THE NATURE OF CRYSTAL IMPERFECTION

1. SYNGENETIC IMPERFECTIONS OF CRYSTALS

A. M. KUZMIN

Introduction

Among crystals one distinguishes perfect (ideal) and imperfect (real) crystals. Perfect, or ideal, crystals include crystals which in all respects appear externally geometrically regular*), and whose constituent substances—atoms, ions, complexes and their groups—are distributed throughout the mass of the crystal relative to one another in a strictly spatially regular manner, i.e., ideal crystals throughout their entire mass are spatially, physically, and geometrically constructed homogeneously. Ideal crystals are characterized also by an ideal spatial lattice**).

Imperfect, or, as they are often called, real polyhedra include crystals which, by their external form, cannot be recognized as geometrically perfect; moreover, they bear various kinds of defects that disturb their physical homogeneity. The internal inhomogeneity of such crystals is often reflected both in their external form and in their physical properties. Such crystals are often, explicitly or implicitly, blocky (mosaic), and their spatial lattice also proves to be mosaic. It is therefore quite natural that the properties of real crystals, possessing lattice defects, differ radically from the properties of ideal crystals.

Perfect crystals occur in natural and laboratory conditions only exceptionally rarely. According to A. V. Shubnikov, the ideal form is one of the possible forms of crystals of a given substance [23], while Van Buren asserts that such crystals do not exist [1]. Moreover, crystals that are externally perfect in form are not always physically homogeneous. The overwhelming majority of crystals—real crystals, with which one has to deal in practice—bear, as a rule, various kinds of both external and internal imperfections.

The imperfections of real crystals are closely connected with the conditions under which the crystals themselves are formed and with the conditions of their existence in subsequent life. In other words, disturbances of the homogeneity of the structure of crystals depend on physicochemical conditions, i.e., on the temperature, pressure, and composition of the medium, which at the stage of crystallization do not remain strictly constant; this applies especially to the medium and its tempe-

*) For a crystal that is physically homogeneous in all respects, an external ideal form is not obligatory.

**) According to Bernal [2].

temperature. Using the example of the formation of magma, one can concretely imagine the entire course of the process of mineral formation, which is accompanied by an inexorable drop in temperature within the range \(1500—50^\circ\), by pressure, and by a constant and successive change in the composition of the medium, beginning with the formation of magmatic rocks and ending with low-temperature hydrothermal deposits of crystals of mineral matter. Moreover, the pressure throughout does not remain constant.

After crystals have formed, the physicochemical environment for their subsequent life, as a rule, also changes to varying degrees, and the crystals themselves, as is said, age; this is correspondingly reflected in them both in the form of changes in the crystal lattice and in physical properties, and in the appearance within them of various forms of defects as a consequence of deformations arising in the crystal for various reasons.

Thus, during the period of formation of a real crystal, a number of different kinds of defects arise in it in the form of vacancies at lattice sites, the capture of foreign ions whose sizes do not correspond to the sizes of the host ions, and the capture of foreign crystals. In the course of its subsequent life the crystal is subjected to various kinds of deformation, changes in its composition, and restructuring of the crystal structure, which in general may be regarded as its dislocations.

The term “dislocation” of crystals was introduced into crystallography, into solid-state physics, by metallophysicists studying the plastic properties of metals and alloys subjected to deformation. In this connection it was believed that, for example, the plasticity of metals is favored by dislocations present in metallic crystals.

According to Buerger, dislocations are structural defects in crystal lattices that arise in them during the growth of a crystal, and dislocations are created in a crystal as a result of plastic deformation [3]. These include point dislocations, vacancies at lattice sites, atoms and ions captured during crystal growth that are arranged in the cells between lattice sites if their sizes are small, and, finally, linear and screw dislocations are also included here [1, 3, 4, 16, etc.]. As a result of deformation of a crystal, linear dislocations appear in it as a consequence of slip. Spiral dislocations in crystals arise as a result of its growth. Without going into the details of what is understood by dislocations, to the consideration of which an enormous literature is devoted [8], for our part we propose to broaden the concept of “dislocation” as applied to our object of study, and to refer to dislocations all those disturbances of the homogeneity of crystals that arise in them both during the period of their formation and later, during the period of their existence, under the influence of various physical, chemical, and physicochemical causes. I consider it necessary to dwell on the theory of crystal dislocations after the extensive factual material on the study of defects in natural crystals has been presented.

On the basis of what has just been said, imperfections and dislocations appearing in crystals should be divided, according to the time of their occurrence, into two groups: syngenetic and epigenetic [12].

Syngenetic imperfections and dislocations should include those types of imperfections and dislocations that form in crystals simultaneously with their growth and throughout the entire period of their formation.

Epigenetic imperfections and dislocations include those disturbances of homogeneity that arise and develop in crystals after their formation or after they have become part of ...

environment, which, as a result of changes in physicochemical conditions, undergoes various kinds of deformation. In this process there occurs an intensification and superposition, upon syngenetic disturbances and dislocations, of epigenetic deformations.

In speaking of the imperfections of natural crystals, the author of the present work would like below to show, through a number of examples, how these imperfections are formed at the stage of creation of the crystal itself, what deformations it undergoes during its life after formation, and, in conclusion, to dwell briefly on how nature uses defects in minerals in its laboratory.

The material offered to the readers’ attention will be presented in four chapters as separate articles. In the first of them: I. Syngenetic imperfections of crystals. II. Epigenetic imperfections of crystals during polymorphic transformations. III. Epigenetic imperfections during plastic deformations. IV. Epigenetic imperfections during dehydration of crystals (published in “Materials on the Mineralogy, Petrography, and Useful Minerals of Western Siberia and Krasnoyarsk Territory” [28]).

