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Crystal structure

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In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. [1]

125 relations: Adsorption, Allotropy, Alloy, Alternating group, Amorphous solid, Atom, Atomic packing factor, Axial ratio, Bipyramid, Bravais lattice, Brillouin zone, Brittleness, Burgers vector, Canadian Journal of Physics, Cartesian coordinate system, Centrosymmetry, Chemical element, Chirality (chemistry), Cleavage (crystal), Close-packing of equal spheres, Coordination number, Creep (deformation), Crystal, Crystal engineering, Crystal growth, Crystal habit, Crystal optics, Crystal system, Crystallite, Crystallographic database, Crystallographic defect, Crystallographic point group, Crystallography, Crystallography Open Database, Cube, Cubic crystal system, Cyclic group, Deformation (engineering), Diamond, Diamond cubic, Dielectric, Diffusion, Dihedral group, Dislocation, Electrical resistivity and conductivity, Electronic band structure, Evolutionary algorithm, Ferroelectricity, Ferromagnetism, Fractional coordinates, ..., Frank Kasper phases, Germanium, Grain boundary, Grain boundary strengthening, Hermann–Mauguin notation, Hexagonal crystal family, Improper rotation, Integer, Ion, Journal of the American Chemical Society, Klein four-group, Laser-heated pedestal growth, Lattice constant, Line (geometry), Linus Pauling, Liquid crystal, Melting point, Metal, Miller index, Mineral, Molecule, Monoclinic crystal system, Optics, Orthorhombic crystal system, Parallelepiped, Patterson function, Pauling's rules, Periodic table (crystal structure), Perovskite (structure), Piezoelectricity, Plane (geometry), Plasticity (physics), Point group, Polar point group, Polymer, Polymorphism (materials science), Precipitation (chemistry), Primitive cell, Prism (geometry), Proceedings of the Royal Society, Pyramid (geometry), Pyroelectricity, Quartz, Quasicrystal, Reactivity (chemistry), Reciprocal lattice, Refractive index, Resonating valence bond theory, Rotational symmetry, Schoenflies notation, Seed crystal, Semiconductor, Shear stress, Silicate, Silicon, Silicon dioxide, Sintering, Space group, Stable, Supercell (crystal), Surface tension, Symmetric group, Symmetry, Symmetry number, Tetragonal crystal system, Tetrahedron, Thermal conductivity, Three-dimensional space, Tin, Translation (geometry), Translational symmetry, Triclinic crystal system, Wigner–Seitz cell, William Hume-Rothery, X-ray crystallography. Expand index (75 more) »


Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface.

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Allotropy or allotropism is the property of some chemical elements to exist in two or more different forms, in the same physical state, known as allotropes of these elements.

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An alloy is a combination of metals or of a metal and another element.

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Alternating group

In mathematics, an alternating group is the group of even permutations of a finite set.

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Amorphous solid

In condensed matter physics and materials science, an amorphous (from the Greek a, without, morphé, shape, form) or non-crystalline solid is a solid that lacks the long-range order that is characteristic of a crystal.

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An atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element.

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Atomic packing factor

In crystallography, atomic packing factor (APF), packing efficiency or packing fraction is the fraction of volume in a crystal structure that is occupied by constituent particles.

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Axial ratio

Axial ratio, for any structure or shape with two or more axes, is the ratio of the length (or magnitude) of those axes to each other - the longer axis divided by the shorter.

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An n-gonal bipyramid or dipyramid is a polyhedron formed by joining an n-gonal pyramid and its mirror image base-to-base.

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Bravais lattice

In geometry and crystallography, a Bravais lattice, named after, is an infinite array of discrete points in three dimensional space generated by a set of discrete translation operations described by: where ni are any integers and ai are known as the primitive vectors which lie in different directions and span the lattice.

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Brillouin zone

In mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell in reciprocal space.

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# A material is brittle if, when subjected to stress, it breaks without significant plastic deformation.

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Burgers vector

In physics, the Burgers vector, named after Dutch physicist Jan Burgers, is a vector, often denoted as b, that represents the magnitude and direction of the lattice distortion resulting from a dislocation in a crystal lattice.

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Canadian Journal of Physics

The Canadian Journal of Physics is a peer-reviewed scientific journal covering a broad range of physics.

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Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

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In crystallography, a point group which contains an inversion center as one of its symmetry elements is centrosymmetric.

