Intensity & Amplitude of Scattered Wave by Atoms
- Practical Electron Microscopy and Database -
- An Online Book -

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The intensity of scattered wave, for an isolated atom, is given by,

          intensity of scattered wave, for an isolated atom ---------------------------------- [2670a]

where,
          f(θ) -- The atomic scattering factor.

Considering the scattering contribution of all the atoms in an unit cell, the atomic scattering factors for each atom should be multiplied by a phase factor to account for the difference in phases between the waves scattered on different planes with Miller indices, (hkl). Therefore, the total amplitude of the scattered wave, summed over all the atoms within the unit cell, is given by,

          intensity of scattered wave, for an isolated atom ---------------------------------- [2670b]
                         intensity of scattered wave, for an isolated atom ---------------- [2670c]
where,
          xi, yi, and zi -- The positions of the atoms in the unit cell.

Certain lattice, such as body centered cubic (Cubic I) and face centered cubic (Cubic F), have "kinematically" forbidden reflections. In other words, due to the arrangements of the atoms in the unit cell, these are reflections where the intensity of the scattered wave is zero, given by,

         Conditions of forbidden and allowed reflections (h k l) of common crystal structures ---------------------------- [2670d]

 

 

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