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# Topic: Bravais lattice

###### In the News (Tue 21 May 19)

 3D crystal models Bravais lattice is a lattice with translation symmetry which consists of equivalent nodes. The Wigner-Zeitz cell for the Simple Cubic lattice is cube (the cell coincides with the unit cell). The Wigner-Zeitz cell for the BCC lattice is truncated octahedron www.ibiblio.org /e-notes/Cryst/Cryst.htm   (551 words)

 Spartanburg SC | GoUpstate.com | Spartanburg Herald-Journal   (Site not responding. Last check: 2007-10-06) In geometry and crystallography, a Bravais lattice is a category of symmetry groups for translational symmetry in three directions, or correspondingly, a category of translation lattices. These lattices are classified by space group of the translation lattice itself; there are 14 Bravais lattices in three dimensions; each can apply in one crystal system only. For convenience a Bravais lattice is depicted by a unit cell which is a factor 1, 2, 3 or 4 larger than the primitive cell. www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=crystal_system   (662 words)

 Lattice (group) Information The number of lattice points contained in a polytope all of whose vertices are elements of the lattice is described by the polytope's Ehrhart polynomial. In a rhombic lattice, the shortest distance may either be a diagonal or a side of the rhombus, i.e., the line segment connecting the first two points may or may not be one of the equal sides of the isosceles triangle. The rectangular lattices are at the imaginary axis, and the remaining area represents the parallelogrammetic lattices, with the mirror image of a parallelogram represented by the mirror image in the imaginary axis. www.bookrags.com /wiki/Lattice_(group)   (1439 words)

 Bravais Lattices   (Site not responding. Last check: 2007-10-06) Note that the Bravais lattice is not the same as the periodic function, but is the framework on which the periodic function is built. For example, the hexagonal lattice is an example of a 2-dimensional Bravais lattice, but the honeycomb lattice is not since neighboring points are not equivalent (it is an example of a compound structure, which we will discuss next). For the bcc lattice, a point is added to the center of each cube; alternatively, this lattice can be viewed as two sets of sc sublattices, A and B, that inter-penetrate (however, note that there is no way to distinguish these two sets). carini.physics.indiana.edu /p615/lattices.html   (773 words)

 Spartanburg SC | GoUpstate.com | Spartanburg Herald-Journal In geometry and crystallography, a Bravais lattice, named after Auguste Bravais, is an infinite set of points generated by a set of discrete translation operations. Related to Bravais lattices are Crystallographic point groups of which there are 32 and Space groups of which there are 230. The 14 Bravais lattices are arrived at by combining one of the seven crystal systems (or axial systems) with one of the lattice centerings. www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Bravais_lattice   (318 words)

 Reference.com/Encyclopedia/Reciprocal lattice In crystallography, the reciprocal lattice of a Bravais lattice is the set of all vectors K such that The reciprocal lattice is itself a Bravais lattice, and the reciprocal of the reciprocal lattice is the original lattice. The direction of the reciprocal lattice vector corresponds to the normal to the real space planes, and the magnitude of the reciprocal lattice vector is equal to the reciprocal of the interplanar spacing of the real space planes. www.reference.com /browse/wiki/Reciprocal_space   (676 words)

 BritenySpears.ac: Semiconductor Crystal Structure The lattice is an ordered arrangement of points in space, while the basis consists of the simplest arrangement of atoms which is repeated at every point in the lattice to build up the crystal structure. Lattice vectors are the shortest distances to the nearest neighbouring points on the lattice and are conventionally denoted by a, b and c. In the cubic lattice, for example, (100) is equivalent to five other planes, (010), (001), (100), (010), (001) and to acknowledge this, the set of Miller indices is written {100} which means the set of (100) planes equivalent by virtue of symmetry. britneyspears.ac /physics/crystals/wcrystals.htm   (1587 words)

 Crystallographic Topology - Lattice Complexes Lattice complexes are configurations of points that recur at least once but usually repeatedly throughout the family of all space groups. Those equivalent to Bravais lattices are P, C, I, R, and F. Assigning all Wyckoff positions of all space groups to lattice complexes produces a total of 402 lattice complexes which are tabulated in Fischer, Burzlaff, Hellner, and Donnay (1973) and Fischer and Koch (1995). For the body-centered lattice complex I, this correlation does not hold since the bcc peaks, passes, pales, and pits are on the center, 8 hexagonal faces, 24 vertices, and 6 square faces, respectively, rather than on the 14 faces, 36 edges, and 24 vertices of the bcc truncated octahedron Dirichlet polyhedron. www.ornl.gov /sci/ortep/topology/lattice.html   (2532 words)

