Quasiperiodic crystals, or quasicrystal , are structures that are ordered but not periodic. The quasicrystalline pattern can continue to fill all available space, but does not have symmetrical translation. While the crystals, according to the classical crystallographic restoration theorem, can have only two, three, four, and six-fold rotational symmetry, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry commands, eg fivefold.
The Aperiodic tunic was invented by mathematicians in the early 1960s, and, some twenty years later, they were found to be applied to the study of quasicrystals. The discovery of these aperiodic forms in nature has resulted in a paradigm shift in the field of crystallography. Quasicrystals had been investigated and observed before, but, until the 1980s, they were ignored for the prevailing view of the atomic structure of matter. In 2009, after a special search, mineralogical findings, icosahedrite, offer evidence of natural quasicrystals.
Roughly speaking, ordering is not periodic if it does not have symmetrical translation, which means that the shifted copy will never match exactly to the original. A more precise mathematical definition is that there is never a symmetry translation in more than n Ã,-1 independent linear directions, where n is the dimension of filled space, for example, tiles the three dimensions shown in quasicrystal may have translational symmetry in two dimensions. The symmetric diffraction pattern is generated from the existence of a large number of unlimited elements with regular distances, a property that is loosely described as a long-term sequence. Experimentally, aperiodicity is expressed in the symmetry of an unusual diffraction pattern, ie symmetry of orders other than two, three, four, or six. In 1982, materials scientist Dan Shechtman observed that certain aluminum-manganese alloys produce an unusual difractogram that is currently seen as a revelation of quasicrystal structures. Fearful of the reaction of the scientific community, it took him two years to publish the results in which he was awarded the Nobel Prize in Chemistry in 2011.
Video Quasicrystal
Histori
In 1961, Hao Wang asked whether determining whether a set of tiles acknowledged tiles from a plane was an issue that had not been solved algorithmically or not. He suspects that it can be solved, depending on the hypothesis that any set of tiles that can compact the aircraft can do so periodically (hence, it will be enough to try to arrange larger and larger patterns until the tiles get acquired periodically). However, two years later, his student, Robert Berger, built a set of about 20,000 square tiles (now called Wang tiles) that can compact aircraft but not periodically. When the next aperiodic tile set is found, the set with fewer and fewer forms is found. In 1976 Roger Penrose discovered a set of only two tiles, now referred to as Penrose tiles, which only produce non-periodic tilings of aircraft. This slope shows a fivefold symmetry sample. One year later Alan Mackay demonstrated experimentally that the diffraction pattern of the Penrose layer has a two-dimensional Fourier transform consisting of a sharp 'delta' peak arranged in a fivefold symmetrical pattern. Around the same time Robert Ammann created a set of aperiodic tiles that produced eight-fold symmetry.
Mathematically, quasicrystals have been proven to be derived from common methods that treat them as projections of higher dimensional lattices. Just as circles, ellipses, and hyperbolic curves in planes can be obtained as part of three-dimensional three-dimensional cones, as well as various (aperiodic or periodic) arrangements in two and three dimensions can be derived from hyperlipins postulated with four or more dimensions.. Icosahedral quasicrystals in three dimensions is projected from a six-dimensional hypercubation lattice by Peter Kramer and Roberto Neri in 1984. The tile is formed by two tiles with a rhombohedral shape.
Shechtman first observed ten times the electron diffraction pattern in 1982, as described in his notebook. Observations were made during routine investigations, with electron microscopy, of rapidly cooled aluminum and manganese alloys prepared at the US National Standards Agency (later NIST).
In the summer of the same year, Shechtman visited Ilan Blech and recounted his observations to him. Blech replied that such diffraction had been seen before. Around that time, Shechtman also linked his findings with John Cahn of NIST who offered no explanation and challenged him to complete his observations. Shechtman quoted Cahn as saying: "Danny, this material tells us something and I challenge you to find out what it is".
Observations of tenfold diffraction patterns were inexplicable for two years until spring 1984, when Blech asked Shechtman to show the results again. A quick study of Shechtman's results shows that the general explanation for ten-fold symmetrical diffraction patterns, the existence of twins, is ruled out by his experiments. Since periodicity and twins are ruled out, Blech, unaware of the work of two-dimensional tiles, seeks another possibility: a completely new structure containing cells connected to each other with clear angles and distances but without translational periodicity. Blech decided to use computer simulations to calculate the intensity of diffraction from a group of such materials without a long-distance translation order but still not random. He termed this new structure some polyhedral.
