Perfect crystals monochromators

The channel-cut monochromator is the simplest type employed experimentally. A channel is cut in a perfect crystal (e.g.. Si) to provide two parallel reflecting surfaces that have a particular crystal plane [e.g., the Si (220)] parallel to the surface. The Bragg condition is used to select a particular wavelength and the reflected beam emerges parallel to the incident beam but is vertically displaced by 2D cos d, where D is the distance between the two faces and 0 is the angle between the beam and the Bragg planes. The accuracy of data collected using channel-cut crystal monochromators may be limited due to harmonic con-... 

Even though the diffracted beam is not perfectly monochromatic at any specific angle due to various imperfections (defects, distortions, stresses, etc.) present in the crystal monochromator, the separation of Ka and Kp wavelengths is large enough so that the elimination of the Kp and nearly all... 

A higher-resolution setup exploits a perfect-crystal pre-sample monochromator (Figure 2.11) to remove the K0C2 radiation. To achieve this and maintain a reasonable X-ray intensity, the monochromator crystal is curved so as to satisfy... 

Figure 2.11 Bragg Brentano geometry with a pre sample monochromator. A near perfect crystal, e.g. quartz or germanium, is required to separate Kai and Ka2.

Figure 5.6 The single perfect crystal as monochromator for use with SR (a) flat crystal (b) curved crystal for minimum reflected dXIX (Guinier setting) (c) curved crystal at overbend (d) finite source size contribution to 6X/X in the reflected beam (monochromator at Guinier setting). From Helliwell (1984) and reproduced with permission of the Institute of Physics.

The effect of the degree of perfection of monochromator crystals on the basic characteristics of focusing monochromators, and particularly on the intensity of the reflected beam, has not received its due attention in the literature. For example, it has been considered [5] that tubes with small focus dimensions and the most perfect crystals must be used to obtain a narrow intense beam of monochromatic radiation. However, measurements made on quartz of different degrees of perfection [6] showed that the maximum intensity of a monochromatic beam is observed for "average" degrees of perfection of the monochromator crystal. 

The reflection intensity is zero for rays for which the angle a is higher in absolute value than the integrated width of the reflection from the monochromator crystal. The effective width of the focus area whose intensity will make a contribution to the reflected beam will evidently decrease with decreasing integrated width of the reflection curve, i.e., the more perfect the monochromator crystal. Consequently, to obtain the maximum intensity for the reflected monochromatic beam, it is necessary to establish a definite optimum relationship between the effective width of the focus and the integrated width of the reflection curve of the monochromator crystal. 

If the monochromating crystal is bent but not cut, some concentration of energy will be achieved inasmuch as the reflected beam will be convergent, but it will not converge to a perfect focus. 

Figure 2.10 Bragg Brentano geometry with a diffracted beam monochromator. The crystal is usually graphite, which has a low degree of crystalline perfection, and hence a large acceptance angle (tenths of a degree). Thus a flat crystal is adequate.

For some specific applications, they can be associated with traditional monochromators. An illustration of a typical configuration of this kind is shown in Figure 2.16a. A parabohc artificial crystal is irradiated by a divergent source, and the beam diffracted by this element is then diffracted by a monochromator comprised of two or four plane crystals [SCH 95]. The beam resulting from this system, sometimes referred to as a hybrid monochromator, is perfectly monochromatic and much more intense than in the absence of a parabolic artificial crystal. Note, however, that this beam is much wider than the initial beam produced by the source. Therefore, this monochromator is only used for particular types of configurations and these hybrid monochromators are essentially used for certain studies of epitaxial thin films [STO 97]. 

The raw data were corrected for Lorentz and polarization effects, including that due to incident beam monochromatization (assuming the graphite monochromator crystal to be half perfect and half mosaic in character). Standard deviations were assigned to individual reflections by the formula... 

There are quite a number of possible configurations of perfect single crystals as monochromators. Detailed reviews have been given by Hart (1971), Barrington-Leigh and Rosenbaum (1974), Beaumont and Hart (1974), Bonse, Materlik and Schroder (1976), Hastings (1977) and Kohra et al (1978). Witz (1969) reviewed the use of monochromators for conventional sources of X-rays. Underwood and Turner (1977) discussed the use of differently shaped materials for producing specific curvature optical elements. 

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