Absorption of X rays

For an imperfect crystal, a would be cos220M- Azaroff et al (1974) discussed the possibility of an intermediate power of n in cos 20M between 1 and 2 for intermediate monochromator crystal states. This would apply if graphite is used, for instance, when tests for the mosaic character of the monochromator crystal would be needed. 

An X-ray beam passing through a material suffers absorption and its intensity is attenutated. The absorbed X-rays cause thermal heating and radiation damage we will discuss these in detail in section 6.5. In the context of the current discussion the derivation of F from E(hM) requires an absorption correction to be applied. The simplest situation is for the case of a spherical crystal (without a capillary) completely bathed in a uniform X-ray beam. In such a case all the reflections would be equally reduced in intensity. The situation of such a spherical crystal never exists in macromolecular crystallography. 

For a beam of monochromatic X-rays passing through an isotropic material the transmitted beam has intensity 

For a material consisting of a number of elements, N, the overall mass absorption coefficient [im is given by 

The mass absorption coefficient, /im, varies with wavelength according to the following relationship, in the absence of elemental absorption edges, 

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Ema data can be quantitated to provide elemental concentrations, but several corrections are necessary to account for matrix effects adequately. One weU-known method for matrix correction is the 2af method (7,31). This approach is based on calculated corrections for major matrix-dependent effects which alter the intensity of x-rays observed at a particular energy after being emitted from the corresponding atoms. The 2af method corrects for differences between elements in electron stopping power and backscattering (the correction), self-absorption of x-rays by the matrix (the a correction), and the excitation of x-rays from one element by x-rays emitted from a different element, or in other words, secondary fluorescence (the f correction). 

Absorption of x-rays by a powdered sample of soHd fat has been a useful method for determination of polymorphic character as discussed eadier. The a, and P forms may be distinguished however, interpretation is made more difficult because subsets of the P and P forms have often been encountered. Also, a fat may contain mixtures of polymorphic forms and properties may therefore be difficult to relate to the spectra. 

Physical Properties. The absorption of x-rays by iodine has been studied and the iodine crystal stmcture deterrnined (12,13). Iodine crystallizes in the orthorhombic system and has a unit cell of eight atoms arranged as a symmetrical bipyramid. The cell constants at 18°C (14) are given in Table 1, along with other physical properties. Prom the interatomic distances of many iodine compounds, the calculated effective radius of the covalently bound iodine atom is 184 pm (15). 

A consequence of absorption of X rays is the inner shell ionization of the absorbing atoms and the subsequent generation of characteristic X rays from the absorbing atoms, called secondary fluorescence, which raises the generated intensity over that produced by the direct action of the beam electrons. Secondary fluorescence can be induced by both characteristic and bremsstrahlung X rays. Both effects are compo-sitionally dependent. 

Both inner-shell (K and L) and outer-shell (M, N, etc.) electrons can be excited by the absorption of X rays and by the inelastic scattering of electrons. In either instance, at an electron binding energy characteristic of an element in a sample. 

The classical approach for determining the structures of crystalline materials is through diflfiaction methods, i.e.. X-ray, neutron-beam, and electron-beam techniques. Difiiaction data can be analyzed to yield the spatial arrangement of all the atoms in the crystal lattice. EXAFS provides a different approach to the analysis of atomic structure, based not on the diffraction of X rays by an array of atoms but rather upon the absorption of X rays by individual atoms in such an array. Herein lie the capabilities and limitations of EXAFS. 

Whenever the appropriate specimens can be prepared, this mode is normally the one preferred for trace-element analysis in geoscience, air polludon and atmospheric science, biology, medicine, water analysis, and forensic science. In this case, the ions pass through the specimen with negligible energy loss and there is minimal absorption of X rays. 

The absorption of x-rays influences their detection in two important and obvious ways Absorption on the way to the detecting medium reduces the measured intensity and is undesirable this includes absorption by the detector window. Conversely, absorption within the detecting medium produces the effect to be measured and is desirable. 

Three important detectors make use of the ionization, called here the initial ionization, that follows the absorption of x-rays by a gas and the ejection ol photoelectrons from the molecules involved. These photoelectrons subsequently ionize other molecules. The relatively large energy of the x-ray quantum thus leads to the production of a number of ion pairs, each consisting of an electron and a relatively immobile positive ion. if these ion pairs do not recombine, the extent of this initial ionization is determined by (and measures) the energy of the x-ray quantum. 

Both variations referred to above are due to the absorption of x-rays... 

