Electron-counting in intermetallics made easy: the 18-n rule and isolobal bonds across the Os–Al system

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Abstract Electron count is one of the key factors controlling the formation of complex intermetallic structures. The delocalized nature of bonding in metals, however, has made it difficult to connect these electron counts to the various structural features that make up complex intermetallics. In this article, we illustrate how structural progressions in transition metal-main group intermetallics can in fact be simply understood with the 18-n bonding scheme, using as an example series the four binary phases of the Os–Al system. Our analysis begins with the CsCl-type OsAl phase, whose 11 electrons/Os count is one electron short of that predicted by the 18-n rule. This electron deficiency provides a driving force for Al incorporation to make more Al-rich intermetallic phases. In the structures of Os2Al3 (own type) and OsAl2 (MoSi2 type), each additional Al atom contributes three electrons, two of which go towards cleaving Os–Os isolobal bonds, with the third alleviating the original electron deficiency of OsAl. Across the series, the framework of isolobal Os–Os bonds is reduced from a primitive cubic network (n=6, OsAl) to layers of cubes (n=5, Os2Al3) to individual square nets (n=4, OsAl2). Upon adding more Al to form Os4Al13, the Os–Os contacts are further reduced to dumbbells at the interfaces between fluorite-type columns. At this point, the added Al raises the electron count beyond that needed for filled octadecets on the Os atoms; the excess electrons are accommodated by Al–Al bonds. Throughout this work, we emphasize how the 18-n scheme can be applied from structural inspection alone, with theoretical calculations confirming or refining these conclusions.