Absorption length
The absorption length or attenuation length in x-ray scattering is the distance over which the x-ray beam is absorbed. By convention, the absorption length ϵ is defined as the distance into a material where the beam flux has dropped to 1/e of its incident flux.
Contents
Absorption
The absorption follows a simple Beer-Lambert law:
The attenuation coefficient (or absorption coefficient) is simply the inverse of the absorption length;
Calculating
The absorption length arises from the imaginary part of the atomic scattering factor, f_{2}. It is closely related to the absorption cross-section, and the mass absorption coefficient. Specifically, the atomic photoabsorption cross-section can be computed via:
Where λ is the x-ray wavelength, and r_{e} is the classical electron radius. The attenuation coefficient is given by:
where ρ is density, N_{a} is the Avogadro constant, and m_{a} is the atomic molar mass. Note that the mass attenuation coefficient is simply .
Elemental dependence
Energy dependence
Notice that the absorption undergoes sharp increases when passing through an absorption edge.
Examples
silicon
gold
Elemental/Energy dependence
Related forms
As can be seen, there are many related quantities which express the material's absorption:
- Absorption length , the distance over which the intensity falls to 1/e.
- Attenuation coefficient , the characteristic inverse-distance for attenuation.
- Mass attenuation coefficient , the density-scaled attenuation.
- Absorptive atomic scattering factor , the intrinsic dissipative interaction of the material.
- Atomic photoabsorption cross-section , the cross-section ('effective size') of the atom's x-ray absorption (capture) efficiency.
- Imaginary refractive index , the resonant component of the refractive index.
- Imaginary Scattering Length Density , the absorptive component of the scattering contrast.
See also scattering factors for a comparison of the quantities related to f_{1}.