Instrument smearing effects

2 INSTRUMENT SMEARING EFFECTS 6.2.1 Prediction of partiality and angular reflecting range 

There are important differences in the diffraction geometry with SR optical systems compared with a conventional laboratory arrangement (Greenhough and Helliwell, 1982a,b). In particular, at an SR source the 

For this reason and the interest in the dispersive setting (section 

In order to decide whether a reflection is partial or not for a given crystal orientation the sample reflection rocking width A or a spherical reciprocal lattice volume of radius E can be compared with a unit Ewald sphere these are given by  

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Table 6.1. Instrument smearing effects Example instrument settings based on a bent triangular monochromator (section 5.2.3) focussing in the horizontal plane and a horizontal rotation axis of the crystal sample. 

Figure 7.12 shows examples of experimental I(q) as measured at different temperature and fits using the analytical Leibler function. The experimental data are indeed fitted very well by the structure factor of the RPA theory. The solid curves shown in the figure represents best fits convoluted by the experimental resolution function. In the insert is shown the effect of instrumental smearing. In typical data analysis, both the polymer radius of gyration Rg and the Flory-Huggins interaction parameter x are used as adjustable parameters. 

Cosine smearing. Because instrument volume and experiment time must both be minimized for a planetary Mossbauer spectrometer, it is desirable in backscatter geometry to illuminate as much of the sample as possible with source radiation. However, this requirement at some point compromises the quality of the Mossbauer spectrum because of an effect known as cosine smearing [327, 348, 349] (see also Sects. 3.1.8 and 3.3). The effect on the Mossbauer spectrum is to increase the linewidth of Mossbauer peaks (which lowers the resolution) and shift their centers outward (affects the values of Mossbauer parameters). Therefore, the diameter of the source y-ray beam incident on the sample, which is determined by a... 

Fig. 21. Palladium L,-XANES and K-XANES are compared with the calculated theoretical p(E) from the p-like partial density of states taking account of the matrix element of the Pd crystal before and after it has been smeared to account for lifetime effects. The difference between the L, and the K-edge is due to the better instrumental energy resolution in the energy range of the Lj edge and shorter core hole lifetime at the K-edge...

A diffraction line may be broadened as a result of instrumental effects, such as an imperfection in the collimation geometry, the finite width of the detector window, imperfect focusing, less than perfect monochromatization of the incident beam, etc. Suppose that I(s) represents the intensity pattern that could be obtained under an ideal instrumental condition producing no instrumental broadening, and f0bs(s) represents the smeared intensity pattern that is actually observed. The relationship between these two can be expressed in most cases as... 

Fig. 2. Current-voltage and derivative curves for lET junctions. lETS peaks (c) are broadened by thermal smearing of electron energies (dashed line) and also instrumental effects (not shown)...

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