Impingement factor in the case of phase transformations governed by spatially correlated nucleation

The Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory fails to treat nonrandom nucleation and overgrowth processes. However, the very tractability of their solution in describing experimental data caused researchers to slightly modify KJMA's differential equation so as to extend the applicability of the model. In doing this a phenomenological parameter is introduced, named as the impingement factor. Here we analyze, in depth, the limits within which the phenomenological approach is suitable for sidestepping the difficulty of nonrandom nucleation. In particular we tackled two cases: instantaneous cluster growth where cluster overgrowth prevails and the constant nucleation rate of spatially correlated nuclei according to the hard-core model. In the last part of the paper we show that Avrami's general set theory is equivalent to the statistical mechanics of rigid disks. This permits a deeper appreciation of the KJMA theory and the nonrandom nonsimultaneous kinetics