Title: A model of the AlMnSi quasicrystal derived from the α AlMnSi crystal structure
Abstract: Abstract Abstract The α AlMnSi crystal structure consists of two kinds of polyhedra: Mackay icosahedra (MI) and double Mackay icosahedra (DMI). An MI and a DMI both have icosahedral symmetry and consist of 54 and 156 atoms respectively. They are similar to each other, but a DMI is 1•618 times bigger than an MI. If these polyhedra connect with each other along the two-, three- and fivefold axes, an AlMnSi quasicrystal can be built up. We term the MI and the DMI the first-order icosahedron and the first-order DMI respectively. The second-order icosahedron consists of 12 first-order DMIs and 20 first-order icosahedra. The second-order DMI consists of 31 first-order DMIs and 32 first-order icosahedra. The second-order icosahedron and DMI are 2•618 times bigger than the first-order ones. In general, the Nth-order icosahedron consists of 12 (N−1)th-order DMIs and 20 (N−1)th-order icosahedra; the Nth-order DMI, 31 (N−1)th-order DMIs and 32 (N−1)th-order icosahedra. The Nth-order icosahedron and DMI are 2•618 times bigger than the (N−1)th ones. This can go on continuously to fill expanding space.
Publication Year: 1988
Publication Date: 1988-07-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 27
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