Role of dislocations in the growth of single crystals of potash alum

摘要

Faraday Discuss., 1993,95, 173-1 82 Role of Dislocations in the Growth of Single Crystals of Potash Alum J. N. Sherwood and T. Shripathi? Department of Pure and Applied Chemistry, University of Strathclyde, Glasgow, UK GI IXL Using a combination of growth kinetics and X-ray topographic studies an assessment has been made of the role of growth dislocations in the growth process on the ( 111) and (1 10) surfaces of seeded potash alum single crystals. (111) Growth sectors contain few dislocations which initiate at the seed interface. Most growth dislocations enter these sections at later stages of growth from adjacent { 110) and (100)sections. These dislocations appear to have little influence on the growth process, the kinetics and mechanism being defined at an early stage of growth to give a constant growth rate.The (110) sectors contain dislocations of all types which initiate at the seed crystal interface and influence the growth process. Identification of the numbers of different types of growth dislocation and the correlation of their density with growth rate shows no distinct and regular variation of growth rate with the number of screw and/or mixed dislocations. Edge dislocations must be included in the total to yield a regular and potentially dominant influence. Studies of the supersaturation dependence of the growth rate of (1 10) faces yields a behaviour consistent with growth by a two-dimensional nucleation mechanism. This is additional evidence to that already noted in growth of the (100) sectors for a strong contributory role of edge dislocations to crystal growth in some sectors of this material.Dislocation-controlled crystal growth is proposed to nucleate at the emergence points of screw and mixed types of dislocations at the growth These dislocations which have a component of the Burgers vector normal to the growth front provide the continuous regenerative step which is needed for the easy attachment of growth units to the surface. Much experimental evidence has accumulated to confirm this the~ry.~ Pure edge dislocations or any other types of dislocation which do not have a component of the Burgers vector normal to the growth front do not provide such a step and until recently it was believed that they played no role in the growth of crystals.Evidence does exist, however, for their influence. Growth features such as closed-loop patterns on crystal surfaces have been observed and which could be centred at the emergent end of such dislocations.46 Also Bauser and Strunk' have demonstrated using an electron microscope the presence of growth hillocks at the emergent end of mixed dislocations which have no component of the Burgers vector normal to the growth front on the (001) surfaces of gallium arsenide. Following this last observation, attempts to rationalise nucleation and growth at outcrops of edge dislocations have been made by Franks for the general case and by Bauster and Strunk7 and Giling and van Dam9 for the particular case of gallium arsenide.An attempt by Kuznetsov and ChernovIo to confirm an influence of single edge t Present address: Inter University Consortium for DAE Facilities, University Campus, Khandwa Road, Indore (M.P.)452001, India. 173 Dislocations and the Growth of Potash Alum dislocations on crystal growth in ADP was unsuccessful. More recently Sherwood and Shripathil have presented alternative evidence for the involvement of edge dislocations in the crystal growth process. Following an observation1I that edge dislocations are the dominant line defects in the (100) growth sectors of potash alum they found it possible to generate only this type of defect in these sectors. Additionally, by changing growth conditions they were able to vary the number of these dislocations and hence to demonstrate that the growth rate of the (100) faces increased with increasing edge dislocation density.In support of their conclusion they observed closed-loop patterns on the (100) surfaces of the crystals. It was suggested that growth occurred by the enhanced two-dimensional nucleation mechanism proposed by Frank.8 This work has now been extended to examine the potential role of dislocations in the growth of the (1 10) and (111) surfaces of potash alum. Previous studies indicate that dislocations in these sectors should be predominantly of screw character.12 Experimental Large (25-30 cm3) high-quality crystals of potash alum were grown by the controlled slow cooling of seeded saturated solutions.13 These crystals were cut using a solvent saw into smaller pieces of size 1.2 x 0.5 x 0.1 cm3 with the I .2 x 0.1 cm2 surface parallel either to a { 111) or a { 110) plane.These cut crystals were then polished flat on a solvent-soaked filter paper (Fig. 1). Separate cut crystals were mounted in a growth cell similar in construction to that described previo~sly.'