TY - JOUR
T1 - Self-consistent modeling of anisotropic interfaces and missing orientations
T2 - Derivation from phase-field crystal
AU - Ofori-Opoku, N.
AU - Warren, J. A.
AU - Voorhees, P. W.
N1 - Funding Information:
We acknowledge the following financial assistance Award No. 70NANB14H012 from the U. S. Department of Commerce, National Institute of Standards and Technology (NIST) as part of the Center for Hierarchical Materials Design (CHiMaD). This research was supported in part through the computational resources and staff contributions provided for the Quest high performance computing facility at Northwestern University which is jointly supported by the Office of the Provost, the Office for Research, and Northwestern University Information Technology, and the resources at the NIST Center for Theoretical and Computational Materials Science (CTCMS).
Publisher Copyright:
© 2018 American Physical Society. US.
PY - 2018/8/20
Y1 - 2018/8/20
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevMaterials.2.083404
DO - 10.1103/PhysRevMaterials.2.083404
M3 - Article
AN - SCOPUS:85059621255
VL - 2
JO - Physical Review Materials
JF - Physical Review Materials
SN - 2475-9953
IS - 8
M1 - 083404
ER -