Dependence of growth rate on solution velocity in growth of NH4H2PO4 crystal

Journal of Crystal Growth 72 (1985) 631—638 North-Holland, Amsterdam

631

DEPENDENCE OF GROWTh RATE ON SOLUTION VELOCITY IN GROWTh OF NH4H2PO4 CRYSTAL Hiroshi TAKUBO College of General Education, Osaka Unk~ersity,Toyonaka -s/u, Osaka 560, Japan Received 6 November 1984; manuscript received in final form 26 April 1985 NH4H2PO4 crystals were grown by using a constant-temperature method in order to clarify the relationships between growth rate, solution velocity, supersaturation and growth temperature. Seed grains fixed on the plates were cultivated in flowing solutions of various supersaturations and temperatures. At higher supersaturations, the growth rate increases in proportion to the square root of the solution velocity, without approaching a constant value. Respecting the supersaturation dependency of the growth rate, rapid solution flow is effective in differentiating between parabolic and linear dependency. The upper critical supersaturation limiting the parabolic relation decreases with increasing solution velocity. The activation energy for growth decreases as the solution velocity increases. These phenomena become indistinct as the supersaturation decreases. The various phenomena observed in a former (1] and in the present study are compiled in a summary table.

1- Introduction In order to study the relationship between growth rate and solution velocity, we have carried out experiments on the growth of NH4H2PO4 crystals in flowing solutions, by using a tank crystallizer and seed particles. In an earlier paper [1], we reported the result of crystallization by cooling and classified the course of crystallization into four stages, a, y and 6, according to their characteristic features. In addition to crystallization by cooling, we have grown crystals by using the constant-temperature method. This paper mainly concerns the constanttemperature method and compiles experimental data in graphic forms which show the relationships between growth rate, solution velocity, supersaturation and growth temperature. As a summary of the earlier and the present study, the general features of the crystal growth of NH4H2PO4 in flowing solutions are compiled. ~,

2. Experimental NH4H2PO4 crystals were grown in a tank crystallizer which was designed to make simulta-

neously runs at various solution velocities. The details of the apparatus and general experimental procedures were described in a previous paper [1]. Solution velocities as high as 14 rn/s were obtamed by reducing the inside diameter of the crystallization pipe to 15 mm. However, most runs at velocities higher than about 10 rn/s were not successful. Above these velocities, the seed crystals on the holder plate were frequently blown away and, at much higher supersaturations, the suspending microcrystals mechanically corroded the edges of growing crystals. Runs in stagnant solutions were simultaneously made in a cylinder immersed in the tank. Even in stagnant solutions, irregular local flows up to about 3 cm/s were confirmed by adding a small amount of ink. In preliminary experiments, it was observed that the larger seeds grew faster than the smaller. Therefore, in this study, all seed particles were prepared by pulverizing to a size under 200 mesh (<0.075 mm). Seeds were scrubbed into several grooves on both sides of plastic plates and held in the crystallization pipes. The experimental procedures for the constanttemperature method are as follows (see ref. [1] for details): 35 to 45 liters of NH4H2PO4 solutions

0022-0248/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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Dependence of growth rate ofNH

(pH 3.9—4.1) were kept at temperatures about 5°C above saturation temperatures. At these temperatures, the solutions were allowed to circulate for 30 mm, passing through a filtrating basket to separate solid impurities. Then, the solutions were rapidly cooled at rates of —1 to 3°C/mm by operating a cooling circuit and by floating ice bags. As soon as the required growth temperature was obtained, the pump was stopped. Three or four crystallization pipes containing the seed holder plates were quickly connected to the guide pipes from the pump and two or three pipes (30 mm in inside diameter) were fixed alongside the tank wall. Then the solution velocity in each crystaffization pipe was raised in a few minutes up to the desired value by regulating the power supply to the pump and by adjusting the valve cocks of the guide pipes. The solution velocities along the tank wall were adjusted by panel boards and by guide funnels attached to the inlets of the crystallization pipes (see Nos. 13, 24 and 7 in fig. 1 of ref. [11). During the runs, the solution temperatures were kept constant with an accuracy of 0.1°Cfor lower supersaturations and of 0.2—0.5°C for higher supersaturations where spontaneous nucleation proceeds, by manually operating the cooling and heating circuits, The supersaturations, which are defined as the excess solute weight percent in the working solution, were monitored by hydrometers. Estimation of supersaturation was made by using the specific gravity change and the followin.g fundamental relations: Solubility increase: 0.455 wt%/°C. Specific gravity increase at fixed temperature: 0.006/wt%. Specific gravity increase for saturated solutions: 0.0237/°C. Specific gravity increase for unsaturated solution of fixed concentration: 0.045/°C. These relations were confirmed for solutions of pH 3.9—4.1 and temperatures 10—40°C. Some difficulties occurred during runs. It was difficult to keep the solution velocity constant for a long time, because the area of pipe section decreased with increasing crystal size. At higher supersaturations and solution velocities, supersaturations were rapidly decreased by pronounced —