~ Saturated solution at 304 K from a thermostatically controlled bath Fig. 1 End-on diagrammatic view of the growing interface showing the adjacent growth facets: (a) (1 10) and (b)(1 1 1) seed crystals. The dotted rectangle shows the projection of the boundary of the seed crystal. Dashed lines AA' define the section taken for topography. J. N. Sherwood and T. Shripathi was pumped through a heat exchanger to the thermostatically controlled growth cell.This heat exchanger was used to induce and control (amp; 0.02 K) the supersaturation of the solution reaching the cell. The solution then passed through another heat exchanger (warmed to dissolve all spontaneous nuclei formed during passage) and returned to the crystallizer through a flowmeter control. The growth rate of a particular face was monitored using a microscope with a calibrated eyepiece. Studies were made of the influence of solution flow rate on growth to ensure that the rates used were sufficiently high to eliminate the possibility of diffusion-controlled growth. Two sets of experiments were carried out. The growth kinetics of several seed crystals were measured at a constant supersaturation of 6.4 following initial facetting at different supersaturations (in the range 0.1-6.4).In a second set of experiments the seed crystals were facetted at a particular supersaturation and the growth rates assessed at different supersaturations in the range 0.1-9. Growth rates were usually followed for periods up to 36 h. During growth (which is unconstrained) the polished seed crystals developed all normal (1 1l}, { 1lo} and (100) habit faces (Fig. 1). On completion of growth, each crystal was removed from the cell and thinned by polishing on a solvent-soaked filter paper to a thickness slightly greater than the extent of the original 1.2 x 0.1 cm2 face (Fig. 1). For the ( 1 lo} faces, which decrease in area during growth, this left the complete growth sector intact but bounded by the residue of the adjacent (1 1l} and {loo}sectors which formed during growth Fig.l(a). For crystals in which the ( 1 1 l} growth rate was monitored, the thinning process removed major volumes of the sector under examination but left the original extent of the growth front intact Fig. l(h). This is because unlike the other two growth fronts ((1 lo} and {loo}),the area of the (1 1l} surface increases due to its relatively slow growth rate. The thinned samples were then examined by X-ray topography15 using Mo-Ka radiation. Under the conditions of the experiment the product of absorption coefficient p and thickness t (ca.1 mm), pt = 0.7. Topographs were recorded on Ilford L4 nuclear plates or Agfa Structurix D4 film.Results Growth Kinetics Growth kinetics experiments on the (loo} surfaces Fig. 2(a)showed a similar pattern to that reported earlier by Human16 and Sherwood and Shripathi" for (100) surfaces. The growth rate in the region A (facetting region) was variable and then became constant (region B) for a period of time before oscillating (region C)with the average growth rate decreasing with time. This decrease continued for ca. 15-20 h, following which the crystal grew in short bursts with variable intervals of zero growth. This process continued for the remainder of the time of the experiments. In contrast, following facetting (region A), the growth rate of the dominant ( 1 1 l} faces Fig. 2(b)remained almost constant for long periods of time.The growth rate of the { 11l} face is much lower however (ca. 1 pm min-I, 18 = 6.4) than that of the initial growth rates of the other two faces, ca. 2 and 3 pm min-l, respectively, for the {l lo} and (100) faces. Morphology of the Crystal Interface When growth was initiated on a particular cut and polished seed crystal, the development of the habit faces took place in a way similar to that reported for the (100) surfaces.Il Microscopic pyramidal structures bounded by {loo}/( 11 l} and {loo}/{ 1lo} faces developed on both ( 1lo} and ( 11l} surfaces. After ca. 5-10 min these microstructures merged to give a smoother growth front, which advanced with a growth rate which depended upon the supersaturation of the growth medium.Dislocations and the Growth of Potash Alum Al B IC-I 2.0 -I.z 1.5 t/min Fig. 2 Variation of growth rate with time for the propagation of (a){I lo and (b){ 11Ifaces of potash alum. Region A corresponds to variations in growth rate during facetting of the crystal. Region B is the uniform growth rate region corresponding to constant dislocation content for the { 1lo face. Region C shows the oscillating decrease in growth rate which correlates with the decrease in dislocation content in the { 1 101 sector. In addition to the above feature, and as for the (100) growth sectors, an additional high- index face formed between the (1 lo} and the developing { 1 1 l} surfaces during the initial stages of growth. The growth rate of this face was slightly higher than that of the (100) growth surface.This