Morphological Instability of Grain Boundaries in Two-Phase Coherent Solids

Geslin, Pierre-Antoine; Yi, Xu

doi:10.1103/physrevlett.114.105501

Cited by 13 publications

(32 citation statements)

References 46 publications

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“…This work paves further the way to detailed investigations of 3D systems by APFC including also other physical contributions already shown to be correctly modeled by this approach in 2D such as binary systems [33,34] or the presence of both GBs and compositional domains [30,31]. Further work will be devoted to the optimization of the numerical approach in order to provide even more efficient calculations to enable simulations of grain growth in polycrystalline materials, similar to Ref.…”

Section: Discussionmentioning

confidence: 74%

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

Salvalaglio

Backofen

Elder

et al. 2018

Phys. Rev. Materials

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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. arXiv:1803.03233v2 [cond-mat.mtrl-sci]

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Section: Discussionmentioning

confidence: 74%

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

Salvalaglio

Backofen

Elder

et al. 2018

Phys. Rev. Materials

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“…For instance, it would be interesting to examine the tuning of defects energies and interfaces in binary systems as in Refs. [20,26] or at GBs when compositional domains are also present [24,25].…”

Section: Conclusion and Remarksmentioning

confidence: 99%

“…The method has also been extended to binary systems [20][21][22]. Moreover, it has been used to examine the influence of compositional strains on interfaces [23], heteroepitaxy in binary systems [20,21] and the elastically induced interaction of GBs and compositional interfaces [24,25]. While the original APFC model was introduced for two-dimensional systems with triangular symmetry the method has been extended to fcc and bcc systems in three dimensions [20,26] and honeycomb lattices in two dimensions [16,19].…”

Section: Introductionmentioning

confidence: 99%

Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model

et al. 2017

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One of the major difficulties in employing phase field crystal (PFC) modeling and the associated amplitude (APFC) formulation is the ability to tune model parameters to match experimental quantities. In this work we address the problem of tuning the defect core and interface energies in the APFC formulation. We show that the addition of a single term to the free energy functional can be used to increase the solid-liquid interface and defect energies in a well-controlled fashion, without any major change to other features. The influence of the new term is explored in 2D triangular and honeycomb structures as well as bcc and fcc lattices in 3D. In addition, a Finite Element Method (FEM) is developed for the model that incorporates a mesh refinement scheme. The combination of FEM and mesh refinement to simulate amplitude expansion with a new energy term provides a method of controlling microscopic features such as defect and interface energies while simultaneously delivering a coarse-grained examination of the system.

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“…The concentrations at which this mode is unstable lay between the classical (chemical) spinodal and the spinodal modified by elastic effects (coherent spinodal). This type of localized instabilities seem to underly a number of fundamental processes such as the stability of grain boundaries in phase-separating systems that is currently receiving much attention [15,53], where an understanding of localized instabilities in the presence of coherency strain is of capital importance.…”

Section: Introductionmentioning

confidence: 99%

Localized instabilities and spinodal decomposition in driven systems in the presence of elasticity

Meca¹,

Münch²,

Wagner³

2018

Phys. Rev. E

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We study numerically and analytically the instabilities associated with phase separation in a solid layer on which an external material flux is imposed. The first instability is localized within a boundary layer at the exposed free surface by a process akin to spinodal decomposition. In the limiting static case, when there is no material flux, the coherent spinodal decomposition is recovered. In the present problem stability analysis of the time-dependent and non-uniform base states as well as numerical simulations of the full governing equations are used to establish the dependence of the wavelength and onset of the instability on parameter settings and its transient nature as the patterns eventually coarsen into a flat moving front. The second instability is related to the MullinsSekerka instability in the presence of elasticity and arises at the moving front between the two phases when the flux is reversed. Stability analyses of the full model and the corresponding sharp-interface model are carried out and compared. Our results demonstrate how interface and bulk instabilities can be analysed within the same framework which allows to identify and distinguish each of them clearly. The relevance for a detailed understanding of both instabilities and their interconnections in a realistic setting are demonstrated for a system of equations modelling the lithiation/delithiation processes within the context of Lithium ion batteries.

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Morphological Instability of Grain Boundaries in Two-Phase Coherent Solids

Cited by 13 publications

References 46 publications

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

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

Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model

Localized instabilities and spinodal decomposition in driven systems in the presence of elasticity

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