Diffuse diffraction

Polymer or Fiber Diffraction. Polymers and fibers are often ordered ia one or two dimensions but not ordered ia the second or third dimension. The resulting diffraction patterns have broad diffuse diffraction maxima. The abiHty to coUect two dimensional images makes it possible to coUect and analyze polymer and fiber diffraction patterns. 

N are more or less disintegrated, yielding very diffuse diffractions, apparently due in part to very small crystalline elements of mercerized cellulose... 

In an atmosphere of carbon dioxide, filings from the reguli were screened through a 200-mesh sieve and collected in thin-walled glass capillaries about mm. in diameter. The capillaries were then evacuated and sealed, and the specimens were annealed at 280° C. for 40 hr. and allowed to cool at the rate of about 0-001 ° C./ sec. (It was observed that specimens which were not annealed gave diffuse diffraction lines the lines were made sharp by the process of annealing as described above.)... 

Certain crystals give diffuse X-ray reflections there are various possible causes for this—small crystal size, structural irregularities, or thermal movements. The consideration of these phenomena in Chapter XI leads on to a brief introduction to the interpretation of the very diffuse diffraction patterns given by non-crystalline substances. 

Hall, Dieter, Hofer, and Anderson (19) studied reactions of nitrides and carbonitrides in a reduced, fused iron catalyst (Bureau of Mines number D3001). The results of these experiments were in general similar to those of Jack, and most of the differences may be explained by the differences in the type of iron employed. The major discrepancy was that in the catalyst of large surface area and small crystallite size, the <-carbonitride phase was found under conditions under which massive iron is converted to the f-phase. Since the transformation of the - to the f-phase involves only slight changes in the lattice positions of iron atoms and small changes in the x-ray pattern, it is possible either that this transformation did not occur in the catalyst or that the pattern of the f-phase could not be distinguished from that of the e-phase in the diffuse diffraction patterns. 

Diffusive diffraction experiments in interconnected porous structures have been carried out in close-packed polymer sphere arrays (Callaghan et al., 1992 Coy and Callaghan, 1994a) as well as in emulsions (Soderman and Stilbs, 1994). An example is shown in Fig. 9. 

Coy, A., and Callaghan, P. T. (1994a). Pulsed gradient spin echo NMR diffusive diffraction experiments on water surrounding close-packed polymer spheres. J. Colloid Interface Sci. 168, 373-437. 

The determination of quartz dust in the air samples in industrial workplace is an established procedure. Although capable of collecting the particulates, organic polymer membranes can not be employed as an XRD substrate since the diffuse diffraction lines at or near the 10 angle of quaru makes polymeric membtanes not suitable for this application [Minneci and Paulson, 1988]. It is possible to quantify as low as 0.005 mg quartz under well controlled conditions (Bumsted, 1973]. Similarly, silver membranes can also be used as a collecting medium and XRD substrate for measuring crystalline and amorphous silica, lead sulfide, boron carbide and chrysotile asbestos [Leroux and Powers. 1970]. 

Very recently, the Kuchel group has been applying a new form of analysis called diffusion-diffraction to suspensions of red blood cells. This approach is based on the pulsed-Eeld gradient diffusion NMR experiment and... 

As mentioned previously, CTRs arise as a result of the abrupt termination of a crystal lattice, and the diffuse diffracted intensity connects Bragg points in reciprocal space. In this case, the scattering vector is normal to the surface, and as a result, this technique is very sensitive to surface and interface roughness but not to in-plane atomic correlations. Thus, it yields information that is complementary to that obtained by grazing incidence diffraction. The most important feature of CTR is the characteristic decay of the scattered intensity described by Eq. (38). For surfaces that are not perfectly terminated (i.e., rough) the intensity will decay faster than predicted by this equation, and this can be used as a measure of root-mean-square surface roughness. 

The radial distribution function, g(r), can be determined experimentally from X-ray diffraction patterns. Liquids scatter X-rays so that the scattered X-ray intensity is a function of angle, which shows broad maximum peaks, in contrast to the sharp maximum peaks obtained from solids. Then, g(r) can be extracted from these diffuse diffraction patterns. In Equation (273) there is an enhanced probability due to g(r) > 1 for the first shell around the specified molecule at r = o, and a minimum probability, g(r) < 1 between the first and the second shells at r = 1.5cr. Other maximum probabilities are seen at r = 2(7, r = 3 o, and so on. Since there is a lack of long-range order in liquids, g(r) approaches 1, as r approaches infinity. For a liquid that obeys the Lennard-Jones attraction-repulsion equation (Equation (97) in Section 2.7.3), a maximum value of g(r) = 3 is found for a distance of r = <7. If r < cr, then g(r) rapidly goes to zero, as a result of intermolecular Pauli repulsion. 

It should be noted that any defects and imperfection in structure and orientation would give rise to rather coarse points and doughnut-shaped zones in the reciprocal lattice rather than clearly defined points and circles. This is the case for oriented liquid crystals and polymer fibers. Diffused diffraction patterns are therefore obtained for these specimens. 

Examples of diffuse diffraction patterns in monochromatic geometry 323... 

EXAMPLES OF DIFFUSE DIFFRACTION PATTERNS IN MONOCHROMATIC GEOMETRY... 

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