Neutron scattering patterns

From these spectra, one can calculate information about the microscopic structure using mathematical transformations. Nonetheless, the scattering spectra preserve the symmetry of the system and are little works of art in themselves. Figure 8 shows an example, the neutron scattering pattern of a typical lamellar phase. Note the asymmetry of the spectrum it indicates that there is a preferred ordering direction in the system. From the distance of the bright circles to the center, the distance between two lamellae can be calculated. 

Fig. 8 Small-angle neutron scattering pattern of a lamellar phase...

Fig. 4.1 Top schematic illustration of micellar phases formed by the Pluronic copolymer P85 (PE 026PP0i9 PEO,6) with increasing temperature. Bottom small-angle neutron scattering patterns from sheared solutions in D20 of this copolymer (25wt%). The three columns (left-right) correspond to a liquid spherical micelle phase at 25 °C, a cubic phase of spherical micelles at 27 °C and a hexagonal phase of rod-like micelles at 68 °C (Mortensen 1993a).

FIGURE 5.1 (a) The geometry of the LOQ scattering experiments, (b) A contour plot of a typical neutron-scattering pattern. The momentum transfers (A-1) perpendicular and parallel to the silicate layers lie along the vertical and horizontal axes, respectively. 

FIGURE 8.2 Structure factors S(QZ) obtained from neutron-scattering patterns of butylam-monium vermiculite gels (upper panels) and from a 0.1 M protonated butylammonium salt solution with no clay (lowest panel). The upper panels show S(QZ) for gels prepared in a 0.1 M deuterated salt solution and in 0.1 and 0.01 M protonated salt solutions. The momentum transfer Q was perpendicular to the clay plates, and the structure factor S(QZ) has been normalized after correction for background scattering and absorption. 

FIGURE 11.1 Contour plots of typical neutron-scattering patterns for r = 0.01 and c = 0.1 M gels at T = 8°C. (Figure legend shows the pixel codes.) (a) No added polymer the arrow marks the first-order diffraction maximum at 0max = 0.5 nm. (b) With 1% PVME. The arrows mark the first maximum at Qnml = 0.7 nm-1 and the second maximum at = 1.4 nm-1. 

Fig. 1.17 Small-angle neutron scattering pattern for a sample of per-deuterated lightly branched polyethylene containing 10% of hydrogen containing linear polyethylene. The sample is molten and has just been subjected to deformation in a channel die. The flow axis is horizontal and the effective extension ratio is 3.

Figure 2.27 Neutron scattering pattern of vanadium at 20 K, showing the extremely weak coherent scattering. (From Shull and Wilkinson.22)...

The position of aluminum cations can be detennined experimentally by Al NMR spectra (Figure 3.8) and by Rietveld analysis of X-ray and neutron scattering patterns (H7). The results indicate that in Y-AI2O3, 25—33% of all Al " ions are in tetrahedral positions, whereas the rest are almost exclusively in octahedral positions, with a few Al ions in fivefold (149,150) or highly distorted tetrahedral coordination. It has been reported that milling can increase the firaction ofpentacoordinated aluminum up to a value of 20% (151) the fivefold coordinations arise through an increased disorder similar to that discussed above for amorphous alumina. 

Figure 63 (a) X-ray diffraction patterns of organically modified Closite-30B nanoclay and nanocomposites, (b) small-angle neutron scattering patterns I(q) versus q (wave vector) plot of indicated PU and nanocomposites, (c, c ) AFM image of PU and its nanocomposites with height profile, and (d) POM image PU-nanoclay composite [9]. 

Because of the similarities in wavelengths of X-rays and neutrons used in scattering experiments, the sizes of structures accessible to X-rays and neutron are similar. In polymeric materials, the substitution of deuterium for hydrogen in a structure dramatically changes its neutron scattering pattern, while the X-ray scattering remains unchanged because the... 

Neutron scattering methods provide the best experimental means cnr-rently available to probe the atomic strncture of aqueous solutions. It can be proved that a formal mathematical (Fourier transformation) link can be formed between the neutron scattering pattern obtained experimentally and the pair radial distribution functions Sotfi r) of pairs of atoms a and of the system. Knowledge of these functions, either individn-ally or as combinations [G (r)] specific to a particular atom (or ion), a,... 

Moreover, the strength of interaction, which is characterised by the scattering length parameter , varies from isotope to isotope. Therefore, two solutions with the same composition of atomic material but containing isotopically different nuclei (e.g. H for D, Cl for Cl, etc.) will give different neutron scattering patterns. This enables detailed information to be obtained which is specific to a particular isotopically substituted species. 

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