Response to comment on “The irrelevance of phantom nuclei in crystallization kinetics: An integral equation approach”

Abstract In a recent article I have concluded that phantom nuclei are irrelevant for an isothermal crystallization process that consists of nucleation and spherical growth, and for the type of growth rates considered in my study. I illustrated phantom irrelevance by comparing two solutions of the crystallization formulation I introduced: the first one is a constant nucleation rate model, which can be represented by the Avrami equation and does not excludes phantoms; the second is a solution with a varying nucleation rate that is proportional to the fraction of untransformed material. I maintain that this latter case excludes phantoms. In a Comment on my article by Tomellini and Fanfoni it is claimed that my comparison is invalid. Their main argument is that a varying nucleation rate solution does not exclude phantoms. To refute this claim, I present arguments supporting my assertion that a phantom-excluding model can be obtained by introducing a nucleation rate proportional to the fraction of untransformed phase.