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Chemical element

A chemical element is a species of atoms having the same number of protons in their atomic nuclei (that is, the same atomic number, or Z).

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Chirality (chemistry)

Chirality is a geometric property of some molecules and ions.

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Cleavage (crystal)

Cleavage, in mineralogy, is the tendency of crystalline materials to split along definite crystallographic structural planes.

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Close-packing of equal spheres

In geometry, close-packing of equal spheres is a dense arrangement of congruent spheres in an infinite, regular arrangement (or lattice).

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Coordination number

In chemistry, crystallography, and materials science the coordination number, also called ligancy, of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it.

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Creep (deformation)

In materials science, creep (sometimes called cold flow) is the tendency of a solid material to move slowly or deform permanently under the influence of mechanical stresses.

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A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions.

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Crystal engineering

Crystal engineering is the design and synthesis of molecular solid state structures with desired properties, based on an understanding and use of intermolecular interactions.

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Crystal growth

Crystal growth is the process where a pre-existing crystal becomes larger as more molecules or ions add in their positions in the crystal lattice.

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Crystal habit

In mineralogy, crystal habit is the characteristic external shape of an individual crystal or crystal group.

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Crystal optics

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.

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Crystal system

In crystallography, the terms crystal system, crystal family and lattice system each refer to one of several classes of space groups, lattices, point groups or crystals.

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A crystallite is a small or even microscopic crystal which forms, for example, during the cooling of many materials.

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Crystallographic database

A crystallographic database is a database specifically designed to store information about the structure of molecules and crystals.

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Crystallographic defect

Crystalline solids exhibit a periodic crystal structure.

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Crystallographic point group

In crystallography, a crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a central point fixed while moving other directions and faces of the crystal to the positions of features of the same kind.

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Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure).

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Crystallography Open Database

The Crystallography Open Database (COD) is a database of crystal structures.

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In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

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Cubic crystal system

In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube.

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Cyclic group

In algebra, a cyclic group or monogenous group is a group that is generated by a single element.

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Deformation (engineering)

In materials science, deformation refers to any changes in the shape or size of an object due to-.

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Diamond is a solid form of carbon with a diamond cubic crystal structure.

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Diamond cubic

The diamond cubic crystal structure is a repeating pattern of 8 atoms that certain materials may adopt as they solidify.

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A dielectric (or dielectric material) is an electrical insulator that can be polarized by an applied electric field.

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Diffusion is the net movement of molecules or atoms from a region of high concentration (or high chemical potential) to a region of low concentration (or low chemical potential) as a result of random motion of the molecules or atoms.

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Dihedral group

In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.

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In materials science, a dislocation or Taylor's dislocation is a crystallographic defect or irregularity within a crystal structure.

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Electrical resistivity and conductivity

Electrical resistivity (also known as resistivity, specific electrical resistance, or volume resistivity) is a fundamental property that quantifies how strongly a given material opposes the flow of electric current.

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Electronic band structure

In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energies that an electron within the solid may have (called energy bands, allowed bands, or simply bands) and ranges of energy that it may not have (called band gaps or forbidden bands).

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Evolutionary algorithm

In artificial intelligence, an evolutionary algorithm (EA) is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm.

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Ferroelectricity is a characteristic of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field.

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Ferromagnetism is the basic mechanism by which certain materials (such as iron) form permanent magnets, or are attracted to magnets.

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Fractional coordinates

In crystallography, a fractional coordinate system is a coordinate system in which the edges of the unit cell are used as the basic vectors to describe the positions of atomic nuclei.

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Frank Kasper phases

Topologically close pack (TCP) phases or Frank-Kasper (FK) phases are one of the largest groups of intermetallic compounds, known for their complex crystallographic structure and physical properties.

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Germanium is a chemical element with symbol Ge and atomic number 32.

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Grain boundary

A grain boundary is the interface between two grains, or crystallites, in a polycrystalline material.

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Grain boundary strengthening

Grain-boundary strengthening (or Hall–Petch strengthening) is a method of strengthening materials by changing their average crystallite (grain) size.

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Hermann–Mauguin notation

In geometry, Hermann–Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups.

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Hexagonal crystal family

In crystallography, the hexagonal crystal family is one of the 6 crystal families, which includes 2 crystal systems (hexagonal and trigonal) and 2 lattice systems (hexagonal and rhombohedral).

