View source for Debye-Waller factor

The '''Debye-Waller factor''', also known as the '''B-factor''' or the '''temperature factor''' describes the decrease in scattering intensity (either from x-ray or neutron scattering) due to the thermal motion of the atoms, or due to crystal disorder. The thermal motion, or disorder, in some sense reduces the validity of the Laue diffraction condition which is based on fixed atoms.

<!--:<math>I=I_{{0}} \mathrm{e}^{-1/3\,  \left| \vec G \right|^{2}\overline {{u}^{2}}}</math>-->
 I = I_0 * exp(-1/3 * |G|^2 * u^2)

I is the weakened intensity and I<sub>0</sub> the source intensity. G is a [[Reciprocal lattice|reciprocal lattice vector]] and u the thermally enhanced oscillation amplitude of the atoms. 

Higher orders of Bragg reflection are weakened more.

== Restrictions ==
Normally, the following restrictions apply to the anisotropic B-factor tensor
{| align="center" style="border: 1px solid #999; background-color:#FFFFFF"
|--bgcolor="#eeeeee"
| [http://en.wikipedia.org/wiki/Triclinic Triclinic]
|| none
|-----
| [http://en.wikipedia.org/wiki/Monoclinic Monoclinic]
|| B13 = B23 = 0 when &beta; = &alpha; = 90°<br/>
B12 = B23 = 0 when &gamma; = &alpha; = 90°<br/>
B12 = B13 = 0 when &gamma; = &beta; = 90°
|--bgcolor="#eeeeee"
| [http://en.wikipedia.org/wiki/Orthorhombic Orthorhombic]
|| B12 = B13 = B23 = 0
|-----
| [http://en.wikipedia.org/wiki/Tetragonal Tetragonal]
|| B11 = B22 and<br/> B12 = B13 = B23 = 0
|--bgcolor="#eeeeee"
| [http://en.wikipedia.org/wiki/Rhombohedral Rhombohedral]
|| B11 = B22 = B33 and<br/> B12 = B13 = B23
|-----
| [http://en.wikipedia.org/wiki/Hexagonal_%28crystal_system%29 Hexagonal]
|| B11 = B22 and<br/> B13 = B23 = 0
|--bgcolor="#eeeeee"
| [http://en.wikipedia.org/wiki/Cubic_crystal_system Cubic]
|| B11 = B22 = B33 and<br/> B12 = B13 = B23 = 0
|}

== External links ==
* [http://en.wikipedia.org/wiki/Debye-Waller_factor Wikipedia article on '''Debye-Waller factor''']

[[Category:Academic Research]]
[[Category:Crystallography]]