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4H2PO4 on solution velocity

spontaneous nucleation. In longer runs at higher supersaturations and lower solution velocities, suspending microcrystals tended to cluster or polygonize on the surface of growing crystals. To avoid these troubles, most runs were stopped when the crystals grew up to 1.5 to 2 mm in size. The run duration needed for growing crystals of these sizes were, for example, about 5—12, 20—25, 60—90 and 120—180 mm for supersaturations of about 0.085, 0.04, 0.02 and 0.015 respectively at solution velocities of 5—6 rn/s. The duration was extended up to 480 mm in runs at 0.008, the lowest supersaturation examined. In runs at higher supersaturations, active spontaneous nucleation lowers the degree of supersaturation. Therefore, in such runs, the following efforts were necessary to keep the supersaturation constant: (i) Run duration was shortened as described above. (ii) Working temperature was slowly dropped 0.5—1.0°Cduring the run. (iii) Clear solutions, higher by 0.5—1.5 wt% in concentration than the working solutions, were fed into the sub-tank (15 cm x 20 cm x 15—20 cm) around the pump (see fig. 1 in ref. [1J),by using a 1000 ml pear-shaped separating funnel with a stop cock. In order to keep the feed solution at the desired temperature and concentration, a 200 W heater insulated with a Teflon tube and a glass thermometer was put in the funnel. The temperature difference between the feed and the working solution was from 2 to 3°C.The rate of solution feed, about 5—50 ml/min, was regulated by monitoring the specific gravity and the temperature of the working solution. (iv) In order to separate the suspended microcrystals from the working solution, the flow pattern throughout the tank was regulated by moving the panels and shutters, so as to make low-velocity zones where the microcrystals could settle to the tank bottom. In addition to this, polyester wool and net were often used for trapping microcrystals in the low velocity zones. (v) The seed holder plates immersed in the lowvelocity zones were held, horizontally in order to protect the undersides of the plates from settling and covering microcrystals. At the end of each run, the seed holder plates

H. Takubo

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Dependence of growth rate of NH

were drawn out of the pipes, wiped with filter paper and cotton, and then dried. The crystal size ing ways. Both sides of seed holder plate, about 10—15 cm long, were divided into ten sections of equal interval. The maximum length along the c-axis direction for every section was measured under microscope (X 100) with in a micrometer and thea growth rate were measured the followeyepiece and averaged over a plate. The standard deviations were within the range 0.09—0.11 for 1.5 mm and 0.16—0.23 for 2 mm average crystal length. Linear growth rates in mm/h were calculated by subtracting 0.075 mm, the maximum size of the seed, from the average values and normalizing the working durations •to 1 h. In the runs at low velocity and high supersaturation, growth rates were measured only for the crystals grown on the undersidesoftheplates, sincetheuppersideswere covered with a number of crystals which nucleated spontaneously in the solutions. In runs at the lowest supersaturations corresponding to those of the a-stage, the growth occurred sporadically along the seed holder plates and gave large deviations in the growth rates as described below,

3. Results and discussion A number of runs were made under conditions of various solution velocities, supersaturations and growth temperatures. 3.1. Effect of solution velocity on growth rate Fig. 1 is an example showing the relationship between growth rate and solution velocity. The data points were obtained at the growth temperatures of about 30 ±1°Cand supersaturations from 0.016 to 0.085. Data of Mullin and Amatavivadhana [2] are also shown in the left part of the diagram. In fig. 1, the supersaturation for the respective lines are (A) 0.085 ±0.006, (B) 0.061 ±0.005, (C) 0.047 ±0.004, (D) 0.041 ±0.002, (E) 0.027 ± 0.002, (F) 0.022 ±0.001 and (G) 0.016 ±0.001. The data at lower supersaturations are omitted because of wide fluctuations. Horizontal bars

