Editing Cubic crystal system (section)

==Bravais lattices==
{{further information|Bravais lattice}}
The three Bravais latices in the cubic crystal system are:

{| class="wikitable skin-invert-image"
! Bravais lattice
! Primitive<br/>cubic
! Body-centered<br/>cubic
! Face-centered<br/>cubic
|- align=center
! [[Pearson symbol]]
| ''cP''
| ''cI''
| ''cF''
|-
! [[Crystal structure#Unit cell|Unit cell]]
| [[File:Cubic.svg|100px]]
| [[File:Cubic-body-centered.svg|100px]]
| [[File:Cubic-face-centered.svg|100px]]
|}

The primitive cubic lattice (cP) consists of one [[Lattice (group)|lattice]] point on each corner of the cube; this means each simple cubic unit cell has in total one lattice point. Each atom at a lattice point is then shared equally between eight adjacent cubes, and the unit cell therefore contains in total one atom ({{frac|8}}&nbsp;×&nbsp;8).<ref name=IUCnames>{{cite journal|title=Nomenclature for crystal families, Bravais-lattice types and arithmetic classes. Report of the International Union of Crystallography Ad-Hoc Committee on the Nomenclature of Symmetry|year=1985|journal=[[Acta Crystallographica Section A]]|volume=41|issue=3|page=278|doi=10.1107/S0108767385000587|doi-access=free|last1=De Wolff |first1=P. M. |last2=Belov |first2=N. V. |last3=Bertaut |first3=E. F. |last4=Buerger |first4=M. J. |last5=Donnay |first5=J. D. H. |last6=Fischer |first6=W. |last7=Hahn |first7=Th. |last8=Koptsik |first8=V. A. |last9=MacKay |first9=A. L. |last10=Wondratschek |first10=H. |last11=Wilson |first11=A. J. C. |last12=Abrahams |first12=S. C. }}</ref>

The body-centered cubic lattice (cI) has one lattice point in the center of the unit cell in addition to the eight corner points. It has a net total of two lattice points per unit cell ({{frac|8}}&nbsp;×&nbsp;8 +&nbsp;1).<ref name=IUCnames />

The face-centered cubic lattice (cF) has lattice points on the faces of the cube, that each gives exactly one half contribution, in addition to the corner lattice points, giving a total of four lattice points per unit cell ({{frac|8}}&nbsp;×&nbsp;8 from the corners plus {{frac|2}}&nbsp;×&nbsp;6 from the faces).

The face-centered cubic lattice is closely related to the [[Hexagonal crystal system|hexagonal close packed]] (hcp) system, where two systems differ only in the relative placements of their hexagonal layers. The [[Miller index|[111]]] plane of a face-centered cubic lattice is a hexagonal grid.

Attempting to create a base-centered cubic lattice (i.e., putting an extra lattice point in the center of each horizontal face) results in a simple [[Tetragonal crystal system|tetragonal]] [[Bravais lattice]].

[[Coordination number]] (CN) is the number of nearest neighbors of a central atom in the structure.<ref name=IUCnames /> Each sphere in a cP lattice has coordination number 6, in a cI lattice 8, and in a cF lattice 12.

[[Atomic packing factor]] (APF) is the fraction of volume that is occupied by atoms. The cP lattice has an APF of about 0.524, the cI lattice an APF of about 0.680, and the cF lattice an APF of about 0.740.