Nucleation kinetics in phase transformations with spatially correlated nuclei

Phase transitions by nucleation, growth and impingement between growing nuclei can occur by nonrandom arrangement of the nuclei. In this contribution, a theoretical approach for the kinetics of phase transition with spatially correlated nuclei by progressive nucleation is developed. The approach is based on the assumptions by Kolmogorov, Johnson, Mehl and Avrami (KJMA) for phase transition kinetics, except for the randomness condition on nucleation that is removed. The work focuses on the rate of formation of the actual nuclei, a quantity that is necessary for describing the transformation kinetics. The approach uses correlation functions, and it is applied to treat hard-sphere interaction between nuclei. Computations have been performed for 2D and 3D growths by truncation of the series expansion in correlation functions up to second order terms. It is shown that the nucleation kinetics undergoes a transition from a typical Random Sequential Adsorption (RSA) behavior to one that is like the KJMA kinetics. The time evolution of the volume fraction of the new phase is found to depend slightly on correlation radius. Such behavior is explained by the partial balancing between the reduction in number density of nuclei and the decrease in impingement events, which have opposite effects on the kinetics.