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

Abstract

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.

Atomistic investigation of coarsening kinetics of supported nanoparticles using the phase field crystal model

“…31 Moreover, the existence of the moiré pattern also contributes to the decrease of the coarsening rate. 9 Sprodowski et al 5 investigated the decay of supported nano-islands with a lattice mismatch equal to 13% and reported similar conclusions.…”

“…The reduced curvature will decrease the atom density or concentration near the surface, which further reduces the density gradient between the particles and suppress the atom diffusion from small particles to larger ones. 44,45 Secondly, the growth of these particles on the (110) and (100) faces is layer by layer, and the formation of new layers needs to overcome an energy barrier additionally, as discussed by Guo et al 9 As for K (110) > K (100) , this is due to the PSD being wider for the coarsening on the (110) substrate.…”

“…The rotation phenomenon during coarsening has been widely investigated by experimental and numerical methods, 8,16,32 and it is generally believed that the rotation is driven by gradients in interface energy concerning the misorientation. 9 However, as the interface energy is composed of grain boundary energy and phase boundary energy, the properties of grain boundaries and the interaction strength between the substrates and the particles could affect the rotation process; 7,8,32 thus it is hard to reveal the rotation kinetic mechanism for real multi-particle coarsening systems. Herein, we examined the effect of lattice mismatch on the rotation process of supported nanoparticles at the atomic scale.…”

“…[26][27][28][29][30] Recently, Guo and Moats et al 31,32 extended the PFC model to the simulation of the coarsening process of nanocrystals. By adding pinning potentials to the free energy function of the PFC model, our previous work 9 checked the influence of interaction strength on the coarsening of supported nanoparticles. Herein, we further simulated the coarsening of supported particles on substrates with different lattice structures ((111), (110), and (100) of a face-centred cubic crystal), investigated the coarsening kinetics and the atomistic growth mechanism of supported nanoparticles, and examined the influence of lattice mismatch on coarsening.…”

“…Recent atomistic simulation results showed that supported particles with smaller radii or lower misorientations usually rotate faster to a stable state and then inverse growth might occur. 9 As the performance of nanoparticles drops dramatically with size, further studies on the effect of substrates on nanocrystal growth are needed.…”