Scale Invariant Fractal and Slow Dynamics in Nucleation and Growth Processes

Details Scale Invariant Fractal and Slow Dynamics in Nucleation and Growth Processes Scale Invariant Fractal and Slow Dynamics in Nucleation and Growth Processes

2004-07-28

arxiv.org/abs/cond-mat/0407715v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, no figure, Submitted to publication

Scientific paper

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 $v=x/\tau(x)$ where $\tau(x)$ 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 $d_f$ helps generalising the exponent $(1+d_f)$ of the power-law decay. However, when either $v=v_0$ (constant) or $v=\sigma/t$ ($\sigma$ is a constant) the decay is exponential and it is accompanied by the violation of scaling.

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