I. Syngenetic Imperfections of Crystals

Since the time of T. Lovitz [17, 18] it has been known that the most regular crystals are obtained from weakly supersaturated solutions. Later, Frankenheim, O. Lehmann, and then V. G. Wulff [5] investigated the conditions of crystal growth and, on the basis of theoretical and experimental studies, found that during crystallization a crystallization courtyard [5] is created around the growing crystal, within which, owing to the high supersaturation of the solution, crystallites are formed; some of them are adsorbed by the growing crystal on its surface, while another part floats away. It is natural to expect that the size of the crystallites relative to their neighbors may be unequal, and that the crystallites adsorbed by the crystal do not lie on its surface in a dense and even layer. A. V. Shubnikov [23], relying on experiments, asserts that the degree of perfection of crystals is determined entirely by the size of aggregates of molecules (submicrons), which, differing from one another in their dimensions by even a very small amount and being deposited in parallel, cannot form a perfectly even layer even on an initially flat face, and cannot fit upon it tightly, without gaps. The next layer of such “submicrons,” likewise unequal in size, will cause still greater disturbances in the packing of the face, and so on. In real crystals constructed in this way there will always be voids between the imperfectly fitted submicrons of different sizes; and the superposition of later layers of submicrons upon the preceding ones leads to the burial of voids with the remaining mother liquor in them, in the form of bubbles in a cavity with geometric walls (negative crystals), or in the form of inclusions of various shapes.

What has just been said makes it possible simply and naturally to imagine a real crystal as mosaic; its space lattice in this case must likewise be mosaic, and therefore differs sharply from the lattice characteristic of an ideal crystal.

To this type of imperfection should be assigned the phenomenon of bunching, by which M. V. Erofeev first attempted to explain the formation of large tourmaline crystals [11].

The author has at his disposal, from druse formations, several intergrowths consisting of three galena crystals in the form of cubes

with truncation of the vertices of the trihedral angles by the faces of the octahedron (Fig. 1).

The three crystals of the intergrowth as a whole are arranged spatially parallel to one another. Each of the crystals, in turn, consists of a large number of smaller crystals of the 2nd order, in the form of cubes with octahedral faces. Since there is no strict spatial parallelism in their packing, they are quite readily distinguishable. The galena crystals of the 2nd order themselves, in turn,

Fig. 1. Surface of a cube of a galena crystal composed of crystallites of several orders

consist of still smaller crystallites of the 3rd order, which are also readily distinguishable under a magnifying glass. The latter, in turn, consist of still smaller block-crystallites distinguishable under a microscope. When these latter are studied on an MIM-8M at magnifications of 150–300×, they prove to consist of crystals of the 4th order, and the latter sometimes even of the 5th order.

Considering the position of galena crystals of the 2nd order relative to crystals of the 1st order, the relation of crystals of the 3rd order to crystals of the 2nd order, etc., as was already noted above, it is clearly visible even to the unaided eye that the crystals of each subsequent order, relative to the crystal of the preceding order, are located within it and, relative to crystals of the corresponding order, are not strictly spatially parallel and therefore are distinctly noticeable, but the general orientation of such a mosaic galena crystal as a whole is preserved.

Another example of clustering may be fluorites from Cumberland (Fig. 2). On one of the cube faces it is clearly visible that it consists of crystals and plates of various sizes with cube and octahedron faces, arranged relative to one another not strictly spatially parallel.

Between the crystals just mentioned there are gaps—cracks and voids. On the surface of the growing crystals of the 2nd

a

Fig. 2. Surface of a cube of fluorite crystals a and b, composed of crystals of several orders.

order on the face of the cube, it is clearly noticeable that they too are mosaic, composed of finer crystals of the 3rd order. On the cleavage plane {111}, passing almost through the center of the crystal, it is clearly seen from the production of a reflection that, in its inner part, the crystal consists of a large number of blocks, each of which is inclined with respect to its neighbor by a very small angle; that is, simply speaking, the octahedral plane of each block in the given section does not lie in the same cleavage plane, as it should in a single crystal. On the adjacent face of the cube of the same crystal the mosaic structure is not so striking in comparison with that described above, since the small cubes of the mosaic are smaller; although they are visible, they barely protrude above the common face of the cube. On three other faces there are isolated visible defects; the faces themselves as a whole are smooth and even, but in the pits the block structure of the other faces of the crystal is also clearly visible. The violet fluorite crystals from Cumberland are often called zonal; this feature is clearly noticeable from the alternating change of zones with different intensity of coloration. The zonal structure, parallel to the smooth faces, remains strictly parallel to them. On distinctly mosaic faces the external, sharply expressed zones of zonality within 3 mm noticeably repeat the configuration of the complex surface of the cube.

Fig. 3. Sketch of the surface of a fluorite cube composed of lamellar crystallites of several orders (a); b—detail of the structure of one of the portions of the fluorite described.

As the next example, let us cite pyrite crystals from the clayey-marly Ordovician shales of the Kulombe River (basin of the Lower Tunguska River), collected by B. V. Oleinikov. Hundreds of crystals, from a centimeter and smaller up to 5 cm across, were studied. One feature common to them is their mosaic structure, which can be illustrated by the drawings given below (Fig. 4). The pyrites of B. V. Oleinikov under consideration initially consisted of a fine-grained aggregate of cubic grains, the size of which did not exceed one millimeter, and was often smaller. The pyrite grains in the aggregate are arranged relative to one another in an entirely disorderly manner. With the growth of the crystals in the aggregate, and with the enlargement of such an aggregate to 0.5–2.5 cm across, some part of its grains proves to be arranged in a spatially parallel orientation, and this part of the grains receives preferential growth. As a result of such selective growth, instead of a very large number of grains, several comparatively large, misoriented pyrite crystals grow. Then, among these latter crystals, those close in orientation receive preferential growth and tend to form a single crystal, while the growth of other pyrite crystals with a different orientation does continue, but proves to be more retarded. Therefore, in rel-

in individual cases, crystals that have not had time to develop or that grow slowly are captured by rapidly growing ones. In the photograph in Fig. 4 of a cubic pyrite crystal with octahedral faces, its block structure is clearly visible; in the central part of the cube face two pyrite crystals stand out distinctly. One of them, darker, at the stage of complete overgrowth is represented by an edge of the cube and by an octahedral face; the other, to the right of it, is in the form of a large cubic crystal, whose cubic and

