Finite Volume Kolmogorov-Johnson-Mehl-Avrami Theory

Details Finite Volume Kolmogorov-Johnson-Mehl-Avrami Theory Finite Volume Kolmogorov-Johnson-Mehl-Avrami Theory

2008-02-05

arxiv.org/abs/0802.0535v2

Phys.Rev.Lett.100:165702,2008

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures. Additions after referee reports: Scaling of the variable q is proven. Additional references are added

Scientific paper

10.1103/PhysRevLett.100.165702

We study Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory of phase conversion in finite volumes. For the conversion time we find the relationship $\tau_{\rm con} = \tau_{\rm nu} [1+f_d(q)]$. Here $d$ is the space dimension, $\tau_{\rm nu}$ the nucleation time in the volume $V$, and $f_d(q)$ a scaling function. Its dimensionless argument is $q=\tau_{\rm ex}/ \tau_{\rm nu}$, where $\tau_{\rm ex}$ is an expansion time, defined to be proportional to the diameter of the volume divided by expansion speed. We calculate $f_d(q)$ in one, two and three dimensions. The often considered limits of phase conversion via either nucleation or spinodal decomposition are found to be volume-size dependent concepts, governed by simple power laws for $f_d(q)$.

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