Finite size corrections for the Johnson-Mehl-Avrami-Kolmogorov equation

The Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation is frequently used to describe phase transformations involving nucleation and growth. The assumptions used in the derivation of this equation, however, are frequently violated when making experimental measurements; use of the JMAK equation for analyzing such data can often produce invalid results. Finite-size effects are among the most serious of these problems. We present modified analytic JMAK equations that correct for the finite-size effects and are roughly independent of both the sample shape and the shape of the growing nuclei. A comparison with computer simulations shows that these modified JMAK equations accurately reproduce the growth behavior over a wide range of conditions.