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Growth rate enhancement by microcrystals and the quality of resulting potash alum crystals
Journal of Crystal Growth 192 (1998) 439—447
Growth rate enhancement by microcrystals and the quality of resulting potash alum crystals H. Takiyama!,*, N. Tezuka!, M. Matsuoka!, R.I. Ristic", J.N. Sherwood" ! Department of Chemical Engineering, Tokyo University of Agriculture and Technology, 24-16 Nakacho-2, Koganei, Tokyo 184-8588, Japan " Department of Pure and Applied Chemistry, University of Strathclyde, Glasgow G1 1XL, Scotland, UK Received 15 December 1997; accepted 12 April 1998
Abstract Growth rate enhancement resulting from the addition of ground powder crystals to a growing larger crystal has been examined for the potash alum—water system. The crystal quality of the large crystal after the addition and subsequent growth rate enhancement was evaluated in terms of the formation of inclusions and dislocations. Inclusions were observed with an optical microscope and the dislocations were analysed using X-ray transmission topography. It was found that the development of inclusions occurs at the time of the addition to the solution of the ground powder crystals and their attachment to the growing crystal surface. Simultaneously, dislocation bundles were generated. It is proposed that the inclusions form as the growing crystal surface envelopes the adhering particles and that the dislocations form both as a consequence of the strain that develops and the lattice mismatch required to refacet the surface. Both result in the development of additional growth centres which cause the growth rate enhancement. ( 1998 Elsevier Science B.V. All rights reserved. PACS: 61.72.Ff; 81.10.Dn Keywords: Growth rate enhancement; Microcrystal; Inclusions; X-ray topography; Potash alum
1. Introduction The phenomenon of growth rate enhancement of a fixed single crystal in the presence of freshly nucleated microcrystals has been observed for the potash alum—water [1], the sodium chloride—water
* Corresponding author. Fax: #81 42 387 7944; e-mail: [email protected].
[2] and the organic m-chloronitrobenzene—acetone systems [3]. The details of this type of growth rate enhancement are not understood at present. In particular, the effects of growth rate enhancement on the quality, purity and perfection of crystals and the role of supersaturation and size of the microcrystals in the rate enhancement process are not known. It is well known that crystal quality decreases with increasing growth rate for single crystals [4]
0022-0248/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 0 4 5 6 - 4
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and that the development of inclusions affects purity in industrial crystallisation [5,6]. Therefore, it might be expected that enhancement in this case may also influence the crystal quality in the same way. Similarly, using X-ray topography, Ristic et al. [7] observed that dislocations can form readily at deformed and refacetted surfaces and at inclusions in several solids. They discussed [8,9] their role in growth rate dispersion at all surfaces of potash alum crystals. Again, surface changes due to growth rate enhancement by added particles may cause similar changes in dislocation content which may play an important role in the enhancement process. This study deals with some of the above unanswered questions by combining an examination of the relationship between growth rate enhancement, inclusion formation and defect generation for the potash alum—water system. This system was chosen because of the transparency of the solution which is advantageous in the observation of inclusions in the bulk of the crystals following the enhancement process.
achieved in the present system. The solvent was filtered with a 0.1 lm membrane filter prior to making up solutions. The saturated solutions were prepared at each temperature given in Table 1 and were also filtered before experiments with a 0.45 lm membrane filter to prevent nucleation by foreign particles. The saturated solution concentration was determined by the temperature [1]. The solution was placed in the crystalliser and kept at the operating temperature. The prepared solutions and experimental conditions are shown in Table 1. The initial supersaturation p was calculated from the 0 saturation and the operating temperatures. 2.2. Procedure Single fixed seed crystals were prepared by the methods outlined in Section 2.3. A seed was washed by using filtered water and ethanol immediately
2. Experimental procedures 2.1. Apparatus and solutions The experimental equipment shown in Fig. 1 is based on a 720 ml jacketed stirred tank. An internal plate made of teflon was included to prevent evaporation and hence nucleation during experiments. The solution was stirred at 0.7 Hz by a paddletype impeller made of glass and the temperature was controlled by a thermostat. The stability of the operating temperature within $0.05 K was
Fig. 1. Experimental set-up for crystal growth.
Table 1 Experimental conditions Run No.
Saturation temperature (K)
Operating temperature (K)
Supersaturation p 0
Ground powder crystal addition time (h)
Run 1—1 Run 1—2 Run 1—2
303.3 304.1 303.9
302.7 303.4 303.9
0.0210 0.0208 0.000798
44 67 213
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before each experiment to remove extraneous surface nucleation. Growth was monitored with a CCD camera and recorded on a video recorder. Size changes were calculated from the images on the TV screen (Section 2.4). After the confirmation of steady growth, 0.2 g of ground powder crystals prepared using an agate mortar were added to the supersaturated solution to induce nucleation in solution, i.e. for the generation of microcrystals. The size of the microcrystals is, therefore, expected to mimic that of secondary nuclei. The growth experiment was continued for at least 100 h and then the single fixed crystal was taken out to evaluate its quality.