Inasmuch as the thickness measurement depends on the absorption of x-rays by iron, the results of Figure 6-2 ought to be in accord with the known mass absorption coefficients of that element. Whether such accord exists can be determined by using the exponential absorption law in the form... 

It is convenient to use the absorption of x-rays (1.11) as a point of departure for the discussion of 7-ray absorption. According to Equation... 

Fortunately, some simplifications are possible. Carbon, nitrogen, and oxygen in tissue proteins are the elements principally responsible for the absorption of x-rays by the different biological structures. Further-... 

Slices of the body are irradiated from one side. X-ray detectors quantify the remaining intensity of the X-rays after passing through the various tissues. The X-ray tube and the detectors are rotating around the body. The data are used to calculate images of the corresponding slice which reflect the absorption of X-rays in a great number of pixels of an individual slice. 

Limitations are obvious if the diseased tissue does not differ from normal tissue or successfully treated tissue in respect of the above-mentioned criteria. Under these conditions, even a contrast agent with high absorption of X-rays is of no help. Another drawback is the short-lasting contrast which requires repeated injections if the diagnosis is missed during the first scan or if persistent visualization of a lesion is required during an interventional procedure. 

Figure 4.10. Absorption of X-rays as a function of photon energy E = hv by a free atom and by atoms in a lattice. The fine structure, due to the interference of waves...

In the case of thin samples described so far, the absorption of x-rays in the sample is negligible, and it is not necessary to apply any corrections for the slowing down of the particles or the absorption of X-rays. 

Absorption of X-ray radiation of energy well above the threshold for an X-ray transition will result in the ejection of a photoelectron since the initial unoccupied band stale to which the transition takes place will be above the vacuum level. The Kronig fine structure is due to oscillations induced in the absorption cross-section of the absorbing atom as a result of interference... 

In samples consisting of fine particles, not only is preferred orientation minimized, but there is also satisfactory averaging of the absorption process. Assuming that absorption of x-rays within each particle is 1%, the maximum acceptable particle size, fmax, for quantitative studies can be calculated using the following equation [62] ... 

The absorption of X-rays by a target is described by an exponential expression akin to the Beer-Lambert law (p. 357)... 

As illustrated in Fig. 7.15, the electromagnetic radiation measured in an XRF experiment is the result of one or more valence electrons filling the vacancy created by an initial photoionization where a core electron was ejected upon absorption of x-ray photons. The quantity of radiation from a certain level will be dependent on the relative efficiency of the radiationless and radiative deactivation processes, with this relative efficiency being denoted at the fluorescent yield. The fluorescent yield is defined as the number of x-ray photons emitted within a given series divided by the number of vacancies formed in the associated level within the same time period. 

In order to estimate the photoelectron yield from a chemisorbed layer we follow the approach of Henke (S), applied by Madey et al. (9), and modified by Carley and Roberts (10). A monoenergetic beam of x rays strike a surface at an angle 0 to the surface normal the photoelectrons, assumed to be generated in a layer of depth X and thickness dx, escape from the sample to a detector positioned at an angle with respect to the surface normal. The differential probability dP of absorption of x rays at depth X within the thickness dx is... 

The thin film approximation assumes that absorption of X-rays within the sample (and any second order efifeet ensuing from absorption) is negligible. It is a good approximation for many of the TEM samples. Within this approximation the detected intensity (Iac) for the analytical line (a) of element A is proportional to the number of generated X-rays (Gao) and the detection efficiency (Pao) for this line. 

The Fe EXAFS data from inactive aconitase and its Fourier transform are shown in Figure 6. EXAFS of metal complexes arises from the interference of outgoing photoelectron waves (generated from the absorption of X-rays by the Is electrons of the metal) with waves back-scattered from neighboring atoms. 

K EDGE ABSORPTION SPEGTRA. The absorption of x-rays in the vicinity of the K absorption edge of transition metals gives information on both oxidation state and coordination geometry of the central absorbing atom. The energy positions of various absorption features have been demonstrated to be correlated to the formal valence of V in an extensive series of oxides, vanadates and intermetallics (13"). 

Edge Spectroscopy (XANES) can be used to estimate the expected absorption energy of the anomalous atoms. Eor example, SGX has determined the energy that corresponds to the maximum absorption of X-rays by pure selenomethionine. This value is used for all experiments that utilize selenomethionine to determine the required phases. With this approach, the limited X-ray lifetime of protein crystals can be devoted to determination of diffraction. In addition to preserving crystals, this approach maximizes the time devoted to data-collection in high-throughput mode. 

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