|
List Of Space Groups
There are 230 space groups in three dimensions, given by a number index, and a full name in Hermann–Mauguin notation, and a short name (international short symbol). The long names are given with spaces for readability. The groups each have a point group of the unit cell. Symbols In Hermann–Mauguin notation, space groups are named by a symbol combining the point group identifier with the uppercase letters describing the lattice type. Translations within the lattice in the form of screw axes and glide planes are also noted, giving a complete crystallographic space group. These are the Bravais lattices in three dimensions: *P primitive *I body centered (from the German ''Innenzentriert'') *F face centered (from the German ''Flächenzentriert'') *A centered on A faces only *B centered on B faces only *C centered on C faces only *R rhombohedral A reflection plane m within the point groups can be replaced by a glide plane, labeled as a, b, or c depending on which axis the gli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space Group
In mathematics, physics and chemistry, a space group is the symmetry group of an object in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of an object that leave it unchanged. In three dimensions, space groups are classified into 219 distinct types, or 230 types if chiral copies are considered distinct. Space groups are discrete cocompact groups of isometries of an oriented Euclidean space in any number of dimensions. In dimensions other than 3, they are sometimes called Bieberbach groups. In crystallography, space groups are also called the crystallographic or Fedorov groups, and represent a description of the symmetry of the crystal. A definitive source regarding 3-dimensional space groups is the ''International Tables for Crystallography'' . History Space groups in 2 dimensions are the 17 wallpaper groups which have been known for several centuries, though the proof that the list was complete was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shubnikov
Shubnikov (russian: Шубников) is a Russian surname. Notable people with the surname include: * Alexei Vasilievich Shubnikov Alexei Vasilievich Shubnikov (russian: Алексей Васильевич Шубников; 29March 1887 – 27April 1970) was a Soviet crystallographer and mathematician. Shubnikov was the founding director of the Institute of Crystallograph ... (1887–1970), Soviet crystallographer and mathematician * Lev Shubnikov (1901–1937), Soviet experimental physicist {{surname Russian-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetragonal Crystal System
In crystallography, the tetragonal crystal system is one of the 7 crystal systems. Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base (''a'' by ''a'') and height (''c'', which is different from ''a''). Bravais lattices There are two tetragonal Bravais lattices: the primitive tetragonal and the body-centered tetragonal. The base-centered tetragonal lattice is equivalent to the primitive tetragonal lattice with a smaller unit cell, while the face-centered tetragonal lattice is equivalent to the body-centered tetragonal lattice with a smaller unit cell. Crystal classes The point groups that fall under this crystal system are listed below, followed by their representations in international notation, Schoenflies notation, orbifold notation, Coxeter notation and mineral examples.Hurlbut, Cornelius S.; Klein, Cornelis, 1985, ''Manual of Mineralogy'', 20th ed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetragonal
In crystallography, the tetragonal crystal system is one of the 7 crystal systems. Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base (''a'' by ''a'') and height (''c'', which is different from ''a''). Bravais lattices There are two tetragonal Bravais lattices: the primitive tetragonal and the body-centered tetragonal. The base-centered tetragonal lattice is equivalent to the primitive tetragonal lattice with a smaller unit cell, while the face-centered tetragonal lattice is equivalent to the body-centered tetragonal lattice with a smaller unit cell. Crystal classes The point groups that fall under this crystal system are listed below, followed by their representations in international notation, Schoenflies notation, orbifold notation, Coxeter notation and mineral examples.Hurlbut, Cornelius S.; Klein, Cornelis, 1985, ''Manual of Mineralogy'', 20th ed., ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. 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 described with primitive rhombic axes. Note that the length a of the primi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthorhombic
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. 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 described with primitive rhombic axes. Note that the length a of the prim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monoclinic Crystal System
In crystallography, the monoclinic crystal system is one of the seven crystal systems. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal lengths, as in the orthorhombic system. They form a parallelogram 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. Note that the length a of the primitive cell below equals \frac \sqrt of the conventional cell above. Crystal classes The table below or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