441
Fig. 2. Determination of the size of two different positions of a growing crystal observed on the monitor: (a) two octahedron apices seen and (b) an octahedron apex seen in the front. Distance: (a) ¸ (t )"(1/2) (¸ (t )#¸ (t )) and (b) ¸ (t )" W1 1 1 X i 1 i 2 i W1 1 1 X i (1/2) (¸@ (t )#¸@ (t )) cos /. 1 i 2 i
2.3. Single fixed seed crystals A seed crystal was fixed to a support by the following three methods: Method 1: A clear crystal with a well-defined shape and about 4 mm in size was fixed to a platinum wire of 0.3 mm in diameter by applying sufficient heat to melt the wire into the surface. Method 2: A crystal that nucleated spontaneously at the tip of a cotton thread was allowed to grow to about 4 mm. Method 3: A crystal that nucleated spontaneously at the tip of a platinum wire of 0.3 mm in diameter was allowed to grow to about 4 mm. The surfaces of seed crystals prepared by Methods 1 and 2 were observed by SEM. When a platinum wire was used with heating (Method 1), the surface of the crystal around the wire was changed. Therefore, crystals that nucleated spontaneously at the tip of the cotton thread or the platinum wire (i.e. Methods 2 and 3) were used as seed crystals in the present experiments. 2.4. Growth rate The calculation of crystal size from video images depends on how a seed crystal is fixed relative to the TV camera. Since the growth rate of the (1 1 1) face was needed, the procedures, presented in Fig. 2, for the calculation of the crystal length along the S1 1 1T axis were used. The interplanar distance ¸ between the two (1 1 1) faces of a crystal W1 1 1X fixed as shown in Fig. 2a was measured directly.
For the case when an apex of the octahedron could be seen in the front (Fig. 2b), the distances of the two sides along the S1 1 0T directions (¸@ and ¸@ ) 1 2 were measured, and the average length was then converted into the length in the S1 1 1T direction by using the conversion factor of cos /, where / is the angle between the (1 1 1) and the (1 1 0) faces. The instantaneous growth rate G in the direcW1 1 1X tion S1 1 1T is one-half of the increment *¸ W1 1 1X of the crystal size divided by the time *t, G "1 (*¸ /*t), W1 1 1X 2 W1 1 1X
(1)
where *¸ "¸ (t )!¸ (t ) and W1 1 1X W1 1 1X 2 W1 1 1X 1 *t"t !t . 2 1 2.5. Crystal quality The quality of crystals after the growth rate enhancement was evaluated in terms of the existence of inclusions and dislocations. The grown crystals were either observed under an optical microscope after washing and drying or analysed by X-ray transmission topography. Two of the crystals were grown at almost the same value of the supersaturation (Runs 1—1 and 1—2). One of the crystals was analysed by X-ray topography, while the other crystal was observed by microscope. Run 2—2 was carried out at a supersaturation lower (about 1) than that for Runs 1—1 and 1—2. This crystal was 3 also analysed by X-ray topography.
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3. Results 3.1. Growth enhancement phenomena Growth rate enhancement phenomena observed under each set of experimental conditions are shown in Fig. 3. The abscissa shows experimental time and the ordinate growth increments of the fixed crystals. The arrows indicate when the powder crystals were added. The addition was accompanied by the nucleation of microcrystals in the solution. Although there were differences in the degree of growth rate enhancement effects, enhancement phenomena by microcrystals were observed in all experiments. The degree of growth rate enhancement has been defined [1] by the coefficient e "(growth rate in the presence of microcrystals)/ 0 (growth rate in the absence of microcrystals). (2) In this present case, e is the ratio of the growth rate 0 G immediately after the addition of the !&5%3W1 1 1X powder crystals to the steady growth rate G before their addition. The incremental "%&03%W1 1 1X increase in the crystal size was fitted to a thirdorder polynomial equation. G was cal!&5%3W1 1 1X
Fig. 3. Increase in crystal size ¸ with time t for three runs. W1 1 1X Arrows indicate when powder crystals were added.
culated from the derivative of this function. These results (shown as open symbols) are compared with previous experiments [1] for the same system in Fig. 4. It can be seen that these results lie well within the range of the previous experimental results. The crystals represented by the symbols n and h were those analysed by X-ray topography, and the one with the symbol L (Run 1—1) was analysed optically to determine the distribution of inclusions. 3.2. Inclusions Video images of the crystal of Run 1—1 during the experiment are shown in Fig. 5. The apex of the regular octahedron of the potash alum crystal is seen at the front. The seed crystal was prepared by Method 2, i.e. at the tip of a cotton thread. Fig. 5a is a video image before the addition of the powder crystals while Fig. 5b is that after the addition. The powder crystals are seen to have attached to the upper (1 1 1) faces soon after they were added to the solution. No attachment was observed to the lower faces. Fig. 6a is a micrograph taken when the optical microscope was focused at 1.0 mm depth from the (1 1 1) surface of the crystal where the attached crystals were observed. Fig. 6b is taken at 0.8 mm
Fig. 4. Comparison of the growth rate before and after the nucleation. These results lie in the range of the previous data.
