Diffraction rods

Diffraction is usefiil whenever there is a distinct phase relationship between scattering units. The greater the order, the better defined are the diffraction features. For example, the reciprocal lattice of a 3D crystal is a set of points, because three Laue conditions have to be exactly satisfied. The diffraction pattern is a set of sharp spots. If disorder is introduced into the structure, the spots broaden and weaken. Two-dimensional structures give diffraction rods, because only two Laue conditions have to be satisfied. The diffraction pattern is again a set of sharp spots, because the Ewald sphere cuts these rods at precise places. Disorder in the plane broadens the rods and, hence, the diffraction spots in x and y. The existence of streaks, broad spots, and additional diffuse intensity in the pattern is a common... 

W21 beamline and diffractometer [33]. A large number, 366 of which 267 were non-equivalent, of in-plane reflections arising from the reconstruction were measured. All peaks were exactly centred at the expected positions to within 0.001° of azimuthal rotation, which showed that the surface reconstruction is perfectly commensurate with the underlying bulk lattice. Their width and Lorentzian shape indicated an exponential decay in correlations with the decay length of -500 A. Several reconstruction diffraction rods were also measured. The absence of symmetry of the rod intensity with respect to =0 showed that the reconstruction has the minimal hexagonal symmetry p3. 

The behaviour of the intensities of the Bragg peaks and diffraction rods of the rock-salt and spinel structures allows to conclude that the oO(lll) (resp. MnO(l 11)) polished surface is stabilised by the presence of a spinel 0304(111) (resp. Mn304(l 11)) surface layer. 

Fig. 25 Potential step experiment of the transition between the commensurate Cu(l X 1) and the incommensurate CuCi UPD adlayer on Pt(ni) in 0.1 M H2SO4 + 1.0 mM Cu + (a) potential perturbation, (b) current transients (the inset shows a magnified region of the entire transient) and (c) time dependence of the scattered X-ray intensity at (0.765, 0, 0.5), which represents a characteristic diffraction rod of the incommensurate CuCi bilayer (reprinted from Ref [200], copyright 1998 by American Physical Society).

Experimental results are available for the diffraction rods and structure of an overlayer of Pb on Ag(l 11)[23, 24]. Since these measurements are very accurate it is also possible to measure the compression of the UPD overlayer of Pb as the potential is changed[25, 26]. The compressibility is certainly related to the electrosorption valency, discussed in another section of this book. 

Figure 3A2.5 Real and reciprocal space of a crystal with a flat top surface. Reciprocal space consists of crystal truncation rods, that is, diffraction rods in which the strong bulk Bragg peaks are connected by weak tails of diffuse intensity. The specular rod, or (00) rod, has no in-plane momentum transfer.

Figure 3.4.2.13 Three types of ordering of a single layer on top of a crystal (a) a fully ordered solid layer in which the layer contributes to all substrate diffraction rods (b) a completely liquid layer that contributes to the specular rod only and (c) a layer with...

The situations in Figure 3.4.2.13 all correspond to a small value of B . For the 2D Hquid, B// is infinitely large for the quasi Hquid, B// is large and for the solid, it is smaU. Thus, the only difference between the Hquid atoms and the solid surface atoms is found in the values of the Debye-Waller parameters in all other aspects, they are treated the same in the calculation of the surface structure factor. The effective density distribution pz across the interface contributing to a diffraction rod with in-plane momentum transfer Q// can be calculated by weighting the electron density of each atom with its Debye-Waller factor ... 

Figure 3.4.2.14 The direction of the diffraction rods is, in principle, perpendicular to the crystal surface, but the actual direction depends on the smoothness and step-step correlation on the surface, (a) The ideal case of a flat surface without misorientation. (b)...

Figure 3.4.2.19 When the exit angle is large enough, the intersection of the Ewald sphere with a diffraction rod is small. In that case, the integrated intensity over the intersection can be measured without scanning. When this is done using an area detector, the full profile and background can be measured simultaneously.

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