 Set of 14 Bravais Type Lattices   (Site not responding. Last check: 2007-10-06) The set of 14 Bravais space lattices was designed for use in the teaching and study of fundamental lattice types. Bravais space lattices represent the 14 basic lattice types from which according to Bravais, practically all natural crystals originate. The models have an edge length of approximately 15cm, and are assembled of 25 mm wood spheres, connected by metal rods. www.klingereducational.com /Products/Crystal_Models/Set_of_14_Bravais_Type_Structu/set_of_14_bravais_type_structu.html   (101 words)

 Bravais lattice   (Site not responding. Last check: 2007-10-06) In geometry and crystallography, a Bravais lattice is an infinite set of points generated by a set of discrete translation operations. The position vectors of a Bravais lattice in three dimensions are given by : The 14 Bravais lattices are: The Bravais lattices were studied by M. Frankenheim in 1842, who found that there were 15 Bravais lattices. bravais-lattice.iqnaut.net   (146 words)

 BALSAC Version 2.15 Manual, Section 6.2.1 LATTICE OPTION, [L] next, previous Section / Table of Contents / Index [L] This option allows you to select the crystal lattice by defining lattice vectors and lattice basis vectors. This is followed by a prompt Global lattice scaling constant a= asking for a global lattice constant a to scale all lattice and lattice basis vectors (a = 1.0 yields no scaling). However, lattice plane directions are denoted by Miller indices using the hexagonal 4-index notation which is confirmed by the lattice code -10 in the message free lattice selected, code = -10 and becomes useful for non-primitive hexagonal lattices, see Sec. www.fhi-berlin.mpg.de /th/balsac/balm.56.html   (1516 words)

 Bravais lattices All other cubic crystal structures (for instance the diamond lattice) can be formed by adding an appropriate base at each lattice point to one of those three lattices. The three cubic Bravais lattices are the simple cubic lattice, the body centered cubic lattice and the face centered cubic lattice. The face centered lattice equals the simple cubic lattice with the addition of a lattice point in the center of each of the six faces of each cube. ece-www.colorado.edu /~bart/book/bravais.htm   (680 words)

 III.C. CRYSTALS, SYMMETRY, AND DIFFRACTION   (Site not responding. Last check: 2007-10-06) Bravais lattice: One of the 14 possible arrays of points repeated periodically in 3D space in such a way that the arrangement of points about any one of the points in the array is identical in every respect to that about any other point in the array. The repeat distance between points in a particular row of the reciprocal lattice is inversely proportional to the interplanar spacing between the nets of the crystal lattice that are normal to this row of points. The lattice is a rule for translation and the motif is the object that is translated. em-outreach.ucsd.edu /web-course/Sec-III.C.1-C.5/Sec-III.C.1-C.5.html   (3671 words)

 Bravais lattice - Definition, explanation In geometry and crystallography, a Bravais lattice is an infinite set of points generated by a set of discrete translation operations. The position vectors of a Bravais lattice in three dimensions are given by The Bravais lattices were studied by M. Frankenheim in 1842, who found that there were 15 Bravais lattices. www.calsky.com /lexikon/en/txt/b/br/bravais_lattice.php   (164 words)

 Bravais Lattice   (Site not responding. Last check: 2007-10-06) A Bravais lattice is an infinite array of discrete points with an arrangement and orientation that appears exactly the same viewed from any point of the array. The primitive lattice vectors can be used to generate the lattice by varying the integers. The smallest parallelepiped with a lattice point at each corner is called the primitive unit cell of the crystal. www.neutron.anl.gov /hyper-physics/bravais.html   (162 words)

 Bravais lattices   (Site not responding. Last check: 2007-10-06) The simple tetragonal is made by pulling on two opposite faces of the simple cubic and stretching it into a rectangular prism with a square base, but a height not equal to the sides of the square. And the face-centered orthorhombic is obtrained by adding one lattice point in the center of each of the object's faces. The simple hexagonal bravais has the hexagonal point group and is the only bravais lattice in the hexagonal system. phycomp.technion.ac.il /~sshaharr/intro.html   (352 words)

 Lattice and Crystal   (Site not responding. Last check: 2007-10-06) The periodicity is described by a mathematical lattice (which are mathematical points at specific coordinates in space), the identical structural units (or base of the crystal) are the atoms in some specific arrangement which are unambiguously placed at every lattice point. lattices, which are commonly used to describe lattice types. Whereas, for example, it shows best the cubic symmetry of the cubic lattices, its elementary cell is not a primitive unit cell of the lattice, i.e. www.tf.uni-kiel.de /matwis/amat/def_en/kap_1/basics/b1_3_1.html   (381 words)

