Crystallization kinetics and the JMAK equation

In the present work the application of the Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory for the calculation of the volume fraction crystallized is discussed for several particular cases of isothermal transformations. In particular, the following three situations, for which the JMAK theory requires extensions, are considered: (1) finite size effects and non-uniform nucleation, (2) anisotropic particle formation, and (3) transient nucleation. We present new equations which describe these three situations. In general, we find that anisotropic particle formation, finite size effects and non-uniform nucleation lead to a reduction of the crystallization rate. Furthermore, transformations which produce anisotropic particles are characterized by reduced values of the Avrami exponents. Finally, we demonstrate that corrections to the JMAK f⁴ law arising from time dependent nucleation must include size-dependent growth effects to obtain a logically consistent result.