Spatial distribution of nuclei in progressive nucleation: modeling and application

TL;DR

This paper presents an analytical model for the spatial distribution of nuclei in progressive nucleation, accounting for correlations due to non-simultaneous nucleation and growth, with applications to electrochemical nucleation.

Contribution

It introduces a novel analytical approach to compute the pair-correlation function and spatial distribution of nuclei in progressive nucleation, validated against simulations and experiments.

Findings

Model accurately predicts transition from Poissonian to correlated distributions.

Comparison with experiments confirms the model's effectiveness.

Provides insights into spatial correlations in electrochemical nucleation.

Abstract

Phase transformations ruled by non-simultaneous nucleation and growth do not lead to random distribution of nuclei. Since nucleation is only allowed in the untransformed portion of space, positions of nuclei are correlated. In this article an analytical approach is presented for computing pair-correlation function of nuclei in progressive nucleation. This quantity is further employed for characterizing the spatial distribution of nuclei through the nearest neighbor distribution function. The modeling is developed for nucleation in 2D space with power growth law and it is applied to describe electrochemical nucleation where correlation effects are significant. Comparison with both computer simulations and experimental data lends support to the model which gives insights into the transition from Poissonian to correlated nearest neighbor probability density.