STUDY OF CRYSTAL SURFACES USING X-RAYS

It is generally known that a number of the most important properties of crystalline bodies are radically dependent on the state of the surface. Thus, for example, the lowering of the mechanical strength of crystalline substances is to a considerable degree determined by the presence of defects on the surface of the initial specimens, or by their occurrence in the course of plastic deformation. This latter circumstance was recently confirmed by M. V. Klassen-Neklyudova¹ on the example of zinc monocrystals.

It is quite probable that, when piezoelectric oscillations are excited in quartz plates, the uniformity of these oscillations depends on the state of the crystal surface. The numerous questions connected with the theory of deformation of crystalline substances, in turn, make it necessary to develop methods that would make it possible to judge the character of the structure of the crystal surface and the change in the degree of its perfection in the process of deformation. On the other hand, the possibility of studying the state of the crystal surface by X-ray methods opens up certain prospects also in the sense of an experimental substantiation of the basic theoretical propositions of the modern theory of the scattering of X-rays by real crystals, developed mainly in three successive papers by Darwin.

According to Darwin, the surface layer of a real crystal should be regarded as an aggregate of individual, small-sized, ideally perfect blocks, slightly rotated with respect to one another. In this case, if the number of atomic planes composing each of the ideal crystallites does not exceed several thousand, then their mutual influence on one another in the reflection of X-rays may be neglected. Otherwise it is necessary to take into account the so-called extinction—the diminution of the amplitude of a wave incident on successive atomic planes of the crystal as a result of reflection from the overlying ones. In this case, within the limits of one ideal block one speaks of so-called primary extinction, and for the entire volume of the crystal—of secondary extinction. In essence, both the one and the other extinction depend on the degree to which the lower-lying layers of atoms of the crystal are screened by the upper ones, which take upon themselves part of the incident radiation. In the case of primary extinction, the layers belong to the same homogeneous crystallite, and therefore there exist constant phase relations between the reflected waves. In the case of sec…

rical—these layers belong to different blocks of the crystal, and therefore there are no constant phase relations between the reflected waves.

From the point of view of these conceptions, it is extremely important to study separately the effects associated with the presence of secondary and primary extinction under various kinds of action on crystals, especially since the substantial role of primary extinction in the reflection of x-rays from deformed crystals is disputed by a number of authors.

Investigations in White Light

The influence of the state of the surface of a reflecting crystal on the appearance and character of the reflection has been observed repeatedly by many authors working by the Laue method, and at first did not arouse any special interest among investigators. Even Leonhard², who had addressed the question of the form of Laue spots in the case of a divergent beam of x-rays and wide slits, pointed to the influence of the degree of homogeneity of a crystal through its thickness on the appearance and character of the radiograph. Later Barrett³ showed that, when x-rays are reflected by a crystal whose surface layer is disturbed considerably more than the rest of its volume, a peculiar distribution of intensity along the Laue spots is observed. He observed radial splitting of the Laue spots of quartz, appearing as a result of polishing its surface. Such splitting of spots differs qualitatively from the well-known⁴ splitting that accompanies plastic deformation of crystals in that the distance between the individual portions of a split spot does not depend on their position relative to the axis about which the exposure was made.

The magnitude of this splitting is determined only by the relation between the thickness of the crystal and the width of the slit limiting the beam of rays incident on the crystal, and by the Bragg angle at which reflection occurs. If one assumes the incident beam of x-rays to be parallel but of finite width \(a\), and if the thickness of the crystal \(d\) is taken into account, then purely geometrical considerations lead to a formula, verified experimentally, which relates the splitting \(p\) to the above-mentioned parameters by the relation

\[ p = d \operatorname{tg} 2\theta, \]

where \(p\) is the magnitude of the splitting, \(d\) is the thickness of the crystal, and \(\theta\) is the Bragg angle. At the same time, of course, it is necessary that the width of the x-ray beam be sufficiently small in comparison with \(p\). Barrett assumed that, owing to a considerable difference in the degree of perfection of the inner and outer regions of the polished quartz, reflection occurs practically only at the points of entry and exit of the x-ray beam. Rock salt, owing to its greater degree of imperfection, should not have shown splitting at all. However, later Cork⁵ obtained splitting in good specimens of freshly cleaved rock salt, although it was not so sharply expressed.