Fig. 4. Pyrite crystal. The surface (001) has a block structure.
At the center of the face two differently oriented crystals protrude.

octahedral faces are not precisely oriented with the octahedral and cube faces of the large crystal. On the left there is a third crystal, protruding as a trigonal vertex of a cubic crystal.

Another characteristic of the crystals being described is that pyrite crystals build up on the cube face in the form of parallel \(\{100\}\) plates (Fig. 5), which are bounded by traces of the octahedron and cube faces and are often elongated in the directions \([110]\) and \([100]\). Such plate-crystals, of unequal thickness, are superposed on one another, and therefore channels and fissures naturally exist between the plate-blocks, which are covered by other plate-blocks. On the octahedral faces (Fig. 5, g, d, e) it is also clearly visible that pyrites in their development have a block structure and that between the blocks there are triangular voids and voids of more complex shape. On the block faces of the octahedron the same feature stands out distinctly: the face of each block is composed of faces of microblocks, and each block and microblock grows by the superposition of triangular plates one upon another. The spatially parallel arrangement of plate-blocks on the cube and octahedron faces does not always prove to be strictly oriented. Similar platy overgrowth on the cube face can also be seen in the photograph (Fig. 4). In the NE part of the crystal, the platy overgrowth is

Fig. 5. Block structure of pyrite crystals.
a—plate-like blocks of pyrite composing the cube face; b, c, d—block structure of octahedron faces; e—detail of the structure of the surface of one of the blocks, on which concentric growth layers are visible; f—detail explaining the character of the structure of the concentric growth layers of the cube surface.

Fig. 6. Block structure of pyrite crystals.

obvious; it accordingly found reflection in other crystals as well, in Figs. 6, a; 5, a, and others.

Looking closely at the surface of a block of a crystal (Fig. 4, Fig. 6, a), which at first glance appears smooth, one finds that, when studied with a goniometer, this surface in fact has a more complex structure. Thus, in Fig. 5, d, the growing plate of pyrite consists, in turn, of separate, smaller blocks (vicinals). In each such block there is a center of its growth, which, in the form of a protrusion, is the apex of a very obtuse cone. At the apex of the cone there is usually one or several microscopic crystallites (Fig. 5, e). Around the center of growth, at various distances from it, there are concentric rings—blocks numbering from 2 to 7—which illustrate, as it were, a system of flat cones nested one within another. The complex contours of the rings—the serration—are caused by the combination of traces of faces of the cube and the octahedron. Straight lines indicate the boundaries of the blocks.

To conclude the consideration of the features of the formation of pyrite crystals, let us give one more example. From the Atasuy deposit in Kazakhstan, large crystals of cubic pyrite, up to 20 cm and more in size, were obtained. A feature of these crystals was the complete absence of the pentagonal-dodecahedral striation typical of pyrites. At first glance the surface of such crystals seemed mirror-smooth. However, a somewhat more attentive study was sufficient to make one convinced of its block structure (Fig. 7): each block has its own outlines, the character of which is determined by the interdependent conditions of their growth. Each block bears on its surface a very fine striation, corresponding to the faces of the octahedron and, to a lesser degree, to the faces of the cube. The clearly distinguishable striation on the surface of each block (in Fig. 7, g, it is shown selectively, to illustrate the character of its manifestation) is essentially the boundary of very thin plates superposed one upon another and decreasing in area toward the center of growth of the block.

The described examples of crystals once again confirm the idea that block structure is one of nature’s ways of forming large crystals. The pyrites of B. V. Oleinikov show nature’s tendency to build single crystals, proceeding in a number of cases from aggregates through polycrystals. The studied pyrites from many other deposits, for the most part, indicate that their crystals are not distinguished by homogeneity either in their external manifestation or in their internal structure.

In the 1920s Prof. A. V. Lavrskii, during the crystallization of K- and NH₄-alums in the presence of borax, obtained crystals of cubic form. A feature of these crystals was that the cube faces were composed of small cubes with edges of 0.1–0.05 mm (Fig. 8). The cubes on the (100) face were arranged, in the general space, in rows. In each of them the cubes were of different sizes; for this reason the common faces of the cube were not ideally smooth, nor were the edges linearly even. The cubes were sometimes packed tightly against one another, while more often there were gaps between them of thousandths of a millimeter. Each face could be likened to a city built up with cubes of different sizes. The gaps between them are streets, whose width is determined both by the arrangement of the cubes and by their sizes; the streets either pass from one row to another, or, when continued, run into a cube of a neighboring row, or go around the cubes if this is possible. In this city there are, in places, squares free of cubes; the size of the squares corresponds to the dimensions of one, two, or even three cubes. The streets, as ca-

channels; in this city they enter the underlying layer of cubes; here they either partly wedge out in the form of dead ends, or can be traced for some distance into the crystal, then finally branch and wedge out. In the lower layers of cubes there are also their own streets, and their own dead ends. Taken all together, this gives a clear idea that this entire structure is composed of cubes of different sizes, and in such a structure it is difficult to expect that the cubes composing it would be arranged with respect to one another in any strictly spatially parallel way. The octahedron face, which developed on some crystals, is covered with small projections of the trihedral vertices of the cubes.

