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Mass transport limitation of top-seeded solution growth rate
Journal of Crystal Growth 32 (1976) 287 292 © North-Holland Publishing Company
MASS TRANSPORT LIMITATION OF TOP-SEEDED SOLUTION GROWTH RATE C.M. LAWRENCE and D. ELWELL Department of Physics, Portsmouth Polytechnic, Portsmouth, England Received 28 September 1975 The growth rate of garnet crystals growing by top-seeding with supersaturation produced by thermal gradient transport has been found to decrease progressively. This decrease has been attributed to poor mixing in the solutions, and simulation experiments are in agreement with this postulate. The application of time markers to top-seeded solution growth is described.
I. Introduction
a crystal inserted just below the surface of a high temperature solution has been determined by three independent methods. In each case the solution was maintamed in a temperature gradient, with undissolved nutrient material present in a layer deposited at the base of the crucible. With the temperature, temperature gradient and seed rotation rate maintained constant, the crystal growth rate should, after an initial tran-
In the model of top-seeded solution growth with thermal gradient transport of Dawson et al. [1], it was assumed that the bulk solution is well mixed by thermal convection and particularly by the stirring action of the rotating seed crystal. The assumption of relatively efficient stirring appears to be justified for NaNbO3/NaBO2 solutions [1], and solution flow rates
sient, attain a steady value with the deposition rate balanced by dissolution of the nutrient at the higher temperature. If the seed is not slowly withdrawn from the solution to maintain the lower surface at a constant position, the growth rate may decrease because of a dedine in the effective supersaturation in a constant external (to the crucible) temperature gradient. The magnitude of the latter effect is calculable and is small compared with that observed in the various experiments.
predicted [2, 3] by theory are much higher than those required for crystallization at linear crystal growth rates of typically a few mm per day. Particularly in the case of viscous solutions, boundary effects associated with the crucible base and walls may reduce the flow rate to a value well below that predicted by the theory, which assumes an infinite crucible. In this paper, evidence is presented for relatively poor mixing in solutions of the garnets Y3A15 012 and Y3Fe5 012 in BaO/B203 and BaOI B203/BaF2 solvents. The lack of mixing manifests itself in a decrease with time of the isothermal growth rate by top-seeding, which indicates that the solution in the vicinity of the crystal becomes depleted of solute which is not replenished by flow from the nutrient material at the crucible base. The flow patterns predicted from the growth rate behaviour have been confirmed by simulation experiments using liquids of the appropriate kinematic viscosity,
2.1. Intermittent removal In the earliest experiments, the linear advance of the crystal over 24 h intervals was determined by removing the crystal from the solution and monitoring the point at which it just contacted the melt on the re-insertion. The point of contact was determined electrically through the closed circuit formed between the crystal and its support, the solution and a platinum wire welded to the crucible base, and the growth was determined by a sensitive displacement gauge attached to the crystal support. This method is maccu-
2. Growth rate determination The variation with time of the linear growth rate of 287
G.M. Lawrence, D. Elwell / Mass transport limitation of top-seeded solution growth rate
288
8-
I I.-
4.
-J 0) >-
o
2-
U
I
2
4
____________________
6
2
4 TIME
6 DAYS
Fig. 1. Thickness of material deposited on Y
3AI5 °i2 seed. The interval between initial growth and re-growth was two days.