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Fig. 6. Inclusions observed at a depth l from the (a) upper and (b) lower faces of the crystal of Run 1—1. Note that a large number of inclusions appear in the upper face, while they are less in the lower.
Fig. 5. Video images for the crystals of Run 1—1 grown at initial supersaturation p "0.0210 with growth rate G " 0 "%&03% 9.23]10~9 (m/s): (a) before and (b) after the addition of powder crystals. Growth rate enhancement coefficient e "1.26. 0
depth from the lower surface. Both micrographs show that many inclusions have developed inside the crystal. Large inclusions with a network structure were observed in the upper face of the crystal. On the other hand, small inclusions were observed in the lower faces. To evaluate the amount of inclusions, a quantity al was defined: i
al "(Area of inclusions in observed inner plane i
at the depth l from the crystal surface)/ i (Total area of observed plane),
(3)
where al is the fraction of the area that inclusions i occupy at the depth l . The total area of the obi served plane was 1.6]10~6 m2. Micrographs were taken at every 0.1 mm depth by adjusting the focal distance of the microscope. The outline of inclusions was extracted from each micrograph. The total area of inclusions was then summed and al was calculated. The relationships between the i distance from the surface of the crystal and the area fraction of inclusions al are shown in Fig. 7 for i both the upper and the lower faces. The depth from the upper surface was denoted as lu , while the iW1 1 1X depth from the lower surface was defined as ll . The left end of the abscissa represents the iW1 1 1X crystal surface after the growth experiment. The arrows on the graphs indicate the point at which the ground powder crystals were added. Both diagrams show sudden increases in al at the time when i growth rate enhancement phenomena were observed. Then, al decreases with the decrease of the i growth rate enhancement effect. The area fraction of inclusions al in the upper face at the point of the i generation of micro crystals was larger than at the equivalent point in the lower face.
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Fig. 8. Plot of the dependence of area fraction of inclusions al on growth rate enhancement effect gl . i
Fig. 7. Dependence of area fraction of inclusions al on depth of i observation region from (a) the upper and (b) the lower face of the crystal of Run 1—1. Arrows indicate the surface positions when powder crystals were added.
The relationship between the changes in the growth rate and the area fraction of the inclusions was calculated to clarify the effect of the growth rate enhancement phenomena on the occurrence of inclusions. These are shown in Fig. 8. The change in the local growth rate enhancement effect gl was i evaluated from the relation gl "Gl /G
, (4) "%&03%W1 1 1X where Gl is the instantaneous crystal growth rate i at the position l in Fig. 7, calculated as the derivai tive of the growth curve shown in Fig. 3. The numbers in Fig. 8 correspond to those in Fig. 7. At the start the enhancement effect gl increased i abruptly. The maximum value of gl was 1.26 ("e ) 0 i for Run 1—1. The area fraction of inclusions al bei gan to increase after gl . Then, al decreased with the i i disappearance of the growth rate enhancement effects. The value of l , which gave the maximum i value of gl , does not correspond to that which gave i the maximum value of a because of the time delay li in the formation of inclusions. Even when the value of gl dropped below 1.0, the values of al were not i i zero. i
i
i
Run 1—1, to which the above method of analysis was applied, shows a lower growth rate enhancement compared with other runs as seen in Fig. 3. Moreover, in the later period of the experiment the growth rate G became lower than !&5%3W1 1 1X G . Similar but less marked effects were "%&03%W1 1 1X also observed for other crystals. 3.3. X-Ray topography Fig. 9a and Fig. 9b are video images taken before and after the addition of the powder crystals, respectively. The growth conditions of the crystal are almost the same as those used for the crystal shown in Fig. 5 for which inclusions were measured. It can be seen that the powder crystals are attached only to the upper faces of the crystal (Fig. 9b). The crystal was allowed to grow further and removed from the solution after it had reached the size shown in Fig. 9c. It was sectioned along the broken line indicated in Fig. 9c and the dislocation distribution was analysed by X-ray topography of the resulting slice. The results are shown in Fig. 9d where u indicates the diffraction vector. The dark outline seen close to the centre of the crystal defines the surface of the seed crystal. This arises from the strain developed in the surface during the refacetting of the seed. At the centre of the seed is a dark volume that represents strain
H. Takiyama et al. / Journal of Crystal Growth 192 (1998) 439–447
445
Fig. 9. Video images (a)—(c) and X-ray transmission topograph (d) for the crystal of Run 1—2 grown at initial supersaturation p "0.0208 with growth rate G "7.57]10~9 (m/s): (a) before, (b) after the addition of powder crystals and (c) final crystal. 0 "%&03% Growth rate enhancement coefficient e "2.13. The broken line indicated in (c) shows the cutting plane. Bold arrow represents 0 observation direction for X-ray topographs ((21 2 0) reflection).
