Atomic-scale investigation of coarsening kinetics by the phase-field crystal model

Abstract

Coarsening is a common physical process that occurs in polydisperse two-phase mixture systems, which had been widely studied for decades. However, accurate prediction of the volume fraction dependence of the diffusion-controlled coarsening kinetic process is still very difficult. In this work, by using the atomic-scale phase-field crystal model, we investigated the coarsening kinetics of crystalline nanoparticles in the semi-solid region. The results showed that the details of the atomic-scale nature of particles do not affect the kinetics of coarsening for low solid volume fractions and the coarsening process of the nanoparticles is in agreement with the classical coarsening theory. While, for high solid volume fractions, our simulation results show that the coarsening rates of crystalline particles decrease with the solid volume fraction, which runs counter to the theoretical models based on mean-field theories. By checking the competitive growth process of all the particles, we found the appearance of grain rotation and volume diffusion mechanisms leads to the failure of the classical coarsening models.

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

“…The grain rotation phenomenon during coarsening has been reported widely by experimental and numerical investigations, and it is generally believed that the rotations are driven by gradients in the grain boundary energy with respect to the misorientation. However, as the rotations are often influenced by many factors, such as the volume fractions of particles, the property of neighboring particles, the structure of grain boundaries, the substrates, and so forth, ,, it is a daunting task to reveal the rotation kinetic mechanism for real coarsening systems. In this work, the rotation process of nanoparticles on fcc (111) surface substrates was checked by the phase-field crystal model.…”

“…Comparing the parallel runs with different initial conditions (particle position and lattice orientation), for f = 0.2 and σ = 0.2, the initial particle distribution does not affect the atomistic mechanisms and the kinetic process of the coarsening of nanoparticles. As for high volume fraction conditions, the rotation of the particles could be affected by the neighbor particles 14 and the substrates 19 both, and the atomistic mechanism of coarsening would be different for different initial conditions.…”

“…Therefore, a deep understanding of the coarsening kinetics of nanoparticles on substrates is of great fundamental and critical importance for controlling the material properties. The current model to describe the coarsening kinetics is based on the classical work of Lifshitz and Slyozov and Wagner which is known as the LSW theory; however, it cannot quantitatively describe the coarsening process of nanoparticles because the model ignores the effect of the crystallographic characteristics of the particles. , During the past decade, the coarsening of nanoparticles on substrates was widely investigated by scanning tunneling microscopy, transmission electron microscopy, , scanning transmission electron microscopy, and atomic resolution transmission electron microscopy . However, observing the coarsening process in situ on an atomic scale is still very difficult, and the atomistic coarsening mechanism of nanoparticles on substrates remains largely unknown.…”

“…The PFC model is a simplified classical density functional theory; as all higher-order gradient terms in this model are omitted, the PFC model allows the modeling of material systems with atomic-scale spatial resolution, while diffusive timescales examine complex dynamical processes. The PFC model has been successfully used in the study of crystal nucleation, growth, − and Ostwald ripening with different volume fractions. , Here, we simulate the coarsening process of multiparticle systems on the (111) surface of face-centered cubic (fcc) by a modified PFC model, examine the strength of the interaction between the substrate and the nanoparticles on the coarsening kinetics, and provide dynamic imaging of the nanoparticle coarsening process at the atomic scale.…”

“…The PFC model has been successfully used in the study of crystal nucleation, growth, 24−26 and Ostwald ripening with different volume fractions. 14,27 Here, we simulate the coarsening process of multiparticle systems on the (111) surface of face-centered cubic (fcc) by a modified PFC model, examine the strength of the interaction between the substrate and the nanoparticles on the coarsening kinetics, and provide dynamic imaging of the nanoparticle coarsening process at the atomic scale.…”