rate 1~ecauseof adhesion of solution to the lower face of the crystal, but the quantity of adhered solution shou~dbe approximately constant at constant tempera~ureand crystal rotation rate. Fig. 1 shows the variation over a period of several days of the linear growth at 12500 C of an yttrium aluminium garnet (Y3A15 012) crystal rotated at 45 rpm in a splution of molar composition 0.5OBaO ‘0.41B203 ‘0.09BaF~.The viscosity of this solution is about 3 poise [4]. At the start of growth, the supercooling may be approximately given by the temperature difference between crystal and nutrient, 4°Cin this experiment. The linear growth rate is seen to fall progressively over 6 days to roughly 20% of the initial value, After the first 6 days, the crystal was withdrawn to a point immediately above the melt for two days and the solution maintained at constant temperature prior to reinsertion of the crystal. This procedure is seen to result in a temporary increase in the growth rate, mdicating that some increase in surface supersaturation had occurred. The time constants for solution equilibrium and depletion are clearly very long,
[5] permits a continuous determination of the rate of weight increase of a rotating seed. This apparatus was used to investigate the time dependence of the growth rate of yttrium iron garnet (Y3Fe5012) from a 0.78Ba0 ‘0.22B203 solution at 1062°C.The viscosity of the solution is about 2.5 poise, and the temperature difference across the solution 11.8°C. Fig. 2 shows the variation of growth rate with rotation rate as the latter was increased continuously from 0 60 rpm, over a period of 2 days and then returned to zero in a similar period. The points on the graph represent averages over a period of about 3 h and show scatter due to electrical and thermal noise inherent in the system. The growth rate is normally expected to increase as the rotation rate increases but the trend in fig. 2 is dominated by the tendency of the growth rate to decrease with time. This long term effect, associated with bulk transport, prevents the determination of the influence of boundary layer or interface kinetic effects on the crystallization rate, except over very short periods following a change in supersaturation. The latter technique was adopted in our initial study using the thermobalance [5] but is
2.2.
clearly unsatisfactory for systematic investigations which inevitably involve measurements on one crystal over extended periods.
Thermogravimetry
The thermogravimetric apparatus described earlier
G.M. Lawrence, D. Elwell / Mass transport limitation of top-seeded solution growth rate
6
-
t ~
289
+
12-
+
I
+ +
+
Ui I—
a
I I-
0
I
10
I
I
20
30
40
50 ROTATION RATE
60 R.P.M.
Fig. 2. Growth rate of Y
3FesOi2 crystal during programmed increase and decrease of rotation rate.
The general trends of the data shown in figs. 1 and 2 have been confirmed by observations on several other crystals. 2.3. Time markers
The use of time markers in crystals was reported by Kroko [6] and their use to determine crystal growth rates from high temperature solution has been described by Damen and Robertson [7] and by Görnert and Hergt [8]. A particularly attractive method of inserting impurity striations involves the application of electrical current pulses between the crystal and the melt, as proposed by Witt and Gatos [9]. Attempts were made using the latter method to introduce time markers into Y 3A15012 crystals during top-seeded growth from a 0.5OBaO ‘0.41B203 ‘0.09BaF~solution. For doping purposes, 0.5% of the ~203 was replaced by Cr203, which introduces a pale green colouration. It was intended to introduce, by the application of sharp current pulses passing through the seed and the solution, darker green bands of sufficient intensity to be visible by optical microscopy. In addition to Joule heating and Peltier heating or
cooling, the flow of current through the solution will cause Faradaic effects, and these are expected to be dominant. Cathodic pulses were therefore applied to produce density the order 50 mA! 2 for 1a current mm every hour.of Slices 1 mm of in 10 thickness cm cut perpendicular to the growth surface, polwere ished and examined by optical microscopy. Great difficulty was experienced in reproducible insertion of time markers, because of the low conductivity of the crystals in comparison with the solution. The solution has a very high surface tension [41and tends to form a meniscus some mm in height, so causing the current flow to by-pass the lower face of the crystal. Attempts to circumvent this effect were made by drilling a hole through the crystal so that an electrode could be inserted immediately behind the lower surface, and also by raising the seed above the melt so that contact with the bulk liquid was maintamed only through a meniscus some 2 mm in thickness. Fig. 3 shows the best-defined striations which were introduced into a Y3A15 012 crystal of 1 cm diameter using a pulse of 60 V, corresponding to a current of 50 mA. The bands are seen to be very faint, although they could be easily observed in the microscope.
G.M. Lawrence, D. Elwell / Mass transport limitation of top-seeded solution growth rate
290
-w
Fig. 3. Section through Y
3A15 012 crystals showing induced striations. The darkest line shows the boundary between initial slower growth (left) and more rapid re-growth. Dark patches are caused by diffraction from surface scratches.
