# Mass attenuation coefficient

### From Online Dictionary of Crystallography

##### Revision as of 12:38, 16 November 2017 by BrianMcMahon (talk | contribs) (Added German and Spanish translations (U. Mueller))

Massenschwächungskoeffizient (*Ge*). Coeficiente másico de atenuación (*Sp*).

## Definition

The mass attenuation coefficient in cm^{2} g^{−1} can be written as a sum of separated photoelectric mass absorption coefficients [math][\mu/\rho]_{PE}[/math] and coherent [math][\sigma/\rho]_{coh}[/math] and incoherent [math][\sigma/\rho]_{incoh}[/math] scattering contributions:

[math][\mu/\rho]_{TOT}=[\mu/\rho]_{PE} +[\sigma/\rho]_{coh} +[\sigma/\rho]_{incoh}[/math]

or equivalently

[math][\mu/\rho]_{TOT}=[\mu/\rho]_{PE} +[\mu/\rho]_{coh} +[\mu/\rho]_{incoh}.[/math]

It is recommended that [math][\mu/\rho]_{TOT}[/math] be used to distinguish this from the mass absorption coefficient [math][\mu/\rho]_{PE}[/math] (*q.v.*) as they are both commonly presented as [math][\mu/\rho][/math].

The last two contributions are angle-dependent. Note that while absorptive processes are linear (see absorption coefficient), coherent scattering (and incoherent scattering) are not linear and hence the attenuation coefficient does not obey the Beer–Lambert Law.

The mass attenuation coefficient is conventionally given by the symbol [math][\mu/\rho] = \sigma/(uA)[/math], where [math]\sigma[/math] is the cross-section in barns/atom (1 barn = [math]10^{-24}[/math] cm^{2}), [math]u[/math] is the atomic mass unit, and [math]A[/math] is the relative atomic mass of the target element (*i.e.* in amu; the mass relative to 12 for carbon 12).

Where a material is composed of separate layers, the total *absorption* is given by the sum

[math]\ln\Big({I\over{I_0}}\Big)\Big|_{PE} = -\sum_i \Big[{\mu\over\rho}\Big]_{PE,i}[\rho t]_i.[/math]

Sometimes mass fractions are used as an approximation for a mixture, assuming that each atomic scatterer is independent.