The idea of ​​a new structure is a necessary paradigm shift to breaking the deadlock. "When Eureka" came when computer simulations showed a sharp tenfold diffraction pattern, similar to the one observed, derived from a three-dimensional structure without periodicity. The structure of some polyhedral is then termed by many researchers as icosahedral glass but basically it embraces a polyhedra arrangement that is connected to a definite angle and distance (this common definition includes tiles, for example).
Shechtman accepted Blech's discovery of a new kind of material and gave him the courage to publish his experimental observations. Shechtman and Blech jointly wrote a paper entitled "The Microstructure of Rapidly Al ( 6 Mn") and submitted it for publication around June 1984 to the Journal of Applied Physics (JAP). The JAP editor immediately rejected the paper as being more suitable for metallurgical readers. As a result, the same paper is sent back for publication to the Metallurgy Transaction A , where it is received. Although not recorded in the body of published texts, the published papers were slightly revised before they were published.
Meanwhile, when looking at the draft of Shechtman-Blech paper in the summer of 1984, John Cahn suggested that the results of the Shechtman experiment deserve a quick publication in a more precise scientific journal. Shechtman agrees and, in hindsight, calls this quick publication "a victory step". This paper, published in Physical Review Letters (PRL), repeats Shechtman's observations and uses the same illustrations as the original Shechtman-Blech paper in Metallurgical Transactions A . PRL papers, which first appeared in print, caused great excitement in the scientific community.
Next year Ishimasa et al. reported twelve-fold symmetry in Ni-Cr particles. Soon, eight-fold diffraction patterns were recorded in V-Ni-Si and Cr-Ni-Si alloys. Over the years, hundreds of quasicrystals with different compositions and symmetries have been found. The first quasicrystalline material is thermodynamically unstable - when heated, they form ordinary crystals. However, in 1987, the first of many stable quasicrystals was invented, making it possible to produce large samples for learning and opening the door for potential applications. In 2009, after a 10-year systematic search, scientists reported the first natural quasicrystal, a mineral found in the Khatyrka River in eastern Russia. This natural quasicrystal shows high crystal quality, matching the best artificial example. Natural quasicrystal phase, with the composition of Al 63 Cu 24 Fe 13 , was named icosahedrite and approved by the International Mineralogical Association in 2010. Furthermore, probably from meteorites, possibly sent from carbon chondrite asteroids.
A further study of the Khatyrka meteorite revealed micron-sized grains of another natural quasicrystal, which has ten-fold symmetry and chemical formula Al 71 Ni 24 Fe 5 . Quasicrystal is stable in a narrow temperature range, from 1120 to 1200 K at ambient pressure, indicating that natural quasicrystals are formed by rapid quenching of heated meteorites during the impact of induction shocks.
In 1972 de Wolf and van Aalst reported that the diffraction patterns generated by sodium carbonate crystals can not be labeled with three indices but required one more, which implies that the underlying structure has four dimensions in the reciprocal space. Other confusing cases have been reported, but until the concept of quasicrystal appears, they are described or rejected. However, in the late 1980s the idea was acceptable, and in 1992, the International Crystallization Union changed its definition of crystal, extending it as a result of Shechtman's findings, reducing it to the ability to produce a distinct pattern of diffraction. and acknowledge the possibility of ordering to be periodic or aperiodic. Now, symmetry corresponding to the translation is defined as "crystallography", leaving room for other "non-crystallographic" symmetry. Therefore, aperiodic or quasiperiodic structure can be divided into two main classes: that is, with the symmetry of the crystal point group, where the unsuitable modulated structures and composite structures are included, and those with the non-crystallographic point-crystalline point, where the quasicrystal structure belongs.
Originally, a new form of material was nicknamed "Shechtmanite". The term "quasicrystal" was first used in print by Steinhardt and Levine shortly after the paper Shechtman was published. The quasicrystalline adjectives are already used, but they are now applied to any pattern with unusual symmetry. The 'quasiperiodical' structure is claimed to be observed in several decorative tilings designed by the architects of medieval Islam. For example, Girih tiles in the medieval Islamic mosque in Isfahan, Iran, are structured in two-dimensional quasicrystallals patterns. However, these claims have been disputed.
Shechtman was awarded the Nobel Prize in Chemistry in 2011 for his work on quasicrystals. "The discovery of quasicrystals reveals a new principle for atom and molecular packing," the Nobel Committee said and pointed out that "this causes a paradigm shift in chemistry."
