Hume-Rothery rule in V–VI compounds

• Published in: Solid state communications Vol. 84; no. 8; pp. 839 - 842
• Main Authors: Gaspard, J.-P., Ceolin, R.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.11.1992; Elsevier
• Subjects: Condensed matter: structure, mechanical and thermal properties; Crystal binding; cohesive energy; Crystalline state (including molecular motions in solids); Exact sciences and technology; Physics; Structure of solids and liquids; crystallography; Electronic structure; Semiconductor materials; Peierls transition; Theoretical study; Covalent bond; Hume Rothery phase; Crystalline structure
• ISSN: 0038-1098; 1879-2766
• DOI: 10.1016/0038-1098(92)90102-F

The crystal structures of compounds of the right hand side of the Mendeleiev table can be easily understood in terms of their electronic structure. The bonding mechanism is of ppσ type and the expected simple cubic structure is subsequently deformed by a Peirls transition: some bonds are shortened and some others are elongated among the directions of the axes of the cube. The alternation of short and long bonds is driven by the electron/atom ratio. Using simple theoretical arguments, we show that the periodicity of deformation is simply related to the average number Np of p electrons. If the filling of the p band isNp6=nmwhere n and m are prime numbers, the structure shows a m-fold periodicity. We show that, up to very large m values, this rule is confirmed without any exception by an important series of compounds including AsxTe1-x, SbxTe1-x, BixSe1-x, BixTe1-x and As2GexTe3+x.