N. H. Agnew
Rhodes University Grahamstown, south Africa
A Solid State Chemistry Experiment Dislocations in etched calcite by Polaroid photomicrography
Today the role of lattice imperfections in many physical and chemical changes occurring in solids is being increasingly appreciated by chemists (1). In crystal growth (2) and dissolution ( I ) , the photographic process (S), thermal decomposition of solids (4), and addition polymerization (5), to mention only a few processes, the role of defects is well established. The reasons for the pervading influence of defects in solid state processes are to be sought in the enhanced diffusion (6) along dislocation lines, in the extra energy available in defect regions, and in the abnormal stereochemistry (7) associated with certain types of imperfection. It seems advisable, therefore, to give more prominence in undergraduate curricula to some aspects of imperfections in crystals than has been prcviously the case. At the pre-graduate level the crystalline state is frequently treated in terms of the perfect lattice, with perhaps only passing reference to the many types of imperfection such as point and line defects. In an attempt to balance this situation part of a laboratory period devoted to chemical microscopy in the author's final year undergraduate course is used to demonstrate the existence of dislocations in etched cleavage fragments of calcite. The purpose of the present paper is to discuss some aspects of dislocations in crystals, and to present details of the photomicrographic method of demonstrating dislocations used in our undergraduate laboratory. Of the various types of common defect recognized in solids (S), e.g., vacancies, interstitial atoms, line defects or dislocations, and plane defects such as grain boundaries, dislocations are often the most easily observed. The classic experimental technique is by etching, and although other more sophisticated ways arc being increasingly used [see (I)], the etch-pit method remains the simplest in many instances. For this reason it is clearly the method of choice in the teaching laboratory where time and inexpensive equipment are important factors in determining the selection of experiments. Geometrical Aspects of Dislocations
For the purpose of a teaching experiment such as the one outlined here some geometrical properties of dislocations in crystals are worth discussing. Advanced theoretical treatment has been given by Cottrell (9). Line defects, or dislocations, extend along straight or curved lines in the crystal. Two extreme types of dislocation are distinguished. The edge dislocation, EE' in Figure 1, can be regarded as an extra half plane
Figure 1. A unit edge didocation EE'. is perpendicular to the dislocation line.
The Burgers' vector lorrow)
Figwe 2. A unit screw dislocation emergent at S on the crystal surface. The Burgen' vector btraight arrow) is porollel to the didocation line.
inserted into the lattice resulting in distortion of the adjacent planes along the dislocation line. The screw dislocation (Fig. 2 ) is in effect a lateral shift or slip of one half of a crystal plane relative to the other. The name arises because movement of this type converts the entire crystal into a single helicoidal surface. In Figure 2 the course of the curved arrow runs from the surface plane dovn a ramp to the adjacent plane. Repitition of this operation traces out the helical path of a screw thread. The screw dislocation in Figure 2 thus traverses the entire crystal and emerges on the opposite crystal face. For topological reasons, which are no>y discussed, dislocations must either emerge at crystal surfaces or close in upon themselves to form loops. I t is impossible Volume
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for a dislocation lime to end within the crystal itself. Thus, in Figure 1 the edge dislocation line emerges a t E and E' on the crystal surfaces; alternatively, if one considers a shortened plane, say EXYZ in Figure 1, the dislocation emerges a t Y on the top surface. The dislocation line is now EXY. Further, if one imagines the crystal to be extended in space, on the front and top surfaces of the crystal, it is readily seen that EXYZ defines a dislocation loop which lies within the body of the crystal. Similar arguments may he applied to the screw dislocation to show that it must likewise either emerge a t a free surface or close in upon itself. For example, in Figure 3 is shown the interaction between screw and edge dislocations. What is purely screw dislocation emergent a t S on one face is changed, along the curved dislocation line, into pure edge dislocation at I3 on another face. Slip of the crystal planes has taken place over the shaded area. It is apparent that the situation here is similar to that shown in Figure 2, except that the screw dislocation, by not traversing the