Abstract
More than 35 years and 11 000 publications after the discovery of quasicrystals by Dan Shechtman, quite a bit is known about their occurrence, formation, stability, structures and physical properties. It has also been discovered that quasiperiodic self-assembly is not restricted to intermetallics, but can take place in systems on the meso- and macroscales. However, there are some blank areas, even in the centre of the big picture. For instance, it has still not been fully clarified whether quasicrystals are just entropy-stabilized high-temperature phases or whether they can be thermodynamically stable at 0 K as well. More studies are needed for developing a generally accepted model of quasicrystal growth. The state of the art of quasicrystal research is briefly reviewed and the main as-yet unanswered questions are addressed, as well as the experimental limitations to finding answers to them. The focus of this discussion is on quasicrystal structure analysis as well as on quasicrystal stability and growth mechanisms.
Highlights
Dan Shechtman was the first to identify a rapidly solidified intermetallic phase as a representative of a novel class of longrange-ordered (LRO) phases with icosahedral diffraction symmetry (Shechtman et al, 1984)
No devil’s staircase of approximant crystals (ACs) to a particular QC has been identified, as is known for IMSs (Bak, 1982, and references therein). This can be interpreted in such a way that once the chemical composition approximates that needed for the formation of a pseudogap at EF, the close-tospherical pseudo-Brillouin zone of an IQC lowers the energy more than the less-symmetric cubic Brillouin zone of even a high-order AC
Why are we interested in the analysis of crystal structures at all? At present, the main structural databases contain more than 1 200 000 entries for periodic crystal structures [>188 000 inorganics/intermetallics in the Inorganic Crystal Structure Database (ICSD); >875 000 organics/metalorganics in the Cambridge Structural Database (CSD); >107 000 proteins in the RCSB Protein Data Bank (PDB)] and 145 of incommensurate structures in the Bilbao Incommensurate Structures Database (B-IncStrDB)
Summary
Dan Shechtman was the first to identify a rapidly solidified intermetallic phase as a representative of a novel class of longrange-ordered (LRO) phases with icosahedral diffraction symmetry (Shechtman et al, 1984). In most cases, only X-ray powderdiffraction methods were routinely used for sample characterization at that time, the fivefold diffraction symmetry characteristic of icosahedral QCs did not immediately catch the eye, unlike Shechtman’s electron diffraction patterns. It seems that nature created QCs aeons earlier. We do not know enough about the thermodynamic stability of QCs, and the way they form and grow from the melt These are the main unanswered questions from my point of view. The other two classes of aperiodic crystals, incommensurately modulated structures (IMSs) and composite or host–guest structures (CSs), which have been known for longer, are not as far away from average periodicity as QCs
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