Aperiodic Structures in Condensed Matter

Chemical Bonding and Physical Properties in Quasicrystals and Their Related Approximant Phases: Known Facts and Current Perspectives

“…It should be highlighted that the term quasicrystal (QC) is just a shorthand for "quasiperiodic crystal", envisioned as a natural extension of the classical crystal notion, now embodying quasiperiodic arrangements of matter as well [2]. Therefore, this class of solids has nothing to do with amorphous or disordered materials [3][4][5][6].…”

“…The growth of relatively large, high structural quality samples, exhibiting pentagonal dodecahedron or triacontahedral shapes in the case of icosahedral symmetry QCs (usually denoted i-QCs) and octagonal, dodecagonal, or decagonal prismatic habits (Figure 1b) in the case of axial symmetry QCs (denoted o-, dd-, and d-QCs, respectively), allowed for the detailed experimental study of intrinsic physical properties of QCs, including their electrical, thermal, magnetic, optical, and mechanical properties. From the experimental results collected during the last thirty years on the physical properties of stable QCs one concludes that these intermetallic compounds certainly possess a remarkable set of unique features, which significantly differ from those observed in their periodic counterparts [3,6,10]. Indeed, metallic substances show a number of characteristic physical attributes stemming from the presence of a specific kind of chemical bond among their atomic constituents: the so-called metallic bond [11].…”

“…Furthermore, their electrical conductivity significantly decreases as the structural quality of the sample is improved (e.g., by annealing), in striking contrast with periodic metallic alloys, whose electrical transport properties improve when structural imperfections are removed upon heating [12], thereby providing additional evidence on the role played by the novel kind of order present in these materials. Another suitable example is provided by the extremely low thermal conductivity measured for QCs over the wide temperature interval 1-400 K [3,6,10], which could be explained in terms of an enhanced Umklapp process stemming from the dense filling of Bragg reflections in reciprocal space (Figure 1a).…”

Quo Vadis Quasicrystals?

“…In light of the experimental knowledge gained during the last twenty five years on the intrinsic properties of stable QCs, it is now clear that they exhibit a remarkable number of unique physical properties [20,42,43], which significantly differ from those observed in their periodic counterparts.…”

“…According to this view, a more appropriate term for these solids would probably be hypercrystals [19][20][21]. By adopting the hyperspace perspective, the contribution by Farhad A. Namin and Douglas H. Werner exploits the unit cell in the higher dimensional space to obtain the atomic surfaces' Fourier series expansion in closed-form [22].…”