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

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