entire crystal, emerges as an edge on the front face. Edge and screw dislocations frequently interact in this way in crystals. An important property of dislocations is the Burgers' vector (10) which describes the magnitude and direction of the slip that has occurred. In Figure 1the Burgers' vector of the unit edge dislocation is shown by the arrow perpendicular to the dislocation line; in Figure 2 the vector is parallel to the unit screw dislocation. A Burgers' vector inclined to the direction of slip designates a combination of edge and screw. Due to distortion of the lattice the region of a dislocation line is one of higher energy than perfect regions in the crystal. The extra energy is proportional to the square of the Burgers' vector (11). As a consequence of this, and probably also because of abnormal stereochemistry a t the dislocation line (I), chemical reactivity a t the point of emergence of a dislocation on the crystal surface is enhanced. Thus, crystal surfaces frequently develop etch pits when treated with a suitable reagent or poor solvent. The pits demarcate the points of emergence of dislocation lines. It is clear, then, that if a crystal is cleaved the cleavage plane will generally intersect dislocation
lines and loops. By etching the matched cleavage faces a 1:1 correspondence of pits should be apparent. The present experiment depends upon this assumption. Historical
It is of interest to trace briefly the evolution of ideas leading to an appreciation of the relationship between line defects, the mechanism of crystal growth a t the screw dislocation, and etch figures on crystal surfaces, since, as discussed below, etch figures have been known and used for a long time but the experimental connection with dislocations has only been realized relatively recently. Etch pits may be defined as cavities of dpfinite shape on crystal surfaces. It has long been known that etch figures result from the preferential action of a solvent or reagent on crystals, and the relationship between the shapes of etch pits and the external symmetry class of crystals has bccn used extensively in mineralogy since the early part of the nineteenth century (12). An explanation, in terms of the dislocation, of the enhanced reactivity a t the sit? of the etch pit was not forthcoming, however, until the early nincteen fifties, although the concept of an imperfection of some sort or another had been put forward much earlier. Thus, Honess (1%)in 1927 thought that etch figures were due to a "slight mpture or other irregularity of the molecular plane forming the surface, or (to) differential cohesion ~ i t h i nthe surface." During the 1930's the model of the edge (13) and the screw (10) dislocation provided significant advances in the theory of the defect crystalline state. The screw dislocation creates a permanent step on the crystal surface, and the mechanism of crystal growth at the step, giving rise to spiral g r o ~ t hpattern on the surface, was introduced simultan~ouslyby Frank (2) and Burton and Cabrera (14) in 1949. This rapidly led to an understanding of the relationship betaeen screw dislocations and etch figures. In an elegant series of experiments Horn, in 1952, sho~ved (15) that when silicon carbide crystals with surface spiral gro~vth patterns are etched for increasing periods the dislocation spiral is first removed. This is followed, on prolonged treatment, by the etching of a pit a t the origin of the spiral. Thus the etch pit may be used to identify the point of emergence of a screw dislocation a t a crystal surface. Further, it was observed (15) that crystals which do not display growth spirals develop identical etch pits, the explanation being that such crystals have smooth surfaces because of the inter growth of the spiral patterns of many screw dislocations. It is now well established that etch pits occur a t the points of emergence of dislocations on the surface of crystals. The defect region of the lattice a t a dislocation line is characterized by higher energy and enhanced reactivity, and inde~dthe important consequences of dislocations in solid state chemistry are being increasingly realized, as stressed recently by Thomas (1). The Experiment
Figwe 3. Interaction of unit edge and x r e w dislocations. At S the didocotion is pure screw; a t E pure edge. Along the curved line it is a mixture of m e w and edge. Slip has occurred over the shaded area.
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By etching two matched cleavage fragments from the same face of a calcite rhomb, and then photographing the opposing surfaces a 1 :1 correspondence of the etch pits (Fig. 4) demonstrates the presence of
Figure 5. (A) mnd (81 Makhed cleavage rhombohedra of calcite. Ekh pits hove differently oriented internal rtrvstvrer due to the inclination of the carbonate ions to the cleavage turfose ABCD.
