Editing Quasicrystal (section)

==Materials science==
[[Image:frustrationPentagons.jpg|thumb|Tiling of a plane by regular pentagons is impossible but can be realized on a sphere in the form of pentagonal dodecahedron.]]
[[File:Ho-Mg-ZnQuasicrystal.jpg|thumb|A [[holmium–magnesium–zinc quasicrystal|Ho–Mg–Zn dodecahedral quasicrystal]] formed as a pentagonal [[dodecahedron]], the [[dual polyhedron|dual]] of the [[icosahedron]]. Unlike the similar [[pyritohedron]] shape of some cubic-system crystals such as [[pyrite]], the quasicrystal has faces that are true regular pentagons]]
[[File:TiMnImage2y.png|right|thumb|TiMn quasicrystal approximant lattice]]

Since the original discovery by [[Dan Shechtman]], hundreds of quasicrystals have been reported and confirmed. Quasicrystals are found most often in aluminium alloys (Al–Li–Cu, Al–Mn–Si, Al–Ni–Co, Al–Pd–Mn, Al–Cu–Fe, Al–Cu–V, etc.), but numerous other compositions are also known (Cd–Yb, Ti–Zr–Ni, Zn–Mg–Ho, Zn–Mg–Sc, In–Ag–Yb, Pd–U–Si, etc.).<ref>{{cite journal|doi=10.1088/0034-4885/69/2/R03|title=The role of aperiodic order in science and technology|year=2006|last1=MacIá|first1=Enrique|journal=Reports on Progress in Physics|volume=69|pages=397–441|bibcode = 2006RPPh...69..397M|issue=2|s2cid=120125675 }}</ref>

Two types of quasicrystals are known.<ref name="comp" /> The first type, polygonal (dihedral) quasicrystals, have an axis of 8-, 10-, or 12-fold local symmetry (octagonal, decagonal, or dodecagonal quasicrystals, respectively). They are periodic along this axis and quasiperiodic in planes normal to it. The second type, icosahedral quasicrystals, are aperiodic in all directions. Icosahedral quasicrystals have a three dimensional quasiperiodic structure and possess fifteen 2-fold, ten 3-fold and six 5-fold axes in accordance with their icosahedral symmetry.<ref>{{cite journal |last1=C |first1=Cui |last2=M |first2=Shimoda |last3=AP |first3=Tsai |title=Studies on icosahedral Ag-In-Yb: A prototype for Tsai-type quasicrystals |journal=RSC Advances |date=2014 |volume=4 |issue=87 |pages=46907–46921 |doi=10.1039/C4RA07980A|bibcode=2014RSCAd...446907C }}</ref>

Quasicrystals fall into three groups of different thermal stability:<ref>{{cite journal|doi=10.1088/1468-6996/9/1/013008|pmc=5099795|title=Icosahedral clusters, icosaheral order and stability of quasicrystals – a view of metallurgy|year=2008|last1=Tsai|first1=An Pang|journal=Science and Technology of Advanced Materials|volume=9|issue=1|page=013008|bibcode = 2008STAdM...9a3008T|pmid=27877926}}</ref>
* Stable quasicrystals grown by slow cooling or [[casting (metalworking)|casting]] with subsequent [[annealing (metallurgy)|annealing]],
* Metastable quasicrystals prepared by [[melt spinning]], and
* Metastable quasicrystals formed by the [[crystallization]] of the [[amorphous]] phase.

Except for the Al–Li–Cu system, all the stable quasicrystals are almost free of defects and disorder, as evidenced by [[X-ray diffraction|X-ray]] and [[electron diffraction]] revealing peak widths as sharp as those of perfect crystals such as Si. Diffraction patterns exhibit fivefold, threefold, and twofold symmetries, and reflections are arranged quasiperiodically in three dimensions.

The origin of the stabilization mechanism is different for the stable and metastable quasicrystals. Nevertheless, there is a common feature observed in most quasicrystal-forming liquid alloys or their undercooled liquids: a local icosahedral order. The icosahedral order is in equilibrium in the ''liquid state'' for the stable quasicrystals, whereas the icosahedral order prevails in the ''undercooled liquid state'' for the metastable quasicrystals.

