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Monoclinic crystal An example of the monoclinic crystal orthoclase. 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 ...
Crystal systems that have space groups assigned to a common lattice system are combined into a crystal family. The seven crystal systems are triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. Informally, two crystals are in the same crystal system if they have similar symmetries (though there are many exceptions).
Twenty of the 32 crystal classes are piezoelectric, and crystals belonging to one of these classes (point groups) display piezoelectricity. All piezoelectric classes lack inversion symmetry . Any material develops a dielectric polarization when an electric field is applied, but a substance that has such a natural charge separation even in the ...
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 ...
The hexagonal crystal family consists of two crystal systems: trigonal and hexagonal. A crystal system is a set of point groups in which the point groups themselves and their corresponding space groups are assigned to a lattice system (see table in Crystal system#Crystal classes ).
Crystallography ranges from the fundamentals of crystal structure to the mathematics of crystal geometry, including those that are not periodic or quasicrystals. At the atomic scale it can involve the use of X-ray diffraction to produce experimental data that the tools of X-ray crystallography can convert into detailed positions of atoms, and ...
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.
These groups may contain only two-fold axes, mirror planes, and/or an inversion center. These are the crystallographic point groups 1 and 1 (triclinic crystal system), 2, m, and 2 / m , and 222, 2 / m 2 / m 2 / m , and mm2 (orthorhombic). (The short form of 2 / m 2 / m 2 / m is mmm.)