developed around the string on which the crystal nucleated. From this central dark volume welldefined alignments of growth dislocations develop and propagate towards the bounding facets of the growing crystal. Many of these continue through the seed interface into the newly developed crystal. New growth dislocations are also generated at the seed interface. Variation in the number and type of these dislocations from sector to sector implies that each M1 1 1N sector grows at a similar but different rate. The black volumes around the edge of the crystal mark is the point at which the powder
crystals were added to the system. They represent the generation of dislocations and comprise bundles of dislocations nucleated at a point and fanning out towards the surface. The fact that these volumes are observed in the topographs presented is strong evidence that they comprise predominantly dislocations of mixed character. As expected, the density of dislocations is greatest at the upper ( ) surfaces and lower at the ( ) lower surfaces. A similar comparison for a crystal grown under conditions of lower supersaturation was carried
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out. In this case (Run 2—2) a crystal nucleated spontaneously at the tip of the platinum wire was used for the experiment. After a short period of growth, the powder crystals were added and the growth continued as before. The powder attached principally to the upper face. On completion of growth the crystal was sectioned parallel to the broken line (Fig. 10a) and topographed. The topograph is shown in Fig. 10b. Fig. 10b shows that in the original seed crystal the principal dislocation structure springs from the point of contact of the wire with the seed crystal and develops principally towards the upper facet. New dislocation bundles emanate from the surface of the seed to form the basic defect structure of the specimen. In this experiment it is difficult to see the point at which the powder crystals were added since there is less dislocation formation than before. This reflects the much lower growth rate of this specimen. The nature of the defect structure is similar to before and the relative width of the dark volumes on the upper and lower surfaces is again consistent with the observed enhancement.
4. Discussion and conclusions The following results were obtained between the growth rate enhancement and the formation of inclusions and/or dislocation for the potash alum crystals. 1. Growth rate enhancement occurs immediately following the generation of microcrystals in the solution. 2. Inclusions and hence solvent become incorporated in the crystal at this point resulting in a lowering of the perfection of the material. 3. There is a simultaneous generation of dislocations that causes a decrease in perfection of the growing crystal. 4. The degree to which these changes occur depends on supersaturation being worst at high and least at low supersaturation. The addition of the powder crystals to the growing crystal system brings about well-defined changes to the defect structure of the crystal. These changes result principally from the attachment to
Fig. 10. Video images (a) and X-ray transmission topograph (b) for the crystal of Run 2—2 grown at initial supersaturation p "0.00798 with growth rate G "1.40]10~9 (m/s). Growth rate enhancement coefficient e "1.81. The broken line indicated in 0 "%&03% 0 (a) shows the cutting plane. The bold arrow represents observation direction for X-ray topographs ((21 2 0) reflection).
H. Takiyama et al. / Journal of Crystal Growth 192 (1998) 439–447
the crystal surface of either the added powder or microcrystals produced by secondary nucleation from solution on addition of the powder. The advancing crystal surface grows to surround and incorporate these particles and in doing so leaves voids in the structure which will inevitably contain included solution. In this way the perfection of the growing crystal will be decreased. The healing of the lattice as it develops to include the growing surface particle results in the development of strain and dislocation structure. The latter are formed both as a consequence of the strain and also to accommodate the mismatch of the healing lattice. The growth rate enhancement process varies with supersaturation producing a higher degree of solvent incorporation and defect formation at higher supersaturations than at lower supersaturations. These results are not inconsistent with the discussion about the growth kinetics for dislocations [10]. Regarding the eventual decrease in growth rate following the enhancement period, we see two principal explanations. (1) Mainly the density of dislocations was decreased. A detailed examination of the defect structure in the enhanced growth region shows that this comprises bundles of dislocations each nucleating at a point and fanning out as growth progresses. The closeness of the dislocations at the start is sufficient to yield cooperating and rapidly propagating growth sources; hence the enhancement. As growth continues they separate to yield more slowly propagating single sources. In such circumstances, as single sources, they may add little power to the sources originally present and hence have little additional influence on the growth rate, particularly since by now the area of the growing face will have increased and it is the density of dislocation sources at the surface which defines the rate of growth. Hence the growth rate will fall with time and could well become lower than that before enhancement. (2) Alternatively, there is the possibility that the presence of such increased amounts of small crystals in solution and their growth will remove solute
447
from the solution and hence reduce the concentration and hence supersaturation at the surface. A lower growth rate would result. In general, we feel that the principal cause of microcrystal induced growth rate enhancement is the formation of a dislocation structure around the voids generated in the crystal surface following the adhesion of microcrystals. These results and conclusions have important ramifications for the growth of crystals in industrial crystallisers where the inevitability of producing large numbers of growing and colliding primary and secondary particles will yield variations in the purity and perfection of the crystals produced.
Acknowledgements The X-ray topographs presented in this paper were recorded at the UK EPSRC at Daresbury Laboratory. J.N.S. and R.I.R. thank the director and his staff for providing the facilities used in this characterisation.
