Transformations, diffraction geometr

It will be assumed here that the X-ray diffraction data were collected on flat films with a point focus camera. This simplifies the theoretical presentation. The TMV data analyzed in the results section were collected on cylindrical films with Guinier cameras, but positions on the cylindrical films can be mapped onto positions on a flat film by a simple geometric transformation. In general, the form of the optical density, D(r,), in a fiber diffraction pattern can be expressed in film coordinates as the sum of contributions from all reflections, I (r,iJ> ), plus a background term, B(r,) ... 

Tabic l.l gives those crystal data for the C,S polymorphs that have been obtained using single crystal methods. The literature contains additional unit cell data, based only on powder diffraction evidence. Some of these may be equivalent to ones in Table 1.1, since the unit ceil of a monoclinic or triclinic crystal can be defined in different ways, but some are certainly incorrect. Because only the stronger reflections are recorded, and for other reasons, it is not possible to determine the unit cells of these complex structures reliably by powder methods. The unit cells of the T, Mj and R forms are superficially somewhat different, but all three are geometrically related transformation matrices have been given (12,HI). 

It is possible to include phase transformers in scalar diffraction theory. The calculations are lengthy, however, and we refer the reader to Anan ev (1992) and Martin and Bowen (1993) for details. An alternative approach exists that is equivalent to the transfer matrix method of geometrical optics, although the results are justifiable in terms of diffraction theory (Anan ev, 1992 Martin and Bowen, 1993). The formalism is discussed, for example, in Hecht and Zajac (1979, pp. 171-175) and we will briefly outline the necessary results. 

The structural model proposed in [260] is based on accurate X-ray diffraction measurements over regions of the reciprocal lattice larger than those sampled in the preceding literature (shown in Fig. 31) and on geometrical and conformational analyses and calculations of Fourier transforms of model structures. 

There is a strong emphasis on the (typically small-angle X-ray or neutron) diffraction features of the mesophases, and most mesophases are conventionally distinguished on that basis. Diffraction, a Fourier-transform technique, probes the geometric correlations within the material. Detailed models of the idealized mesostructure can therefore be constructed. For this reason, mesophase structure is dominated by such an approach. 

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