Scattering in diffraction

In between the ideal crystalline and the purely amorphous states, most real crystals contain degrees of disorder. Two types of statistical disorder have to be distinguished chemical disorder and displacive disorder (Fig. 1.3-14). Statistical disorder contributes to the entropy S of the solid and is manifested by diffuse scattering in diffraction experiments. It may occur in both periodic and aperiodic materials. 

The intensity in the diffraction channel is defined by 5ocP where Sqg is an element of the scattering S-matrix. The probability for scattering in diffraction channel G, IS ogI is obtained as the ratio between the outgoing and incoming fluxes, i.e.. 

Electrons interact with solid surfaces by elastic and inelastic scattering, and these interactions are employed in electron spectroscopy. For example, electrons that elastically scatter will diffract from a single-crystal lattice. The diffraction pattern can be used as a means of stnictural detenuination, as in FEED. Electrons scatter inelastically by inducing electronic and vibrational excitations in the surface region. These losses fonu the basis of electron energy loss spectroscopy (EELS). An incident electron can also knock out an iimer-shell, or core, electron from an atom in the solid that will, in turn, initiate an Auger process. Electrons can also be used to induce stimulated desorption, as described in section Al.7.5.6. 

A number of reviews have appeared covering the various aspects of borate glasses. The stmcture, physical properties, thermochemistry, reactions, phase equihbria, and electrical properties of alkah borate melts and glasses have been presented (73). The apphcation of x-ray diffraction, nmr, Raman scattering, in spectroscopy, and esr to stmctural analysis is available (26). Phase-equihbrium diagrams for a large number of anhydrous borate systems are included in a compilation (145), and thermochemical data on the anhydrous alkah metal borates have been compiled (17). 

Figure 1 Plane wave scattering from two consecutive iines of a one-dimensionai diffraction grating. The wave scatters in-phase when the path difference (the difference in iength of the two dotted sections) equais an integrai number of waveiengths.

For a given structure, the values of S at which in-phase scattering occurs can be plotted these values make up the reciprocal lattice. The separation of the diffraction maxima is inversely proportional to the separation of the scatterers. In one dimension, the reciprocal lattice is a series of planes, perpendicular to the line of scatterers, spaced 2Jl/ apart. In two dimensions, the lattice is a 2D array of infinite rods perpendicular to the 2D plane. The rod spacings are equal to 2Jl/(atomic row spacings). In three dimensions, the lattice is a 3D lattice of points whose separation is inversely related to the separation of crystal planes. 

Order and polydispersity are key parameters that characterize many self-assembled systems. However, accurate measurement of particle sizes in concentrated solution-phase systems, and determination of crystallinity for thin-film systems, remain problematic. While inverse methods such as scattering and diffraction provide measures of these properties, often the physical information derived from such data is ambiguous and model dependent. Hence development of improved theory and data analysis methods for extracting real-space information from inverse methods is a priority. 

Diffraction is a scattering phenomenon. When x-rays are incident on crystalline solids, they are scattered in all directions. In some of these directions, the scattered beams are completely in phase and reinforce one another to form the diffracted beams [1,2]. Bragg s law describes the conditions under which this would occur. It is assumed that a perfectly parallel and monochromatic x-ray beam, of wavelength A, is incident on a crystalline sample at an angle 0. Diffraction will occur if... 

The use of a STEM instrument allows the controlled movement of a very fine electron beam in relation to the specimen and the efficient detection of the scattering and energy losses of the beam. We have outlined here a few of the possible applications arising from this capability. Other applications, of increasing sophistication and power will undoubtedly follow in time. In particular a range of phenomena, resulting from coherent interference effects in diffraction patterns produced by coherent convergent beams, have been observed (26) but not yet exploited. 

The structure of a liquid is conventionally described by the set of distributions of relative separations of atom pairs, atom triplets, etc. The fundamental basis for X-ray and neutron diffraction studies of liquids is the observation that in the absence of multiple scattering the diffraction pattern is completely determined by the pair distribution function. 

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. ... 

Z.L. Wang, Elastic and Inelastic Scattering in Electron Diffraction and Imaging, Plenum, New York (1995)... 

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