What can we learn from the exclusion volume of fluctuations and precipitates?

Abstract

ABSTRACT In the literature, the volume of a cluster (i.e. a fluctuation of the solid solution or a precipitate) is identified as the volume of a sample of the bulk precipitate phase containing the same number of solute atoms (i.e. of the same size). This approximation is suitable for macroscopic precipitates but is debatable for a rigorous description of microscopic clusters, especially during the nucleation and growth stages. To go beyond this simplification, this work focuses on the notion of ‘exclusion volume’, a volume which accounts for real cluster configurations in a given 3D lattice. The exclusion volume normalised by the cluster size is a complex function of the cluster size, which, like the cluster free energy, evolves during precipitation kinetics and converges toward an asymptote in the long-time limit. Furthermore, this asymptote exhibits a bifurcation which clearly separates fluctuations from precipitates, for a cluster size which is found equal to the minimum value of the critical size for nucleation. With the help of Atomistic Kinetic Monte Carlo (AKMC) simulations, it is shown that the evolution of cluster volume during precipitation can be accurately predicted.