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.

Absorption

The absorption follows a simple Beer-Lambert law:

${\frac {I(x)}{I_{0}}}=e^{-x/\epsilon }$

The attenuation coefficient (or absorption coefficient) is simply the inverse of the absorption length; $\mu =1/\epsilon$

${\frac {I(x)}{I_{0}}}=e^{-\mu x}$

Calculating

The absorption length arises from the imaginary part of the atomic scattering factor, f₂. It is closely related to the absorption cross-section, and the mass absorption coefficient. Specifically, the atomic photoabsorption cross-section can be computed via:

$\sigma =2r_{e}\lambda f_{2}$

Where λ is the x-ray wavelength, and r_e is the classical electron radius. The attenuation coefficient is given by:

Failed to parse (unknown function "\begin{alignat}"): {\displaystyle \begin{alignat}{2} \mu & = \frac{\rho N_a}{m_a} \sigma \\ & = \frac{\rho N_a}{m_a} \2 r_e \lambda f_2 \end{alignat} }

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 $\mu /\rho$.

See Also

• LBL X-Ray Attenuation Length calculator
• [http://11bm.xray.aps.anl.gov/absorb/absorb.php APS absorption calculator
• Wikipedia: Mass attenuation coefficient
• NIST tables of x-ray mass attenuation coefficient