A report on 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 .

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

14 related topics with Alpha

Overall

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

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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 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

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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.

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

Crystallography

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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.

Bravais lattice

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Infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by

Infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by

In two-dimensional space there are 5 Bravais lattices, grouped into four lattice systems, shown in the table below.

Relation between the two settings for the rhombohedral lattice

Hexagonal crystal family

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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).

Subgroup relations of the 32 crystallographic point groups<BR>(rows represent group orders from bottom to top as: 1,2,3,4,6,8,12,16,24, and 48.)

Crystallographic point group

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Set of symmetry operations, corresponding to one of the point groups in three dimensions, such that each operation would leave the structure of a crystal unchanged i.e. the same kinds of atoms would be placed in similar positions as before the transformation.

Set of symmetry operations, corresponding to one of the point groups in three dimensions, such that each operation would leave the structure of a crystal unchanged i.e. the same kinds of atoms would be placed in similar positions as before the transformation.

Subgroup relations of the 32 crystallographic point groups<BR>(rows represent group orders from bottom to top as: 1,2,3,4,6,8,12,16,24, and 48.)

For the correspondence of the two systems below, see crystal system.

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

Crystal structure

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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.

An example of the triclinic crystals, microcline

Triclinic crystal system

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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.

Monoclinic crystal

Monoclinic crystal system

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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.

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

Orthorhombic crystal system

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

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