Effect of Growth Rate History on Current Crystal Growth. 2. Crystal

Effect of Growth Rate History on Current Crystal Growth. 2. Crystal Growth of Sucrose, Al(SO4)2 · 12H2O, KH2PO4, and K2SO4 Pareena Pantaraks,†,‡ Masakuni Matsuoka,§ and Adrian E. Flood*,† School of Chemical Engineering, Suranaree UniVersity of Technology (SUT), 111 UniVersity AVenue, Muang District, Nakhon Ratchasima 30000, Thailand, and Department of Chemical Engineering, Tokyo UniVersity of Agriculture and Technology (TUAT), 24-16 Nakacho-2, Koganei, Tokyo 184-8588, Japan

CRYSTAL GROWTH & DESIGN 2007 VOL. 7, NO. 12 2635–2642

ReceiVed March 18, 2007; ReVised Manuscript ReceiVed August 13, 2007

ABSTRACT: The current study investigated a potential mechanism of growth rate dispersion (GRD) by determining the effect of a crystal’s “growth rate history” on its current crystal growth, for sucrose, potash alum, potassium dihydrogen phosphate (KDP), and potassium sulfate crystals, using a combination of growth kinetic analysis and surface analysis via atomic force microscopy (AFM) and scanning electron microscopy (SEM). The growth history of a crystal had a significant effect on the future crystal growth rate: if a crystal had a period of high growth in a high supersaturation environment, the subsequent growth of the crystal in a lower supersaturation had a lower rate than a crystal that had been kept in the lower supersaturation environment. These results can be explained by the effect of high growth rates on the growing surface of a crystal: crystals grown in high supersaturation solutions had a rougher surface (on a macroscopic rather than molecular scale) than those grown in low supersaturation solutions. This phenomenon occurs if growth occurs above a critical level of the supersaturation, which we term the roughening transition. The level of GRD is shown to be related to the surface energy of the crystal, with high surface energy species also displaying higher levels of growth rate dispersion at the same relative supersaturation. Introduction Crystal growth rate dispersion (GRD), first noted by White and Wright,1 is where individual crystals of the same size exhibit different growth rates in spite of the fact that the temperatures, hydrodynamics, and supersaturations of the solutions they are grown from are the same. The phenomenon causes considerable problems in industrial crystallization from solution, making crystallizer design more difficult and also degrading the quality of the product in relation to the crystal size distribution. The differences in the growth rates of crystals from the same population can be very significant: a recent study on glucose monohydrate showed that the growth rate of crystals in the fastest five percent of the population was more than eight times the growth rate of the slowest five percent.2 Many inorganic crystals such as Gibbsite also have considerable levels of GRD.3 Growth rate dispersion causes a significant problem in the crystal size distribution (CSD) of crystalline products, giving a wide range of crystal product sizes even when the process starts with a narrow CSD. A further consequence of GRD is an increase in the amount of small, slow-growing crystals and, therefore, a reduction of mean particle size.4 An excellent review of the phenomenon of crystal growth rate dispersion was presented by Ulrich in 1989;5 however, a reasonably large number of papers has also been published in the area since this time, and it is useful to present a short summary of the research in the area. The original mechanism proposed for GRD involved the surface integration step and was related to the concentration of screw dislocation steps on the crystal surface, an idea directly based on the Burton-Cabrera-Frank (BCF) theory of crystal * Corresponding author. Phone: +66 44 224497. Fax: +66 44 224609. E-mail: [email protected]. † Suranaree University of Technology (SUT). ‡ Current address: Michelin Research Asia (Thailand) Co. Ltd., 252 SPE Tower 15th Floor, Phaholyothin Rd., Samsaen Nai, Pauathai, Bangkok 10400, Thailand. § Tokyo University of Agriculture and Technology (TUAT).

