Effect of noise-induced nucleation on grain size distribution studied via the phase-field crystal method

Abstract

We contribute to the more detailed understanding of the phase-field crystal model recently developed by Elder et al (2002 Phys. Rev. Lett. 88 245701), by focusing on its noise term and examining its impact on the nucleation rate in a homogeneously solidifying system as well as on successively developing grain size distributions. In this context we show that principally the grain size decreases with increasing noise amplitude, resulting in both a smaller average grain size and a decreased maximum grain size. Despite this general tendency, which we interpret based on Panfilis and Filiponi (2000 J. Appl. Phys. 88 562), we can identify two different regimes in which nucleation and successive initial growth are governed by quite different mechanisms.

Effect of noise on ordering of hexagonal grains in a phase-field-crystal model

“…It seems likely that this is a time range of observation reported in Ref. [11]. At the later times, by contrast, the coarsening dynamics have sped up, and we have in fact found that a higher value of ζ results in a configuration with a larger average domain size.…”

“…In this paper, we will focus exclusively on the case where η is conserved, which is of particular interest in relation to the recent simulation result [11]. We note in passing that the previous work [2,9,10] referred to in the Introduction all focused on the nonconserved version of Eq.…”

“…This is attributed to the fact that noise can provide a source of depinning for topological defects, the interaction of which is known to predominantly drive the coarsening process [7]. Since there is no obvious reason that this constructive effect of * Corresponding author: shiway@kit.ac.jp noise would not occur in the ordering of hexagonal domains, the recent claim [11] to the contrary is disturbing. In this paper, we dispute this claim since we observe similar slowing of the coarsening with increasing noise strength in our grain growth simulations, but with a subsequent crossover to the speeding-up behavior at late times.…”

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

“…-dendrites [26][27][28][29][30] -eutectics [26,28,29,31] -homogeneous nucleation [28,[30][31][32][33]] -heterogeneous nucleation [30,31,34,35] -grain-boundary melting [36,37] -fractal growth [38,39] -crystal anisotropy [33,38,[40][41][42][43][44]] -density/solute trapping [38,39,45] -glass formation [35,46,47] -surface alloying [48,49] Colloid patterning [33] Grain-boundary dynamics [50] Crack propagation [50] Elasticity, plasticity, dislocation dynamics [12,[50][51][52][53][54] Kirkendall effect [55] Vacancy transport [56] Liquid phase separation with colloid accumulation at phase boundaries …”

Nucleation, growth, and coarsening of crystalline domains in order-order transitions between lamellar and hexagonal phases

“…For example, in the growth of domains of lamellae from random initial conditions, the addition of a small amount of noise is consistently shown to increase the growth exponent and leads to enhanced pattern orientation with increasing noise strength [43]. In a recent paper [44], an additive noise effect in the disorder-to-hexagonal pattern formation has been studied by simulations of Eq. (10).…”