Central diffuse scattering

The two components of the CDS can be analyzed to determine the sizes of the entities that give rise to these features. The isotropic scattering can yield an estimate of the size of voids or particulate defects. The equatorial scattering can be analyzed to determine the orientation distribution of the scattering entities [93] and, when appropriate, the size and length of the elongated scattering entities such as microfibrils 

---

Voids Size and distribution Height (length) when voids are elongated Misoiientation Characteristics of the decay in central diffuse scattering Width of the diffuse scattering along the meridian extrapolated from a series of meridional shces Azimuthal intensity distribution of diffuse streak... 

DF imaging using the inelastic, diffusely scattered electrons (near the central beam), which, it is assumed, arise predominantly from noncrystalline regions of the specimen (Clarke 1979a McLaren and Etheridge 1980). 

FIGURE 6-20. Electron diffraction pattern from a pillared rectorite crystal. The diffuse scattering appears mainly in the central disc and in the symmetrical spots outside the first ring. 

This variation in chemical composition, whilst the basic lattice remains unaltered, requires explanation. The diffuse nature of the X-ray diffraction pattern was attributed, some fifty years ago, to the size of the crystals which are so small that each one contains only a few hundred unit cells. More recent studies by both X-ray diffraction and electron microscopy have suggested that, in addition to the minute hydroxyapatite crystals, bone mineral contains a substantial proportion of small particles which do not give a systematic diffraction pattern but only diffuse scattering. This component, amorphous calcium phosphate (ACP), has been estimated to form as much as 68% of the mineral in the femur of very young rats, some 35% in adult rats and about 40% in human adults. When prepared in the laboratory, it exists as minute spheroids, about 20 nm in diameter, each with a denser outer shell enclosing a less dense central portion. Little is known about the arrangement of ions within them, except that the structure is not apatite. The Ca P ratio is about 1-5. When such an amorphous component is present, it will give the mineral a lower overall Ca P ratio than that of an ideal calcium hydroxyapatite (1-67). 

Wang W, Murthy NS, Grubb DT. Central small-angle diffuse scattering from fibers is made of two components. J Polym Sci B 2012 50 797-804. 

The Q and ft) dependence of neutron scattering structure factors contains infonnation on the geometry, amplitudes, and time scales of all the motions in which the scatterers participate that are resolved by the instrument. Motions that are slow relative to the time scale of the measurement give rise to a 8-function elastic peak at ft) = 0, whereas diffusive motions lead to quasielastic broadening of the central peak and vibrational motions attenuate the intensity of the spectrum. It is useful to express the structure factors in a form that permits the contributions from vibrational and diffusive motions to be isolated. Assuming that vibrational and diffusive motions are decoupled, we can write the measured structure factor as... 

In Sect. 7.4.6, we discussed various stochastic simulation techniques that include the kinetics of recombination and free-ion yield in multiple ion-pair spurs. No further details will be presented here, but the results will be compared with available experiments. In so doing, we should remember that in the more comprehensive Monte Carlo simulations of Bartczak and Hummel (1986,1987, 1993,1997) Hummel and Bartczak, (1988) the recombination reaction is taken to be fully diffusion-controlled and that the diffusive free path distribution is frequently assumed to be rectangular, consistent with the diffusion coefficient, instead of a more realistic distribution. While the latter assumption can be justified on the basis of the central limit theorem, which guarantees a gaussian distribution for a large number of scatterings, the first assumption is only valid for low-mobility liquids. 

An alternative to the common device of determining relative intensities is a study of the fine structure of the scattered beam. This entails resolving the spectrum of scattered light into its three peaks, viz. a central peak and two side ones. The need is thus obviated to refer to I0 or, according to the apparatus, the scattering power of a standard calibration material. The method is used mainly for determining diffusion constants and thermodynamic properties of liquids. 

The damping factors take into account 1) the mean free path k(k) of the photoelectron the exponential factor selects the contributions due to those photoelectron waves which make the round trip from the central atom to the scatterer and back without energy losses 2) the mean square value of the relative displacements of the central atom and of the scatterer. This is called Debye-Waller like term since it is not referred to the laboratory frame, but it is a relative value, and it is temperature dependent, of course It is important to remember the peculiar way of probing the matter that EXAFS does the source of the probe is the excited atom which sends off a photoelectron spherical wave, the detector of the distribution of the scattering centres in the environment is again the same central atom that receives the back-diffused photoelectron amplitude. This is a unique feature since all other crystallographic probes are totally (source and detector) or partially (source or detector) external probes , i.e. the measured quantities are referred to the laboratory reference system. 

In real fluids, low-frequency light-scattering reveals a central Rayleigh peak, due to heat diffusion, and two symmetrically displaced Brillouin peaks, due to sound waves, such that... 

Fig. 6. Low energy electron diffraction patterns at normal incidence from clean tungsten surfaces, (a) Ball model of W(llO) face. Some of the net lines (hk) are indexed in terms of a centered rectangular unit mesh (outlined), (b) Clean W(llO), 75 V. Diffuse brightness and central bright spot are caused by light from electron gun filament, (c) Clean W(llO), 300 V. (d) Ball model of (112) surface, the third densest of the boo lattice, (e) Clean W(112) at 90 V. Note the asymmetric intensities of the A/c and hA beams. The unit mesh contains only a single mirror plane perpendicular to surface. There is a strong scattering contribution from the exposed second layer which is asymmetrically positioned.

---