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Space fullerenes: a computer search for new Frank-Kasper structures.
Mathieu Dutour Sikirić1, Olaf Delgado-Friedrichs, Michel Deza
1Rudjer Bosković Institute, Bijenicka 54, 10 000 Zagreb, Croatia. mdsikir@irb.hr
A new computational method identified 84 Frank-Kasper structures, advancing the understanding of these complex geometric tilings found in materials science. This research compares these novel findings with existing crystallographic data.
Area of Science:
- Crystallography
- Computational Geometry
- Materials Science
Background:
- Frank-Kasper structures are 3-periodic Euclidean tilings by tetrahedra.
- These structures are crucial in understanding metallic alloys and clathrates.
- Vertex figures in Frank-Kasper structures exhibit specific face counts (20, 24, 26, 28).
Purpose of the Study:
- To develop a novel computer enumeration method for Frank-Kasper structures.
- To generate and analyze Frank-Kasper structures within a reduced fundamental domain.
- To compare newly generated structures with known physical and constructed examples.
Main Methods:
- Employed a new computer enumeration technique.
- Focused on obtaining structures with up to 20 cells.
- Utilized a reduced fundamental domain for efficiency.
Main Results:
- Successfully enumerated 84 new Frank-Kasper structures.
- Compared these 84 structures against 27 known physical structures.
- Validated findings against established special constructions (e.g., Frank-Kasper-Sullivan).
Conclusions:
- The new enumeration method is effective for discovering Frank-Kasper structures.
- The study expands the known catalog of Frank-Kasper structures.
- Provides a basis for further crystallographic and materials science research.
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