Interface Mobility from Interface Random Walk

Abstract

Computational studies aimed at extracting interface mobilities require driving forces orders of magnitude higher than those occurring experimentally. We present a computational methodology that extracts the absolute interface mobility in the zero driving force limit by monitoring the one-dimensional random walk of the mean interface position along the interface normal. The method exploits a fluctuation-dissipation relation similar to the Stokes-Einstein relation, which relates the diffusion coefficient of this Brownian-like random walk to the interface mobility. Atomic-scale simulations of grain boundaries in model crystalline systems validate the theoretical predictions and highlight the profound effect of impurities. The generality of this technique, combined with its inherent spatiotemporal efficiency, should allow computational studies to effectively complement experiments in understanding interface kinetics in diverse material systems.

Directional grain growth from anisotropic kinetic roughening of grain boundaries in sheared colloidal crystals

“…Polycrystals are pervasive as engineering materials and elucidating mechanisms that determine the structure and dynamics of their GBs continue to be a central goal of materials research (9). Advances in computer simulation methods (2,10,11) and experiments (12,13) have provided substantial insights into the microscopic origins of these mechanisms. In conventional materials, nevertheless, establishing a direct link between the dynamics at the single/few atom length scale and the collective behavior of the many thousands of atoms that constitute GBs and grains poses a serious challenge (14).…”

“…Despite its technological relevance, the implications of kinetic roughening for GB mobility and grain growth remain poorly understood. Although molecular dynamics simulations can model atomistic phenomena realistically, they often are limited to small system sizes (19) and short time scales (11), which may influence measurements of GB roughness (15) and predictions of grain growth laws (2,20). Kinetic Monte Carlo simulations (21) and phase field models (22) are insensitive to microscopic details.…”

Colloidal Crystallization in 2D for Short-Ranged Attractions: A Descriptive Overview

“…At the particle level, it was observed a glassy type dynamics of the particles confined in the grain boundaries, due to transient caging of them by their nearest neighbors [59,60]. It has been seen, both by simulations [61] and experiments [62], how a grain boundary diffuses back and forth on a direction roughly perpendicular to the boundary, as if performing a one-dimensional random walk, although it was observed for short periods of time.…”

“…This mathematical development was validated with moleclular dynamics (MD) simulations of an initially flat grain boundary, with an attractive potential between the particles, and it was observed that the average interface position <h(t)> maintains a normal (Gaussian) distribution within each time interval considered [61]. It should be said, however, that their simulations were very short-what the MD simulations permitted-and lasted on the order of a few hundreds of picoseconds, corresponding to a movement of the mean interface position by several interatomic distances only.…”

“…Among the dynamical processes performed by a whole GB (i.e., the colective behavior of the particles that constitute the GB) that have been advanced, in the absence of an applied strain as in our case, that is, in the zero driving force limit [57,58,61,62,98], a one-dimensional random walk perpendicular to the GB has been highlighted by several researchers [57,61,62]. In their 3D computer simulations, Trautt et al [61] were able to relate the interface mobility to the diffusion coefficient of this one-dimensional random walk, by exploiting a fluctuation-dissipation relation similar to the Stokes-Einstein relation. Starting with a planar interface perpendicular to the z direction and denoting the interface height profile as h(r,t), where r = (x, y) is restricted to the interfacial plane, and by averaging over the x and y coordinates they obtain a mean square displacement on the z direction as < h 2 >= D t, with the diffusion coefficient…”