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Zeolites and tetrahedral packings

Banff International Research Station for Mathematical Innovation and Discovery

Zeolites (zeo = boil; lithos = stone) are microporous, aluminosilicate minerals commonly used as commercial adsorbents and catalysts. In 1973 the book "Zeolite molecular sieves: structure, chemistry and use" (771pp) by Donald W. Breck appeared. At that time 27 zeolite framework types were known. In 2007, the 6'th edition of the Atlas of Zeolite Framework Types describes 176 known distinct approved types. Zeolites occur naturally but are also produced industrially on a large scale. Combinatorially, zeolites are line graphs of 4-regular graphs and may be finite. However, it is not always possible to realize a combinatorial zeolite as a unit distance graph in 3-space. Mike Winkler found a saturated tetrahedral packing consisting of only 12 tetrahedra. It is not known yet if the packing is rigid. A 16 vertex model was shown to have at least two degrees of freedom. We try to give an overview of recent results and open problems.

Mathematics; Convex and discrete geometry; Statistical mechanics, structure of matter; Discrete mathematics

video/mp4

Author affiliation: Worcester Polytechnic Institute

2020-03-31

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73864

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/