Boron-based quasicrystals with sevenfold symmetry

Abstract

It is not too surprising that 5-fold symmetry is the symmetry of quasicrystals since icosahedral coordination is the most frequent atomic environment type (AET) in intermetallic phases. What about AETs with 7-fold symmetry? Whereas no regular or semi-regular polyhedra (Platonic or Archimedean solids) exist with rotational symmetry larger than 5-fold, polyhedra with only axial n-fold symmetry (e.g. pyramids) are possible for arbitrary n. Indeed, (distorted) seven-membered rings are very common in ternary borides and borocarbides such as the YCrB₄, ThB₄, ThMoB₄, Y₂ReB₆ structure types. The possibility to find heptagonal quasicrystals related to these phases will be discussed.