Pendellösung Fringes in Crystals
- Practical Electron Microscopy and Database -
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Figure 4147 shows the transmitted (I0) and diffracted (Ig) intensities have a periodicity of ξg in TEM specimen depth in two beam condition. The exchange of intensity between the forward and diffracted beams in dynamical theory is called pendellösung. Pendellösung is not a kinematical effect because it does not allow such large change in intensity.

diffracted intensity (Ig) showing a periodicity of ξg

Figure 4147. The diffracted intensity (Ig) showing a periodicity of ξg in TEM
specimen depth in two beam condition. Ig is the intensity of transmitted beam.

For CBED, the Bragg spots are extended to disks. CBED patterns contain Pendellösung fringes representing dynamical phenomenon. These fringes give information about the TEM specimen thickness and the real and imaginary Fourier coefficients, Vg and V’g, of the potential of the crystal lattice. With the illumination geometry of CBED, the incident beam directions vary continuously within the cone. The continuous variation of incident beam directions induces a continuous variation of the excitation error of the Bragg reflection and the observed intensity distribution in the CBED disks corresponds to a two-dimensional rocking curve (pendellösung) of the dynamical theory of electron diffraction.

 

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