Sakisaka and Sumoto⁶ subsequently also studied the dependence of the intensity of x-ray reflection on the perfection of crystals in their surface layers. The experiments were carried out parallel on crystals of rock salt and calcite, which, as is known, are sufficiently perfect. The surface was polished and then radiographed. The Laue spots were found to be doubled. Then, imposing a temperature gradient of about 160°/cm along one of the crystallographic axes, the investigators obtained coalescence of the spots. Fox and Carr⁷ observed the same phenomenon. They studied the influence of piezo-oscillations on the intensity of spots. Bringing quartz into a state of piezoelectric oscillation, the authors obtained a blurring of the previously split spots. Further work by Barrett and Howe⁸ led to the establishment of a fine structure of Laue spots on radiographs obtained from oscillating quartz. Colby and Harris⁹ etched the surface of quartz plates and found, in agreement with the data of other authors, an increase in the intensity of the Laue spots. In explaining the observed phenomena, they adopted the assumption that

the increase in reflection intensity in these experiments is due to significant disturbances of the perfection of the corresponding regions of the crystal. Barrett and Hough associate this with a decrease in primary extinction, whereas Kolby and Harris—with secondary extinction. Berch\(^{10}\) further found that the intensity of Laue spots and Bragg reflections from an oscillating quartz depends on the frequency of its vibrations; moreover, according to the author’s notions, the regions of the crystal that give the most intense reflexes are those parts of it that coincide with the nodes of the standing waves established in the volume of the specimen. In this connection a number of works by Jones\(^{11}\) and co-workers are of great interest. The investigators studied the influence of piezoelectric vibrations on diffuse reflection from quartz. The experiments yielded a negative result. Comparing the results of their work with known data on the influence of piezo-vibrations on the intensity of Laue spots, the authors are inclined to think that the disturbances occurring in a crystal in a state of piezo-vibrations may basically be characterized by a decrease in the coefficient of secondary extinction, and not primary extinction, as Barrett had proposed.

Recently the method of studying crystal perfection by the splitting of Lauegram spots was applied by Gogoberidze\(^{12}\) to determine the state of the lattice along the twinning plane in a polysynthetic twin. The author succeeded in observing splitting on NaCl crystals, even without polishing them. If a crystal is split in two perpendicularly to the beam, or if it has a natural crack, then the Lauegram spots double. With a somewhat greater separation of the split parts from each other and the creation, in this way, of one more surface with large disturbances in the path of the beam, the Lauegram spot is quadrupled. If a crystal having an internal crack is dissolved from the surface, then on the Lauegram this leads to a weakening of two extreme spots of the reflex, while the internal one, caused by the presence of cracks, remains unchanged. By artificially changing the lengths of the paths traversed by rays reflected at the entrance to and exit from the crystal, one can change the relative intensity of the spots in the doubled Laue spot. If a bundle of X-rays passes through a polysynthetic twin, representing from our point of view a multilayer formation whose degree of perfection changes in passing from layer to layer, then the spot on the Lauegram must have a multiplet structure. This is precisely what Gogoberidze observed. This work shows that observation of the nature of the splitting of Lauegram spots makes it possible to judge the degree of perfection of normally and deformed crystals, since the presence of planes on which there are significant lattice distortions affects the multiplicity of the spots of the resulting Lauegrams.

It may be that in the future this method will make it possible to overcome one of the fundamental difficulties of the Laue method in its classical formulation, namely the impossibility of studying elastic stresses and local disturbances of the lattice in the investigated volume of the substance.

Berg\(^{13}\) was the first to attempt to obtain an X-ray photograph of a surface by directly observing the reflection of white X-ray radiation from the surface of a NaCl crystal that had previously been subjected to deformation. After an exposure of 20 hours he succeeded in obtaining a reflectogram, the appearance of which was directly dependent on the character of the surface change as a result of deformation.

