Proceedings of the Tomsk Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov

Vol. 165 — 1969

THE NATURE OF CRYSTAL IMPERFECTION

II. Epigenetic dislocations of crystals in connection with their polymorphic transformations

A. M. KUZMIN

All disturbances that cause the appearance of various types of imperfections in a crystalline structure, according to the time of their formation, have been divided into syngenetic and epigenetic [2]. Syngenetic imperfections of crystals and their dislocations were considered in another article. Here we shall dwell on those imperfections of crystals which, by their origin, are connected with the epigenetic conditions of life. In comparison with syngenetic dislocations, epigenetic dislocations, in the character of their manifestation, are also diverse and are widespread. Epigenetic dislocations, or disturbances of the homogeneity of the structure of crystals, as was noted above, include imperfections that develop in crystals after their formation has been fully completed, after which the finished crystals, during their subsequent life, find themselves in different, highly variable physicochemical conditions and undergo polymorphic changes.

Polymorphic transformations, as is known, are closely connected with changes in the physicochemical conditions of existence of the crystal. E. S. Fedorov drew attention to the fact that “under temperature changes the majority of crystals, if not all in general, undergo substantial changes that transform the given body into an entirely different one.” Such polymorphic transformations, as he wrote, are closely connected with new regroupings of molecules or parts of molecules [6]¹).

Polymorphic transformations may be monotropic and enantiotropic. The transition of diamond into graphite is considered the classical example of a monotropic transformation.

Table 1

Diamond is characterized by perfect cleavage along {111}. Optically it is isotropic, more often anisotropic, revealing anomalous birefrin-

...cleavage, polysynthetic twinning, and asterism. The transition of diamond to graphite is accompanied by an elongation of the diagonal of the cubic cell of diamond, equal to 6.166 Å, along the third-order axis to \(C_0 = 6.701\) of graphite and by some compression in the direction perpendicular to this axis, which, taken together, leads to an increase in the unit cell and to the creation of a looser structure, to a sharp decrease in density and refractive index, and to the appearance of very perfect cleavage along \(\{0001\}\), in whose plane packets of graphite are able to slide relative to one another; diamond crystals, for the same reason, not infrequently exhibit an optical anomaly, while sliding [5] along \(\{111\}\) leads to the formation of polysynthetic domain twinning. Diamond is metastable under normal conditions; however, owing to the large internal friction in this state it can exist for an indefinitely long time. At \(1400^\circ\) in vacuum or in an inert medium, diamond graphitizes from the surface. At \(2000^\circ\mathrm{C}\) it is completely transformed into graphite. According to Bundy, at present experimental paths have been found for the direct transformation of graphite into diamond in an apparatus with high static pressure. In this case, the complete spontaneous transformation of graphite into diamond occurs at 125 kb and a temperature on the order of \(3000^\circ\mathrm{K}\). The diamond obtained in this way can, with lowering of the temperature, be returned to the initial state.

An example of an enantiotropic transformation is sulfur. The latter occurs in 6 polymorphic modifications, of which \(\alpha\)-sulfur and \(\beta\)-sulfur are the best known.

Table 2

Rhombic sulfur, when heated to \(95.5^\circ\mathrm{C}\), first expands slowly. Above this temperature, cracking into a powder, it passes into the monoclinic form, and then melts at about \(119^\circ\). In the reverse process, from the molten mass below a temperature of \(119^\circ\), sulfur crystallizes in the form of slender prismatic and tabular crystals of monoclinic symmetry, which below \(95.5^\circ\) crack with a clearly distinguishable noise and turn into a powder of crystals of rhombic syngony. Thus, sulfur crystals undergo deformation during their enantiotropic transformations.

The two examples just considered clearly show that polymorphic transformations of a crystalline substance, in the transition from one modification to another, are accompanied by deformation of the crystals, which necessarily lead to the destruction of the old phase and the formation in its place of a new one. However, the rebuilding of one modification into crystals of another occurs at different points of the former, especially at its defects, at different rates, and, naturally, the crystal lattice of the new modification is blocky, bearing a number of defects characteristic of it. There are numerous cases, similar to quartz, leucite, boracite, and many other minerals, when, in the form of their crystals, they turn out to be pseudomorphs after the original form and domain-blocky in their internal structure.

