PID from the diffraction pattern

A particularly intriguing case may occur when polytypes with different periodicities are in relation of homomorphy. As shown above, this may happen if a sub-periodicity exists in the sequence of V2 ,2 +i displacement vectors of meso-octahedral polytypes, or in the sequence of T2 ,T2 +i orientation vectors of hetero-octahedral polytypes when the chirality of the packets is neglected. In general, the number of reflections in the c repeat corresponds to the number of layers in the full-period polytype. However, when the chemical difference between the family of the full-period polytype and the family of the shorter homomorphous polytype becomes smaller, some of the reflections weaken if these weak reflections are overlooked, the homo-octahedral stacking sequence obtained from the PID analysis corresponds to an apparent periodicity shorter than the correct one. The visual comparison of the intensities, if performed, involves only the meso-octahedral polytypes homomorphous with the homo-octahedral polytype indicated by the PID, but with the same number of layers and the mistake may be overlooked. Special attention is necessary not to miss weak reflections along X rows. 

The general guidelines for the PID derivation from the diffraction pattern is summarized as follows  

For X-ray diffraction, the effect of the absorption on the PID is normally negligible for the purpose of polytype identification, if a sufficient number (e.g., four or more) of periods along the same row are considered and the corresponding PIDs are weighted. The LP factors are critical, however, if the diffraction pattern is taken with a precession camera, because the Lorentz-polarization effect in the precession motion is severe. 

For electron diffraction, the near-flatness of the Ewald sphere reduces greatly the effect of the experimental factors on the intensities. The pattern is, however, no longer kinematical, and the dynamical effects in general must be taken into account. However, the intensity ratio between adjacent reflections in a reciprocal lattice row can be treated as kinematical, and the PID analysis applies to electron diffraction as well (Kogure and Nespolo 1999b). 

The square root of the intensities, partially reduced when necessary, gives an approximant of the structure factors. By dividing these by the Fourier transform of the layer, an un-weighted, un-scaled PID is obtained. The mean value of PID along several period of the same reciprocal lattice row is computed, and the result is brought on the same scale [see Appendix B, Eqn. (B.4)]. 

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