Fig. 7. Large pyrite crystal with a mirror surface. Visible on its \((001)\), \((100)\), and \((010)\) are the microplaty structure and the corresponding striation along \((111)\) and \((100)\)

Fig. 8. Sketch of a cubic quartz crystal with a clearly expressed block structure

The crystals described by A. V. Lavrsky were essentially models of Haüy’s ideas [6]. Thus, the crystals of A. V. Lavrsky are analogous formations of fluorite, galena, pyrite, and other minerals described above. They represented a comparatively coarse mosaic of the structure of a crystal, but at the same time they may be a natural prototype of the micromosaic structure of crystalline bodies. Incidentally, the model of two-dimensional single crystals in the form of accumulations of Bragg and Nye bubbles of identical size [25], proposed by these scientists for understanding the dislocations themselves in the deformation of atomic and ionic structures, is most likely a model of molecular-mosaic structures of the galena-, fluorite-, and quartz-type arrangements discussed above.

Let us give one more example, which vividly shows how mosaic crystals originate. In limestones, under metasomatic conditions of formation of garnets of the grossular–andradite series, garnet nuclei often arise (Fig. 9). At the initial stage of crystal formation, garnet nuclei \(0.5\)—\(1.5\) mm in diameter appear in the form of separate grains, arranged chaotically with respect to one another, but with an obvious tendency toward a common crystallographic orientation (Fig. 9, \(a\)); some of these grains clearly have a block structure and complex serrated outlines, but at the same time there are also grains in the form \(\{110\}\). Then the number of grains and the sizes of the crystallites formed earlier increase, but the grains still remain isolated. However, in their relative position an ordering is outlined, with a tendency toward the establishment of the face of the future crystal in the form \(\{110\}\). Judging by the reflection of light from

surfaces of the grains, the latter prove to be noticeably spatially disoriented. At one of the subsequent stages (Fig. 9, б) the formation of a crystal of clearly mosaic structure takes place. On its {110} face the blocks predominantly coalesce along the edges and as islands within the face. Later, on the continuous surface (Fig. 9, в) of the fully formed garnet crystal, blocks of several orders can be observed on the {110} face.

The block structure is no less clearly expressed in quartz crystals. Especially suitable for studying the block structure are crystals of rock crystal, amethyst, smoky quartz, citrine, and morion, on whose prismatic and rhombohedral faces both macroblocks and microblocks can be distinguished. Macroblocks are readily distinguished by visual examination of the crystal surface and are comparatively easily recognized when light is reflected from a face.

Fig. 9. Formation of a garnet (andradite) metacrystal in granular marble. а — appearance of nuclei—crystallites; б and в — successive shaping of the {110} faces of garnet.

Quartz microblocks require, for their study, the use of a goniometer, a microscope, and obligatory etching with hydrofluoric acid. One of the characteristic features of quartz crystals is the presence of frequently encountered growth striation or induction striation perpendicular to the edge of the hexagonal prism. Each macroblock present in the structure of a prismatic face bears striation which, along its length, does not pass from one block to another: it terminates at the block boundary. This feature very easily makes it possible to isolate the individual elements of the block structure of the crystal surface. Study of the character of the striation on a face within a block, with the aid of a magnifying glass and microscope, makes it possible to speak with some confidence about blocks of the second order. Their existence is indicated by a certain waviness of especially very fine striation.

Fig. 10 gives a clear idea of the block structure of prismatic faces. Such a block structure of crystals arises, on the one hand, through the accretion of individual crystallites on the crystal face at many points. Such crystallites, growing together with the host, merge into a single common crystal with clear isometric outlines of the blocks. In other cases, the block structure is caused by the growth of separate six-sided crystals along the edges and faces of the prism, beginning from the base. In this case the strict orientation of these six-sided forms is absent. Therefore, by their striation the six-sided forms, merging in the plane of the prism, are sufficiently well notice—

Fig. 10. Block structure of the faces $(11\bar{0}0)$, $(10\bar{1}0)$, and $(01\bar{1}0)$ of a rock-crystal crystal.

and their boundary is visible. Further growth of the rods proceeds intermittently, and the crystal nucleus that appears on the head of a rod differs somewhat in its orientation from that of the crystal whose growth it ought to continue. Therefore, naturally, in Fig. 10 a horizontal boundary is shown between the rods, along with a vertical one. As a result of such crystal growth, pseudomonocrystals are obtained. In transparent crystals, “empty” gaps remain at the boundary of blocks that are not strictly oriented; these are clearly visible when light is reflected from the surface of two adjacent blocks.

K. M. Melkova and J. Lhamsuren [19] cite well-known data and thereby recall views on the formation of large quartz crystals through the coalescence and overgrowth of crystals of smaller size; the illustrations they give convincingly support what has been said. The authors further indicate that such a block structure leads to the formation, in quartz crystals, of voids, cracks, and tubular channels with triangular, rectangular, oval, and irregular—angular—cross-sectional shapes, signs of whose emergence can be found on the faces of the rhombohedron [19]. To this it should be added that the so-called vicinal spherical convex triangles with growth traces constitute the termination of the growth of a prismatic block of the general plane \(\{10\overline{1}1\}\). It is precisely at the boundaries of such figures that the outlets of pores and channels are associated.

A. V. Shubnikov [24] gives a number of photographs of the etched surface of quartz crystals by hydrofluoric acid, from which their block structure is clearly visible.

Thus, from examples of the formation of “large” quartz crystals, one may with full justification assume that “small” quartz crystals are also, on the whole, composed of crystallites which in general coalesce not so ideally in spatially parallel fashion. This latter circumstance makes entirely understandable the presence in quartz of pores and voids, which to varying degrees prove to be filled with gas–liquid inclusions. The latter, being distributed in a number of cases parallel to the faces of the crystal, account for the emergence in them of zonal structure.