Among metals with pronounced polymorphic properties, let us cite tin, which occurs in nature in the native state. Tin melts at a temperature of 231.9°C. On cooling in the range 231.9–161° it, as the $\gamma$-modification, has a rhombic lattice, possesses very brittle properties, and is easily ground into a powder with a specific gravity of 6.6 g/cm$^3$. In the range 161–13.2°C tin is known as the $\beta$-polymorphic variety, as white tin. Its crystalline structure corresponds to the tetragonal system and has a density of 7.30 g/cm$^3$. When rods of such tin are bent, a crackling sound is clearly heard; its appearance is explained by the friction of individual crystals during deformation. The causes of this crackling may be those stresses that arise as a result of the rapid cooling of tin in the mold, which to a certain extent retards its transition from the $\gamma Sn$ phase to the $\beta Sn$ phase. Deformation, however, promotes the “violent” transition of one modification into another, which bears clear traces of dislocations in the form of slip along a clearly expressed cleavage.

Below 13.2° white tin passes into the gray modification $\alpha Sn$, whose density is 5.7–5.8 g/cm$^2$, and whose lattice is cubic of the diamond type. The transition of $\beta Sn$ to $\alpha Sn$ at 13.2° occurs slowly, but is accelerated with decreasing temperature and reaches a maximum at $(-)30^\circ\mathrm{C}$. The transformation of white tin into gray is accompanied by an increase in volume of 25.6%. This transition begins with the appearance on the surface of white tin of the gray variety, the “tin pest,” in the form of patches and furrows of various sizes, which increase in size over time. Tin pest develops not only on the surface of tin but penetrates into the metal along pores and cracks that arise in it both during the transition of $\gamma$-tin to $\beta$-tin and during the transition of $\beta$-tin to $\alpha$-tin.

White tin itself at 13.2° and below becomes unstable, and contact with gray tin is sufficient to accelerate the transition of $\beta Sn$ to $\alpha Sn$. In our, for example, Siberian conditions in winter, the modification of white tin readily passes into a finely dispersed state, in which it is physically and chemically dispersed.

Among the boromagnesian salts let us cite boracite—$\mathrm{Mg_3B_7O_{13}Cl}$, which forms two polymorphic modifications, while the polymorphic transformations are accompanied by the appearance of new dislocation elements of the crystals. The $\beta$-boracite modification is stable above 265°C; its crystals with parameter $a_0 = 12.10\ \text{\AA}$ [9] belong to the polygyral-planar class of symmetry. The second modification, $\alpha$-boracite, stable below 265°, belongs to the digyral, probably tetragonal, system with constants $a_0 = 8.54\ \text{\AA}$, $b_0 = 8.54\ \text{\AA}$, $c_0 = 12.07\ \text{\AA}$, and their ratio $a_0 : b_0 : c_0 = 1 : 1 : 1.413$. The starting material for the formation of $\beta$-boracite is fibrous stassfurtite, whose composition and properties correspond to $\alpha$-boracite. Recrystallization of the latter under conditions of elevated temperature and pressure [9] leads to the formation of $\beta$-boracite$^{1)}$, which, in the form of well-formed crystals with faces $\{100\}$, $\{110\}$, $\{111\}$, occurs embedded in anhydrite. However, such crystals represent a paramorph of secondary $\alpha$-boracite after $\beta$-boracite [9]. Therefore the crystals have a block structure and often consist of 12 irregularly bounded ribbed pyramids, whose apices are directed toward the center of the crystal, while the bounding planes of the crystal are the bases of the pyramids. Each pyramid of the block

$^{1)}$ The possibility of the formation of $\beta$-boracite at 265° and above under the conditions of formation of the Stassfurt salt deposit is doubtful.

in turn, as in many paramorphs, breaks up into a system of parallel bars (domains).

M. Memel’ [10] writes that, upon heating $\alpha$-boracite, as the temperature rises the cell dimensions increase linearly, while near the transition point at 265° the change of the anisotropic $\alpha$-modification into the isotropic $\beta$-modification occurs discontinuously. Hence it is natural to suppose that the reverse transition of cubic boracite into rhombic boracite will be accompanied by structural changes: a breakdown into blocks—pyramids, each of which moreover becomes polysynthetically twinned (domain-like) parallel to the base, i.e., $\alpha$-boracite as a paramorph physically becomes inhomogeneously constructed. The formation of blocks and of a domain structure in a block leads simultaneously to the appearance of new dislocations in the crystal.

