Rapid Geometric Screening of Low-Energy Surfaces in Crystals
Abstract
:1. Introduction
2. Methods
2.1. A Simple Model of Surface Energy
- There are an infinite number of possible surface directions.
- For a given direction, there are an infinite number of possible locations at which to cut the crystal to make a surface.
2.2. Wulff Construction
- 1.
- The crystal’s Wulff shape , alternatively described by:
- (a)
- The set of facets of , encoded as vectors , (with K as small as possible) defining the convex hull . Note that gives the facet k’s unit normal and gives its surface energy.
- (b)
- The set of vertices of , denoted , .
- 2.
- The full orientation-dependence of the surface energy, encoded as a function of a normal unit vector u.
- 1.
- Construct the convex hull of the points and express it in terms of the minimal number of vectors such that .
- 2.
- Compute the convex hull of the points and express it in terms of the minimal number of vectors such that .
- 3.
- For any given unit vector u, compute .
3. Results
4. Discussion
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
DFT | Density Functional Theory |
ATAT | Alloy Theoretic Automated Toolkit |
FCC | Face-Centered Cubic |
HCP | Hexagonal Close-Packed |
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Liu, H.; van de Walle, A. Rapid Geometric Screening of Low-Energy Surfaces in Crystals. Symmetry 2022, 14, 2067. https://doi.org/10.3390/sym14102067
Liu H, van de Walle A. Rapid Geometric Screening of Low-Energy Surfaces in Crystals. Symmetry. 2022; 14(10):2067. https://doi.org/10.3390/sym14102067
Chicago/Turabian StyleLiu, Helena, and Axel van de Walle. 2022. "Rapid Geometric Screening of Low-Energy Surfaces in Crystals" Symmetry 14, no. 10: 2067. https://doi.org/10.3390/sym14102067
APA StyleLiu, H., & van de Walle, A. (2022). Rapid Geometric Screening of Low-Energy Surfaces in Crystals. Symmetry, 14(10), 2067. https://doi.org/10.3390/sym14102067