Primary X-ray beam

The primary X-ray beam is directed onto the solid surface in grazing incidence. The angle of incidence is kept below the critical angle at which total reflection occurs. The critical angle is given by... 

The cross-section of the primary X-ray beam is extended and not an ideal point. This fact results in a blurring of the recorded scattering pattern. By keeping the cross-section tiny, modern equipment is close to the point-focus collimation approximation - because, in general, the features of the scattering patterns are relatively broad. Care must be taken, if narrow peaks like equatorial streaks (cf. p. 166) are observed and discussed. The solution is either to desmear the scattering pattern or to correct the determined structure parameters for the integral breadth of the beam profile (Sect. 9.7). 

X-ray radiation wavelength—that is, 1/ X. When the crystal is rotated, the reciprocal lattice rotates with it and different points within the lattice are brought to diffraction. The diffracted beams are called reflections because each of them can be regarded as a reflection of the primary X-ray beam against planes in the crystal. 

Figure 2.9 Interaction of the primary X-ray beam with a solid sample. See text for discussion. (After Jenkins, 1974 Fig. 3-3. John Wiley Sons Limited. Reproduced with permission.)...

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.

It shall be assumed in this chapter that molecular arrangement in the bulk of solid explosives, and all amorphous and liquid explosives, has no preferred orientation direction. The diffraction patterns in this case are isotropic around the primary X-ray beam, and the vector quantity, x, can be replaced by its scalar magnitude. It is customary to speak of diffraction profiles, rather than patterns, when isotropy obtains and the diffraction profiles are derived by integration of the (circularly-symmetric) diffraction pattern over the azimuthal component of the scattering angle. 

Until 1977 no crystal structure analyses were known for highly reactive diacetylene monomers. Polymerization in the primary x-ray beam proceeds in these cases so rapidly that data collection on the monomer crystal is impossible. This experimental difficulty was overcome by carrying out the data collection at low temperatures. At 110 K the polymerization rate is sufficiently low to maintain a polymer content at below 5 percent during the time necessary to collect the data for an average structure. The first monomer crystal structure which was solved using this technique was PTS... 

FIGURE 1.14 Seen here is the hk0 zone diffraction pattern from a crystal of M4 dogfish lactate dehydrogenase obtained using a precession camera. It is based on a tetragonal crystal system and, therefore, exhibits a fourfold axis of symmetry. The hole at center represents the point where the primary X-ray beam would strike the film (but is blocked by a circular beamstop). Note the very predictable positions of the diffraction intensities. All the intensities, or reflections, fall at regular intervals on an orthogonal net, or lattice. This lattice in diffraction space is called the reciprocal lattice. 

Figure 6.11 Geometric construction of a total reflection fluorescence spectrometer. The incident angle is less than 0.1° so that the primary X-ray beam is totally reflected from the flat substrate. (Reproduced with permission from R. Klockenkamper, Total-Reflection X-ray Fluorescence Analysis, John Wiley Sons Inc., New York. 1997 John Wiley Sons Inc.)...

The EDS type of X-ray spectrometer is commonly included as a part of SEMs and TEMs. The reason for using EDS rather than WDS is simply its compactness. With EDS in an electron microscope, we can obtain elemental analysis while examining the microstructure of materials. The main difference between EDS in an electron microscope and in a stand-alone XRF is the source to excite characteristic X-rays from a specimen. Instead of using the primary X-ray beam, a high energy electron beam (the same beam for image formation) is used by the X-ray spectrometer in the microscopes. EDS in an electron microscope is suitable for analyzing the chemical elements in microscopic volume in the specimen because the electron probe can be focused on a very small area. Thus, the technique is often referred to as microanalysis. 

Figure 14.5 A circular conic section resulting from an orthogonal detector to primary X ray beam setting. On the left is a view perpendicular to the detector, on the right is a side view, showing the primary beam entering from the right. The primary and diffracted beams from the sample S intersect the detector on the detector plane. The primary beam intersects the detector at the centre of the circle. For clarity only one diffraction cone has been drawn. The distance from the sample to the detector along the primary beam is given by D. The detector coordinate system is denoted in x and y relative to the beam centre.