growth. A significant body of work has shown that this mechanism is not related to GRD and suggested that there is no connection between the number of dislocation steps and the crystal growth rate.6–9 The concept of varying degrees of “internal crystal perfection” in terms of strain in the crystal lattice has previously been investigated to explain the mechanism behind GRD. A clear tendency for a reduction in growth rate with increasing amount of overall lattice strain (as measured by mosaic spread) has been revealed in experimental studies.10 Subsequent studies have both demonstrated similar results4,11 and disagreed with this result. For example, Harding et al.12 concluded that, for ammonium dihydrogen phosphate (ADP), sodium chlorate, and sucrose, “no correlation existed between the growth rates of crystals of these simple systems and their mosaic spread”. In addition, Herden and Lacmann9 found no correlation between face-specific growth rates of KNO3 and Laue quality and concluded that this was likely due to growth rates being face-specific, while Laue quality is determined over the entire crystal. The authors did conclude that lattice strain was significant in the mechanism of GRD, however. Models predicting the effect of lattice strain on the crystal growth rate have also been produced.13 Wang et al.14 observed the growth rates of potash alum (KAl(SO4)2 · 12H2O) when the supersaturation levels were subjected to a pulse change σ1:σ2:σ1 (with σ2 more than or less than σ1). The results showed that the growth rate decreases with decreasing σ2 and increases with increasing σ2, but it does not return to the previous value after the second supersaturation change (returning to σ1) in a short time period. Tanneberger et al.8 repeated these experiments and found similar results. Both works concluded that these effects might be explained by changes of the surface structure of the crystal due to changes in the supersaturation level. It has recently been shown that growth history, the record of previous growth rates of a crystal, has a significant effect on the crystal’s current growth kinetics and that this may be a significant factor in the mechanism of crystal growth rate

10.1021/cg070265q CCC: $37.00  2007 American Chemical Society Published on Web 11/20/2007

2636 Crystal Growth & Design, Vol. 7, No. 12, 2007

Figure 1. Seed crystals of (a) potash alum and (b) KDP.

dispersion.15 On the basis of this evidence, it was decided to investigate the surface of crystals growing under a variety of conditions using atomic force microscopy (AFM) to more fully elucidate the changes in the surface of the growing crystals and also to determine the significance of the surface energy of the crystal on the growth rate dispersion. In addition, the current research extends the previous paper to also include inorganic molecules, such as potassium dihydrogen phosphate (KDP), potash alum, and potassium sulfate. The current study is to investigate whether changes in supersaturation levels can influence the surface structure of the crystal and to study the effect of growth rate history, by modifying the supersaturation level during growth, on current crystal growth rates. The results from this study can help to conclude whether the growth rate history of individual crystals is related to the phenomenon of crystal growth rate dispersion. Experimental Section Materials. The materials used in this study are sucrose, potash alum (KAl(SO4)2 · 12H2O), potassium sulfate (K2SO4), and KDP (KH2PO4). Solutions of sucrose were produced from commercial grade refined sugar of approximately 99.95% purity (Mitr Phol, Thailand) and distilled water. Solutions of potash alum, KDP, and potassium sulfate were prepared from ACS grade reagents (Wako Industry) of approximately 99.5%, 99%, and 99.9% purity, respectively, and distilled water. Sucrose seed crystals were taken from commercial grade white sugar in the size range of 600-850 µm. The seed crystals of potash alum, KDP, and potassium sulfate were obtained by recrystallization. The sizes of potash alum crystals used in the experiment were 550-700 µm, those of KDP were 650-800 µm, and potassium sulfate seed crystals were 550-1000 µm. Narrower seed crystal size distributions (approximately 200-500 µm) were used in experiments to characterize the level of GRD in various systems to enable more accurate characterization of the GRD. Examples of seed crystals for potash alum and KDP are shown in Figure 1. Supersaturated solutions were produced by creating a solution of the necessary concentration at a temperature above its equilibrium temperature and then cooling the solution to the experimental temperature. Apparatus. Crystallization experiments were performed in both a single crystal growth cell (for surface analysis of individual crystals after growth) and a batch crystallizer. The single crystal growth cell is depicted in Figure 2. A single crystal was mounted between two pins, at the center of the pipe cross-section, in a flow of mother liquor. The crystal holder was positioned toward the end of the pipe in order to minimize end effects on the fluid flow at the crystal. The outer jacket was used to maintain the experimental temperature by flow of water from a constant temperature bath. The crystal size can be determined either from direct measurement or image analysis. The batch crystallizer was a 300 mL, glass batch crystallizer equipped with a constant temperature jacket and agitated with a magnetic stirrer. Effect of Supersaturation Levels on the Crystal Surface. The surfaces of three species of crystal, sucrose, potash alum, and KDP were observed after growth at low and high supersaturation by using a scanning electron microscope (SEM). To produce the same history for the seed crystals, all types of seed crystals were first dissolved with a slightly undersaturated solution, followed by further growth in a

