- Primitive cell
geometry, solid state physicsand mineralogy, particularly in describing crystal structure, a primitive cell, is a minimum cell corresponding to a single lattice pointof a structure with translational symmetryin 2D, 3D, or other dimensions. A lattice can be characterized by the geometry of its primitive cell.
The primitive cell is a
fundamental domainwith respect to translational symmetry only. In the case of additional symmetries a fundamental domain is smaller.
crystalcan be categorized by its lattice and the atoms that lie in a primitive cell (the "basis"). A cell will fill all the lattice space without leaving gaps by repetition of crystal translation operations.
"Primitive translation vectors" are used to define a crystal translation vector, , and also gives a lattice cell of smallest volume for a particular lattice. The "lattice" and translation vectors , , and are "primitive" if the atoms look the same from any lattice points using integers , , and .
The primitive cell is defined by the primitive axes (vectors) , , and . The volume, , of the primitive cell is given by the parallelepiped from the above axes as,
Wigner-Seitz cellis an example of another kind of primitive cell. In certain circumstances, "primitive cell" is synonymous with "unit cell". However, the conventional description of cubic lattices, such as body centered cubic (BCC) and face centered cubic (FCC) lattices, relies on a cubic unit cell. In the BCC and FCC cases, the primitive cell is distinct from this "conventional unit cell".
The general mathematical concept behind the primitive cell is termed the
fundamental domainor the Voronoi cell. The primitive cell of the reciprocal latticein momentum spaceis called the Brillouin zone.
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