An efficient numerical framework for the amplitude expansion of the phase-field crystal model

Abstract

The study of polycrystalline materials requires theoretical and computational techniques enabling multiscale investigations. The amplitude expansion of the phase field crystal model (APFC) allows for describing crystal lattice properties on diffusive timescales by focusing on continuous fields varying on length scales larger than the atomic spacing. Thus, it allows for the simulation of large systems still retaining details of the crystal lattice. Fostered by the applications of this approach, we present here an efficient numerical framework to solve its equations. In particular, we consider a real space approach exploiting the finite element method. An optimized preconditioner is developed in order to improve the convergence of the linear solver. Moreover, a mesh adaptivity criterion based on the local rotation of the polycrystal is used. This results in an unprecedented capability of simulating large, three-dimensional systems including the dynamical description of the microstructures in polycrystalline materials together with their dislocation networks.

12 pages, 7 figures

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Cited by in corpus (13)

• A coarse-grained phase-field crystal model of plastic motion
• Closing the gap between atomic-scale lattice deformations and continuum elasticity
• Coarse-grained modeling of crystals by the amplitude expansion of the phase-field crystal model: an overview
• Disconnection-Mediated Migration of Interfaces in Microstructures: II. diffuse interface simulations
• Mesoscale Defect Motion in Binary Systems: Effects of Compositional Strain and Cottrell Atmospheres
• Field Dislocation Mechanics and Phase Field Crystal models
• A unified field theory of topological defects and non-linear local excitations
• The elastic inclusion problem in the (amplitude) phase field crystal model
• Amplitude expansion of the phase-field crystal model for complex crystal structures
• Magnetic APFC modeling and the influence of magneto-structural interactions on grain shrinkage
• Hybrid-PFC: coupling the phase-field crystal model and its amplitude-equation formulation
• Mesoscale Field Theory for Quasicrystals
• Mesoscale modeling of deformations and defects in thin crystalline sheets