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Improper rotation

In geometry, an improper rotation,.

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An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

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An ion is an atom or molecule that has a non-zero net electrical charge (its total number of electrons is not equal to its total number of protons).

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Journal of the American Chemical Society

The Journal of the American Chemical Society (also known as JACS) is a weekly peer-reviewed scientific journal that was established in 1879 by the American Chemical Society.

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Klein four-group

In mathematics, the Klein four-group (or just Klein group or Vierergruppe, four-group, often symbolized by the letter V or as K4) is the group, the direct product of two copies of the cyclic group of order 2.

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Laser-heated pedestal growth

Laser-heated pedestal growth (LHPG) or laser floating zone (LFZ) is a crystal growth technique.

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Lattice constant

The lattice constant, or lattice parameter, refers to the physical dimension of unit cells in a crystal lattice.

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Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

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Linus Pauling

Linus Carl Pauling (February 28, 1901 – August 19, 1994) was an American chemist, biochemist, peace activist, author, educator, and husband of American human rights activist Ava Helen Pauling.

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Liquid crystal

Liquid crystals (LCs) are matter in a state which has properties between those of conventional liquids and those of solid crystals.

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Melting point

The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid at atmospheric pressure.

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A metal (from Greek μέταλλον métallon, "mine, quarry, metal") is a material (an element, compound, or alloy) that is typically hard when in solid state, opaque, shiny, and has good electrical and thermal conductivity.

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Miller index

Miller indices form a notation system in crystallography for planes in crystal (Bravais) lattices.

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A mineral is a naturally occurring chemical compound, usually of crystalline form and not produced by life processes.

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A molecule is an electrically neutral group of two or more atoms held together by chemical bonds.

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Monoclinic crystal system

In crystallography, the monoclinic crystal system is one of the 7 crystal systems.

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Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it.

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Orthorhombic crystal system

In crystallography, the orthorhombic crystal system is one of the 7 crystal systems.

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In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning).

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Patterson function

The Patterson function is used to solve the phase problem in X-ray crystallography.

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Pauling's rules

Pauling's rules are five rules published by Linus Pauling in 1929 for predicting and rationalizing the crystal structures of ionic compounds.

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Periodic table (crystal structure)

For elements that are solid at standard temperature and pressure the table gives the crystalline structure of the most thermodynamically stable form(s) in those conditions.

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Perovskite (structure)

A perovskite is any material with the same type of crystal structure as calcium titanium oxide (CaTiO3), known as the perovskite structure, or XIIA2+VIB4+X2−3 with the oxygen in the edge centers.

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Piezoelectricity is the electric charge that accumulates in certain solid materials (such as crystals, certain ceramics, and biological matter such as bone, DNA and various proteins) in response to applied mechanical stress.

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Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.

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Plasticity (physics)

In physics and materials science, plasticity describes the deformation of a (solid) material undergoing non-reversible changes of shape in response to applied forces.

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Point group

In geometry, a point group is a group of geometric symmetries (isometries) that keep at least one point fixed.

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Polar point group

In geometry, a polar point group is a point group in which there is more than one point that every symmetry operation leaves unmoved.

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A polymer (Greek poly-, "many" + -mer, "part") is a large molecule, or macromolecule, composed of many repeated subunits.

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Polymorphism (materials science)

In materials science, polymorphism is the ability of a solid material to exist in more than one form or crystal structure.

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Precipitation (chemistry)

Precipitation is the creation of a solid from a solution.

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Primitive cell

In geometry, crystallography, mineralogy, and solid state physics, a primitive cell is a minimum volume cell (a unit cell) corresponding to a single lattice point of a structure with discrete translational symmetry.

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Prism (geometry)

In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases.

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Proceedings of the Royal Society

Proceedings of the Royal Society is the parent title of two scientific journals published by the Royal Society.

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Pyramid (geometry)

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.

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Pyroelectricity (from the Greek pyr, fire, and electricity) is the property of certain crystals which are naturally electrically polarized and as a result contain large electric fields.

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Quartz is a mineral composed of silicon and oxygen atoms in a continuous framework of SiO4 silicon–oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical formula of SiO2.

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A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic.

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Reactivity (chemistry)

In chemistry, reactivity is the impetus for which a chemical substance undergoes a chemical reaction, either by itself or with other materials, with an overall release of energy.

