Discovering Hierarchies Among Intermetallic Crystal Structures

Abstract

The crystal structure of a compound plays an important role in determining its properties. Here we analyze over four thousand intermetallic compounds and identify a hierarchical relationship between their crystal structures. By considering each intermetallic compound as a particular chemical ordering over the sites of a higher symmetry crystal structure, we determine that most intermetallic compounds can be derived from a small number of parent crystal structures. While many compounds can be considered as chemical orderings over the sites of simple crystal structures such as BCC and FCC, the majority map onto more complex parent crystal structures. Surprisingly, many intermetallic compounds map onto parent crystal structures that differ from those of the elemental constituents. Nevertheless, the occurrence of particular parent crystal structures within the same alloy system is highly correlated with simple atomic descriptors such as the ratio of atomic radii and electronegativity differences. The hierarchical organization of crystal structures provides an atlas from which to make sense of correlations between chemistry and structure, thus revealing useful trends to guide design and structure prediction of multi-component alloys.