Frank introduced in 1965 the novel idea of projection from a four-dimensional cube to recover the points of a hexagonal lattice with a special c/a ratio of (3/2)1/2. This was called a cubic hexagonal crystal, as there was a similarity to the conventional cubic crystals in that directions were perpendicular to planes with the same Miller-Bravais indices. While a number of crystals in the NiAs-Ni2In family have been reported with this special axial ratio, the number of atoms in the unit cell is small. As the first example of an intermetallic cluster compound, we identify μ-Al4Mn, μ-Al4Cr, Zn-Mg-Sm and a host of related intermetallics featuring a special aggregate of icosahedra as Frank's 'cubic' hexagonal phase or its variant. The metric is generated by the Friauf polyhedra and the icosahedral linkages and leads to a multimetric crystal and several interesting connections with hexagonal quasicrystals, hexagonal phases and derivative orthorhombic and lower-symmetry structures.
ASJC Scopus subject areas
- Condensed Matter Physics