HUME-ROTHERY RULE IN V-VI COMPOUNDS

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 ppsigma type and the expected simple cubic structure is subsequently deformed by a Peierls 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 N(p) of p electrons. If the filling of the p band is N(p)/6 = n/m where 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.