Rose des Sables (Sand Rose), formed of gypsum 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 are 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. Download high resolution version (1842x1737, 701 KB) Wikipedia does not have an article with this exact name. ... Download high resolution version (1842x1737, 701 KB) Wikipedia does not have an article with this exact name. ... 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 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. ... Properties For alternative meanings see atom (disambiguation). ... In geometry and crystallography, a Bravais lattice is an infinite set of points generated by a set of discrete translation operations. ... Square with symmetry group D4 Symmetry is a characteristic of geometrical shapes, equations, and other objects; we say that such an object is symmetric with respect to a given operation if this operation, when applied to the object, does not appear to change it. ... The space group of a crystal is a mathematical description of the symmetry inherent in the structure. ... Cleaveage, 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. ...

Unit cell

A unit cell is a spatial arrangement of atoms which is tiled in three-dimensional space to describe the crystal. The positions of the atoms inside the unit cell are described by the asymmetric unit or basis, the set of atomic positions (x_i,y_i,z_i) measured from a lattice point. Properties For alternative meanings see atom (disambiguation). ... 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. ...

For each crystal structure there is a conventional unit cell, usually chosen to make the resulting lattice as symmetric as possible. 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. 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. ...

Crystal system

The crystal system is the point group of the lattice (the set of rotation and reflection symmetries which leave a lattice point fixed), not including the positions of the atoms in the unit cell. There are seven unique crystal systems. The simplest and most symmetric, the cubic (or isometric) system, has the symmetry of a cube. 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. 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. ... 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 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. ...

Classification of lattices

Crystal system	Lattices
triclinic
monoclinic	simple	centered
orthorhombic	simple	base-centered	body-centered	face-centered
hexagonal
rhombohedral (trigonal)
tetragonal	simple	body-centered
cubic (isometric)	simple	body-centered	face-centered

A Bravais lattice is a set of points constructed by translating a single point in discrete steps by a set of basis vectors. In three dimensions, there are 14 unique Bravais lattices (distinct from one another in that they have different space groups) in three dimensions. All crystalline materials recognised till now (not including quasicrystals) fit in one of these arrangements. The fourteen three-dimensional lattices, classified by crystal system, are shown to the right. In crystallography, the triclinic crystal system is one of the 7 lattice point groups. ... Triclinic crystal structure File links The following pages link to this file: User:DrBob/Figures Crystal structure Triclinic Categories: GFDL images ... 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. ... Orthorhombic crystal structure. ... Orthorhombic base-centred crystal File links The following pages link to this file: User:DrBob/Figures Crystal structure Orthorhombic Categories: GFDL images ... Orthorhombic body-centred crystal File links The following pages link to this file: User:DrBob/Figures Crystal structure Orthorhombic Categories: GFDL images ... Orthorhombic face-centred crystal File links The following pages link to this file: User:DrBob/Figures Crystal structure Orthorhombic Categories: GFDL images ... In crystallography, the hexagonal crystal system is one of the 7 lattice point groups. ... Hexagonal crystal structure. ... In crystallography, the rhombohedral (or trigonal) crystal system is one of the 7 lattice point groups. ... Rhombohedral crystal structure. ... In crystallography, the tetragonal crystal system is one of the 7 lattice point groups. ... Tetragonal crystal structure. ... Tetragonal body-centred crystal File links The following pages link to this file: User:DrBob/Figures Crystal structure Tetragonal Categories: GFDL images ... In crystallography, the cubic crystal system (or isometric crystal system) is the most symmetric of the 7 crystal systems. ... Cubic crystal structure. ... In geometry and crystallography, a Bravais lattice is an infinite set of points generated by a set of discrete translation operations. ... The space group of a crystal is a mathematical description of the symmetry inherent in the structure. ... Quasicrystals are a peculiar form of solid in which the atoms of the solid are arranged in a seemingly regular, yet non-repeating structure. ...

The crystal structure is one of the lattices with a unit cell, which contains atoms at specific coordinates, at every lattice point. Because it includes the unit cell, the symmetry of the crystal can be more complicated than the symmetry of the lattice.

Point and space groups

The crystallographic point group or crystal class is the set of non-translational symmetries that leave a point in the crystal fixed. There are 32 possible crystal classes. 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 symmetries in addition to the symmetries of the point group. There are 230 distinct space groups. The space group of a crystal is a mathematical description of the symmetry inherent in the structure. ...

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. 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. ... For the syntaxic operation, see Dislocation (syntax) For the medical term, see Dislocation (medicine) In materials science a dislocation is a linear crystallographic defect, or irregularity, in 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). ...

See also

• Crystal
• Crystallography
• Crystallographic point group
• Crystallographic defect
• Crystal growth
• Liquid crystal
• Cleavage (crystal)
• Seed crystal
• Quasicrystals

For more detailed information in specific technology applications see materials engineering, materials science, ceramics, metallurgy, or materials physics. Quartz crystal 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. ... 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. ... 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. ... Cleaveage, 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. ... Materials engineering is a discipline related to materials science which focusses on materials design, processing techniques (casting, rolling, welding, ion implantation, crystal growth, thin film deposition, sintering, glassblowing, etc. ... The Materials Science Tetrahedron Materials science is a multidisciplinary field focusing on functional solids, whether the function served is structural, electronic, thermal, chemical, magnetic, optical, or some combination of these. ... The word ceramic is derived from the Greek word Κεραμεικος (the name of a suburb of Athens), and in its strictest sense refers to clay in all its forms. ... Metallurgy is a domain of materials science and of materials engineering that studies the physical and chemical behavior of metallic elements and their mixtures, which are called alloys. ... Materials physics is a field of physics concerned with the physical properties of materials. ...

External links

• Appendix A from the manual for Atoms, software for XAFS
• Intro to Minerals: Crystal Class and System
• Introduction to Crystallography and Mineral Crystal Systems
• Crystal planes and Miller indices