Connection between phantom and spatial correlation in the Kolmogorov–Johnson–Mehl–Avrami-model: a brief review

The goal of this minireview is restricted to describe how the theoretical basis of Kolmogorov (1937)–Johnson-Mehl (1939) –Avrami (1939–41) model has evolved from its birth up to the present day. The model, which dates back to the late of 1930s, has the purpose of describing the kinetics of a phase transformation. Given the nature of this article, although there are hundreds (if not thousands) of experimental data concerning the most disparate topics, which are interpreted on the basis of the KJMA model, no arguments relating to these, will be touched upon. Starting from the ingenious concept of phantom nuclei, firstly introduced by Avrami to get the exact kinetics, we review theoretical approaches which overcome such concept. We will show how spatial correlation among nuclei plays a fundamental role in these modelings.