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Misorientation
In materials science, misorientation is the difference in crystallographic orientation between two crystallites in a polycrystalline material. In crystalline materials, the orientation of a crystallite is defined by a transformation from a sample reference frame (i.e. defined by the direction of a rolling or extrusion process and two orthogonal directions) to the local reference frame of the crystalline lattice, as defined by the basis of the unit cell. In the same way, misorientation is the transformation necessary to move from one local crystal frame to some other crystal frame. That is, it is the distance in orientation space between two distinct orientations. If the orientations are specified in terms of matrices of direction cosines and , then the misorientation operator going from to can be defined as follows: :\begin & g_B = \Delta g_ g_A \\ & \Delta g_ = g_B g_A^ \end where the term is the reverse operation of , that is, transformation from crystal frame back t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axis Angle
An axis (plural ''axes'') is an imaginary line around which an object rotates or is symmetrical. Axis may also refer to: Mathematics * Axis of rotation: see rotation around a fixed axis *Axis (mathematics), a designator for a Cartesian-coordinate dimension * Axis, a line generated by basis vector in a linear algebra Politics *Axis powers of World War II, 1936–1945. *Axis of evil (first used in 2002), U.S. President George W. Bush's description of Iran, Iraq, and North Korea *Axis of Resistance (first used in 2002), the Shia alliance of Iran, Syria, and Hezbollah *Political spectrum, sometimes called an axis Science *Axis of rotation: see rotation around a fixed axis *Axis (anatomy), the second cervical vertebra of the spine * ''Axis'' (genus), a genus of deer *Axis, an anatomical term of orientation *Axis, a botanical term meaning the line through the centre of a plant *Optical axis, a line of rotational symmetry * ''Axis'' (journal), online journal published by The Mineralo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orientation Matrix
In geometry, the orientation, angular position, attitude, bearing, or direction of an object such as a line, plane or rigid body is part of the description of how it is placed in the space it occupies. More specifically, it refers to the imaginary rotation that is needed to move the object from a reference placement to its current placement. A rotation may not be enough to reach the current placement. It may be necessary to add an imaginary translation, called the object's location (or position, or linear position). The location and orientation together fully describe how the object is placed in space. The above-mentioned imaginary rotation and translation may be thought to occur in any order, as the orientation of an object does not change when it translates, and its location does not change when it rotates. Euler's rotation theorem shows that in three dimensions any orientation can be reached with a single rotation around a fixed axis. This gives one common way of representin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mackenzie Plot
Mackenzie, Mckenzie, MacKenzie, or McKenzie may refer to: People * Mackenzie (given name), a given name (including a list of people with the name) * Mackenzie (surname), a surname (including a list of people with the name) * Clan Mackenzie, a Scottish clan Places Cities, towns and roads Australia * Mackenzie, Queensland, a suburb of Brisbane * Mackenzie, Queensland (Central Highlands), a locality in the Central Highlands Region * Lake McKenzie, a perched lake in Queensland Canada * Mackenzie (provincial electoral district), a former constituency in British Columbia * Mackenzie, British Columbia, near Williston Lake in east central British Columbia * Mackenzie, Ontario, on Thunder Bay in west central Ontario * Mackenzie Mountains, a mountain range in northern Canada * District of Mackenzie, a former administrative district of Canada's Northwest Territories ''Alberta'' * Mackenzie County, a specialized municipality in northwestern Alberta * Mackenzie Highway, in Alberta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Harmonics
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. Since the spherical harmonics form a complete set of orthogonal functions and thus an orthonormal basis, each function defined on the surface of a sphere can be written as a sum of these spherical harmonics. This is similar to periodic functions defined on a circle that can be expressed as a sum of circular functions (sines and cosines) via Fourier series. Like the sines and cosines in Fourier series, the spherical harmonics may be organized by (spatial) angular frequency, as seen in the rows of functions in the illustration on the right. Further, spherical harmonics are basis functions for irreducible representations of SO(3), the group of rotations in three dimensions, and thus play a central role in the group theoretic discussion of SO(3). Spherical harmonics originate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orientation Distribution Function
In physical chemistry and materials science, texture is the distribution of crystallographic orientations of a polycrystalline sample (it is also part of the geological fabric). A sample in which these orientations are fully random is said to have no distinct texture. If the crystallographic orientations are not random, but have some preferred orientation, then the sample has a weak, moderate or strong texture. The degree is dependent on the percentage of crystals having the preferred orientation. Texture is seen in almost all engineered materials, and can have a great influence on materials properties. The texture forms in materials during thermo-mechanical processes, for example during production processes e.g. rolling. Consequently, the rolling process is often followed by a heat treatment to reduce the amount of unwanted texture. Controlling the production process in combination with the characterization of texture and the material's microstructure help to determine the materi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MDF Rodrigues AA5083
