Quasicrystal
A
Aperiodic tilings 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,[4]—that also brought in 1982, with the crystallographic Fourier transform of a Penrose tiling,[5] the possibility of identifying quasiperiodic order in a material through diffraction.
Quasicrystals had been investigated and observed earlier,[6] 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.[7]
Roughly, an ordering is non-periodic if it lacks
History
The first representations of perfect quasicrystalline patterns can be found in several early Islamic works of art and architecture such as the Gunbad-i-Kabud tomb tower, the Darb-e Imam shrine and the Al-Attarine Madrasa.[12][13] On July 16, 1945, in Alamogordo, New Mexico, the Trinity nuclear bomb test produced icosahedral quasicrystals. They went unnoticed at the time of the test but were later identified in samples of red Trinitite, a glass-like substance formed from fused sand and copper transmission lines. Identified in 2021, they are the oldest known anthropogenic quasicrystals.[14][15]
In 1961,
In 1972, de Wolf and van Aalst[17] reported that the diffraction pattern produced by a crystal of sodium carbonate cannot be labeled with three indices but needed one more, which implied that the underlying structure had four dimensions in reciprocal space. Other puzzling cases have been reported,[18] but until the concept of quasicrystal came to be established, they were explained away or denied.[19][20]
Shechtman first observed ten-fold
The observation of the ten-fold diffraction pattern lay unexplained for two years until the spring of 1984, when Blech asked Shechtman to show him his results again. A quick study of Shechtman's results showed that the common explanation for a ten-fold symmetrical diffraction pattern, a type of
Shechtman accepted Blech's discovery of a new type of material and chose to publish his observation in a paper entitled "The Microstructure of Rapidly Solidified Al6Mn", which was written around June 1984 and published in a 1985 edition of
Originally, the new form of matter was dubbed "Shechtmanite".[28] The term "quasicrystal" was first used in print by Steinhardt and Levine[2] shortly after Shechtman's paper was published.
Also in 1985, Ishimasa et al. reported twelvefold symmetry in Ni-Cr particles.[29] Soon, eightfold diffraction patterns were recorded in V-Ni-Si and Cr-Ni-Si alloys.[30] Over the years, hundreds of quasicrystals with various compositions and different symmetries have been discovered. The first quasicrystalline materials were thermodynamically unstable—when heated, they formed regular crystals. However, in 1987, the first of many stable quasicrystals were discovered, making it possible to produce large samples for study and applications.[31]
In 1992, the International Union of Crystallography altered its definition of a crystal, reducing it to the ability to produce a clear-cut diffraction pattern and acknowledging the possibility of the ordering to be either periodic or aperiodic.[8][32]
In 2001, Paul Steinhardt of Princeton University hypothesized that quasicrystals could exist in nature and developed a method of recognition, inviting all the mineralogical collections of the world to identify any badly cataloged crystals. In 2007 Steinhardt received a reply by Luca Bindi, who found a quasicrystalline specimen from Khatyrka in the University of Florence Mineralogical Collection. The crystal samples were sent to Princeton University for other tests, and in late 2009, Steinhardt confirmed its quasicrystalline character. This quasicrystal, with a composition of Al63Cu24Fe13, was named icosahedrite and it was approved by the International Mineralogical Association in 2010. Analysis indicates it may be meteoritic in origin, possibly delivered from a carbonaceous chondrite asteroid. In 2011, Bindi, Steinhardt, and a team of specialists found more icosahedrite samples from Khatyrka.[34] A further study of Khatyrka meteorites revealed micron-sized grains of another natural quasicrystal, which has a ten-fold symmetry and a chemical formula of Al71Ni24Fe5. This quasicrystal is stable in a narrow temperature range, from 1120 to 1200 K at ambient pressure, which suggests that natural quasicrystals are formed by rapid quenching of a meteorite heated during an impact-induced shock.[33]
Shechtman was awarded the Nobel Prize in Chemistry in 2011 for his work on quasicrystals. "His discovery of quasicrystals revealed a new principle for packing of atoms and molecules," stated the Nobel Committee and pointed that "this led to a paradigm shift within chemistry."[8][35] In 2014, Post of Israel issued a stamp dedicated to quasicrystals and the 2011 Nobel Prize.[36]
While the first quasicrystals discovered were made out of intermetallic components, later on quasicrystals were also discovered in soft-matter and molecular systems. Soft quasicrystal structures have been found in supramolecular dendrimer liquids[37] and ABC Star Polymers[38] in 2004 and 2007. In 2009, it was found that thin-film quasicrystals can be formed by self-assembly of uniformly shaped, nano-sized molecular units at an air-liquid interface.[39] It was demonstrated that these units can be both inorganic and organic.[40] Additionally in the 2010s, two-dimensional molecular quasicrystals were discovered, driven by intermolecular interactions[41] and interface-interactions.[42]
In 2018, chemists from Brown University announced the successful creation of a self-constructing lattice structure based on a strangely shaped quantum dot. While single-component quasicrystal lattices have been previously predicted mathematically and in computer simulations,[43] they had not been demonstrated prior to this.[44]
Mathematics
There are several ways to mathematically define quasicrystalline patterns. One definition, the "cut and project" construction, is based on the work of Harald Bohr (mathematician brother of Niels Bohr). The concept of an almost periodic function (also called a quasiperiodic function) was studied by Bohr, including work of Bohl and Escanglon.[45] He introduced the notion of a superspace. Bohr showed that quasiperiodic functions arise as restrictions of high-dimensional periodic functions to an irrational slice (an intersection with one or more hyperplanes), and discussed their Fourier point spectrum. These functions are not exactly periodic, but they are arbitrarily close in some sense, as well as being a projection of an exactly periodic function.
