Difference between revisions of "Mass attenuation coefficient"
From Online Dictionary of Crystallography
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== Definition == | == Definition == | ||
| − | The mass attenuation coefficient in cm<sup>2</sup>/ | + | The mass attenuation coefficient in cm<sup>2</sup> g<sup>&minu;1</sup> can be written as a sum of separated photoelectric mass [[absorption coefficient]]s <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> | <math>[\mu/\rho]_{TOT}=[\mu/\rho]_{PE} +[\sigma/\rho]_{coh} +[\sigma/\rho]_{incoh}</math> | ||
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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>. | 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 ( | + | 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<sup>2</sup>), <math>u</math> is the atomic mass unit, and <math>A</math> is the relative atomic mass of the target element (''i.e'' | + | 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<sup>2</sup>), <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 | Where a material is composed of separate layers, the total ''absorption'' is given by the sum | ||
Revision as of 09:11, 20 May 2017
Definition
The mass attenuation coefficient in cm2 g&minu;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] 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.