The geometry, topology and structure of amorphous solids

Clusters of atoms can be divided into three categories depending on their topology. One of the categories provides the basis for development of a model of a perfectly random structure (ideal amorphous solid) using the non-equilateral triangle topology in the coordination shell. Metallic glasses solidify as amorphous solids with random arrangement of atoms. A model of Zr-based metallic glass has been constructed and described in terms of cluster topology, and compared with a recently published dynamic molecular model of the same alloy. It is shown that the pair distribution function for the ideal amorphous model relates to the pair correlation function obtained from the dynamic model. Debye X-ray scattering computations reveal the presence of vacancies and other flaws relative to the ideal amorphous solid. A shift in the peak position can be predicted using the Erhenfest formula. Two atomic displacement mechanisms involving a five-atom sub-cluster are identified as the fundamental means of compositional redistribution between clusters in the alloy.