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Gamma Point
In mathematics and solid state physics, the first Brillouin zone (named after Léon Brillouin) is a uniquely defined primitive cell in reciprocal space. In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice is broken up into Brillouin zones. The boundaries of this cell are given by planes related to points on the reciprocal lattice. The importance of the Brillouin zone stems from the description of waves in a periodic medium given by Bloch's theorem, in which it is found that the solutions can be completely characterized by their behavior in a single Brillouin zone. The first Brillouin zone is the locus of points in reciprocal space that are closer to the origin of the reciprocal lattice than they are to any other reciprocal lattice points (see the derivation of the Wigner–Seitz cell). Another definition is as the set of points in ''k''-space that can be reached from the origin without crossing any Bragg plane. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brillouin Zone
In mathematics and solid state physics, the first Brillouin zone (named after Léon Brillouin) is a uniquely defined primitive cell in reciprocal space Reciprocal lattice is a concept associated with solids with translational symmetry which plays a major role in many areas such as X-ray diffraction, X-ray and Electron diffraction, electron diffraction as well as the Electronic band structure, e .... In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice is broken up into Brillouin zones. The boundaries of this cell are given by planes related to points on the reciprocal lattice. The importance of the Brillouin zone stems from the description of waves in a periodic medium given by Bloch's theorem, in which it is found that the solutions can be completely characterized by their behavior in a single Brillouin zone. The first Brillouin zone is the locus of points in reciprocal space that are closer to the or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Materials Science
Computational materials science and engineering uses modeling, simulation, theory, and informatics to understand materials. The main goals include discovering new materials, determining material behavior and mechanisms, explaining experiments, and exploring materials theories. It is analogous to computational chemistry and computational biology as an increasingly important subfield of materials science. Introduction Just as materials science spans all length scales, from electrons to components, so do its computational sub-disciplines. While many methods and variations have been and continue to be developed, seven main simulation techniques, or motifs, have emerged. These computer simulation methods use underlying models and approximations to understand material behavior in more complex scenarios than pure theory generally allows and with more detail and precision than is often possible from experiments. Each method can be used independently to predict materials properties and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simple Orthorhombic Lattice (Brillouin Zone)
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Orthorhombic
In crystallography, the orthorhombic crystal system is one of the 7 crystal systems. Orthorhombic Lattice (group), lattices result from stretching a cubic crystal system, cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular Prism (geometry), prism with a rectangular Base (geometry), 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. Bravais lattices There are four orthorhombic Bravais lattices: primitive orthorhombic, base-centered orthorhombic, body-centered orthorhombic, and face-centered orthorhombic. For the base-centered orthorhombic lattice, the primitive cell has the shape of a right rhombic prism;See , row oC, column Primitive, where the cell parameters are given as a1 = a2, α = β = 90° it can be constructed because the two-dimensional centered rectangular base layer can also be descr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monoclinic
In crystallography, the monoclinic crystal system is one of the seven crystal systems. A crystal system is described by three Vector (geometric), vectors. In the monoclinic system, the crystal is described by vectors of unequal lengths, as in the orthorhombic system. They form a parallelogram prism (geometry), prism. Hence two pairs of vectors are perpendicular (meet at right angles), while the third pair makes an angle other than 90°. Bravais lattices Two monoclinic Bravais lattices exist: the primitive monoclinic and the base-centered monoclinic. For the base-centered monoclinic lattice, the primitive cell has the shape of an oblique rhombic prism;See , row mC, column Primitive, where the cell parameters are given as a1 = a2, α = β it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. The length a of the primitive cell below equals \frac \sqrt of the conventional cell above. Crystal class ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triclinic Lattice Type 2b (Brillouin Zone)
class=skin-invert-image, 180px, Triclinic (a ≠ b ≠ c ≠ a and α, β, γ, 90° pairwise different) In crystallography, the triclinic (or anorthic) crystal system is one of the seven crystal systems. A crystal system is described by three basis vectors. In the triclinic system, the crystal is described by vectors of unequal length, as in the orthorhombic system. In addition, the angles between these vectors must all be different and may not include 90°. The triclinic lattice is the least symmetric of the 14 three-dimensional Bravais lattices. It has (itself) the minimum symmetry all lattices have: points of inversion at each lattice point and at 7 more points for each lattice point: at the midpoints of the edges and the faces, and at the center points. It is the only lattice type that itself has no mirror planes. Crystal classes The triclinic crystal system class names, examples, Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Cryst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
