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.

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

• Wikipedia article on Debye-Waller factor