The Ruland Streak Method

For a unimodal equatorial reflection the treatment is more involved. If the distribution is narrow, it follows from Fig. 9.5 an approximation p n/l, which can be used to obtain an approximative solution, in turn (Ruland cited by Thunemann [257], 

On each side of the meridian, only a distorted image of the orientation distribution is observed. Nevertheless, even equatorial reflections can generally be used for the purpose of orientation-desmearing if we make assumptions concerning the analytical type of the orientation distribution. The corresponding method is demonstrated in the following section. 

Motivation and Principle. Broadened reflections are characteristic for soft matter. The reason for such broadening is predominantly both the short range of order among the particles in the structural entities, and imperfect orientation of the entities themselves. A powerful method for the separation of these two contributions is Ruland s streak method [30-34]. Short range of order makes that the reflection is considerably extended in the radial direction of reciprocal space - often it develops the shape of a streak. This makes it practically possible to measure reflection breadths separately on several nested shells in reciprocal space. As a function of shell diameter one of the contributions is constant, whereas the other is changing. If the measurement is performed on spheres (azimuthal), the orientation component is constant. 

History. Wilke [129] considers the case that different orders of a reflection are observed and that the orientation distribution can be analytically described by a Gaussian on the orientation sphere. He shows how the apparent increase of the integral breadth with the order of the reflection can be used to separate misorientation effects from size effects. Ruland [30-34] generalizes this concept. He considers various analytical orientation distribution functions [9,84,124] and deduces that the method can be used if only a single reflection is sufficiently extended in radial direction, as is frequently the case with the streak-shaped reflections of the anisotropic 

Structural entities observed in fiber materials. In recent publications [34,258,259] several authors demonstrate, both how this concept is flexibly modified, and how it helps to characterize the perfection of nanostructured materials. 

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The influence of finite size and imperfect orientation of the entities on the shape of the reflections. Separation of unimodal orientation distributions by means of Ruland s streak method, and assessment of the analytical shape of the orientation distribution (Sect. 9.7). 

Figure 9.7. Separation of misorientation (Bg) and extension of the structural entities (1/ (L)) for known breadth of the primary beam (Bp) according to Ruland s streak method. The perfect linearization of the observed azimuthal integral breadth measured as a function of arc radius, s, shows that the orientation distribution is approximated by a Lorentzian with an azimuthal breadth Bs... 

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