Kinetic Monte Carlo simulation of the effective diffusivity in grain boundary networks

Abstract

The effective diffusivity in grain boundary networks of polycrystalline materials is evaluated using a kinetic Monte Carlo model. This model connects the atomic hopping processes with the coarse-grained diffusion so that the macroscopic simulations can be conducted without the need to resolve atomic details. The effects of various properties of the grain boundary network on the effective diffusivity have been examined, including grain size, two-vs. three-dimensional networks, and distribution of grain boundary diffusivities. It is shown that the effective diffusivity does not depend on the grain size when grain boundary diffusion is the dominant diffusion mechanism in a polycrystalline sample. We find that the behavior of the effective diffusivity is qualitatively the same for two-and three-dimensional models, except that the percolation threshold and the critical exponents need to be changed accordingly when using empirical functions to characterize the effective diffusivity. In addition, we find that the effective diffusivity exhibits large fluctuations due to its dependence on the grain boundary distributions, and therefore the details of the materials microstructure can significantly impact the effective diffusivity in a specific finite-size sample. Finally, we check the applicable range of the effective medium theory and discuss the effects of modeling different grain boundary types with varying diffusivities using just two vs. many types.

Small-Angle Twist Grain Boundaries as Sinks for Point Defects

“…The time of interstitials diffusion along dislocation grid to reach edges of GBs is denoted as t sink and it has the units of seconds. To determine t sink , we employ a similar strategy for coarse grained modeling of GBs as implemented in ref 36 . First of all, we use the nudged elastic band (NEB) method 37 to obtain the energy landscape for interstitials diffusion along a dislocation lines between two intersections of dislocations.…”

Grain boundary diffusion of Ag through polycrystalline SiC in TRISO fuel particles

“…However, it has been demonstrated in Ref. [32] that with the appropriate hopping rate, the kMC model with coarse-grained hops yields the same effective diffusivity as a model with atomic resolution. Thirdly, the difference between the diffusion of Ag along GB junctions and within GB planes is ignored here.…”

“…It is emphasized here that although the diffusivity ratio in our model can be as large as 10 2 or 10 3 , it does not mean that the effective diffusivity D eff will vary 2 or 3 orders of magnitude. The actual fluctuation of D eff , which is one of the main interests of this study, remains to be examined because D eff is not only dependent on D L and D H , but it is also affected by f H , as well as by the connectivity of GBs [32,37]. We note that by fitting the values of diffusivities to release data from Refs.…”

“…The present study focuses on GB diffusion of Ag in the SiC layer and aims to test two hypotheses: (i) the variation in GB structures may be the origin of some or all of the scatter in diffusivity and release fraction of Ag in TRISO fuel particles; (ii) GB diffusion in polycrystalline SiC is fast enough to explain experimentally observed Ag release. To test these hypotheses, we use our recently developed kinetic Monte Carlo (kMC) model [32] for diffusion through polycrystalline materials and calculate the effective diffusivity of Ag in heterogeneous GB networks in SiC. The model is also further extended to evaluate the release fraction of Ag in fuel particles with time-dependent generation of Ag.…”

Hydrogen diffusion and hydride formation in grain boundary rich magnesium

“…They found that the movement does not change the diffusion speed in regime C. This is not true for Regime B, where the penetration depth is lower for a moving grain boundary [174]. Deng et al studied the diffusion in Regime C for more than one type of grain boundary [175]. They studied how grain boundaries with fast and slow diffusion lead to an effective diffusion coefficient of the overall grain boundary network (the effective diffusion coefficient should not be confused with D ef f in Regime A).…”