ABSTRACTS

LAUE DIAGRAMS WITH OPTICAL WAVES

Until recently, many attempts had been made to construct a spatial grating for visible light. However, the high degree of accuracy required in the relative arrangement of the elements of such a grating made its realization by mechanical means difficult.

Quite numerous experiments on the diffraction of light by ultrasonic waves (some of them have already been reported in Uspekhi Fizicheskikh Nauk1) showed that the condensations and rarefactions arising in liquids and solids during the propagation of ultrasonic waves through them can serve as the elements of a diffraction grating. For the first time Debye and Sears2 obtained in this way a one-dimensional diffraction grating, passing through a liquid enclosed in a plane-parallel vessel a plane ultrasonic wave from a piezoquartz plate connected to a high-frequency generator. Then Bär, Meyer, Hiedemann, and Asbach showed that a region of liquid in which two plane ultrasonic waves propagating at an angle to one another are superposed acts on a light beam passing through it as a diffraction grating with two periods. Finally, Schaefer and Bergmann3 used ultrasonic waves to create in a liquid a structure resembling the spatial grating of crystals. For this purpose they produced in the liquid, with the aid of three piezoquartz plates, three beams of ultrasonic waves propagating in mutually perpendicular directions. As a result of the superposition of these waves, a system of regularly arranged points is obtained, at which the liquid has a higher density than at other points. The totality of these condensed places in the liquid forms a spatial structure, the constant of which is determined by the wavelength of the ultrasonic wave. When a light beam passes through such a grating, phenomena are observed analogous to those that occur when an X-ray beam passes through crystals. Thus Laue diagrams with optical waves are obtained. Fig. 1 gives the Laue diagram of a liquid in which a spatial structure has been created by means of three mutually perpendicular piezoquartz plates oscillating with the same frequency; in this case the direction of the light beam is perpendicular to one of the piezoquartz plates. The diagram clearly indicates the symmetry of the spatial structure.

If the quartz plates are placed at different angles to one another and different frequencies are applied to the individual plates, it is possible to obtain still more complex spatial structures.

The diagrams of a liquid, however, are very imperfect, since the currents caused by heating of the liquid by the transmitted light blur the picture, reducing its sharpness.

In their most recent work,4 a review of which constitutes the subject of the present note, Schaefer and Bergmann obtained, with the aid of ultrasonic waves, a spatial structure in solid bodies. First of all, experiments were carried out with a small glass cube, on two adjacent faces of which piezoquartz plates were glued. The dimensions of the cube were selected so that the overtones of the entire system coincided with the overtones of the piezoquartz plate. In this case the system

was in strong oscillatory motion. The oscillation of the cube in the third direction was established automatically by virtue of the presence of transverse compression arising from oscillations propagating in other directions. The optical arrangement for observation was as follows: a small diaphragm, illuminated by an arc lamp, was focused by a long-focus objective onto ground glass or a photographic plate. The solid body under investigation was placed between the ground glass and the objective, immediately in front of the latter. Fig. 2 gives an example of a diagram obtained on the glass with the aid of a light beam. Fig. 3 shows a Laue diagram obtained on a calcite cube cut in such a way that one system of ribs is parallel to the optical axis, and the other to one

Fig. 1.

Fig. 2.

Fig. 3.

of the double axes; excitation of the crystal was produced in the direction of this double axis, while illumination was in a direction perpendicular to the optical and double axes.

The most interesting results were obtained when illuminating piezoelectric quartz crystals set into oscillatory motion by means of a high-frequency generator. Above all, in quartz one may observe a transition from a two-dimensional diffraction grating to a spatial grating. If a hexagonal prism is cut from quartz, with its axis coinciding with the direction of the optical axis, and each

Fig. 4.

Fig. 5.

Fig. 6.

pair of side faces perpendicular to one of the double (electric) axes, and it is excited with the same frequency along the directions of three electric axes, then conditions can be selected such that oscillations parallel to the axis of the prism will be very small. Fig. 4 shows the Laue diagram obtained on such a prism when it is illuminated along the optical axis. The diffraction pattern corresponds to a grating with two periods. Fig. 5 corresponds to the case when, by changing the electrical conditions, the prism is also brought into strong oscillations along the axis (the illumination conditions are the same as before). Here the spatial structure is already fully manifested, and the pattern from the plane grating recedes into the background. We note that when thinner diaphragms and higher overtones are used to excite the crystals, the apparently continuous lines of the diffraction pattern clearly break up into separate points.

In studying the quartz diagrams, several important points were established. First of all, it was shown that the form and arrangement of the curves of the diffraction pattern change when the direction of illumination is changed, but remain the same when passing from one form of the surface bounding the quartz crystal to another. A round quartz plate, a quartz parallelepiped, a cube, a hexagonal prism, and a circular cylinder give one and the same figure if they are illuminated and excited in one and the same direction.

Fig. 7.

Fig. 8.

Fig. 9.