A sphalerite crystal from the Darasun deposit, up to 6 cm in diameter, spherical in form and with a large number of faces, was accidentally subjected to all-round compression, as a result of which it broke up into a large number of blocks ranging from 10 to 5 mm and smaller in diameter, and split along the cleavage. The surface of each block bore contact growth striation. In other words, the sphalerite crystal had an obviously coarse-mosaic (block) structure. The nuclei of the blocks of the future crystal, just as in the case of garnet nucleation, were initially arranged disorderly relative to one another, but in general they were crystallographically spatially oriented; and, owing to this, as each block grew separately, such a large single crystal could form.

The block structure of relatively large crystals can be observed both in natural crystals and in crystals obtained under laboratory conditions. For example, such a structure can be seen in crystals of potassium bichromate—\(K_2Cr_2O_7\)—the flat surface of which is partly composed of flattened prismatic crystallites with somewhat different orientations. The entire mass of a potassium bichromate crystal is composed of exactly the same crystallite blocks; as is clearly visible in a fracture, it is filled with macro- and micropores. Study of the surface of large sugar crystals measuring up to \(2.0 \times 1.6 \times 1.2\) cm

before etching and after etching also prove to be constructed of blocks (Fig. 11).

Crystals of sodium and potassium halides, grown from saturated aqueous solutions in the presence of ethyl alcohol, in the form of thin plates and long prisms \(2 \times 2\) mm in cross section, often proved to be composed of cubes of various sizes that were not always ideally oriented. The block structure of the crystals described is especially

Fig. 11. Block structure of sugar crystals

clearly visible on their surface (Figs. 12, 13), which, as in the case of the cubic crystals of alum of A. V. Lavrsky, is made up of plates with clearly square outlines. Such plates either are in close contact with one another, and in their field, at the contact of individual plates, voids have been preserved in the form of elongated or spherical outlines, or else there are salt-free gaps between the plates, which on the surface form a complex rectangular network of channels.

Such a sculptured surface of one growth layer of the crystal is overlain by another similar sculptured layer, and this latter in turn is overlain by a third, a fourth, and so on. As a result, each layer deposited on the surface of the crystal “slams shut” all the defects of the surface of the preceding layer, together with the remnants of mother liquor in them. The defects themselves in this case have the form of negative cubes, prisms, and various kinds of streaks, all such formations being located only in the plane of crystal growth. Individual surface channels communicate by fissures with the channels of the underlying preceding growth surface.

Thus, the study of halide crystals clearly shows us that a block structure is characteristic not only of the surface

Fig. 12. Block structure of the {100} face of prismatic crystals of potassium and sodium chloride salts. Magnification 200×

Fig. 13. Block structure of the cleavage plane of rock salt. Carbon replica, shadowed with chromium. Electron magnification 6000×

parts of them, but it is also indispensable for the internal structure of the crystalline edifice, a phenomenon that very simply and naturally explains the appearance of many defects in crystals.

A. E. Fersman, in his work Crystallography of Diamond, gives many examples of the fact that natural diamonds are intergrowths of a large number of crystals. Thus, a cube face [22, Figs. 140 and 141] is covered with quadrangular etch pits, the details of whose structure are illustrated by sketches of the picture seen under the microscope. These dissolution pits are negative octahedral crystals (Fig. 14) [22, Figs. 153, 155]. In Fig. 15 A. E. Fersman [22, Fig. 43] showed schematically that, in a particular case,

Fig. 14. Pits between tetrahedral blocks of diamond crystals

Fig. 15. Overgrowth of “octahedral” faces of diamond by platy crystallites

an octahedral face is an aggregate of triangular faces of different sizes superposed upon one another. In Fig. 16 [22, Fig. 37] a polycrystal is shown on which faces {100}, {110}, {111} are outlined. In general, however, a diamond crystal is an aggregate of intergrown and accreted, in enormous number, misoriented plates {111} of different sizes. For such reasons the faces {111} are composed of noticeably misoriented plates. The face {110} is ribbed, owing to projections of one side of the plates along the octahedron. The faces {100} are pitted, owing to the emergence of the vertices of triangular plates. Therefore, naturally, a crystal of such structure is sufficiently porous and spatially, physically, and geometrically inhomogeneous.

A large number of the crystals presented in the atlas [22] are in complex twinned intergrowth and are composed of 48, 24, and 12 individual blocks.

Crystals of dolomite, siderite, and rhodochrosite are well known in the form of curved rhombohedra resembling the shells of bivalve mollusks. Such crystals turn out to consist of smaller rhombohedral crystallites of different sizes, which, relative to their neighbors, do not fit into dense rows in the plane of the rhombohedron, but are displaced somewhat with respect to one another in one direction; this also causes, as it were, a regular bending of the rhombohedral crystals. The smaller crystallites of the indicated rhombohedra, in turn, are composed of still smaller submicron crystallites, which likewise do not have a strict spatially parallel orientation, as a result of which they can be distinguished.

Incidentally, crystals of many zeolites behave in the same way.

A similar picture can be observed quite clearly in gaylandite in platy crystals; however the crystals of desmine may split, they nevertheless tend to acquire the collective form of a mosaic crystal.

