Superstructure reflections

In fig. 6a.b we can observe as examples how the user can define different areas of the ED pattern (lines, or regions around spots ) can select in order to speed up time of measurement and avoid unnecessary beam damage, or concentrate the study in selected group of reflections ( e.g symmetry-related reflections or superstructure reflections). 

The SAED patterns consist of an intense base set of a - PbO subcell reflections and weak superstructure reflections hV4, kV3, T/2 referring to the a - PbO cell due to a modulation of the structure. To determine the Pb and Mo positions in PbsMoOg on the base of the relative intensities of the SAED reflections a multislice dynamic calculation [12] was performed. The calculations were performed separately for each of the 6 experimental microdiffraction patterns. The thickness of the specimen was determined independently for each of the patterns. The performed procedure is close to the published idea by Bing - Dong et al. [13]. 

Figure 22. Phases in the muscovite-pyrophyllite join. M = mica-like phase ML = mixed layered phase Mo = fully expandable beidellite Py = pyro-phyllite Kaol = kaolinite Q = quartz All = ordered phase with superstructure reflection.

Mixed layered clays, most often ordered, are present up to temperatures near 200°C at depths of 500 to 1500 meters. The minerals form in two distinct zones. At shallow depths (between 100 and 200°C) mixed layering is between 90 and 0% montmorillonite. Above 200°C or so no expandable minerals are present. In the second zone (1.5Km. depth) one finds ordered interlayering showing the superstructure reflection... 

Figure 29. Possible general phase relations for illite and associated phyllosilicates as a function of varying P-T conditions. Ill = illite, either predominantly IMd or 2M in polymorph I = illite, 2M mica ID = k layer ordered mixed layered phase MLSS = mixed layered 3 or 2 layer ordering giving a superstructure reflection ML0 = mixed layered, ordered structure with no superstructure MLr = mixed layered non-ordered M, = fully expandable montmorillonite Chi = chlorite Kaol = kaolinite Exp 3 " expanding chlorite and/or corrensite.

In 1923 CeC>2 was found to have the fluorite structure (Goldschmidt and Thomas-sen, 1923), and in 1926 PrC>2 was found to have the same structure (Goldschmidt, 1926). In 1950 the intermediate compositions in the PrO system were reported to have the fluorite structure of variable lattice parameters (the superstructure reflections were not observed). In 1951 TbC>2 was also shown to have the fluorite structure (Gruen et al., 1951). By this time the basic fluorite structure had been established for all the known higher oxides of cerium, praseodymium and terbium. 

Notes 1. Preparation All preparations are by equilibration of the oxide with oxygen at temperatures and oxygen pressure predetermined from experimental data. 2. The diffraction patterns all show strong face-center-cubic reflections with commensurate, weak, superstructure reflections by whatever means they are taken. 

Unlike TiN0.26H0.15, in TiN0.26D0.15, the appearance of superstructural reflections in the neutron diffraction patterns is not preceded by diffuse scattering. 

Up to now we have seen how lattice distortions are detected and characterized. This does not provide a direct observation of the molecular translations, rotations, and deformations associated with the distortion. However, for a few compounds it has been possible to measure a large enough number of satellite or superstructure reflections so that the distorted structure can be parametrized and refined (rigid-body or full structural study). We consider below four examples, taken from materials selected in Section IV. A, which show that such studies are not easy and that the data collection requires special attention. Indeed, it is generally difficult to measure enough satellite reflections, especially if several kinds of the latter coexist (e.g., 2kp and 4kF satellites, high-order satellites, etc.). 

What is apparent from the examples above is that, in most cases, the key problem is the measuring of a large enough number of weak (or even very weak) satellites or superstructure reflections. A limited data set forces the use of rigid-body refinements and may lead to inaccurate results. However, we may expect that new, very high flux synchrotron sources may help to solve this problem in the near future. 

Figure 23 Electron microdiffraction study of TMA.TCNQ.I. Changes in superstructure reflections at about 40 K as a function of the irradiation dose. (From Ref. 190.)...

Fig. 25. Temperature dependence of the a ( ) and c ( ) lattice parameters of PTS polymer. The superstructure reflections appear in the shaded temperature range...

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. 

The above expression gives fundamental reflections (h = H) when all tnn = fcn + A = 0- For all other cases the Equation (34) corresponds to satellite or superstructure reflections. 

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