P. B. V. PRASAD

Dcpartrnent of Physics, Govornmont Polytechnic, Warangal, India

The Effect of Decrease in Supercooling on the Growth Rates: n-Pentadecanoic Acid

The Growth rates of crystals fluctuate randoiiily. In view of such fluctuations, it is inore appropriate if a statistical approach is adopted to describe the growth rates of crystals.

1. Introduction

It is well known that if the supercooling j3 is Ti/T, (where Ti is actual crystallization temperature and T , is saturation temperature), then growth or equilibrium or dis- solution takes place depending upon the condition /3 3 1. It is interesting t o study the crystallization behaviour (a) when the crystallization temperature TI is changed to T,, such that T , > T, > T , and (b) T, > T , > TI . Because, in such case, one might expect to get some information on the behaviour of diffusion field that sur- rounds a crystal and also further information 011 the nature of the fluctuations in the growth rates (PRASAD). The present study is made on n-penta decanoic acid (briefly C15). The crystals of C15 were grown froin two such solvents which yield rhombic and hexagonal crystal forms, so that four and six lion basal faces are available for the examination.

2. Naterials

C l 5 (99.5o/b pure) , Xylene (analytical grade, Glaxo made) 2,2,4-Triiiiethyl pentane, briefly 224 T M P (Loba Chemie, Indo Austraiiol Co. made).

3. Experimental and observat,ions

3.1.a. Experimental

water circulation type therniostat, which provides 0.01 "C coiistaiicy of teiiiperature was employed in the present studies. Crystallization was carried out in a home made growtll cell, through wliich circulated the theriiiostated water. An inverted niicroscope, fitted with very high quality surface reflecting iiiirrors, was employed for observing the cr>stals. A 500 W halogen larrip was used for illuinination. A 10 ciii thick water mass was used as infrared filter. Either the crystals were photographed on 400 A S S film or their projections were recorded vis-a-vis iiieasuremeiit of time. The growth rates were evaluated from the measured dimension of the crystals.

780 PRASAD : Effect of Decrease in Supercooling on Growth Rates

3.1.b. Habit

Crystallography of n-penta decanoic acid was reviewed by SATO and KOBAYASHI. The B' form crystals have rhombic habit when grown from xylene, with average acute angle 70", and average obtuse angle 110.5". The values of angles were found to be variable, as in case of hydrocarbon crystals (BOISTELLE). The A' form crystals have highly elongated rhombic shape. The A' and B' crystals, when grown from 224 TMP, were observed to have their acute vertices truncated. The B' form crystals appear almost like hexagons.

3.2. Observations

3.2.a. C15-xylene system

Crystals of C15 were grown in xylene. The saturation temperature (T,) of the solution was 27.9 "C. The crystallization temperature (T,) initially was 26.8 "C, and it was changed to 27.0 "C, while crystallization was in progress, so a supercooling AT = = 1.1 "C was decreased to 0.9 "C in a span of 4 min. The changes in the growth rate of faces were recorded. The results are shown in Figure 1.

fime/min Fig. 1. Changes in the growth rates introduced by dccrease in supcrcooling. Insct: rhombic form of a crystal of C16

Figure 1 shows the placement of line and solid circles. The solid circles represent the perpendicular distances between two (a,a,) opposite non-basal faces. The line circle represents the perpendicular distance between the rest of the two (b,b,) non- basal faces (see the inset of Fig. 1). Thus in the present study, the overall growth rate of the pair of corresponding faces is only known. Such growth rate is the sum of the growth rates of the two individual faces. The segment AB in Figure 1 shows that both the pairs of faces have equal growth rates (9.1 x 10-7m/s) a t 26.8 "C and A T = 1.1 "C. The change in the temperature was brought a t 4 min, and it took another 4 min for the establishment of a temperature of 27 "C; the raise in temperature was 0.2 "C and AT = 0.9 "C. There were changes in ths growth rates from 5 min onwards under changing temperature.

During the unsteady condition, the (blb2) faces assumed a lower growth rate (4.1 x 10-7m/s) for a brief period (BC segment); then the growth rate changed to 14.3 x lW7 m/s (CD). During this period the growth rate of (a,a2) faces has steadily

Cryst. Res. Technol. '24 (1989) 8 781

decreased (BC'). From 8 min onwards the temperature was constant a t 27 "C. HOT- ever the (b,b,) faces still showed fluctuations in growth rates. The faces assumed a growth rate of 2.9 x m / s for a brief period (Segment DE). From 12 mill onwards the growth rate was steady at 5.8 x mjs for a considerable period (Segment EF). The gron th rate of faces (ap,) was constant almost from the moment the temperature 27 "C was estPblished: the gron-th rate being 1 x 10-'m/s (Segment C'D'); after some time, the growth rate increased to 8.3 x 10-7 inis (Segment D'E'). It can be noticed that whereas (b,b,) faces were growing at 5.8 x 10-'m/s, the (ala2) faces grew at a rate of 1 x 10-'m/s and subsequently the rate increased to a value of 8.3 x lo-' mis which is larger than that of (b,b,) faces

3.2.b. C15-224 TMP system

Crystals of C15 were grown in 224 TMP. Saturation temperature of the solution mas 27.3 "C. Crystals were allowed t o grow for some time a t 27.1 "C. Then the crystal- lization temperature was raised to 28.2 "C. Thus the supercooling AT = 0.2 "C was changed to an undercooling of 0.9 "C. The dimensions of the crystals were recorded. The results are shown in Figure 2. C15 grown in 224 TMP have hexagonal habit. The three pairs of faces are labelled as (a,a,), (b,b,! and (c1c2) (see the inset of Fig. 2). The growth rates and dissolution rates are shown in Table 1.

