# Centrosymmetry

In crystallography, a point group which contains an inversion center as one of its symmetry elements is centrosymmetric.[1] In such a point group, for every point (x, y, z) in the unit cell there is an indistinguishable point (-x, -y, -z). Such point groups are also said to have inversion symmetry.[2] Point reflection is a similar term used in geometry. Crystals with an inversion center cannot display certain properties, such as the piezoelectric effect.

The following space groups have inversion symmetry: the triclinic space group 2, the monoclinic 10-15, the orthorhombic 47-74, the tetragonal 83-88 and 123-142, the trigonal 147, 148 and 162-167, the hexagonal 175, 176 and 191-194, the cubic 200-206 and 221-230.[3]

Point groups lacking an inversion center (non-centrosymmetric) can be polar, chiral , both or neither.

A polar point group is one whose symmetry operations leave more than one common point unmoved. A polar point group has no unique origin because each of those unmoved points can be chosen as one. The unmoved points collectively make one or more unique anisotropic axes. Polar point groups in crystal include 1, 2, 3, 4, 6, m, mm2, 3m, 4mm, and 6mm.

A chiral (often also called enantiomorphic) point group is one containing only proper (often called "pure") rotation symmetry. No inversion, reflection, roto-inversion or roto-reflection (i.e., improper rotation) symmetry exists in such point group. Chiral point groups in crystal include 1, 2, 3, 4, 6, 222, 422, 622, 32, 23, and 432. Chiral molecules such as proteins crystallize in chiral point groups.

Non-centrosymmetric point groups in crystal 1, 2, 3, 4, 6 are both polar and chiral.

Non-centrosymmetric point groups in crystal -4, -42m, -6, -6m2, -43m are neither polar nor chiral. On the other hand, polar and chiral point groups must be non-centrosymmetric.

Benzene is a centrosymmetric molecule having a centre of symmetry at the centre

## References

1. ^ Tilley, Richard (2006). "4". Crystals and Crystal Structures. John Wiley. pp. 80–83. ISBN 978-0-470-01821-7.
2. ^ Fu, Liang; Kane, C. "Topological insulators with inversion symmetry". Physical Review B. 76 (4). arXiv:cond-mat/0611341. Bibcode:2007PhRvB..76d5302F. doi:10.1103/PhysRevB.76.045302.
3. ^ Cockcroft, Jeremy Karl. "The 230 3-Dimensional Space Groups". Birkbeck College, University of London. Retrieved 18 August 2014.
Anomalous photovoltaic effect

The anomalous photovoltaic effect (APE), also called the bulk photovoltaic effect in certain cases, is a type of a photovoltaic effect which occurs in certain semiconductors and insulators. The "anomalous" refers to those cases where the photovoltage (i.e., the open-circuit voltage caused by the light) is larger than the band gap of the corresponding semiconductor. In some cases, the voltage may reach thousands of volts.

Although the voltage is unusually high, the short-circuit current is unusually low. Overall, materials that exhibit the anomalous photovoltaic effect have very low power generation efficiencies, and are never used in practical power-generation systems.

There are several situations in which APE can arise.

First, in polycrystalline materials, each microscopic grain can act as a photovoltaic. Then the grains add in series, so that the overall open-circuit voltage across the sample is large, potentially much larger than the bandgap.

Second, in a similar manner, certain ferroelectric materials can develop stripes consisting of parallel ferroelectric domains, where each domain acts like a photovoltaic and each domain wall acts like a contact connecting the adjacent photovoltaics (or vice versa). Again, domains add in series, so that the overall open-circuit voltage is large.Third, a perfect single crystal with a non-centrosymmetric structure can develop a giant photovoltage. This is specifically called the bulk photovoltaic effect, and occurs because of non-centrosymmetry. Specifically, the electron processes—photo-excitation, scattering, and relaxation—occur with different probabilities for electron motion in one direction versus the opposite direction.

