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Deriving surface-energy anisotropy for phenomenological phase-field models of solidification
Sami Majaniemi1, Nikolas Provatas
1Department of Materials Science and Engineering, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S-4L7, Canada. majaniem@physics.mcgill.ca
Summary
This study describes solidification in 2D hexagonal crystals using classical density functional theory. Researchers derived an analytic expression for surface energy, linking it to liquid phase properties.
Area of Science:
- Condensed matter physics
- Statistical mechanics
- Materials science
Background:
- Classical density functional theory (DFT) is a powerful tool for studying phase transitions in inhomogeneous systems.
- Understanding solidification in two-dimensional (2D) systems is crucial for designing novel materials and understanding fundamental physical phenomena.
- Hexagonal crystal structures are common in 2D materials and exhibit unique anisotropic properties.
Purpose of the Study:
- To develop a theoretical framework for describing solidification in 2D hexagonal crystals using classical DFT.
- To provide a coarse-graining method that bridges the microscopic DFT description to a macroscopic order parameter.
- To derive an analytic expression for the surface energy and its angular dependence.
Main Methods:
- Utilized the free energy functional of classical density functional theory for an inhomogeneous fluid at coexistence with its solid.
- Developed a coarse-graining formalism to transition from microscopic density variations to a macroscopic order parameter.
- Performed analytical derivations to obtain expressions for surface energy and its anisotropy.
Main Results:
- Successfully described the solidification process in 2D hexagonal crystals.
- Provided a coarse-graining formalism connecting microscopic and macroscopic descriptions.
- Derived an analytic expression for the surface energy, including its angular dependence.
- Established a relationship between the surface energy coefficients and the two-point direct correlation function of the coexisting liquid phase.
Conclusions:
- The developed classical DFT approach accurately describes solidification in 2D hexagonal crystals.
- The coarse-graining method offers a simplified yet effective way to model macroscopic solidification phenomena.
- The derived analytic expression for surface energy provides valuable insights into the anisotropic behavior of 2D crystals and their interfacial properties.
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