Pantaraks et al. slightly supersaturated solution for a short period. In the experiment, individual crystals were grown under a specific supersaturation in a single crystal growth cell for a period of 2-3 h. The solution flow rate used was very high for each case (200 mL/min) to ensure that the growth rate was entirely controlled by the surface integration step. Ex-situ observation of the surface of potash alum during growth was also performed using an atomic force microscope (AFM). The crystal was removed from the solution at each time period and was washed with ethanol before scanning. A small area (about 50 µm × 50 µm) of the crystal’s surface was scanned and analyzed. Effect of Growth History on Current Crystal Growth. Experiments for sucrose, potash alum, and KDP crystals were carried out in a batch crystallizer under isothermal conditions with stirring at 500 rpm for periods of 2-3 h. Two groups of 200 crystals were each initially grown at low (1.5%) and high (5.0%) supersaturation to produce different growth histories. The crystals in each group were then separated into equal batches to be subsequently grown under different supersaturation levels. For example, a group of 200 crystals grown for 2 h in 1.5% relative supersaturation were separated into four groups, which were subsequently grown for 2 h at 1.50, 2.20, 3.60, and 5.10% relative supersaturation. Separation was achieved by manual separation after filtration to remove the mother liquor. Filtration using a vacuum pump was required in the case of sucrose crystals due to the high viscosity of the solution. Effect of Growth Time at High Supersaturation on Subsequent Growth Rate. Populations of potash alum crystals were grown in the 300 mL batch crystallizer. Initially, the crystals were grown under a high level of supersaturation (8.5% relative supersaturation) at 24.3 °C for periods of either 20, 40, or 60 min, after which the crystals were grown for 60 min under a low level of supersaturation (3.8% relative supersaturation) at the same temperature. Crystal growth rates were determined by removing crystals from the crystallizer, filtering them under vacuum, and sizing them using photomicroscopy. Image analysis software was used to analyze the photomicrograph to determine the particle size distribution, and this distribution was used to determine the crystal growth rate. Effect of Surface Energy on GRD. Constant composition batch crystallizations (using low seeding rates) were performed with potash alum, KDP, and potassium sulfate at 5% relative supersaturation for all species in order to determine whether surface energy could be correlated with levels of GRD. The crystal size distributions (CSDs) of the seed crystals were compared to the CSDs of the product crystals after 3 h of growth. The change in the width of the distribution due to the 3 h of growth was used as a measure of the level of GRD in the system.

Results and Discussion Effect of Supersaturation Levels on the Surface Structure of Crystals. SEM micrographs of the product crystals grown from low and high relative supersaturation for sucrose, potash alum, and KDP are shown in Figures 3, 4, and 5, respectively. The results from the SEM micrographs show that the level of supersaturation during growth has a significant effect on the surface structure, or the surface roughness of the crystals. The surfaces of all three crystals grown from low supersaturation display a smooth surface, whereas those grown from high supersaturation have a rougher surface: it should be noted that the scale of the surface roughness observed in this case is on the microscopic level, not the molecular or macroscopic levels. According to the review paper of Garside on industrial crystallization from solution,16 roughness at the molecular level is related to the nature of solute and solvent as well as their interactions, while that at the macroscopic level relates to the change in morphology of the crystals. In our experiment, the roughness in the molecular scale should not vary, because the two crystals being compared are of the same species and were grown in aqueous solutions with identical hydrodynamics and temperatures, but with different supersaturation levels. The SEM micrographs are also unlikely to distinguish roughness

Growth Rate History and Crystal Growth

Crystal Growth & Design, Vol. 7, No. 12, 2007 2637

Figure 2. Single crystal growth cell.