Maps Quasicrystal
Math
There are several ways to mathematically define the quasicrystalline pattern. One definition, "cut and project" construction, is based on the work of Harald Bohr (brother of mathematician Niels Bohr). The almost periodic concept of function (also called quasiperiodic function) was studied by Bohr, including the works of Bohl and Escanglon. He introduced the idea of ​​superspace. Bohr shows that the quasiperiodic function arises as a limitation of high-dimensional periodic functions to irrational slices (intersections with one or more hyperplanes), and discusses the spectrum of their Fourier points. These functions are not periodically correct, but they are arbitrarily close in some sense, as well as being a projection of a completely periodic function.
In order for the quasicrystal itself to be aperiodic, this slice should avoid the lattice planes of the high dimensional grid. De Bruijn points out that Penrose's tilings can be seen as two-dimensional slices of the structure of five-dimensional hyperkubs. Equivalently, Fourier's transformation of such quasicrystal is zero only in a solid set of points spanned by integer multiples of a finite set of base vectors (projection of the primitive reciprocal lattice vector of the high dimensional grid). The intuitive considerations derived from a simple aperiodic tycoon model are formally expressed in the concept of Meyer and Delone sets. The mathematical pair of physical diffraction is the Fourier transform and the qualitative description of the diffraction image as 'clear-cut' or 'sharp' means the singularity is present in the Fourier spectrum. There are various methods for building quasicrystals models. This is the same method that generates an aperiodic furnace with additional constraints for the diffraction property. Thus, for the substitution of substitution eigenvalues ​​â € <â € The classical theory of crystals reduces the crystals to the point of the lattice where each point is the center of the mass of one of the identical crystal units. The crystal structure can be analyzed by defining the associated group. Quasicrystals, on the other hand, consist of more than one type of unit, so instead of lattice, quasilattices should be used. Instead of groups, groupoids, generalizations of group maths in category theory, is the right tool for studying quasicrystals. Using mathematics for construction and quasicrystal structure analysis is a difficult task for most experimentalists. Computer modeling, based on existing quasicrystals theory, however, greatly facilitates this task. An advanced program has been developed that allows one to build, visualize and analyze their quasicrystal structures and diffraction patterns. Swivel interacting is also analyzed in quasicrystals: The AKLT model and the 8-vertex model are solved in analytic quasicrystals. The study of quasicrystals can explain the most fundamental ideas associated with the quantum critical point observed in heavy metal fermions. Experimental measurements on the gold-aluminum-ytterbium quasicrystal have revealed the quantum critical point that defines the magnetic susceptibility divergence when temperatures tend to be zero. It is recommended that several quasicrystals electronic systems are located at a quantum critical point without tuning, while quasicrystals exhibit scaling behavior typical of their thermodynamic properties and belong to the well-known family of heavy fermion metals.
Materials science
Since the original discovery by Dan Shechtman, hundreds of quasicrystals have been reported and confirmed. Undoubtedly, quasicrystals are no longer a unique solid form; they exist universally in many metal alloys and some polymers. Quasicrystals are found most often in aluminum alloys (Al-Li-Cu, Al-Mn-Si, Al-Ni-Co, Al-Pd-Mn, Al-Cu-Fe, Al-Cu-V, etc.), Other compositions are also known (Cd-Yb, Ti-Zr-Ni, Zn-Mg-Ho, Zn-Mg-Sc, In-Ag-Yb, Pd-U-Si, etc.).
Two types of quasicrystals are known. The first type, polygonal (dihedral) quasicrystals, has a local symmetry axis 8, 10, or 12 fold (octagonal, desagonal, or dodecagonal quasicrystals, respectively). They are periodic along this axis and quasiperiodic in a normal plane. The second type, icosahedral quasicrystals, is aperiodic in all directions.
Quasicrystals are divided into three different thermal stability groups:
- Quasicrystals that grow slowly with slow cooling or casting with the next annealing,
- Metas quasicrystals prepared with melt rounds, and
- Metas quasicrystals formed by amorphous phase crystallization.
Except for the Al-Li-Cu system, all stable quasicrystals are almost free of defects and disturbances, as evidenced by X-rays and electron diffraction revealing peak widths as sharp as perfect crystals such as Si. The Diffraction pattern shows fivefold, three folds, and two symmetries, and the reflections are arranged in a stepwise quasi in three dimensions.
