Modelling of grain boundary dynamics using amplitude equations

Abstract

We discuss the modelling of grain boundary dynamics within an amplitude equations description, which is derived from classical density functional theory or the phase field crystal model. The relation between the conditions for periodicity of the system and coincidence site lattices at grain boundaries is investigated. Within the amplitude equations framework, we recover predictions of the geometrical model by Cahn and Taylor for coupled grain boundary motion, and find both 100 and 110 coupling. No spontaneous transition between these modes occurs due to restrictions related to the rotational invariance of the amplitude equations. Grain rotation due to coupled motion is also in agreement with theoretical predictions. Whereas linear elasticity is correctly captured by the amplitude equations model, open questions remain for the case of nonlinear deformations.

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

“…In addition, by means of η j 's it is also possible to compute a scalar order parameter (referred to as A 2 in the following) that is maximum within the crystal, decreases at defects and at crystal-melt or ordered-disordered interfaces, and vanishes for disordered-liquid phases, so that it can be thought of as being related to the order parameter that enters standard phase-field approaches. Although the APFC approach does not provide an accurate description of the atomic rearrangement at dislocation cores, it is known to give good coarse-grained approximations of PFC for small deformations or tilts and has been already adopted to investigate GBs in two dimensions [24,[30][31][32]. Moreover, the original model has been extended to binary systems and to body-centered cubic (bcc) and face-centered cubic (fcc) symmetries [33,34].…”

Nonlinear elastic effects in phase field crystal and amplitude equations: Comparison toab initiosimulations of bcc metals and graphene

“…One of the advantages of the PFC model is that it automatically contains elasticity, as a deformation of the lattice, expressed through a change of the lattice constant, raises the energy. For small deformations this energy change is quadratic, hence linear elasticity is captured, and for larger deformations non-linear effects appear 9,10 . Whereas the original PFC model is fully phenomenological, later extensions have shown that it can be linked to the classical density functional theory of freezing [11][12][13] , which allows to determine the model parameters from fundamental physical quantities, which can for example be determined from molecular dynamics simulations [14][15][16][17] .…”

Snaking without subcriticality: grain boundaries as non-topological defects

“…In the materials science context these results show that in this parameter regime grain shrinkage is a thermally activated process. Note that PFC models have previously been applied to study grain rotation (Radhakrishnan et al, 2012;Hüter et al, 2017) and also other, more complex grain boundary and defect dynamics that occur, for example, when a material is sheared (Chan et al, 2010). Our results identify the parameter regime where grains in a polycrystalline material are dynamically stable and so identifies the regime in which grain rotation is an activated process.…”