high-index face persisted for a period of ca. 1 h. During this period of growth which corresponded to region B of Fig. 2(a)the growth rate and area of the (1 10) face remained constant. No such additional face was observed on the { 111) growth surface. At longer times, the relative growth rates of the ( 1lo} and adjacent (1 111 faces led to a decrease in area of the (1 lo face and hence to a convergence of the growth sector boundaries separating these sectors. X-Ray Topography Fig. 3 and 4 show X-ray topographs of typical crystals grown on (1lo} and (11l} surfaces, respectively. The extent of the original (1 lo} seed crystal is defined by the dark lines XXrsquo; which reflect the strain developed during the facetting of the polished surface. Careful examination of Fig.3 and 4 show that, contrary to expectation,12 crystals grown along the (1 10) direction contain edge and/or screw dislocations (normal to the growth front) and mixed dislocations (angled to the growth front) whereas crystals grown along (111) contain only mixed dislocations. The number and hence the density of dislocations in the (1 lo} growth sectors remained constant for a period corresponding to region B, Fig. 2(a).Thereafter some became refracted to the adjacent (1 1 l} sectors as they cross the converging growth sector boundaries. The Burgers vectors of these dislocations are potentially, (1 lo} sector; edge b( loo), screw b( 110) and mixed b( 100) and (1 1l} sector; mixed b( 010).l2 Few, if any, of the total number of dislocations eventually found in the (1 11) sectors were noted to form at the seed interface. The dominant growth dislocation structure of these sectors was formed by the continuously increasing number refracted in from adjacent (1 lo} and (100) sectors. It is likely that, in the initial stages of growth the formation of the pyramidal microstructures in the growth front, their propagation and eventual smoothing will lead to considerable lattice strain. The dislocations will then be formed either as a consequence of J. N. Sherwood and T. Shripathi Fig. 3 X-Ray topographs: (a)220 and (b) 220 reflections of a typical crystal regrown along 1 101 large face (OOl). XX' represents the boundary of the extent of the seed crystal in the direction of growth which was studied (scale mark 1 mm).this strain or as misfit dislocations to allow the smoothing to occur. Whatever the reason, it seems logical that refacetting at various rates of supersaturation should produce various numbers of nuclei or varying strain. This in turn should yield a variation in growth dislocation number. This speculation is confirmed in Fig. 5, which shows the variation in total dislocation number in the { 110) sectors assessed from X-ray topographs of crystals produced at different facetting supersaturations. Similar experiments are not possible with the { 11 1) sectors since few (if any) dislocations are formed at the initial interface.It is perhaps worth noting that the strain developed on refacetting the { 111) sectors is significantly less than for {loo} and (1 10) as exemplified by the topograph in Fig. 4. No equivalent dark contrast can be observed at the interface XX'. The position of the interface can be defined by the left-hand edge of the fringe pattern which marks the initiation of the expanding growth-sector boundary. The presence of the growth-sector boundary confirmed that the sections used for topography included the original { 11 1) growth faces. Dependence of Growth Rate on Dislocation Density { 1 10) Sectors As noted above, the { 110) sectors contain dislocations of mixed, edge and screw character. Distinction can be made between the last two types using orthogonal X-ray reflections of the types shown in Fig.3. For the case shown, dislocations normal to the growth interface (line direction 1 1 lo) will show strong contrast in 220 reflections and zero constant in 220 reflections if of edge character (gab x 1 = 0) and the reverse if of screw character.15 Such analysis of a series of crystals initially developed under a range of supersaturations allowed us to identify the number of dislocations of various types and to correlate these with the Dislocations and the Growth of Potash Alum Fig. 4 X-Ray topograph, 333 reflection of a crystal grown along 1 1I showing mixed dislocations (b(010)I2) entering the growth sector across the growth-sector boundary (fringe pattern).XX' represents the boundary of the seed crystal in the direction of growth (scale mark 1 mm). growth rates of the crystals in region B Fig. 2(a)during which the numbers of dislocations in the sector and growth rate remained constant. The data are summarised in Fig. 6 which correlates the growth rates of a series of crystals with the density of screw, screw and mixed, edge and total dislocations emerging at the growing face of the (110) sectors during the constant growth rate period e.g.B, Fig. 2(a). (1 1l} Sectors Similar experiments