5 fold diffraction pattern symmetries were discovered in 1982 by dan shechtman when he discovered this phase which opened new field of study in quasiperiodic crystals
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Crystallographic restriction theorem The crystallographic restriction theorem in its basic form was based on the observation that the rotational symmetries of a crystal are usually limited to 2-fold, 3-fold, 4-fold, and 6-fold. However, quasicrystals can occur with other diffraction pattern symmetries, such as 5-fold; these were not discovered until 1982 by Dan Shechtman.
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Dan Shechtman Dan Shechtman (Hebrew: דן שכטמן; born January 24, 1941) is the Philip Tobias Professor of Materials Science at the Technion – Israel Institute of Technology, an Associate of the US Department of Energy's Ames Laboratory, and Professor of Materials Science at Iowa State University. On April 8, 1982, while on sabbatical at the U.S. National Bureau of Standards in Washington, D.C., Shechtman discovered the icosahedral phase, which opened the new field of quasiperiodic crystals. Shechtman was awarded the 2011 Nobel Prize in Chemistry for the discovery of quasicrystals, making him one of six Israelis who have won the Nobel Prize in Chemistry.
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Surface freezing Surface freezing is the appearance of long-range crystalline order in a near-surface layer of a liquid. The surface freezing effect is opposite to a far more common surface melting, or premelting. Surface Freezing was experimentally discovered in melts of alkanes and related chain molecules in the early 1990s independently by two groups. John Earnshaw and his group (Queen's University of Belfast) used light scattering, which did not allow a determination of the frozen layer's thickness, and whether or not it is laterally ordered. A group led by Ben Ocko (Brookhaven National Laboratory), Eric Sirota (Exxon) and Moshe Deutsch (Bar-Ilan University, Israel) discovered independently the same effect, using x-ray surface diffraction which allowed them to show that the frozen layer is a crystalline monolayer, with molecules oriented roughly along the surface normal, and ordered in an hexagonal lattice. A related effect, the existence of a smectic phase at the surface of a nematic liquid bulk was observed in liquid crystals by Jens Als-Nielsen (Risø National Laboratory, Denmark) and Peter Pershan (Harvard University) in the early 1980s. However, the surface layer there was neither ordered, nor confined to a single layer. Surface freezing has since been found in a wide range of chain molecules and at various interfaces: liquid-air, liquid-solid and liquid-liquid.
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Victor Anatolyevich Vassiliev Victor Anatolyevich Vassiliev or Vasilyev (Russian: Виктор Анатольевич Васильев ; born April 10, 1956), is a Soviet and Russian mathematician. He is best known for his discovery of the Vassiliev invariants in knot theory (also known as finite type invariants), which subsume many previously discovered polynomial knot invariants such as the Jones polynomial. He also works on singularity theory, topology, computational complexity theory, integral geometry, symplectic geometry, partial differential equations (geometry of wavefronts), complex analysis, combinatorics, and Picard–Lefschetz theory.
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Lattice constant The lattice constant, or lattice parameter, refers to the physical dimension of unit cells in a crystal lattice. Lattices in three dimensions generally have three lattice constants, referred to as "a", "b", and "c". However, in the special case of cubic crystal structures, all of the constants are equal and we only refer to "a". Similarly, in hexagonal crystal structures, the "a" and "b" constants are equal, and we only refer to the "a" and "c" constants. A group of lattice constants could be referred to as lattice parameters. However, the full set of lattice parameters consist of the three lattice constants and the three angles between them.
