Unit cell

In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice.^[1] Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessarily have unit size, or even a particular size at all. Rather, the primitive cell is the closest analogy to a unit vector, since it has a determined size for a given lattice and is the basic building block from which larger cells are constructed.

The concept is used particularly in describing crystal structure in two and three dimensions, though it makes sense in all dimensions. A lattice can be characterized by the geometry of its unit cell, which is a section of the tiling (a parallelogram or parallelepiped) that generates the whole tiling using only translations.

There are two special cases of the unit cell: the primitive cell and the conventional cell. The primitive cell is a unit cell corresponding to a single lattice point, it is the smallest possible unit cell.^[2] In some cases, the full symmetry of a crystal structure is not obvious from the primitive cell, in which cases a conventional cell may be used. A conventional cell (which may or may not be primitive) is a unit cell with the full symmetry of the lattice and may include more than one lattice point. The conventional unit cells are parallelotopes in n dimensions.

^ Ashcroft, Neil W. (1976). "Chapter 4". Solid State Physics. W. B. Saunders Company. p. 72. ISBN 0-03-083993-9.
^ Simon, Steven (2013). The Oxford Solid State Physics (1 ed.). Oxford University Press. p. 114. ISBN 978-0-19-968076-4.

[1] Ashcroft, Neil W. (1976). "Chapter 4". Solid State Physics. W. B. Saunders Company. p. 72. ISBN 0-03-083993-9.

[2] Simon, Steven (2013). The Oxford Solid State Physics (1 ed.). Oxford University Press. p. 114. ISBN 978-0-19-968076-4.

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