Fig. 6 shows the diagram of a quartz cube cut in such a way that one pair of its surfaces is perpendicular to the optical axis of the quartz, while the other is perpendicular to one of the three twofold axes; in this case the cube is excited in the direction of the twofold axis and illuminated in the direction of the optical axis. Comparison of Fig. 6 with Fig. 5, obtained on a hexagonal quartz prism when it was illuminated and excited in the same directions, shows the identity of the diffraction patterns in both cases. These two photographs illustrate the position regarding the independence of the diffraction pattern from the form of the crystals. Fig. 7 differs from Fig. 6 in that the illumination of the crystal is carried out not in the direction of the optical axis, but in the direction of the twofold axis. The considerable change in the appearance of the diffraction pattern shows how strongly it depends on the direction of illumination.

Fig. 10.

It was further established that the appearance of the diffraction pattern depends on the polarization of the light beam if the illumination is not carried out in the direction of the optical axis. Figs. 8 and 9 show Laue diagrams for a quartz cube excited in the direction of the twofold axis and illuminated with polarized light (the direction of the electric vector of the wave is indicated by an arrow) in a direction perpendicular to the direction of excitation and to the optical axis of the quartz. Fig. 10 shows a diagram taken under the same conditions in unpolarized light. Superposition of Figs. 8 and 9 gives exactly Fig. 10.

The most important fact obtained from the study of Laue diagrams with optical waves is the circumstance that the appearance of the diffraction pattern is closely connected with other properties of the crystal under investigation. Fig. 7 gives an example confirming the existence of such a connection. The inclination of the diffraction pattern with respect to the horizontal, approximately \(18^\circ\), corresponds to the fact that the direction of the minimum modulus of elasticity of quartz makes the same angle, \(18^\circ\), with the horizontal (for this orientation of the crystal). The authors cite a number of further analogous comparisons between the arrangement of the diffraction pattern and the elastic properties of the crystal.

The material presented makes it possible to conclude that the method of Laue diagrams with optical waves can to a considerable extent facilitate the study of the elastic properties of transparent solids.

References

1. Uspekhi fizicheskikh nauk XIII, 783, 1933.
2. Debye, Proc. Nat. Acad. Am. 18, 409, 1932.
3. E. Hiedemann and A. Asbach, Phys. Z. 34, 393, 1933.
4. Schaffer and Bergmann, Sitzungsber. d. Preuss Akad. Wiss. X, 152, 1934.
5. Schaffer and Bergmann, Naturwiss. 22, 685, 1934.

L. Groshev

OPTICAL EVIDENCE OF PIEZOQUARTZ OSCILLATIONS IN OVERTONES

By exciting piezoquartz with a variable wavelength and observing the formation of a diffraction pattern when a beam of light is passed through a perpendicularly propagating ultrasonic wave, the author, by the Debye method, demonstrated the excitability of quartz overtones (up to the 69th order). Measuring the distance between the spectra and calculating from it and from the frequency of the oscillations, measured by a wavemeter, the velocity of the ultrasonic oscillations in the liquid, the author found that it is constant in the frequency interval from \(3.65 \cdot 10^5\) to \(2.5 \cdot 10^7\) hertz (for toluene). By an analogous method the velocities of ultrasound in water, aqueous NaCl solutions, and chloroform were measured; the data obtained correspond to those of other authors.

N. Malov

STUDY OF QUARTZ OSCILLATIONS WITH AN OPTICAL INTERFEROMETER

To determine the distribution of nodal lines and loops on the surface of oscillating quartz, Osterberg (Osterberg, Phys. Rev. 43, 819, 1933) used a quartz plate as one mirror of an interferometer, positioning it at a slight angle to the other mirror. In the absence of oscillations, parallel interference fringes were obtained, which broke up into separate sections when quartz oscillations were excited in a direction perpendicular to its surface. With such an arrangement it was impossible to obtain whole nodal lines. Therefore Straubel (H. Straubel, Phys. Z. 34, 894, 1933) placed the quartz strictly parallel to the interferometer mirror, and in the absence of oscillations the entire field of view was dark. When oscillations were excited, the nodal lines remained dark, while the moving regions were illuminated. By this method, the study is being carried out of oscillations of plates of various orientation, size, and shape, preliminary results of which are given in the cited work.

N. Malov

FREQUENCY CONTROL BY MEANS OF A SINGLE-FILAMENT ELECTROMETER

To control the constancy of the frequency of alternating current, an ohmic resistance and a capacitance connected in series are included in the circuit; their magnitudes are selected in such a way that the voltage drops across both, at the given frequency, are equal. The filament of a single-filament electrometer is connected to the common point of the resistance and capacitance, and the plates of the electrometer are connected to the opposite ends of the resistance and capacitance. In this case the filament is set at a certain position, which it may leave when the voltage distribution across the resistance and condenser changes, owing to changes in the frequency of the current. It can be shown that the deflection of the filament is proportional to the change in frequency, so long as these changes are small relative to the magnitude of the initial frequency (C. Hagen, Z. techn. Phys. 15, 231, 1934).

N. Malov