Diffuse scatter

Broadening of spots can result from themial diffuse scattering and island fomiation, among other causes. The themial effects arise from the disorder in atomic positions as they vibrate around their equilibrium sites the sites themselves may be perfectly crystalline. 

The transition from smectic A to smectic B phase is characterized by tire development of a sixfold modulation of density witliin tire smectic layers ( hexatic ordering), which can be seen from x-ray diffraction experiments where a sixfold symmetry of diffuse scattering appears. This sixfold symmetry reflects tire bond orientational order. An appropriate order parameter to describe tlie SmA-SmB phase transition is tlien [18,19 and 20]... 

Here f denotes the fraction of molecules diffusely scattered at the surface and I is the mean free path. If distance is measured on a scale whose unit is comparable with the dimensions of the flow channel and is some suitable characteristic fluid velocity, such as the center-line velocity, then dv/dx v and f <<1. Provided a significant proportion of incident molecules are scattered diffusely at the wall, so that f is not too small, it then follows from (4.8) that G l, and hence from (4.7) that V v° at the wall. Consequently a good approximation to the correct boundary condition is obtained by setting v = 0 at the wall. ... 

Any perturbation from ideal space-group symmetry in a crystal will give rise to diffuse scattering. The X-ray diffuse scattering intensity at some point (hkl) in reciprocal space can be written as... 

Displacements correlated within unit cells but not between them lead to very diffuse scattering that is not associated with the Bragg peaks. This can be conveniently explored... 

Figure 3 Calculated X-ray diffuse scattering patterns from (a) a full molecular dynamics trajectory of orthorhombic hen egg white lysozyme and (b) a trajectory obtained by fitting to the full trajectory rigid-body side chains and segments of the backbone. A full description is given in Ref. 13.

A dynamic transition in the internal motions of proteins is seen with increasing temperamre [22]. The basic elements of this transition are reproduced by MD simulation [23]. As the temperature is increased, a transition from harmonic to anharmonic motion is seen, evidenced by a rapid increase in the atomic mean-square displacements. Comparison of simulation with quasielastic neutron scattering experiment has led to an interpretation of the dynamics involved in terms of rigid-body motions of the side chain atoms, in a way analogous to that shown above for the X-ray diffuse scattering [24]. 

Usually, the collection of LEED 7-Vcurves requires single crystal surfaces with long-range order in the upper-most layers. Structural information can, however, also be obtained in a similar way for certain disordered surfaces, when the energy dependence of the diffusely scattered intensity is analyzed (diffuse LEED [2.264, 2.265]). 

The occurrence of the mesophase in the fiber is confirmed by x-ray diffraction examination. The occurrence of three equatorial reflections 010, 110, and 100, the absence of layer and meridional reflections, and the manifestation of the intensity maximum of diffusively scattered radiation at 20 = 19 in the fiber diffraction pattern are the criterion for the presence of the mesophase. The... 

For local deviations from random atomic distribution electrical resistivity is affected just by the diffuse scattering of conduction electrons LRO in addition will contribute to resistivity by superlattice Bragg scattering, thus changing the effective number of conduction electrons. When measuring resistivity at a low and constant temperature no phonon scattering need be considered ar a rather simple formula results ... 

It is simplest to consider these factors as they are reflected in the entropy of the solution, because it is easy to subtract from the measured entropy of solution the configurational contribution. For the latter, one may use the ideal entropy of mixing, — In, since the correction arising from usual deviation of a solution (not a superlattice) from randomness is usually less than — 0.1 cal/deg-g atom. (In special cases, where the degree of short-range order is known from x-ray diffuse scattering, one may adequately calculate this correction from quasi-chemical theory.) Consequently, the excess entropy of solution, AS6, is a convenient measure of the sum of the nonconfigurational factors in the solution. 

A. Plech, R. R. A. Geis, and M. Wulff, Diffuse scattering from hquid solutions with white-beam undulator radiation for photoexcitation studies. J. Synchrotron Radiation 9(5), 287-292 (2002). 

Diffuse Reflectance IR Fourier Transform Spectroscopy (DRIFTS) can be employed with high surface area catalytic samples that are not sufficiently transparent to be studied in transmission. In this technique, the diffusely scattered IR radiation from a sample is collected, refocussed, and analysed. Samples can be measured in the form of loose powders. 

Hall, C.R. and Hirsch, P.B. (1965) Effect of thermal diffuse scattering on propagation of high energy electron through crystals, Proc. R. Soc. London A, 286, 158-177. 

Rossouw, C.J. and Bursill, L.A. (1985) Interpretation of dynamical diffuse scattering of fast electrons in rutile, Acta Cryst. A, 41, 320-327. 

Pure liquids can be used for the purpose of calibration to absolute intensity, because their diffuse scattering Ipi (0) = limv qIFi (s) caused from density fluctuations can be computed theoretically. Some examples are in the literature [91,93-95],... 

Figure 8.8. Important components of diffuse scattering in the SAXS of polymer materials with two or more phases. Only for fractals Porod s law is fundamentally changed...

Diffuse scattering is always present in the SAXS of polymer materials. In Fig. 8.8 its most important components are sketched45. The density fluctuation background re-... 

It is assumed that the machine background has separately been measured and properly been subtracted under consideration of the absorption factor (Sect. 7.6). In particular it is not allowed to take the diffuse scattering background of a molten or amorphous sample for the machine background. 

Other effects contribute to the diffuse scattering, as well. In particular, a smooth density transition zone between the phases (e.g., at particle surfaces) and a rough particle surface must be mentioned. 

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