CRYSTAL DEFECTS

D. B. Gozoberdze, Leningrad

Up to the present time, the question of crystal defects and their classification has still not been sufficiently clarified. In the Russian literature on this question there is complete divergence of views, and there is not a single more or less satisfactory system for classifying crystal defects, although attempts in this direction have been made repeatedly.¹˒² In particular, the author of the present article also proposed, albeit in a very incomplete form, a scheme for classifying these defects.³

The increase in the experimental material at our disposal has made it possible to set forth the indicated questions in considerably greater detail and to attempt to broaden the classification of crystal defects and to characterize each of them more fully. At the same time, the proposed classification is by no means exhaustive; however, it seems to us that it embraces the majority of frequently encountered defects. Our investigations have shown that very often defects of one and the same character may arise for different reasons: thus, for example, defects of an entirely similar character may arise as a result of irregularities of growth and of mechanical deformation.

For this reason it would seem to us incorrect, and even impossible, in classifying crystal defects to proceed from the genetic principle. On the contrary, the geometrical character of the changes in the crystal that accompany one or another defect is quite definite, and therefore the classification must be built precisely on this feature. This is what we do. Accordingly, we begin our classification with defects of a surface character, and then pass on to volumetric ones. In doing so, we have tried as far as possible to deviate less from generally accepted terminology.

1. COMBINATION STRIATION¹

On growth planes and on the faces of vicinal pyramids, one often observes the appearance of a peculiar striation which, as Groth believes, is the result of the corresponding face not being completely flat and being formed, as it were, by a series of steps. Thus, for example, in quartz crystals on prism faces, combination striation

¹ The term is borrowed from Groth.⁴

formed by planes of rhombohedra alternating with planes of the prism (Fig. 1). Sometimes all these striations are parallel to one another. In this case, in the goniometer they give a single common reflection; we shall call such striation parallel (it is found in calcite). Sometimes, however, these striations are inclined to one another; such striation we shall call nonparallel. It must be noted, however, that very often on a crystal it is very difficult to establish by the combination of precisely which planes the combinational striation is formed, since sometimes the planes in the combinational striation, especially in the nonparallel one, differ noticeably from the “corresponding” planes in the crystal. Nonparallel striation gives not one but several reflections in the goniometer. A special investigation carried out by us by the Laue method³ makes it possible to assert that parallel combinational striation in calcite is not connected with a disturbance of the crystal lattice and is a purely surface formation. Combinational striation is a characteristic defect associated with growth conditions, namely, for the most part with concentration currents.

Fig. 1. Quartz crystal with parallel combinational striation. The protruding part with bevels on both sides is visible

We were able to observe combinational striation on one of the crystals of Caucasian calcite. It was also observed on the faces of a so-called negative crystal (as is known, a negative crystal is a cavity inside an ordinary crystal, having a regular shape and bounded by crystallographically possible planes). Since it is usually considered that a negative crystal arises as a result of dissolution or a combination of dissolution with growth, apparently the conditions promoting the appearance of striation may occur not only during growth, but also during dissolution, or, more precisely, during a combination of growth and dissolution, owing to which a “similar” negative crystal is formed.

It is interesting to note that sometimes, even in the presence of parallel combinational striation, one may observe how some part of the crystal protrudes above the plane and has a bevel on both sides, as is clearly visible in Fig. 1.

Ansheles⁵ indicates that on the faces of growing hyposulfite crystals, combinational striation begins to form from the edges toward the middle of the face, so that the entire face acquires, as it were, a curved shape.

2. Striation

On cleavage chips of crystals of NaCl, calcite, and gypsum, appreciable irregularities can sometimes also be observed. These irregularities do not show up on the X-ray photograph and do not cause the appearance of double refraction. The presence or absence of striation is not noticeably reflected in the spectrogram taken with the aid of the given crystal, either during oscillation or even with a stationary crystal. The formation of striation can be induced mechanically; when even very perfect NaCl crystals are split, it is almost unavoidable, and it sometimes also appears when calcite is split.

The direction of the irregularities of striation is not associated with any definite crystallographic direction. For the most part it consists of a series of curved lines diverging like a fan over the cube face from that vertex of the crystal against which the knife rested during cleaving. Striation can be detected only with difficulty and only in light reflected from the crystal.