Audio Video Standard

Audio Video Coding Standard (AVS) refers to the digital audio and digital video series compression standard formulated by Audio and Video coding standard workgroup of China according to the open international rules. At present, the formulation of two-generation AVS standards has been completed.The first generation AVS standard includes “Information Technology, Advanced Audio Video Coding, Part 2: Video” (AVS1 for short) and “Information Technology, Advanced Audio Video Coding Part 16: Radio Television Video” (AVS+ for short).

For the second generation AVS standard, referred to as AVS2, the primary application target is Ultra HD (High Definition) video, supporting the efficient compression of ultra high-resolution (4K above), HDR (High Dynamic Range) videos, and it has been submitted to the IEEE international standard (Standard No.: IEEE1857.4) for application.

The “AVS Patent Pool” provides one-stop authorization for AVS standard, which charges only a small amount of royalties for terminal products, excluding content providers and operators. The royalty for the first generation AVS standard is one yuan per terminal.In order to propel the development and promotion of the AVS standard, Huawei, TCL, Skyworth and other companies established Zhongguancun audiovisual industry technology innovation alliance (abbreviation: AVS industry alliance), which is devoted to the development and promotion of the AVS standard.

Flexoelectricity

Flexoelectricity is a property of a dielectric material whereby it exhibits a spontaneous electrical polarization induced by a strain gradient. Flexoelectricity is closely related to piezoelectricity, but while piezoelectricity refers to polarization due to uniform strain, flexoelectricity refers specifically to polarization due to strain that changes from point to point in the material. This nonuniform strain breaks centrosymmetry, meaning that unlike in piezoelectiricty, flexoelectric effects can occur in centrosymmetric crystal structures. Flexoelectricity is not the same as Ferroelasticity.

The electric polarization due to mechanical stress in a dielectric is given by

${\displaystyle P_{i}=d_{ijk}\sigma _{jk}+\mu _{ijkl}{\frac {\partial \epsilon _{jk}}{\partial x_{l}}}}$

where the first term corresponds to the direct piezoelectric effect and the second term corresponds to the flexoelectric polarization induced by the strain gradient.

Here, the flexoelectric coefficient, ${\displaystyle \mu _{ijkl}}$, is a fourth-rank polar tensor and ${\displaystyle d_{ijk}}$ is the coefficient corresponding to the direct piezoelectric effect.

Indenofluorene

Indenofluorenes (IFs) are members of the family of polycyclic hydrocarbons which incorporate a core Indene and a core Fluorene to form a 6-5-6-5-6 ring system. While IFs are members of the polycyclic hydrocarbon family, they are not necessarily members of the polycyclic aromatic hydrocarbon family. For example, the fully conjugated versions, shown below, have 20π electrons making them formally anti-aromatic. Depending on the way that the indene and fluorene are connected, five regioisomers can be formed where each regioisomer has unique properties, applications and extent of study.

Despite being first synthesized in the late 19th century by Dr. S. Gabriel when he synthesized the substituted indeno [1,2-a] fluorene (shown right), the lack of robust synthesis routes left this family of molecules unexplored until the mid 20th century. After Gabriel, the next major step was the synthesis of the indeno [2,1-a] fluorene in 1939 by Weizmann et al. Next major advances came from Chardonens and Ritter with the synthesis the indeno [1,2-b] fluorene and indeno [2,1-b] fluorene in 1951. Continuing with their work, Chardonens and Ritter, synthesized indeno [1,2-a] fluorene in 1955. The final regioisomer, the indeno [2,1-c] fluorene was synthesized in 1961 by Ginsburg and Altman. Since the fifties and sixties, when these molecules were first being synthesized and discovered, improved synthetic routes and instrumentation have allowed IFs to be explored for uses in organic electronics including organic photovoltaics, organic light emitting diodes, and organic field effect transistors. Even with these advancements, the properties of IFs have remained largely unexplored. This is likely to change, however, as improvements on synthesis and expansion of IF examples continues to be an active area of research.

