Monochromatic beam

For this calculation, let us assume a simple case in which a suitable monochromatic beam of intensity /x falls perpendicularly upon unit area (1 square centimeter) of a monolayer of cobalt atoms resting upon a transparent substrate. The first term in Equation 4-9, A I, is given by... 

The assumption implicit above, that the x-ray source delivers a monochromatic beam of wavelength 1.00 A, is unrealistic. It will be discussed later. 

To summarize Filtering is an effective way of producing intense monochromatic beams, but it is severely limited because it cannot be used at all wavelengths and cannot achieve high spectral purity at any wavelength. The analysis of a spectrum, that is, the selection of a line and the measurement of its intensity, requires Bragg reflection. 

Fig. 4-9. This diagram shows the intensity variation with angle for a rock salt crystal in the region near the Bragg angle, 0q, for an incident monochromatic beam. The area under the mosaic crystal curve could be thirty times greater than the ideal. (After Renninger, Z. Krist. 89, 344.)...

The following generalization, though imperfect, is justified as a means of orienting the reader new to the field. Polychromatic beams are intense, complex, but require little equipment if the y are to be used in absorptiometry. Monochromatic beams are weak, simple, and demand more equipment if they are to be obtained from an x-ray tube for this use. 

The reduction in intensity concomitant upon the monochromatization of a polychromatic beam depends, of course, upon how nearly monochromatic the beam is made usually, however, the intensity will be reduced by about 3 powers of ten (4.5). Another imperfect generalization is that polychromatic beams are susceptible of instantaneous intensity measurement whereas monochromatic beams must be integrated (4.5). 

If the equipment required for absorptiometry with monochromatic beams is at hand, this method should be tried whenever instantaneous readings are not required. The simplicity of the experimental results is a powerful argument for the method. 

The relationships valid for absorptiometry with monochromatic beams are analogous to those in Chapter 3 (Equations 3-1, 3-2, 3-3). With such beams, there is generally no need to worry about an effective wavelength, about filtration of the beam, or about difficulties resulting... 

Absorptiometry with monochromatic beams subdivides logically into (1) simple absorptiometry, which is not generally specific and yields much the kind of information described in Chapter 3 for absorptiometry with polychromatic beams and (2) differential absorptiometry across an absorption edge,2 which is in principle specific for every element. 

For the purposes of analytical chemistry, four kinds of monochromatic beams need to be considered. (The quotation marks are to remind the reader that the beams under discussion are not always truly monochromatic.) Three kinds of beams—those produced by Bragg reflection (4.9), filtered beams (4.6), beams in which characteristic lines predominate over a background that can be neglected— will be discussed later ( 6.2). The fourth kind of beam contains monochromatic x-rays that are a by-product of our atomic age and that promise to grow in importance they are given off by radioactive isotopes. These x-rays must not be confused with 7-rays (11.1), which also originate from radioactive atoms but which differ from x-rays because the transformation that leads to radiation involves the nucleus. 

The relationship between g, and k must reflect the fact that nickel is being used to determine / . As monochromatic beams arc being used, thP matter ma be ignored. With polychromatic beams, it might need to be taken into account. 

Glocker and Frohnmayer determined the characteristic constant c for nine elements (Reference 2, Table 4) ranging in atomic numbers from 42 (molybdenum) to 90 (thorium). They proved that identical results could be obtained with the sample in the primary (polychromatic) or in the diffracted (monochromatic) beam. The method was applied with good results to the determination of barium in glass of antimony in a silicate of hafnium in the mineral alvite and of molybdenum, antimony, barium, and lanthanum in a solution of their salts—for example, 5.45% barium was found on 90-minute exposure by the x-ray method for a glass that yielded 5.8% on being analyzed chemically. 

The determination of chlorine in resins is an example of a simple, industrially important determination of a light element. The same determination can be carried out successfully by absorptiometry with polychromatic (3.8) or monochromatic beams (5.3), but x-ray emission spectrography must be regarded as the preferred method unless the matrix (all the sample except the chlorine) varies little in composition, or unless a suitable standard sample is available for comparison with the unknown. 

As might have been expected from the interrelationship of the various x-ray instruments (Figure 4-14), the XRD-5 D/S is easily converted into a spectrophotometer for absorptiometry with monochromatic beams (Chapter 5). To make this conversion, in principle, it is only... 

Broadening, of monochromatic beams by crystals, 115, 116, 118 of pulse-size range, 47 Bromine, as internal standard in tungsten analysis, 194-196 determination, by absorption-edge method, 138-142... 

Crystal broadening of monochromatic beams, 115, 116, 118 Crystal reflection of x-rays, efficiency, 116... 

XRD on battery materials can be classified as powder dififaction, a technique developed by Peter Debye and Paul Scherrer. In powder dififaction the material consists of microscopic crystals oriented at random in all directions. If one passes a monochromatic beam of X-rays through a fiat thin powder electrode, a fraction of the particles will be oriented to satisfy the Bragg relation for a given set of planes. Another group will be oriented so that the Bragg relationship is satisfied for another set of planes, and so on. In this method, cones of reflected and transmitted radiation are produced (Fig. 27.2). X-ray diffraction patterns can be recorded by intercepting a... 

---