The origin of different stabilization mechanisms for stable and metastable quasicrystals. However, there is a general feature observed in most quasicrystal-forming liquid alloys or their un-cooled liquids: local icosahedral orders. The icosahedral sequence is in equilibrium in the liquid state for stable quasicrystals, whereas the icosahedral sequence is applicable under the undercooled liquid conditions for metastable quasicrystals.
The nanoscale icosahedral phase is formed in massive Zr-, Cu- and Hf-based metal glasses mixed with precious metals.
Most quasicrystals have properties such as ceramics including high thermal and electrical resistance, hardness and brittleness, corrosion resistance, and non-stick properties. Many of the 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 to 700 ° C, are the exception.
Apps
Quasicrystalline substances have potential applications in several forms.
Quasicrystalline metal coatings can be applied by plasma-coating or magnetron sputtering. The problem to be solved is the tendency to crack due to the extreme fragility of the material. Cracking can be reduced by reducing sample dimension or layer thickness. Recent studies show typically fragile quasicrystals can show tremendous ductility of more than 50% of strains at room temperature and sub-micrometer scale (& lt; 500 nm).
Application is the use of low-friction Al-Cu-Fe-Cr quasicrystals as a coating for frying pan. Food does not stick as well as in stainless steels that make the pan less sticky and easy to clean; heat transfer and better durability of PTFE non-stick cookware and the pot is free of perfluorooctanoic acid (PFOA); the surface is very hard, claimed ten times harder than stainless steel, and not harmed by metal equipment or cleaning in a dishwasher; and the pot can withstand temperatures of 1,000 Â ° C (1,800 Â ° F) without harm. However, cooking with lots of salt will etch the quasicrystalline layer used, and the pan is eventually withdrawn from production. Shechtman has one of these pans.
The Nobel quote says that quasicrystals, while fragile, can strengthen steel "like armor". When Shechtman was asked about potential applications of quasicrystals he said that stainless steels produced precipitation were reinforced by small quasicrystalline particles. It does not corrode and is very strong, suitable for razors and surgical instruments. Small quasicrystalline particles inhibit the movement of dislocations in the material.
Quasicrystals are also used to develop heat insulation, LEDs, diesel engines, and new materials that convert heat into electricity. Shechtman suggests new applications take advantage of the low coefficient of friction and hardness of some quasicryine materials, for example implanting particles in plastics to make strong, wear resistant and low friction plastic teeth. The low thermal conductivity of some quasicrystals makes them good for heat insulation coating.
Other potential applications include selective solar absorber for power conversion, wavelength reflector width, and bone repair and prosthesis applications where biocompatibility, low friction and corrosion resistance are required. Magnetron sputtering can be easily applied to other stable quasicrystalline alloys such as Al-Pd-Mn.
While saying that the discovery of icosahedrite, the first quasicristal found in nature, is important, Shechtman does not see any practical application.
See also
- Archimedean solid
- Damage to hyperagamitas
- Fibonacci quasicrystal
- Phason
- Tessellation
- Crystal time
- The Icosahedral twins
Note
References
External links
- Partial Bibliography of Literature on Quasicrystals (1996-2008).
- BBC web page displaying Quasicrystals images
- What is it... Quasicrystal?, AMS Notice 2006, Volume 53, Number 8
- Gateways to quasicrystals: a brief history by P. Kramer
- Quasicrystals: introduction by R. Lifshitz
- Quasicrystals: introduction by S. Weber
- Steinhardt's proposal
- Quasicrystal Research - Documentary 2011 at the University of Stuttgart research
- Thiel, P.A. (2008). "Quasicrystal Surface". Physical Chemical Annual Review . 59 : 129-152. Bibcode: 2008ARPC... 59..129T. doi: 10.1146/annurev.physchem.59.032607.093736. PMID 17988201.
- The Crystallography Foundation.
- Quasicrystals: What are they, and why are they there ?, Marek Mihalkovic and many others. (Microsoft PowerPoint format)
- "Indiana Steinhardt and Quest for Quasicrystals - Conversation with Paul Steinhardt", Ideas Roadshow , 2016
- Shaginyan, V. R.; Msezane, A. Z.; Popov, K. G.; Japaridze, G. S.; Khodel, V. A. (2013). "Common quantum phase phases in quasi crystal and heavy metal fermions". Physical Review B . 87 (24). arXiv: 1302.1806 . Bibcode: 2013PhRvB..87x5122S. doi: 10.1103/PhysRevB.87.245122.
Source of the article : Wikipedia
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