On the validity of the Avrami theorem in the case of decelerating growth

It is argued that the use of the Avrami theorem, S(t) = 1−e^−S_x(t), is in principle not allowed when applied to overlapping diffusion zones or, more generally, in all cases where the phantom nuclei overtake the front of their parent nuclei. Via computer simulations the overtake effect is shown to exist and is found to be surprisingly small. The use of a modified Avrami equation, S(t) = FS_x(t)·1 −e^−S_x(t)], is suggested for such cases and the function FS_x(t)] pertaining to diffusion-controlled growth is reported.