Here, Professor of Physics Zbigniew M. Stadnik at the University of Ottawa, explores research into the unusual physical properties and potential applications of Quasicrystals
Solids are traditionally divided into two groups: crystalline and amorphous. The dramatic discovery of an icosahedral Al-Mn alloy in 1984 by Daniel Shechtman (the 2011 Nobel Prize in Chemistry) extended this dichotomous division by introducing the notion of quasicrystals (QCs). These compounds possess a new long-range translational order, quasiperiodicity, and non-crystallographic orientational order associated with the classically forbidden fivefold, eightfold, tenfold, and twelvefold symmetry axes. One of the central problems in condensed-matter physics is determining whether quasiperiodicity leads to novel physical properties that are significantly different from those of crystalline and amorphous materials.
QCs indeed exhibit some unusual physical properties. Perhaps the most noteworthy is a simple electrical resistivity ρ. For some QCs, ρ is orders of magnitude larger than ρ of constituent elements of a QC (the Al-Fe-Re QC can even be considered an electrical insulator). For QCs composed of metallic constituents, the temperature dependence of ρ is surprising; it increases with decreasing temperature at low temperatures, contrary to what is expected for a metallic system. Furthermore, the ρ of a QC increases with improved sample quality, which cannot be explained within our traditional understanding of the physical mechanism of ρ. Other electrical and heat transport physical properties of QCs also exhibit various anomalies. There are a plethora of theoretical explanations of these anomalies. It seems fair to state that our understanding of these anomalies and their relation to quasiperiodicity is only fragmentary.
The electronic structure of solids determines many of their fundamental physical properties. The significant finding in that area was the discovery of a theoretically predicted pseudogap in the density of states (DOS) at or around the Fermi energy in many QCs. This pseudogap, via a Hume-Rothery-type electronic mechanism, is one factor responsible for stabilising the quasiperiodic structure in QCs. Some theoretical studies also make a surprising prediction of a fine, spiky structure of DOS around the Fermi energy, which is seemingly the signature of quasiperiodicity. However, convincing experimental evidence for the existence of such spikiness is still lacking.
The magnetism of QCs is similar to that of crystalline or amorphous compounds in that all known QCs are either diamagnets, paramagnets, or spin glasses. An essential experimental discovery was the observation that the nature of the spin-glass state in QCs is different from that found in the canonical spin glasses of crystalline or amorphous systems. Numerous theoretical studies suggest that long-range magnetic order (antiferro- magnetism, ferromagnetism, etc.) ubiquitous in crystalline and amorphous systems should also occur in QCs. Yet, to date, no such magnetic order has been discovered. Could its absence be the consequence of quasiperiodicity?
QCs have hitherto been found as synthetic solids in more than a hundred systems and few natural minerals. Recently, it has been demonstrated that they can also form in some soft-matter systems, such as liquid dendritic systems, polymeric star systems or self-assembled nanoparticle (colloidal) systems. Another recent development was that quasiperiodicity could be realised in so-called photonic QCs. These are artificial quasiperiodic heterostructures constructed from two or more types of dielectric material; they are a quasiperiodic equivalent of photonic crystals. Enormous research interest in these photonic QCs stems from their significant potential applications in the field of modern optics. Perhaps the most exotic realisation of quasiperiodicity occurs in time QCs; these are the quasiperiodic analogs of time crystals. Time QCs, which have been realised experimentally, are quasiperiodic structures in time that form spontaneously in quantum many-body systems.
Because of their low friction, high hardness, and low surface reactivity, Al-Fe-Cu QCs found their first technological application, which later was discontinued, as coatings in non-stick frying pans, aiming to replace Teflon. Tiny particles of QCs can harden steel, which can be used in needles for acupuncture, surgeon and dental instruments, or razor blades. More generally, to overcome their inherent brittleness via the presence of a ductile matrix, QCs can be used to reinforce Al-matrix composites. There are other potential applications of solid QCs, especially photonic and possibly time QCs. This, however, requires significant developments and seems far from realisation on a mass scale. It appears that technological applications of QCs have not yet come of age.
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