3. Overgrowths

On cleavage layers of rock-salt crystals one can often observe characteristic curved lines, leading to the fact that the plane loses its regularity. These irregularities appear in the process of growth and are apparently caused by concentration fluxes during growth. In Fig. 2 a photograph of such overgrowths on a cleavage face of an NaCl crystal is shown. Besides NaCl crystals, they are also observed on many other crystals [calcite (Iceland spar), gypsum, barite, etc.]. The overgrowths are volume defects of the crystal, as Laue diagrams taken from such crystals show (a change in the spots is clearly visible).

Fig. 2. Overgrowths on a cleavage face of an NaCl crystal

If a very thin plate (0.3–0.2 mm thick) is cleaved from an NaCl crystal with overgrowths, it is easy to notice that, changing gradually, the overgrowths extend into the depth of the crystal. This proves still more clearly that the overgrowths have a volume character.

We,⁶ ⁷ developed a method that makes it possible to photograph the surface of a crystal in reflected X-ray light; in the reflexogram obtained in this way all lattice defects near the surface are clearly visible. In this case, in the photograph all dimensions on the crystal along the direction of the beam decrease in the ratio of the cosine of the Bragg angle, while the transverse dimensions remain unchanged. As a result, the image is obtained slightly distorted—

... compared with optical ones, but it is very easy to establish the connection between them. Such reflection patterns are photographed by means of a monochromatic, weakly divergent beam of X-rays in a strongly asymmetric spectrograph. The distance from the X-ray source to the crystal must be considerably greater than the distance from the crystal to the plate.

We took such reflection patterns from an NaCl crystal that had clearly pronounced growth build-ups. In these photographs the image of the build-ups is plainly visible. If such a crystal, having build-ups, is polished, then the inhomogeneity in the structure of the reflection pattern due to the build-ups does not disappear, which once again indicates their volumetric character.

4. VICINALS

Vicinals are irregularities on the external faces of certain crystals, for example alum, quartz, etc., which appear in the process of growth and are such that their shape depends on the symmetry of the face on which they arise. For the most part vicinals are a pyramid, sometimes a pronounced one, i.e. with an incomplete number of faces, appearing on the principal face of the crystal. In this case, on one face there may form either one or several vicinal pyramids. It has been established that vicinals also formed in the case where some foreign body falls onto the face of a growing crystal. Thus, for example, small pyrite crystals cause the formation of vicinals on the face of quartz ^8.

Reflection of an X-ray beam from the surface of a crystal face can be used to find out whether vicinals are a surface formation or are connected with a disturbance of the lattice.

For quartz crystals this was done by us. In order to show that the image of a vicinal on an X-ray reflection does not depend on the protrusion of the vicinal at this place above the flat surface of the face, we polished the surface of the face so that it became completely smooth and matte, and after this took an X-ray photograph of the surface. In such photographs the vicinal is visible quite clearly. It may therefore be assumed that, in the quartz crystals studied, the vicinals are not a purely surface formation, but are connected with a disturbance of the lattice (cf. ^9–11).

On the basis of these experiments, carried out on quartz, one cannot, of course, categorically assert the same for other crystals as well and, in particular, for alums, which were studied by Shubnikov and Brunovskii ^11.

5. COARSE MOSAIC STRUCTURE1 (VICINALOIDS)

By coarse mosaic structure ^12 we mean the complex structure of a crystal formed as if from a series of separate large blocks—

blocks rotated relative to one another by angles on the order of several (a few) degrees.

Mosaic crystals of NaCl are usually characterized by a nonuniform block structure on the different faces of the cube. However, on each pair of opposite faces this structure is almost the same and, in sufficiently thin crystals, becomes identical. Usually, on four of the six faces of the cube in rock salt the mosaic appears in the form of elongated blocks with a common axis of rotation, while on the other two faces it appears in the form of blocks of irregular shape (Fig. 3).

The mosaic structure is the result of disturbances that arise during growth. According to the experiments of Leonhardt and Timmeier[^13], carried out on crystals of saltpeter, the mosaic structure is expressed the more strongly, the greater the rate of growth. During crystallization of zinc[^14] we likewise observed that the mosaic structure is expressed the more strongly, the greater the rate of crystallization and the dirtier the material.