The mosaic structure of crystals is very characteristic and is encountered quite often among minerals of the garnet, tourmaline, orthoclase, albite-cleavelandite, zeolite, dolomite, siderite, aragonite, cerussite, barite, gypsum, magnetite, tremolite, actinolite, augite, and

Fig. 16. Platy blocks of tetrahedra \(\{\bar{1}11\}\) and \(\{111\}\), growing together, cause the appearance, in one case, \(a\)—of pitted cube faces, ribbed \(\{110\}\) and platy \(\{111\}\) faces, and in the other, \(b\)—of octahedral diamond crystals

many other mineral formations. It should be assumed that macro- and micromosaic structures of crystals are a very widespread feature of them; at the same time, as M. V. Erofeev [11] first showed, it represents a mode of formation of real crystals of large and all small sizes, a circumstance that casts doubt on the existence in nature, laboratories, and factories of single crystals with a single spatial lattice characteristic of them, as is accepted by many. In mosaic-built crystals the lattice is likewise mosaic-built. In a mosaic crystal the elementary particles that compose it, moreover, are not arranged strictly parallel throughout and side by side; at mosaic boundaries there is a series of defects of both point, linear, and more complex character.

The next group of minerals whose imperfections are created during crystallization will be the group of zonal crystals. Zoning of growth is a basic feature of any crystal. If the physicochemical growth conditions remain the same during the formation of a crystal, then the zonal structure of the crystal is difficult to detect, although theoretically it goes without saying. But if, during crystal growth, the chemical solution changes somewhat, the crystallization temperature fluctuates, and, consequently, the concentration of the solution feeding the crystals does not remain constant, then all this taken together is reflected in the fact that the chemical composition of the deposited zones is noticeably different; one zone, in comparison with another, the preceding one, was deposited from a solution of different saturation, and each of them naturally carries a different number of defects. Finally, fluctuation in the saturation of the solution may lead to a temporary cessation of grow-

… and even partial dissolution of the already formed surface of the crystal, upon which, with a subsequent increase in supersaturation, the next growth zone will begin to be deposited. Often, crystals of another composition are deposited on the surface of a zone with traces of dissolution; for example, in zonal orthoclases, one may find on the surfaces of such zones flakes of biotite, prisms of hornblende, and grains of quartz.

It follows from what has been said that zonality is an obligatory property of crystals, but in each particular case it manifests itself differently.

Let us turn to some facts.

An excellent example of zonality is provided by zonal plagioclases. The latter, as is known, are a solid solution of substances corresponding to the composition of albite \(Ab—\mathrm{NaAlSi_3O_8}\) and anorthite \(An—\mathrm{CaAl_2Si_2O_8}\); the general composition in this case may be expressed by the formula \(n\mathrm{CaAl_2Si_2O_8}(100-n)\mathrm{NaAlSi_3O_8}^{*}\). Zonal crystals of plagioclase are of two kinds [14]. In some cases the zonality changes gradually from plagioclase of a higher number to plagioclase with a lower content of the anorthite molecule, for example, from No. 62 to No. 37, or from No. 37 to No. 20–18. The boundaries between zones, as a rule, are not sharply expressed; the change in chemical composition from zone to zone takes place gradually and smoothly, and therefore the optical properties change from number to number gradually, regularly, without any noticeable jumps. However, with slow rotation of the stage of the polarizing microscope, even in this case one can observe boundaries between zones, although weakly expressed.

In another case the zonal structure of plagioclase is clearly manifested in a stepwise manner [14]. This is so-called repeating (recurrent) zonality. Thus, for example, in one of the numerous cases the inner part of a plagioclase grain, in its optical properties, corresponds to No. 37 (Fig. 17); externally it is embraced by a zonal band, the inner zone of which corresponds to plagioclase No. 52, and the outer one to No. 42. The transition from No. 52 to No. 42, as can be judged from the optical properties, is gradual, which is closely connected with the gradual change in the composition of the plagioclase zones within the band itself. Upon this latter there is superposed the next band of zones, the inner part of which consists of a zone of plagioclase No. 52, and the outer part—No. 37, and so on. In general, the scheme of the zonality described may be expressed by the following formula: core No. 37 \(|\) No. 52—No. 37 \(|\) No. 48—No. 37 \(|\) No. 42—No. 33 \(|\) No. 37—No. 27. From what has just been said it follows that in passing from No. 37 to No. 52, from No. 42 to No. 52, from No. 37 to No. 42, etc., a jump is clearly manifested, caused by a sharp change in composition, which is quite clearly reflected in the optical properties of the two neighboring zones of adjacent bands.

Fig. 17. Zonal plagioclase

From consideration of Table 1 of the mean geometric constants of plagioclase crystals [26], it follows that in zonal crystals, within the zonal band, the dimensions of the space lattice change gradually—

* \(n\) is a number in % expressing the content of the anorthite molecule in the given plagioclase: \(nAn(100-n)Ab\).

over a span of several minutes. In fact, within the limits of belts No. 52—No. 42, No. 52—No. 37, etc., the angular constants change by no more than 7–8 minutes on average¹, but this is quite sufficient to have a corresponding effect on the optical properties, for example, on extinction in polarized light and on the definition of the zonal belt itself.

Table I

The transition from one zonal belt to another is always sharply expressed and has a discontinuous character, which is a consequence of the abrupt transition step from zone No. 37 to zone No. 52, from No. 42 to No. 52, from No. 37 to No. 48, and so on.

Therefore one must suppose that at the boundary of two adjacent zonal belts, in contact with one another, the boundary zones have noticeable discrepancies in the dimensions of the lattice cells, which is correspondingly reflected, for example, in the optical properties. This boundary between the belts of zones is, moreover, the place along which plagioclases are later most readily subjected to various subsequent alterations: for example, sericitization, chloritization, epidotization. In the case of sharply expressed recurrent zoning of plagioclase, it can often be observed that the surface of the preceding zonal belt is, to varying degrees, subjected to dissolution, and on this dissolved uneven surface the next belt of zones is deposited. For this reason the boundary between zonal belts often looks emphatically sharp, because in the boundary regions of two adjacent zones there are certain structural and physical discrepancies.