could not be carried out for the { 1 1l} sectors since it was not possible to assess the total numbers of dislocations. Some general comments can be made however. Dislocations in the { 11l} sectors are mixed in character as evidenced by the observation that the line directions do not lie normal to the growing interface.Their numbers increase significantly during the course of growth by refraction of dislocations from adjacent sectors to provide a change in number which can be estimated to be ca. 10-fold. Despite this increase, the growth rates of specific { 11l} faces show no change with time, which suggests that the kinetics of the growth of this face are determined at the earliest stages of growth and that the additional dislocations play no significant part in the process. Despite this apparent lack of dependence on dislocation content, the growth rate of different crystals does show a significant variation (ca. 10-fold) with facetting supersatu- ration (Fig.7). This presumably reflects variations in the number of nuclei formed in the developing surface. J. N. Sherwood and T. Shripathi 1 1 I I I I 500 ;lsquo;E 400 .-A U 2 300 0.rdquo;c) 02 200 100 00123456 initiating supersaturation () Fig. 5 Relationship between the supersaturation at which refacetting was carried out and dislocation density for crystals grown along (1 10) ic *gE 2*512.0:::k$+-0.5 ++ -I *sE 1 E E 5 U M 2.5 2.0 1.5 1.0 0.5 0.0 0 50 100 150 0.0 1 0 100 200 300 400 1 500 dislocation density/cm-rsquo; dislocation density/cm-2 Fig. 6 Relationship between the growth rate and density of different dislocations in the constant growth region (B in Fig. 3) for crystals grown along (1 10).The growth measurements were carried out at a constant supersaturation of 6.4 after refacetting. (a) Growth rate vs. screw (0)and screw + mixed dislocation (0)density; (6) growth rate vs. pure edge (0)and total ( x ) dislocation density. Dislocations and the Growth of Potash Alum 1.o 0.8 0.6 0.4 0.2 0.0 initiating supersaturation () Fig. 7 Relationship between refacetting supersaturation and growth rate in the constant-growth region for crystals grown along 1 I 13. The growth-rate measurements were carried out at a constant supersaturation of 6.4 after refacetting. Dependence of Growth Rate on Supersaturation It is of interest to examine the role of supersaturation on the growth rates since this in turn can be related to potential mechanisms.Fig. 8 shows the variation in growth rate of the { 1101 face with supersaturation for one particular crystal refacetted at a supersaturation of 6.4. All measurements were made in the constant-growth region B, Fig. 2(a). The two basic mechanisms usually considered for crystal growth are the dislocation- controlled mechanism of Burton et aL2and the two-dimensional nucleation mechanism. According to the former model the growth rate Rshould depend on supersaturation /3 according to the equation R=C-tanh' BB2 Bc B where C is a constant and /Ic a critical supersaturation required to produce nuclei. At low supersaturations, i.e. ,8 Bc, eqn. (1) reduces to R= CB2/BC (2) and at high supersaturations, i.e.p pc it becomes R= C/3 (3) For two-dimensional nucleation the growth rate is proposed to follow R= A,/35'6exp (-A2/,8) (4) where A, and A2 are constants. At low supersaturations the exponential term will dominate whilst at high supersatu- rations characteristic of the present experiments the rate can be expressed as R= (5) J. N. Sherwood and T. Shripathi 5 1 5 1.5 c z 1.0 0.5 0.0 0 2 4 6 8 10 supersaturation p and p5rsquo;6 (YO) Fig. 8 Relationship between growth rate and supersaturation /3 (0)and /35rsquo;6 (0),showing the dependence of growth rate on /35/6rather than on /3 Fig. 8 confirms that the experimental data follow the last behaviour which suggests that growth on the (110) faces follows a two-dimensional growth mechanism.A similar conclusion was reached for much more limited data on the growth of (100) faces.rsquo; No assessment was made of the dependence of the growth rate of the (1 1 l} faces on supersaturation at this time. Later studies by Ristic and Sherwood17 indicate that growth on this face follows more complicated kinetics. Discussion The nature of the growth of the { 1111faces precludes any definite conclusions on the role of dislocations in crystal growth on these faces. It is quite certain, however, that the rate and mechanism are defined at the earliest stages of growth. Facetting of the surface occurs with little strain and potentially without the formation of growth dislocations. Despite this, variation of the supersaturation at facetting yields a range of growth rates (Fig.7) and thus it must influence and define the number of growth nuclei on the developing face. Subsequent significant increases in mixed dislocation content in these sectors have no influence on growth rate. This would appear to suggest that the mechanism is not dislocation controlled. Certainly