MDF may refer to: Computing * Master Database File, a Microsoft SQL Server file type * ''MES Development Framework'', a .NET framework for building manufacturing execution system applications * ''Message Development Framework'', a collection of models, methods and tools used by Health Level 7 v3.0 methodology * Media Descriptor File, a proprietary disc image file format developed for Alcohol 120% * Measurement Data Format, one of the data formats defined by the Association for Standardisation of Automation and Measuring Systems (ASAM) * Multiple Domain Facility; see Logical partition Medicine * Map-dot-fingerprint dystrophy, a genetic disease affecting the cornea * ''Mean Diastolic Filling'' of the heart * Myocardial depressant factor, a low-molecular-weight peptide released from the pancreas into the blood in mammals during various shock states Organizations * Hungarian Democratic Forum (Hungarian: ''Magyar Demokrata Fórum''), a political party * Maraland Democratic Fro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystal Symmetry
In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter. The smallest group of particles in the material that constitutes this repeating pattern is the unit cell of the structure. The unit cell completely reflects the symmetry and structure of the entire crystal, which is built up by repetitive translation of the unit cell along its principal axes. The translation vectors define the nodes of the Bravais lattice. The lengths of the principal axes, or edges, of the unit cell and the angles between them are the lattice constants, also called ''lattice parameters'' or ''cell parameters''. The symmetry properties of the crystal are described by the concept of space groups. All possible symmetric arrangements of particles ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quaternions And Spatial Rotation
Unit quaternions, known as ''versors'', provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. Specifically, they encode information about an axis-angle rotation about an arbitrary axis. Rotation and orientation quaternions have applications in computer graphics, Presented at SIGGRAPH '85. computer vision, robotics, navigation, molecular dynamics, flight dynamics, orbital mechanics of satellites, and crystallographic texture analysis. When used to represent rotation, unit quaternions are also called rotation quaternions as they represent the 3D rotation group. When used to represent an orientation (rotation relative to a reference coordinate system), they are called orientation quaternions or attitude quaternions. A spatial rotation around a fixed point of \theta radians about a unit axis (X,Y,Z) that denotes the ''Euler axis'' is given by the quaternion (C, X \, S, Y \, S, Z \, S), where C = \cos(\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler Angles
The Euler angles are three angles introduced by Leonhard Euler to describe the Orientation (geometry), orientation of a rigid body with respect to a fixed coordinate system.Novi Commentarii academiae scientiarum Petropolitanae 20, 1776, pp. 189–207 (E478PDF/ref> They can also represent the orientation of a mobile frame of reference in physics or the orientation of a general Basis (linear algebra), basis in 3-dimensional linear algebra. Alternative forms were later introduced by Peter Guthrie Tait and George H. Bryan intended for use in aeronautics and engineering. Chained rotations equivalence Euler angles can be defined by elemental geometry or by composition of rotations. The geometrical definition demonstrates that three composed ''elemental rotations'' (rotations about the axes of a coordinate system) are always sufficient to reach any target frame. The three elemental rotations may be #Conventions by extrinsic rotations, extrinsic (rotations about the axes ''xyz'' of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystallography
Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The word "crystallography" is derived from the Greek word κρύσταλλος (''krystallos'') "clear ice, rock-crystal", with its meaning extending to all solids with some degree of transparency, and γράφειν (''graphein'') "to write". In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming that 2014 would be the International Year of Crystallography. denote a direction vector (in real space). * Coordinates in ''angle brackets'' or ''chevrons'' such as <100> denote a ''family'' of directions which are related by symmetry operations. In the cubic crystal system for example, would mean 00 10 01/nowiki> or the negative of any of those directions. * Miller indices in ''parentheses'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotation Matrix
In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix :R = \begin \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end rotates points in the plane counterclockwise through an angle with respect to the positive axis about the origin of a two-dimensional Cartesian coordinate system. To perform the rotation on a plane point with standard coordinates , it should be written as a column vector, and multiplied by the matrix : : R\mathbf = \begin \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end \begin x \\ y \end = \begin x\cos\theta-y\sin\theta \\ x\sin\theta+y\cos\theta \end. If and are the endpoint coordinates of a vector, where is cosine and is sine, then the above equations become the trigonometric summation angle formulae. Indeed, a rotation matrix can be seen as the trigonometric summation angle formulae in matrix form. One w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
