[Paper Review] Coupled motion of asymmetrical tilt grain boundaries: molecular dynamics and phase field crystal simulations

Zachary Trautt, Ari Adland+2 more|arXiv (Cornell University)|Jun 15, 2012

Microstructure and mechanical properties39 references3 citations

TL;DR

This study investigates stress-driven motion of asymmetrical tilt grain boundaries using molecular dynamics (MD) and phase field crystal (PFC) simulations, revealing that coupling to shear stress is widespread and exhibits a non-trivial dependence on misorientation and inclination angles. The key finding is a discontinuous sign change in the coupling factor β near a transition region, leading to divergent β values and sliding-like behavior, with distinct coupling modes governed by crystallographic symmetry and dislocation dynamics.

ABSTRACT

Previous simulation and experimental studies have shown that some grain boundaries (GBs) can couple to applied shear stresses and be moved by them, producing shear deformation of the lattice traversed by their motion. While this coupling effect has been well confirmed for symmetrical tilt GBs, little is known about the coupling ability of asymmetrical boundaries. In this work we apply a combination of molecular dynamics and phase field crystal simulations to investigate stress-driven motion of asymmetrical GBs between cubic crystals over the entire range of inclination angles. Our main findings are that the coupling effect exists for most of the asymmetrical GBs and that the coupling factor exhibits a non-trivial dependence on both the misorientation and inclination angles. This dependence is characterized by a discontinuous change of sign of the coupling factor, which reflects a transition between two different coupling modes over a narrow range of angles. Importantly, the magnitude of the coupling factor becomes large or divergent within this transition region, thereby giving rise to a sliding-like behavior. Our results are interpreted in terms of a diagram presenting the domains of existence of the two coupling modes and the transition region between them in the plane of misorientation and inclination angles. The simulations reveal some of the dislocation mechanisms responsible for the motion of asymmetrical tilt GBs. The results of this study compare favorably with existing experimental measurements and provide a theoretical ground for the design of future experiments.

Motivation & Objective

• To investigate the coupling behavior of asymmetrical tilt grain boundaries to applied shear stresses, which remains poorly understood despite known coupling in symmetrical boundaries.
• To determine how the coupling factor β depends on misorientation and inclination angles across the full range of boundary configurations.
• To identify the underlying dislocation mechanisms enabling coupled motion in asymmetrical boundaries, especially where dislocations on intersecting slip planes may impede motion.
• To compare MD and PFC simulation results to assess consistency in predicting coupling behavior and to validate the models against experimental data.
• To provide a theoretical framework for designing future experiments on stress-driven grain boundary motion in polycrystalline materials.

Proposed method

• Molecular dynamics (MD) simulations were performed on FCC Cu and Al to study atomic-scale mechanisms of stress-driven grain boundary motion at varying temperatures and applied shear stresses.
• Phase field crystal (PFC) simulations were used to model grain boundary dynamics over longer timescales, incorporating diffusive processes such as dislocation climb.
• The coupling factor β = v|| / v_n was computed from the ratio of tangential grain translation velocity to normal grain boundary velocity to quantify shear coupling.
• The simulations systematically varied both misorientation angle θ and inclination angle φ to map the dependence of β across the full parameter space of asymmetrical tilt boundaries.
• Dislocation structures and reactions were analyzed in MD to identify mechanisms such as dislocation reactions and avoidance that enable motion despite intersecting slip planes.
• The results from MD and PFC were compared to assess consistency in predicting the sign, magnitude, and angular dependence of β, particularly near transition regions.

Experimental results

Research questions

• RQ1 Does the coupling effect persist for asymmetrical tilt grain boundaries across the full range of misorientation and inclination angles?
• RQ2 How does the coupling factor β depend on the inclination angle φ and misorientation angle θ, and what causes its non-trivial angular dependence?
• RQ3 What are the dominant dislocation mechanisms responsible for coupled motion in asymmetrical boundaries, especially when dislocations on intersecting planes may block each other?
• RQ4 Why does β exhibit a discontinuous sign change between positive and negative values, and what physical mechanism underlies the divergent β values near this transition?
• RQ5 To what extent do MD and PFC simulations yield consistent predictions for β, and how do they compare with experimental measurements?

Key findings

• The coupling effect exists for most asymmetrical tilt grain boundaries, with β values varying significantly with both misorientation and inclination angles.
• A discontinuous sign change in β occurs over a narrow range of inclination angles, marking a transition between two distinct coupling modes.
• The magnitude of β becomes large or divergent near the transition region, leading to sliding-like behavior of the grain boundary.
• The regions of positive and negative β are bounded by a transition line in the θ–φ parameter space, with shapes consistent with crystallographic symmetry and Peierls barrier differences.
• MD simulations reveal that dislocation reactions and avoidance mechanisms enable motion despite intersecting slip planes, while PFC simulations show that dislocation climb facilitates collective motion and avoids locking.
• The simulation results from both MD and PFC methods show strikingly similar qualitative and quantitative trends in β’s dependence on angle, validating the findings across different modeling approaches.