FROM THE CURRENT LITERATURE

NEW IDEAS IN X-RAY SPECTROSCOPIC TECHNIQUES

Works by a number of investigators have very recently demonstrated the possibility of successfully applying X-ray spectral methods in a whole series of areas of physical research. In addition to the use of these methods for quantitative and qualitative analysis, for solving a number of problems in the theory of aggregate states and in the physics of X-rays, the possibility of successfully using X-ray spectral methods to study the mechanism of deformation has apparently been proven in recent times.^1 The diversity of directions in which the application of spectral methods has proved fruitful has determined the abundance of new ways of improving spectroscopic technique that have characterized the last five years.

In a number of reviews,^2 which appeared several years ago, the fundamental questions connected with the use of spectrographs operating on the Johann or Cauchois principle—whose very successful structural design is due to Siegbahn—are discussed in detail. Let us point out only, in addition, the works of Borisov and Fogel,^3 who described a spectrograph of their own design, somewhat different from Siegbahn’s. In this spectrograph the crystal holder is not a separate part, and therefore it is not necessary to center it specially with respect to the cassette. However, this indisputable advantage of the spectrograph in express surveys cannot be regarded as decisive in laboratory practice.

Spectrographs using a plane crystal

Despite the great successes in the field of spectroscopy with a bent crystal, in solving a number of physical problems the application of this method proves impossible. The problem of creating high-luminosity spectrographs providing greater intensity without the bending of the reflecting crystal, which is impermissible in a number of cases, was, as far as we know, first posed and acutely solved by Fankuchen.^4 Using an ordinary Bragg spectrograph, Fankuchen proposed cutting the crystal that reflects the X-rays so that its surface should be at an angle to the reflecting planes. In this case the reflected beam makes a smaller angle with the surface of the crystal than the incident beam. It is easy to calculate the intensity of the reflected beam. If $\Phi$ is the angle formed by the surface of the crystal with the reflecting planes (Fig. 1), and $\theta$ is the Bragg angle for the incident rays, then the ratio of the widths of the incident and reflected beams

Fig. 1. Path of rays in a spectrograph by Fankuchen’s method.

is given by the formula

\[ \frac{W_0}{W_{\Phi}}=\frac{\sin \alpha}{\sin \beta}, \]

where \(\alpha=\theta+\Phi\) and \(\beta=\theta-\Phi\).

Fankuchen showed that, after allowance for absorption, the effective gain in intensity with his method, as compared with the ordinary Bragg method, is given by the expression

\[ P=\frac{2\sin \alpha}{\sin \alpha+\sin \beta}, \]

which, for \(\beta=0\) or \(\Phi=0\), attains the maximum value, equal to 2.

In an analogous way, work was carried out by D. Gogoberidze\(^{5}\). The author arranges the apparatus in such a way that the axis of the spectrograph slit is parallel to the surface of the anticathode, which, in the case of Hadding tubes, has the form of a circle 2–3 mm in diameter, observed through a window in the form of a strongly elongated ellipse. Such an arrangement of the slit should therefore, in the author’s opinion, lead to a more rational use of the focal spot.

In Fig. 2 we give a schematic view of a spectrograph designed at the L. Kh. T. I., with a horizontal axis of rotation. To further increase the intensity, the author uses a spectrograph whose reflecting crystal is cut parallel to various crystallographic directions having a small interplanar spacing. In the case of NaCl crystals cut along the rhombic dodecahedron, LiF cut along the (110) plane, and galena crystals, the author was indeed able to obtain a considerable gain in intensity, making it possible, for example, for galena crystals to reduce the required exposure by a factor of 6–7 in comparison with rock salt reflecting from one of the planes (100), (010), or (001). Owing to this gain in intensity it proved possible to proceed to photographing higher orders of reflection with increased resolving power.

Fig. 2. Spectrograph with a flat crystal and a horizontal axis

a—diaphragm limiting the primary beam, b—crystal holder, c—cassette, d—horizontal axis of the spectrograph, fixed immovably on the stand (e)

Spectrographs with bent crystals

a) Spectrograph with so-called horizontal focusing

Since the appearance of the first works of Iogann and Koshu, who developed the geometrical conditions of focusing in spectrographs with a bent crystal, the efforts of investigators have proceeded, on the one hand, toward

directions of creating designs most suitable for solving particular physical problems, and, on the other hand, toward creating a universal X-ray spectrograph permitting a considerable wavelength interval to be covered.