A more perfect method, although also requiring long exposures, proved to be the method proposed by de Laue\(^{14}\). The crystal under study is placed relative to the X-ray source in a position in which one of the Lauegram spots proves to be the most intense. The other, less intense reflexes are then screened off. If the cassette and the crystal are now moved synchronously along mutually perpendicular directions in a plane perpendicular to the beam of X-rays, and in this way the primary beam of X-rays is made to be reflected from different parts of the crystal, then, in the case of complete homogeneity of its surface, two parallel lines will be obtained on the plate, owing their origin to the primary and reflected beams.

Disturbed areas of the crystal surface will reflect the beam into a position not lying on a straight line. In this way a whole series of spots is obtained on the plate, the mutual arrangement of which will characterize the topographic features of the crystal surface. The method described found successful application in the work of Brilliantov and Obreimov[^15], who investigated the consequences of plastic deformation of NaCl. As is known, deformation leads either to the slipping of some parts of the crystal relative to others along so-called slip planes, or to the rotation of separate regions of the crystal through discrete angles, to so-called twinning along “irrational planes,” in the authors’ terminology. The predominance of one or another process in the course of deformation of a crystal can be judged by the state of its surface and can be checked by the method described above.

Investigation in monochromatic rays

In recent years several attempts have been made to create a method for investigating the surface of a crystal using monochromatic radiation. This alone would make it possible to shorten the exposure greatly. It turned out that when using a Bragg spectrograph, in which the distance from the crystal to the cassette and to the slit of the instrument must be strictly the same, it is not possible to obtain reflexograms whose appearance would reflect the state of the surface.

Fig. 1. “Photograph” of the NaCl surface (according to Bakovsky). Ratio of the spectrograph arms 60:40 cm

Fig. 2. Photograph of the same NaCl surface as in Fig. 1. Ratio of the arms 60:20 cm

The latter begins to play a decisive role in the reflection from the crystal if one uses the so-called asymmetric method, to which, for example, the Zeeman method belongs. Under these conditions, by creating a sharp asymmetry of the spectrograph arms, it was possible to obtain “photographs” that reflected in detail the distribution of defects along the surface of the reflecting crystal. Using this principle and placing the slit of the spectrograph (or of the X-ray tube in the so-called slitless method of exposure) at a distance of 3 m from the crystal, and the photographic plate in its immediate vicinity, Bakovsky[^16] obtained a series of images of the surface of rock salt. As can be seen from the figures presented (1, 2, 3, 4), the sharpness of the reflexogram increases as the asymmetry of the method increases. Some authors, using such a method, “photographed” the surface of multifrequency piezoquartz plates. In this case the reflexogram acquired a complex structure, indicating, apparently, the presence on the surface of the quartz crystal under study of defects of the mosaic-structure type. It was further found that similar X-ray photographs of the surface can also be observed in spectrographs with a bent crystal under somewhat modified exposure conditions. We[^17] observed a similar picture in studying the surface of a bent—

mica plates. The exposure was carried out immediately behind the spectrograph crystal. Let us point out here an obvious shortcoming of the described possibilities connected with the use of Seemann’s method, in which, as is known, the slit is formed by the edge of a wedge lying on the crystal, and the deepest-lying layer of atoms participating in the reflection of the X-rays lies deepest. Therefore, any changes in the degree of perfection of the surface layers of the crystal, connected either with the natural conditions of growth of the crystal or with artificial action upon it, must have a substantial effect on the depth of penetration of the rays into the crystal and, consequently, on the width of the reflected reflex. By moving the crystal relative to the wedge, one can study in detail the features of the crystal surface. Thus, the method presented here makes it possible, by direct measurements, to estimate the character of the change in primary extinction as a result of action upon the crystal. The author’s preliminary experiments show the complete possibility of using this method in studying the state of the surface of a number of natural crystals.

Fig. 3. Same as Fig. 2. Ratio of arms 60:10 cm

Fig. 4. “Photograph” of the surface of NaCl. Distance from the tube to the crystal 3 m; photographic film at the crystal

E. E. Vainshtein, Moscow

REFERENCES

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