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Reciprocal lattice

In physics, the reciprocal lattice represents the Fourier transform of another lattice (usually a Bravais lattice).

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Refractive index

In optics, the refractive index or index of refraction of a material is a dimensionless number that describes how light propagates through that medium.

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Resonating valence bond theory

In condensed matter physics, the resonating valence bond theory (RVB) is a theoretical model that attempts to describe high temperature superconductivity, and in particular the superconductivity in cuprate compounds.

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Rotational symmetry

Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn.

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Schoenflies notation

The Schoenflies (or Schönflies) notation, named after the German mathematician Arthur Moritz Schoenflies, is one of two conventions commonly used to describe point groups.

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Seed crystal

A seed crystal is a small piece of single crystal or polycrystal material from which a large crystal of typically the same material is to be grown in a laboratory.

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A semiconductor material has an electrical conductivity value falling between that of a conductor – such as copper, gold etc.

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Shear stress

A shear stress, often denoted by (Greek: tau), is the component of stress coplanar with a material cross section.

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In chemistry, a silicate is any member of a family of anions consisting of silicon and oxygen, usually with the general formula, where 0 ≤ x Silicate anions are often large polymeric molecules with an extense variety of structures, including chains and rings (as in polymeric metasilicate), double chains (as in, and sheets (as in. In geology and astronomy, the term silicate is used to mean silicate minerals, ionic solids with silicate anions; as well as rock types that consist predominantly of such minerals. In that context, the term also includes the non-ionic compound silicon dioxide (silica, quartz), which would correspond to x.

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Silicon is a chemical element with symbol Si and atomic number 14.

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Silicon dioxide

Silicon dioxide, also known as silica (from the Latin silex), is an oxide of silicon with the chemical formula, most commonly found in nature as quartz and in various living organisms.

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Clinker nodules produced by sintering Sintering is the process of compacting and forming a solid mass of material by heat or pressure without melting it to the point of liquefaction.

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Space group

In mathematics, physics and chemistry, a space group is the symmetry group of a configuration in space, usually in three dimensions.

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A stable is a building in which livestock, especially horses, are kept.

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Supercell (crystal)

In solid-state physics and crystallography, a crystal structure is described by a unit cell.

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Surface tension

Surface tension is the elastic tendency of a fluid surface which makes it acquire the least surface area possible.

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Symmetric group

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.

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Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance.

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Symmetry number

The symmetry number or symmetry order of an object is the number of different but indistinguishable (or equivalent) arrangements (or views) of the object, i.e. the order of its symmetry group.

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Tetragonal crystal system

In crystallography, the tetragonal crystal system is one of the 7 crystal systems.

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In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.

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Thermal conductivity

Thermal conductivity (often denoted k, λ, or κ) is the property of a material to conduct heat.

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Three-dimensional space

Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).

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Tin is a chemical element with the symbol Sn (from stannum) and atomic number 50.

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Translation (geometry)

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction.

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Translational symmetry

In geometry, a translation "slides" a thing by a: Ta(p).

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Triclinic crystal system

Triclinic (a ≠ b ≠ c and α ≠ β ≠ γ) In crystallography, the triclinic (or anorthic) crystal system is one of the 7 crystal systems.

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Wigner–Seitz cell

The Wigner–Seitz cell, named after Eugene Wigner and Frederick Seitz, is a type of Voronoi cell used in the study of crystalline material in solid-state physics.

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William Hume-Rothery

William Hume-Rothery OBE FRS (15 May 1899 – 27 September 1968) was an English metallurgist and materials scientist who studied the constitution of alloys.

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X-ray crystallography

X-ray crystallography is a technique used for determining the atomic and molecular structure of a crystal, in which the crystalline atoms cause a beam of incident X-rays to diffract into many specific directions.

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Assymetric unit, Asymmetric unit, Basal Plane, Basal plane, Basis (crystal structure), Crystal Structure, Crystal axis, Crystal lattice structure, Crystal lattices, Crystal pattern, Crystal structure of a mineral, Crystal structures, Crystal symmetry, Crystalline lattice, Crystalline structure, Crystallographic lattice, Crystallographic structure, Crystallographic system, Lattice structure, Mineral structure, Mineral structures, Principal axis (crystallography), Space lattice, Types of crystals, Unit Cell, Unit cell, Unit cell length.


[1] https://en.wikipedia.org/wiki/Crystal_structure

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