Origin of the DOS pseudogap and Hume–Rothery stabilization mechanism in RT-type Al₄₈Mg₆₄Zn₄₈ and Al₈₄Li₅₂Cu₂₄ 1/1-1/1-1/1 approximants

Abstract

Full-potential linearized plane wave (FLAPW) band calculations with subsequent FLAPW-Fourier analyses have been performed for two RTtype Al 48 Mg 64 Zn 48 and Al 84 Li 52 Cu 24 1/1-1/1-1/1 approximants containing 160 atoms per unit cell. The FLAPW-Fourier analysis revealed that the Fermi surface-Brillouin zone (FsBz) interactions involving more than two sets of lattice planes are responsible for the formation of a pseudogap across the Fermi level in both compounds. The most critical sets of lattice planes interfering with electrons at the Fermi level are deduced to be {543} þ {710} þ {550} with jGj 2 ¼ 50 in the former and {631} with jGj 2 ¼ 46 in the latter. The square of the Fermi diameter ð2k F Þ 2 is determined to be 49.9 AE 0.1 and 47.1 AE 0.4 in units of ð2=aÞ 2 , respectively, where a is the lattice constant. Hence, the matching condition ð2k F Þ 2 ¼ jGj 2 holds well in both compounds. It is also shown that, while a shallow pseudogap in the Al 48 Mg 64 Zn 48 approximant can be ascribed solely to the FsBz interactions, a much deeper one in the Al 84 Li 52 Cu 24 approximant is explained as a superposition of the FsBz interactions and the formation of strongly directional bonding states between Cu-4p and Al-3p orbitals.

The Physics of the Hume-Rothery Electron Concentration Rule

“…The determination of both (2k F ) 2 and e/a becomes unstable in A-P (A = Li, Na, K, given by equation (20). This has been referred to as the "3/2-power law".…”

“…In the present article, both electron wave vector k and reciprocal lattice vector G in the reciprocal space are expressed in units of 2π a for a cubic lattice with the lattice constant a [11][12][13][14][15][16][17][18][19][20]. Hence, the reciprocal lattice vector G = 2π a (h k l) is simply given by G = (h k l), where integers h, k and l represent the set of Miller indices and…”

“…Figure 56 is constructed to show how the data for families of gamma- uc represents the effective lattice constant for any crystals. The interference condition given by Equation (20) has been referred to as the "3/2-power law". No correlation is found between |G| 2 c and e/a, which is plotted using the ordinate in the right-hand side.…”

“…It allows us to efficiently perform the FLAPW electronic structure calculations even for a compound with a giant unit cell like 2/1-2/1-2/1 approximants containing 680 atoms per unit cell. The FLAPW-Fourier theory discussed in the present Section has been elaborated since 2011 by using the WIEN2k program package [11][12][13][14][15][16][17][18][19][20]. In the WIEN2k-FLAPW electronic structure calculations, we have exclusively employed the GGA-PBE (Generalized Gradient Approximation-Perdew, Burke and Ernzerhof) for exchange-correlation energy and dealt with only non-magnetic states even for 3d-TM elements like Fe, Co and Ni.…”

Fermi Surface-Brillouin Zone Interactions in 2/1-2/1-2/1 Bergman-Type Approximant Na27Au27Ga31

“…For example, we have the 1/1-1/1-1/1 approximants Na 26 Au 24 Ga 30 (e/a = 1.75) [1,2] and Al 48 Mg 64 Zn 48 (e/a = 2.31) [3,4,6] with space group Im3 and Pearson symbol cI160. The reason why more than two e/a values can occur in systems with the same space group and Pearson symbol is discussed in [11].…”