Kinetics and mechanism of barium tungstate crystal growth from sodium tungstate melts in platinum crucibles

BIMALENDU NARAYAN ROY' A N D MANJU RANI ROY Deprrrtmetrt of Chetnis~ry, Utliuersity of Science otrrl Techt~ology, K~rmnsi, Ghnt~n

Received May 12, 1980

BIMALENDU NARAYAN ROY and MANJU RANI ROY. Can. J. Chem. 60,2321 (1982). Kinetics and mechanism of barium tungstate crystal growth from sodium tungstate melts in platinum crucibles were investigated

by DTA at crystallization temperatures To = 800 to lOOODC by continuous cooling at rates RT = 0.67 to 3.37'C min-I. During an induction period (5) small crystallites (I =-0.003 to 0.03cm) developed in the solution but the main growth occurred only after sufficient excess solute concentrations (AC) developed at the end of_?. For crystallizations <80%, the average crystal lengths (I,) varied with the growth time ( 5 ) according to IT2 = (I)2 + 4kD,MAC, kD, being the diffusion rate constant and M the metal salt molecular weight. The last 20% growth was rate-controlled only by the development rate of excess solute concentration.

BIMALENDU NARAYAN ROY et MANJU RANI ROY. Can. J. Chem. 60, 2321 (1982). Faisant appel a I'ATD, on a CtudiC la cinCtique et le mecanisme de la croissance de cristaux de tungstate de baryum a partir de

masse fondue de tungstate de sodium prCsents dans des creusets de platine; les temperatures de cristallisation s'etalent de To = 800 1000°C et le taux de refroidissement continue varie de RT = 0,67 a 3,37"C min-I. Au cours de la pkriode d'induction (I) des petits cristaux se developpent dans la solution mais lacroissance principale ne se produit que lorsqu'un exces suffisant de la concentration du solute (AC) se manifeste a la fin de I. Pour des criztallisations <80%, la longueur moyenne des cristaux (I,) varie avec le temps de croissance selon I'Cquation IT2 = + 4ko,MAC ou kD, est la constante de vitesse de diffusion et M la masse molaire du sel metallique. Les derniers 20% de la croissance se font a une vitesse qui est contr61Ce que par le taux d'Cvolution de la concentration du solute en exces.

[Traduit par le journal]

Introduction crystal length at z; (ACSoI), is the residual excess In recent years crystallization kinetics of a large solute concentration at z; and and PSOI are the

number of inorganic salts have been reported densities of the crystal and solution respectively. (1-10). In any crystallization from aqueous solu- When the natural convection in an unstirred ~ 0 1 ~ - tions or melts, the growth process may occur tion is poor, the dimensionless Sherwood function practically immediately after the onset of cooling or approximately equals 2 and then eq. [I] becomes the system may exhibit induction periods of differ- (11) ent lengths during which only the excess solute concentration develops without any significant [21 d1,ldz =

~DM+(A~SOI), (p / ) sol P

growth - the actual growth occurs only after the I T

induction period. In both cases, the growth mecha- [31 - - 2 k ~ , M(ACS0l)T

nism may be identical but the kinetic relations will 4 differ depending upon the length of induction periods. where kD, = 2D+(psol/p) is the rate constant for

For a diffusion-controlled crystal growth exhibit- diffusion-controlled growth of the "wider" crystal ing induction periods, the rate of the main growth of face. the "major" side of the main crystal face at any Generally, in crystallizations from melts, the growth time z after the induction period (I) would excess solute concentration at any would be be expressed (1 1) [41 (Acs0~), = (ACT - WT/M)

[I.] dl, /dz = 2(Sh)DMO(AC,l), (p /

sol P) where AC, is the overall excess solute concentra- 1 , tion up to z and W, is the crystal weight deposited at

different growth time z. This equation may be where Sh is the Sherwood function; D is the ,itten as diffusion coefficient of the metal salt cations; M is the molecular weight of the solute; + is the overall [51 (AcsodT = (AC + R,r - pl?) permeability factor; z (=t - I) is the actual growth time; t is the total crystallization time; 1, is the where AC is the excess solute concentration Up to

i; R, is the development rate of excess solute IPresent address: 47 Arlesford Road, LondonSW99JS, U.K. concentration; N is the crystal number at any

0008-4042/82/ 182321-04$0 1 .OO/O @I982 National Research Council of Canada/Conseil national de recherches du Canada

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2322 CAN. J. CHEM. VOL. 60, 1982

crystallization time t ; f , is a shape factor; and P (= Npf, /M) is a function of the crystal number. Combining eqs. [3] and [5]

Integrating, one gets

[7] lT2 = ( iy + AT + B T ~

where is the maximum crystal length up to the end of f , and for any To and RT, A and B are constants given by

If (AC,,,), = AC, eq. [3] becomes

Integrating, one gets

where A' (= ~ ~ , , M A C ) is a function of AC and constant for any To and RT.