It should be noted that the unsubstituted, also called parent, indenofluorenes are rarely synthesized due to instability issues. Instead, syntheses tend to focus on the dione substituted IFs, the fully conjugated IF, or the methylene bridged IFs. Even in these molecules, though, stability remains a problem so it is not uncommon to stabilize the core indenofluorene with aromatic or bulky substituents, such as mesityl or triisopropyl silyl. Similarly, the scope of indenofluorenes have been increasing over the decades to include heteroatoms, such as sulfur, within the ring system. Other structural expansions include addition of rings to the outer edges, off the center and expanding the center core.

Index of physics articles (C)

The index of physics articles is split into multiple pages due to its size.

To navigate by individual letter use the table of contents below.

List of Greek and Latin roots in English/A–G

The following is an alphabetical list of Greek and Latin roots, stems, and prefixes commonly used in the English language from A to G. See also the lists from H to O and from P to Z.

Some of those used in medicine and medical technology are not listed here but instead in the entry for List of medical roots, suffixes and prefixes.

Metal K-edge

Metal K-edge spectroscopy is a spectroscopic technique used to study the electronic structures of transition metal atoms and complexes. This method measures X-ray absorption caused by the excitation of a 1s electron to valence bound states localized on the metal, which creates a characteristic absorption peak called the K-edge. The K-edge can be divided into the pre-edge region (comprising the pre-edge and rising edge transitions) and the near-edge region (comprising the intense edge transition and ~150 eV above it).

Nambulite

Nambulite is a lithium bearing manganese silicate mineral with formula: (Li,Na)Mn4Si5O14(OH). It is named after the mineralogist, Matsuo Nambu (born 1917) of Tohoko University, Japan, who is known for his research in manganese minerals. The mineral was first discovered in the Funakozawa Mine of northeastern Japan, a metasedimentary manganese ore.Nambulite is formed from the reaction between a hydrothermal solution and rhodonite, and commonly creates veins in the host rock. Other than a collector’s gem, however, it has little economic value.

It belongs to the triclinic-pinacoidal crystal system (or triclinic-normal), meaning that it has three axes of unequal length (a, b, c), all intersecting at oblique angles with each other (none of the angles are equal to 90°). It belongs to the crystal class 1, meaning that any point on the crystal that is rotated 360° and then completely inverted will meet with an equal (but opposite) point on the crystal (see centrosymmetry). Its space group is P 1.

The three axes (a, b, c) have different indices of refraction, na=1.707, nb=1.710, nc=1.730. The index of refraction (RI) can be defined as n = cair/cmineral, where “n” is the index of refraction and “c” is the speed of light. The maximum birefringence is .023, the difference between the highest (nc=1.730) and lowest (na=1.707) indices of refraction within the mineral.

In a medium with an index of refraction equaling 1.53, Nambulite has a calculated relief of 1.71-1.73, giving it a moderate to high relief. Relief is a measure of the difference between the index of refraction of the mineral and that of the medium (often Canada balsam or other epoxy with an RI of around 1.53-1.54).Nambulite is an anisotropic crystal, where the velocity of light that passes through the crystal varies depending on the crystallographic direction. In contrast, an isotropic crystal includes all isometric crystals, and the velocity of light is equal in all directions. The mineral exhibits slight pleochroism. Pleochroism is an optical property observed when the mineral is viewed under the microscope in plane polarized light, and when it the stage of the microscope is rotated the observed colors change. The color change is due to different wavelengths being absorbed in different directions, and the color of the mineral depends on the crystallographic orientation.

Patterson function

The Patterson function is used to solve the phase problem in X-ray crystallography. It was introduced in 1935 by Arthur Lindo Patterson while he was a visiting researcher in the laboratory of Bertram Eugene Warren at MIT.