In order that the quasicrystal itself be aperiodic, this slice must avoid any
Classical theory of crystals reduces crystals to point lattices where each point is the center of mass of one of the identical units of the crystal. The structure of crystals can be analyzed by defining an associated group. Quasicrystals, on the other hand, are composed of more than one type of unit, so, instead of lattices, quasilattices must be used. Instead of groups, groupoids, the mathematical generalization of groups in category theory, is the appropriate tool for studying quasicrystals.[49]
Using mathematics for construction and analysis of quasicrystal structures is a difficult task for most experimentalists. Computer modeling, based on the existing theories of quasicrystals, however, greatly facilitated this task. Advanced programs have been developed[50] allowing one to construct, visualize and analyze quasicrystal structures and their diffraction patterns. The aperiodic nature of quasicrystals can also make theoretical studies of physical properties, such as electronic structure, difficult due to the inapplicability of Bloch's theorem. However, spectra of quasicrystals can still be computed with error control.[51]
Study of quasicrystals may shed light on the most basic notions related to the
Materials science
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.).[53]
Two types of quasicrystals are known.[50] 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.[54]
Quasicrystals fall into three groups of different thermal stability:[55]
- Stable quasicrystals grown by slow cooling or annealing,
- Metastable quasicrystals prepared by melt spinning, and
- Metastable quasicrystals formed by the amorphousphase.
Except for the Al–Li–Cu system, all the stable quasicrystals are almost free of defects and disorder, as evidenced by 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.[56]
Most quasicrystals have ceramic-like properties including high thermal and electrical resistance, hardness and brittleness, resistance to corrosion, and non-stick properties.[57] Many metallic quasicrystalline substances are impractical for most applications due to their 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 °C, are notable exceptions.
The quasi-ordered droplet crystals could be formed under Dipolar forces in the Bose Einstein condensate.[58] While the softcore Rydberg dressing interaction has forms triangular droplet-crystals,[59] 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.[58]
Applications
Quasicrystalline substances have potential applications in several forms.
Metallic quasicrystalline coatings can be applied by
An application was the use of low-friction Al–Cu–Fe–Cr quasicrystals
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.[63]
Quasicrystals were also being used to develop heat insulation,
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.[57]
Non-material science applications
Applications in macroscopic engineering have been suggested, building quasi-crystal-like large scale engineering structures, which could have interesting physical properties. Also, aperiodic tiling lattice structures may be used instead of isogrid or honeycomb patterns. None of these seem to have been put to use in practice.[65]
See also
- Aperiodic crystal – Crystal type lacking 3D periodicity
- Archimedean solid – Polyhedra in which all vertices are the same
- Crystallography – Scientific study of crystal structures
- Disordered hyperuniformity– A state similar to a liquid and a crystal in properties.
- Fibonacci quasicrystal– Binary sequence from Fibonacci recurrence
- Fiveling – Five crystals arranged round a common axis
- Icosahedral twins – Structure found in atomic clusters and nanoparticles
- Phason – Collective excitation in aperiodic materials
- Tessellation – Tiling of a plane in mathematics
- Time crystal – Structure that repeats in time; a novel type or phase of non-equilibrium matter
References
- S2CID 53382207.
- ^ .
- OCLC 847002667.
- ^ Alan L. Mackay, "De Nive Quinquangula", Krystallografiya, Vol. 26, 910–919 (1981).
- ^ Alan L. Mackay, "Crystallography and the Penrose Pattern", Physica 114 A, 609 (1982).
- .
- S2CID 14512017.
