Anomalous diffraction approximation

Box and McKellar (1978) derived the sum rule (4.81) under the assumption of a constant refractive index and within the framework of the anomalous diffraction approximation of van de Hulst (1957, Chap. 11). 

In addition, the anomalous diffraction approximation can also be used to predict the cross-sections of spherical cells based on the facts that (i) their relative complex index of refraction is such that 1 - 1 and (ii)... 

This appendix reports the weights for the moments of the particle size distribution obtained from an eight order Taylor Series approximation to the scattering efficiency for the anomalous diffraction case... 

The newer la.ser diffraction instrument allows measurement for particle sizes ranging from 0.1 pm to 8 mm (7). Most of the laser diffraction instruments in the pharmaceutical industry use the optical model based on several theories, either Fraunhofer, (near-) forward light scattering, low-angle laser light scattering, Mie, Fraunhofer approximation, or anomalous diffraction. These laser diffraction instruments assume that the particles measured are spherical. Hence, the instrument will convert the scattering pattern into an equivalent volume diameter. A typical laser diffraction instrument consists of a laser, a sample presentation system, and a series of detectors. 

Since anomalous diffraction is only relevant for forward scattering, it is not meaningful to discuss other cross sections than the extinction one. A first order approximation for real refractive indices was provided by van de Hulst (1981, p. 176) ... 

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. 

Fig. 15 shows the diffraction efficiency and the room temperature during 3 hours. As can be seen, the temperatures have the same behavior and are 25 °C approximately, the DE has a similar values but temperature fluctuations modifies it behavior. When the temperature is almost constant the DE has a softly grow, but when the temperature has some change, the DE show an anomalous behavior. The same behavior for 27 im and 17 (im was observed as is shown in Fig. 16 and 17. 

Figures 28.7, 28.8, and 28.9 show the results of three recent but quite independent studies of the system ThOz-LazOz. These have been redrawn from the published data in such a way as to facilitate comparison, and the designations used throughout for the lanthana-rich intermediate phases of closely similar composition are those of Sibieude and Foex (1975). However, this is not to say that phases with the same designation are necessarily identical. Thus in the paper by Keller et al. (1972) it is stated that X-ray diffraction data for the phases found at 91.7 mole % LaOi.5 are in approximate agreement with those reported by Sibieude and Chaudron (1970) for the iP i-phase, hut that a similar correspondence between data for the phase found in this work at 75.0 mole % LaOi.5 and the metastable I 3-phase found by the French workers was anomalous in that the IP s composition was given as 85-87 mole % LaOij. No such correspondence with the data of Diness and Roy (1969) could be found.

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