References [1] M. Matsuoka, T. Kamada, H. Takiyama, J. Crystal Growth 158 (1996) 322. [2] M. Matsuoka, K. Tanishima, 7th Symp. on Salt, vol. II, 1993, p. 177. [3] M. Matsuoka, N. Eguchi, J. Phys. D 26 (1993) B162. [4] M. Matsuoka, N. Kanekuni, H. Tanaka, J. Crystal Growth 73 (1985) 563. [5] J.W. Mullin, in: Crystallisation, 3rd ed., ButterworthHeinemann, London, 1993, p. 260. [6] A. Mersmann, in: A. Mersmann (Ed.), Crystallization Technology Handbook, Marcel Dekker, New York, 1995, p. 201. [7] J.N. Sherwood, T. Shripathi, J. Crystal Growth 88 (1988) 358. [8] R.I. Ristic, J.N. Sherwood, T. Shripathi, J. Crystal Growth 102 (1990) 245. [9] R.I. Ristic, J.N. Sherwood, T. Shripathi, Advances in Industrial Crystallization, Butterworth-Heinemann, London, 1991, p. 77. [10] A.A. Chernov, L.N. Rashkovich, I.L. Smol’skii, Yu.G. Kuznetsov, A.A. Mkrtchyan, A.I. Malkin, Growth of Crystal 15 (1885) 43.
Growth rate enhancement by microcrystals and the quality of resulting potash alum crystals H. Takiyama!,*, N. Tezuka!, M. Matsuoka!, R.I. Ristic", J.N. Sherwood" ! Department of Chemical Engineering, Tokyo University of Agriculture and Technology, 24-16 Nakacho-2, Koganei, Tokyo 184-8588, Japan " Department of Pure and Applied Chemistry, University of Strathclyde, Glasgow G1 1XL, Scotland, UK Received 15 December 1997; accepted 12 April 1998
Abstract Growth rate enhancement resulting from the addition of ground powder crystals to a growing larger crystal has been examined for the potash alum—water system. The crystal quality of the large crystal after the addition and subsequent growth rate enhancement was evaluated in terms of the formation of inclusions and dislocations. Inclusions were observed with an optical microscope and the dislocations were analysed using X-ray transmission topography. It was found that the development of inclusions occurs at the time of the addition to the solution of the ground powder crystals and their attachment to the growing crystal surface. Simultaneously, dislocation bundles were generated. It is proposed that the inclusions form as the growing crystal surface envelopes the adhering particles and that the dislocations form both as a consequence of the strain that develops and the lattice mismatch required to refacet the surface. Both result in the development of additional growth centres which cause the growth rate enhancement. ( 1998 Elsevier Science B.V. All rights reserved. PACS: 61.72.Ff; 81.10.Dn Keywords: Growth rate enhancement; Microcrystal; Inclusions; X-ray topography; Potash alum
1. Introduction The phenomenon of growth rate enhancement of a fixed single crystal in the presence of freshly nucleated microcrystals has been observed for the potash alum—water [1], the sodium chloride—water
* Corresponding author. Fax: #81 42 387 7944; e-mail: [email protected].
[2] and the organic m-chloronitrobenzene—acetone systems [3]. The details of this type of growth rate enhancement are not understood at present. In particular, the effects of growth rate enhancement on the quality, purity and perfection of crystals and the role of supersaturation and size of the microcrystals in the rate enhancement process are not known. It is well known that crystal quality decreases with increasing growth rate for single crystals [4]
0022-0248/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 0 4 5 6 - 4
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and that the development of inclusions affects purity in industrial crystallisation [5,6]. Therefore, it might be expected that enhancement in this case may also influence the crystal quality in the same way. Similarly, using X-ray topography, Ristic et al. [7] observed that dislocations can form readily at deformed and refacetted surfaces and at inclusions in several solids. They discussed [8,9] their role in growth rate dispersion at all surfaces of potash alum crystals. Again, surface changes due to growth rate enhancement by added particles may cause similar changes in dislocation content which may play an important role in the enhancement process. This study deals with some of the above unanswered questions by combining an examination of the relationship between growth rate enhancement, inclusion formation and defect generation for the potash alum—water system. This system was chosen because of the transparency of the solution which is advantageous in the observation of inclusions in the bulk of the crystals following the enhancement process.
achieved in the present system. The solvent was filtered with a 0.1 lm membrane filter prior to making up solutions. The saturated solutions were prepared at each temperature given in Table 1 and were also filtered before experiments with a 0.45 lm membrane filter to prevent nucleation by foreign particles. The saturated solution concentration was determined by the temperature [1]. The solution was placed in the crystalliser and kept at the operating temperature. The prepared solutions and experimental conditions are shown in Table 1. The initial supersaturation p was calculated from the 0 saturation and the operating temperatures. 2.2. Procedure Single fixed seed crystals were prepared by the methods outlined in Section 2.3. A seed was washed by using filtered water and ethanol immediately
2. Experimental procedures 2.1. Apparatus and solutions The experimental equipment shown in Fig. 1 is based on a 720 ml jacketed stirred tank. An internal plate made of teflon was included to prevent evaporation and hence nucleation during experiments. The solution was stirred at 0.7 Hz by a paddletype impeller made of glass and the temperature was controlled by a thermostat. The stability of the operating temperature within $0.05 K was
Fig. 1. Experimental set-up for crystal growth.
Table 1 Experimental conditions Run No.
