Weak superlattice reflections

All of the I/S produced by WD are randomly interstratified, with the possible exception of the Black Jack sample (Figure 3) and the most illitic Kinney sample (Figure 4), both of which show signs of partial R1 ordering between illite and smectite layers. For these samples, the 001 XRD reflections are displaced towards larger angles, and a very weak superlattice reflection is visible at small angles. 

Fig. 5 Diffraction profiles collected from the same powdered sample of InSb at 2 GPa, using (top) energy- and (bottom) angle-dispersive diffraction. The angle-dispersive data clearly have higher angular resolution, and are not contaminated by X-ray fluorescence peaks. The tick marks below the angle-dispersive data mark the positions of some of the weak superlattice reflections that were essential to determining the structure of the InSb-IV phase [165]...

Single-crystal X-ray results (9) point to strict alternation of Si and Al (the 4 0 ordering scheme) in accordance with Loewenstein s rules (10), but this model was recently challenged on the basis of 29si NMR measurements (1, 2) and our discovery that the sodium derivative can be rhombohedral (11,12). However, the controversy has now been resolved and the correctness of the X-ray model reaffirmed (13,14). A consequence of the Si, Al ordering is that the lattice parameter of the cubic cell is ca. 24.6 A, not 12.3 A as reported in earlier work, a feature reflected in weak superlattice reflections. The space group is Fm3c. 

Exposure times up to 30 s with high-speed film plates were necessary to observe very weak superlattice reflections. 

Figure 4. A small portion of the powder X-ray diffraction pattern of zeolite (K, Ba)-

Structure of -EucryplHe Considerable structural understanding has developed concerning the most highly stuffed derivative of P-quartz, namely P-eucryptite (LiAlSiO ). The structure of P-eucryptite was first shown to be based on that of p-quartz by Winkler (1948). A complete ordering of A1 and Si over the tetrahedral sites produces a doubling of the c-axis as revealed by weak superlattice reflections of the type hkl. I = odd. 

In any situation where there is substitutional disorder of any kind in a crystal the diffraction pattern consists of two parts the diffraction pattern of the averaged structure, which is confined to the Bragg reflections and whose analysis in terms of occupancy I have discussed and superimposed on this the diffraction pattern of the difference structure i.e. a distribution of electron density everywhere equal to the difference between the average and the actual structure. Even in the case of complete disorder this will be non-zero, but its diffraction pattern will be very weak everywhere because it will be diffused over all diffraction directions. Only if there is some kind of ordering on subsets of the crystallographic sites, which subsets define a superlattice of the crystal lattice, will the intensity of the difference pattern concentrate into definite directions and be easily detectable and interpretable. However if such a superlattice regularity is confined to 1 or 2 dimensions or to very small 3-dimensional domains then the difference diffraction will be smeared out. It may then be difficult to detect, and even when detected it can be difficult to interpret unambiguously. 

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