Quasicrystal is a kind ofcrystalandAmorphousSolids between.Quasicrystals have long range orderedatomHowever, quasicrystals do not possess translational symmetry of crystals.[1]Therefore, it can have macroscopic symmetry that is not allowed by crystals.
Quasicrystals, also known as "quasicrystals" or "quasicrystals", arecrystalandAmorphousSolid structure between.In the atomic arrangement of quasicrystals, their structure is long range ordered, which is similar to that of crystals;But quasicrystals do not have translational symmetry, which is different from crystals.Ordinary crystals have quadratic, cubic, quartic or sixth rotational symmetry, but the Bragg diffraction patterns of quasicrystals have other symmetries, such as quintic symmetry or higher than sixth symmetry.[1]
The composition of a substance depends on the arrangement of its atoms.The solid matter whose atoms are arranged in a periodic manner is called crystal, the one whose atoms are arranged in disorder is called amorphous, and the one between the two is called quasicrystal.The discovery of quasicrystals was in the 1980sCrystallographyA breakthrough in research.
On April 8, 1982, Shechtman firstelectron microscopeAn "abnormal" phenomenon was observed below:Aluminium manganese alloyThe atoms of are arranged in a non repetitive, non periodic, but symmetrical and orderly manner.At that time, it was generally believed that the atoms in the crystal were arranged in a symmetrical pattern that was periodically repeated. This repeated structure was necessary for the formation of the crystal. There could be no crystal with the atomic arrangement found by Shechtman in nature.Subsequently, scientists produced more and more quasicrystals in the laboratory, and discovered pure natural quasicrystals for the first time in 2009.[2]
This quasicrystal is also related to the Fibonacci sequence, in which each number is the sum of the first two numbers.In 1753,University of GlasgowRobert Simpson, a mathematician ofGolden ratio(a similar to piInfinite acyclic decimal, its value is about 0.618).Scientists later proved that the distance between atoms in quasicrystals also fully conforms to the golden section.In 1982, when Shechtman conducted the experiment of "diffraction grating", he let electrons diffract through aluminum manganese alloy, and found that innumerable concentric circles were surrounded by 10 light points, which was exactly a 10th symmetry.At that time, Shechtman thought "this is impossible" and wrote on his notebook: "10 times?" However, in 1987, French and Japanese scientists successfully manufactured quasicrystal structures in the laboratory;In 2009, scientists found the "trace" of natural quasicrystals in the mineral samples obtained from Lake Khatelka in eastern Russia. This new mineral named icosahedrite (taken from the icosahedron) is composed of aluminum, copper and iron;A Swedish company also found quasicrystals in the most durable steel, which is used in razor blades and surgical needles for ophthalmic surgery.[2]
nature
Announce
edit
Quintic rotational symmetry
Fig. 2 Atomic model of silver aluminum quasicrystal
In classical crystallography, no matter 14 Braffie lattices or 230 space groups, quintic symmetry is not allowed, because quintic symmetry will breakSpatial latticeIt is impossible to fill the two-dimensional plane with a regular pentagon, or fill the three-dimensional space with an icosahedron.The discovery of quasicrystals has overturned this idea. One of the characteristics of quasicrystals is the quintic symmetry.In fact, opal in the ore world, boron ring compounds in organic chemistry, and viruses in biology all show five symmetry characteristics. Mathematicians have already made theoretical preparations for quasicrystals. In 1974, Roger Penrose, an Englishman, based on previous work, proposed a solution to pave the plane with two quadrilateral puzzles, as shown in Figure 2.For Shechtman's quasicrystal diffraction pattern and Penrose's puzzle, there is a fascinating property, that is, there is a wonderful mathematical constant τ hidden in their shape, that isGolden section0.618……。Penrose puzzle is a mosaic of two quadrangles, one fat and one thin (the internal angles are 72 degrees, 108 degrees and 36 degrees, 144 degrees respectively). The ratio of the number of the two quadrangles is just τ;Similarly, in quasicrystals, the ratio of the distances between atoms tends to approach this value.Then, in 1981-1982, Mackay extended the concept of Penrose to three-dimensional space. The icosahedral symmetry was obtained by inserting two kinds of tridecahedrons, and the optical diffraction pattern of quintic symmetry was obtained by using an optical transformation instrument.[1]
Quasi periodicity
As we all know, quintic symmetry and periodicity cannot coexist.If we insist on quintic symmetry, we must consider quasi periodicity.,Seen from an axis orthogonal to the 5th axis, the length of the line segment is not random, but there are only one long and one short. Their ratio is exactly 0.618... of the golden section, and all included angles in the figure are integral multiples of/5.That is to say, although there is no periodicity in this two-dimensional structure, it is not completely disordered, whether in length orincluded angleAll have fixed values.
Quasi periodicity is characterized byIrrational numberIn the one-dimensional quasi periodic lattice, in addition to the translation unit 1, it can also be translated.A two-dimensional square lattice, select a strip with a slope of, and project the points on it into the one-dimensional space E//(horizontal space) to form a one-dimensional quasi periodic lattice with lengths of L and S, LSLLSLSL.... This one-dimensional quasi periodic lattice is characterized by that there is no S nearest neighbor on either side of S, and there is only one L nearest neighbor on either side of L.Since the slope of the strip is an irrational number, its sideline can only pass through one arraySlopeIf the rational number is changed to 2/1, then the projection of the strip in the parallel space becomes a periodic LLSLLS.It can be seen from this that both one-dimensional periodic lattice and one-dimensional quasi periodic lattice can be obtained by the projection of a two-dimensional periodic lattice. The only difference is the slope of the selected projection band. The former is a rational number, and the latter is an irrational number.[1]
Quasicrystal and Art
Interestingly, the combination of the rich colors of light and the unique geometric structure of quasicrystals will show extraordinary artistry.The quasicrystal patterns presented in many fields of research, such as quasicrystal polymer structure, quasicrystal diffraction patterns, and the distribution intensity of resonant states in photonic quasicrystals, are of high artistic appreciation value.
