Mass attenuation coefficient
From Online Dictionary of Crystallography
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Definition
The mass attenuation coefficient in cm2/g 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] cm2), [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.