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A crystal's structure and symmetry play a role in determining many of its properties, such as cleavage, electronic band structure, and optical properties.
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 measured from a lattice point.
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.
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, tetragonalIn crystallography, the tetragonal crystal system is one of the 7 lattice point groups. Tetragonal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base a by a and, rhombohedralIn crystallography, the rhombohedral (or trigonal crystal system is one of the 7 lattice point groups. A crystal system is described by three basis vectors. In the rhombohedral system, the crystal is described by vectors of equal length, all three of whic (also known as trigonal), orthorhombicIn crystallography, the orthorhombic crystal system is one of the 7 lattice point groups. Orthorhombic lattices result from stretching a cubic lattice along two of its lattice vectors by two different factors, resulting in a rectangular prism with a recta, monoclinicIn crystallography, the monoclinic crystal system is one of the 7 lattice point groups. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal length, as in the orthorhombic system. Two of and triclinicIn crystallography, the triclinic crystal system is one of the 7 lattice point groups. A crystal system is described by three basis vectors. In the triclinic system, the crystal is described by vectors of unequal length, as in the orthorhombic system.. Some crystallographers consider the hexagonal crystal system not to be its own crystal system, but instead a part of the trigonal crystal system.
| Crystal system | Lattices | |||
| triclinicIn crystallography, the triclinic crystal system is one of the 7 lattice point groups. A crystal system is described by three basis vectors. In the triclinic system, the crystal is described by vectors of unequal length, as in the orthorhombic system. | ||||
| monoclinicIn crystallography, the monoclinic crystal system is one of the 7 lattice point groups. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal length, as in the orthorhombic system. Two of | simple | centered | ||
| orthorhombicIn crystallography, the orthorhombic crystal system is one of the 7 lattice point groups. Orthorhombic lattices result from stretching a cubic lattice along two of its lattice vectors by two different factors, resulting in a rectangular prism with a recta | 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.
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.
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