The aperiodic mosaics in Alhambra Palace in Spain and Darb iImam Mosque in Iran reflect the perfect combination of quasicrystal patterns and architectural art.
Akio Hizume, a Japanese artist, drew inspiration from quasicrystals and created three-dimensional quasicrystals with 510 small bamboo poles.[1]
development history
Announce
edit
Quasicrystal diffraction pattern
The structure of quasicrystals was well known by architects before the 20th century, for example, in IranIsfahanThe pattern of the tiles on the mosque is arranged according to the quasicrystal pattern.
In 1961, mathematician Wang Hao put forward the problem of using different shapes of puzzles to cover the plane.Mathematicians have known that a plane can be filled with a single shape puzzle, such as a quadrilateral orRegular hexagon, but when you increase the types of puzzle units, you can construct more methods to fill a plane.Two years later, Wang Hao's student Robert Berger constructed a series of non cyclical puzzle methods.After that, the types of puzzles needed to pave the plane became less and less. In 1976, Roger Penrose constructed a series of methods that only needed two kinds of puzzles. The patterns created by this method had quintic symmetry.
At the end of 1984,D.ShechtmanEt al. announced that they have found a five foldRotational symmetryHowever, there is no alloy image with translational periodicity, that is, 20 faceted quasicrystal. The puzzle form of this quasicrystal consists of two different rhombic shapes.This article was published in 1984 under the title "ALong-range orderBut the metallic phase with Long Range Oriental Order and No Translational Symmetry.The quintic symmetry structure they found was produced in the rapidly cooled Al Mn alloy after melting.stayCrystallographyAnd related academic circles caused a great shock.Soon, this kind of crystal without translation periodicity but with position order is called quasicrystal.
Quasicrystals were discovered in 1982 and haveConvex polyhedronRegular shape, but different from crystal solid materials, they have a five fold axis that crystal materials do not have.QuasicrystallineRegular dodecahedronAppearance.All known quasicrystals areIntermetallic compound。All hundreds of quasicrystals discovered before 2000 contain at least three metals, such as Al65Cu23Fe12, Al70Pd21Mn9, etc.However, it is almost found that only two metals can also form quasicrystals, such as Cd57Yb10 [Nature, 2000408:537].
In 2009, a discovery in mineralogy provided evidence for the formation of quasicrystals under natural conditions: quasicrystal particles composed of Al63Cu24Fe13 were found on an aluminum zinc copper deposit in Russia.As synthesized in the laboratory, the crystallinity of these particles is very good.
The composition and structure of quasicrystals are still under study.For example, Al70Pd21Mn9 is a quasicrystal, while Al60Pd25Mn15 is a crystal.With regard to the structure, it is generally believed that quasicrystals have a three-dimensional periodic structure that deviates from the crystal, because the monotonous periodic structure cannot have a five fold axis, but the structure of quasicrystals is still regular, unlikeAmorphous substanceThat kind of close-up disorder is still some kind of close-upOrdered structure。
Although the composition and structure of quasicrystals have not yet been fully clarified, their discovery has theoreticallyCrystallographyIt has a great impact, so thatInternational Union of CrystallographyRecently, it was suggested thatcrystalDefined asA solid with a well-defined pattern(any solid having an essentially discrete diffusion diagram) to replace the original definition of the periodic structure of micro space.In fact, quasicrystals have been developed as useful materials.For example, quasicrystals composed of aluminum copper iron chromium have been found to have low frictioncoefficient, high hardness, low surface energy and low heat transfer, is being developed for cooking potPlating；Al65Cu23Fe12 is very wear-resistant and has been developed as the coating of high-temperature arc nozzle.
application
Announce
edit
Quasicrystals have unique properties, hard and elastic, very smooth, and different from most metals, they conduct electricityThermal conductivityIt is very poor, so it can be used in daily life.Scientists are trying to apply it to other products, such as non stick pan andlight-emitting diodeEtc.In addition, although their thermal conductivity is poor, because they can convert heat into electricity, they can be used as ideal thermoelectric materials to recycle heat. Some scientists are trying to use them to capture the heat of car waste.[2]
Discoverer
Announce
edit
Daniel Shechtman, an Israeli scientist, enjoyed 2011 alone because of the discovery of quasicrystalsNobel Prize in Chemistry。
In 2011, 70 year old Shechtman will receive 10 million yuanSwedish krona(about 1.4 million US dollars).Shechtman discovered quasicrystals, which have a strange structure and overturn the concept established in crystallography.For many years, condensed matter physicists only cared aboutCrystalline stateSolid matter.However, in the past few decades, they have gradually turned their attention to "amorphous" materials, such as liquid or amorphous, in which the atoms are onlyShort-range order, known as lack of "spacePeriodicity”。
In 1982, Shechtman found quasicrystals when he worked at Hopkins University in the United States. This new structure is not crystal because of the lack of spatial periodicity, but unlike amorphous, quasicrystals show perfectLong-range orderThis fact has brought a huge impact to the crystallography community, which challenges the basic concept of the equivalence of long-range order and periodicity.
