X-RAY OPTICAL “MICROSCOPE”

The desire to see individual atoms directly has long prompted researchers to persistently seek a way to construct an X-ray microscope. However, the devices proposed up to the present time have not been able to solve this problem completely (see, for example, \(^{1,2}\)). Nor is the problem solved by the device proposed

by the author of the work being reviewed. Moreover, the idea of this device, which only with great reservations can be called a “microscope,” is by no means new. Nevertheless, both it and the results obtained with its aid, as it seems to us, deserve attention.

The essence of the device is as follows. Suppose that the object under consideration is located in the focal plane \(P_1\) of lens \(L_1\) (Fig. 1). Lens \(L_2\), separated from lens \(L_1\) by the distance \(F_1+F_2\), forms in its focal plane \(P_2\) an image of the object, magnified

\[ \frac{F_2}{F_1} \]

times, where \(F_1\) and \(F_2\) are the focal lengths of the lenses. The process of image formation may be regarded as consisting of two stages: 1) the formation by lens \(L_1\) of a diffraction image of the object in plane \(P'\), and 2) the formation by lens \(L_2\) in plane \(P_2\) of the diffraction image of plane \(P'\). This is illustrated in Fig. 1 by solid lines.

Fig. 1.

Both stages, generally speaking, can be separated in time; namely, one can first obtain the diffraction image of the object in plane \(P'\), and then independently obtain its diffraction image in plane \(P_2\). In doing so, however, it is necessary not only to reproduce the distribution of intensities in the intermediate diffraction image, but also to preserve the phase relations between its parts.

Finally, one may take a further step by obtaining a secondary diffraction pattern with the aid of rays of another wavelength. A simple calculation shows that the linear magnification thereby achieved is equal to

\[ \frac{F_2}{F_1}\,\frac{\lambda_2}{\lambda_1}, \]

where \(\lambda_1\) and \(\lambda_2\) are the wavelengths of the radiations with which, respectively, the first and second stages of obtaining the image are carried out. In particular, if the first stage is carried out by means of X-rays (\(\lambda_1 \sim 7\cdot 10^{-9}\ \text{cm}\); the author used the \(K_{\alpha}\)-line of molybdenum), and the second by means of visible light (\(\lambda_2 \sim 5\cdot 10^{-5}\ \text{cm}\)), then for \(F_1=5\ \text{cm}\) and \(F_2=200\ \text{cm}\) the magnification will be about \(3\cdot 10^5\) times. Thus an atom, whose dimensions are of the order of \(1\ \text{Å}\), will be represented by a circle about \(0.03\ \text{mm}\) in diameter, readily visible in a microscope of low magnification. In this case the resolving power of the device is determined by the quantity \(\lambda_1\), and the indicated magnification is by no means fictitious,

The impossibility of using lenses for X-ray radiation, as well as the complications associated with the three-dimensionality of the periodic structures under consideration (the Wulff–Bragg condition), are not so essential; for, with the aid of generally known methods of X-ray structural analysis, one can obtain a reproduction of the diffraction pattern that fully imitates the diffraction pattern which would have been obtained with the aid of a lens. In other words, the first stage of the process—the obtaining of an intermediate image in X-rays—can be carried out without difficulty.

The second stage is carried out just as simply. For this purpose an optical bench is used, at one end of which is placed a point source of light (a quartz lamp, covered by an opaque screen with an aperture about 30 μ in diameter). The light from the point source is transformed by a long-focus lens into a parallel beam, then collected by a second long-focus lens at the other end of the bench, where a horizontal microscope is placed, into which the light beam enters. A reproduction of the intermediate diffraction pattern is placed between the lenses, and the final image is observed (or photographed) in the microscope. Here, however, a fundamental difficulty arises which so far cannot be overcome effectively. As has already been pointed out, in order to obtain a complete image it is necessary to observe the phase relations between the various parts of the intermediate diffraction pattern. In the device described, however, the phase relations are disturbed—all parts of the image turn out to be in phase. Thus, in essence, the optical device performs Patterson synthesis, with all its inherent shortcomings. (At the same time, one also has to overcome difficulties connected with the fact that the interfering beams pass through a film of diapositive, and special measures are needed to eliminate the influence of its inhomogeneities.)

The author sees the solution in artificially recreating the real phase relations in those cases where they can be determined, proceeding from X-ray structural and crystallographic data. To this end he abandons the use of a reproduction of the real intermediate diffraction pattern and turns to its rough modeling. As a model he uses an opaque metallic screen in which, at those places where diffraction maxima should have been located, holes are drilled with an area proportional to the amplitudes \(F_{hkl}\), calculated from X-ray data. To obtain a better imitation it proves necessary to use from 100 to 400 holes, depending on the complexity of the structure. The holes are then covered with “phase shifters,” selected so as to reproduce phases expected according to old or other considerations. Thin sheets of mica, with variable angle of rotation relative to the ray, are used as phase shifters. Such modeling is especially simple in the case of crystals with a centrosymmetric structure, since in this case the phases of the separate diffraction maxima differ by 0 or π. One of the manufactured simple metal models of the diffraction pattern (Fig. 2) contained 150 holes, of which 32 were covered with mica plates shifting the phase by π. For details we refer the reader to the original work.

With the aid of the described method the author obtained excellent “microphotographs” of the crystal structure of certain compounds (see the plate at the end of the issue). Individual atoms appear with exceptional clarity, and the difference in electron densities is clearly visible, manifesting itself in differences in image intensity.

However, the term “microphotograph” is scarcely applicable to an image obtained in this way. It is rather a “photomontage” or an “engraving.” From a scientific point of view its value is small, for it contains nothing that could not be derived from the X-ray structural data underlying the preparation of the metallic model of the intermediate diffraction pattern.

Fig. 2. Metallic model of an intermediate diffraction pattern. Some of the holes are closed by mica phase shifters enclosed in metal frames.

It is also not entirely clear how expedient it is to replace mathematical calculations by the process of making a model, which is evidently rather painstaking and laborious. However, the vividness of the images obtained with the aid of the device described speaks for itself and undoubtedly justifies the search for further improvements of the X-ray optical “microscope.”

G. R.

CITED LITERATURE

1. UFN 42, 577 (1950).
2. UFN 35, 595 (1948).
3. M. J. Buerger, J. Appl. Phys. 21, 909 (1950).

For the abstract “X-ray Optical Microscope.”