Figure 3. SEM micrographs of the surface of a sucrose crystal15 after (a) growth at 2.2% relative supersaturation and (b) growth at 5.1% relative supersaturation.

Figure 4. SEM micrographs of the surface of a potash alum crystal after (a) growth at 2.6% relative supersaturation and (b) growth at 7.5% relative supersaturation.

Figure 5. SEM micrographs of the surface of a KDP crystal after (a) growth at 2.0% relative supersaturation and (b) growth at 5.0% relative supersaturation.

at a molecular level. The morphology of the product crystals was also not changed, so it also cannot be explained using the macroscopic scale. At the microscopic scale, the size range of 1-10 µm, the roughness is possibly caused by

groups of clusters, step bunches, or surface nuclei formed on the surface of the crystals. The results of a study of the surface of potash alum from AFM confirmed that the roughness of the crystals grown in high


Pantaraks et al.

Figure 6. AFM images of 50 µm × 50 µm areas of the surface of potash alum after (a) growth at 2.6% relative supersaturation and (b) growth at 7.5% relative supersaturation. Table 1. Effect of Crystal Growth History on Current Crystal Growth Rates of Sucrose growth at σ1

growth at σ2 (%): G2 (nm/s)

Table 2. Effect of Crystal Growth History on Current Crystal Growth Rates of Potash Alum growth at σ1


σ1 (%)

G1 (nm/s)

σ2 ) 1.50

σ2 ) 2.20

σ2 ) 3.60

σ2 ) 5.00

σ1 (%)

G1 (nm/s)

σ2 ) 1.50

σ2 ) 3.50

σ2 ) 5.90

σ2 ) 7.60

1.50 5.00

8.0 32.5

7.7 4.3

12.0 7.7

19.8 14.0

33.3 31.8

1.50 5.00

8.0 51.7

8.3 5.3

32.5 23.7

84.0 73.3

103.8 101.3

supersaturation was due to irregular growth patterns on the surface of the crystal, possibly large surface nuclei with an imperfect lattice forming on the surface. Figure 6a is a region (50 µm × 50 µm in size) of the surface of potash alum scanned by AFM after growth in low supersaturation, and Figure 6b shows the result of growth at high supersaturation. The AFM micrographs show that irregular growth patches occur at low concentrations on the surface of the crystal even after growth in low supersaturation, but more of these surface imperfections occur when the supersaturation level is high. Plots of the height of roughness as a function of distance for each supersaturation are also in Figure 6. Note that the vertical axis is greatly magnified with respect to the horizontal axes to better display surface irregularity. The height per scale division in Figure 6a is 50 nm while the height per scale division in Figure 6b is 200 nm indicating a much larger variation in the topography of the crystal grown under high supersaturation. Effect of Growth History and Supersaturation on the Current Crystal Growth. On basis of the results from the previous section, crystals grown more quickly at higher super-

Table 3. Effect of Crystal Growth History on Current Crystal Growth Rates of KDP growth at σ1


σ1 (%)

G1 (nm/s)

σ2 ) 2.50

σ2 ) 3.80

σ2 ) 5.00

1.50 5.00

19.5 50.8

31.3 5.30

46.7 19.0

54.8 52.3

saturation have a surface that is significantly rougher on a microscopic level than the seed crystals that they were grown from. Therefore, crystals grown from different supersaturation levels must have different microscopic surface roughness, and previous results on sucrose suggest that this affects the later growth of the crystals.15 The result of batch crystallizations performed to show the effect of growth history on the current crystal growth of sucrose, potash alum, and KDP are summarized in Tables 1, 2, and 3, respectively. When crystals were grown at the same supersaturation for two periods of growth, the average growth rates of the crystals (for all species) were not significantly different, representing



Figure 7. Effect of growth history of (a) sucrose crystals, (b) potash alum crystals, and (c) KDP crystals on their current crystal growth: previous growth under (b) 1.5% relative supersaturation and (O) 5.0% relative supersaturation.

