Spatially resolved distribution function and the medium-range order in metallic liquid and glass.

The structural description of disordered systems has been a longstanding challenge in physical science. We propose an atomic cluster alignment method to reveal the development of three-dimensional topological ordering in a metallic liquid as it undercools to form a glass. By analyzing molecular dynamic (MD) simulation trajectories of a Cu(64.5)Zr(35.5) alloy, we show that medium-range order (MRO) develops in the liquid as it approaches the glass transition. Specifically, around Cu sites, we observe "Bergman triacontahedron" packing (icosahedron, dodecahedron and icosahedron) that extends out to the fourth shell, forming an interpenetrating backbone network in the glass. The discovery of Bergman-type MRO from our order-mining technique provides unique insights into the topological ordering near the glass transition and the relationship between metallic glasses and quasicrystals.