Modeling total scattering

Based on their measurements of North African dust transported to the Barbados, Li et al. (1996) estimate that over a 10-year period, dust contributed about 56% of the total light scattering. Similarly, Tegen et al. (1997) estimate using a global transport model that scattering and absorption of light by submicron soil... 

The presence of a minor second phase impurity can be added either in the form of the actual structural model of Ni or as a Le Bail s phase, where only the unit cell and peak shape parameters are taken into account. The latter option has been chosen since we are not interested in the crystal structure of this minor impurity, and it may be a difficult task given its small contribution to the total scattered intensity. 

Figures 2 and 3 compare measured and simulated total scattering functions (tsf) for ice Ih at 120 and 200 K, respectively. The upper panels of Figures 2 and 3 compare tsf s for the initial stages of the RMCPOW modelling. It is obvious that Bragg scattering, as far as peak positions are concerned, is well described by the starting configurations, although intensities may not always match the measured values. Note, however, that the shape and intensity of the diffuse part had to change enormously between the initial and final states of the calculations.

It is shown that both the Bragg and the diffuse scattering parts of neutron powder diffraction data on ice Ih can be interpreted simultaneously by constructing large models of the structure that are consistent with the measured total scattering functions within errors. The RMCPOW algorithm proved to be readily applicable for the purpose. 

Total scattering data can be analyzed by fitting models directly in reciprocal-space [i.e., the S Q) function is fit]. However, an alternative and intuitive approaeh is to Fourier transform the data to real-spaee to obtain the atomic pair distribution function (PDF), which is then fit in real-space. The reduced pair distribution function, G r), is related to S Q) through a sine Fourier transform aeeording to ... 

Fig. 20. The reflected energy fraction is shown as a function of the total scatter angle for both the single-scatter and the double half-scatter BC models. Mass ratios /x = 1.43. (From Helmer and Graves, 1998.)...

Fig. 21. The histograms show the distributions of total scattering angle a for the reflected atoms, (a) Ar+, 50 eV, 85°, bare Si and (b) C1+, 50 eV, 85°, 2.3-MI. Si -Cl. Filled circles represent the average reflected energy fraction corresponding to the reflection angle. Single-scatter (SS) soft-soft branch and double half-scatter (DHS) soft-soft branch model predictions for (a) jjL = 1.43 and (b) jjL = 1.0 also shown for comparison with data from simulation.

The latter assumption has been verified within experimental error from an analysis of the total scattering invariant which has been calculated from the absolute intensity of scattering. The results for n listed in Table II show an apparent increase at low water contents and then a slight decrease at large water contents. It is noted that this decrease in H implying particle coalescence is in apparent contradiction to the hard sphere model used above. 

The reality, which was reflected by the string-and-bead model, was of a polymer chain separating into several discreet regions ( beads ) interconnected by a length of the polymer chain, which had a negligible contribution to the total scattering. The distance between the beads was calculated to be about 150 A. 

One calculates transport properties by correlating the resistivity with the total scattering cross-section. The electrical resistivity is found to be temperature insensitive at low temperatures, has the ln T/T ) dependence near T , and decreases steadily for T > Tq. The shape of the resistivity curve will be discussed in section 3.3. Clearly the low-temperature resistivity is in disagreement with experiments, which indicate the type Fermi liquid behavior. The discrepancy comes from the implicit assumption that the impurity atoms scatter the conduction electrons Incoherently. How the system achieves coherence at low temperatures is now studied in terms of the spin fluctuation resonance model, but the analysis has not yet reached the level of sophistication of the single-impurity problem. 

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