Experimental Barium tungstate was prepared in situ in sodium tungstate

melts from equimolecular mixtures of the metal carbonate and tungsten trioxide. The saturated solutions were prepared at temperatures slightly higher than the initial crystallization temperature by heating for several hours inside a "Carbolite" electric furnace (Carbolite Co. Ltd., Sheffield, U.K.). These solutions were then cooled down rapidly to room temperature and the solidified melt was ground well and dried at 100°C for 24h to remove any moisture absorbed during grinding. The requisite amount of this sample was then taken in a small platinum crucible inside a differential thermal analyser (No. 990, E.I. du Pont de Nemours & Co., Wilmington, DE, U.S.A.) and the temperature was gradually raised to slightly higher than the crystallization temperature To at a rate of 20"lmin. It was held constant at that temperature for sufficient time to ensure complete melting. Then the crystallization was canied out by gradually reducing the temperature from To (=800 to 10000C) down to below 300°C at cooling rates RT = 40, 120, and 200°C per h according to a pre-assigned automatic cooling programme. The temperatures were recorded automatically on the chart. The DTA curves were traced on standard millimeter graph papers.

From the DTA curves, the eutectic temperature (T,) was determined as the initial melting temperature of the mixtures of metal tungstate and sodium tungstate. The degree of crystalliza- tion (a,) at different crystallization time (t) was calculated using a, = Al/Atotal, where A, is the area under the thermogram at any time t and is the total area under the same thermogram. From these a, values the length (I,) of barium tungstate crystals at any time was estimated using a, = (1,/1 I)3, where I, is the final crystal length. l1 values were measured by optical microscopy from separate crystallization runs in the "Carbolite" electric furnace mentioned above (12).

The rates (R,) of development of excess solute concentration were estimated from the product aR,, where a = dC/dT, C being the concentration. Induction periods (i) were determined

by extrapolation of the linear parts ofthe I, vs. t plots backjo the t-axis; the induction temperatures (T) were thengiven by T = To - RT7. The actual growth time (r) and the overall excess solute concentration (AC,) at different r were evaluated respectively from .r = t - i and ACT = Co - C,, where Co is the initial concentration and C, the concentration at r. The residual excess solute concentrations, (ACsOI),, were evaluated from eq. [4], and W,/M and the final overall excess solute concentrations, ACI, were respectively given by

and

ACf = (Co - C,,)

where C,, is the solubility at the eutectic temperature (T,,).

Results Developtnent of supersaturation

Overall excess solute concentrations, residual excess solute concentrations, and total crystal weights

The overall excess solute concentrations (AC,) increased linearly with cooling time t and attained the maximum value, ACf, at the eutectic tempera- ture. The total crystal weights W,IM increased significantly only after the induction periods. Some typical results for AC, and W,/M are shown in Figs. 1 and 2. The amount of excess solute concentration developed at any t and also the final amount was higher than those for barium tungstate crystalliza- tion under identical conditions from sodium tung- state melts in alumina crucibles (12).

(0,Ol I 2 3 t ( h )

FIG. 1. Crystallization of barium tungstate from sodium tungstate melts at To = 900°C and RT = 40"C/h. Overall excess solute concentrations (AC,), residual excess solute concentra- tions, (AC,,,),, and total crystal weights at different times (W,IM has no dimensions).

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ROY AND ROY 2323

FIG. 2. Crystallization of barium tungstate from sodium tung- state melts at To = 1000°C and R, = 120"Clh. Overall excess solute concentrations (AC,), residual excess solute concentra- tions (AC,,,),, and total crystal weights at different times ( K I M has no dimensions).

The AC, and K I M values show that at the early stages the amount of residual excess solute concen- trations was high. Total crystal weights were very low at the early stages; however, these weights increased with decreasing temperatures up to the time t* (over 75% crystallization), when all the excess solute deposited on thegrowing crystals and probably no further growth occurred. This was also observed in the case of barium tungstate crystalli- zation from sodium tungstate melts in alumina crucibles (12).

Very little (or perhaps none at all) material deposited on the early nuclei until the excess solute co_ncentrations in the-solution attained some value AC at temperature T. As the crystallization pro- ceeded, the residual excess solute concentrations in the solution at any t deviated more and more from AC,, gradually reached the final value, and then sharply dropped to very low values at t*.

