On modifications of the well-known Hume-Rothery rules: Amorphous alloys as model systems

Structure formation in condensed matter physics is still far from being understood. One important approach, for a limited class of systems selected by some exclusion rules, goes back to Hume-Rothery. Here we review on measurements of the static structure, electronic properties, and the thermal stability of amorphous TM-Al (TM: Ti, V, Cr, Mn, Fe, Co, Ni) and Na–Sn alloys. Concluding from the results, we postulate that the Hume-Rothery rules can be lifted in some cases, extending the Hume-Rothery scheme, i.e., the opening of band gaps at the Fermi energy, to a much wider class of materials, making it more general.