Many examples of the zonal structure of crystals can be cited from the mineral kingdom. Thus, for example, zonal structure is very often encountered among garnets, which, moreover, quite often turn out to be sectorial-zonal formations. Magnetites from metasomatic iron deposits are, as a rule, zonal; moreover, the zoning may be simple, when one zone grows upon another, and it may be complex, when upon a simple ordinary zone there grows a zone

typically encrustational, and on this latter simple zones are deposited, and on them, in turn, encrustational zones grow, etc. [30].

In magnetite, both with simple zones and with encrustational ones, zones of the first order are readily distinguished; and in first-order zones very fine zones of the second order are distinguishable. In first-order zones of magnetite the following feature very often attracts attention: the inner part of the zones in well-polished and etched sections appears dense, whereas the outer part is porous and contains relics of the replaced rock.

In some crystals of radioactive cassiterite the thickness of the zones varies within the limits of 0.25–0.0005 mm; among them, first-order zones from 0.30 to 0.05 mm and thinner, and second-order zones from 0.02 to 0.005 mm and thinner, are clearly distinguished. The inner part of this zonal crystal is in a metamict state; in separate areas, fragments with zonal structure have been preserved.

Fig. 18. Zonal magnetite.

A number of literature data are cited concerning the polycrystalline and heterogeneous structure of crystals of muscovite and phlogopite [7, 9, 20, 21]. Thus, N. M. Uspenskii and V. D. Nikitin describe large zonal crystals, brown and red-brown in color, known as “ruby muscovite,” for which zonality is characteristic, visible in plates 2–3 mm thick. In addition to zonality, both authors provide data indicating that relatively large muscovite crystals have a reticulate-banded structure, a circumstance illustrated by sufficiently clear photographs. The reticulate-banded structure itself is a combination of zonal banding and intersecting banding parallel to {010} and {221}. According to V. D. Nikitin, zonality in ruby micas, owing to a change in color, is clearly expressed; the number of zones in individual cases reaches 150. The width of first-order zones varies over broad limits, from 1 to 25 mm. The boundaries of the zones in plates 2–3 mm thick are clearly expressed. Within the colored zones the intensity changes both on passing from zone to zone and within each zone. In the latter case, the inner part of the zone proves to be relatively densely colored, and its inner boundary is sharply expressed. Toward the outer edge of the zone the intensity of the color decreases. V. D. Nikitin explains the brown coloration itself by the replacement of part of the aluminum by iron. Therefore the more internal part of the zone has a higher refractive index than the refractive index of its outer part. Judging by the color of the zones and the iron content in them, the amount of the latter changed slowly and regularly within the zones and abruptly from zone to zone.

I. Ya. Dyadkina (the third author), who devoted considerable attention to the morphology and genesis of muscovite from the Slyudyanogorsk deposit (Middle Urals), showed that the large crystals of this mica formed as the result of a complex process of potassium metasomatism at the stage of granitization of rocks in the place of amphibole gneisses. Such transformations began with the biotitization of amphibole and the formation of micaceous gneiss with fine-scaled biotite; the continuing process of introduction of potassium and aluminum led to the removal of iron and magnesium and to the formation of fine-scaled muscovite gneiss. This same process subsequently leads, on the one hand, to the overgrowth of individual scales with the formation of zones, and, on the other, to the coalescence of small mica scales and the formation of large ones, which are surrounded by a belt of fine-scaled aggregate. I. Ya. Dyadkina, describing large plates of mica, notes that within their mass there are also differently oriented scales of muscovite, i.e., the formation of large mica plates proceeds according to the same plan as that of large crystals of pyrite, quartz, tourmaline, garnet, and many other minerals: first, individual crystals arise with the same spatial orientation; then, as their growth continues, they acquire the visible character of a single crystal.

Zonal structure is known for calcites, barites, galenites, smaltines, pyrites, fahlores, orthoclases, corundums, hematites, pyroxenes, quartzes, for crystals of sodium chloride, potassium chloride, for fluorites, tourmalines, disthenes, and many other minerals.

Finally, an example may be cited of recrystallization in the solid state with the formation of a complex crystalline construction having a polycrystalline character of aggregation. I have in mind rock salt, which is well known to everyone. For example, cleavage pieces of it from the Artemovsk deposit in the Donbas.

When etched, cleavage pieces of NaCl no more than one centimeter thick, when examined under the microscope at low magnifications, often prove to consist of blocks of various sizes, whose configuration is sometimes irregular and sometimes regularly cubic. In this latter case, a cleavage piece of rock salt proves to consist of a series of parallel-arranged cubes of crystals, more or less identical or different in size. Sometimes, upon etching, on the cubic forms one can distinguish, in addition to the face (100), the faces (210) and (110). The dimensions of the blocks range from 1–0.8 mm to 0.1–0.05–0.01 mm and even 0.001 mm. On some etched crystals, very small NaCl crystallites in the form of cubes form parallel rows and a parquet-like arrangement of cubes measuring 0.01–0.005 mm and less (Figs. 19 and 20).

Among the imperfections of crystals must be included inclusions that form in them during the period of crystal formation. A large number of such examples can be given from the field of magmatic formations, in which, during the crystallization of one of the minerals being formed, another is captured. For example, crystals of basic plagioclase often contain needles of rutile; crystals of oligoclase may be found enclosed in orthoclase; quartz is often captured by orthoclase; grains of apatite and zircon are often found enclosed in biotite and hornblende. In hydrothermal formations there are also frequent cases of inclusions: stannine in chalcopyrite, sphalerite and, conversely, pyrrhotite, chalcopyrite, stannine in sphalerite; in pyrite—grains of chalcopyrite; in galena—enclosed argentite; in magnetite—ilmenite; in ilmenite—hematite; in titanaugite—grains of plagioclase. A classic example of regular dis-

Fig. 19. Block structure of rock-salt crystals. Magnification 150×

Fig. 20. Block-packet structure of crystals. Magnification 200×

...the determination of carbonaceous (graphitic) pigment are andalusites, known as chiastolites.