 Lattice and Crystal   (Site not responding. Last check: 2007-10-06) The periodicity is described by a mathematical lattice (which are mathematical points at specific coordinates in space), the identical structural units (or base of the crystal) are the atoms in some specific arrangement which are unambiguously placed at every lattice point. lattices, which are commonly used to describe lattice types. Whereas, for example, it shows best the cubic symmetry of the cubic lattices, its elementary cell is not a primitive unit cell of the lattice, i.e. www.techfak.uni-kiel.de /matwis/amat/def_en/kap_1/basics/b1_3_1.html   (381 words)

 Crystal Structures   (Site not responding. Last check: 2007-10-06) It is important to emphasize that the symmetries of the Bravais lattice are intimately related to the symmetries of the original lattice. For example, the three-fold rotational symmetry of the honeycomb lattice results in the requirement that its Bravais lattice must have three-fold rotational invariance (which leaves the hexagonal lattice as the only choice, see Figure 1.2). The WS cell is a primitive unit cell that preserves the symmetries of the Bravais lattice. solidstate.physics.sunysb.edu /book/prob/node3.html   (2041 words)

 7 - Lecture notes for GEOL3010 In fact any of the 14 Bravais lattice types may be referred to a primitive cell. These are applied to a point of origin, in the directions of the crystallographic axes to generate the lattice points in 3-D space. Mathematically, the [uvw] direction in a lattice with a, b and c lattice parameters is parallel to the vector ua + vb + wc. www.gly.uga.edu /schroeder/geol3010/3010lecture07.html   (875 words)

 Appendix A: Denoting Space Groups The Bravais lattices are constructed from the simplest translational symmetries applied to the seven crystal systems. In cubic or rhombohedral lattices the axes are equivalent, thus the primary axis is arbitrary. For orthorhombic lattices the third and fourth symbols specify the symmetries of the a and b axes respectively. www.planewave.de /icp/atoms/atoms.sgml-7.html   (2481 words)

 LatticeData - Wolfram Mathematica Lattices can be specified by standard names such as "FaceCenteredCubic" and "CoxeterTodd". LatticeData[patt] gives a list of all named lattices that match the string pattern patt. LatticeData[lattice, "class"] gives True or False depending on whether lattice is in the specified class. reference.wolfram.com /mathematica/ref/LatticeData.html   (161 words)

 The MOE Crystal Builder   (Site not responding. Last check: 2007-10-06) All points in the lattice have identical "environments" --- the view from every point in the lattice is identical to that from any other point in the lattice. The absolute positions of the points of a lattice, and hence the unit cell, are arbitrary with respect to a pattern. Lattices can be classified into "systems", each system being characterized by the shape of its associated unit cell. www.chemcomp.com /feature/crysbld.htm   (1784 words)

 Bravais lattice Details, Meaning Bravais lattice Article and Explanation Guide The position vectors of a Bravais lattice in three dimensions are given by The Bravais lattices were studied by M. Frankenheim in 1842, who found that there were 15 Bravais lattices. This was corrected to 14 by A. Bravais in 1845. www.e-paranoids.com /b/br/bravais_lattice.html   (152 words)

 EULER Record Details The Bravais lattices of the PAs are tetragonal, rectangular, hexagonal and rhombic. The mother lattice \$L\$ of a non-Bravais-type quasilattice (NBTQL) is a non-Bravais-type periodic lattice with higher dimensionality and has an associated Bravais lattice \$L\sb 0\$. The second important Bravais lattice \$L\sb h\$ called the host lattice is associated with \$L\$ and we have clarified the difference in roles between \$L\sb 0\$ and \$L\sb h\$ in the theory of PAs to the NBTQL. www.emis.de /projects/EULER/detail?ide=1992niiztheoselfperi&matchno=82&matchtotal=190&q=subseries   (295 words)

 Bravais Lattices   (Site not responding. Last check: 2007-10-06) The last is often described as a "centered" lattice, a rectangle with an extra point in the middle, to bring out the rectangular nature of the pattern. For this reason, three-dimensional lattices must often be described as unit cells with additional points. This is the only Bravais lattice with more than one interior point. www.uwgb.edu /DutchS/SYMMETRY/bravais.htm   (295 words)

 Bravais Lattice We treat trigonal (rhombohedral) lattice as a hexagonal crystal system with sublattices at The prm and abc coordinate systems are identical for simple and hexagonal lattices. We must distinguish them for body centered, face centered, base centered and trigonal lattices. homepage2.nifty.com /a-m/bandmemo/node1.html   (67 words)

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