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e/a classification of Hume-Rothery Rhombic Triacontahedron-type approximants based on all-electron density functional theory calculations

Titlee/a classification of Hume-Rothery Rhombic Triacontahedron-type approximants based on all-electron density functional theory calculations
Publication TypeJournal Article
Year of Publication2014
AuthorsMizutani, U, Inukai, M, Sato, H, Zijlstra, ES, Lin, Q
JournalPhilosophical Magazine
Volume94
Pagination2571-2594
Date Published07
Type of ArticleArticle
ISBN Number1478-6435
Accession NumberWOS:000340050200007
Keywords2/1-2/1-2/1 approximants, cluster, cu-ru, elements, FLAPW-Fourier method, Hume-Rothery electron concentration rule, Hume-Rothery stabilization mechanism, interference condition, Intermetallic compounds, metal, mg, phase, quasi-crystals, RT-type approximants, sn, stabilization mechanism, zn
Abstract

There are three key electronic parameters in elucidating the physics behind the Hume-Rothery electron concentration rule: the square of the Fermi diameter (2k(F))(2), the square of the critical reciprocal lattice vector vertical bar G vertical bar(c)(2) and the electron concentration parameter or the number of itinerant electrons per atom e/a. We have reliably determined these three parameters for 10 Rhombic Triacontahedron-type 2/1-2/1-2/1 (N = 680) and 1/1-1/1-1/1 (N = 160-162) approximants by making full use of the full-potential linearized augmented plane wave-Fourier band calculations based on all-electron density-functional theory. We revealed that the 2/1-2/1-2/1 approximants Al13Mg27Zn45 and Na27Au27Ga31 belong to two different sub-groups classified in terms of vertical bar G vertical bar(c)(2) equal to 126 and 109 and could explain why they take different e/a values of 2.13 and 1.76, respectively. Among eight 1/1-1/1-1/1 approximants Al3Mg4Zn3, Al9Mg8Ag3, Al21Li13Cu6, Ga21Li13Cu6, Na26Au24Ga30, Na26Au37Ge18, Na26Au37Sn18 and Na26Cd40Pb6, the first two, the second two and the last four compounds were classified into three sub-groups with vertical bar G vertical bar(c)(2) = 50, 46 and 42; and were claimed to obey the e/a = 2.30, 2.10-2.15 and 1.70-1.80 rules, respectively.

DOI10.1080/14786435.2014.913820
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