Multiple diffraction effect

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. 

According to kinematic theory the intensity of diffraction spots is proportional to the square of the structure factor (Eq. 4). This simple proportionality is lost in reality because of multiple diffraction effects, which are taken into account adequately in dynamic theory [149]. 

Figure 11.11 Examples of RHEED patterns obtained during non-equilibrium MBE growth of GeSn alloys, (a) Pattern for a very smooth surface as in left side of Figure 11.10 showing points on an arc. The diagonal streaks are multiple diffraction effects known as Kikuchi bands.

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]. 

In some crystalline materials a phase transition on lowering the temperature may produce a modulated structure. This is characterized by the appearance of satellite or superstructure reflections that are adjacent reflections (called fundamental reflections) already observed for the high temperature phase. The superstructure reflections, usually much weaker than fundamental reflections, can in some cases be indexed by a unit cell that is a multiple of the high temperature cell. In such a case the term commensurate modulated structure is commonly used. However, the most general case arises when the additional reflections appear in incommensurate positions in reciprocal space. This diffraction effect is due to a distortion of the high temperature phase normally due to cooperative displacements of atoms, ordering of mixed occupied sites, or both. Let us consider the case of a displacive distortion. 

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... 

In the self-consistent approach of McRae (54, 55, 58, 59,177) and others (43, 68) the complete multiple diffraction problem, with attenuation of the wave by elastic backscattering alone, has been solved in self-consistent fashion for certain idealized cases. Inelastic losses were not included in the theory at all. However, in the recent work of Duke and Tucker (179) and of Jones and Strozier (66) inelastic absorption is treated as the dominant effect, and this is nearer reality when considering the LEED problem at all but the lowest energies. 

In this resin film are hundreds of interfaces or boundaries between the two resins. If the resins differ in refractive index, refraction will occur at every interface. Fig. 19 shows how light can be returned from a film by successive refractions. Reflection will also occur and by this means some of the light will be returned towards the surface of the film. It is often forgotten that diffraction will also occur at the edges of the droplets. The net effect of multiple diffractions is extremely complex it is sufficient to say that diffraction can play an important part in turning the light back towards the film surface. 

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