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Laves Phases, γ ‐Brass, and 2×2×2 Superstructures: A New Class of Quasicrystal Approximants and the Suggestion of a New Quasicrystal
Author(s) -
Berger Robert F.,
Lee Stephen,
Johnson Jeffreys,
Nebgen Ben,
So Adrian ChiYau
Publication year - 2008
Publication title -
chemistry – a european journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.687
H-Index - 242
eISSN - 1521-3765
pISSN - 0947-6539
DOI - 10.1002/chem.200800336
Subject(s) - quasicrystal , perpendicular , atom (system on chip) , intermetallic , crystallography , crystal structure , translational symmetry , projection (relational algebra) , brass , penrose tiling , symmetry (geometry) , materials science , condensed matter physics , geometry , physics , chemistry , mathematics , copper , metallurgy , computer science , alloy , algorithm , embedded system
Of the most common cubic intermetallic structure types, several (MgCu 2 , Cu 5 Zn 8 , Ti 2 Ni, and α ‐Mn) have superstructures with unusual symmetry properties. These superstructures (Be 5 Au, Li 21 Si 5 , Sm 11 Cd 45 , and Mg 44 Ir 7 ) have the unusual property of pairs of perpendicular pseudo fivefold axes, most apparent in their X‐ray diffraction patterns. The current work shows that an 8D to 3D projection method cleanly describes most (and in one case, all) of the atomic positions in the four superstructures mentioned above. This type of projection, which maps the E 8 lattice (a mathematically simple 8D crystal) into 3D space, combines the desired higher dimensional point group's perpendicular fivefold rotations with 3D translational symmetry—exactly what we see in the experimental crystal structures. The projection method successfully accounts for all heavy atom positions in the four superstructures, and at least 60–70 % of the light atom positions. The results suggest that all of these structures, previously known to be connected only by qualitative similarities in their atomic “clusters”, are approximants of a single, as‐yet unknown, class of quasicrystal.