An example of polymorphic changes with multistage transformations may be silica. The series of its principal polymorphic modifications and the relationships between them are illustrated in Table 3.

Table 3

However, within the scope of the present work we shall confine ourselves to consideration of two sufficiently well studied modifications, $\beta$- and $\alpha$-quartz, whose principal features are correspondingly reflected in Table 4.

Table 4

From this table it follows that the transformation of the $\beta$-modification of quartz into the $\alpha$-modification in connection with a lowering of temperature leads to a lowering of the crystal symmetry, to a decrease in the lattice dimensions, and to densification of $\alpha$-quartz in comparison with the $\beta$-variety by 5.8%. At the same time the parameter $c_0$ in the direction of the principal crystallographic axis is shortened by 0.052 Å, or by 0.97%; while in the direction perpendicular to it the parameter $a_0$ decreases by 0.086 Å, or by 1.79%; i.e., during the transition of $\beta$-quartz into $\alpha$-quartz the lattice cells and the lattice itself as a whole undergo nonuniform compression, which to a relatively greater extent takes place in the direction of $a_0$.

Such compression of crystals leads to deformation which, in crystals of mathematical quartz, accounts for the appearance in it of a distinctly expressed wavy extinction. The axis of the wave of such extinction is generally parallel to the direction of the optical axis \(Ng\), i.e., the wavy extinction of quartz in polarized light is a consequence of a regular change in the structure of the crystal during its polymorphic transformations. In some cases the wavy extinction is sharply expressed; in others it often has a blurred character and appears in the form of spotted or mosaic, cloudy and dispersion-like extinction, and in the form of annular extinction from the periphery toward the center or vice versa, sometimes in the form of sectorial extinction resembling an hourglass type of extinction.

A. E. Fersman, referring to Sosman, indicates [7] that when the temperature falls from 1000 to \(575^\circ\), the volume of quartz increases by no more than 0.3%; but at the moment of transition of the \(\beta\)-modification of quartz into the \(\alpha\)-modification, the volume contracts by 0.86% relative to the initial value. On cooling within the range \(600—300^\circ\)C, quartz crystals undergo a further contraction of \(4.5—5\%\); below \(300^\circ\), the decrease in the volume of \(\alpha\)-quartz continues very slowly. Such compression of the spatial lattice within \(1000—25^\circ\)C is quite sufficient to cause the corresponding deformation in the mass of the crystal. At the same time, the decrease in the volume of quartz takes place over a shorter period (according to A. E. Fersman, “catastrophically” rapidly) than is required for the rearrangement of the lattice of \(\beta\)-quartz into \(\alpha\)-quartz. This contradiction between the necessity of reducing the volume relatively rapidly in accordance with the lowering of temperature and the relatively slow rate of rearrangement of the lattice is resolved by deformation of the quartz, by the appearance of a disturbance of homogeneity and by the emergence of wavy extinction.

As for the factor of tectonic pressure, which causes the appearance of mechanical deformation and to which the occurrence of wavy extinction in quartz is usually ascribed, it by itself is hardly capable of producing such a phenomenon\(^1\), apart from crushing it. However, by virtue of the retardation and hence the delay in the development of the transition of one modification into another, wavy extinction may appear in weakly expressed forms. In this case, external pressure may accelerate the deformation process and the rearrangement of the lattice that has begun, and thereby, as it were, promote the occurrence of wavy extinction in quartz. Thus, during the transition of \(\beta\)-quartz into \(\alpha\)-quartz, its block structure is often revealed, which under tectonic pressures is emphasized throughout, while the blocks themselves undergo a certain displacement relative to one another.

A clearer picture of polymorphic transformation can be shown in leucite—\(\mathrm{KAlSi_2O_6}\), which, for example, occurs in sufficiently well-formed crystals in the lavas and tuffs of Vesuvius. At temperatures above \(620^\circ\)C, \(\beta\)-leucite is distinctly cubic; it is characterized by a tetragontetrahedral crystal habit, its geometrical constant \(a_0 = 13.40\) Å, and it is optically isotropic. At temperatures below \(600^\circ\) and under ordinary conditions it is anisotropic; in polarized light, under crossed nicols, it breaks up into separate blocks\(^1\), and each block consists of parallel square bars (domains). The bars of neighboring blocks are arranged mutually perpendicular (Fig. 1). In sections \(\{111\}\), the structural pattern of leucite, as is evident from Fig. 2, is—

\(^1\) However, in the case of the manifestation of general plastic deformation, for example, of granites, wavy extinction occurs equally in quartz, feldspars, mica, and hornblende.