Fig. 3 also shows the boundary between the initial growth and material grown after reinsertion of the crystal into remelted solution. The separation between the striations is clearly much greater in the latter case although the time interval and temperature difference (10°C)were the same in both cases. The values of linear growth rate of this crystal are plotted in fig. 4. After an initial increase during the
6
~I 4
3
2
4
8
I
I
I
I
2
16
20
24
I 26
TIME HRS
Fig. 4. Variation with time of the growth rate of the crystal of fig. 3, after re-insertion,
first hour following the introduction of the seed, the grnwth rate falls steadily apart from two rather sharp peaks. The origin of these irregularities is unknown, but they may have arisen from sudden disturbances of a thermal or mechanical nature. Attempts to reproduce the intensity of the time markers of fig. 3 were generally unsuccessful, in spite of several changes in operating parameters and seed or electrode configuration. Alternative methods of introducing time markers involving the use of temperature pulses (cooling the crystal or heating the nutrient) were also tried. These were unsatisfactory since they resulted either in an unobservable effect or in major disturbances of the crystal surface, leading to a high concentration of solvent inclusions. Mechanical disturbances, such as interrupting the crystal rotation, were found to have a similar effect. The powerful nature of the time marker technique, in revealing the position and shape of the growth interface at known and relatively short time intervals, is such that it cannot be abandoned, but it is particularly difficult to apply to insulating materials. Further studies will be based upon the use of X-ray topography to detect the growth striations, which may then be detected in both optically transparent and opaque crystals.
G.M. Lawrence, D. Elwell / Mass transport limitation of top-seeded solution growth rate
291
3. Interpretation of the decrease in growth rate A possible cause of the tendency of the growth rate to decrease to very low values over a period of several days is the reduction in the number of screw dislocations which intersect the growing crystal surface. The strong dependence of the growth rate of facetted crystals upon the presence of dislocations has been established by Mussard and Goldsztaub [10] in the case of sodium chlorate crystals growing from aqueous solution. Although a detailed examination of the density and nature of dislocations in the garnet crystals has not yet been made, they do grow with well-developed habit faces as in the example of fig. 5. It is, however, unlikely that no dislocations (other than pure edge) intersect the crystal surface and the change in growth rate on reinsertion (fig. 1) supports the hypothesis that the decrease in growth rate occurs because of local depletion of the solution. Confirmation of poor mixing in the relatively viscous liquids used was provided by simulation experiments at room temperature using a water—glycerol mixture of the same kinematic viscosity (~—1stokes)
Fig. 6. Flow patterns in water glycerol mixture of I stokes kinematic viscosity. “Crystal” rotation rate 45 rpm. as the high-temperature solutions. The crystal was simulated by a perspex cylinder 1 cm in diameter and rotating at the same speeds (0—60 rpm) used for crystal growth. The volume of liquid and the crucible diameter corresponded to those used during growth. The flow pattern was made visible by the introduction of a small quantity of potassium permanganate solution and the flow behaviour was confirmed by observations using alternative particles of neutral buoyancy, such as small segments of human hair. It is clear from observations such as that shown in fig. 6 that non-mixing surfaces exist within the liquid. The liquid within a fairly well-defined region in contact with the crystal is made to flow at rates compara ble with those predicted by theory, but this liquid is recycled, with very little mixing in the bulk of the liquid. Calculations for the crystal growth experiments suggest that 40 50% of the solution is depleted of supersaturated material before the growth rate falls to a negligibly low value. Simulation experiments using a temperature gradient have shown that thermal convection does help to improve the degree of mixing, but not to any major extent.
a
4. Summary and conclusions Fig. 5. Y3Fe5052
crystal
used for data of fig.
2.
