Editing Crystal structure (section)

===APF and CN===
{{main|Atomic packing factor|Coordination number}}
One important characteristic of a crystalline structure is its atomic packing factor (APF). This is calculated by assuming that all the atoms are identical spheres, with a radius large enough that each sphere abuts on the next. The atomic packing factor is the proportion of space filled by these spheres which can be worked out by calculating the total volume of the spheres and dividing by the volume of the cell as follows:
:<math>\mathrm{APF} = \frac{N_\mathrm{particle} V_\mathrm{particle}}{V_\text{unit cell}}</math>

Another important characteristic of a crystalline structure is its coordination number (CN). This is the number of nearest neighbours of a central atom in the structure.

The APFs and CNs of the most common crystal structures are shown below:

{| class=wikitable
! Crystal structure
! Atomic packing factor
! Coordination number<br/>([[Coordination geometry|Geometry]])
|-
! [[Diamond cubic]]
| 0.34
| 4 ([[Tetrahedron]])
|-
! [[Simple cubic]]
| 0.52<ref name=Ellis>{{cite book|first1=Arthur B.|display-authors=etal|last1=Ellis|title=Teaching General Chemistry: A Materials Science Companion|date=1995|publisher=American Chemical Society|location=Washington, DC|isbn=084122725X|edition=3rd}}</ref>
| 6 ([[Octahedron]])
|-
! [[Body-centered cubic]] (BCC)
| 0.68<ref name=Ellis/>
| 8 ([[Cube]])
|-
! [[Face-centered cubic]] (FCC)
| 0.74<ref name=Ellis/>
| 12 ([[Cuboctahedron]])
|-
! [[Hexagonal crystal system|Hexagonal close-packed]] (HCP)
| 0.74<ref name=Ellis/>
| 12 ([[Triangular orthobicupola]])
|}

The 74% packing efficiency of the FCC and HCP is the maximum density possible in unit cells constructed of spheres of only one size.