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Muffin-tin approximation The muffin-tin approximation is a shape approximation of the potential field in an atomistic environment. It is most commonly employed in quantum mechanical simulations of electronic band structure in solids. The approximation was proposed by John C. Slater. Augmented plane wave method is a method which uses muffin-tin approximation. It is a method to approximate the energy states of an electron in a crystal lattice. The basic approximation lies in the potential in which the potential is assumed to be spherically symmetric in the muffin-tin region and constant in the interstitial region. Wave functions (the augmented plane waves) are constructed by matching solutions of the Schrödinger equation within each sphere with plane-wave solutions in the interstitial region, and linear combinations of these wave functions are then determined by the variational method Many modern electronic structure methods employ the approximation. Among them are the augmented plane wave (APW) method, the linear muffin-tin orbital method (LMTO) and various Green's function methods. One application is found in the variational theory developed by Korringa (1947) and by Kohn and Rostoker (1954) referred to as the KKR method. This method has been adapted to treat random materials as well, where it is called the KKR coherent potential approximation.
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Hannay angle In classical mechanics, the Hannay angle is a mechanics analogue of the whirling Geometric phase (or Berry phase). It was named after John Hannay of the University of Bristol, UK.
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Glauber–Sudarshan P representation The Glauber–Sudarshan P representation is a suggested way of writing down the phase space distribution of a quantum system in the phase space formulation of quantum mechanics. The P representation is the quasiprobability distribution in which observables are expressed in normal order. In quantum optics, this representation, formally equivalent to several other representations, is sometimes championed over alternative representations to describe light in optical phase space, because typical optical observables, such as the particle number operator, are naturally expressed in normal order. It is named after George Sudarshan and Roy J. Glauber, who were working on the topic in 1963. It was the subject of a controversy when Glauber was awarded a share of the 2005 Nobel Prize in Physics for his work in this field and George Sudarshan's contribution was not recognized.
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57-cell In mathematics, the 57-cell (pentacontakaiheptachoron) is a self-dual abstract regular 4-polytope (four-dimensional polytope). Its 57 cells are hemi-dodecahedra. It also has 57 vertices, 171 edges and 171 two-dimensional faces. Its symmetry group is the projective special linear group L(19), so it has 3420 symmetries.
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Davydov soliton Davydov soliton is a quantum quasiparticle representing an excitation propagating along the protein α-helix self-trapped amide I. It is a solution of the Davydov Hamiltonian. It is named for the Soviet and Ukrainian physicist Alexander Davydov. The Davydov model describes the interaction of the amide I vibrations with the hydrogen bonds that stabilize the α-helix of proteins. The elementary excitations within the α-helix are given by the phonons which correspond to the deformational oscillations of the lattice, and the excitons which describe the internal amide I excitations of the peptide groups. Referring to the atomic structure of an α-helix region of protein the mechanism that creates the Davydov soliton (polaron, exciton) can be described as follows: vibrational energy of the C=O stretching (or amide I) oscillators that is localized on the α-helix acts through a phonon coupling effect to distort the structure of the α-helix, while the helical distortion reacts again through phonon coupling to trap the amide I oscillation energy and prevent its dispersion. This effect is called "self-localization" or "self-trapping". Solitons in which the energy is distributed in a fashion preserving the helical symmetry are dynamically unstable, and such symmetrical solitons once formed decay rapidly when they propagate. On the other hand, an asymmetric soliton which spontaneously breaks the local translational and helical symmetries possesses the lowest energy and is a robust localized entity.
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Holmium–magnesium–zinc quasicrystal A holmium–magnesium–zinc (Ho–Mg–Zn) quasicrystal is a quasicrystal made of an alloy of those three metals that has the shape of a regular dodecahedron, a Platonic solid with 12 five-sided faces. Unlike the similar pyritohedron shape of some cubic-system crystals such as pyrite, this quasicrystal has faces that are true regular pentagons.
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Single-mode optical fiber In fiber-optic communication, a single-mode optical fiber (SMF) is an optical fiber designed to carry light only directly down the fiber - the transverse mode. Modes are the possible solutions of the Helmholtz equation for waves, which is obtained by combining Maxwell's equations and the boundary conditions. These modes define the way the wave travels through space, i.e. how the wave is distributed in space. Waves can have the same mode but have different frequencies. This is the case in single-mode fibers, where we can have waves with different frequencies, but of the same mode, which means that they are distributed in space in the same way, and that gives us a single ray of light. Although the ray travels parallel to the length of the fiber, it is often called transverse mode since its electromagnetic oscillations occur perpendicular (transverse) to the length of the fiber. The 2009 Nobel Prize in Physics was awarded to Charles K. Kao for his theoretical work on the single-mode optical fiber.
