Hard tetrahedron model: Difference between revisions
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<ref>[http://dx.doi.org/10.1063/1.3651370 Amir Haji-Akbari, Michael Engel, and Sharon C. Glotzer "Phase diagram of hard tetrahedra", Journal of Chemical Physics '''135''' 194101 (2011)]</ref> | <ref>[http://dx.doi.org/10.1063/1.3651370 Amir Haji-Akbari, Michael Engel, and Sharon C. Glotzer "Phase diagram of hard tetrahedra", Journal of Chemical Physics '''135''' 194101 (2011)]</ref> | ||
==Truncated tetrahedra== | ==Truncated tetrahedra== | ||
Dimers composed of | Dimers composed of Archimedean Truncated Tetrahedra <ref>[http://dx.doi.org/10.1103/PhysRevLett.107.155501 Joost de Graaf, René van Roij, and Marjolein Dijkstra "Dense Regular Packings of Irregular Nonconvex Particles", Physical Review Letters '''107''' 155501 (2011)]</ref> are able to achieve packing fractions as high as <math>\phi= 207/208 \approx 0.9951923</math> | ||
<ref>[http://dx.doi.org/10.1063/1.3653938 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)]</ref> | <ref>[http://dx.doi.org/10.1063/1.3653938 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)]</ref> while a Nonregular Truncated Tetrahedra can completely even tile space.<ref>[http://dx.doi.org/10.1021/nn204012y 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)]</ref> | ||
==References== | ==References== | ||
<references/> | <references/> | ||
Revision as of 04:10, 21 November 2012
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 [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 [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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