Ruland’s method

Methods for estimating lattice distortion generally require two or more orders of a particular reflection to be present, and most polymers have only one order available. A method for estimating both crystallinity and lattice disorder, which does not need higher orders of a reflection, and indeed takes into account the whole of the diffraction trace, is that due to Buland (27). This method has been applied to many different fibres by Sotton and his colleagues, who have discussed their results both here (28) and elsewhere (12). The major problem with Ruland s method is that an arbitrary separation of the crystalline scatter from the non-crystalline scatter must be made other restrictions are that the method cannot be used to measure crystallite size and cannot give any indication of the presence of paracrystalline or intermediate-phase material. 

Nevertheless, when we carry out x-ray crystallinity measurements on textile fibers, we must consider distortions that always affect crystalline material. Even in a completely crystalline material, the scattered x-ray intensity is not located exclusively in the diffraction peaks. That is because the atoms move away from their ideal positions, owing to thermal motion and distortions. Therefore, some of scattered x-rays are distributed over reciprocal space. Because of this distribution, determinations of crystallinity that separate crystalline peaks and background lead to an underestimation of the crystalline fraction of the polymer. In this paper, we attempt to calculate the real crystallinity for textile fibers from apparent values measured on the x-ray pattern. This is done by taking into account the factor of disorder following Ruland s method (3). 

Corrections of the apparent crystallinity values of fibers materials have been carried out by taking into account a disorder parameter k, following Ruland s method. Peculiar care was taken about samples preparation (cutting and pelleting of fibers), data collection and reduction, which will be briefly described. Crystallinity and disorder parameter measurements have been performed on main textile fibers (polyester, polyamide, aramid, polypropylene, cellulosic fibers) and the results will be discussed comparatively, with those got by more conventional x-ray crystallinity determinations. The complementarities of these different approaches will be illustrated with several examples. For instance,... 

Electron diffraction crystallinity X-Ray crystallinity (RULAND s Method)... 

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). 

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 several11 nested shells in reciprocal space. As a function of shell diameter one of the contributions is constant, whereas the other is changing12. If the measurement is performed on spheres (azimuthal), the orientation component is constant. 

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... 

A modd-free analysis approach of the stacking statistics of tmdecorated lamdlar two-phase systems is given by Ruland s interface distribution function (IDF), which consists of a superposition of first- and higher-order (i.e., spanning multiple lamellae) lamella thickness distributions. Since the IDF is equivalent to a second-order derivative of a ID autoconelation function, the requirements for the data quality are quite high for this method to produce significant results. 

Figure 7.6 Minimal and maximal values of crystallinity index [CrI] of MCC Avicel PH-101 obtained by various researchers using different methods Segal [S], Ruland [R], Deconvolution (DC], Subtraction of amorphous fraction [SA] and Jayme-Knolle [JK] in comparison with degree of crystallinity X).

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