- ^ a b c Gerlin, Andrea (October 5, 2011). "Tecnion's Shechtman Wins Nobel in Chemistry for Quasicrystals Discovery". Bloomberg. Archived from the original on December 5, 2014. Retrieved January 4, 2019.
- ^ .
- ^ "The Nobel Prize in Chemistry 2011". Nobelprize.org. Retrieved 2011-10-06.
- S2CID 10374218.
- ISBN 978-94-007-6431-6.
- ^ "Islamic Quasicrystal Tilings | Paul J. Steinhardt". paulsteinhardt.org. Retrieved 2023-05-29.
- PMID 34001665.
- ^ Mullane, Laura (May 18, 2021). "Newly discovered quasicrystal was created by the first nuclear explosion at Trinity Site". Phys.org. Retrieved May 21, 2021.
- .
- ^ de Wolf, R.M. & van Aalst, W. (1972). "The four dimensional group of γ-Na2CO3". Acta Crystallogr. A. 28: S111.
- .
- PMID 10034915.
- ^ Kenneth Chang (October 5, 2011). "Israeli Scientist Wins Nobel Prize for Chemistry". NY Times.
- ^ "QC Hot News". Archived from the original on 2011-10-07.
- ISSN 0031-9015.
- .
- .
- ^ "NIST and the Nobel (September 30, 2016, Updated November 17, 2019) The Nobel Moment: Dan Shechtman". NIST. 30 September 2016.
- ISBN 9780120406036.
- S2CID 136733193.
- ^ Browne, Malcolm W. (1989-09-05). "Impossible' Form of Matter Takes Spotlight In Study of Solids". New York Times.
- PMID 10032372.
- PMID 10035936.
- ISSN 0031-9228.
- ^ "Quasicrystal - Online Dictionary of Crystallography". dictionary.iucr.org. Retrieved 2024-04-04.
- ^ PMID 25765857.
- PMID 22215583.
- ^ "Nobel win for crystal discovery". BBC News. 2011-10-05. Retrieved 2011-10-05.
- ^ Crystallography matters ... more! iycr2014.org
- S2CID 4429689.
- PMID 17677627.
- S2CID 4344953.
- PMID 30573624.
- S2CID 4401013.
- S2CID 22736155.
- PMID 25485986.
- PMID 30573624.
- .
- ^ de Bruijn, N. (1981). "Algebraic theory of Penrose's non-periodic tilings of the plane". Nederl. Akad. Wetensch. Proc. A84: 39.
- .
- ISBN 978-3-540-64224-4.
- ISBN 978-0-8176-4051-4.
- ^ PMID 27877919.
- S2CID 198463498.
- S2CID 7686382.
- S2CID 120125675.
- .
- PMID 27877926.
- .
- ^ .
- ^ S2CID 220301701.
- S2CID 1782501.
- ^ PMID 27515779.
- .
- ^ Widjaja, Edy (2004). Quasicrystalline thin films: growth, structure and interface. Evanston, Illinois, USA: Northwestern University. pp. Appendix A.
- ^ a b Kalman, Matthew (12 October 2011). "The Quasicrystal Laureate". MIT Technology Review. Retrieved 12 February 2016.
- ^ Bakhtiari, H. "An Overview of Quasicrystals, Their Types, Preparation Methods, Properties" (PDF). Journal of Environmental Friendly Materials. 5: 69–76.
- ^ Kayser, Lin (2023-03-20). "Could centuries-old islamic patterns be the key to hypersonic flight?". Josefine Lissner and Lin Kayser. Retrieved 2023-03-20.
External links
- A Partial Bibliography of Literature on Quasicrystals (1996–2008).
- What is... a Quasicrystal?, Notices of the AMS2006, Volume 53, Number 8
- Gateways towards quasicrystals: a short history by P. Kramer
- Quasicrystals: an introduction by R. Lifshitz
- Quasicrystals: an introduction by S. Weber
- Steinhardt's proposal Archived 2016-10-18 at the Wayback Machine
- Quasicrystal Research – Documentary 2011 on the research of the University of Stuttgart
- Thiel, P.A. (2008). "Quasicrystal Surfaces". PMID 17988201.
- "Indiana Steinhardt and the Quest for Quasicrystals – A Conversation with Paul Steinhardt" Archived 2016-11-04 at the Wayback Machine, Ideas Roadshow, 2016
- Shaginyan, V. R.; Msezane, A. Z.; Popov, K. G.; Japaridze, G. S.; Khodel, V. A. (2013). "Common quantum phase transition in quasicrystals and heavy-fermion metals". Physical Review B. 87 (24): 245122. S2CID 119239115.
- BBC webpage showing pictures of Quasicrystals
- Quasicrystal Blocks: Description and Cut & Fold Instructions Space-filling models