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Comparison of theory with experiment in convectionless growth of crystals from solution
Journal of Crystal Growth 71 (1985) 791-794 North-Holland, Amsterdam
791
LETTER TO THE EDITORS COMPARISON OF THEORY WITH EXPERIMENT IN CONVECTIONLESS GROWTH OF CRYSTALS FROM SOLUTION * Darrell G. SCHLOM ** Student Space Organization, California Institute of Technology, Pasadena, California 91125, USA
and
Paul J. SHLICHTA Jet Propulsion Laboratory California Institute of Technology, Pasadena, California 91109, USA Received 19 November 1984; .manuscript received in final form 25 March 1985
Wilcox's computer program for predicting the growth rates of crystals in convectionless supersaturated solution has been shown to
give good agreement with the best available experimental data. Slight modificationsin the original program were made to accommodatethe changeof diffusioncoefficientwith temperature. Several attempts have been made to measure the growth rates of crystals growing from solution under conditions of suppressed or minimized buoyant convection [1-4]. Of these experiments, those of Simon [1] appear to come the closest to convectionless conditions. Simon's experiment consisted of placing a 0.8 mm capillary tube, containing a NaC103 seed crystal in contact with solution saturated at 20°C, into a temperature bath set at a lower temperature, thereby initiating growth of the crystal. When the crystal grew upward into the solution, the resultant solute depletion near the interface caused a positive density gradient which initiated convection. In contrast, downward growth caused a negative density gradient ( d p / d z < 0) which was stable and inhibited convection. Simon measured growth rates after three or four days, when steady-state conditions had been established, and noted that the down-
* The publication of this paper was supported by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. ** Present address: Center for Materials Research, Stanford University, Stanford, California 94305, USA.
ward convectionless growth was two orders of magnitude slower than upward growth at comparable supersaturations. The experiments of Nerad and Shlichta [2,3] also used downward unidirectional growth to stabilize the interface concentration gradient. These experiments, however, were macroscopic (4 × 75 mm cross section) and conducted in a special experiment cell designed to minimize horizontal thermal gradients. The experiments were monitored with a schlieren system which showed that, although convection was not entirely eliminated, it was reduced to velocities below 50 #m/s, which is at least an order of magnitude less than conventional earth-based experiments. Other experiments, such as those of Shiomi, Kuroda and Ogawa [4], were not monitored by schlieren and, in view of the non-inverted configuration and large diameter, were probably accompanied by considerable convection. Thus, in comparing these experimental results to theory, the agreement or disagreement with Simon's results is the most significant. Many theoretical models for convectionless solution growth have been proposed [5-10]. One of the most general, in terms of its assumptions, is the model proposed by Wilcox [11]. Wilcox's model
0022-0248/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
D.G. Schlorrg P.J. Shlichta / Convectionless growth of crystals from solution
792
Table 1 Parametric equations used in Wilcox's crystal growth program Diffusion coefficient Solubility Partial molar volume in solution Interface kinetics Concentration in solid
cm2/s m o l / c m3 cm3/mol cm4/mol • s m o l / c m3
D = Ad + BdT + GdC Ce = A~e exp( - E~ / T )
V = A,~ + BvT B =Bvc e x p ( - Eve~T)
Q = Ac~ +BcsT
C = concentration ( m o l / c m 3). T = temperature (K).
requires that the properties of the solution system, specific to each crystal, be represented in equation form with empirically derived coefficients. These equations are shown in table 1. In the present paper, we have used Wilcox's program to model the experiments of Simon and of Nerad and Shlichta and compared the results with the experimental data. The coefficients of fit to Wilcox's parametric equations for the diffusion coefficient, solubility, partial molar volume, and concentration in solid were determined by fitting his equations to the values given in the literature. For KDP the diffusion coefficient as a function of concentration and temperature was fit to the data in refs. [13-18]. The diffusion coefficient of sodium chlorate was assumed to have the same temperature dependence (B d) as KDP, and was fit to the data of Campbell and Oliver [19]. The solubility as a function of temperature was fit to the data given in refs. [20-31] for KDP and in refs. [32,33] for sodium
Table 2 Parametric equation fit coefficients for sodium chlorate and KDP Fit coefficients
NaCIO 3
KDP
A0 Bd Go Ace E~¢ Av Bv Bye Eve Ac~
- 4 . 1 4 × 1 0 -5 2.06x 10 -~ - 2 . 0 4 × 1 0 -3 0.0457 569 43.6 0 > 0.01 0 0.02339
- 5.29 × 10- 5 2.06 × 10- 7 - 1.36 × 10- a 0.418 1640 15.3 0.108 >0.1 0 0.01718 0
Bc~
0
chlorate. The molar volume of KDP as a function of temperature was determined from the solub~ty and density data of refs. [20-31] and the equation: PsolutionWKDP
V~olutio,= ] [ (MoI.Wt.)KDp Psolution( 1 __ W ) K D P ] - l
+
(Mol.Wt.)H2o
]
"
The partial molar volume was obtained by linearly extrapolating to zero weight fraction (WKDP = 0). The values obtained are in good agreement with Rutskov [34]. The partial molar volume of sodium chlorate, which was assumed to be independent of temperature and constant at concentrations near saturation, was obtained from ref. [35]. The concentration of solute in the solid crystal was obtained from ref. [36] for both crystals. The temperature dependence of the concentration in solid was taken to be zero (Bcs = 0) since the temperature excursions and the thermal expansion coefficient are small. Table 2 lists the resultant coefficients of fit used for Wilcox's program. Since the diffusion coefficient was assumed to be a function of temperature, the differential and finite difference equations given by Wilcox had to be adjusted to take this into account [12]: Specifically, his equations (1), (5), and (6) were changed to the following:
o (DBc)
Bc
-~y ~ -~y _ + Vcf By D(1
Bc
Bt '
+(1 -
+o (1 \
BC °c l a z f = 0-7'
(1) BC
(5)
793
D.G. Schlom, P.J. Shlichta / Convectionless growth of crystals from solution
At Cl = P1 + ( - ~ D ( 1
- Zt)2(P,+, - 2P I + P,_,)
at + 2-'~( 1 - Z/)(Vcf- D)(PI+I - PI-1) At + ~ G d (
1 _ Z t ) 2 ( p , + l _ p,_,)2.
