Evidence of the Relationship of the Electronic Properties of Icosahedral Boron-Rich Solids and Icosahedral Quasicrystals

Werheit, H.; Schmechel, Roland; Kimura, Kaoru; Tamura, Ryuji; Lundström, Torsten

doi:10.1006/jssc.1997.7337

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“…Recently, dodecagonal quasiperiodic ordering was even observed in supramolecular dentritic liquid crystals [3]. There have also been predictions of icosahedral [4][5][6][7][8] as well as of decagonal boron-based QCs [9]. Thus, there are clear indications that quasiperiodic self-organization may not be limited to intermetallics.…”

Section: Introductionmentioning

confidence: 97%

Boron-based quasicrystals with sevenfold symmetry

Steurer

2007

Philosophical Magazine

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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 YCrB 4 , ThB 4 , ThMoB 4 , Y 2 ReB 6 structure types. The possibility to find heptagonal quasicrystals related to these phases will be discussed.

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