The observed decrease with time of the linear
292
G.M. Lawrence, D. Elwell
/ Mass transport limitation of top-seeded solution growth rate
growth rate of garnet crystals grown by top-seeding with supersaturation produced by a temperature gradient is attributed to poor mixing within the solution. Several alternative strategies exist to overcome this problem. Ideally a solution should be chosen with a kinematic viscosity well below 1 stokes (e.g. a lead salt), but the tess viscous solvents are often rather volatile. The
rapid seed rotation is unlikely to result in high-quality crystals because of turbulence in the solution. In conclusion, it might be mentioned that the experience reported here illustrates the value of simulation experiments, which have provided a more valid insight into the behaviour of our system than the results of theory based upon an idealised case.
use of slow cooling rather than a temperature gradient
to produce the supersaturation will reduce though not eliminate the problem arising from non-mixing. This alternative is, however, often unattractive when doped materials or solid solutions are to be crystallized, since the resulting crystals are normally inhomogeneous. If isothermal growth is considered desirable, the best alternative appears to be to use some stirring action more effective than that provided by crystal rotation or thermal convection. Immersed stirrers fabricated from platinum or its alloys ar normally too soft for prolonged use, and accelerated rotation [11] of the crucible appears to offer the most promising alternative. This technique suffers from the disadvantage that the meniscus is moved vertically with the period of
References
the rotation programme, but this variation may not be serious in solution growth since the amount of
[8] P. Görnert and R. Hergt, Phys. Status Solidi (a) 20 (1973) 577. [9] A.F. Witt and H.C. Gatos, J. Electrochem. Soc. 115 (1968) 70. [10] F. Mussard and S. Goldsztaub, J. Crystal Growth 13/14
crystal deposited in one period is small (typically ~1 pm). Experiments to assess the viability of this stirring technique in top-seeded solution growth of Y3A15012 are now in progress. The alternative of very
[1] R.D. Dawson, D. Elwell and J.C. Brice, J. Crystal Growth
23 (1974) 65. [2] W.G. Cochran, Proc. Cambridge Phil. Soc. 30 (1934) 365. [3] P. Capper and D. Elwell, J. Crystal Growth 30 (1975) 352.
[4] D. Elwell, P. Capper and C.M. Lawrence, J. Crystal Growth 24/25 (1974) 651. [5] D. Elwell, P. Capper and M. D’Agostino, J. Crystal Growth 29 (1975) 321.
[6] L.J. Kroko, J. Electrochem. Soc. 113 (1966) 801. [7] J.P.M. Damen and J.M. Robertson, J. Crystal Growth 16 (1972) 50.
(1971) 445.
[11] H.J. Scheel, J. Crystal Growth 13/14 (1971) 560.
MASS TRANSPORT LIMITATION OF TOP-SEEDED SOLUTION GROWTH RATE C.M. LAWRENCE and D. ELWELL Department of Physics, Portsmouth Polytechnic, Portsmouth, England Received 28 September 1975 The growth rate of garnet crystals growing by top-seeding with supersaturation produced by thermal gradient transport has been found to decrease progressively. This decrease has been attributed to poor mixing in the solutions, and simulation experiments are in agreement with this postulate. The application of time markers to top-seeded solution growth is described.
I. Introduction
a crystal inserted just below the surface of a high temperature solution has been determined by three independent methods. In each case the solution was maintamed in a temperature gradient, with undissolved nutrient material present in a layer deposited at the base of the crucible. With the temperature, temperature gradient and seed rotation rate maintained constant, the crystal growth rate should, after an initial tran-
In the model of top-seeded solution growth with thermal gradient transport of Dawson et al. [1], it was assumed that the bulk solution is well mixed by thermal convection and particularly by the stirring action of the rotating seed crystal. The assumption of relatively efficient stirring appears to be justified for NaNbO3/NaBO2 solutions [1], and solution flow rates
sient, attain a steady value with the deposition rate balanced by dissolution of the nutrient at the higher temperature. If the seed is not slowly withdrawn from the solution to maintain the lower surface at a constant position, the growth rate may decrease because of a dedine in the effective supersaturation in a constant external (to the crucible) temperature gradient. The magnitude of the latter effect is calculable and is small compared with that observed in the various experiments.
