Coarsening Process of Nanoparticles on Substrates by the Phase-Field Crystal Model

A deep understanding of the coarsening kinetics of nanoparticles on substrates is of great fundamental and critical importance for controlling the material properties. However, in situ observation of the coarsening process at the atomic scale is still very difficult, and the influence of the substrate on coarsening kinetics remains largely unknown. In this work, by using an atomic-scale phase-field crystal model, we investigated the coarsening kinetics of nanoparticles on fcc (111) surface substrates. The results showed that the number of steps and local curvature near the particle surface increase with the pinning potential of substrates, leading to an increase in the coarsening rate. By examining the particles' atomic configurations during coarsening, we find that the particles rotate with time and the speed of rotation is influenced by the particle radius and the initial misorientations. In addition, we observe inverse coarsening behavior in the initial state of coarsening. We find that the particles with smaller radii or lower misorientations rotate faster to the stable state and then grow continuously at the expense of the surrounding particles. Our simulations in this work provide dynamic imaging of the coarsening process of nanoparticles on the substrates and show that crystalline characteristics or atomic scale nature have significant influences on the coarsening kinetics.