Editing Quasicrystal (section)

{{Short description|Ordered chemical structure with no repeating pattern}}
{{Distinguish|Quasi-crystals (supramolecular)}}
{{use mdy dates|date=September 2024 |cs1-dates=sy }}
[[File:Quasicrystal1.jpg|thumb|Potential energy surface for silver depositing on an [[aluminium]]–[[palladium]]–[[manganese]] (Al–Pd–Mn) quasicrystal surface. Similar to Fig. 6 in Ref.<ref>{{cite journal|last=Ünal|first=B|author2=V. Fournée|author3=K.J. Schnitzenbaumer|author4=C. Ghosh|author5=C.J. Jenks|author5-link=Cynthia Jenks|author6=A.R. Ross|author7=T.A. Lograsso|author8=J.W. Evans|author9=P.A. Thiel|title=Nucleation and growth of Ag islands on fivefold Al-Pd-Mn quasicrystal surfaces: Dependence of island density on temperature and flux|journal=Physical Review B|year=2007|volume=75|pages=064205|doi=10.1103/PhysRevB.75.064205|bibcode=2007PhRvB..75f4205U|issue=6|s2cid=53382207|url=http://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1034&context=chem_pubs|access-date=2018-12-21|archive-date=2020-07-28|archive-url=https://web.archive.org/web/20200728104031/https://lib.dr.iastate.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=1034&context=chem_pubs|url-status=live}}</ref>]]

A [[quasiperiodicity|quasiperiodic]] [[crystal]], or '''quasicrystal''', is a [[structure]] that is [[Order and disorder (physics)|ordered]] but not [[Bravais lattice|periodic]]. A quasicrystalline pattern can continuously fill all available space, but it lacks [[translational symmetry]].<ref name="r9" /> While crystals, according to the classical [[crystallographic restriction theorem]], can possess only two-, three-, four-, and six-fold [[rotational symmetries]], the [[Bragg diffraction]] pattern of quasicrystals shows sharp peaks with other [[symmetry]] orders—for instance, five-fold.<ref>{{Cite book|last1=Lifshitz|first1=Ron|last2=Schmid|first2=Siegbert|last3=Withers|first3=Ray L.|url=http://worldcat.org/oclc/847002667|title=Aperiodic crystals|date=2013|publisher=Springer|oclc=847002667|access-date=2022-12-13|archive-date=2024-09-18|archive-url=https://web.archive.org/web/20240918002535/https://search.worldcat.org/title/847002667|url-status=live}}</ref>

[[Aperiodic tiling]]s were discovered by mathematicians in the early 1960s, and some twenty years later, they were found to apply to the study of natural quasicrystals. The discovery of these aperiodic forms in nature has produced a [[paradigm shift]] in the field of [[crystallography]]. In crystallography, the quasicrystals were predicted in 1981 by a five-fold symmetry study of [[Alan Lindsay Mackay]],<ref>Alan L. Mackay, "De Nive Quinquangula", ''Krystallografiya'', Vol. 26, 910–919 (1981).</ref>—that also brought in 1982, with the crystallographic [[Fourier transform]] of a [[Penrose tiling]],<ref name=":1">Alan L. Mackay, "Crystallography and the Penrose Pattern", ''Physica'' 114 A, 609 (1982).</ref> the possibility of identifying quasiperiodic order in a material through diffraction.

Quasicrystals had been investigated and observed earlier,<ref name=":2">{{cite journal|author=Steurer W.|journal= Z. Kristallogr. |volume=219 |year=2004|pages= 391–446|doi=10.1524/zkri.219.7.391.35643|title=Twenty years of structure research on quasicrystals. Part I. Pentagonal, octagonal, decagonal and dodecagonal quasicrystals|issue=7–2004|bibcode = 2004ZK....219..391S |doi-access=free}}</ref> but, until the 1980s, they were disregarded in favor of the prevailing views about the atomic structure of matter. In 2009, after a dedicated search, a mineralogical finding, [[icosahedrite]], offered evidence for the existence of natural quasicrystals.<ref name="r5" />

Roughly, an ordering is non-periodic if it lacks [[translational symmetry]], which means that a shifted copy will never match exactly with its original. The more precise mathematical definition is that there is never translational symmetry in more than ''n''&nbsp;–&nbsp;1 [[linear independence|linearly independent]] directions, where ''n'' is the dimension of the space filled, e.g., the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two directions. Symmetrical diffraction patterns result from the existence of an indefinitely large number of elements with regular spacing, a property loosely described as [[long-range order]]. Experimentally, the aperiodicity is revealed in the unusual symmetry of the diffraction pattern, that is, symmetry of orders other than two, three, four, or six.

In 1982, [[materials science|materials scientist]] [[Dan Shechtman]] observed that certain [[aluminium]]–[[manganese]] alloys produced unusual diffractograms, which today are seen as revelatory of quasicrystal structures. Due to fear of the scientific community's reaction, it took him two years to publish the results.<ref name="bloomberg" /><ref name="s" /> Shechtman's discovery challenged the long-held belief that all crystals are periodic. Observed in a rapidly solidified Al-Mn alloy, quasicrystals exhibited [[icosahedral symmetry]], which was previously thought impossible in crystallography.<ref>{{Cite journal |last1=Blech |first1=Ilan A. |last2=Cahn |first2=John W. |last3=Gratias |first3=Denis |date=2012-10-01 |title=Reminiscences About a Chemistry Nobel Prize Won with Metallurgy: Comments on D. Shechtman and I. A. Blech; Metall. Trans. A, 1985, vol. 16A, pp. 1005–12 |url=https://link.springer.com/article/10.1007/s11661-012-1323-1 |journal=Metallurgical and Materials Transactions A |language=en |volume=43 |issue=10 |pages=3411–3422 |doi=10.1007/s11661-012-1323-1 |bibcode=2012MMTA...43.3411B |issn=1543-1940}}</ref> This breakthrough, supported by theoretical models and experimental evidence, led to a paradigm shift in the understanding of solid-state matter. Despite initial skepticism, the discovery gained widespread acceptance, prompting the [[International Union of Crystallography]] to redefine the term "[[crystal]]."<ref>{{Cite web |title=articles |url=https://www.iucr.org/news/newsletter/etc/articles?issue=151351&result_138339_result_page=17 |access-date=2024-11-22 |website=www.iucr.org}}</ref> The work ultimately earned Shechtman the 2011 [[Nobel Prize in Chemistry]]<ref name="nobel" /> and inspired significant advancements in materials science and mathematics.

On 25 October 2018, [[Luca Bindi]] and [[Paul Steinhardt]] were awarded the Aspen Institute 2018 Prize for collaboration and scientific research between Italy and the United States after discovering [[icosahedrite]], the first quasicrystal known to occur naturally.