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Theoretical Foundation for the Hume-Rothery Electron Concentration Rule for Structurally Complex Alloys

100%

Mizutani U., Sato H., Inukai M., Zijlstra E.

Acta Physica Polonica A

2014

vol. 126

issue 2

531-534

An electron concentration parameter, expressed as the number of itinerant electrons per number of atoms N in a structural unit cell of an alloy, e/uc, is a useful parameter that can be used in interpreting the origin of a band structure pseudogap often evident at the Fermi level for structurally complex metallic alloy phases. It can be expressed in terms of the interference condition e/uc=π/3[|G|_{c}^2]^{3/2}, where |G|_{c}^2 is the square of the critical reciprocal lattice vector associated with the specific set of lattice planes interfering with electrons at the Fermi level. This parameter is similar to the well-known Hume-Rothery electron concentration parameter e/a, which represents the number of electrons per atom and is linked with e/uc through the relation e/uc = N(e/a). We have demonstrated that certain complex metallic alloy structures appear to be stable at or near certain values of e/a. We show that the e/a=1.60 rule holds for the sub-group of gamma-brasses with space group I4̅3m and Pearson symbol cI52, the e/a=4.34 rule for skutterudite compounds with Im3̅ and cI32, the e/a=2.74 rule for Al_6TM (TM = Mn, Tc, Re, Fe, and Ru) compounds with Cmcm and oC28, the e/a=1.62 rule for the sub-group of the Heusler compounds with Fm3̅m and cF16, and the e/a=2.09 rule for the sub-group of Zintl compounds MX_1 (M = Li and Na, X_1 = Al, Ga, In, and Tl) with Fd3̅m and cF32. The e/a rule holds in sub-groups of isostructural compounds, regardless of the degree of orbital hybridizations and the polarity involved.

Fermi Surface-Brillouin Zone Interactions in 2/1-2/1-2/1 Bergman-Type Approximant Na_{27}Au_{27}Ga_{31}

76%

Mizutani U., Sato H., Inukai M., Zijlstra E., Lin Q., Corbett J., Miller G.

Acta Physica Polonica A

2014

vol. 126

issue 2

535-538

The X-ray diffraction studies on a newly synthesized Na_{26}Au_{25}Ga_{29} single crystal revealed the formation of a single phase 2/1-2/1-2/1 Bergman-type approximant and the presence of Au/Ga mixed occupancies in its unit cell containing 680 atoms. The structure model of the 2/1-2/1-2/1 approximant with composition Na_{27}Au_{27}Ga_{31} was constructed by eliminating the chemical disorder with a minimum sacrifice of composition displacement. The full potential linearized augmented plane wave electronic structure calculations with subsequent full potential linearized augmented plane wave-Fourier analysis were performed for the 2/1-2/1-2/1 approximant Na_{27}Au_{27}Ga_{31} with space group Pa3̅. The square of the Fermi diameter (2k_{F})^2, electrons per atom ratio e/a and the critical reciprocal lattice vector |G|^2 are determined. A shallow pseudogap at the Fermi level was interpreted as originating from interference of electrons having (2k_{F})^2=109.2±1.0 with sets of lattice planes with |G|^2's centered at 108. The effective e/a value for the compound is found to be 1.76 in good agreement with 1.73 derived from a composition average of (e/a)_{Na}=1.0, (e/a)_{Au}=1.0 and (e/a)_{Ga}=3.0.

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2 Acta Physica Polonica A

2 2014

2 Inukai M.

2 Mizutani U.

2 Sato H.

2 Zijlstra E.

1 Corbett J.

1 Lin Q.

1 Miller G.

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Theoretical Foundation for the Hume-Rothery Electron Concentration Rule for Structurally Complex Alloys

Fermi Surface-Brillouin Zone Interactions in 2/1-2/1-2/1 Bergman-Type Approximant Na_{27}Au_{27}Ga_{31}