Without touching on the special designs described by various authors,^6 let us dwell on the recent work of Ingelshtam,^7 who has described his universal spectrograph with high luminosity. The author sets himself the goal of creating a universal X-ray spectrograph, convenient in operation and capable of covering a wavelength region up to 2,500 X.E. The latter includes

Fig. 3. Schematic representation of reflection by the methods of Cauchois and Johann

a—Cauchois method, b—Johann method

Fig. 4. Reflecting planes of quartz used in Ingelshtam’s universal spectrograph

P—plate

the entire K-spectrum of elements with atomic number exceeding 24. It is known that in the region 1100–1500 X.E. the geometrical conditions of recording make the use of Cauchois-type spectrographs, working on the principle of “external reflection,” more applicable. On the other hand, in the region of longer wavelengths it is preferable to use the Johann method (Fig. 3). In the first of these methods a system of planes perpendicular to the surface of the bent crystal is used; in the second, one parallel to it. The author sets himself the problem of designing a universal spectrograph that could with equal success be used both as a Johann spectrograph and as a Cauchois spectrograph, by choosing such crystals as would have a small interplanar spacing for the planes participating in reflection according to Johann (to obtain sufficient dispersion in the region of very small \(\lambda\)), and a somewhat larger spacing for the planes working in the Cauchois method. It turned out that a quartz plate, cut in the manner shown in Fig. 4, possesses sufficient symmetry and makes it possible to reflect X-rays, as needed, from either one system of planes or the other, practically without changing the position of the crystal. The angle between the two systems of planes differs little from a right angle and is \(92^\circ 2'\).

In Ingelshtam’s spectrograph (a photograph of which is given in Fig. 5) the angle between the normal to the surface of the crystal at its midpoint and the incident rays can be varied up to \(65^\circ\). The author shows that such a spectrograph makes it possible to study the K-spectra of elements \(92 \geq Z \geq 24\) and the L-spectra of all elements with \(Z\) lying between 62 and 92. As may be seen, in the region of \(\lambda\) corresponding to the K- and L-spectra of light elements with \(Z < 24\), it is still necessary to use special spectrographs with crystals possessing a large \(d\). The radius of curvature of Ingelshtam’s spectrograph is 30 cm. The carefully fitted crystal holder, measuring \(80 \times 34 \times 36\) mm, is made of specially hardened steel to prevent possible deformation.

b) Spectrographs with vertical focusing. Along with the development of the methods of Kossel and Yohan, which pertain to devices with so-called horizontal focusing, Kunzel,^8 Daleyzhek and Taerl^9 developed in their works the theory of the method of vertical focusing. Recently the authors described in sufficient detail an improved construction of a spectrograph based on this principle. In such instruments the crystal is placed in a vertical plane, and its focusing action amounts to reducing the height of the reflection from the crystal. Thus the total energy of the reflected rays, distributed upon reflection from a plane crystal (in the Bragg method) over a length equal to the height of the reflecting portion of the crystal, is in our case distributed along a line of considerably smaller length. Owing to such a reduction in the height of the reflection it is possible, theoretically speaking, to obtain an infinitely large gain in intensity. This enormous luminosity, which does not depend on the radius of curvature of the crystal reflecting the rays, permits the use of very large distances between the slit, the crystal, and the photographic film, so that in practice the line width in the focus becomes independent of the depth of penetration of the X-rays into the crystal. On the other hand, this makes it possible to bring the resolving power of the spectrograph to a value comparable with the value

\[ \frac{\lambda}{\Delta \lambda} \]

for a double-crystal spectrograph. As Bakovskii^10 showed, in the case of focusing by this method the magnitude of the imperfection of the crystal used as a reflector is practically without effect. All the foregoing makes this method very promising and especially suitable for measuring such effects in which independence of the line width from secondary and difficult-to-allow-for influences of geometrical factors and of the factor of crystal imperfection is particularly desirable.

