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Encyclopedia > Crystal structure
Enargite crystals
Enargite crystals

In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. A crystal structure is composed of a unit cell, a set of atoms arranged in a particular way; which is periodically repeated in three dimensions on a lattice. The spacing between unit cells in various directions is called its lattice parameters. The symmetry properties of the crystal are embodied in its space group. A crystal's structure and symmetry play a role in determining many of its properties, such as cleavage, electronic band structure, and optical properties. Image File history File links Enargite_crystals. ... Image File history File links Enargite_crystals. ... Mineralogy is an earth science that involves the chemistry, crystal structure, and physical (including optical) properties of minerals. ... Crystallography (from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and graphein = write) is the experimental science of determining the arrangement of atoms in solids. ... Quartz crystal Copper(II) sulfate and iodine crystal Synthetic bismuth crystal Insulin crystals Gallium, a metal that easily forms large single crystals A huge monocrystal of potassium dihydrogen phosphate grown from solution by Saint-Gobain for the megajoule laser of CEA. In chemistry and mineralogy, a crystal is a solid... “Atomic” redirects here. ... 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. ... Sphere symmetry group o. ... The space group of a crystal is a mathematical description of the symmetry inherent in the structure. ... Cleavage, in mineralogy, is the tendency of crystalline materials to split along definite planes, creating smooth surfaces, of which there are several named types: Basal cleavage: cleavage parallel to the base of a crystal, or to the plane of the lateral axes. ... In solid state physics, the electronic band structure, or simply band structure, refers to the dispersion relation (the relation between energy versus momentum) of electrons in a crystal. ... Crystal optics is the branch of optics that describes the behaviour of light in anisotropic media, that is, media (such as crystals) in which light behaves differently depending on which direction the light is propagating. ...

Contents

Unit cell

The crystal structure of a material is often discussed in terms of its unit cell. The unit cell is a spatial arrangement of atoms which is tiled in three-dimensional space to describe the crystal. The unit cell is given by its lattice parameters, the length of the cell edges and the angles between them, while the positions of the atoms inside the unit cell are described by the set of atomic positions (xi,yi,zi) measured from a lattice point. “Atomic” redirects here. ... In geometry, a tiling (also called tessellation, mosaic or dissection) of a given shape S consists of a collection of other shapes which precisely cover S. Often the shape S to be tiled is the Euclidean plane, but other shapes and three-dimensional objects are considered as well. ... In geometry, a Miller index is used to describe sets of planes in a crystal. ...


For each crystal structure there is a conventional unit cell, which is the smallest unit that has the full symmetry of the crystal (see below). However, the conventional unit cell is not always the smallest possible choice. A primitive unit cell of a particular crystal structure is the smallest possible unit cell one can construct such that, when tiled, it completely fills space. This primitive unit cell does not, however, display all the symmetries inherent in the crystal. A Wigner-Seitz cell is a particular kind of primitive cell which has the same symmetry as the lattice. A Wigner-Seitz cell, in solid state physics, is a primitive lattice cell. ... In solid state physics and mineralogy, particularly in describing crystal structure, a primitive cell is a minimum volume cell corresponding to a single lattice point. ...


There are only seven distinct shapes that can pack together into an infinite 3D space lattice in such a way that each lattice point has an identical environment to that around every other lattice point.


Classification of crystals by symmetry

The defining property of a crystal is its inherent symmetry, by which we mean that under certain operations the crystal remains unchanged. For example, rotating the crystal 180 degrees about a certain axis may result in an atomic configuration which is identical to the original configuration. The crystal is then said to have a twofold rotational symmetry about this axis. In addition to rotational symmetries like this, a crystal may have symmetries in the form of mirror planes and translational symmetries, and also the so-called compound symmetries which are a combination of translation and rotation/mirror symmetries. A full classification of a crystal is achieved when all of these inherent symmetries of the crystal are identified.


Crystal system

The crystal systems are a grouping of crystal structures according to the axial system used to describe their lattice. Each crystal system consists of a set of three axes in a particular geometrical arrangement. There are seven unique crystal systems. The simplest and most symmetric, the cubic (or isometric) system, has the symmetry of a cube, that is, it exhibits four threefold rotational axes oriented at 109.5 degrees (the tetrahedral angle) with respect to each other. These threefold axes lie along the body diagonals of the cube. This definition of a cubic is correct, although very many textbooks incorrectly state that a cube is defined by three mutually perpendicular axes of equal length - if this were true there would be far more than 14 Bravais lattices. The other six systems, in order of decreasing symmetry, are hexagonal, tetragonal, rhombohedral (also known as trigonal), orthorhombic, monoclinic and triclinic. Some crystallographers consider the hexagonal crystal system not to be its own crystal system, but instead a part of the trigonal crystal system. The crystal system and Bravais lattice of a crystal describe the (purely) translational symmetry of the crystal. A crystal system is a category of space groups, which characterize symmetry of structures in three dimensions with translational symmetry in three directions, having a discrete symmetry group. ... In crystallography, the cubic crystal system (or isometric crystal system) is the most symmetric of the 7 crystal systems. ... Three dimensions A cube (or hexahedron) is a Platonic solid composed of six square faces, with three meeting at each vertex. ... 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. ... In crystallography, the hexagonal crystal system is one of the 7 lattice point groups. ... In crystallography, the tetragonal crystal system is one of the 7 lattice point groups. ... In crystallography, the rhombohedral (or trigonal) crystal system is one of the 7 lattice point groups. ... In crystallography, the orthorhombic crystal system is one of the 7 lattice point groups. ... In crystallography, the monoclinic crystal system is one of the 7 lattice point groups. ... In crystallography, the triclinic crystal system is one of the 7 lattice point groups. ...


