Crystal system

The diamond crystal structure belongs to the face-centered cubic lattice, with a repeated two-atom pattern.
Hexagonal hanksite crystal, with threefold c-axis symmetry

Set of point groups (a group of geometric symmetries with at least one fixed point).

- Crystal system
The diamond crystal structure belongs to the face-centered cubic lattice, with a repeated two-atom pattern.

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The space group of hexagonal H2O ice is P63/mmc. The first m indicates the mirror plane perpendicular to the c-axis (a), the second m indicates the mirror planes parallel to the c-axis (b), and the c indicates the glide planes (b) and (c). The black boxes outline the unit cell.

Space group

Symmetry group of an object in space, usually in three dimensions.

Symmetry group of an object in space, usually in three dimensions.

The space group of hexagonal H2O ice is P63/mmc. The first m indicates the mirror plane perpendicular to the c-axis (a), the second m indicates the mirror planes parallel to the c-axis (b), and the c indicates the glide planes (b) and (c). The black boxes outline the unit cell.

The space groups in three dimensions are made from combinations of the 32 crystallographic point groups with the 14 Bravais lattices, each of the latter belonging to one of 7 lattice systems.

A crystalline solid: atomic resolution image of strontium titanate. Brighter spots are columns of strontium atoms and darker ones are titanium-oxygen columns.

Crystallography

Experimental science of determining the arrangement of atoms in crystalline solids .

Experimental science of determining the arrangement of atoms in crystalline solids .

A crystalline solid: atomic resolution image of strontium titanate. Brighter spots are columns of strontium atoms and darker ones are titanium-oxygen columns.
Molecular model of penicillin by Dorothy Hodgkin, 1945
Photograph of DNA (photo 51), Rosalind Franklin, 1952
Octahedral and tetrahedral interstitial sites in a face centered cubic structure
Kikuchi lines in an electron backscatter diffraction pattern of monocrystalline silicon, taken at 20 kV with a field-emission electron source

Coordinates in angle brackets or chevrons such as <100> denote a family of directions which are related by symmetry operations. In the cubic crystal system for example, would mean or the negative of any of those directions.

Crystals of amethyst quartz

Crystal

Solid material whose constituents are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions.

Solid material whose constituents are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions.

Crystals of amethyst quartz
Microscopically, a single crystal has atoms in a near-perfect periodic arrangement; a polycrystal is composed of many microscopic crystals (called "crystallites" or "grains"); and an amorphous solid (such as glass) has no periodic arrangement even microscopically.
As a halite crystal is growing, new atoms can very easily attach to the parts of the surface with rough atomic-scale structure and many dangling bonds. Therefore, these parts of the crystal grow out very quickly (yellow arrows). Eventually, the whole surface consists of smooth, stable faces, where new atoms cannot as easily attach themselves.
Ice crystals
Fossil shell with calcite crystals
Vertical cooling crystallizer in a beet sugar factory.
Two types of crystallographic defects. Top right: edge dislocation. Bottom right: screw dislocation.
Twinned pyrite crystal group.
The material holmium–magnesium–zinc (Ho–Mg–Zn) forms quasicrystals, which can take on the macroscopic shape of a pentagonal dodecahedron. Only quasicrystals can take this 5-fold symmetry. The edges are 2 mm long.
Insulin crystals grown in earth orbit.
Hoar frost: A type of ice crystal (picture taken from a distance of about 5 cm).
Gallium, a metal that easily forms large crystals.
An apatite crystal sits front and center on cherry-red rhodochroite rhombs, purple fluorite cubes, quartz and a dusting of brass-yellow pyrite cubes.
Boules of silicon, like this one, are an important type of industrially-produced single crystal.
A specimen consisting of a bornite-coated chalcopyrite crystal nestled in a bed of clear quartz crystals and lustrous pyrite crystals. The bornite-coated crystal is up to 1.5 cm across.
Needle-like millerite crystals partially encased in calcite crystal and oxidized on their surfaces to zaratite; from the Devonian Milwaukee Formation of Wisconsin

These are grouped into 7 crystal systems, such as cubic crystal system (where the crystals may form cubes or rectangular boxes, such as halite shown at right) or hexagonal crystal system (where the crystals may form hexagons, such as ordinary water ice).

Monoclinic crystal

Monoclinic crystal system

Monoclinic crystal
An example of the monoclinic crystal orthoclase

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

Rectangular vs rhombic unit cells for the 2D orthorhombic lattices.

Orthorhombic crystal system

Rectangular vs rhombic unit cells for the 2D orthorhombic lattices.

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

An example of the tetragonal crystals, wulfenite

Tetragonal crystal system

An example of the tetragonal crystals, wulfenite

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

An example of the triclinic crystals, microcline

Triclinic crystal system

An example of the triclinic crystals, microcline
Triclinic (a ≠ b ≠ c and α ≠ β ≠ γ )

In crystallography, the triclinic (or anorthic) crystal system is one of the 7 crystal systems.

A rock containing three crystals of pyrite (FeS2). The crystal structure of pyrite is primitive cubic, and this is reflected in the cubic symmetry of its natural crystal facets.

Cubic crystal system

A rock containing three crystals of pyrite (FeS2). The crystal structure of pyrite is primitive cubic, and this is reflected in the cubic symmetry of its natural crystal facets.
A network model of a primitive cubic system
The primitive and cubic close-packed (also known as face-centered cubic) unit cells
Visualisation of a diamond cubic unit cell: 1. Components of a unit cell, 2. One unit cell, 3. A lattice of 3 x 3 x 3 unit cells
A caesium chloride unit cell. The two colors of spheres represent the two types of atoms.
This graphic shows the interlocking simple cubic lattices of cesium and chlorine. You can see them separately and as they are interlocked in what looks like a body-centered cubic arrangement
The rock-salt crystal structure. Each atom has six nearest neighbours, with octahedral geometry.
A zincblende unit cell
The structure of the Heusler compounds with formula X2YZ (e. g., Co2MnSi).
Diagram of the iron monosilicide structure.
Weaire–Phelan structure

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

Crystal structure of table salt (sodium in purple, chloride in green)

Crystal structure

Description of the ordered arrangement of atoms, ions or molecules in a crystalline material.

Description of the ordered arrangement of atoms, ions or molecules in a crystalline material.

Crystal structure of table salt (sodium in purple, chloride in green)
Planes with different Miller indices in cubic crystals
Dense crystallographic planes
The hcp lattice (left) and the fcc lattice (right)
Quartz is one of the several crystalline forms of silica, SiO2. The most important forms of silica include: α-quartz, β-quartz, tridymite, cristobalite, coesite, and stishovite.
Simple cubic (P)
Body-centered cubic (I)
Face-centered cubic (F)

They are similar to, but not quite the same as the seven crystal systems.

Relation between the two settings for the rhombohedral lattice

Hexagonal crystal family

Relation between the two settings for the rhombohedral lattice
Hexagonal close packed (hcp) unit cell
Wurtzite unit cell as described by symmetry operators of the space group.
Another representation of the wurtzite unit cell
Another representation of the wurtzite structure
The unit cell of nickeline

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