Wide-angle diffraction Theory

The diffraction maxima in the wide-angle diffraction pattern derive from the periodicity of the crystal lattice (Cullity and Stock 2001). Their angular pattern is characteristic of the crystal lattice, so is ideal for identification and detection purposes. For monochromatic radiation (X-rays, neutrons or electrons) of wavelength X, Bragg s Law gives 

The widths of the diffraction maxima give information about the size and perfection (e.g., microstrain) of the crystals (Cullity and Stock 2001, Snyder et al. 1999). Assuming perfect crystals apart from a small size, the Scherrer formula is, 

If a crystal is bent or otherwise mechanically distorted, the lattice spacing d of the diffracting planes will vary over the crystal. If the range in d is Ad, and the resultant spread in the positions of the diffraction maxima is A2 0, then by differentiating Bragg s Law 

This equation allows the spread in microstrain, AdId, to be calculated from the observed broadening assuming that size broadening is absent. 

In practice in biological apatites, it is most likely that both size- and microstrainbroadening are present. Inhomogeneities in the chemical composition of the crystals may also cause broadening of maxima, particularly those maxima whose positions are mainly 

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Although it may be possible to measure this orientation using wide angle X-ray diffraction techniques, we present here only a qualitative comparison between the theory and experimental results. In Figure 10 we present the theoretical predictions of the shear stress at the start up of flow. We have assumed values of unity for... 

Wide- and small-angle scattering are fully developed X-ray techniques for studying structural features. The theory is complete, the experimental devices are well developed, laboratory systems are commercially available, and dedicated X-ray facilities for special applications exist in several international research centers. Data analysis techniques have improved substantially in the last two decades through computers use of numerical methods. By nature, SAXS is used in the study of relatively large-scale structures, while wide-angle X-ray diffraction (WAXD) deals mainly... 

P. H. Hermans and co-workers described how the orientation factor /h may be computed from wide-angle x-ray diffraction, and developed a simple theory of birefringence (45-47). Orientation measured by x-rays and by birefringence were distinguished (46). The former represents the orientation of the crystalline regions and the latter the total orientation, including amorphous regions ... 

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