Fig. 3. Photograph of a NaCl mosaic with irregular blocks

According to observations by M. V. Klassen-Neklyudova, during annealing of mosaic NaCl crystals one can sometimes observe darkening of the boundaries between individual blocks, which makes them easy to notice. This observation indicates that the boundaries between blocks are regions with a somewhat disturbed lattice, in which diffusion processes can occur especially readily.

We carried out a detailed study of the influence of various defects in crystals on the structure of Laue spots[^15]. The Laue spot of a good crystal of great thickness usually splits into two parts. If, however, imperfect crystals are used—for example, those having an internal crack—then this crack causes the formation of a new surface inside the crystal, where the lattice is disturbed, and as a result the structure of the Laue spot becomes more complicated; in addition to the two spots, another reflection[^11] appears from planes near the crack, and the spot then consists of three spots.

The presence of a boundary between the blocks of the mosaic has exactly the same effect on the structure of the Laue spot as a crack. In this case as well, a thin interlayer of disturbed lattice causes the appearance of an additional spot, as a result of the fact that the reflection from the disturbed lattice is much more intense than from the normal one. This circumstance once again confirms what was said about the presence, along the boundary of the mosaic blocks, of layers of disturbed lattice.

We also took reflectograms (X-ray) from mosaic crystals. These reflectograms showed (as, incidentally, already followed with certainty from our previous work) that the mosaic blocks are bounded by cube planes, rotated relative to one another by some angle of the order of 3–4°. By grinding off a thin layer (the surface) from a mosaic NaCl crystal, we can make the crystal surface perfectly even. There will be no irregularities on it, except for scratches from grinding. Nevertheless, on the reflectogram we still obtain an image of the mosaic blocks, although more blurred than in the unground crystal. During polishing, the sharpness of the image of the blocks on the reflectogram is again partially restored. This indicates that, during polishing, the small NaCl particles torn from their places are, as it were, arranged in the same order as that of the lattice of the crystal itself. In the case of a mosaic, these particles during polishing apparently become arranged on the blocks in the order of the lattice of each of them.

During plastic deformation by compression in NaCl, as is known^16, analogous formations arise. They were called (not very successfully)^1) by the physicists who discovered them “twins along irrational planes.” These twins, or deformation blocks, are entirely analogous to the blocks of the mosaic structure, with the sole difference that the blocks in a mosaic are usually larger and their angles of rotation greater.

Quite often analogous deformation blocks also form when NaCl crystals are cleaved, especially in the case where the knife with which the crystal is cleaved is not particularly sharp. In this case, if the blade of the (blunt) knife forms an angle close to 45° with the edge of the crystal, then an irregular mosaic structure of the type shown in Fig. 3 forms on the cleavage plane. If, however, the knife blade is placed parallel to the edge of the cube, then a different system of blocks arises. In this case the formation of characteristic “wedging-out twins” is often observed, i.e., blocks whose angle of rotation gradually decreases and finally becomes equal to zero; however, the size of the blocks and the angles of rotation are smaller than in a mosaic structure.

6. TWINS

Twins are crystals in which two parts of the lattice are arranged in mirror symmetry with respect to one another relative to some plane, called the twinning plane. In this case it is not necessary that the twinning plane serve as the boundary of separation between the twins; such a boundary may be

^1) In saying that the name “twins along irrational planes” is not very successful, we have in mind the circumstance that the possibility of the formation of twins of such a type, in which the plane and direction of twinning are irrational, is not provided for by the classical theory of twinning. For our part, we prefer to call them deformation blocks.

and any other surface completely unlike the twinning plane.

The angles of rotation of one part of the lattice relative to its other part are strictly determined and follow from geometrical considerations.

Twins can arise both during the growth of crystals (growth twins) and under mechanical deformation (deformation twins). However, as a result of deformation, by no means all forms corresponding to growth twins can arise here, but only some of them. Yet, apparently, during deformation no forms arise that do not occur during growth. According to the concepts of geometrical crystallography, in twins either the twinning plane or the twinning direction must necessarily be rational.