633

4H2PO4 on solution velocity

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above the abcissa indicate the fluctuation range of solution velocities. Data points 1—3 show the results at 0.15 m/s, 30°Cby Mullin and Amatavivadhana [2]. The supersaturations estimated from their data are (1) 0.045, (2) 0.03 and (3) 0.02. The thick bar (4) shows their data at 0.025, 25°C. From fig. 1, it is evident that the growth rates increase in proportion to the square root of solution velocities at supersaturations higher than 0.027. For convenience, this relationship will be called the “square root law”, hereafter. The data points, 1 to 3, given by Mullin and Amatavivadhana [2] seem to show reasonable values estimated from lines with corresponding supersaturations. The square root law at higher supersaturations has been confirmed at growth temperatures around 12.5 and 22.5°Cas well. In fig. 1, the slopes of the lines become steeper, especially at lower solution velocities, at supersaturations ranging from 0.016 to 0.025. The cause of this phenomenon may be attributed partly to the increasing mass transfer rate and partly to the changing crystal habit with increasing solution velocity. In this supersaturation range corresponding to the fl-stage, longer prismatic crystals

634

H. Takubo

/ Dependence of growth rate ofNH4H2PO4

with curved faces tend to grow at higher solution velocities [1]. At supersaturations less than 0.016, detectable growth occurred only on several seed particles. Their growth rates were independent of the solution velocities and the data points randomly scattered in the region below about 1 mm/h growth rate. The bar (4) given by Mullin and Amatavivadhana [2] also shows a similar result, though the supersaturation is a little higher than our data stated above.

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suits by other authors [2—6]are shown for cornIn fig. 2, the solution velocity (m/s) and growth parison. temperature (°C) for the respective lines are as follows: filled circles (5 ±0,52, 30 ±1), open circles (1 ±0.28, 30 ±1), filled squares (0.3 ± 0.12, 30 ±1), open squares (0.15, 30, by Mullin and Amatavivadhana [2]), crosses (about 0.05, 31, by Kunisaki [3]) and open triangles (stagnant, virtually 0—0.03, 30 ±1). The hatched area a shows the region where the growth rates deviate, being independent of supersaturation and solution velocities. Here only sporadic growth was observed. The area b covers the data ranges given by Alexandru [4], Bo~inand ~i~iC [5] and Garside and RistiC [6]. The bars a, fl,y and 6 show ranges where the characteristic features described in ref. [1] were observed in runs at solution velocities around 1 rn/s. From fig. 2, the following can be said: (1) The growth rates increase with supersaturation as well as solution velocities. In flowing solutions with lower supersaturations corresponding to the fl-stage, the growth rate increases following a parabolic law. At the higher supersaturations, the rate follows a linear law. The transitional regions of the curves can be referred to as the y-stage where visible spontaneous nucleation starts. (2) In so-called “stagnant solutions”, where the virtual flow is about a few cm/s, the growth rate

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Fig. 2 shows the relationships between growth flowing solutions rates and supersaturations in flowing solutions with velocities 5, 1, 0.3 and nearly zero rn/s. Re-

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follows the parabolic law only at the higher supersaturations tested and rapidly decreases with decreasing supersaturations, approaching nearly zero at supersaturations around 0.03. As shown in the area b, the same trend is seen for the data given by

H. Takubo

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Dependence ofgrowth rate of NH

other authors. The effective solution velocities used by these authors must have been less than several cm/s. From the trend of the curve for the stagnant solution, it seems that, in the strictly stagnant solutions free from forced flow and convection, growth detectable on the laboratory time scale may hardly occur even at higher supersaturations. (3) The critical supersaturation separating the parabolic law and the linear law region decreases with increasing solution velocity. This implies that the start of visible spontaneous nucleation characterizing the ‘i-stage is advanced by rapid solution flow. This is concordant with the well-known rule that strong agitation enhances spontaneous nucleation. Mullin and Amatavivadhana [2] gave results concordant with the present results. However, Kunisaki [3] gave “abnormal” data at lower supersaturations as shown by crosses in fig. 2. The discrepance may be attributed to his inadequate estimation of supersaturation.

