Soller slits

A beam from an actual sample will require a more elaborate slit S3rstem for collimation if the sample is broad. The Soller slit (Figure 4-7), a stack of thin parallel plates, is such a system. The reasoning that supports this construction is as follows. Were the sample a point or a line source, a slit between sample and crystal or a slit between crystal and detector would be enough for satisfactory collimation. With a two-dimensional sample, both slits would be needed to get this done. But this arrangement is wasteful of emitted intensity because the detector sees the sample as a line source. To use all the sample area effectively, a system of parallel slits is needed. To eliminate the divergent rays in such a system, the slits must be extended in the direction of the beam, and this leads to the parallel-plate construction in the Seller slit system. 

Fig. 4-7. Diffraction of a divergent beam from a broad sample by a large crystal. Collimation of this beam requires the Soller slit system shown. This system is equivalent to simple slits at A and B with separators provided to make certain that only parallel rays leave the exit slit.

Spectrographs sometimes have two Soller slits. The first, whose function it is to collimate the desired x-ravs, is then placed between crystal and detector. The second and wider-angled slit is interposed... 

In this second class of spectrometers, X-ray radiation emitted by the sample, after it has been filtered by a sheet collimator (Soller slits), impacts on a crystal analyser... 

Figure 13.9—Schematic of a sequential, crystal-based spectrometer and the spectrum obtained using the sequential method with an instrument having a goniometer. The Soller slit collimator, made of metallic parallel sheets, collimates the primary X-ray beam emitted by a high power source (SRS 300 instrument, reproduced by permission of Siemens). A typical spectrum of an alloy, obtained by an instrument of this category, having an LiF crystal (200) with 26 angle in degrees as the abscissa and intensity in Cps as the ordinate). Model Philips PW2400 Spectrum, reproduced with permission of VALDI-France.

Fig. 63. X-ray optical system of a Geiger-counter diffractometer by Xorth American Philips Co. Inc. A, X-ray tube target B, Soller slits <7, scatter slit D, specimen Et diffractometer axis F, Soller slits G> counter entrance slit.

The mineralogical composition of all the samples included in the study was determined by XRD, using the same powdered sample prepared for XRF analysis. Measurements were performed using a PANalytical X Pert PRO alphal powder diffractometer (radius = 240 mm) using the Cu Ka radiation (A. = 1.5418 A), with a working power of 45 kV - 40 mA. The incident beam was passed through a 0.04 radians Soller slit, and the diffracted beam passed through a second slit. Moreover, the diffracted beam was Ni filtered. An X Celerator... 

X-Ray diffraction data of atenolol are presented in Table 7 (5) The diffraction spectrum was produced by monochromatic radiation from the CuK line (1.542 a) which was obtained by excitation at 55 kV and 2o mA. Recording conditions were as follows. Optics detector slit o.2° M.R. soller slit, 5° beam slit, o.ooo7 Ni filter, 3° take off angle. Goniometer scan at 2°, 2o/min. Detector amplifier gain 16 coarse, 9 1 fine. Scintillation co-... 

In its simplest form, direct X-ray scatter imaging relies on the use of simple mechanical collimation elements such as pinholes, Soller slits and the like to determine the origin coordinates of a scattered photon. They all achieve spatial resolution of the scatter field at the detector by restricting the angular range over which radiation can reach the detector. Examples of direct tomography in the explosives detection field include the... 

Figure 2.10. The schematic showing how the x-ray beam is collimated by using both the divergence and Soller slits (top). The beam, collimated in-plane by the divergence slit, is further collimated axially by the Soller slits. The coordinates in the middle of the drawing indicate the corresponding directions. The bottom part of the figure illustrates the analogy of Eq. 2.6 with Eq. 2.5.

A proper configuration of the instrument and its alignment can substantially reduce peak asymmetry but unfortunately, they cannot eliminate it completely. The major asymmetry contribution, which is caused by the axial divergence of the beam, can be successfully controlled by Soller slits especially when they are used on both the incident and diffracted beam s sides. The length of the Soller slits is critical in handling both the axial divergence and asymmetry however, the reduction of the axial divergence is usually accomplished at a sizeable loss of intensity. 

The slit box located between the x-ray source and the sample Figure 3.12, left) contains two divergence slits, which control the aperture and the divergence of the incident beam in the vertical plane. The two divergence slits are separated by a set of Soller slits, which limit the divergence of the incident beam in the horizontal plane. The sample holder here is an automatic four-specimen sample changer. 

The second slit box is located on the detector arm between the sample and the detector. The slit nearest to the sample serves as a scatter slit. It is followed by another Soller slit and a receiving slit positioned just before the detector. The detector in this case is a solid-state detector, which is cooled by a built-in Peltier refrigerator enabling to adjust and maintain the detector sensitivity at extremely narrow width to allow only x-ray photons of specific energy to be registered. Monochromatization of the diffracted x-ray beam is, therefore, achieved electronically rather than by physical means (e.g. by a P-filter or a crystal monochromator), which increases the registered diffracted intensity by eliminating losses in the filter or in the monochromator. 

The beam diffracted by the specimen passes through another Soller slit and the receiving slit F before entering the counter (Fig. 7-8). Since the receiving slit defines the width of the beam admitted to the counter, an increase in its width will increase the maximum intensity of any diffraction line being measured but at the expense of some loss of resolution. On the other hand, the relative integrated intensity of a diffraction line is independent of slit width, which is one reason for its greater fundamental importance. ... 

The main difficulties encountered in numerical calculations of the instrumental function are associated with the wide range of instrumental parameters [diffractometer radius, sizes of X-ray source, sample, receiving slit, using (or not using) Soller slits in incident and/or diffracted beam, using (or not using) monochromator], the contributions of some of which differ by three orders of magnitude. 

There are two different approaches for calculation of the instrumental function. The first is the convolution approach. Proposed more than 50 years ago, initially to describe the observed profile as a convolution of the instrumental and physical profiles, it was extended for the description of the instrumental profile by itself According to this approach the total instrumental profile is assumed to be the convolution of the specific instrumental functions. Representation of the total instrumental function as a convolution is based on the supposition that specific instrumental functions are completely independent. The specific instrumental functions for equatorial aberrations (caused by finite width of the source, sample, deviation of the sample surface from the focusing circle, deviation of the sample surface from its ideal position), axial aberration (finite length of the source, sample, receiving slit, and restriction on the axial divergence due to the Soller slits), and absorption were introduced. For the main contributors to the asymmetry - axial aberration and effect of the sample transparency - the derived (half)-analytical functions for corresponding specific functions are based on approximations. These aberrations are being studied intensively (see reviews refs. 46 and 47). 

The effects of misalignment and Soller slits can also be included in the calculation as well as a different diffractometer geometry. For the case of the diffractometer equipped with a crystal monochromator it is also possible to provide a solution in the context of the proposed method. For reasons of space, we outline here the possible treatment of these effects without going into details. 

For the case of Soller slits in the incident beam, the condition of rays passing through the slits is given by the inequality ... 

For Soller slits in the diffracted beam each point A2 on the sample sees only parts of the receiving slit (Figure 6.22). 

Therefore, instead of one full receiving slit, several (the number depends on the positions and geometrical parameters of the Soller slits) smaller receiving slits should be considered. The corner points of these new sub-receiving slits for given Soller slits depend on the position of point A2 and angle (p and can be... 

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