X-ray diffusion

Other techniques such as X-ray diffusion or small angle neutron diffusion are also used in attempts to describe the size and form of asphaltenes in crude oil. It is generally believed that asphaltenes have the approximate form of very flat ellipsoids whose thicknesses are on the order of one nanometer and diameters of several dozen nanometers. 

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... 

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]. 

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. 

There is actually no sharp distinction between the crystalline and amorphous states. Each sample of a pharmaceutical solid or other organic material exhibits an X-ray diffraction pattern of a certain sharpness or diffuseness corresponding to a certain mosaic spread, a certain content of crystal defects, and a certain degree of crystallinity. When comparing the X-ray diffuseness or mosaic spread of finely divided (powdered) solids, the particle size should exceed 1 um or should be held constant. The reason is that the X-ray diffuseness increases with decreasing particle size below about 0.1 J,m until the limit of molecular dimension is reached at 1-0.1 nm (10-1 A), when the concept of the crystal with regular repetition of the unit cell ceases to be appropriate. 

X-Ray Diffuse Scattering from Self-Oi anized Mesoscopic Semiconductor Structures... 

In the case of structural studies with x-rays, sample size is rarely a serious problem since single crystals as small as about 0.001 mm3 (sealed x-ray tube) or 10-9 mm3 (synchrotron radiation) will do. In the case of x-ray diffuse scattering measurements with the assembly described in Section VI.D, the crystal must be 2 mm long at least but can be relatively thin. With neutrons, however, sample size is more critical. Indeed, for structure measurements, 0.1 mm3 is a minimum, with the highest neutron fluxes available nowadays, and more usual sizes are in the range of several cubic millimeters to several tens of cubic millimeters. For polarized neutrons or inelastic scattering studies, much larger samples are necessary. 

Because the amplitude of the lattice distortion in the Peierls insulator is very small, the X-ray scattering associated with it is weak. Furthermore the one-dimensional nature of this distortion gives rise to diffuse Bragg planes instead of the usual well-defined Bragg reflections. These two facts have led to the development of a special diffuse X-ray photographic technique often referred to as the monochromatic Laue technique or XDS (for X-ray diffuse scattering) (64). 

Below Tp, the static ( locked ) CDW of the conduction electrons at 2 kp (or 4 kp), couple with the other atomic or molecular electrons in the lattice, cause a slight lattice distortion, and gives rise to extra X-ray reflections. Above Tp, these CDW are mobile, with no phase locking between excitations on nearby chains one sees X-ray diffuse reflections, similar to thermal diffuse scattering, which sharpen as T is lowered. Below Tp the static distortion produces new, usually weak, reflections between reciprocal-lattice layer lines. When the band filling is a rational fraction (1/4, 1/2, 2/3,1, etc.) then these reflections overlap with certain Bragg reflections of the background lattice, and are more difficult to detect. 

Renaud G, Belakhovsky M, Lefebvre S, Bessiere M (1995) Correlated chemical and positional fluctuations in the gold-nickel system-a synchrotron X-ray diffuse-scattering study. J Phys III 5 1391-1405... 

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