predicted [2, 3] by theory are much higher than those required for crystallization at linear crystal growth rates of typically a few mm per day. Particularly in the case of viscous solutions, boundary effects associated with the crucible base and walls may reduce the flow rate to a value well below that predicted by the theory, which assumes an infinite crucible. In this paper, evidence is presented for relatively poor mixing in solutions of the garnets Y3A15 012 and Y3Fe5 012 in BaO/B203 and BaOI B203/BaF2 solvents. The lack of mixing manifests itself in a decrease with time of the isothermal growth rate by top-seeding, which indicates that the solution in the vicinity of the crystal becomes depleted of solute which is not replenished by flow from the nutrient material at the crucible base. The flow patterns predicted from the growth rate behaviour have been confirmed by simulation experiments using liquids of the appropriate kinematic viscosity,
2.1. Intermittent removal In the earliest experiments, the linear advance of the crystal over 24 h intervals was determined by removing the crystal from the solution and monitoring the point at which it just contacted the melt on the re-insertion. The point of contact was determined electrically through the closed circuit formed between the crystal and its support, the solution and a platinum wire welded to the crucible base, and the growth was determined by a sensitive displacement gauge attached to the crystal support. This method is maccu-
2. Growth rate determination The variation with time of the linear growth rate of 287
G.M. Lawrence, D. Elwell / Mass transport limitation of top-seeded solution growth rate
288
8-
I I.-
4.
-J 0) >-
o
2-
U
I
2
4
____________________
6
2
4 TIME
6 DAYS
Fig. 1. Thickness of material deposited on Y
3AI5 °i2 seed. The interval between initial growth and re-growth was two days.
rate 1~ecauseof adhesion of solution to the lower face of the crystal, but the quantity of adhered solution shou~dbe approximately constant at constant tempera~ureand crystal rotation rate. Fig. 1 shows the variation over a period of several days of the linear growth at 12500 C of an yttrium aluminium garnet (Y3A15 012) crystal rotated at 45 rpm in a splution of molar composition 0.5OBaO ‘0.41B203 ‘0.09BaF~.The viscosity of this solution is about 3 poise [4]. At the start of growth, the supercooling may be approximately given by the temperature difference between crystal and nutrient, 4°Cin this experiment. The linear growth rate is seen to fall progressively over 6 days to roughly 20% of the initial value, After the first 6 days, the crystal was withdrawn to a point immediately above the melt for two days and the solution maintained at constant temperature prior to reinsertion of the crystal. This procedure is seen to result in a temporary increase in the growth rate, mdicating that some increase in surface supersaturation had occurred. The time constants for solution equilibrium and depletion are clearly very long,
[5] permits a continuous determination of the rate of weight increase of a rotating seed. This apparatus was used to investigate the time dependence of the growth rate of yttrium iron garnet (Y3Fe5012) from a 0.78Ba0 ‘0.22B203 solution at 1062°C.The viscosity of the solution is about 2.5 poise, and the temperature difference across the solution 11.8°C. Fig. 2 shows the variation of growth rate with rotation rate as the latter was increased continuously from 0 60 rpm, over a period of 2 days and then returned to zero in a similar period. The points on the graph represent averages over a period of about 3 h and show scatter due to electrical and thermal noise inherent in the system. The growth rate is normally expected to increase as the rotation rate increases but the trend in fig. 2 is dominated by the tendency of the growth rate to decrease with time. This long term effect, associated with bulk transport, prevents the determination of the influence of boundary layer or interface kinetic effects on the crystallization rate, except over very short periods following a change in supersaturation. The latter technique was adopted in our initial study using the thermobalance [5] but is
2.2.
clearly unsatisfactory for systematic investigations which inevitably involve measurements on one crystal over extended periods.
Thermogravimetry
The thermogravimetric apparatus described earlier
G.M. Lawrence, D. Elwell / Mass transport limitation of top-seeded solution growth rate
6
-
t ~
289
+
12-
+
I
+ +
+
Ui I—
a
I I-
0
I
10
I
I
20
30
40
50 ROTATION RATE
60 R.P.M.
Fig. 2. Growth rate of Y
3FesOi2 crystal during programmed increase and decrease of rotation rate.
