Spherical periodicity as structural homology of crystalline and amorphous states

It has been widely accepted that spherical periodicity generally dominates liquid and amorphous structure formation, where atoms tend to gather near spherically periodic shells according to Friedel oscillation. Here we revealed that the same order is just hidden in the atomic global packing modes of the crystalline phases relevant to bulk metallic glasses. Among the nearest-neighbor clusters developed from all the non-equivalent atomic sites in a given phase, there always exists a principal a principal cluster, centered by which the spherical periodicity, both topologically and chemically, is the most distinct. Then the principal clusters plus specific glue atoms just constitute the cluster-plus-glue-atom structural units shared by both metallic glasses and the corresponding crystalline phases. It is further pointed out that the spherical periodicity order represents a common structural homology of crystalline and amorphous states in the medium-range through scrutinizing all binary bulk-glass-relevant phases in Cu-(Zr, Hf), Ni-(Nb, Ta), Al-Ca, and Pd-Si systems.