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

Abstract

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 newly added term is explored in two-dimensional triangular and honeycomb structures as well as bcc and fcc lattices in three dimensions. In addition, a finite element method (FEM) is developed for the model that incorporates a mesh refinement scheme. The combination of the 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.

14 pages, 9 figures

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• Defects at grain boundaries: A coarse-grained, three-dimensional description by the amplitude expansion of the phase-field crystal model
• Mesoscale Defect Motion in Binary Systems: Effects of Compositional Strain and Cottrell Atmospheres
• An efficient numerical framework for the amplitude expansion of the phase-field crystal model
• 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
• Grain extraction and microstructural analysis method for two-dimensional poly and quasicrystalline solids
• Hybrid-PFC: coupling the phase-field crystal model and its amplitude-equation formulation