Improved scattering models

The use of more sophisticated scattering models, in which bonding effects on the charge density are taken into account, discussed in chapter 3, leads to a significant improvement in the results of the rigid-bond test. An example, based on a low-temperature analysis of p-nitropyridine-N-oxide, is given in Table 2.3. 

Concerning the nuclear data in the JEF-2.2 library, a general conclusion was that the inelastic scattering cross-sections for many even mass nuclides were about a factor of 2 low because of the neglect of direct interaction effects in the nuclear models used to calculate these cross-sections. The contribution of inelastic scattering is of the order of 15% of the total fission product reactivity effect. The most important even mass nuclei are Mo-98, - 100, Ru-102, - 104, - 106, Pd-106, - 108, Xe-132, - 134, Nd-146, - 148 and Sm-152. Improved theoretical models have now been developed and validated by direct measurements of the differential cross-sections of Pd isotopes. As a consequence of the analyses of the integral measurements, it has been concluded that the contribution of fission products to the variation of reactivity with bum-up can be predicted to within 5% (Is) for a conventional fast reactor. 

Pretreatment of the spectroscopic data is usually carried out to improve the model. A first derivative can be applied to remove sloping backgrounds and offset errors. This is a very common method of pretreating MR spectra. The data can be centred about its mean. Routines are available to smooth the data and remove spectroscopic scatter. 

The idea of the Rietveld method is to do a step-by-step refinement of the whole powder diffraction pattern. One can constmct an initial stmctural model from a partial knowledge of the phases detected in a pattern and, gradually and progressively, improve the model in order to compare it to the experimental diffraction pattern. One of the main advantages of the method is, in principle, that it can deal with heavily overlapped peak patterns. There is no need to separate peaks, since the scattering contributions from the various phases are all summed up to calculate the intensities at each diffractogram step, not attributing a particular peak to a specific phase or a crystal plane. ... 

K. C. Hickman, S. M. Caspar, S. S. H. Naqvi, K. P. Bishop, J. R, McNeil, G. D. Tipton, B. R, Stallard, and B. L. Draper. Use of Diffraction From Latent Images to Improve Lithogrophy Control. Presented at the SPIE Technical Conference 1464 Symposium on I.C. Metrology, Inspection, and Process Control, San Jose, CA, 1991, Proc. SPIE. 1464, pp. 245-257, 1991. Another application is presented of scattering characterization and modeling from periodic structures for process control. 

The temperature dependence of the thermal conductivity of CBCF has been examined by several workers [10,13,14]. Typically, models for the thermal conductivity behavior include a density term and two temperaUrre (7) terms, i.e., a T term representing conduction within the fibers, and a term to account for the radiation contribution due to conduction. The thermal conductivity of CBCF (measured perpendicular to the fibers) over the temperature range 600 to 2200 K for four samples is shown in Fig. 6 [14]. The specimen to specimen variability in the insulation, and typical experimental scatter observed in the thermal conductivity data is evident in Fig. 6. The thermal conductivity of CBCF increases with temperature due to the contribution from radiation and thermally induced improvements in fiber structure and conductivity above 1873 K. 

Further improvements on the previously discussed models were proposed in the latest model for y - and e - Mn02 by Chabre and Pannetier [12, 43, 44], Starting from De Wolff s model they developed a structural description of manganese dioxides that accounts for the scattering function of all y - and e - Mn02 materials and provides a method of characterizing them quantitatively in terms of structural defects. All y — and e - Mn02 samples can be described on the basis of an ideal ramsdellite lattice affected by two kinds of defects ... 

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. 

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