Difference between revisions of "Absorption length"
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\begin{alignat}{2} | \begin{alignat}{2} | ||
\mu & = \frac{\rho N_a}{m_a} \sigma \\ | \mu & = \frac{\rho N_a}{m_a} \sigma \\ | ||
| − | & = \frac{\rho N_a}{m_a} | + | & = \frac{\rho N_a}{m_a} 2 r_e \lambda f_2 |
\end{alignat} | \end{alignat} | ||
</math> | </math> | ||
where ''ρ'' is density, ''N<sub>a</sub>'' is the Avogadro constant, and ''m<sub>a</sub>'' is the atomic molar mass. Note that the '''mass attenuation coefficient''' is simply <math>\mu/\rho</math>. | where ''ρ'' is density, ''N<sub>a</sub>'' is the Avogadro constant, and ''m<sub>a</sub>'' is the atomic molar mass. Note that the '''mass attenuation coefficient''' is simply <math>\mu/\rho</math>. | ||
| + | |||
| + | ==Related forms== | ||
| + | As can be seen, there are many related quantities which express the material's absorption: | ||
| + | * '''Absorption length''' <math>\epsilon</math>, the distance over which the intensity falls to 1/''e''. | ||
| + | * '''Attenuation coefficient''' <math>\mu</math>, the characteristic inverse-distance for attenuation. | ||
| + | * '''Mass attenuation coefficient''' <math>\mu/\rho</math>, the density-scaled attenuation. | ||
| + | * '''Absorptive [[atomic scattering factor]]''' <math>f_2</math>, the intrinsic dissipative interaction of the material. | ||
| + | * '''Atomic photoabsorption cross-section''' <math>\sigma</math>, the cross-section ('effective size') of the atom's x-ray absorption (capture) efficiency. | ||
| + | * '''Imaginary [[refractive index]]''' <math>\beta</math>, the resonant component of the refractive index. | ||
| + | * '''Imaginary [[Scattering Length Density]]''' <math>\mathrm{Im}(\mathrm{SLD})</math>, the absorptive component of the scattering contrast. | ||
==See Also== | ==See Also== | ||
Revision as of 13:55, 6 June 2014
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:
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, 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:
Where λ is the x-ray wavelength, and re is the classical electron radius. The attenuation coefficient is given by:
where ρ is density, Na is the Avogadro constant, and ma is the atomic molar mass. Note that the mass attenuation coefficient is simply .
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.