Gypsum and calcite crystals, developing in a mass of sand, prove to be filled with inclusions of sand grains. Calcite crystals, forming in sandstones, become poikilitic. In this case, on the cleavage planes of calcite, disorderly included grains of quartz sand are clearly visible. During the development of calcite there is at the same time partial dissolution of the surface of the grains of the captured mineral. If we cite the coefficients of linear expansion for quartz, $\perp c = 13.24 \cdot 10^{-6}$ and $\parallel c = 6.99 \cdot 10^{-6}$, and for calcite, $\perp c = -5.75 \cdot 10^{-6}$ and $\parallel c = 25.57 \cdot 10^{-6}$, then it is clear to us that, at the boundary of quartz and calcite grains, temperature changes create stresses of different magnitude, which are intensified at the epigenetic stage of existence of poikilitic formations.

As is evident from what has been said above, the nature of the imperfections of crystal structures formed at the stage of syngenetic crystal formation is extremely diverse; their defects are likewise diverse, and their character depends on the physicochemical setting and on the character of the imperfection itself. These imperfections affect the density of crystals. Thus, a study of the microhardness of crystals, using zircon as an example, showed that it varies within the range from 750 to 2800 kg/sq. mm [10]. The data cited indicate that the density of packing of crystals in the plane of a face is not ideal. In those cases, as occurred in A. V. Lavrsky’s crystals (Fig. 8), if the crystallites in the crystal structure are packed as tightly as possible, then the hardness in this case is the highest; but if defects occur between the crystallites in the packing—lack of strict parallelism, fissures of various forms, voids—then, naturally, the hardness at these points will be below the average.

By a special method of crystallization it is possible to obtain crystals, for example, of sodium and potassium halides, with a large number of pores. Such crystals have a reduced density. For example, sodium chloride, instead of a specific gravity equal to 2.165 g/cm³, may have from 2 to 1.8 g/cm³; potassium chloride, instead of 1.99 g/cm³, has 1.90–1.8; the specific gravity of potassium bromide is 2.52 g/cm³ instead of 2.75. Owing to this feature, such crystals lose transparency and acquire a pearly luster.

Thus, on the preceding pages a large and varied body of material has been considered concerning syngenetic imperfections of crystals of certain compounds, formed in the course of their growth. From the examples considered it follows that the principal element of crystal structure is macro- and microcrystallites (submicrons) of several orders. The latter, being of different size, are not arranged on the faces, and consequently also in the mass of the crystal, spatially in a strictly parallel and equally dense manner. This circumstance, as follows from the examples considered above, leads to the formation of macro- and micromosaic crystals expressed to varying degrees, which carry defects both in the continuity of the crystal structure and in their general homogeneity.

Thus, the nature of crystal imperfection at the stage of their formation in the process of growth is determined by the imperfection of the packing of crystallites in the mass of the crystal as a whole and, in particular, by the imperfection of the packing of crystallites on the faces of the growing polyhedron.

At the boundaries of crystallites there arise defects, different both in form and in magnitude. Among them the most frequent are pores, which are located between individual crystallites and especially readily along

faces, along the boundaries between zones that contain a sufficiently large number of voids. In addition, individual voids are elongated in one direction and are, in essence, linear defects—linear dislocations.

Furthermore, crystals contain two-dimensional defects in the form of gaps between crystallites, between rows of crystallites. Linear and point defects, merging, form simple channels, twists, or networks of channels. Defects of one layer of crystallites, joining with defects of layers situated below and above, form a complex labyrinth network in three dimensions.

The presence of point and linear dislocations is judged from defects revealed by etching the surface of a crystal. The emergence of linear dislocations onto the crystal surface is registered by the appearance of etch pits having the form of negative pyramids, with their apex directed into the crystal. As our experiments show, such pits readily arise at the contact of four crystallites, at the point where four edges meet, which in essence form a linear dislocation. Such a dislocation may be confined to a single layer of crystallites, or it may be continued along parallel edges closely adjoining one another. Incidentally, it should be noted that pits of four-faced pyramids of negative sign were first recorded at the beginning of our century as etch pits by A. E. Fersman on diamond crystals, on the faces of every four macrocrystallites out of 24, or on the faces of every 8 crystallites out of 48 \[22, figs. 159, 166, pls. 82, 59, etc.\].

One of the curious features of mosaic crystals is the tendency, during continued growth, toward ordering of the microcrystallites, toward a transition from macromosaic to micromosaic crystals. Similar phenomena can be observed, for example, in polychrome tourmalines from Zavitaya, when several prismatic crystals in their distal parts tend to become a single crystal; prismatic crystals of quartz behave similarly in parallel; so do polycrystalline crystals of fluorite, gypsum, garnets, pyrites, and many other minerals. Therefore, naturally, many real crystals that are often called single crystals are in fact polycrystals composed of crystallites insufficiently ordered in space.

Finally, the porosity of crystals, expressed to varying degrees, ensures the loss of gas–water inclusions and the repeated filling of pores by them. This circumstance plays an enormous role in the life of crystals, in metasomatic processes of transformation of mineral substance, and in the appearance, in place of one mineral, of another with a different composition.

All imperfections of crystals, examples of which have been given in sufficient number, arise in crystals during the period of their formation, and these imperfections, with all their defects, manifest themselves to one degree or another at the epigenetic stages of existence of the crystalline structure created at the syngenetic stage.

LITERATURE

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1. The average magnitude of the fluctuation of the angular constant between two adjacent plagioclase numbers n and n + 1 is, for ∠α, 0.26′; ∠β, 0.45′; and ∠γ, 1.47′. ↩