Recently a number of authors have studied in detail the phenomenon of the formation of deformation twins in crystals of calcite \(^{15,17}\) and quartz \(^{18}\). These investigations have shown that during deformation twinning there is no very strong disruption of the lattice. A Lauegram of twinned quartz or calcite, taken in such a way that the beam of X-rays passes along the boundary between the normal crystal and the twin, including both the one and the other, is a superposition of two X-ray patterns of the usual type, rotated relative to each other. During twinning nothing similar to the phenomena of asterism is observed.

Apparently, in the lattice of the twin no changes other than rotation occur. Only at the boundary between the normal crystal and the twin in calcite is a certain lattice disturbance observed, arising as a result of the presence of elastic stresses \(^{19}\). As a result of this, along the plane of separation between the normal crystal and the twin there is a layer with excess free energy. It is clear that the strength along this layer must be considerably smaller and, consequently, a new plane of secondary cleavage—or, more precisely, parting—must appear in the crystal along the boundary between the normal crystal and the twin. As our experiments have shown, such a phenomenon is indeed observed. Knaper \(^{19}\) calculated the magnitude of this excess free energy and came to the conclusion that it should cause a work of separation along the twinning plane even somewhat smaller than along the cleavage plane \((100)\).

If one considers the displacement of atomic groups in calcite during twinning, one notices that the Ca and \(\mathrm{CO}_3\) ions (if they are regarded as points) are displaced longitudinally (undergo shear) parallel to the twinning plane, along its direction. If, however, it is taken into account that the \(\mathrm{CO}_3\) ion is a triangle at whose vertices the O atoms are located and at whose center is the C atom, then it turns out that the plane of this triangle in the twin has changed its position in comparison with its position in the normal crystal (it makes an angle of \(38^\circ\) with it). Thus, in calcite the displacement of atoms is not limited to a single displacement, but represents, generally speaking, a special kind of rotation.

With an analogous phenomenon we encounter quartz, where the displacement of atoms during twinning cannot be explained by shear alone. The theory of twinning is obliged to reckon with this fact. Meanwhile neither the geometrical theory of Boas and Schmid^20, nor the theory of Kontorova and Frenkel^21 takes this into account and therefore does not give a complete picture of the phenomenon.

7. BENDING OF PLANES

In many crystals a peculiar growth defect is observed, consisting in the bending (sometimes screw-like) of its planes. Such defects are observed in quartz (in the form of screw-like bending of a prism plane around the hexagonal axis), in gypsum [in the form of screw-like bending of the plane (010)], in NaCl, and in a number of other crystals.

Under mechanical action, as our experiments on gypsum have shown, bending of atomic planes may arise, analogous to the bending observed as the result of growth irregularities in the same substance.

In NaCl crystals, especially upon deformation at elevated temperature, screw-like bending of atomic planes may also arise^6.

8. SUBINDIVIDUALS (OVERGROWTHS)

Quite often on the faces of crystals one can observe, as it were, separate small crystals stuck to its faces in such a way that their faces and edges are not parallel to the faces and edges of the principal crystal. In this case we are for the most part dealing with a small crystal whose lattice is not parallel to the lattice of the principal crystal. Sometimes this lattice is in a twin position with respect to it, but more often it is simply a small crystal oriented in a random manner with respect to the principal crystal. In this case we essentially no longer have a single crystal (Fig. 1).

There are, however, also such overgrowths in which the lattice of the overgrowth is parallel or nearly parallel to the lattice of the principal crystal. The overgrowths have formed as the result of the accretion of a small crystal onto the face of a large growing crystal. If the size of the overgrowth is so great that it is close to the dimensions of the principal crystal, then it is said that we have an irregular intergrowth of subindividuals. Irregular intergrowths also include such formations as spherulites and dendrites of various types.

Spherulites and dendrites are, as it were, a transitional stage between single crystals and polycrystals, since in this case we have a series of comparatively large crystals that have grown together at small angles to one another. However, these crystals are still arranged relative to one another with some regularity; that is why we mention them here, although, of course, dendrites and especially spherulites cannot be regarded as irregular-

properties of single crystals, but as intergrowths of different crystals at an angle to one another.