Fig. 2 . The growth, no growth, an& dissolntion bchaTiour of a hexagonal C l 5 crystal. In&: hexagonal form of a crystal of C15. The lower part of the figure shows the temperature profile

Table 1

Faces growth ra te ~~ -~ ~~

dissolution ra te

2.3 x ni/s 2.0 x m/s 2.6 x lo-? injs (81%) (bib,) 3.6 x nijs 2.0 x injs 2.2 x lo-? nijs

2.6 x riijs 4.1 x 10-7 llljs 2.8 x m/s ( % C J . -

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782 PRASAD: Effect of Decrease in Supercooling on Growth Rates

It can be noticed in Figure2 that reaching the equillibrium state (or no growth condition) is different for different (pairs of) faces (from 6 to 12 min). Whereas (ala2) faces cease to grow, the (blbz) were persuing a slow growth and the growth of (c1c2) was oscillatory. From 12 to 14 min, (a,a2), (b,b2) and (c1c2) faces grew in unison. Then the (a,a,) faces assumed equilibrium, whereas (b,b,) were slowly growing, with a falling growth rate, and (c1c2) faces produced a final peak. All the three faces started to dissolve from 19 min onwards. The (ala2) faces were steady for 5 min whereas (b,b,), (clcz) were dynamic.

4. Discussion

An examination of fluctuations in the growth rates of the crystal, in the circumstances of a drop in supercooling (as seen in Fig. 1) indicate that the influencing factor is not only the defect substructure of the crystal faces but also the fluctuations in the dif- fusion fields around the crystal.

It is known that the anisotropic shape of a crystal increases when the supersatu- ration is incrcased aiid this i s explained (PSTROV et al.) by two-dimensional nucleation, which is different for different faces. As different faces have different potential reliefs. the rate of formation of 2D nuclei on different faces a t a given supersaturation can be niuch different (PETROV et al.). Therefore, one can expect that the anisotropy in growth rates should decrease mith a decrease in the supersaturation. How ever, the situation observed in case of Figure 1 is contrary to such an expectation. In fact an anisotropy in the growth rates was introduced in the crystal, which had uniform groki th rates (Segment AB of Fig. l), due to a lowering of the supercooling. However, an answer can be given to this discrepancy.

In stagnant solution experiments, the molecular diffusion is always accompanied by the natural convective transport of matter promoted by the density differences in the solution, near and away from the growing crystals. Further, during initial time interval in which a boundary diffusion layer forms, the rate of growth varies considerably (PXTBOV et al.). After such an initial period, if the supersaturation of mother liquor is maintained constant, then steady state conditions are reached and the time needed for the establishment of such a boundary and natural convective layer varies from a few minutes to tens of ininutes for crystals of 1.5 mm size (PETROV et al.). It is assumed here that the general nature of this description should also be applicable to sub-millimeter size crystals. It can then be assumed that the segments BE and BI)' on Figure 1 correspond to the growth rates in the regime of non-steady state conditions. However, the segments EF and D'E' which are fairly stable have 5.8 x 10-7in/s and 8.3 x lO-'m/s growth rates, respectively. This difference may be indicative of difference in the surface itriicture of the crystal faces in the new environment (i.e., in low supercooled solution) or in the symmetry of the difftision field itself n hich can cause a difference in growth rates (PETROV et al.).

It is known that when the temperature is increased the chemical binding becomes 'cx eaker and consequeritly the thickness of the boundary layer decreases (PETROV et al.). Reduetjon, in the thickness of the boundarg layer should promote an enhanced mass transport n hich naturally leads to increased growth ratc. We think that the increase in the grovth rates, observed in case of Figure 2 , from the 12th minute to 18th minute could be a manifestation of such a process. It can also be noticed that all the three sets offaces, (a,a,), (b,b,), and (c1c2) have different growth rates and dis- solution rates.

Cryst. Res. Technol. 24 (1989) 8 783

5. Conclusion

The growth rates of crystals fluctuate randomly. In view of such fluctuations, i t is more appropriate if a statistical approach is adopted t o describe the growth rates of crystals.

The author is thankful t o Dr. A. Purushothania Rao, Department of Zoology, Kakatiya University, Sri M. Vijaya Rurnar, Department of Mechanical Engineering, Qoveriirrient Polytechnic, Warangal, for their helpful cooperation.

References

BOISTELLE, R.: in: Current Topics in Materials Science, Vol. 4. ed. El. KALDIS, 1980 PETROV, T. G . , TREIVUS, E. B., K a s a T K r N , A. P.: in: C:rowing crystals frorir solution;

PRASAD, P. B. V. : paper cominunicated to J. Cryst. Growth SATO, K., KOBAYASHI, M.: in: Organic Crystals, ed. Dr. N. KARL (in press)

translated from Russian by Albin TYRULEWICZ, New York 1969

(Received February 1, 1989; accepted February 9, 1989)

Authors' address:

Dr. P. B. V. PRASAD Department of Physics, Government Polytecliriic Warangal - 506007 India

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