FIGURE 6.28 Effects in a sample irradiated with x-rays. The characteristic (fluorescence) emission is the desired analytical effect that needs to be separated from the other secondary emissions. The primary x-ray beam scatters coherently (without loss in energy) and incoherently (losing energy) and is recorded to a small amount in the detector. The characteristic fluorescence beam not only undergoes absorption by other metals in the sample but may also be excited by secondary or tertiary fluorescence from other elements. 

X-ray Fluorescence Spectroscopy is an analytical method for automated sequential analysis of major and trace elements in metals, rocks, soils, and other usually solid materials. The technique is based on the absorption of a primary x-ray beam that leads to secondary fluorescence that is specific for the atoms in a compound. 

S.R. often for the first time opens up the possibility of performing time resolved measurements. It shall be emphasized, however, that the synchrotron light could produce artifacts, too. The question of molecular degradation due to the intensive primary X-ray beam must be carefully noticed, especially when the measurements are carried out at elevated temperatures above glass transition. 

Penetration of an incident low energy electron beam (say 100 eV) is only a few layers, unlike X rays with radiation so penetrating that the surface region has negligible effect on the diffraction pattern. A primary X-ray beam is hardly attenuated after passage through thousands of crystal planes. In LEED, the interaction with the uppermost layers is intense, and a diffraction pattern corresponds to interference of waves scattered by superficial planes only. Reciprocal space is diperiodic for slow electron diffraction from a regular surface, and is modulated in... 

X-ray fluorescence spectrometry is based upon the excitation of a sample by X-rays. A primary X-ray beam excites secondary X-rays (X-ray fluorescence) which have wavelengths characteristic of the elements present in the sample. The intensity of the secondary X-rays is used to determine the concentrations of the elements present by reference to calibration standards, with appropriate corrections being made for instrumental errors and the effects the composition of the sample has on its X-ray emission intensities. Alternatively, the X-rays may be detected without... 

The quantity of both, fluorescent photons and Auger electrons, is directly related to the number of core holes created, i.e., to the absorption, and is thus a direct measure of the absorption. In cases where the usual X-ray absorption measurement in transmission is not feasible, determination of the intensity of X-ray fluorescence or of Auger electrons as a function of the energy of the primary X-ray beam will give absorption spectra. 

The primary X-ray beam is first monochromatized using a double-crystal monochromator, usually made of Si or Ge single crystals. The intensities Zq and Ii of the X-ray beam before and behind the sample are determined using ionization chambers. To detect instabilities in the energy scales of subsequent measurements, a reference sample that exhibits an edge in the scanned region can be measured simultaneously using a third ionization chamber. 

The value of p at a given point (x,y,z) in the unit cell depends directly upon the measured intensities / oc The intensities, in turn, depend upon the relative position of all atoms in the unit cell, but also upon the exposure time, the intensity of the primary X-ray beam, the size and shape of the crystal, etc., thus making the results of the experiment accurate only in a relative and not an absolute way. This means that without proper scaling the electron density as determined by the X-ray diffraction experiment is very hard to interpret. In order to assign meaningful dimensions like electrons per cubic Angstrom to the density values, the measured intensities (or F values in the. hkl file) have to be scaled properly. This scaling... 

Wavelength-dispersive XRF instramentation is almost exclusively used for (highly reliable and routine) bulk-analysis of materials, e. g., in industrial quality control laboratories. In the field of energy-dispersive XRF instrumentation, next to the equipment suitable for bulk analysis, several important variants have evolved in the last 20 years. Both total reflection XRF (TXRF) and micro-XRF are based on the spatial confinement of the primary X-ray beam so that only a Hmited part of the sample (+ support) is irradiated. This is realized in practice by the use of dedicated X-ray sources. X-ray optics, and irradiation geometries. 

The collimated primary X-ray beam on the left is partially reflected on the different lattice planes of the crystal at an angle Q. Addition of the multitude of different secondary (diffracted) beams leads to the interference. Only if A, shown at the bottom, is a multiple n... 

Fig. 27. 1) = X-ray tube 2) = Primary X-ray beam 3) = Sample 4) = Fluorescence radiation 5) = Collimator 6) = Analyzer crystal 7) = Receiver...

The specific hazards of analytical X-ray equipment can include exposure to an intense, localized primary X-ray beam, exposure to diffracted and/or scattered portions of the primary X-ray beam (includes X-ray leakage), and the high voltages used in generating the X-ray themselves. 

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