Difference between revisions of "Debye-Waller factor"

From Christoph's Personal Wiki
Jump to: navigation, search
 
 
(3 intermediate revisions by the same user not shown)
Line 4: Line 4:
 
  I = I_0 * exp(-1/3 * |G|^2 * u^2)
 
  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.  
+
''I'' is the weakened intensity and ''I<sub>0</sub>'' the source intensity. ''G'' is a [http://en.wikipedia.org/wiki/Reciprocal_lattice reciprocal lattice vector] and ''u'' the thermally enhanced oscillation amplitude of the atoms.  
  
 
Higher orders of Bragg reflection are weakened more.
 
Higher orders of Bragg reflection are weakened more.
  
 
== Restrictions ==
 
== Restrictions ==
Normally, the following restrictions apply to the anisotropic B-factor tensor
+
Normally, the following restrictions apply to the [http://en.wikipedia.org/wiki/Anisotropic anisotropic] B-factor tensor
 
{| align="center" style="border: 1px solid #999; background-color:#FFFFFF"
 
{| align="center" style="border: 1px solid #999; background-color:#FFFFFF"
 
|--bgcolor="#eeeeee"
 
|--bgcolor="#eeeeee"
Line 38: Line 38:
 
== External links ==
 
== External links ==
 
* [http://en.wikipedia.org/wiki/Debye-Waller_factor Wikipedia article on '''Debye-Waller factor''']
 
* [http://en.wikipedia.org/wiki/Debye-Waller_factor Wikipedia article on '''Debye-Waller factor''']
 +
* [http://www.ocms.ox.ac.uk/mirrored/xplor/manual/htmlman/node296.html Overall B-Factor Refinement]
  
[[Category:Academic Research]]
 
 
[[Category:Crystallography]]
 
[[Category:Crystallography]]

Latest revision as of 06:42, 15 October 2021

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.

I = I_0 * exp(-1/3 * |G|^2 * u^2)

I is the weakened intensity and I0 the source intensity. G is a 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

Triclinic none
Monoclinic B13 = B23 = 0 when β = α = 90°

B12 = B23 = 0 when γ = α = 90°
B12 = B13 = 0 when γ = β = 90°

Orthorhombic B12 = B13 = B23 = 0
Tetragonal B11 = B22 and
B12 = B13 = B23 = 0
Rhombohedral B11 = B22 = B33 and
B12 = B13 = B23
Hexagonal B11 = B22 and
B13 = B23 = 0
Cubic B11 = B22 = B33 and
B12 = B13 = B23 = 0

External links