9. FINE MOSAIC STRUCTURE

Somewhat apart from other defects stands the fine mosaic structure of crystals.

When Laue²² first published the theory of the interference of X-rays, it turned out that this theory did not give sufficiently good agreement with experiment for a whole series of quantities and, in particular, that the decrease in the intensity of reflection as a function of order, calculated theoretically, was smaller than that given by experiment. In order to avoid this disagreement, Darwin²³ suggested that an ordinary real crystal is not an ideal lattice, and that the arrangement of atoms in it differs from the ideal. To simplify the calculation, the assumption was made that the crystal consists of separate, quite perfect small blocks, rotated relative to one another by certain small angles. These microblocks were called a fine mosaic structure, and the assumption of their existence made it possible to explain the discrepancy between the theoretically expected and experimentally observed width of spectral lines and the dependence of the intensity of a spectral line on the order of reflection.

Physically, however, a more natural assumption is that the crystal consists not of separate ideal blocks rotated relative to one another, but that the atoms lying in different crystallographic planes are displaced relative to one another in different ways. Attempts to construct a theory on this basis have been made recently, and some of them seem to us very successful²⁴.

Thus, it seems to us that in reality the assumption of a fine mosaic structure is simply a method that makes it possible to facilitate the mathematical part of the calculations; however, we do not insist on this. In any case, by fine mosaic structure we shall call the cause that produces an increase in the intrinsic width of a spectral line and a change in the decrease of intensity with the order of reflection, as compared with an ideal crystal. Such phenomena were studied in detail in the well-known works of James²⁵ and others, and, with the aid of a double spectrometer, by Allison and Compton²⁶ and their followers.

An analogous effect is observed in reflexograms, where polishing causes a strong blurring of the pattern and at the same time a large increase in the fine mosaic structure.

LITERATURE

1. Sheftal, Classification of Accessory Minerals, reported at the Fedorov Institute, 1938.
2. Ansheles, Open letter to Sheftal concerning his report.
3. Gogoberidze, Proceedings of the Vses. Mineral. Society, 1938.
4. Grot, Physical Crystallography, St. Petersburg, Rikkert Publishing House, 311, 1897.

1. Anschles, Uchenye zapiski LGU, issue 5, No. 21, 1939.
2. Gogoberidze, ZhETF, 10, 96, 1940.
3. Gogoberidze, ZhETF, 10, 232, 1940.
4. Lemlein, Report at the Fedorov Day in May 1938.
5. Anschles, ZhRKhO, physical section, 60, 27, 1928.
6. Anschles, Z. Krist., (A) 95, 150, 1936.
7. Schubnikow and Brunowski, Z. Krist., 77, 337, 1931.
8. Gogoberidze, Mechanical Twinning, DNTVU, 1938.
9. Leonhard and Timmeier, Z. Physik, 102, 781, 1936.
10. Unpublished work by the author.
11. Gogoberidze, Construction of Laue X-ray diffraction spots, Zhurnal tekhnicheskoi fiziki, 9, 205, 1939.
12. Obreimov and Brilliantov, ZhETF, 5, 330, 1935; 7, 978, 1937; 9, 592, 1939.
13. Yakutovich and Yakovleva, Zhurnal tekhnicheskoi fiziki, 6, 1936.
14. Shubnikov, Trudy Lomonosovskogo instituta, issue 3, pp. 5 and 67.
15. Kaner, ZhETF, 9, 218, 1939.
16. Schmid and Boas, Kristallplastizität, Springer, 1934.
17. Kontorova and Frenkel, ZhETF, 8, 89, 1340, 1349, 1938.
18. Laue, Encyklop. Exakt. Naturwiss. Wellenoptik, 5, 3, 1915.
19. Darwin, Phil. Mag., 27, 315, 175, 1914; 43, 800, 1922.
20. Boas, Z. Krist., 97, 354, 1937.
21. Tans and Brindles, Proc. Roy. Soc., London, A 149, 121, 1928.
22. Kompton and Allison, X-Rays in Theory and Experiment, New York, Van Nostrand Co., 1935.

1. The term “mosaic structure” has long been in use among physicists to denote defects of this type. The term “vicinaloids” is used by some mineralogists. ↩