The crystal structure of a compound plays an important role in determining its properties. Here we analyze over 4000 intermetallic compounds, and we 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 are chemical orderings over the sites of simple crystal structures such as body-centered-cubic (bcc) and face-centered-cubic (fcc) structures, the majority map onto more complex parent crystal structures. Surprisingly, many intermetallic compounds map onto parent crystal structures that differ from those of their elemental constituents. We find that the occurrence of several of the more complex parent crystal structures, such as the Laves phases, can be understood in terms of simple descriptors such as the ratio of atomic radii and electronegativity differences.

中文翻译：

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在金属间晶体结构之间发现层次

化合物的晶体结构在确定其性质方面起着重要作用。在这里，我们分析了4000多种金属间化合物，并确定了它们的晶体结构之间的等级关系。通过将每种金属间化合物视为在较高对称性晶体结构的位点上的特定化学顺序，我们确定大多数金属间化合物可源自少数母体晶体结构。尽管许多化合物在简单的晶体结构（如体心立方（bcc）和面心立方（fcc）结构）上都是化学有序的，但大多数化合物映射到更复杂的母体晶体结构上。令人惊讶的是，许多金属间化合物映射到与其元素成分不同的母体晶体结构上。