Multiple diffraction

There are only three equatorial spots. Each of the three can be accounted for by double diffraction (of 330, 5 50, and 880, with the factor for R of 1.9021 —2sin72°). By vector addition it is seen that the other spots can be accounted for by multiple diffraction of hh 0. 

Most of the applications of electron diffraction intensities for structure analysis rely on a kinematical approximation and thus do not account for the effects of dynamical multiple diffraction. The use of intensities which may be strongly perturbed by multiple scattering results in many cases in poor or misleading structure indications in the direct methods results. One approach which can be shown to reduce dynamical effects somewhat is to use precession electron diffraction (RED) [67] which involves conical rotation of the incident beam about a zone axis direction and thus avoids the strongly dynamical direct zone axis orientation. Although the intensities collected with this technique are still significantly perturbed by dynamical effects [68, 69] results obtained by this approach for zeoHtes are encouraging [70-72]. 

Fig. 3.5. Real space (left) and reciprocal space (right) applicable to Pd(lOO) + (2>/2 X yj2) R45° 2C0. Substrate (overlayer) atoms and diffraction spots are indicated by crosses (circles). Large filled circles represent kinematically produced spots, small filled circles represent multiple-diffraction spots...

However, diffraction methods have severe drawbacks. Disordered crystals are often difficult to tackle. If the disorder is of dynamic nature, e.g. arising from small-or large-amplitude motions in the crystal, the use of devices for variable-temperature measurements is compulsory and can also yield very useful information (see below for some examples) on the existence of enantiotropic systems related by phase transitions. In some, not frequent, cases the crystals are sufficiently robust to be used for direct phase transition measurements on the diffractometer. Figure 3 shows an example of multiple diffraction data sets collected on the same specimen... 

Chang, S.-L. Multiple Diffraction of X-rays in Crystals. Springer-Verlag Berlin, Heidelberg, New York, Tokyo (1984). 

Colella, R. Multiple diffraction of X-rays and the phase problem. Computational procedures and comparison with experiment. Acta Cryst. A30, 413-423 (1974). 

Colella, R. Multiple diffraction of X-rays and the phase problem. In P. P. Ewatd and his Dynamical Theory of X-ray Diffraction. A memorial Volume for Paul P. Ewald. S3 January 1888 — SS August 1985. (Eds., Cruickshank, D. W.. 1 Juretschke, H. J., and Kato, N.) International Union of Crystallography/OxforJ University Press Oxford (1992). 

Chang, S-L. Solution of the X-ray phase problem using multiple diffraction - a review. Cryst. Rev. 1, 87-187 (1987). 

For quick checking of single and multiple diffraction data files, the author has a bias for the XFIT/Koalariet software, but this software is no longer developed (Table 17.9). WinPLOTR, part of the Fullprof Rietveld Suite, is an excellent program for data visualization and processing. It imports various common... 

FIGURE 6 (a) Graphical construction for multiple diffraction on a square planar reciprocal lattice net.14 (b) Dependence, on rotation angle around die diffraction vector, of multiple reflection contribution to the apparent reflection intensity of 222, a forbidden reflection, in germanium.9 (c) Multiple reflection effects for several unrelated reflections, in rotation around the diffraction vector, showing peaks and dips. 1... 

SR Laue data were recorded from a crystal of aluminium phosphate and analysed by Wood et al (1983). The R-factor on I in the Laue data refinement was 19% compared with a conventional monochromatic single crystal study (Thong and Schwarzenbach 1979) with an f -factor of 2.2% on F. For the Laue data 20% of the measurements were rejected on the basis of bad intensity agreements. Of the eight refined positional parameters six were within 2a and only one outside 3a. The temperature factors were somewhat less well determined. This was considered to be due to the significant extinction and multiple diffraction effects for a hard material such as aluminium phosphate. 

An alternative interpretation of the LEED pattern may perhaps be found in terms of multiple diffraction of the electron beam by a simple overlay structure in a manner discussed by MacRae 207). The very strong intensity of the half-order beams as compared with the first-order beams possibly supports this analysis, although surface reconstruction is certainly plausible. 

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