constant growth rates at constant conditions over 4 h. For example, the average growth rate of sucrose at 5% relative supersaturation was 32.5 nm/s for the first period of 2 h and 31.8 nm/s for the second period of 2 h. The results in Tables 1–3 show that the crystals initially grown at 1.5% relative supersaturation have higher average growth rates in the second period of growth than those crystals initially grown at 5.0% relative supersaturation. The data in all tables are also plotted in Figure 7, so that the relative difference between the data for crystals previously grown under different supersaturations is more easily visualized. From Figure 7, it can be noted that the crystals grown for significant times at high supersaturation, causing a rough crystal surface, grow slowly during the next period of growth, particularly at lower levels of supersaturation. A proposed mechanism for the lower growth rate is the effect of surface roughness on crystal growth. Very rough surfaces present on the crystals grown at high supersaturation are probably caused by the fact that, at relatively high supersaturation, the concentration of solute molecules in the adsorbed layer is sufficiently high to form groups of islands or clusters (with a size on the microscopic scale) on the surface. Condensation of these clusters into surface nuclei that do not align perfectly with the underlying crystal lattice might therefore be the major cause of the very rough crystal surfaces apparent in the micrographs. When these crystals are subjected to low supersaturation, where the crystals can grow near-ideal lattices due to the slow growth process, the degraded surface or imperfect lattice is improved by filling and covering of the imperfect layers created by the fast growth periods. This healing period requires significant time and thickness of the improved crystal lattice: the required time depends on how much the surface is degraded. It can also be noted that crystals subjected to two periods of growth under high supersaturation grow at essentially the same rate in the two periods. The degree of degradation of the crystal surface for growth at a particular supersaturation may be constant after extended growth in a particular solution, and this condition may be reached relatively quickly during the growth, after which the surface quality and, therefore, the crystal growth rate is constant. When the crystal is subsequently grown under a lower supersaturation, the surface quality of the crystal is poor in comparison to crystals grown previously at the lower level of supersaturation, and hence, its growth rate will be lower than expected. The rate of the surface renewal appears to be far slower than the rate of the surface degradation process. An experiment was performed to check the reliability of this mechanism by observation of the surface of a potash alum

crystal when the supersaturation for crystal growth was changed from 7.5% relative supersaturation (at high supersaturation producing a rough surface) to 2.5% relative supersaturation, where surface healing could occur. The AFM scans of the initial surface of the crystal (crystallized from 7.5% relative supersaturation) and the surface of the crystal after growth in 2.5% relative supersaturation for 30 min and 1 h are shown in Figure 8. The result confirmed the improvement of the degraded surface when the relative supersaturation was changed to a lower supersaturation condition. The results shown in Figure 7 are particularly interesting; although all three crystal types were initially grown at the same supersaturation level, for preparation of groups of crystals with different surface features, the difference in growth rates between the two groups of crystals at various supersaturations in the second period of growth were quite different for the three types of crystals. The difference between the two curves (initially 1.5% supersaturation and initially 5.0% supersaturation) in the plot of potash alum was small compared to that in the plot of sucrose and KDP. There is a particularly large difference between the two sets of data for KDP. The plots of the relative difference in growth rate, calculated using eq 1 for each species as a function of percent relative supersaturation in the second period of growth are illustrated in Figure 9. G1.5 - G5.0 (1) Relative difference in growth rate ) G1.5 If the surface roughening does result in reduced growth rates, it would be expected that the time period allowed for roughening, i.e. the time at which the crystal is grown under the higher level of supersaturation, should also be related to the reduction in the growth rates during the regrowth period. This was investigated by growing potash alum under a high supersaturation, σ ) 8.5%, for varying time periods (20, 40, and 60 min) before regrowing the crystal at σ ) 3.8%. The results are shown in Figure 10, where it is seen that higher periods of imperfect growth result in lower growth rates in subsequent growth periods. The plot in Figure 9 represents the relative difference in growth rate, from low to high levels of initial supersaturation for potash alum, sucrose, and KDP crystals. As discussed earlier, the factor influencing the growth rates is the surface roughness on a microscopic scale, which is related to the clusters or surface nuclei; therefore, the sequence found in the plots should also be linked with a parameter related to surface nucleation. Surface nucleation in crystallization depends on the surface energy of the crystal. The surface energies of potash alum, sucrose, and


Pantaraks et al.

