Debye-Waller factor

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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

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