Diffuse diffraction peaks

Information on the structure and physico-chemical properties of the investigated materials can be obtained on the basis of X-ray diffraction. If the sample under investigation is amorphous, the diffractogram presents a set of very diffuse diffraction peaks whereas, in the case of a crystal structure, a well-defined maximum, which allows estimation of the ordering direction at molecular level and also the type of crystal, appears. 

In this section we will discuss in some detail the application of X-ray diffraction and IR dichroism for the structure determination and identification of diverse LC phases. The general feature, revealed by X-ray diffraction (XRD), of all smectic phases is the set of sharp (OOn) Bragg peaks due to the periodicity of the layers [43]. The in-plane order is determined from the half-width of the inplane (hkO) peaks and varies from 2 to 3 intermolecular distances in smectics A and C to 6-30 intermolecular distances in the hexatic phase, which is characterized by six-fold symmetry in location of the in-plane diffuse maxima. The lamellar crystalline phases (smectics B, E, G, I) possess sharp in-plane diffraction peaks, indicating long-range periodicity within the layers. 

Besides the inelastic component, always a certain number of He atoms are elastically scattered in directions lying between the coherent diffraction peaks. We will refer to this scattering as diffuse elastic scattering. This diffuse intensity is attributed to scattering from defects and impurities. Accordingly, it provides information on the degree and nature of surface disorder. It can be used for example to study the growth of thin films or to deduce information on the size, nature and orientation of surface defects Very recently from the analysis of the diffuse elastic peak width, information on the diffusive motion of surface atoms has been obtained. ... 

Figs. 11.5 and 11.6 show eight XRD patterns as measured along row C. In Fig. 11.5, the dominant (111) diffraction peak for 100% Pt appears at around 20=40°, as expected. The absence of diffraction peaks of pure Pt or Fe in the multi-metal XRD patterns is indicative of complete alloying of the multi-metal thin films by interlayer diffusion. 

If one looks between diffraction peaks at high resolution, one finds "streaks" due to lattice phonons, which sharpen gradually at low temperatures this is called thermal diffuse scattering. 

FIGURE 8.1 The ripples of diffuse scattering observed in the first D16 experiment. The gels had been soaked in 0.1 M n-butylammonium chloride solutions in D20 (a) with the usual protonated n-butylammonium ions (b) with deuterated n-butylammonium ions. In (a) the sharp peak at Q = 0.05 A-1 is the first-order diffraction peak the low angle scattering has been scaled down by a factor of 15 with respect to the ripples. 

A comparative study of microsilicas from 18 sources showed considerable variation in composition and properties, one of those examined containing as little as 23% of SiOj and having a specific surface area of only 7.5 m g (A21). The same study showed that in most of the samples the diffuse XRD peak from the glass accounted for 98-99.5% of the total diffracted intensity and that it peaked at the value of 0.405 nm characteristic of vitreous silica. The commonest crystalline impurities detected were KCl, quartz, metallic iron and iron silicide, and pozzolanic reactivity was found to depend more on the chemical composition and nature of impurities than on the fineness or SiOj content. A surface layer of carbon, if present, greatly decreased reactivity. 

In 1979, White [3.2] observed that, by milling elemental Nb and Sn powders, the distinct X-ray diffraction peaks of the elements disappeared and typical diffuse peaks of an amorphous pattern showed up. But these samples did not show the superconducting transition temperature of vapor-quenched amorphous Nb-Sn alloys. In 1983, Koch et al. reported on the Preparation of amorphous Ni60Nb40 by mechanical alloying [3.3]. After the detection of amorphization by solid-state reaction in evaporated multilayer films by Schwarz and Johnson [3.4] (see also Chap. 2), Schwarz et al. [3.5] proposed after investigating glass formation in Ni-Ti alloys, that amorphization by mechanical alloying is also based on the solid-state reaction process. Within the last couple... 

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. 

Conventional X-ray diffraction is carried out on crystalline samples and sharp diffraction peaks are observed due to the underlying periodic crystal structure. With the high intensity X-rays obtained from synchrotron radiation or free-electron lasers it is now possible to extract the scattering/diffraction from solute molecules in dilute solutions. The diffraction pattern from isolated molecules is compared to crystalline samples weak and diffuse. In this review, we do not distinguish between X-ray diffraction and X-ray scattering since both phenomena have the same underlying theoretical framework. 

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