A Compton scattering study on the Hume-Rothery mechanism of AlCu-TM (TM: transition metal) quasicrystals

The electron momentum distributions in icosahedral Al64Cu23Fe13, icosahedral Al63Cu23Ru13 and decagonal Al65Cu15Co20 quasicrystals have been studied using the high-resolution Compton scattering technique. The electron-per-atom ratios (e/a) of the quasicrystals were determined quantitatively for the first time from the Compton profiles. The radii of the Fermi spheres were evaluated from the values of e/a on the basis of the free-electron model. Comparisons between the radius of the Fermi spheres and the size of the quasi-Brillouin zones show that the icosahedral quasicrystals meet the empirical matching condition, while the decagonal quasicrystal does not do this so well. This implies that the Hume-Rothery mechanism works for the formation of the pseudogap near the Fermi level in the icosahedral quasicrystals, although it operates only slightly in the decagonal quasicrystal