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Yablonovite Yablonovite is a photonic crystal structure that has an inverse cylindrical holes arranged in a diamond lattice. It was the first 3D photonic crystal to be fabricated with a complete photonic bandgap. It was created in 1991 by Eli Yablonovitch and his team.
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Anomalous scattering In X-ray crystallography, anomalous scattering refers to a change in a diffracting X-ray’s phase that is unique from the rest of the atoms in a crystal due to strong X-ray absorbance. The amount of energy that individual atoms absorb depends on their atomic number. The relatively light atoms found in proteins such as carbon, nitrogen, and oxygen do not contribute to anomalous scattering at normal X-ray wavelengths used for X-ray crystallography. Thus, in order to observe anomalous scattering, a heavy atom must be native to the protein or a heavy atom derivative should be made. In addition, the X-ray’s wavelength should be close to the heavy atom’s absorption edge.
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Precession electron diffraction Precession electron diffraction (PED) is a specialized method to collect electron diffraction patterns in a transmission electron microscope (TEM). By rotating (precessing) a tilted incident electron beam around the central axis of the microscope, a PED pattern is formed by integration over a collection of diffraction conditions. This produces a quasi-kinematical diffraction pattern that is more suitable as input into direct methods algorithms to determine the crystal structure of the sample.
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Nowotny phase In inorganic chemistry, a Nowotny chimney ladder phase (NCL phase) is a particular intermetallic crystal structure found with certain binary compounds. NLC phases are generally tetragonal and are composed of two separate sublattices. The first is a tetragonal array of transition metal atoms, generally from group 4 through group 9 of the periodic table. Contained within this array of transition metal atoms is a second network of main group atoms, typically from group 13 (boron group) or group 14 (carbon group). The transition metal atoms form a chimney with helical zigzag chain. The main-group elements form a ladder spiraling around the transition metal helix.
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Sayre equation In crystallography, the Sayre equation, named after David Sayre who introduced it in 1952, is a mathematical relationship that allows to calculate probable values for the phases of some diffracted beams. It is used when employing direct methods to solve a structure. Its formulation is the following:
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Supergranulation Supergranulation is a particular pattern of convection cells on the Sun's surface called supergranules. It was discovered in the 1950s by A.B.Hart using Doppler velocity measurements showing horizontal flows on the photosphere (flow speed about 300 to 500 m/s, a tenth of that in the smaller granules). Later work (1960s) by Leighton, Noyes and Simon established a typical size of about 30000 km for supergranules with a lifetime of about 24 hours.
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Diffuson The diffuson is a mathematical object, which often appears in the theory of disordered electronic systems (a part of condensed matter physics).
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Orthorhombic crystal system In crystallography, the orthorhombic crystal system is one of the 7 crystal systems. Orthorhombic lattices result from stretching a cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular prism with a rectangular base ("a" by "b") and height ("c"), such that "a", "b", and "c" are distinct. All three bases intersect at 90° angles, so the three lattice vectors remain mutually orthogonal.
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Cubic crystal system In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals.
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Columnar phase The columnar phase is a class of mesophases in which molecules assemble into cylindrical structures to act as mesogens. Originally, these kinds of liquid crystals were called discotic liquid crystals or bowlic liquid crystals because the columnar structures are composed of flat-shaped discotic or bowl-shaped molecules stacked one-dimensionally. Since recent findings provide a number of columnar liquid crystals consisting of non-discoid mesogens, it is more common now to classify this state of matter and compounds with these properties as columnar liquid crystals.