Intermetallic Crystal Structures as Foams. Beyond Frank–Kasper

In many intermetallic structures, the atoms and bonds divide space into tilings by tetrahedra. The well-known Frank–Kasper phases are examples. The dual tilings divide space into a tiling by polyhedra that is topologically a foam. The number of faces of the dual polyhedron corresponds to the atom coordination number in the direct structure, and face sharing by adjacent polyhedra corresponds to bonds in the direct structure. A number of commonly occurring intermetallic crystal structures are shown as their duals. A major advantage of this alternative mode of depiction is that coordination of all of the atoms can be seen simultaneously.