SAXS Setup

In X-ray diffraction and scattering experiments, several X-ray sources can be employed, from X-ray tubes and rotating anodes to synchrotron radiation. Figure 2 presents in a schematized manner the SAXS setup manipulating collimated beams. An ordinary laboratory SAXS experiment is shown in Fignre 2(a), with a typical size of the beam focused at the detector of the order of a few hundred micrometers. The magnitude of the scattering vector can be written as... 

FigureS-l. (a) Schematic SAXS setup, (b) X-ray beamptUhs from the source to the detector, both elements locatedfar away from the sample. The segment AB + BC is the optical path difference from which the phase shift is determined.

SAXS setup having a Kratky U-sHt system. The incident beam was Cu-Ka radiation with a wavelength of 1.542A. The data were corrected for slit collimation. The Guinier radius, Rg> and the mass fractal dimension, D, were calculated from the Guinier and Porod regions, respectively. 

In order to reduce air absorption in SAXS and USAXS setups, a vacuum tube (cf. Fig. 4.10) is mounted between sample chamber and detector. 

The design and placement of the second beam intensity monitor demands more attention. The definition of X-ray absorption does not discriminate between primary beam, USAXS and SAXS. So the second beam intensity monitor should guide primary beam, USAXS and SAXS through its volume, whereas the WAXS should pass outside the monitor. The optimum setup for SAXS and USAXS measurements is a narrow ionization chamber directly behind the sample. For WAXS measurement a pin-diode in the beam stop is a good solution for WAXS. For USAXS and SAXS it may be acceptable, as long as the relevant part of the primary beam is caught, the optical system is in thermal equilibrium and the synchrotron beam does not jump (cf. Sect. 4.2.3.5). 

General Routes. If a SAXS beamline in normal transmission geometry is used, calibration to absolute intensity is, in general, carried out indirectly using secondary standards. Direct methods require direct measurement of the primary beam intensity under consideration of the geometrical setup of the beamline. On a routine basis such direct calibration was commercially available for the historic Kratky camera equipped with zero-dimensional detector and moving slit device 14. 

The so-called Lupolen standard 25 is a well-known secondary standard in the field of SAXS. In conjunction with the Kratky camera it is easily used, because its slit-smeared intensity J(s) /V is constant over a fairly wide range, and this level is chosen as the calibration constant. In point-focus setups the SAXS of the Lupolen standard neither shows a constant intensity region, nor is the reported calibration constant of any use. 

A proper calibration constant for any beamline geometry is the invariant Q. Thus, the Lupolen standard or any other semicrystalline polymer that previously has been calibrated in the Kratky camera can be made a secondary standard for a point-focus setup, after its invariant Q has been computed in absolute units - based on a measurement of its SAXS in the Kratky camera. 

Practical Value. The presented analytical expressions are very useful, predominantly for the analysis of the scattering from weakly distorted nanostructures. Because of their detailed SAXS curves, direct fits to the measured data return highly significant results (cf. Sect. 8.8.3). Nevertheless, some important corrections have to be applied [84], They comprise deviations from the ideal multiphase structure as well as thorough consideration of the setup geometry and machine background correction (cf. Sect. 8.8). 

In practice, either a pole figure has been measured in a texture-goniometer setup, or a 2D SAXS pattern with fiber symmetry has been recorded. In the first case we take the measured intensity g (pole figure. In the second case we can choose a reflection that is smeared on spherical arcs and project in radial direction over the range of the reflection. From the measured or extracted intensities I (orientation parameter by numerical integration and normalization... 

Fig. 12 Experimental setup for the in situ SAXS measurements. Depending on the type of experiments the capacitor, represented by two electrodes, can be temperature-controlled.

Fig. 1. Simultaneous DSC/WAXS/SAXS design. Experimental setup of the microcalorimeter cell in the time-resolved synchrotron X-ray diffraction environment The cell is positioned with sample-containing capillary perpendicular to the beam in such a way that the diffraction patterns are recorded in the vertical plane including the beam by one or two one-dimensional proportional detectors (Position Sensitive Linear Detector 1 and LD2). Counting Electronic (Counting Elect.), Nanovoltmeter (mVter), and Temperature Controller (T Ctrl) are all monitored by the same PC Computer (PC Comp.). Temperature-Controlled Bath (TCB) is kept at constant temperature (e.g., 20°C). Figure is adapted from Reference 3.

FIGURE 8.33 Schematic representation of the experimental setup used for in situ synchrotron SAXS measurements on the formation of mesoscopically ordered silicate-surfactant mesophases. The reactant solution is pumped through a thin quartz capillary and a diffractogram is recorded every 300 ms. The reaction is initiated by emulsifying a macroscopically phase-separated system of tetraethoxysUane and an aqueous phase, respectively. See text for details. 

Fig. 17a. Double monochromator camera for SAXS studies. The orientation of the reflecting planes is schematically indicated, b. Single monochromator camera for SAXS studies, c. Four-crystal monochromator setup...

Alternatively, an entire XAS spectra acquisition on heterogeneous catalyst samples can be obtained in the subsecond time regime (typically milliseconds although experiments with a time resolution in the microseconds regime have recently been attempted) in energy dispersive mode (EDE) (155). With this propensity for rapid data acquisition, XAS has proven to be an extremely popular method to develop multitechnique setups to study both catalyst solid-state self-assembly processes (when combined with XRD, WAXS, and/or SAXS) and reaction processes (eg, with IR, UV-Vis, and Raman) (18,148,154,161). 

Many combined setups have been developed in the past decades to study catalyst synthesis and reaction processes, many of which employ synchrotron radiation. Perhaps the first example of a successful combination of two techniques is X-ray absorption spectroscopy (XAFS) and diffraction, which was soon followed by the combination of SAXS and WAXS. Other examples in which two techniques have been combined to study systems under reaction include XAFS/FTIR, XRD/Raman, XAFS/UV-Vis, and a number of setups that use non-X-ray based radiation, such as UV-Vis/Raman, FTIR/UV-Vis, NMR/UV-Vis, and EPR/UV-Vis. A number of reports have recently appeared in which the number of combined techniques has been increased to three, including SAXS/WAXS/XAFS, UV-Vis/Raman/XAFS (148), and EPR/UV-Vis/Raman (218), and SAXS/WAXS/XAFS (219). In what follows, we illustrate the power three-in-one in situ spectroscopic methods to unravel chemistry of catalytic solids. 

Fig. 15. Panel A shows a schematic diagram of a combined saxs/waxs experimental station suitable for time-resolved experiments. In this case the sample is placed at the center of a curved waxs detector which is placed such that the saxs scattering pattern is not obscured. The sample-saxs detector distance can be varied depending on the required g-range needed. The two independent detector systems are synchronized by the use of a single time frame generator. In panels B and C the simultaneously collected saxs and waxs curves, produced with the setup shown in panel A, from a heating/cooling experiment on HDPE are shown.

Figure 2 Experimental setup of (a) SAXS with point-focusing optics (conventional X-ray and synchrotron sources) and of (b) microfocus SAXS (synchrotron sources).

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