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A fast algorithm to find reduced hyperplane unit cells and solve N-dimensional Bézout's identities.
1Laboratory of Thermo Mechanical Metallurgy (LMTM), PX Group Chair, EPFL, Rue de la Maladière 71b, Neuchâtel, 2000, Switzerland.
Acta Crystallographica. Section A, Foundations and Advances
|September 2, 2021
Summary
This study presents a new method to identify unit cells involved in deformation twinning. This approach aids in understanding crystallographic models by determining specific unit cells attached to crystallographic planes.
Area of Science:
- Crystallography
- Materials Science
- Solid-State Physics
Background:
- Deformation twinning involves simple shear, transforming unit cells on a plane.
- Crystallographic models of twinning necessitate identifying these specific unit cells.
- Higher dimensional crystallography involves hyperplanes.
Purpose of the Study:
- To introduce a novel method for determining unit cells associated with deformation twinning.
- To provide a computational approach for solving problems in higher-dimensional crystallography.
Main Methods:
- The study develops a method to find short unit cells attached to crystallographic planes (or hyperplanes).
- The method is equivalent to solving the N-dimensional Bézout's identity.
Main Results:
- A systematic method for identifying twinning unit cells has been established.
- The approach provides solutions to the N-dimensional Bézout's identity linked to hyperplane Miller indices.
Conclusions:
- The presented method simplifies the determination of unit cells in deformation twinning.
- This work offers a valuable tool for crystallographic modeling and analysis, especially in higher dimensions.
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