The Bravais lattices

Crystal system Lattices:
triclinic Triclinic
monoclinic simple base-centered
Monoclinic, simple Monoclinic, centered
orthorhombic simple base-centered body-centered face-centered
Orthohombic, simple Orthohombic, base-centered Orthohombic, body-centered Orthohombic, face-centered
hexagonal Hexagonal
rhombohedral
(trigonal)
Rhombohedral
tetragonal simple body-centered
Tetragonal, simple Tetragonal, body-centered
cubic
(isometric)
simple body-centered face-centered
Cubic, simple Cubic, body-centered Cubic, face-centered

When the crystal systems are combined with the various possible lattice centerings, we arrive at the Bravais lattices. They describe the geometric arrangement of the lattice points, and thereby the translational symmetry of the crystal. In three dimensions, there are 14 unique Bravais lattices which are distinct from one another in the translational symmetry they contain. All crystalline materials recognized until now (not including quasicrystals) fit in one of these arrangements. The fourteen three-dimensional lattices, classified by crystal system, are shown to the right. The Bravais lattices are sometimes referred to as space lattices. In crystallography, the triclinic crystal system is one of the 7 lattice point groups. ... Image File history File links No higher resolution available. ... In crystallography, the monoclinic crystal system is one of the 7 lattice point groups. ... Monoclinic crystal structure. ... Monoclinic base-centred crystal structure File links The following pages link to this file: User:DrBob/Figures Crystal structure Monoclinic Categories: GFDL images ... In crystallography, the orthorhombic crystal system is one of the 7 lattice point groups. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... In crystallography, the hexagonal crystal system is one of the 7 lattice point groups. ... Image File history File links No higher resolution available. ... In crystallography, the rhombohedral (or trigonal) crystal system is one of the 7 lattice point groups. ... Image File history File links No higher resolution available. ... In crystallography, the tetragonal crystal system is one of the 7 lattice point groups. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... In crystallography, the cubic crystal system (or isometric crystal system) is the most symmetric of the 7 crystal systems. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... 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. ... Quasicrystals are aperiodic structures which produce diffraction. ...


The crystal structure consists of the same group of atoms, the basis, positioned around each and every lattice point. This group of atoms therefore repeats indefinitely in three dimensions according to the arrangement of one of the 14 Bravais lattices. The characteristic rotation and mirror symmetries of the group of atoms, or unit cell, is described by its crystallographic point group. In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. ... In crystallography, a crystallographic point group or crystal class is a set of symmetry operations that leave a point fixed, like rotations or reflections, which leave the crystal unchanged. ...


Point and space groups

The crystallographic point group or crystal class is the set of non-translational symmetry operations that leave the appearance of the crystal structure unchanged. These symmetry operations can include mirror planes, which reflect the structure across a central plane, rotation axes, which rotate the structure a specified number of degrees, and a center of symmetry or inversion point which inverts the structure through a central point. There are 32 possible crystal classes. Each one can be classified into one of the seven crystal systems. In crystallography, a crystallographic point group or crystal class is a set of symmetry operations that leave a point fixed, like rotations or reflections, which leave the crystal unchanged. ...


The space group of the crystal structure is composed of the translational symmetry operations in addition to the operations of the point group. These include pure translations which move a point along a vector, screw axes, which rotate a point around an axis while translating parallel to the axis, and glide planes, which reflect a point through a plane while translating it parallel to the plane. There are 230 distinct space groups. The space group of a crystal is a mathematical description of the symmetry inherent in the structure. ...


Physical properties

Defects in crystals

Real crystals feature defects or irregularities in the ideal arrangements described above and it is these defects that critically determine many of the electrical and mechanical properties of real materials. In particular dislocations in the crystal lattice allow shear at much lower stress than that needed for a perfect crystal structure[citation needed]. Crystalline solids have a very regular atomic structure: that is, the local positions of atoms with respect to each other are repeated at the atomic scale. ... In materials science, a dislocation is a crystallographic defect, or irregularity, within a crystal structure. ... In physics and mechanics, shear refers to a deformation that causes parallel surfaces to slide past one another (as opposed to compression and tension, which cause parallel surfaces to move towards or away from one another). ...