Procedure
B Figure 4. (A1 and (8) Matched cleovogo faces of etched colcite (ohout 1 8 0 x 1 and enlarged.
dislocations intersecting the cleavage plane. An interpretation of the etch figures of calcite has been given by Thomas and Renshaw (16). Thus, in assisting students to interpret their results the following points are discussed. Enhanced reactivity a t the point of emergence of the dislocations on a cleavage face results in the formation of the etch pits. This, together with the fact that prolonged etching does not increase the number of pits is convincing proof of the presence of dislocations. Furthermore, examination of opposite sides of an etched cleavage fragment shows that there is little or no correlation between the pits, indicating that the dislocations close in upon themselves to form loops. A number of other interesting aspects of the etch figures of calcite may also he discussed. For example, individual etch pits on the matched cleavage fragments are not mirror images (Fig. 4). This has been attributed (16) to the C O P ions at corresponding surface sites being inclined at the same angle to the surface. I n Figure 5 the cleavage rhombohedra shown contain carbonate ions arranged in planes perpendicular to the 3-fold rotational axis CE. Calcium ions (not shown) are sited at corners and centers of faces. On the cleavage surface ABCD in Figure Sa the four carbonate ions shoun all tilt towards AB while on the matched surface A'B'C'D' the ions are tilted towards A'B'. Thus, the etch pits have the differently oriented internal structures shown. Shallow background pits are also a feature of etched calcite (Fig. 4). These are thought to be due to the presence of point defects such as cation and anion vacancies (16). The experiment is popular with students-possibly because of the novelty in the chemical laboratory of photomicrography.
The experiment takes about an hour to perform. A calcite rhomb is cleaved with a. razor blade and a mallet, in a wooden corral1 t o prevent the fragments scattering. Two successive cleavage fragments are cut from the same face of the rhomh. After a few trial attempts good cleavage faces an fragments about 1-2 mm thick are easily produced. The two faces are examined side by side under a stereomicroscope, a t low magnification, to ensure that they are matched. They are then etched far 10-1.5 see in 10% aqueous tartaric acid, with shaking. The fragments are washed successively in water, and in acetone, and are then dried in air. The cleavages are again examined side by side under the microscope with matched faces turned up. I t is convenient to choose some imperfection on the cleavtvage surface. such as the intersect,ion of two lines (or cleavage steps-see Fig. 4), t o enable the corresponding region of the matched face to be located easily. The etch-patterns on the cleavage surfaces may he matched visually under the microscope hut it is more convenient t o phot,ograph corresponding regions at a magnification of about 40X and subsequently to match the prints pit hy pit. Photographic prints make a. permanent record of the results of the experiment and, in addition, allow a much better eompsrison of the matched faces than visual inspection of one face a t a time. The Polaroid Land Instmment Camera (.\lode1 ED-10) with film type 107 (ASA rating 3000) is ideal. The camera has a universnl eyepiece-adapter which fits any microscope eyepiece. We use a stereomicroscope as the instrument of choice since the range of magnifications allows more rapid scanning of the cleavage fragments a t low power than does a. conventional microscope. The camera is slid over one eyepiece for phatographing. The faces of the cleavage fragments, placed side by side are photographed in transmitted light (3 V, 30 W). With an exposure time of 3 see it was found necessary t o reduce the light intensity ( a t 40X magnification) by means of a polarizing or green filter in order to avoid overexposure.
Literature Cited (1) T m n m J. M.. Chcm. Brit., 6 , 6 0 (1970). (2) h m x , F. C.. Discuss. Fmadov Soc 5, 48 (1949). 1.M.. A N D MITCXELL. J. W.. Phi!. MRD.,41.223 (1953). (3) HEDGES, (4) THOMAS, J. M., A N D REL(BHAIV, G. D., J . Chem. Sor. ( A ) , 2058 (1967). ( 5 ) R A ~ F O RC.~ H., , A N D E ~ s ~ r oG. ~ C., o , Quorl. Re"., 23, 271 (1969). ( 6 ) STONE.F. S.. "Mechanism and Kinetios of Reactions in Solida," in "Reactivity ai Solids" (Ermon: on BOER.J. H . ) , Elsevier Publishing Co., Imsterdam. 1961, p. 6. (7) COHEN. M.D., A N D S c ~ n r nG. ~ . M. J.. J . Chem. Soe., I966 (1964). (8) See f a r example, HANNAY.N. B., "Solid-State Chemistry." PrentioeHall. Ino.. New Jersey. 1967. ~ . H.. "Theorv oi Crvatd Dislocations." Blaokie B Son (9) C o m n ~ b A. Ltd.. London. 1964. (10) Bcnoens. J. M.. Pm. Kon. Nod. Akod. Wetenseh, 42, 293 (1938)
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(15) Hona. F. H . Phil. Mou.. 43, 1210 (1952). (16) Tnoma, J. M., A N D R E N B R A w . 0. D., Tian8. Foraday Soc.. 61, 791 (1965).
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