Self-consistent modeling of anisotropic interfaces and missing orientations: Derivation from phase-field crystal

Abstract

Highly anisotropic interfaces play an important role in the development of material microstructure. Using the diffusive atomistic phase-field crystal (PFC) formalism, we determine the capability of the model to quantitatively describe these interfaces. Specifically, we coarse grain the PFC model to attain both its complex amplitude formulation and its corresponding phase-field limit. Using this latter formulation, in one-dimensional calculations, we determine the surface energy and the properties of the Wulff shape. We find that the model can yield Wulff shapes with missing orientations, the transition to missing orientations, and facet formation. We show that the corresponding phase-field limit of the complex amplitude model yields a self-consistent description of highly anisotropic surface properties that are a function of the surface orientation with respect to the underlying crystal lattice. The phase-field model is also capable of describing missing orientations on equilibrium shapes of crystals and naturally includes a regularizing contribution. We demonstrate, in two dimensions, how the resultant model can be used to study growth of crystals with varying degrees of anisotropy in the phase-field limit.

arXiv comment40 pages, 9 Figures, Submitted to Physical Review Materials

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Cited by in corpus (6)

• 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
• An efficient numerical framework for the amplitude expansion of the phase-field crystal model
• Hybrid-PFC: coupling the phase-field crystal model and its amplitude-equation formulation
• A Non-Isothermal Phase-Field Crystal Model with Lattice Expansion: Analysis and Benchmarks
• Explicit temperature coupling in phase-field crystal models of solidification