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An Identical Quasicrystal‐Structure Model for T2‐ (AI 6 CuLi 3 ) from Two Different Six‐Dimensional Crystals
Author(s) -
Pan G. Z.,
Li F. H.
Publication year - 1994
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221820104
Subject(s) - quasicrystal , icosahedral symmetry , phase (matter) , penrose tiling , crystallography , crystal (programming language) , materials science , projection (relational algebra) , space (punctuation) , condensed matter physics , physics , mathematics , chemistry , computer science , algorithm , quantum mechanics , programming language , operating system
Abstract The restriction for obtaining an identical quasicrystal by using the projection method from different high‐dimensional crystals is discussed. Two kinds of six‐dimensional crystal‐structure models, (Al, Cu) 7 Li and (Al, Cu) 7 Li 20 , are used to obtain the icosahedral quasicrystalline phase T2‐ (Al 6 CuLi 3 ). It is demonstrated that an identical idealized icosahedral phase T2‐A1 6 CuLi 3 with the same chemical composition, mass density, and atomic arrangement can be obtained by projecting anyone of two 6D crystals onto the physical space. Idealized projection windows are determined on the basis of the rhombic tiling of body‐centered cubic crystals and similarities between the local atomic arrangement of the icosahedral phase T2‐A1 6 CuLi 3 and that of its crystalline approximant R‐Al 5 CuLi 3 . The chemical formula and the mass density of the idealized T2 phase is given.