Theoretical Intensity of Characteristic X-Rays
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The X-ray spectrum recorded by EDS systems is composed of the characteristic peaks and continuum background. In general, the background of EDS map and profile originates from stray radiation in the TEM column and bremsstrahlung X-rays. The background needs to be removed before the peak intensities are obtained. The peak integration can be done either by fitting a Gaussian profile or by using reference spectra that have been recorded previously and stored in the computer.

Theoretically, the measured intensity of the characteristic X-rays can be given by,
          I = (I0σ(ω)ωpNapCtΩr)/(4πM) --------------------- [4646a]
where,
          I0 -- The total current in the electron probe.
          C -- The content (wt% or at.%).
          σ(ω) -- The ionization cross-section for the inner shell excitation.
          t -- The foil thickness.
          ω -- The X-ray yield.
          Ω -- The detector solid angle.
          p -- The Production fraction of characteristic X-rays to be analyzed.
          r -- The detection efficiency.
          Na -- The Avogadro's number.
          M -- The atomic number.
          p -- The atomic density.

If there is no artifacts in EDS measurements, the intensity of characteristic X-rays produced per incident electron is directly given by,
           IA(ω)=fAσ(ω)nAdtI0 --------------------------------------- [4646b]
where,
           fA -- The X-ray (fluorescence) yield.
           nA -- The atomic density of the element A.
           d -- The effective probe diameter.

Direct measurement of the individual factors involved in Equation [4646a] can be avoided by using the Cliff-Lorimer ratio method,

           Cliff-Lorimer ratio ---------------------------------------------------- [4646c]
where,
           nB -- The atomic density of the element B.

where kAB is a constant, which only depends on the identity of the two elements A and B as well as the accelerating voltage. This constant can be calibrated with a standard containing a known ratio of the two elements. By convention, kAB is normally tabulated for a particular instrument with element B being Si. The choice of Si is partially influenced by the large number of different silicates available.

 

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