Cluster formulas of Hume-Rothery phases

Hume-Rothery phases sharing the same e/a (electron concentration, which usually is 1.50(=21/14), 1.62(=21/13), 1.75(=21/12)) crystallize into many different types of structures based on a common Bravais lattice, hence the e/a alone can not be used as the finger print parameter specifying a Hume-Rothery phase. A refined electronic structure parameter is desirable for the classification of Hume-Rothery phases in a more rigorous manner. So the cluster-plus-glue-atom model is used to decipher the structures of Hume-Rothery phases, from which the cluster formula and relative number of electrons per unit formula, e/u , are derived. Hume-Rothery phases with an identical e/a are classified by e/u , so e/u is a new parameter to specify Hume-Rothery phase structures