Scattering geometry, transmission

Conversion electron Mossbauer spectroscopy (CEMS) measurements with back scattering geometry have the merit that spectra can be obtained from a sample with much less isotope content compared with transmission measurements. Another merit is that a sample, deposited on a thick substrate, could be measured, and that because of the limited escape depth of the conversion electrons, depth-selective surface studies are possible. The CEMS technique was found to be best applicable to specimens of 10-100 pg Au cm, i.e., about two orders of magnitudes thinner than required for measurements in transmission mode [443]. This way (1) very thin films of gold alloys, as well as laser- and in beam-modified surfaces in the submicrometers range of depth [443], and (2) metallic gold precipitates in implanted MgO crystals [444] were investigated. 

We have now surveyed the iron-bearing pigments and, to a limited extent, terra cotta statuary using both transmission and scattering geometry. The results provide information of an extraordinary richness and... 

Most often the transmission mode is found to be the most convenient in Mossbauer spectroscopy, i.e., the y radiation passes from the source through the absorber, and the attenuation of the primary beam is measured at the various Doppler velocities. However, there are a number of cases where a "scattering geometry may be advantageous (SO). The basis for this geometry lies in those processes that take place after resonant absorption of y radiation by the Mossbauer isotope. Specifically, after excitation the Mossbauer isotope may reemit the y ray, or it may decay by emission of internal conversion electrons and X rays [with the probability of internal conversion equal to a/(l + a)]. 

There hence exist two modes of arrangement for the third part of the spectrometer, the detector the transmission geometry and the scattering geometry. The detector of the former counts the number of unaffected transmitted gamma rays whereas that of the latter counts that of re-emitted gamma rays. X-rays or electrons. Since the count rate, I(v), is affected by many factors as shown in the formula below ... 

Figure 2 Experimental arrangements and Mossbauer spectra for a Co (Cr) source and a sample of a-Fe (A) transmission geometry, (B) scattering geometry with the detection of y- or X-rays, (C) backscattering geometry with the detection of X-rays and electrons. The source moves at a velocity v.

In this section we will discuss perturbation methods suitable for high-energy electron diffraction. For simplicity, in this section we will be concerned with only periodic structures and a transmission diffraction geometry. In the context of electron diffraction theory, the perturbation method has been extensively used and developed. Applications have been made to take into account the effects of weak beams [44, 45] inelastic scattering [46] higher-order Laue zone diffraction [47] crystal structure determination [48] and crystal structure factors refinement [38, 49]. A formal mathematical expression for the first order partial derivatives of the scattering matrix has been derived by Speer et al. [50], and a formal second order perturbation theory has been developed by Peng [22,34],... 

Figure 4.1. Typical X-ray setup with 2D detector in normal-transmission geometry. The intensity of the incident X-ray beam is measured in an ionization chamber (a). Thereafter it penetrates the sample which is subjected to some process. At a distance R (cf. Table 2.1 on p. 7) behind the sample the detector is recording the scattering pattern. In its center (b) the detector is protected by a beam stop. It is equipped with a pin-diode which records the intensity of the attenuated beam...

For USAXS and SAXS studies in normal-transmission geometry it is more convenient to carry out this step after the correction for absorption and background, because in these cases absorption and background correction are no function of the scattering angle. 

Figure 7.2. Absorption in normal-transmission geometry. The path of the photon through a sample of thickness t before and after its scattering about the angle 20... 

Direct calibration to absolute intensity is not a usual procedure at synchrotron beamlines. Nevertheless, the technical possibilities for realization are improving. Therefore the basic result for the total scattering intensity measured in normal transmission geometry is presented. At a synchrotron beamline point-focus can be realized in good approximation and the intensity /(s) is measured. Then integration of Eq. (7.19) results in... 

CDFs are computed from scattering data which are anisotropic and complete in reciprocal space. Thus the minimum requirement is a 2D SAXS pattern of a material with fiber symmetry taken in normal transmission geometry (cf. p. 37, Fig. 4.1). Required pre-evaluation of the image is described in Chap. 7. 

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