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We defined a 3-dimensional local number, LN3D, and its probability distribution to describe the spatial distribution of new grains in phase transformation, and suggested a modification of Kolmogorov-Johnson-Mehl-Avrami (KJMA) equation for clustered nucleation using parameters of the probability distribution of LN3D. This modification was validated by computer experiments assuming the isotropic growth of new grains but changing their spatial and size distribution. It was demonstrated that modified KJMA equation could be applied to clustering spatial distribution of new grains, regardless of the size distribution of them. In addition, the effective surface area was derived from the modified KJMA equation and was compared with the previous model.

Modification of Kolmogorov-Johnson-Mehl-Avrami Equation for Clustered Nucleation