The general trends of the data shown in figs. 1 and 2 have been confirmed by observations on several other crystals. 2.3. Time markers
The use of time markers in crystals was reported by Kroko [6] and their use to determine crystal growth rates from high temperature solution has been described by Damen and Robertson [7] and by Görnert and Hergt [8]. A particularly attractive method of inserting impurity striations involves the application of electrical current pulses between the crystal and the melt, as proposed by Witt and Gatos [9]. Attempts were made using the latter method to introduce time markers into Y 3A15012 crystals during top-seeded growth from a 0.5OBaO ‘0.41B203 ‘0.09BaF~solution. For doping purposes, 0.5% of the ~203 was replaced by Cr203, which introduces a pale green colouration. It was intended to introduce, by the application of sharp current pulses passing through the seed and the solution, darker green bands of sufficient intensity to be visible by optical microscopy. In addition to Joule heating and Peltier heating or
cooling, the flow of current through the solution will cause Faradaic effects, and these are expected to be dominant. Cathodic pulses were therefore applied to produce density the order 50 mA! 2 for 1a current mm every hour.of Slices 1 mm of in 10 thickness cm cut perpendicular to the growth surface, polwere ished and examined by optical microscopy. Great difficulty was experienced in reproducible insertion of time markers, because of the low conductivity of the crystals in comparison with the solution. The solution has a very high surface tension [41and tends to form a meniscus some mm in height, so causing the current flow to by-pass the lower face of the crystal. Attempts to circumvent this effect were made by drilling a hole through the crystal so that an electrode could be inserted immediately behind the lower surface, and also by raising the seed above the melt so that contact with the bulk liquid was maintamed only through a meniscus some 2 mm in thickness. Fig. 3 shows the best-defined striations which were introduced into a Y3A15 012 crystal of 1 cm diameter using a pulse of 60 V, corresponding to a current of 50 mA. The bands are seen to be very faint, although they could be easily observed in the microscope.
G.M. Lawrence, D. Elwell / Mass transport limitation of top-seeded solution growth rate
290
-w
Fig. 3. Section through Y
3A15 012 crystals showing induced striations. The darkest line shows the boundary between initial slower growth (left) and more rapid re-growth. Dark patches are caused by diffraction from surface scratches.
Fig. 3 also shows the boundary between the initial growth and material grown after reinsertion of the crystal into remelted solution. The separation between the striations is clearly much greater in the latter case although the time interval and temperature difference (10°C)were the same in both cases. The values of linear growth rate of this crystal are plotted in fig. 4. After an initial increase during the
6
~I 4
3
2
4
8
I
I
I
I
2
16
20
24
I 26
TIME HRS
Fig. 4. Variation with time of the growth rate of the crystal of fig. 3, after re-insertion,
first hour following the introduction of the seed, the grnwth rate falls steadily apart from two rather sharp peaks. The origin of these irregularities is unknown, but they may have arisen from sudden disturbances of a thermal or mechanical nature. Attempts to reproduce the intensity of the time markers of fig. 3 were generally unsuccessful, in spite of several changes in operating parameters and seed or electrode configuration. Alternative methods of introducing time markers involving the use of temperature pulses (cooling the crystal or heating the nutrient) were also tried. These were unsatisfactory since they resulted either in an unobservable effect or in major disturbances of the crystal surface, leading to a high concentration of solvent inclusions. Mechanical disturbances, such as interrupting the crystal rotation, were found to have a similar effect. The powerful nature of the time marker technique, in revealing the position and shape of the growth interface at known and relatively short time intervals, is such that it cannot be abandoned, but it is particularly difficult to apply to insulating materials. Further studies will be based upon the use of X-ray topography to detect the growth striations, which may then be detected in both optically transparent and opaque crystals.
