Abstract
The temporal evolution of the probability density function (PDF) of grain size in phase transformations by nucleation and growth has been computed by means of Kolmogorov’s second equation. The transformation is modeled in accord with the classical KJMA (Kolmogorov-Johnson-Mehl-Avrami) theory for linear growth of nuclei and either simultaneous or progressive nucleation. For 3D growth, it is shown that for progressive nucleation, second order term can be neglected in the differential equation for the PDF of grain volume. For site-saturated nucleation the variance of the distribution increases with time to attain the value of the Gamma distribution at the end of the transformation. It is demonstrated that in this case the PDF is given by convolution of Gaussian-like solutions of Kolmogorov’s equation with Gamma distribution. The validity of the model is checked by computer simulations available in literature.
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