Difference between revisions of "Hard tetrahedron model"

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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 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>
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Dimers composed of Archimedean truncated tetrahedra 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> while a non-regular truncated tetrahedra can completely 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''' pp. 609-614 (2012)]</ref>.
+
<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><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 non-regular truncated tetrahedra can completely 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''' pp. 609-614 (2012)]</ref>.
  
 
==References==
 
==References==

Revision as of 03:32, 4 December 2012

Tetrahedron.png

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 \phi=0.8503[2] (the hard sphere packing fraction is \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

[5]

Truncated tetrahedra

Dimers composed of Archimedean truncated tetrahedra are able to achieve packing fractions as high as \phi= 207/208 \approx 0.9951923 [6][7] while a non-regular truncated tetrahedra can completely tile space [8].

References

Related reading