Fig. 5. Photograph of Ingelstam’s universal spectrograph

a—crystal holder with crystal, b—fluorescent screen, c—cassette with photographic film

As Kunzel showed, a characteristic feature of the geometrical conditions for focusing X-rays in such a spectrograph is that the radius of curvature of the cylindrical surface effecting the focusing \((\rho)\), associated with the radius of the spectrograph \((R)\) and the angle of incidence \(\theta\), is related by

\[ \rho = R \sin \theta, \]

and proves to be different when working in different wavelength intervals corresponding to different \(\theta\). Kunzel bent mica plates between forms curved to a definite radius. He was immediately shown that satisfactory results could be obtained only in the range of angles differing from the calculated \(\theta\) by no more than \(\pm 2^\circ\). This significant inconvenience of the method was overcome successively in two works by Daleyzhek and Taerl,^9 who constructed a spectrograph (Fig. 6) in which the radius of curvature of the mica plate serving as the X-ray reflector was varied. The crystal was clamped between two thin elastic steel plates in such a way that, during motion about the axis of the spectrograph, a special mechanism continuously bent the plates, bringing the radius of curvature of the crystal into correspondence with the angle of incidence of the X-rays upon it. Uniform bending of the support with the crystal was achieved by giving the crystal holder such a form that its moment of inertia with respect to the central axis and the bending

8 Uspekhi fizicheskikh nauk, Vol. XXV, issue 3

ing moment in the formula \(\rho=\dfrac{E\cdot J}{M}\) would vary identically, i.e., linearly, from one end of the support to the other. Therefore the support plates were given the form of triangles. The force was transmitted to the support by a system of gears. Small deviations from the calculated radius of curvature, corresponding to different \(\theta\), did not exceed \(1.5\%\) and did not exert any substantial influence on the line width. On the basis of measurements of the widths of the spectral

Fig. 6. DuMond and Taer spectrograph

1—front view, 2—side view (a—mechanism for continuous bending of the crystal, b—crystal), 3—top view

lines of the Mo \(K\)-series, the authors estimate \(\dfrac{\lambda}{\Delta\lambda}\) for the entire spectrograph at only 2700, which, in order of magnitude, does not differ from the resolving power of existing double-crystal spectrographs.

Spectrographs with a “spherical crystal”

In the preceding sections, modern high-luminosity spectrographs with a cylindrically bent crystal, oriented in various ways with respect to the divergent beam of X-rays emerging from the anticathode of the tube, have been examined. In this case, when reflection occurs from planes perpendicular to the axis of the cylinder, it turns out that all radiation of a definite wavelength which, in the absence of a slit, falls on the surface of the crystal at the Bragg angle is focused into a narrow strip on the focal circle, whose radius is half the radius of curvature of the crystal. Since monochromatic radiation falling on the edges and on the middle point of the crystal is not focused at one point on the circle, the minimum line width is determined by the geometrical dimensions of the spectrograph. On the other hand, the well-known advantages are possessed by the slit method of vertical focusing, in which the gain in intensity is obtained by bringing to a point (within the limits) the rays incident on the crystal and diverging in the vertical plane. Here the line width is determined by the width of the slit

of the spectrograph. Recently an attempt has been made to create a spectrograph whose reflecting surface would itself constitute a sphere. This would make it possible, in a certain sense, to combine the two above-mentioned principles for obtaining spectrographs with high luminosity. Carrying out geometrical calculations analogous to those made by Johann, in our case as applied to an arbitrary section, one can obtain that the relative gain in intensity in a spectrograph with a spherical crystal, obtained at the expense of a more rational use of rays diverging in the vertical plane, is expressed by the formula \(J=\dfrac{J_0}{\cos^2\theta}\), where \(J_0\) is the intensity in Johann’s method and \(\theta\) is the Bragg angle. As was to be expected, at small wavelengths the advantages of a spherical crystal are practically insignificant. But at large \(\lambda\) and, consequently, at \(\theta\) approaching \(90^\circ\), a considerable gain in intensity should be expected in spectrographs with a spherical crystal. At the same time, here, as in the case of vertical focusing already discussed earlier, the radius of curvature \(\rho\) depends on the Bragg angle in such a way that, combining this dependence with Bragg’s formula, we obtain

