Interpretation of the Hume-Rothery electron concentration rule in the T2Zn11 (T=Ni, Pd, Co, and Fe) γ brasses based on first-principles FLAPW calculations -: art. no. 125102

The first-principles full-potential augmented plane wave (FLAPW) band calculations were performed for a series of T2Zn11 (T=Ni, Pd, Co, and Fe) gamma brasses to elucidate the Hume-Rothery electron concentration rule. The pseudogap is found immediately below the Fermi level E-F in the Ni2Zn11 and Pd2Zn11 gamma brasses. A resulting gain in the electronic energy is attributed to their stabilization in the same way as in Cu5Zn8 and Cu9Al4 previously studied. However, the pseudogap is essentially shifted above E-F in both Co2Zn11 and Fe2Zn11. The Fourier analysis of the FLAPW wave function was made at the symmetry point N of the reduced Brillouin zone in the energy range involving the pseudogap. It is found that the plane wave giving rise to the largest Fourier component always resonates with the {330} and {411} zone planes to produce the pseudogap near E-F. Moreover, a single-branch energy dispersion relation was constructed in the extended zone scheme by averaging the wave vector 2(k+G) having the largest Fourier component of the FLAPW wave function over selected electronic states in the Brillouin zone. The e/a value thus deduced is found to be close to 21/13=1.615 for Cu5Zn8, Cu9Al4, Ni2Zn11, and Pd2Zn11 gamma brasses but to be only 1.4 and 1.3 for Co2Zn11 and Fe2Zn11, respectively.