the growth is not limited by the growth rate of adjacent (100) and (110) faces since the growth rate of the (111) faces remains constant despite simultaneous variations in the growth rate of these faces (Fig. 2). Such a constant growth rate, however, could be characteristic of growth on strongly propagating dislocation growth sources formed on facetting and which could vary in strength depending on the facetting supersaturation.Such sources could dominate at all times irrespective of the number of mixed dislocations which enter the sector subsequently. Against this suggestion, however, we must recall that we have never observed such sources in the crystals studied. More detailed topological studies of facetting and growing (1 11) surfaces are being carried out in an attempt to resolve this anomaly. 182 Dislocations and the Growth of Potash Alum In contrast, the { 110) surfaces show a well defined, if complex, growth behaviour. The time-dependent variation in growth rate (Fig. 2) parallels that observed previously for the (100) surface." Dislocations are formed at the earliest stages of growth and appear to contribute significantly to the growth process.That some of these defects leave the sector as they meet the converging growth-sector boundaries correlates well with the decrease in average growth rate at longer growth times. Identification of the various dislocation types and their correlation with growth rates reveals some interesting features. Reference to Fig. 6 shows that there is no strong correlation between the numbers of screw and mixed dislocations and growth rate which would be expected if a screw dislocation-type mechanism dominated. It is only when the numbers of edge dislocations are included that a good correlation arises. Thus we must conclude that these dislocations play a significant and potentially dominant role in the growth process as they do also for the (100) surfaces." If we add to this information the observation that the overall kinetics follow the pattern expected for growth by two-dimensional nucleation, we see a potential role for all emergent dislocation sites as potential nuclei for two-dimensional growth.The mechanistic involvement of screw and mixed dislocations is obvious since they present at the surface, step edges for the attachment of ad-ions. Edge dislocations present no such easy nucleation points and it is not easy to accept why they should develop such a major influence. It is unlikely that they will engender surface reconstructions in potash alum of the type proposed by Giling and van Dam9 for edge dislocation nuclei in gallium arsenside. We favour the proposal of Frank8 that the 'energetically enhanced' region around the emergent points is sufficient to allow the site to act as a two-dimensional nucleation point.Further work is in progress to examine the detailed changes in topology of the growing surfaces of well characterised crystals during growth and the correlation of these changes with X-ray topographic analysis. Initial studies have confirmed the correlation between growth centres and dislocations including edge dislocation^.'^ We gratefully acknowledge the financial support of this work by the SERC through the Specially Promoted Programme in Particulate Technology and by ICI plc through their Joint Research Scheme. The X-ray topographic studies were carried out at the SERC Synchrotron Radiation Source, Daresbury, UK.We thank the Director and his staff for their help in the performance of this work. Finally, we thank Professor R. J. Davey, ICI plc and Professor J. Garside, UMIST for many helpful discussions. References 1 F. C. Frank, Discuss. Faraday SOC.,1949, 5, 48. 2 W. K. Burton, N. Cabrera and F. C. Frank, Philos. Trans. R. SOC.London, Ser. A, 1951,243, 299. 3 B. Mutaftschiev, in Dislocations in Solids, ed. F. R. N. Nabarro, North Holland, Amsterdam, 1980, vol. 5, p. 57. 4 A. R. Verma, Crystal Growth and Dislocations, Butterworths, London, 1955. 5 G. A. Bassett, Philos. Mag., 1958, 3, 1042. 6 H. Bethge, Phys. Status Solidi, 1962, 2, 775; 1964, 3, 33. 7 E. Bauser and H. Strunk, J. Crystal Growth, 1981, 51, 362.8 F. C. Frank, J. Crystal Growh, 1981, 51, 367. 9 L. J. Giling and B. van Dam, J. Crystal Growth, 1984,67,400. 10 Y. Kuznetsov and A. A. Chernov, Sov. Phys. Crystallogr., 1988, 31, 709. 11 J. N. Sherwood and T. Shripathi, J. Crystal Growth, 1988,88, 358. 12 H. L. Bhat, R. I. Ristic, J. N. Sherwood and T. Shripathi, J. Crystal Growth, 1992, 121, 709. 13 R. M. Hooper, B. J. McArdle, R. Narang and J. N. Sherwood, in Crystal Growth, ed. B. R. Pamplin, Pergamon Press, Oxford, 2nd edn., 1980, p. 395. 14 M. Rubbo and J. N. Sherwood, J. Crystal Growth, 1983, 61,210. 15 A. R. Lang, Acta Crystallogr., 1959, 12, 249. I6 H. J. Human, Doctoral Thesis, Catholic University, Nijmegen, The Netherlands, 198 1. 17 R. I. Ristic and J. N. Sherwood, to be published. Paper 3/00075C; Received 31st December, 1992