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

Journal Article · · Philosophical Magazine (2003, Print)

There are three key electronic parameters in elucidating the physics behind the Hume–Rothery electron concentration rule: the square of the Fermi diameter (2kF)2, the square of the critical reciprocal lattice vector 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 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 = 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.

Research Organization:
Ames Lab., Ames, IA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
DE-AC02-07CH11358
OSTI ID:
1157652
Report Number(s):
IS-J 8367
Journal Information:
Philosophical Magazine (2003, Print), Vol. 94, Issue 22; ISSN 1478-6435
Publisher:
Taylor & Francis
Country of Publication:
United States
Language:
English