Saturation temperature (K)
Operating temperature (K)
Supersaturation p 0
Ground powder crystal addition time (h)
Run 1—1 Run 1—2 Run 1—2
303.3 304.1 303.9
302.7 303.4 303.9
0.0210 0.0208 0.000798
44 67 213
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before each experiment to remove extraneous surface nucleation. Growth was monitored with a CCD camera and recorded on a video recorder. Size changes were calculated from the images on the TV screen (Section 2.4). After the confirmation of steady growth, 0.2 g of ground powder crystals prepared using an agate mortar were added to the supersaturated solution to induce nucleation in solution, i.e. for the generation of microcrystals. The size of the microcrystals is, therefore, expected to mimic that of secondary nuclei. The growth experiment was continued for at least 100 h and then the single fixed crystal was taken out to evaluate its quality.
441
Fig. 2. Determination of the size of two different positions of a growing crystal observed on the monitor: (a) two octahedron apices seen and (b) an octahedron apex seen in the front. Distance: (a) ¸ (t )"(1/2) (¸ (t )#¸ (t )) and (b) ¸ (t )" W1 1 1 X i 1 i 2 i W1 1 1 X i (1/2) (¸@ (t )#¸@ (t )) cos /. 1 i 2 i
2.3. Single fixed seed crystals A seed crystal was fixed to a support by the following three methods: Method 1: A clear crystal with a well-defined shape and about 4 mm in size was fixed to a platinum wire of 0.3 mm in diameter by applying sufficient heat to melt the wire into the surface. Method 2: A crystal that nucleated spontaneously at the tip of a cotton thread was allowed to grow to about 4 mm. Method 3: A crystal that nucleated spontaneously at the tip of a platinum wire of 0.3 mm in diameter was allowed to grow to about 4 mm. The surfaces of seed crystals prepared by Methods 1 and 2 were observed by SEM. When a platinum wire was used with heating (Method 1), the surface of the crystal around the wire was changed. Therefore, crystals that nucleated spontaneously at the tip of the cotton thread or the platinum wire (i.e. Methods 2 and 3) were used as seed crystals in the present experiments. 2.4. Growth rate The calculation of crystal size from video images depends on how a seed crystal is fixed relative to the TV camera. Since the growth rate of the (1 1 1) face was needed, the procedures, presented in Fig. 2, for the calculation of the crystal length along the S1 1 1T axis were used. The interplanar distance ¸ between the two (1 1 1) faces of a crystal W1 1 1X fixed as shown in Fig. 2a was measured directly.
For the case when an apex of the octahedron could be seen in the front (Fig. 2b), the distances of the two sides along the S1 1 0T directions (¸@ and ¸@ ) 1 2 were measured, and the average length was then converted into the length in the S1 1 1T direction by using the conversion factor of cos /, where / is the angle between the (1 1 1) and the (1 1 0) faces. The instantaneous growth rate G in the direcW1 1 1X tion S1 1 1T is one-half of the increment *¸ W1 1 1X of the crystal size divided by the time *t, G "1 (*¸ /*t), W1 1 1X 2 W1 1 1X
(1)
where *¸ "¸ (t )!¸ (t ) and W1 1 1X W1 1 1X 2 W1 1 1X 1 *t"t !t . 2 1 2.5. Crystal quality The quality of crystals after the growth rate enhancement was evaluated in terms of the existence of inclusions and dislocations. The grown crystals were either observed under an optical microscope after washing and drying or analysed by X-ray transmission topography. Two of the crystals were grown at almost the same value of the supersaturation (Runs 1—1 and 1—2). One of the crystals was analysed by X-ray topography, while the other crystal was observed by microscope. Run 2—2 was carried out at a supersaturation lower (about 1) than that for Runs 1—1 and 1—2. This crystal was 3 also analysed by X-ray topography.
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3. Results 3.1. Growth enhancement phenomena Growth rate enhancement phenomena observed under each set of experimental conditions are shown in Fig. 3. The abscissa shows experimental time and the ordinate growth increments of the fixed crystals. The arrows indicate when the powder crystals were added. The addition was accompanied by the nucleation of microcrystals in the solution. Although there were differences in the degree of growth rate enhancement effects, enhancement phenomena by microcrystals were observed in all experiments. The degree of growth rate enhancement has been defined [1] by the coefficient e "(growth rate in the presence of microcrystals)/ 0 (growth rate in the absence of microcrystals). (2) In this present case, e is the ratio of the growth rate 0 G immediately after the addition of the !&5%3W1 1 1X powder crystals to the steady growth rate G before their addition. The incremental "%&03%W1 1 1X increase in the crystal size was fitted to a thirdorder polynomial equation. G was cal!&5%3W1 1 1X
Fig. 3. Increase in crystal size ¸ with time t for three runs. W1 1 1X Arrows indicate when powder crystals were added.
culated from the derivative of this function. These results (shown as open symbols) are compared with previous experiments [1] for the same system in Fig. 4. It can be seen that these results lie well within the range of the previous experimental results. The crystals represented by the symbols n and h were those analysed by X-ray topography, and the one with the symbol L (Run 1—1) was analysed optically to determine the distribution of inclusions. 3.2. Inclusions Video images of the crystal of Run 1—1 during the experiment are shown in Fig. 5. The apex of the regular octahedron of the potash alum crystal is seen at the front. The seed crystal was prepared by Method 2, i.e. at the tip of a cotton thread. Fig. 5a is a video image before the addition of the powder crystals while Fig. 5b is that after the addition. The powder crystals are seen to have attached to the upper (1 1 1) faces soon after they were added to the solution. No attachment was observed to the lower faces. Fig. 6a is a micrograph taken when the optical microscope was focused at 1.0 mm depth from the (1 1 1) surface of the crystal where the attached crystals were observed. Fig. 6b is taken at 0.8 mm
Fig. 4. Comparison of the growth rate before and after the nucleation. These results lie in the range of the previous data.
