Overdamped langevin dynamics simulations of grain boundary motion

Carolina Baruffi,Alphonse Finel,Brigitte Bacroix,Yann Le Bouar,Oguz Umut Salman

doi:10.1186/s41313-019-0016-1

Abstract

Macroscopic properties of structural materials are strongly dependent on their microstructure. However, the modeling of their evolution is a complex task because of the mechanisms involved such as plasticity, recrystallization, and phase transformations, which are common processes taking place in metallic alloys. This complexity led to a growing interest in atomistic simulations formulated without any auxiliary hypotheses beyond the choice of interatomic potential. In this context, we propose here a model based on an overdamped stochastic evolution of particles interacting through inter-atomic forces. The model settles to the correct thermal equilibrium distribution in canonical and grand-canonical ensembles and is used to study the grain boundary migration. Finally, a comparison of our results with those obtained by molecular dynamics shows that our approach reproduces the complex atomic-scale dynamics of grain boundary migration correctly.

Highlights

The increase in manufacturing of small-scale metallic crystalline materials and their usage in the current nanotechnology era calls for a deeper understanding of their mechanical behavior (Shan et al 2008; Wang et al 2014; Chen et al 2014; Zhang et al 2017)
A comparison of our results with those obtained by molecular dynamics shows that our approach reproduces the complex atomic-scale dynamics of grain boundary migration correctly
Atomistic modeling techniques become more and more relevant because they are formulated at the appropriate scale (Mishin et al 2010) and they provide information and data for models formulated at mesoscale, e.g., discrete dislocation dynamics (Bulatov et al 1998; Zepeda-Ruiz et al 2017), phase field methods (Finel et al 2010, 2018; Vuppuluri and Vedantam 2016; Salman et al 2012; Ask et al 2018) and non-linear elastic models (Minami and Onuki 2007; Salman and Truskinovsky 2011; Geslin et al 2014; Salman et al 2019)

Summary

Introduction

The increase in manufacturing of small-scale metallic crystalline materials and their usage in the current nanotechnology era calls for a deeper understanding of their mechanical behavior (Shan et al 2008; Wang et al 2014; Chen et al 2014; Zhang et al 2017). This is at the root of the so-called kinetic Monte Carlo (KMC) method, which consists in following a Markov chain with a catalog of predefined diffusion mechanisms to compute at every time step the escape rate from a local minimum (Bortz et al 1975; Yip 2005) Since this catalog is predefined, the system under study has to be discretized and atomic positions are limited to fixed lattice sites. The overdamped Langevin method proposed below and the ART KMC belong to the same category, as both rely on Markov dynamics applied to atomic positions They should give access to the same time scales.

Presentation of the model

Peq xni

Findings

Overdamped LD simulations of grain boundary migration