Orthorhombic point lattice, diffraction pattern

FIGURE 5.9 In (a) an assembly of six scattering points has been convoluted with an orthorhombic point lattice, and in (c) the same arrangement with a monoclinic lattice. The corresponding diffraction patterns are, respectively, orthorhombic and monoclinic as well. The diffraction patterns, however, are very different in their intensities because the point lattices sample the continuous transform of the six scattering points, the asymmetric unit of these two-dimensional crystals, at different places. 

The reader may have noticed in the previous examples that some of the information given was not used in the calculations. In (a), for example, the cell was said to contain only one atom, but the shape of the cell was not specified in (b) and (c), the cells were described as orthorhombic and in (d) as cubic, but this information did not enter into the structure-factor calculations. This illustrates the important point that the structure factor is independent of the shape and size of the unit cell. For example, any body-centered cell will have missing reflections for those planes which have ft + k + 1) equal to an odd number, whether the cell is cubic, tetragonal, or orthorhombic. The rules we have derived in the above examples are therefore of wider applicability than would at first appear and demonstrate the close connection between the Bravais lattice of a substance and its diffraction pattern. They are summarized in Table 4-1. These rules are subject to... 

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