Editing Crystal structure (section)

== Atomic coordination ==
By considering the arrangement of atoms relative to each other, their coordination numbers, interatomic distances, types of bonding, etc., it is possible to form a general view of the structures and alternative ways of visualizing them.<ref name="Physics 1994">{{cite book |title=McGraw Hill Encyclopaedia of Physics |edition=2nd |editor1-first=C.B. |editor1-last=Parker |date=1994 |publisher=McGraw-Hill |isbn=978-0070514003 |url-access=registration |url=https://archive.org/details/mcgrawhillencycl1993park }}</ref>

=== Close packing ===
{{Main|Close-packing of equal spheres}}
[[File:close packing.svg|thumb|upright=1.3|The hpc lattice (left) and the ccf lattice (right)]]
The principles involved can be understood by considering the most efficient way of packing together equal-sized spheres and stacking [[close-packed]] atomic planes in three dimensions. For example, if plane A lies beneath plane B, there are two possible ways of placing an additional atom on top of layer B. If an additional layer were placed directly over plane A, this would give rise to the following series:
:...'''ABABABAB'''...
This arrangement of atoms in a crystal structure is known as '''hexagonal close packing (hcp)'''.

If, however, all three planes are staggered relative to each other and it is not until the fourth layer is positioned directly over plane A that the sequence is repeated, then the following sequence arises:
:...'''ABCABCABC'''...
This type of structural arrangement is known as '''cubic close packing (ccp)'''.

The unit cell of a ccp arrangement of atoms is the face-centered cubic (fcc) unit cell. This is not immediately obvious as the closely packed layers are parallel to the {111} planes of the fcc unit cell. There are four different orientations of the close-packed layers.

===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.

===Interstitial sites===
{{Expand section|date=August 2022}}
{{main|Interstitial site}}
[[Image:Sites interstitiels cubique a faces centrees.svg|thumb|200px|''Octahedral'' (red) and ''tetrahedral'' (blue) interstitial sites in a [[face-centered cubic]] lattice.]]
Interstitial sites refer to the empty spaces in between the atoms in the crystal lattice. These spaces can be filled by oppositely charged ions to form multi-element structures. They can also be filled by impurity atoms or self-interstitials to form [[interstitial defect]]s.
{{clear}}