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Fig. 6. Inclusions observed at a depth l from the (a) upper and (b) lower faces of the crystal of Run 1—1. Note that a large number of inclusions appear in the upper face, while they are less in the lower.
Fig. 5. Video images for the crystals of Run 1—1 grown at initial supersaturation p "0.0210 with growth rate G " 0 "%&03% 9.23]10~9 (m/s): (a) before and (b) after the addition of powder crystals. Growth rate enhancement coefficient e "1.26. 0
depth from the lower surface. Both micrographs show that many inclusions have developed inside the crystal. Large inclusions with a network structure were observed in the upper face of the crystal. On the other hand, small inclusions were observed in the lower faces. To evaluate the amount of inclusions, a quantity al was defined: i
al "(Area of inclusions in observed inner plane i
at the depth l from the crystal surface)/ i (Total area of observed plane),
(3)
where al is the fraction of the area that inclusions i occupy at the depth l . The total area of the obi served plane was 1.6]10~6 m2. Micrographs were taken at every 0.1 mm depth by adjusting the focal distance of the microscope. The outline of inclusions was extracted from each micrograph. The total area of inclusions was then summed and al was calculated. The relationships between the i distance from the surface of the crystal and the area fraction of inclusions al are shown in Fig. 7 for i both the upper and the lower faces. The depth from the upper surface was denoted as lu , while the iW1 1 1X depth from the lower surface was defined as ll . The left end of the abscissa represents the iW1 1 1X crystal surface after the growth experiment. The arrows on the graphs indicate the point at which the ground powder crystals were added. Both diagrams show sudden increases in al at the time when i growth rate enhancement phenomena were observed. Then, al decreases with the decrease of the i growth rate enhancement effect. The area fraction of inclusions al in the upper face at the point of the i generation of micro crystals was larger than at the equivalent point in the lower face.
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Fig. 8. Plot of the dependence of area fraction of inclusions al on growth rate enhancement effect gl . i
Fig. 7. Dependence of area fraction of inclusions al on depth of i observation region from (a) the upper and (b) the lower face of the crystal of Run 1—1. Arrows indicate the surface positions when powder crystals were added.
The relationship between the changes in the growth rate and the area fraction of the inclusions was calculated to clarify the effect of the growth rate enhancement phenomena on the occurrence of inclusions. These are shown in Fig. 8. The change in the local growth rate enhancement effect gl was i evaluated from the relation gl "Gl /G
, (4) "%&03%W1 1 1X where Gl is the instantaneous crystal growth rate i at the position l in Fig. 7, calculated as the derivai tive of the growth curve shown in Fig. 3. The numbers in Fig. 8 correspond to those in Fig. 7. At the start the enhancement effect gl increased i abruptly. The maximum value of gl was 1.26 ("e ) 0 i for Run 1—1. The area fraction of inclusions al bei gan to increase after gl . Then, al decreased with the i i disappearance of the growth rate enhancement effects. The value of l , which gave the maximum i value of gl , does not correspond to that which gave i the maximum value of a because of the time delay li in the formation of inclusions. Even when the value of gl dropped below 1.0, the values of al were not i i zero. i
i
i
Run 1—1, to which the above method of analysis was applied, shows a lower growth rate enhancement compared with other runs as seen in Fig. 3. Moreover, in the later period of the experiment the growth rate G became lower than !&5%3W1 1 1X G . Similar but less marked effects were "%&03%W1 1 1X also observed for other crystals. 3.3. X-Ray topography Fig. 9a and Fig. 9b are video images taken before and after the addition of the powder crystals, respectively. The growth conditions of the crystal are almost the same as those used for the crystal shown in Fig. 5 for which inclusions were measured. It can be seen that the powder crystals are attached only to the upper faces of the crystal (Fig. 9b). The crystal was allowed to grow further and removed from the solution after it had reached the size shown in Fig. 9c. It was sectioned along the broken line indicated in Fig. 9c and the dislocation distribution was analysed by X-ray topography of the resulting slice. The results are shown in Fig. 9d where u indicates the diffraction vector. The dark outline seen close to the centre of the crystal defines the surface of the seed crystal. This arises from the strain developed in the surface during the refacetting of the seed. At the centre of the seed is a dark volume that represents strain
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Fig. 9. Video images (a)—(c) and X-ray transmission topograph (d) for the crystal of Run 1—2 grown at initial supersaturation p "0.0208 with growth rate G "7.57]10~9 (m/s): (a) before, (b) after the addition of powder crystals and (c) final crystal. 0 "%&03% Growth rate enhancement coefficient e "2.13. The broken line indicated in (c) shows the cutting plane. Bold arrow represents 0 observation direction for X-ray topographs ((21 2 0) reflection).
