Defects at grain boundaries: A coarse-grained, three-dimensional description by the amplitude expansion of the phase-field crystal model

TL;DR

This paper presents a three-dimensional, coarse-grained model based on the amplitude expansion of the phase-field crystal framework to describe dislocation networks at grain boundaries, applicable to different crystal symmetries and rotation axes.

Contribution

It introduces a versatile, multiscale modeling approach for grain boundary defects that captures microscopic dislocation features and large-scale defect evolution.

Findings

Dislocation networks at grain boundaries can be effectively modeled using the amplitude expansion approach.

The model's results align with classical grain growth theories and atomistic simulations.

New insights into fcc lattice symmetry grain boundary behavior are provided.

Abstract

We address a three-dimensional, coarse-grained description of dislocation networks at grain boundaries between rotated crystals. The so-called amplitude expansion of the phase-field crystal model is exploited with the aid of finite element method calculations. This approach allows for the description of microscopic features, such as dislocations, while simultaneously being able to describe length scales that are orders of magnitude larger than the lattice spacing. Moreover, it allows for the direct description of extended defects by means of a scalar order parameter. The versatility of this framework is shown by considering both fcc and bcc lattice symmetries and different rotation axes. First, the specific case of planar, twist grain boundaries is illustrated. The details of the method are reported and the consistency of the results with literature is discussed. Then, the dislocation networks forming at the interface between a spherical, rotated crystal embedded in an unrotated crystalline structure, are shown. Although explicitly accounting for dislocations which lead to an anisotropic shrinkage of the rotated grain, the extension of the spherical grain boundary is found to decrease linearly over time in agreement with the classical theory of grain growth and recent atomistic investigations. It is shown that the results obtained for a system with bcc symmetry agree very well with existing results, validating the methodology. Furthermore, fully original results are shown for fcc lattice symmetry, revealing the generality of the reported observations.