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. We postulate that the Hume-Rothery rules can be lifted in some cases, extending the principle behind 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. Beside Na–Sn alloys, where an adjustment, i.e. a drastic rise, of density compensates the large difference in electronegativity, the amorphous TM-Al alloys are of particular interest. In these systems hybridization effects help to achieve the resonance condition. Due to this electronic adjustment to the static structure these alloys show a high thermal stability and high resistivity. During the last ten years we investigated the binary system with TM=Sc, Ti, V, Cr, Mn, Fe, Co, Ni and are currently about to extend the measurements to 4d-, 5d- and 4f-TM.

Another widely known fact about the Al-TM alloys are their tendency to form quasicrystalline structures. Indeed, the first quasicrystal ever, oberserved by Schechtman in 1984, occured in Al₈₄Mn₁₆. Later more stable quasicrystals where found in ternary Al-TM systems. In our group we investigated Al-Cu-Fe, Al-Pd-Mn, Al-Pd-Re and Al-Cu-Li, the latter is especially interesting because of the occurance of both, a density anomaly and hybridization effects.

Another class of materials also consisting of Al-TM alloys are the so-called Heusler- and Half-Heusler alloys like Cu₂MnAl/CuMnAl and Ni₂TiAl/NiTiAl which were also subject of our research.

In the talk we try to explain some common properties of all these system on the basis of our resonance model.