635

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In order to estimate the activation energy for growth, the effect of growth temperature on growth rate at various solution velocities was investigated. Fig. 3 shows the results of the investigation. The data given by other authors [2,3,5] are also shown. In fig. 3, the solution velocity (m/s), supersaturation and activation energy for growth (kcal/ mol) for the respective lines are as follows: (A) 6 ±0.8, 0.062 ±0.035, 5.4, (B) 2 ±0.4, 0.062 ± 0.02, 5.7, (C)1 ±0.5, 0.062 ±0.005, 5.7, (D) 0.25 ± 0.08, 0.062 ±0.005, 8.2, (E) 0.27 ±0.03, 0.04 ± 0.005, 9.5, (F) 0.15, 0.028, 12.2, by Mullin and Amatavivadhana [2], (G) about 0.05, 0.021, 10.6, by Kunisaki [3], (H) stagnant, virtually 0—0.03, 0.062 ±0.002, 12.9. The lines I, J and K show the results by Bo~inand Zthe [5]. The estimated activation energies for the lines I, J and K are 12.9, 4.6 and 9.3, respectively, From fig. 3, the following can be said: The lines A, B, C, D and H were obtained at nearly the same supersaturations, 0.061—0.063, but at different solution velocities. Comparing these

lines, it is clear that the activation energy for growth decreases with increasing solution velocity. This phenomenon agrees with the general rule that strong agitation promotes mass transfer on and around crystal surfaces, causing a decrease in the activation energy for the growth process. The lines D and E were obtained at the same solution velocities, about 0.25 m/s, but at different supersaturations, 0.062 and 0.04. Comparing their activation energies, 8.2 and 9.5 kcal/mol respectively, it is assumed that, in high supersaturations, the activation energy decreases with increasing supersaturation. However, much more data would be necessary for confirming this assumption. At supersaturations less than about 0.02, a relation between growth rate and growth temperature cannot be recognized. The data points scattered in a wide area between the lines G and K. This phenomenon may be explained as described by Bo~inand Zi~sC[5]. They attributed the fluctuation in activation energies, as seen in the lines I, J

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of growth rates of

NH4H2PO4 crystals at various solution velocities.

636

H. Takubo / Dependence of growth rate of NH

4H2PO4 on solution velocity

and K, to the activity of dominant dislocation groups in the growing crystals. It seems likely that laborious experiments using the solutions with various supersaturations would be necessary for estimating the activation energies for a number of processes taking place during growth.

4. General discussion (1) There are two extreme possibilities for the rate determining processes in solution crystal growth: volume diffusion and interface kinetics, For isolating volume diffusion and interface kinetics, Brice [7] stressed the role of the solution flow during growth. The present study demonstrates his views as shown in fig. 2. In this figure, the parabolic and the linear relation between growth rate and supersaturation are clearly differentiated with increasing solution velocities, (2) The relationship between growth rate and solution velocity has been theoretically studied by many authors [7—10].Summarizing their papers, the growth rate at high and constant supersaturation is given by 1”3 1~3V1~2 R0AD where A is a coefficient determined by dislocation densities, shapes and sizes of original seed and growing crystal, D is the diffusion coefficient, p

the kinematic viscosity of the solution and V the solution velocity or crystal rotation rate. In the present study, the coefficient A is negligible, since all runs were made by using seed powder prepared in the same way and the final sizes of grown crystals were fixed at 1.5—2 mm. The contribution of the diffusion coefficient of NH4H2PO4 is difficult to estimate because of scarcity of available data. From the data of Mullin and Amatavivadhana [2], it is assumed that a temperature drop of 1°C causes a decrease in growth rate of less than 1%. However, this contribution may be negligible, since the present results have been obtained by using constant-temperature methods. The contribution of kinematic viscosity at constant supersaturation is also very small. From the measured kinematic viscosities [1], it

is estimated that the contribution of kinematic viscosity to the growth rate is about 0.2% for the temperature variation of 0.5°C which was frequently used to keep the constant and high supersaturation during runs. The contribution of the solution velocity to the growth rate at higher supersaturations is clearly shown in fig. 1. Growth following the square root law can be regarded as volume diffusion-controlled. At lower supersaturations, however, the growth rate does not follow the square root law. In this case, it is assumed that the growth rate is affected mainly by interface kinetics and by other factors such as dislocation density, morphology and flow pattern as well as volume diffusion. The square root law has been confirmed in similar experiments using solutions of KC1, NH4C1 and Mg2SO4 7H~O. However, KA1(S04)2 12H20 does not obey this law. Its growth rate at higher supersaturations increases in proportion to the 3rd to 4th roots of the solution velocity. This abnormal behavior may be attributed to the morphology and the strong instability of KAI(S04)2’ 12H20 solution. KA1(S04)2’ 12H20 tended to grow making one (111) face parallel to the flow direction, and a rapid decrease in supersaturation due to the active spontaneous nucleation was observed when the solution velocity increased. The most abnormal result in the present study is that the growth rate of NH 4H2PO4 increases with increasing solution velocity without approaching a constant value. It has been generally accepted that the growth rate at fixed supersaturation increases with the crystal rotation and stirring rate up to a saturated value, beyond which the growth rate remains constant, due to the controlling influence of interface kinetics and of the integration rate of the solute molecules into the crystal lattice. Many investigators have confirmed the presence of a saturation in growth rate in agitated solutions at rotation rates up to about 50 rpm and relative solution velocity up to several tens of cm/s [2,3,11—15]. The discrepancy stated above may be attributed mainly to the differences in experimental procedures as described in the following: (1) Most investigators have used crystal rotation and crucible rotation which gives solution much .

