New Developments in X-ray Focusing Techniques

In X-ray spectral analysis, the most widely used methods for resolving a heterogeneous beam of X-rays into a spectrum are focusing methods employing a bent crystal. In principle, these methods are divided into two groups: with a crystal operating “in transmission” and “in reflection” (Fig. 1).

In the first case, the reflecting planes of the crystal are crystallographic planes perpendicular to the plane of the crystal plate; in the second, they are parallel to it.

In X-ray structural analysis, for obtaining intense monochromatic beams, monochromators with a bent crystal, operating according to these same principles—

From Current Literature

As reflector crystals, as a rule, crystalline plates of quartz, mica, gypsum, topaz, and other minerals are used. To give such plates the required radius of curvature, they are bent in an elastically curved state in special crystal holders with corresponding radii of curvature. When it is necessary

Fig. 1.

a — Cauchois method; b — Johann method; \(\Phi\) — focus of the tube; \(K\) — crystal.

to change the radius of curvature of the bend of the crystalline plate*) it is necessary to have a whole set of crystal holders of various radii. However, there are a number of inconveniences in using crystal holders of this type, not to mention the fact that the very manufacture of crystal holders with an accurately cylindrical surface of radius \(200—1000\) mm is not a simple matter.

I. B. Borovskii\(^{1}\) and A. B. Gil’varg\(^{2}\) proposed, for bending a crystalline plate along a cylinder, to use the principle that was applied by E. S. Fedorov for making a drafting template with variable radius of curvature (“Fedorov’s ruler”). The principle is clear from Fig. 2: in theoretical mechanics this is the case of a beam resting on two supports, with a concentrated load at the ends (Fig. 2, a); in this case the middle part of the beam bends precisely along the arc of a circle. Thus, if a crystalline plate is secured between four pins, as shown in Fig. 2, b, and one pair of pins (for example, the outer pair) is made movable, then the radius of bending of the middle part of the plate can be varied smoothly.

Fig. 2.

With such an arrangement, focusing of X-rays is possible only by the “transmission” method. Buster, Ramachandran, and Lang\(^{3}\) proposed another device, based on the same principle of elastic bending, but allowing operation by the “reflection” method (Fig. 3). The pair of middle pins is replaced by a movable clamp, while the outer pins are made stationary. Such a device is convenient for use in X-ray structural analysis as a monochromator, especially when using high-aperture (focusing) cameras of the Bolin or Boser\(^{4}\) type for X-ray photographs of powders in monochromatic radiation.

*) The resolving power of the instrument and the radius of the focusing circle \((R_{\text{foc}})\) depend on the bending radius \((R_{\text{bend}})\).

Another example of abandoning focusing methods that have become routine is the use of reflection from oblique planes of a crystal, i.e., crystal planes situated at an angle to the plane of the plate and not perpendicular (Fig. 1, a) or parallel (Fig. 1, b) to it, as is usually done. For purposes of X-ray spectral analysis this was proposed by V. N. Protopopov^5 as a means of eliminating the shortcomings of the Johann method at small angles of reflection, consisting in a sharp defocusing of the spectral line with decreasing angle of reflection and in an additional broadening of the line caused by the oblique incidence of the rays on the film (line \(\lambda_1\) in Fig. 1, b). When reflection from oblique planes is used (Fig. 4), the entire spectrum is rotated by \(15—20^\circ\), and the shortcomings indicated above are eliminated.

Fig. 3.

This method is especially convenient in monochromators used for obtaining strictly monochromatic beams in the study of the scattering of X-rays by a substance at small scattering angles. In this case, owing to the asymmetric arrangement of both focal points \(F_1\) and \(F_2\) (Fig. 4) relative to the crystal, it is possible at the same time to use small distances: tube focus—crystal, thereby ensuring a high luminosity of the method, and large distances: specimen under investigation—film \((D)\), which makes it possible substantially to increase the resolving power of the instrument at the same scattering angle \(\varphi\). At the focal point \(F_1\) (for the given wavelength) a slit \(Щ\) should be placed, the purpose of which is to pass rays of only those directions that can be reflected from the crystal by virtue of the Bragg–Wulff condition; this must ensure good monochromatization of the beam without a noticeable decrease in the luminosity of the arrangement.

Fig. 4.

A third innovation is the use of bent reflecting single-crystal plates made of metals. In particular, Cauchois, Tiedema, and Burgers^6 carried out experiments on the use, for X-ray spectrographs (both “transmission” and “reflection”), of aluminum single crystals* bent plastically over a section of a cylindrical surface with radii of 200 and 400 mm. After plastic deformation the crystalline aluminum plate is subjected to recrystallizing annealing (630°, 24 hours) in order to restore the regularity of the lattice and remove stresses; as a result, the plate, bent to the required radius, proves to consist of small blocks whose reflecting crystallographic planes are tangent to the circle of bending (in “reflection” methods) or parallel to the radial planes (in “transmission” methods). When single-crystal aluminum plates with reflecting planes (111) were used, the authors obtained much more intense (of the order of 10:1) spectral lines for Cu-

*) The method of obtaining large (several square centimeters in area) single-crystal aluminum plates of prescribed orientation was described earlier by one of the authors^7.

and Mo radiation than when using elastically bent mica plates; the broadening of the lines when aluminum is used is only slightly greater than for mica.

B. Ya. Pines^8, for his part, proposed using plastically deformed single crystals of zinc (and rock salt) for application in monochromators. He designed a high-luminosity x-ray monochromator with focusing in two planes, i.e., one that brings an x-ray beam diverging from one point back to a point (Fig. 5). For this purpose the reflecting planes in the crystal must have, as their envelope, a surface of double curvature, which in principle cannot be achieved by elastic bending. After matrices and punches with surfaces in the form of a section of a torus have been made, a single-crystal zinc plate is pressed between them at room temperature without subsequent annealing; rock-salt crystals are pressed at a temperature of 680°. The elimination of the divergence of the monochromatic beam in the second direction (vertical in Fig. 5), which is inevitable when bending along a cylinder, by giving the plate double curvature, and the possibility of obtaining very small bending radii make B. Ya. Pines’s monochromators very high-luminosity. For Cr radiation, zinc plates with an area of several square centimeters and a thickness of 1–1.5 mm were bent with $\rho_1 = 60$ mm and $\rho_2 = 14$ mm, which ensured the convergence of the beam almost to a point at a distance of only 30 mm from the crystal; this is especially important for the very soft radiation of chromium.

Fig. 5.

The use of such a monochromator is most expedient in combination with an x-ray tube having a point focus, as B. Ya. Pines does.

Yu. A. Bagaryatskii

CITED LITERATURE

1. I. B. Borovskii, DAN 72, 485 (1950).
2. A. B. Gil’varg, DAN 72, 489 (1950).
3. W. A. Wooster, G. N. Ramachandran and A. Lang, J. Sci. Instr. 26, 156 (1949).
4. R. M. Bozorth and E. F. Haworth, Phys. Rev. 53, 538 (1938).
5. V. N. Protopopov, Report at the Third Conference on the Application of X-rays to the Study of Materials. Abstracts of reports, USSR Academy of Sciences Press, 1950, p. 106.
6. I. Cauchois, T. J. Tidema et W. G. Burgers, Acta Cryst. 3, 372 (1950).
7. T. J. Tidema, Acta Cryst. 2, 261 (1949).
8. B. Ya. Pines, Collection dedicated to the 75th anniversary of Academician A. F. Ioffe, USSR Academy of Sciences Press, 1950, p. 448.