Structural building principles of complex face-centered cubic intermetallics

Fundamental structural building principles are discussed for all 56 known intermetallic phases with approximately 400 or more atoms per unit cell and space-group symmetry F (4) over bar 3m, Fd (3) over barm, Fd (3) over bar, Fm (3) over barm or Fm (3) over barc. Despite fundamental differences in chemical composition, bonding and electronic band structure, their complex crystal structures show striking similarities indicating common building principles. We demonstrate that the structure-determining elements are flat and puckered atomic {110} layers stacked with periodicities 2p. The atoms on this set of layers, which intersect each other, form pentagon face-sharing endohedral fullerene-like clusters arranged in a face-centered cubic packing (f.c.c.). Due to their topological layer structure, all these crystal structures can be described as (p x p x p) = p(3)-fold superstructures of a common basic structure of the double-diamond type. The parameter p, with p = 3, 4, 7 or 11, is determined by the number of layers per repeat unit and the type of cluster packing, which in turn are controlled by chemical composition.