Practical Electron Microscopy and Database

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):

                    -------------------------------------- [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,

                    -------------------------------------- [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.

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

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

                    -------------------------------------- [1313c]
where,
         N_A -- Avogadro’s number,
         A -- The atomic weight,
         σ_a -- The total atomic absorption cross section (cm²/atom).         

The corresponding mass absorption coefficient of a compound can be calculated by the equation,
                   μ_Compound = W₁μ₁ + W₂μ₂ ... + W_nμ_n -------------------------------------- [1313d]
where,
          W_n -- 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.