2.6 Preferred orientation

Preferred orientation plays an important role in determining the features of scattering patterns, especially of fibers, both biological and synthetic, cf. section 2.4. In order to model the observed peak shapes (usually crescent shaped arcs) it is often sufficient to approximate them by factorizations into a radial and an angular component. However, as figure 8 demonstrates for the case of collagen saxs fiber patterns, this approximation can break down so that a proper analysis of the data requires a thorough treatment of preferred orientation effects, as indicated in figure 8(d). The exact treatment of preferred orientation is usually quite involved but can be significantly simplified when suitable orientation distribution functions are chosen so that a large part of the problem can be handled analytically in closed form.

Figure 8: (a–c) Various collagen saxs patterns showing meridional reflections with different degrees of preferred orientation (unpublished experimental data); (d) normalized calculated exact peak shape corresponding to case (c). Valid approximations would be possible for case (a) on the dotted line or for case (b) on the dashed circle but a quantitative analysis of case (c) appears to require the exact treatment of preferred orientation. Note also that the maximum of the peak distribution is not exactly located at s = (0, 1).

Curiously, very recently the most frequently applied (based on the number of quotations) method for evaluation of systems with cylindrical symmetry turned out to be incorrect [24].