Electron microscopy
Mass Absorption Coefficients of X-Rays
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The intensity of the transmitted X-ray is a function of the intensity of a generated X-ray (I0), mass absorption coefficient μ/ρ (cm2/g), material density ρ (g/cm3), and thickness (cm):

                   Mass Absorption Coefficients of X-Rays -------------------------------------- [1313a]

As an example, page1730 shows X-ray absorption and intensity reduction induced by carbon contamination in EMs.

Equation 1313a can be re-written as,

                   mass absorption coefficient -------------------------------------- [1313b]

Assuming all X-rays, at different wavelengths, penetrating the same materials through the same thickness, e.g. X-rays collected by EDS detector in TEM or SEM systems, then the collected X-ray intensities decreases experientially depending on the corresponding mass absorption coefficient as indicated by Equation 1313b and Figure 1313a.


Figure 1313a. .

Table 1313. Mass absorption coefficients (μ/ρ, cm2/g) of several elements.

  Co Cu Fe Mn Ni          
8.04 keV (Cu Kα) 329 52 306 272 49          


The mass absorption coefficient (e.g. Figure 1313b) can be given by,

                   Mass Absorption Coefficients of X-Rays -------------------------------------- [1313c]
         NA -- Avogadro’s number,
         A -- The atomic weight,
         σa -- The total atomic absorption cross section (cm2/atom).         

Figure . Mass absorption coefficients of .
Figure 1313b. Mass absorption coefficients of Al (aluminum), Cu (copper), C (carbon), W (tungsten), and Si (silicon).

The corresponding mass absorption coefficient of a compound can be calculated by the equation,
                   μCompound = W1μ1 + W2μ2 ... + Wnμn -------------------------------------- [1313d]
          Wn -- The atomic weight fractions

Note that the mass absorption coefficient for a mixture can also be calculated in the same way as shown in Equation 1313c.