Reciprocal lattice mapping

Figure 7.19. Reciprocal lattice mapping. The intensity distribution is measured when the reciprocal lattice node associated with the family of diffracting planes passes through the Ewald sphere...

Figure 7.23. Reciprocal lattice maps in the vicinity, respectively, of the lithium niobate s lattice nodes (0006), (a) map, and (00012), (b) map...

Figure 7.30. Reciprocal lattice maps of the zirconia film s (200) and (400) reciprocal lattice nodes...

From the position (q, q ) of the peaks (centers of the scattering distributions) in the reciprocal lattice map for each layer, the corresponding lattice constant values can be determined along the two orthogonal directions in the graph, namely perpendicular ( ) and parallel ( ) to the surface. For each layer and for each direction, the corresponding strain values and ey) can be calculated ... 

Figure 7.8 A scattering map in reciprocal space. Equal intensity contours are shown schematically, and the Ewald sphere is represented as a plane near reciprocal lattice points 0 and h. The dynamical diffraction from the specimen is displaced slightly from the relp and from the centre of the diffuse scatter by the refractive index effect...

Figure 7.11(b) shows the reciprocal space map after a high temperature anneal of the film. The effect of this has been to precipitate ont the arsenic, resnlting in the lattice parameter of the now stochiometric matrix reverting to that of the substrate. The scattering around the layer peak, which arises from the precipitates, is circnlarly symmetric and mnch more extensive than in the substrate. 

Figure 7.15 Reciprocal space maps of GaAs with graded InGaAs buffer layer around the 224 reciprocal lattice point, (a) [110] direction, (b) [ 10] direction. The 004 maps in those directions are shown in the insets...

In X-ray crystallography, 2-A model" means that analysis included reflections out to a distance in the reciprocal lattice of 1/(2 A) from the center of the diffraction pattern. This means that the model takes into account diffraction from sets of equivalent, parallel planes spaced as closely as 2 A in the unit cell. (Presumably, data farther out than the stated resolution was unobtainable or was too weak to be reliable.) Although the final 2-A map, viewed as an empty contour surface, may indeed not allow us to discern adjacent atoms, structural constraints on the model greatly increase the precision of atom positions. The main constraint is that we know we can fit the map with groups of atoms — amino-acid residues — having known connectivities, bond lengths, bond angles, and stereochemistry. 

The (unfiltered) Fourier transform of this image is reproduced in Fig. 7. It shows a map of the k vectors that contribute to the standing wave pattern. Spots reflecting the reciprocal lattice of the Cu(lll) surface (originating from the atomic resolution) and circles corresponding to the 2D Fermi contour, i.e. the crossing of the Fermi level by the surface state, are... 

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