Cell-size distribution and scaling in a one-dimensional KJMA lattice model with continuous nucleation

Zoltán Néda; Ferenc Járai-Szabó; Szilárd Boda

doi:10.1103/physreve.96.042145

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arXiv · 1706.02983

Cell-size distribution and scaling in a one-dimensional KJMA lattice model with continuous nucleation

Zoltán Néda·Ferenc Járai-Szabó·Szilárd Boda

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Abstract

The Kolmogrov-Johnson-Mehl-Avrami (KJMA) growth model is considered on a one-dimensional (1D) lattice. Cells can growth with constant speed and continuously nucleate on the empty sites. We offer an alternative, mean-field like approach for describing theoretically the dynamics and derive an analytical cell-size distribution function. Our method reproduces the same scaling laws as the KJMA theory and has the advantage that it leads to a simple closed form for the cell-size distribution function. It is shown that a Weibull distribution is appropriate for describing the final cell-size distribution. The results are discussed in comparison with Monte Carlo simulation data.

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Zoltán Néda, Ferenc Járai-Szabó, Szilárd Boda. 2017-06-09. Cell-size distribution and scaling in a one-dimensional KJMA lattice model with continuous nucleation. https://doi.org/10.1103/physreve.96.042145

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