Compton-Modified Scattering

In order to determine the natural structure of the Compton modified line it is necessary to first minimize an experimental cause for the breadth of the line which is ordinarily superposed upon the natural breadth so as to mask the latter. This cause is the unavoidable inhomogeneity of scattering angle. The x-radiation incident upon the scattering material... 

Radiation so scattered is called Compton modified radiation, and, besides having its wavelength increased, it has the important characteristic that its phase has no fixed relation to the phase of the incident beam. For this reason it is also known as incoherent radiation. It cannot take part in diffraction because its phase is only randomly related to that of the incident beam and cannot therefore produce any interference effects. Compton modified scattering cannot be prevented, however, and it has the undesirable effect of darkening the background of diffraction patterns. 

The scattering just discussed, whose amplitude is expressed in terms of the atomic scattering factor, is coherent, or unmodified, scattering, which is the only kind capable of being diffracted. On the other hand, incoherent, or Compton modified, scattering is occurring at the same time. Since the latter is due to collisions of quanta with loosely bound electrons, its intensity relative to that of the... 

Placement of the monochromator in the diffracted beam has the advantage of suppressing background radiation originating in the specimen, such as fluorescent radiation and incoherent (Compton modified) scattered radiation. For example, if a steel specimen or any iron-rich material is examined with copper radiation in an ordinary diffractometer, the background due to fluorescent Fe K radiation will be unacceptably high. But if a monochromator is added and oriented to reflect only Cu Aa, the background is reduced practically to zero, because the fluoresced Fe Kol and Fe K(i do not enter the counter. A monochromator may therefore... 

These effects, however, are all very weak and are masked by the other forms of diffuse scattering which are always present. As a result, the details shown in Fig. 13-9 are never observed in an ordinary powder pattern made with filtered radiation. To disclose these details and so learn something about the structure of the solid solution, it is necessary to use strictly monochromatic radiation and, preferably, single-crystal specimens, and to make allowances for the other forms of diffuse scattering, chiefly temperature-diffuse and Compton modified, that are always present. 

The beam of secondary radiation issuing from the sample consists largely of fluorescent radiation, but there are some other weak components present as well. These are coherent scattered radiation, coherent diffracted radiation, and incoherent (Compton modified) radiation. These components appear as a background on which the spectral lines are superimposed. This background is normally low (see Fig. 15-3), but it may become rather high if the sample contains a large proportion of elements of low atomic number, because the sample will then emit a large amount of Compton modified radiation. 

The scattering of x-rays discussed above is elastic, in the sense that there is no transfer of energy from the photon to the electron, and therefore the scattered x-ray retains the same wavelength. The scattering is also coherent, because the phase relationships between the incident and scattered rays are maintained so that interference phenomena can occur among the scattered rays. There is, however, another mechanism by which the electrons scatter x-rays, and this is called the Compton-modified scattering. This is best explained in terms of the particle nature of the x-rays. 

Figure 1.8 Geometry of the Compton-modified scattering. The electron, initially at rest, moves away at velocity v after having been struck by an x-ray photon of energy hv and momentum h/a.

Figure 1.9 Plot of the Compton-modified scattering intensity /compton for a carbon atom and the square of the atomic scattering factor f(s) of carbon.

Note that the incoherence of the Compton-modified x-ray scattering occurs by a mechanism that is very different from what is considered here. The Compton-modified scattering is incoherent because the phase coherence is lost in the inelastic scat-... 

Compton Scattering. It is difficult to eliminate the Compton-modified x-ray scattering reliably by experimental means, because the wavelength shift of the modified from the coherent scattering is rather small, especially at small scattering angles. The preferred practice is to include all the Compton-modified scattering in the measured intensity and then subsequently to subtract the Compton-modified intensity calculated theoretically from it. 

In the case of a crystalline phase in an amorphous matrix, a rough measure of their ratio can be obtained if the compositions are known. This is accomplished by summing the powder diffraction line intensities, subtracting the amorphous (background) intensity, and correcting for Compton-modified scattering. The fact that there is a continuous spectrum of order from well-crystallized to noncrystalline phases is an inherent limitation to the method. 

In modified scattering, the resulting increase in wavelength (Compton effect) is evidence that the x-ray photon acting as a corpuscle has been scattered by colliding with an electron to which it has lost momentum in the process. The Compton effect is not at present of practical importance in analytical chemistry. 

Figure 2.7 Spectra of x-rays scattered by graphite at different angles showing modified lines wider than primary P and displaced to the theoretical position M. (After COmpton and Allison, Ref. 1.)...

Finally, the Electron Compton Scattering method is a novel method, which employs an Electron microscope specially modified and an electron velocity analyzer,(fig. 3f). 

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