resulting structure exhibits self-similarity and can be best described as a fractal. Interestingly, the fractal dimension df helps generalising the exponent (1+df) of the power-law decay. However, when either v=v₀ (constant) or v=σ/t (σ is a constant) the decay is exponential and it is accompanied by the violation of scaling.