Outer diffuse scattering

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). 

The outer layer (beyond the compact layer), referred to as the diffuse layer (or Gouy layer), is a three-dimensional region of scattered ions, which extends from the OHP into the bulk solution. Such an ionic distribution reflects the counterbalance between ordering forces of the electrical field and the disorder caused by a random thermal motion. Based on the equilibrium between these two opposing effects, the concentration of ionic species at a given distance from the surface, C(x), decays exponentially with the ratio between the electro static energy (zF) and the thermal energy (R 7). in accordance with the Boltzmann equation ... 

To evaluate the crystallinity of the films, Raman spectroscopy is used. A typical Raman spectrum is presented in Fig. 4. Of the crystalline diamond, a narrow peak at a frequency of 1332 cur1 is characteristic, which is caused by the first-order phonon scattering by the crystal lattice. The non-diamond carbon is represented in the spectrum by two diffuse bands at ca. 1350 and 1550 cm-1. When comparing the peaks height, one should keep in mind that the Raman signal is 50 times more sensitive to the non-diamond carbon than to the crystalline diamond [20], In the high-quality diamond films used as electrodes, the non-diamond carbon component rarely exceeds 1%. Raman spectroscopy data have been corroborated by the independent impedance spectroscopy measurements (see below). According to [21], the inner layer of a diamond film is enriched with the admixture of non-diamond carbon as compared to its outer layer. 

These speciation concepts are illustrated in Fig. 3 for the idealized basal-plane surface of a smectite, such as montmorillonite. Also shown are the characteristic residence-time scales for a water molecule diffusing in the bulk liquid (L) for an ion in the diffuse swarm (DI) for an outer-sphere surface complex (OSQ and for an inner-sphere surface complex (ISC). These time scales, ranging from picosecond to nanosecond [20,21], can be compared with the molecular time scales that are probed by conventional optical, magnetic resonance, and neutron scattering spectroscopies (Fig. 3). For example, all three surface species remain immobile while being probed by optical spectroscopy, whereas only the surface complexes may remain immobile while being probed by electron spin resonance (ESR) spectroscopy [21-23]. 

The nucleus, like the atom, also does not have a sharp outer boundary. Its surface, too, is diffuse, although somewhat less than that of an atom. Measurements in which neutrons are scattered from nuclei show that to a first approximation the nucleus may be considered to be a sphere with a radius given by the following formula ... 

No real surface behaves in exactly this way, although some surfaces approach it. Some simultaneously exhibit specular and diffuse reflectance that of a new automobile provides a familiar example. The hard, highly polished outer surface exhibits specular reflectance of some of the incident light. The remainder is refracted into the layers below, which contain diffusely reflecting, spectrally selective absorptive pigments suspended in a binding matrix. Light not absorbed is scattered within this layer with an intensity pattern that may approximate that of a perfectly diffuse reflector. Because of the absorptive properties of... 

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