1. Dynamic scaling and stochastic fractal in nucleation and growth processes
- Author
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Lahiri, Amit, Hassan, Md. Kamrul, Blasius, Bernd, and Kurths, Jürgen
- Subjects
Condensed Matter - Statistical Mechanics ,Condensed Matter - Other Condensed Matter ,Condensed Matter - Soft Condensed Matter - Abstract
A class of nucleation and growth models of a stable phase (S-phase) is investigated for various different growth velocities. It is shown that for growth velocities $v\sim s(t)/t$ and $v\sim x/\tau(x)$, where $s(t)$ and $\tau$ are the mean domain size of the metastable phase (M-phase) and the mean nucleation time respectively, the M-phase decays following a power law. Furthermore, snapshots at different time $t$ are taken to collect data for the distribution function $c(x,t)$ of the domain size $x$ of M-phase are found to obey dynamic scaling. Using the idea of data-collapse we show that each snapshot is a self-similar fractal. However, for $v={\rm const.}$ like in the classical Kolmogorov-Johnson-Mehl-Avrami (KJMA) model and for $v\sim 1/t$ the decay of the M-phase are exponential and they are not accompanied by dynamic scaling. We find a perfect agreement between numerical simulation and analytical results., Comment: 10 pages, 8 captioned figures
- Published
- 2022
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