Editing Unit cell (section)

{{refimprove|date=May 2021}}

{{short description|Repeating unit formed by the vectors spanning the points of a lattice}}

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.<ref>{{cite book |last=Ashcroft |first=Neil W. |title=Solid State Physics |year=1976 |publisher=W. B. Saunders Company|isbn=0-03-083993-9 |pages=72 |chapter=Chapter 4}}</ref> 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.<ref>{{cite book |last1=Simon |first1=Steven |title=The Oxford Solid State Physics |date=2013 |publisher=Oxford University Press |isbn=978-0-19-968076-4 |page=114 |edition=1}}</ref> 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 [[Parallelepiped#Parallelotope|parallelotopes]] in ''n'' dimensions.