The Patterson function is defined as

${\displaystyle P(u,v,w)=\sum \limits _{hkl}\left|F_{hkl}\right|^{2}\;e^{-2\pi i(hu+kv+lw)}.}$

It is essentially the Fourier transform of the intensities rather than the structure factors. The Patterson function is also equivalent to the electron density convolved with its inverse:

${\displaystyle P\left({\vec {u}}\right)=\rho \left({\vec {r}}\right)*\rho \left(-{\vec {r}}\right).}$

Furthermore, a Patterson map of N points will have N(N − 1) peaks, excluding the central (origin) peak and any overlap.

The peaks positions in the Patterson function are the interatomic distance vectors and the peak heights are proportional to the product of the number of electrons in the atoms concerned.

Because for each vector between atoms i and j there is an oppositely oriented vector of the same length (between atoms j and i), the Patterson function always has centrosymmetry.

Polar metal

A polar metal, metallic ferroeletric, or ferroelectric metal is a metal that contains an electric dipole moment. Its components have an ordered electric dipole. Such metals should be unexpected, because the charge should conduct by way of the free electrons in the metal and neutralize the polarized charge. However they do exist. One substance family that can produce a polar metal is the nickelate perovskites. One example interpreted to show polar metallic behavior is lanthanum nickelate, LaNiO3. A thin film of LaNiO3 grown on the (111) crystal face of lanthanum aluminate, (LaAlO3) was interpreted to be both conductor and a polar material at room temperature. The resistivity of this system, however, shows an upturn with decreasing temperature, hence does not strictly adhere to the definition of a metal. Also, when grown 3 or 4 unit cells thick (1-2 nm) on the (100) crystal face of LaAlO3, the LaNiO3 can be a polar insulator or polar metal depending on the atomic termination of the surface. Lithium osmate, LiOsO3 also undergoes a ferrorelectric transition when it is cooled below 140K. The point group changes from R3c to R3c losing its centrosymmetry. At room temperature and below lithium osmate is an electric conductor, in single crystal, polycrystalline or powder forms, and the ferroelectric form only appears below 140K. Above 140K the material behaves like a normal metal.P. W. Anderson and E. I. Blount predicted that a ferroelectric metal could exist in 1965. They were inspired to make this prediction based on superconducting transitions, and the ferroelectric transition in barium titanate. The prediction was that atoms do not move far and only a slight crystal non-symmetrical deformation occurs, say from cubic to tetragonal. This transition they called martensitic. They suggested looking at sodium tungsten bronze and InTl alloy. They realised that the free electrons in the metal would neutralise the effect of the polarization at a global level, but that the conduction electrons do not strongly affect transverse optical phonons, or the local electric field inherent in ferroelectricity.

Silicon photonics

Silicon photonics is the study and application of photonic systems which use silicon as an optical medium. The silicon is usually patterned with sub-micrometre precision, into microphotonic components. These operate in the infrared, most commonly at the 1.55 micrometre wavelength used by most fiber optic telecommunication systems. The silicon typically lies on top of a layer of silica in what (by analogy with a similar construction in microelectronics) is known as silicon on insulator (SOI).

Silicon photonic devices can be made using existing semiconductor fabrication techniques, and because silicon is already used as the substrate for most integrated circuits, it is possible to create hybrid devices in which the optical and electronic components are integrated onto a single microchip. Consequently, silicon photonics is being actively researched by many electronics manufacturers including IBM and Intel, as well as by academic research groups, as a means for keeping on track with Moore's Law, by using optical interconnects to provide faster data transfer both between and within microchips.The propagation of light through silicon devices is governed by a range of nonlinear optical phenomena including the Kerr effect, the Raman effect, two-photon absorption and interactions between photons and free charge carriers. The presence of nonlinearity is of fundamental importance, as it enables light to interact with light, thus permitting applications such as wavelength conversion and all-optical signal routing, in addition to the passive transmission of light.

Silicon waveguides are also of great academic interest, due to their unique guiding properties, they can be used for communications, interconnects, biosensors, and they offer the possibility to support exotic nonlinear optical phenomena such as soliton propagation.

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