Critical time (f), critical temperature (T),-and critical excess solute concentration (AC)

Unlike the crystallization of barium tungstate from sodium tungstate melts in alumina crucibles (12), in this case short to medium induction periods were observed, which were ostensibly modified by the cooling rates but there was no direct relation- ship between R, and i. During the induction periods, heterogeneous nuclei slowly formed onto

the metal platinate particles within the solutions and probably very small crystallites grew on these nuclei up to the end of i. Probably the growth kinetics of these crystallites were rate-controlled by a sluggish secondary mononuclear process (13), which was not the case in the crystallization of the same system in alumina crucibles (12).

Kinetics of crystal growth after the induction periods

It is well known that crystallization at high super- saturation is expected to be diffusion-limited. Also, the growth rate of metal salt crystals in unstirred low permeability solutions is generally controlled by the diffusion rate of metal salt ions into the growing crystal surfaces. As stated earlier, during the induction period probably very small crystal- lites grew on the early nuclei up to i. Since there was n o significant growth occumng during the induction period, sufficient amount of excess so- lute concentration accumulated at the end of i and then the main crystal growth occurred. The aver- age crystal lengths (I ,) at any growth time z after the induction periods were evaluated from the 1, versus t plots; I T Z values were then plotted against z (Figs. 3-5). These plots were linear according to eq. [9] up to 1, = 0.481r; these linear relationships indi- cated that the growth process was probably diffu- sion rate controlled.

The A' values were estimated for different crystallizations (Table 1). These values generally

- (0 ,O) I 2

'i( h)

FIG. 3. Crystallization of barium tungstate from sodium tungstate melts at To = 800°C; square of crystal lengths (1;) at different growth times (7).

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2324 CAN. 1. CHEM. VOL. 60. 1982

I 1200C/h TABLE 1. Kinetics and mechanism of barium tungstate crystal 0.5 - growth from sodium tungstate melts in platinum crucibles

0.4- RT To R c i T AC A' U

W / h ) ("C) (gig-solh) (h) ("C) (gigsol) (cm2/h) - 0.3 - 40 800 0.041 0.50 780 0.0026 1.4

900 1.0 860 0.0510 1.0 (U 1000 1.5 940 0.0869 0.99 0 . 2 - 120 800 0.123 0.50 740 0.0201 1.5 T' 900 0.25 870 0.0385 1.3 o 0.1 - 1000 0.25 970 0.0439 1.1

200 800 0.205 0.25 750 0.0176 4.0 I - 900 0.25 850 0.0585 1.5

(0,o I 2 3 1000 0.25 950 0.0739 2.7

FIG. 4. Crystallization of barium tungstate from sodium tungstate melts at To = 900°C; square of crystal lengths (IT2) at different growth times (T).

FIG. 5. Crystallization of barium tungstate from sodium tungstate melts at To = 1000°C; square of crystal lengths (IT2) at different growth times (r).

increased as To and RT increased but there was no direct correlation.

Thejnal growth It is assumed that at growth times T > T* (over

75% crystallization) some fresh solute continued to

separate out from the solution by further cooling but this was probably immediately used up by deposition on the already developed large crystals. Consequently, the residual excess solute concen- trations were very low and the growth rates became dependent only on the development of further excess solute concentration effected by the de- crease in temperature. For this,

[lo] 1,3 = (1*13 + b ( ~ - T*)

where b (= R,/p) is a constant. Then at T = T*, 1, = I*. This was observed experimentally.

1. A. E. NIELSEN. Acta Chem. Scand. 13, 784 (1957). 2. A. E. NIELSEN. Acta Chem. Scand. 14, 1654 (1960). 3. G. H. NANCOLLAS. Trans. Faraday Soc. 57, 2272 (1961). 4. G. H. NANCOLLAS. Trans. Faraday Soc. 59, 753 (1963). 5. G. H. NANCOLLAS. J. Cryst. Growth, 3, 335 (1968). 6. G. H. NANCOLLAS. J. Phys. Chem. 73, 1735 (1969). 7. A. P A C K T E R ~ ~ ~ B. N. ROY. J. Cryst. Growth, 18,86(1973). 8. A. PACKTER and B. N. ROY. Krist. Tech. 9, 1361 (1974). 9. A. PACKTER and B. N. ROY. Krist. Tech. 10,385 (1975).

10. B. N. ROY and S. APPALASAMI. J. Am. Ceram. Soc. 61,38 (1978).

11. R. E. TREYBAL. Mass transfer operations. McGraw-Hill, New York. 1968. Chapt. 3.

12. B. N. ROY and V. K. HANDA. J. Cryst. Growth, 47, 577 (1979).

13. A. E. NIELSEN. Kinetics of precipitation. Pergamon Press, Oxford. 1964. Chapt. 3.

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