Crystal symmetry and physical properties

Twenty of the 32 crystal classes are so-called piezoelectric, and crystals belonging to one of these classes (point groups) display piezoelectricity. All 20 piezoelectric classes lack a center of symmetry. Any material develops a dielectric polarization when an electric field is applied, but a substance which has such a natural charge separation even in the absence of a field is called a polar material. Whether or not a material is polar is determined solely by its crystal structure. Only 10 of the 32 point groups are polar. All polar crystals are pyroelectric, so the 10 polar crystal classes are sometimes referred to as the pyroelectric classes. Piezoelectricity is the ability of certain crystals to produce a voltage when subjected to mechanical stress. ... Piezoelectricity is the ability of crystals, certain ceramic materials, (and to some degree, all materials) to generate a voltage in response to applied mechanical stress. ... A dielectric, or electrical insulator, is a substance that is highly resistant to electric current. ... Pyroelectricity is the electrical potential created in certain materials when they are heated. ...


There are a few crystal structures, notably the perovskite structure, which exhibit ferroelectric behaviour. This is analogous to ferromagnetism, in that, in the absence of an electric field during production, the ferroelectric crystal does not exhibit a polarisation. Upon the application of an electric field of sufficient magnitude, the crystal becomes permanently polarised. This polarisation can be reversed by a sufficiently large counter-charge, in the same way that a ferromagnet can be reversed. However, it is important to note that, although they are called ferroelectrics, the effect is due to the crystal structure, not the presence of a ferrous metal. Perovskite (calcium titanium oxide, CaTiO3) is a relatively rare mineral occurring in orthorhombic (pseudocubic) crystals. ... In physics, the ferroelectric effect is an electrical phenomenon whereby certain ionic crystals may exhibit a spontaneous dipole moment. ... Ferromagnetism is the phenomenon by which materials, such as iron, in an external magnetic field become magnetized and remain magnetized for a period after the material is no longer in the field. ...


Incommensurate crystals have period-varying translational symmetry. The period between nodes of symmetry is constant in most crystals. The distance between nodes in an incommensurate crystal is dependent on the number of nodes between it and the base node.


See also

For more detailed information in specific technology applications see materials science, ceramic, or metallurgy. Quartz crystal Copper(II) sulfate and iodine crystal Synthetic bismuth crystal Insulin crystals Gallium, a metal that easily forms large single crystals A huge monocrystal of potassium dihydrogen phosphate grown from solution by Saint-Gobain for the megajoule laser of CEA. In chemistry and mineralogy, a crystal is a solid... Crystal engineering is the design and synthesis of molecular solid-state structures with desired properties, based on an understanding and exploitation of intermolecular interactions. ... Crystallography (from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and graphein = write) is the experimental science of determining the arrangement of atoms in solids. ... In crystallography, a crystallographic point group or crystal class is a set of symmetry operations that leave a point fixed, like rotations or reflections, which leave the crystal unchanged. ... Crystalline solids have a very regular atomic structure: that is, the local positions of atoms with respect to each other are repeated at the atomic scale. ... Crystals are entities of atoms, ions or even polymer strings in which the subunits (i. ... Schlieren texture of Liquid Crystal nematic phase Liquid crystals are substances that exhibit a phase of matter that has properties between those of a conventional liquid, and those of a solid crystal. ... Cleavage, in mineralogy, is the tendency of crystalline materials to split along definite planes, creating smooth surfaces, of which there are several named types: Basal cleavage: cleavage parallel to the base of a crystal, or to the plane of the lateral axes. ... A seed crystal is a small piece of single crystal material from which a large crystal of, usually, the same material is to be grown. ... Quasicrystals are a peculiar form of solid in which the atoms of the solid are arranged in a seemingly regular, yet non-repeating structure. ... In geometry, a Miller index is used to describe sets of planes in a crystal. ... The Materials Science Tetrahedron, which often also includes Characterization at the center Materials science is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering. ... Fixed Partial Denture, or Bridge The word ceramic is derived from the Greek word κεραμικός (keramikos). ... Metallurgy is a domain of materials science and of materials engineering that studies the physical and chemical behavior of metallic elements, their intermetallic compounds, and their mixtures, which are called alloys. ...


External links


  Results from FactBites:
 
Crystal - Wikipedia, the free encyclopedia (631 words)
A crystal is a solid in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating pattern extending in all three spatial dimensions.
Under ideal conditions, the result may be a single crystal, where all of the atoms in the solid fit into the same lattice or crystal structure but, generally, many crystals form simultaneously during solidification, leading to a polycrystalline solid.
Which crystal structure the fluid will form depends on the chemistry of the fluid, the conditions under which it is being solidified, and also on the ambient pressure.
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