Direct Evidence of the Hume-Rothery Stabilization Mechanism in Al-Mn-Fe-Si Mackay-Type 1/1-Cubic Approximants

Abstract

The detailed structure analysis for a series of the Al–Mn–Fe–Si Mackay-type 1/1-cubic approximants has been performed by applying the Rietveld method to the x-ray powder diffraction spectra taken with a synchrotron radiation x-ray source. We found that identical Mackay clusters occupy both the body-center and vertex positions of the cubic lattice but that atom distributions in glue sites connecting the Mackay clusters are unique to each alloy. The number of s, p-electrons per unit cell is calculated by assigning the appropriate number of valence electrons to constituent atoms involved in the refined atomic structure. It is shown that, when the Fe atoms are substituted for Mn atoms, the total number of s, p-electrons per unit cell remains unchanged and is always centered at a value satisfying the so called Hume-Rothery matching rule, where the Fermi sphere well coincides with the relevant Brillouin zone planes. We conclude that the Hume-Rothery matching condition stabilizes the ternary Al–Mn–Fe–Si approximants by compensating an increase in the valence electrons due to the replacement of Mn atoms by Fe atoms by an increase in the number of vacancies in the glue sites.