Electron microscopy
 
Beer’s Absorption Law in TEM/STEM Measurements
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The Beer’s absorption law states that the transmission T of light through a substance has a logarithmic dependence. In TEM/STEM measurement, the "light" is the incident electron beam. Then, the Beer’s absorption law is given by the fraction (I/I0) of incident electrons transmitted through a thickness x,

        Beer’s law ----------------------------------------- [1226a]
               Beer’s absorption law ---------------------------------------------------------- [1226b]
where,
         I0 -- The incident intensity of electron beam.
         I -- The transmitted intensity of electron beam.
         x -- The thickness of the specimen.
         ρ -- The atomic density of the material.
         ρx - The mass-thickness.
         μ/ρ -- The mass absorption coefficient, or called absorption cross section (σ).
         n -- The number of atoms per unit volume.

Then, the image contrast C can be given by,
         C = ln(1/T) ------------------------------------------------------------------- [1226c]
             = nσx ---------------------------------------------------------------------- [1226d]
             = n(σe + σi)x -------------------------------------------------------------- [1226e]
where,
          σe -- The cross section for elastic scattering.
          σi -- The cross section for inelastic scattering.

 

 

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