  It has been shown that the KJMA (Kolmogorov-Johnson-Mehl-Avrami) solution of
phase transition kinetics can be set as a problem of correlated nucleation
[Phys.Rev.B65, 172301 (2002)]. In this paper the equivalence between the
standard solution and the approach that makes use of the actual nucleation
rate, i.e. that takes into account spatial correlation among nuclei and/or
grains, is shown by a direct calculation in case of linear growth and constant
nucleation rate. As a consequence, the intrinsic limit of KJMA theory due to
the phenomenon of phantom overgrowth is, at last, overcome. This means that
thanks to this new approach it is possible, for instance, to describe phase
transition governed by diffusion.