A nanoscale icosahedral phase was formed in Zr-, Cu- and Hf-based bulk metallic glasses alloyed with noble metals.<ref>{{Cite journal | doi = 10.1146/annurev.matsci.38.060407.130318| title = Formation and Properties of Quasicrystals| journal = [[Annual Review of Materials Research]]| volume = 38| pages = 403–423| year = 2008| last1 = Louzguine-Luzgin | first1 = D. V. | last2 = Inoue | first2 = A.|bibcode = 2008AnRMS..38..403L}}</ref>

Most quasicrystals have ceramic-like properties including high thermal and electrical resistance, hardness and brittleness, resistance to corrosion, and non-stick
properties.<ref name="mrs" /> Many metallic quasicrystalline substances are impractical for most applications due to their [[Thermal stability|thermal instability]]; the Al–Cu–Fe ternary system and the Al–Cu–Fe–Cr and Al–Co–Fe–Cr quaternary systems, thermally stable up to 700&nbsp;°C, are notable exceptions.

The quasi-ordered droplet crystals could be formed under Dipolar forces in the Bose Einstein condensate.<ref name=":0">{{Cite journal|last=Khazali|first=Mohammadsadegh|date=2021-08-05|title=Rydberg noisy dressing and applications in making soliton molecules and droplet quasicrystals|url=http://dx.doi.org/10.1103/physrevresearch.3.l032033|journal=Physical Review Research|volume=3|issue=3|page=032033|doi=10.1103/physrevresearch.3.l032033|issn=2643-1564|arxiv=2007.01039|bibcode=2021PhRvR...3c2033K|s2cid=220301701|access-date=2021-09-30|archive-date=2024-09-18|archive-url=https://web.archive.org/web/20240918002539/https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.L032033|url-status=live}}</ref> While the softcore Rydberg dressing interaction has forms triangular droplet-crystals,<ref>{{Cite journal|last1=Henkel|first1=N.|last2=Cinti|first2=F.|last3=Jain|first3=P.|last4=Pupillo|first4=G.|last5=Pohl|first5=T.|date=2012-06-26|title=Supersolid Vortex Crystals in Rydberg-Dressed Bose-Einstein Condensates|url=http://dx.doi.org/10.1103/physrevlett.108.265301|journal=Physical Review Letters|volume=108|issue=26|page=265301|doi=10.1103/physrevlett.108.265301|pmid=23004994|issn=0031-9007|arxiv=1111.5761|bibcode=2012PhRvL.108z5301H|s2cid=1782501|access-date=2021-09-30|archive-date=2024-09-18|archive-url=https://web.archive.org/web/20240918002514/https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.265301|url-status=live}}</ref> adding a Gaussian peak to the plateau type interaction would form multiple roton unstable points in the Bogoliubov spectrum. Therefore, the excitation around the roton instabilities would grow exponentially and form multiple allowed lattice constants leading to quasi-ordered periodic droplet crystals.<ref name=":0" />

=== Applications ===
Quasicrystalline substances have potential applications in several forms.

Metallic quasicrystalline coatings can be applied by [[thermal spraying]] or [[magnetron sputtering]]. A problem that must be resolved is the tendency for cracking due to the materials' extreme brittleness.<ref name="mrs" /> The cracking could be suppressed by reducing sample dimensions or coating thickness.<ref name="nature.com" /> Recent studies show typically brittle quasicrystals can exhibit remarkable ductility of over 50% strains at room temperature and sub-micrometer scales (<500&nbsp;nm).<ref name="nature.com" />