\[ \rho=\frac{2da}{n\lambda}, \]

where \(a\) is the arm length from the source to the crystal, and \(d\) is the grating constant. Thus, under constant geometrical conditions of the recording, the radius of curvature of the crystal varies inversely proportionally to the wavelength used. The difficulties encountered in bending crystals according to the requirements of the method led to the necessity of creating artificial reflecting systems by depositing on the spherical surface of lenses uniform multiatomic layers of various organic substances. Using the theoretical indications of Langmuir, Adams, and others, K. Blodgett developed a technology for the process of depositing successive monomolecular layers on the solid surface of glass. In the recent works of the authors mentioned it has been shown that, under certain conditions, the number of layers can be brought up to 200–300. A monomolecular film is formed on glass by applying a small amount of stearic acid, diluted in benzene, to the clean surface of water containing Ca salts. Stearic acid, which rapidly forms a thin surface film, subsequently settles on glass cautiously introduced into the bath. The rate at which the film adheres to the glass depends on the acidity of the medium (its pH), the concentration of Ca ions, and the temperature of the water on whose surface the film is formed. Langmuir showed that molecules of fatty acids tend to orient themselves at a certain angle to the surface of the solid bodies on which they settle, so that the group—COOH is oriented toward the solution. In the case of the compound of Ca with stearic acid, such a “layer” at the glass surface is formed by molecules \((\mathrm{COO})_2\mathrm{Ca}\), which have their external group \(\mathrm{CH}_3\) directed outward. With the observance of known precautions, the authors succeeded in depositing on glass, in the proper order, successive molecular layers, thereby creating a semblance of a space lattice with a lattice constant (according to Bernstein’s data) of the order of 50 Å. The thickness of the layer was measured with an interferometer. Details of the procedure and some new recipes are discussed in the papers of K. Blodgett\(^{11}\), C. Bernstein\(^{12}\), and S. Andrus\(^{13}\).

At the present moment it is still difficult to assess the possibilities and fields of application of spectrographs of the described design. The insufficiently developed and still very complex method for obtaining crystals, together with certain fundamental difficulties of the method (for example, the dependence of \(\rho\) on \(\theta\)), make them as yet little suitable for solving practical problems. However, their use is justified even now in the region of rays whose wavelengths exceed 20 Å.

E. E. Weinstein, Moscow

References

1. E. Weinstein, D. Gogoberidze, M. Flerova, JETP, 10, 350, 1940; E. Weinstein, Uspekhi Fizicheskikh Nauk, 23, 78, 1940.
2. Makhalov, Zhurnal Tekhnicheskoi Fiziki, 4, 895, 1934; Borovsky, Zavodskaya Laboratoriya, No. 2, 1938.
3. Borisov and Fogel, Zhurnal Tekhnicheskoi Fiziki, 7, 165, 1937.
4. Fankuchen, Nature, 139, 193, 1937.
5. D. Gogoberidze, Zhurnal Tekhnicheskoi Fiziki, 9, 2049, 1940.
6. B. W. Watson, Rev. Sci. Instr., 8, 480, 1937; S. T. Stephenson, Rev. Sci. Instr., 10, 45, 1939; E. Weinstein, D. Gogoberidze and M. Flerova, JETP, 10, 350, 1940.
7. E. Ingelstam, Rev. Sci. Instr., 11, 160, 1940.
8. V. Kunzel, C. R., 201, 656, 1935.
9. V. Dalejsek et M. Tayerle, C. R., 205, 605, 1937;
   V. Dalejsek et M. Tayerle, J. Phys. et Rad., 9, 465, 1938.
10. J. Bäckovsky, J. Phys. et Rad., 9, 471, 1938.
11. K. Blodgett, J. Am. Chem. Soc., 57, 1007, 1935; K. Blodgett and J. Langmuir, Phys. Rev., 51, 964, 1937.
12. S. Bernstein, J. Am. Chem. Soc., 60, 1511, 1938.
13. C. L. Andrews, Rev. Sci. Instr., 11, 111, 1940.