Figure 9. Relative difference in the growth rate of crystals that were initially grown at 1.5% and at 5.0% supersaturation during the second period of growth.

Figure 10. Effect of the time period of the previous growth at high supersaturation (8.5% relative supersaturation) on the current crystal growth rate of potash alum at a relative supersaturation of 3.8%.

Figure 8. AFM image of a 50 µm × 50 µm area of the surface of potash alum. (a) Initial surface after growth at 7.5% relative supersaturation. (b) Surface after growth at 2.5% relative supersaturation for 30 min. (c) Surface after growth at 2.5% relative supersaturation for 1 h.

KDP crystals are 2.5, 4.7, and 12–16 erg/cm2, respectively.17,18 The sequence of the surface energy values seemingly corresponds to that of the relative difference in growth rates plotted in Figure 7. The higher the surface energy, the larger the relative difference in crystal growth rate under high and low initial supersaturation. These results suggest a hypothesis that crystals which have high a surface energy should also have high differences in growth rates, or high GRD in the system. In order to characterize the relative GRD in systems of different solutes, the change in the width of the CSD between nuclei and product for the same growth period under the same relative supersaturation is used. A larger difference in the width of the CSD indicates a higher level of GRD in the system. The effect of surface energy on the magnitude of GRD was also studied by performing batch crystallizations of potash alum, KDP, and K2SO4. The surface energies of these three inorganic materials are 2.5, 12–16, and 16–23 erg/cm2, respectively.17 All crystals were grown in 5.0% relative supersaturation for 3 h, and sized via image analysis of photomicrographs as before. According to our hypothesis, the CSD of K2SO4 at the final



Figure 11. CSD from batch crystallizations of (a) potash alum crystals, (b) KDP crystals, and (c) potassium sulfate crystals at 5.0% relative supersaturation: (b) seed crystals; (O) product crystals after 3 h of growth.

time should be the widest followed by those of KDP and Potash alum, respectively. The plots of CSD for initial and final times of all three crystals are depicted in Figure 11. The CSD results very clearly demonstrate that higher GRD was found in the system which has high surface energy. Similar results were also obtained at 2.2% relative supersaturation. Collections of experimental values for the surface energies of many different species of crystals, and methods for prediction of the surface energy from other more easily measurable properties are given in a series of papers by Söhnel and others.17,19,20 It appears that the surface degradation due to growth under high supersaturation is more pronounced if the surface energy of the crystal is high, which is contrary to the expectation that a high surface energy should create a smoother surface under any conditions in order to minimize the amount of energy required to create the surface. Crystals having high surface energies must also have larger sizes for critical nuclei (the smallest three-dimensional particle which is a stable nuclei in the solution), and critical surface nuclei (the smallest two-dimensional particle which is stable on the surface of the crystal). It is possible that the surface degradation, and therefore also the GRD, is more pronounced in crystals with high surface energies because the large surface nuclei fail to properly integrate into the correct crystal lattice as they condense on the surface of the crystal, thus creating areas with significant degrees of lattice imperfection. Further work needs to be performed to validate or reject this hypothesis. A further conclusion from the current study is that crystal growth appears to occur by addition of very smooth layers of solute only at reasonably low growth rates and at low levels of supersaturation. At relatively high levels of supersaturation, the growth occurs primarily by apparently imperfect integration of clusters and surface nuclei into the lattice, creating a very rough surface and reduced future growth rates. Between these different mechanisms, there is a level of the supersaturation where the mechanism changes between these two mechanisms. The authors propose to refer