An application was the use of low-friction Al–Cu–Fe–Cr quasicrystals<ref>{{cite thesis|doi=10.5075/epfl-thesis-2707|author=Fikar, Jan |year=2003|title=Al-Cu-Fe quasicrystalline coatings and composites studied by mechanical spectroscopy|publisher=École polytechnique fédérale de Lausanne EPFL, Thesis n° 2707 (2002)}}</ref> as a coating for [[frying pan]]s. Food did not stick to it as much as to [[stainless steel]] making the pan moderately [[non-stick]] and easy to clean; heat transfer and durability were better than [[PTFE]] non-stick cookware and the pan was free from [[perfluorooctanoic acid]] (PFOA); the surface was very hard, claimed to be ten times harder than stainless steel, and not harmed by metal utensils or cleaning in a [[dishwasher]]; and the pan could withstand temperatures of {{Convert|1000|C|sigfig=2}} without harm. However, after an initial introduction the pans were a chrome steel, probably because of the difficulty of controlling thin films of the quasicrystal.<ref>{{Cite book |last=Widjaja |first=Edy |url=https://www.proquest.com/openview/44d6ab76271620818381a74684e9945a/1?pq-origsite=gscholar&cbl=18750&diss=y&casa_token=9d5DGvy1Q3EAAAAA:InGBLgm8r0b-OQ2GMmc4bosumNpFp5ucdJQzXDqKzTe3fp2Uz5-XVpa2qV5FVNOIBVBb4ZfnQg |title=Quasicrystalline thin films: growth, structure and interface |publisher=Northwestern University |year=2004 |location=Evanston, Illinois, USA |pages=Appendix A |bibcode=2004PhDT........60W |access-date=2023-12-02 |archive-date=2024-09-18 |archive-url=https://web.archive.org/web/20240918002538/https://www.proquest.com/openview/44d6ab76271620818381a74684e9945a/1?pq-origsite=gscholar&cbl=18750&diss=y&casa_token=9d5DGvy1Q3EAAAAA:InGBLgm8r0b-OQ2GMmc4bosumNpFp5ucdJQzXDqKzTe3fp2Uz5-XVpa2qV5FVNOIBVBb4ZfnQg |url-status=live }}</ref>

The Nobel citation said that quasicrystals, while brittle, could reinforce steel "like armor". When Shechtman was asked about potential applications of quasicrystals he said that a precipitation-hardened stainless steel is produced that is strengthened by small quasicrystalline particles. It does not corrode and is extremely strong, suitable for razor blades and surgery instruments. The small quasicrystalline particles impede the motion of dislocation in the material.<ref name="mitrev" />

Quasicrystals were also being used to develop heat insulation, [[LED]]s, diesel engines, and new materials that convert heat to electricity. Shechtman suggested new applications taking advantage of the low coefficient of friction and the hardness of some quasicrystalline materials, for example embedding particles in plastic to make strong, hard-wearing, low-friction plastic gears. The low heat conductivity of some quasicrystals makes them good for heat insulating coatings.<ref name="mitrev" /> One of the special properties of quasicrystals is their smooth surface, which despite the irregular atomic
structure, the surface of quasicrystals can be smooth and flat.<ref>{{cite journal |last1=Bakhtiari |first1=H. |title=An Overview of Quasicrystals, Their Types, Preparation Methods, Properties |journal=Journal of Environmental Friendly Materials |volume=5 |pages=69–76 |url=http://jefm.kiau.ac.ir/article_682540_041d8d272bb5706da2472b22eace5d2c.pdf |access-date=2021-10-31 |archive-date=2021-10-31 |archive-url=https://web.archive.org/web/20211031204626/http://jefm.kiau.ac.ir/article_682540_041d8d272bb5706da2472b22eace5d2c.pdf |url-status=live }}</ref>

Other potential applications include selective solar absorbers for power conversion, broad-wavelength reflectors, and bone repair and prostheses applications where biocompatibility, low friction and corrosion resistance are required. Magnetron sputtering can be readily applied to other stable quasicrystalline alloys such as Al–Pd–Mn.<ref name="mrs" />
[[File:Rendering of quasicrystal structure.jpg|thumb|Rendering of a quasicrystalline structure, created using an open-source model for [[Computational engineering|Computational Engineering]].]]