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

Area of Science:

• Materials Science
• Computational Physics
• Crystallography

Background:

• Highly anisotropic interfaces are crucial for material microstructure development.
• Quantitative modeling of these interfaces is essential for materials design.

Purpose of the Study:

• To assess the phase-field crystal (PFC) formalism's capability in quantitatively describing highly anisotropic interfaces.
• To coarse grain the PFC model into its complex amplitude and phase-field limits.

Main Methods:

• Utilized the diffusive atomistic phase-field crystal (PFC) formalism.
• Coarse-grained the PFC model to obtain complex amplitude and phase-field formulations.
• Performed one-dimensional calculations to determine surface energy and Wulff shape properties.
• Extended the model to two dimensions to study crystal growth.

Main Results:

• The phase-field limit of the PFC model accurately describes anisotropic surface properties dependent on crystal orientation.
• The model predicts Wulff shapes with missing orientations and facet formation.
• Demonstrated the model's capability to study crystal growth with varying anisotropy in 2D.

Conclusions:

• The coarse-grained PFC model provides a self-consistent description of highly anisotropic surface properties.
• The phase-field limit naturally incorporates regularization and describes missing orientations in equilibrium crystal shapes.
• The developed model is suitable for studying anisotropic crystal growth.