Hard tetrahedron model
The hard tetrahedron model. Such a structure has been put forward as a potential model for water[1].
Maximum packing fraction
It has recently been shown that regular tetrahedra are able to achieve packing fractions as high as [2] (the hard sphere packing fraction is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \pi/(3 \sqrt{2}) \approx 74.048%} [3]). This is in stark contrast to work as recent as in 2006, where it was suggested that the "...regular tetrahedron might even be the convex body having the smallest possible packing density"[4].
Phase diagram
Truncated tetrahedra
Dimers composed of Archimedean Truncated Tetrahedra [6] are able to achieve packing fractions as high as Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \phi= 207/208 \approx 0.9951923} [7] while a Nonregular Truncated Tetrahedra can completely even tile space.[8]
References
- ↑ Jiri Kolafa and Ivo Nezbeda "The hard tetrahedron fluid: a model for the structure of water?", Molecular Physics 84 pp. 421-434 (1995)
- ↑ Amir Haji-Akbari, Michael Engel, Aaron S. Keys, Xiaoyu Zheng, Rolfe G. Petschek, Peter Palffy-Muhoray and Sharon C. Glotzer "Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra", Nature 462 pp. 773-777 (2009)
- ↑ Neil J. A. Sloane "Kepler's conjecture confirmed", Nature 395 pp. 435-436 (1998)
- ↑ J. H. Conway and S. Torquato "Packing, tiling, and covering with tetrahedra", Proceedings of the National Academy of Sciences of the United States of America 103 10612-10617 (2006)
- ↑ Amir Haji-Akbari, Michael Engel, and Sharon C. Glotzer "Phase diagram of hard tetrahedra", Journal of Chemical Physics 135 194101 (2011)
- ↑ Joost de Graaf, René van Roij, and Marjolein Dijkstra "Dense Regular Packings of Irregular Nonconvex Particles", Physical Review Letters 107 155501 (2011)
- ↑ Yang Jiao and Salvatore Torquato "A packing of truncated tetrahedra that nearly fills all of space and its melting properties", Journal of Chemical Physics 135 151101 (2011)
- ↑ Pablo F. Damasceno, Michael Engel and Sharon C. Glotzer "Crystalline Assemblies and Densest Packings of a Family of Truncated Tetrahedra and the Role of Directional Entropic Forces", ACS Nano 6 1 (2012)
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