developed around the string on which the crystal nucleated. From this central dark volume welldefined alignments of growth dislocations develop and propagate towards the bounding facets of the growing crystal. Many of these continue through the seed interface into the newly developed crystal. New growth dislocations are also generated at the seed interface. Variation in the number and type of these dislocations from sector to sector implies that each M1 1 1N sector grows at a similar but different rate. The black volumes around the edge of the crystal mark is the point at which the powder
crystals were added to the system. They represent the generation of dislocations and comprise bundles of dislocations nucleated at a point and fanning out towards the surface. The fact that these volumes are observed in the topographs presented is strong evidence that they comprise predominantly dislocations of mixed character. As expected, the density of dislocations is greatest at the upper ( ) surfaces and lower at the ( ) lower surfaces. A similar comparison for a crystal grown under conditions of lower supersaturation was carried
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out. In this case (Run 2—2) a crystal nucleated spontaneously at the tip of the platinum wire was used for the experiment. After a short period of growth, the powder crystals were added and the growth continued as before. The powder attached principally to the upper face. On completion of growth the crystal was sectioned parallel to the broken line (Fig. 10a) and topographed. The topograph is shown in Fig. 10b. Fig. 10b shows that in the original seed crystal the principal dislocation structure springs from the point of contact of the wire with the seed crystal and develops principally towards the upper facet. New dislocation bundles emanate from the surface of the seed to form the basic defect structure of the specimen. In this experiment it is difficult to see the point at which the powder crystals were added since there is less dislocation formation than before. This reflects the much lower growth rate of this specimen. The nature of the defect structure is similar to before and the relative width of the dark volumes on the upper and lower surfaces is again consistent with the observed enhancement.
4. Discussion and conclusions The following results were obtained between the growth rate enhancement and the formation of inclusions and/or dislocation for the potash alum crystals. 1. Growth rate enhancement occurs immediately following the generation of microcrystals in the solution. 2. Inclusions and hence solvent become incorporated in the crystal at this point resulting in a lowering of the perfection of the material. 3. There is a simultaneous generation of dislocations that causes a decrease in perfection of the growing crystal. 4. The degree to which these changes occur depends on supersaturation being worst at high and least at low supersaturation. The addition of the powder crystals to the growing crystal system brings about well-defined changes to the defect structure of the crystal. These changes result principally from the attachment to
Fig. 10. Video images (a) and X-ray transmission topograph (b) for the crystal of Run 2—2 grown at initial supersaturation p "0.00798 with growth rate G "1.40]10~9 (m/s). Growth rate enhancement coefficient e "1.81. The broken line indicated in 0 "%&03% 0 (a) shows the cutting plane. The bold arrow represents observation direction for X-ray topographs ((21 2 0) reflection).
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the crystal surface of either the added powder or microcrystals produced by secondary nucleation from solution on addition of the powder. The advancing crystal surface grows to surround and incorporate these particles and in doing so leaves voids in the structure which will inevitably contain included solution. In this way the perfection of the growing crystal will be decreased. The healing of the lattice as it develops to include the growing surface particle results in the development of strain and dislocation structure. The latter are formed both as a consequence of the strain and also to accommodate the mismatch of the healing lattice. The growth rate enhancement process varies with supersaturation producing a higher degree of solvent incorporation and defect formation at higher supersaturations than at lower supersaturations. These results are not inconsistent with the discussion about the growth kinetics for dislocations [10]. Regarding the eventual decrease in growth rate following the enhancement period, we see two principal explanations. (1) Mainly the density of dislocations was decreased. A detailed examination of the defect structure in the enhanced growth region shows that this comprises bundles of dislocations each nucleating at a point and fanning out as growth progresses. The closeness of the dislocations at the start is sufficient to yield cooperating and rapidly propagating growth sources; hence the enhancement. As growth continues they separate to yield more slowly propagating single sources. In such circumstances, as single sources, they may add little power to the sources originally present and hence have little additional influence on the growth rate, particularly since by now the area of the growing face will have increased and it is the density of dislocation sources at the surface which defines the rate of growth. Hence the growth rate will fall with time and could well become lower than that before enhancement. (2) Alternatively, there is the possibility that the presence of such increased amounts of small crystals in solution and their growth will remove solute
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from the solution and hence reduce the concentration and hence supersaturation at the surface. A lower growth rate would result. In general, we feel that the principal cause of microcrystal induced growth rate enhancement is the formation of a dislocation structure around the voids generated in the crystal surface following the adhesion of microcrystals. These results and conclusions have important ramifications for the growth of crystals in industrial crystallisers where the inevitability of producing large numbers of growing and colliding primary and secondary particles will yield variations in the purity and perfection of the crystals produced.
Acknowledgements The X-ray topographs presented in this paper were recorded at the UK EPSRC at Daresbury Laboratory. J.N.S. and R.I.R. thank the director and his staff for providing the facilities used in this characterisation.
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