\(^1\) We note that leucite crystals from Vesuvius quite often prove to be macrodeformed.

is very complex and changes with rotation of the microscope stage (Fig. 2, b). Thus, with decreasing temperature, β-leucite transforms into α-leucite of tetragonal syngony with geometric constants \(a_0 = 12.95\ \text{Å}\), \(c_0 = 13.65\ \text{Å}\), i.e., such a transformation is accompanied by contraction in the directions [100] and [010] and expansion along [001].

The group of titanates Ca, Ba, Pb generally behaves analogously to leucite. Thus, perovskite—\(\mathrm{CaTiO_3}\)—under ordinary conditions is composed of blocks, and each block proves to be polysynthetic with twinning [6]. Barium titanates—\(\mathrm{BaTiO_3}\)—behave similarly; above \(120^\circ\mathrm{C}\)—the point of polymorphic transformation—they possess the properties of cubic crystals. Below this transformation point the zone axis [001] elongates by 1%,

Fig. 1. Optically anomalous leucite in section [001].
a—a crystal consisting of a large number of blocks with domain structure. Magnification 15×; b—domain structure of one of the blocks of the same leucite crystal at magnification 30×

Fig. 2. Optically anomalous leucite in section [111].
a—domains intersect at angles of \(60^\circ\), \(120^\circ\). Magnification 60×; b—in the same thin section, upon rotation by \(30^\circ\), the domain-structure pattern becomes more complex. Magnification 60×

the crystals become tetragonal and at the same time break up into blocks, and each block into domains—a system of parallel bars, analogous to leucite. Crystals similar to titanobarite possess the properties

ferroelectric. A new phase transformation with lowering of the temperature for this compound occurs at \(+10^\circ\text{C}\) and below.

All other analogues of titanobarium and perovskite also have the same character of changes during polymorphic transformations.

Let us give one more case of polymorphic transformations, the manifestation of which depends on the qualitative features of the medium; in particular, the minerals of iron sulfide, pyrite and marcasite, are meant.

Pyrite crystallizes from neutral or weakly acidic solutions, whereas marcasite crystallizes from more acidic ones. Therefore, naturally, if the acidic medium is neutralized, the marcasite that has formed finds itself in an unstable state and, adapting to the new conditions, undergoes a series of corresponding deformations connected with its transformation into pyrite. This transformation is usually accompanied by loosening of the marcasite.

Table 5

However, marcasite has the possibility of preserving itself for some time by sacrificing part of itself. Thus, with access of oxygen and hydrogen, marcasite, sacrificing one particle of \(\mathrm{FeS_2}\),

\[ n[\mathrm{FeS_2}] + \mathrm{O_2} + \mathrm{H_2O} \to (n-1)[\mathrm{FeS_2}] + \mathrm{FeSO_4 7H_2O} + \mathrm{H_2SO_4}, \]

creates around itself the acidic medium necessary for its existence. Therefore it is quite natural that marcasites become covered with a whitish coating of iron vitriol powder and loosen. Marcasites in museums that have undergone prolonged cooling with an increase of humidity in the rooms also become covered with a needle-like powder of iron vitriol, and the bottom of the cardboard boxes becomes brown from \(\mathrm{H_2SO_4}\).

Let us give one more example of multistage polymorphism for ammonium nitrate \((\mathrm{NH_4NO_3})\).

Table 6

From the table just given it is clear that the existence of each polymorphic modification corresponds to definite physicochemical conditions, and each modification is stable within a definite temperature interval, while its formation is accompanied by a definite amount of heat of transformation. Each phase of a polymorphic transformation corresponds to crystals of a definite crystal system, with geometrical constants specific to them. Hence, naturally, during phase transformations the preceding polymorphic modification, in passing into a new one with a decrease or increase in specific volume, must undergo physical destruction associated with reconstruction.

Examples of polymorphic transformations that are accompanied by rearrangement of the internal structure of the crystal, by various kinds of deformations, and by disturbances of its initial homogeneity can be cited in sufficient number from any class of minerals.

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