Treatment of phantom overgrowth in the kolmogorov-johnson-mehl-avrami kinetics as a correlation problem

In this report we point out that any nucleation and growth kinetics can be treated, in principle, as a problem of correlated nucleation. In other words, against a higher mathematical complexity, one can eliminate the concept of phantoms first introduced by Avrami [J. Chem. Phys. 7, 1103 (1939); 8, 212 (1940)]. In this way the long standing question of phantom overgrowth is solved. The simplest and probably most studied kinetics of overgrowth is the Tobin process which consists of throwing disks at random onto a flat surface, removing any disk whose center falls into an occupied area. We consider this process a paradigmatic case, where phantoms can be avoided treating it as a correlation process. In addition, we give the exact formal solution of the kinetics connected to the process.