Model of Icosahedral Order
Metallic glasses, quasicrystals, and crystals may share identical local icosahedral order. This type of ordering extends to fill a three-dimensional curved space, producing an icosahedral “polytope” with perfect short and long-range icosahedral order. In this paper I demonstrate how to flatten the polytope and fill space with structures possessing the short-range order of the polytope but various types of long-range order. Both the rhombohedral packing units required to construct a three-dimensional Penrose pattern and long-range orientational order arise from rolling the polytope along special paths in three-dimensional flat space.
KeywordsMetallic Glass Flat Space Matching Rule Standard Orientation Icosahedral Cluster
Unable to display preview. Download preview PDF.
- 3.M. Kleman and J.F. Sadoc, J. Phys. (Paris) Lett. 40, L569 (1979);Google Scholar
- 5.H.S.M. Coxeter, “Regular Polytopes” (Dover, N.Y., 1973 )Google Scholar
- 10.P. DuVal, “Homographics, Quaternions, and Rotations” ( Oxford, London, 1964 )Google Scholar
- 11.M. Widom, Phys. Rev. B33, July 15 (1986)Google Scholar
- 12.Actually an imperceptible adjustment must be made because the vertices below the equator of the icosahedron centered at (o,o,d) do not match precisely the locations of the vertices above the equator of the icosahedron at the origin.Google Scholar
- See also article by P. Horn in these proceedings.Google Scholar