G.M. Lawrence, D. Elwell / Mass transport limitation of top-seeded solution growth rate
291
3. Interpretation of the decrease in growth rate A possible cause of the tendency of the growth rate to decrease to very low values over a period of several days is the reduction in the number of screw dislocations which intersect the growing crystal surface. The strong dependence of the growth rate of facetted crystals upon the presence of dislocations has been established by Mussard and Goldsztaub [10] in the case of sodium chlorate crystals growing from aqueous solution. Although a detailed examination of the density and nature of dislocations in the garnet crystals has not yet been made, they do grow with well-developed habit faces as in the example of fig. 5. It is, however, unlikely that no dislocations (other than pure edge) intersect the crystal surface and the change in growth rate on reinsertion (fig. 1) supports the hypothesis that the decrease in growth rate occurs because of local depletion of the solution. Confirmation of poor mixing in the relatively viscous liquids used was provided by simulation experiments at room temperature using a water—glycerol mixture of the same kinematic viscosity (~—1stokes)
Fig. 6. Flow patterns in water glycerol mixture of I stokes kinematic viscosity. “Crystal” rotation rate 45 rpm. as the high-temperature solutions. The crystal was simulated by a perspex cylinder 1 cm in diameter and rotating at the same speeds (0—60 rpm) used for crystal growth. The volume of liquid and the crucible diameter corresponded to those used during growth. The flow pattern was made visible by the introduction of a small quantity of potassium permanganate solution and the flow behaviour was confirmed by observations using alternative particles of neutral buoyancy, such as small segments of human hair. It is clear from observations such as that shown in fig. 6 that non-mixing surfaces exist within the liquid. The liquid within a fairly well-defined region in contact with the crystal is made to flow at rates compara ble with those predicted by theory, but this liquid is recycled, with very little mixing in the bulk of the liquid. Calculations for the crystal growth experiments suggest that 40 50% of the solution is depleted of supersaturated material before the growth rate falls to a negligibly low value. Simulation experiments using a temperature gradient have shown that thermal convection does help to improve the degree of mixing, but not to any major extent.
a
4. Summary and conclusions Fig. 5. Y3Fe5052
crystal
used for data of fig.
2.
The observed decrease with time of the linear
292
G.M. Lawrence, D. Elwell
/ Mass transport limitation of top-seeded solution growth rate
growth rate of garnet crystals grown by top-seeding with supersaturation produced by a temperature gradient is attributed to poor mixing within the solution. Several alternative strategies exist to overcome this problem. Ideally a solution should be chosen with a kinematic viscosity well below 1 stokes (e.g. a lead salt), but the tess viscous solvents are often rather volatile. The
rapid seed rotation is unlikely to result in high-quality crystals because of turbulence in the solution. In conclusion, it might be mentioned that the experience reported here illustrates the value of simulation experiments, which have provided a more valid insight into the behaviour of our system than the results of theory based upon an idealised case.
use of slow cooling rather than a temperature gradient
to produce the supersaturation will reduce though not eliminate the problem arising from non-mixing. This alternative is, however, often unattractive when doped materials or solid solutions are to be crystallized, since the resulting crystals are normally inhomogeneous. If isothermal growth is considered desirable, the best alternative appears to be to use some stirring action more effective than that provided by crystal rotation or thermal convection. Immersed stirrers fabricated from platinum or its alloys ar normally too soft for prolonged use, and accelerated rotation [11] of the crucible appears to offer the most promising alternative. This technique suffers from the disadvantage that the meniscus is moved vertically with the period of
References
the rotation programme, but this variation may not be serious in solution growth since the amount of
[8] P. Görnert and R. Hergt, Phys. Status Solidi (a) 20 (1973) 577. [9] A.F. Witt and H.C. Gatos, J. Electrochem. Soc. 115 (1968) 70. [10] F. Mussard and S. Goldsztaub, J. Crystal Growth 13/14
crystal deposited in one period is small (typically ~1 pm). Experiments to assess the viability of this stirring technique in top-seeded solution growth of Y3A15012 are now in progress. The alternative of very
[1] R.D. Dawson, D. Elwell and J.C. Brice, J. Crystal Growth
23 (1974) 65. [2] W.G. Cochran, Proc. Cambridge Phil. Soc. 30 (1934) 365. [3] P. Capper and D. Elwell, J. Crystal Growth 30 (1975) 352.
[4] D. Elwell, P. Capper and C.M. Lawrence, J. Crystal Growth 24/25 (1974) 651. [5] D. Elwell, P. Capper and M. D’Agostino, J. Crystal Growth 29 (1975) 321.
[6] L.J. Kroko, J. Electrochem. Soc. 113 (1966) 801. [7] J.P.M. Damen and J.M. Robertson, J. Crystal Growth 16 (1972) 50.
(1971) 445.
[11] H.J. Scheel, J. Crystal Growth 13/14 (1971) 560.