Partial Cross-Sections for Inner-Shell Ionization
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A partial cross-section specifies
the probability of a specific shell scattering through angles
up to a specific angle, β, and with energy losses covering an energy range, Δ,
above an ionization energy. For instance, the partial cross-section, σK(β,Δ), of K-shell, EK, can be given by, 
For elements of low atomic number, σK(β,Δ) can be measured by EELS [1, 3-5],
This approximation in Equation 954b is accurate for Δ ≥ 50 eV. [1,5]
Based on Equation 954b, the Areal Density, N, namely the number of atoms per unit area of the TEM sample through the electron beam, can be obtained by, 
In practice, σK(β,Δ) obtained by Equations 954a or 954b can be applied into Equation 954c for Areal Density, N, calculation.
For large collection angles, the partial ionization cross-section, σ(β,Δ), becomes the total ionization cross-section, σ(Δ).
 R. F. Egerton, K-shell ionization cross-sections for use in microanalysis, 4(2), (1979) 169-179.