Alloy phases and metallic glass formation understood via cluster formulas

Alloy phase structures and compositions in glass-forming Al–Ni–Zr system are analyzed by cluster-plus-glue-atom model and cluster line approach. Clusters in crystalline phases are shared with their neighboring clusters and the effective clusters after sharings are used to express the phases: phase = [effective cluster](glue atoms). This cluster formulas similar to molecular formulas for chemicals, contain key structure and composition information of the alloy phases. Cluster phases that require glue atoms and contain periodicity-incompatible clusters have close relationships with metallic glass formation. By avoiding cluster sharings, good glass forming compositions can be expressed by [isolated cluster](glue atom)x, x = 1–3.