The mechanism for the stability of the ${\mathrm{Al}}_8{\mathrm{V}}_5\gamma$-brass containing 52 atoms in its cubic unit cell has been investigated by means of first-principles full-potential linearized augmented plane wave (FLAPW) and linearized muffin-tin orbital-atomic sphere approximation (LMTO-ASA) electronic structure calculations. The LMTO-ASA identified a deep valley at $0.5\mathrm{eV}$ above the Fermi level in its density of states (DOS) as arising from orbital hybridizations between V $3d$ and Al $3p$ states. On the other hand, the FLAPW revealed the V $3d$ states mediated resonance of electrons with different sets of lattice planes. The resonance involved is found to be substantial not only at ${\mid \mathbf{G}\mid }^2=18$ or {330} and {411} zones but also at those in the range $14⩽{\mid \mathbf{G}\mid }^2⩽30$. A comparison with the electronic structure of the CsCl-type AlV compound proved that the V $3d$ states mediated resonance occurs only in ${\mathrm{Al}}_8{\mathrm{V}}_5$ but not in AlV compound. The V $3d$ states mediated resonance is proved to result in a significant suppression of the $sp$-partial DOS over the energy range from the Fermi level up to $+2.2\mathrm{eV}$. A gain in the electronic energy has been attributed to the formation of highly condensed bonding states below the Fermi level, again caused by the V $3d$ states mediated resonance. It is also proposed that the ${\mathrm{Al}}_8{\mathrm{V}}_5$ is stabilized at $e∕a=1.94$ rather than $21∕13$ as is expected from the Hume-Rothery electron concentration rule.

• Received 16 July 2006

DOI:https://doi.org/10.1103/PhysRevB.74.235119