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Prism with tapered faces, changing into habit faces (100) with higher a

Long prismatic, (with curved faces at higher V)

Various (plate, ding on original rod, etc.), depenshapes of seeds

Crystal habit C)

4H2PO4 solution (pH 3.9—4.1)

Dependences oflinear growth rate along the c-axis, R, on b) Supersaturation a Solution velocity,

Ditto, but not so distinct

Ditto, but one or two (101) faces develop, being parallel to flow direction

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Veils and inclusions decrease with increasing solution velocity. The activation energy for the growth process decreases with increasing solution velocity. ~ The activation energy for the growth process is affected by the activity of dislocation groups at this stage. ~ A solution free from solid impurities and a solution flow sustained at constant velocity are necessary for twin formation.

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The critical value for each stage decreases with increasing solution velocity. A and B are proportionality constants. The degree of morphological symmetry decreases with increasing solution velocity.

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Table 1 Characteristic features of crystal growth in flowing NH

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Probably, combined spiral and step growth; surface kinetics> volume diffusion

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/ Dependence of growth rate of NH4H2PO4

less than those in the present study. (2) Much higher supersaturations, which are undesirable for commercial crystal growth because of the active spontaneous nucleation, could be used in the present study by taking special care as described above. (3) The types of solution flows in most runs are not laminar but turbulent [1]. In the crystal rotation at slow rate, laminar flow will occur along the crystal surfaces. In the seeding method used in this study, eddy currents will readily occur along the zigzag surfaces of growing seeds mounted on the holder plate. Such eddy currents will make various surface reactions vigorous and speed the dissipation of the heat of crystallization, as well as the mass transfer to crystal surfaces. Moreover, re-entrant angle corners formed by intersecting the seed facets and the holder plate will provide corners and steps favorable to the deposition of solute. An experimental approach emphasizing hydrodynamics would be necessary to explain the dis-. crepancies in growth rate at high solution velocity.

5. Stimmary Powdered seeds placed on the plastic plates were grown in flowing NH4H2PO4 solution at various supersaturations and solution velocities. A number of phenomena observed in the present and

on solution velocity

in an earlier study are tentatively summarized in table 1.

References [11H.

Takubo, S. Kume and M. Koizumi, J. Crystal Growth 67 (1984) 217. [2] J.W. Mullin and A. Ainatavivadhana, J. Apple. Chem. 17 (1967) 151. [3] Y. Kunisaki, J. Chem. Soc. Japan, Ind. Chem. Sect. 60 (1957) 987. [4] H.V. Alexandru, J. Crystal Growth 10 (1971) 151.

[5] S.E. Bolin and B. Zitie, J. Crystal Growth 52 (1981) 820. [61 J. Garside and R.I. Ristiá, J. Crystal Growth 61(1983) 215. [7] J.C. Brice, J. Crystal Growth 1 (1967) 161. [8] A. Carlson, in: Growth and Perfection of Crystals, Eds. R.H. Doremus, B.W. Roberts and D. Turnbull (Wiley, New York, 1958) p. 421. [9] P. Bennema, J. Crystal Growth 5 (1969) 29. [10] R.L. Parker, in: Solid State Physics, Vol. 25, Eds. F. Seitz and D. Turnbull (Academic Press, New York, 1970) p. 151. [11] A.W. Hixon and K.L. Knox, Lad. Eng. Chem. 43 (1951) 2144. [121 J.W. Mullin, Crystallization (Butterworths, London, 1961) p. 122. [13] R.A. Laudise, R.C. Linares and E.F. Dearborn, J. Appi. Phys. 33 (1962) 1362. [141 R.A. Laudise, in: The Art and Scienceof GrowingCrystals, Ed. JJ. Gilman (Wiley, New York, 1963) p. 252. [15] J.W. Mullin and J. Garside, Trans. Inst. Chem. Engrs. (London) 45 (1967) 285, 291.