to this as the “surface roughening transition”. The transition appears to occur at lower supersaturation levels for species having high surface energies. Conclusions The rate of crystal growth of sucrose, potash alum, and KDP crystals appears to be determined by the relative supersaturation of the solution the crystals are grown from and the growth history of the crystal. The crystals of all species grown from low supersaturation display very smooth surfaces compared to those grown from high supersaturation. At some level of supersaturation, the mechanism of crystal growth changes from smooth addition of solute into the lattice to imperfect integration of clusters or surface nuclei, with this transition depending on the surface energy of the crystal. The results from AFM provided a clear image that the high roughness of a crystal grown from high supersaturation was from the surface nuclei with a size range of 1–10 µm generated on the crystal’s surface. The effect of this microscopic roughness plays important roles for the current crystal growth. Crystals initially grown from high supersaturation have a high surface roughness on the microscopic scale, and grow at a lower rate than smooth surfaced crystals grown from a lower supersaturation level. The improvement of the degraded surface at a lower supersaturation (the process of surface healing) was found as the cause of the low growth rates. The effect of growth history is significant for crystallization during both nucleation and growth periods. In nucleation, the set of initial nuclei must be generated from higher supersaturation levels than that of later nuclei, resulting in differences in surface roughness of nuclei in the system. The effect of microscopic surface roughness in the growth period would also occur in the system that is insufficiently mixed, causing variation of local concentration and, therefore, variations in surface roughness.


The results from this study are likely to show that the GRD is a result of the difference in microscopic surface roughness caused by surface nuclei generated on the surface of the crystals. Thus, the surface energy of the crystalline species and the level of supersaturation during growth are important parameters for the understanding and modeling of GRD. Acknowledgment. The authors wish to thank the Thailand Research Fund for the support of Dr. Pantaraks through the RGJ Ph.D. program, grant number PHD/0086/2544. Nomenclature σ ) relative supersaturation G1.5 ) growth rate of crystals initially grown in low (1.5%) supersaturation (nm/s) G5.0 ) growth rate of crystals initially grown in high (5.0%) supersaturation (nm/s)

References (1) White, E. T.; Wright, P. G. CEP Symp. Ser. 1971, 67, 81–87. (2) Srisa-nga, S.; Flood, A. E.; White, E. T. Cryst. Growth Des. 2006, 6, 795–801. (3) Sweegers, S.; Meekes, H.; van Enckevort, W. J. P.; Hiralal, I. D. K.; Rijkeboer, A. Cryst. Growth Des. 2004, 4, 185–198.

Pantaraks et al. (4) Zacher, U.; Mersmann, A. J. Cryst. Growth 1995, 147, 172–180. (5) Ulrich, J. Cryst. Res. Technol. 1989, 24, 249–257. (6) van Enckevort, W. J. P.; Boeshaar, H. J.; van der Linden, W. H.; van den Hoek, B. Crystal Res. Technol. 1983, 18, 185–193. (7) Ristic´, R. I.; Sherwood, J. N.; Shripathi, T. J. Cryst. Growth 1990, 102, 245–248. (8) Tanneberger, U.; Lacmann, R.; Herden, A.; Klapper, H.; Schmiemann, D.; Becker, R. A.; Mersmann, A.; Zacher, U. J. Cryst. Growth 1996, 166, 1074–1077. (9) Herden, A.; Lacmann, R. J. Cryst. Growth 1997, 179, 592–604. (10) Ristic´, R. I.; Sherwood, J. N.; Wojciechowski, K. J. Cryst. Growth 1988, 91, 163–168. (11) Mitrovic´, M. M. J. Phys. Chem. 1995, 99, 5438–5444. (12) Harding, M. M.; Rule, R. J.; Oldman, R. J.; Davey, R. J. J. Cryst. Growth 1992, 123, 373–384. (13) van den Heijden, A. E. D. M.; van der Eerden, J. P. J. Cryst. Growth 1992, 118, 14–26. (14) Wang, S.; Mersmann, A.; Kind, M. J. Cryst. Growth 1990, 99, 1104– 1170. (15) Pantaraks, P.; Flood, A. E. Cryst. Growth Des. 2005, 5, 365–371. (16) Garside, J. AIChE Symp. Ser. 1984, 80 (240), 23–38. (17) Söhnel, O. J. Cryst. Growth 1982, 57, 101–108. (18) Bourne, J. R.; Davey, R. J. J. Cryst. Growth 1976, 36, 278–286. (19) Nielsen, A. E.; Söhnel, O. J. Cryst. Growth 1971, 11, 233–242. (20) Söhnel, O. J. Cryst. Growth 1983, 63, 174–176.

CG070265Q

Effect of Growth Rate History on Current Crystal Growth. 2. Crystal

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