(6)
"~ E
0.6
~¢ O
0.4
"J
0.2
4(az) 2 ~ ITH CI~LH S N E RI A D
An important variable in Wilcox's model is the interface kinetics parameter. If this is set at or above 0.1 for K D P (or above 0.01 for sodium chlorate), the rate-limiting step of solution growth is bulk diffusion of the solute through the solution; therefore, higher values for the interface kinetics parameter do not affect growth rate predictions. For lower interface kinetics coefficient values, the rate-limiting step becomes incorporation of the solute into the crystal. Substantial reductions in predicted growth rate result if very low values are used, .but these values are not considered realistic. '.*{: Wilcox's model was applied to the growth of sodium chlorate and compared to Simon's results. Fig. 1 shows Simon's observed growth rates compared with the predicted growth rate after 80 h at the constant final temperature. It will be noted that the predicted growth rate levels off after about 50 h, corresponding to Simon's "steady-state conditions". Wilcox's model was also applied to potassium dihydrogen phosphate (KDP) and compared to the results of Nerad and Shlichta. In these experiments, only the total amount of growth on the seed crystal was measured. Fig. 2 shows A ¢o O
10
x
8
o -.. E o
6 4
.< •:
O
2 o
r
i
I
I
I
I
I
0.0
10
20 TIME
4
30
&
I 40
A I 50
(hours)
Fig. 2. Comparisonof theoreticalpredictionwith data of Nerad andShlichta [3].
Nerad and Shlichta's observed growth compared to the prediction of Wilcox's model. Since Wilcox's model only applies to growth on a single face of a crystal, it could not be applied to the results o~ Shiomi, Kuroda and Ogawa. The predictions of Wilcox's model are in remarkably good agreement with the experimental results of Simon, i f one assumes a reasonable (>/0.01) value for the interface kinetics parameter. The data of Nerad and Shlichta are 30 to 90% higher than the predictions of the Wilcox model for Bye >/0.1. This is consistent with the observation of occasional low-level convection in these experiments. These comparisons indicate that the Wilcox model can be used to make reliable order-of-magnitude predictions of growth rates in the absence of convection. This model is currently being used to predict growth rates for a forthcoming "Getaway Special" solution growth experiment being prepared by the Caltech Student Space Organization for a future Space Shuttle flight.
References
I 5
J
I 10
[
I 15
SIMON I 20
o TEMPERATURE
(°C)
Fig. 1. Comparisonof theoreticalpredictionwith data of Simon [1].
[1] B. Simon, J. Crystal Growth 43 (1978) 640. [2] P.J. Shlichta, Crystal Growth in a Spaceflight Environment: MPS 770-100, Final Report (Jet PropulsionLaboratory, California Institute of Technology,December 1984). [3] B.A. Nerad and P.J. Shliehta, J. Crystal Growth, to be published. [4] Y. Shiomi,T. Kuroda and T. Ogawa, J. Crystal Growth 50 (1980) 397. [5] H.T. Minden, J. Crystal Growth 6 (1970) 228.
794 [6] [7] [8] [9] [10] [11] [12] [13]
[14] [15]
[16] [17] [18] [19] [20] [21]
D.G. Schlom, P.J. Shlichta / Convectionless growth of crystals from solution R. Ghez, J. Crystal Growth 19 (1973) 153. R. Ghez and J.S. Lew, J. Crystal Growth 20 (1973) 273. H. Mi~ler-Krumbhaar, J. Chem. Phys. 63 (1975) 5131. R. Ghez, Intern. J. Heat Mass Transfer 23 (1980) 425. M.B. Small and J.F. Barnes, J. Crystal Growth 5 (1969) 9. W.R. Wilcox, J. Crystal Growth 56 (1982) 690. W.R. Wilcox, private communication; W.R. Wilcox, J. Crystal Growth 68 (1984) 71. W.A. Roth and K. Scheel, Eds., Landolt-BOrnstein Physikalisch-chemische Tabellen, Band 2, Tei154 (Springer, Berlin, 1969) p. 624. J.D. Hatfield, O.W. Edwards and R.L. Dunn, J. Phys. Chem. 70 (1966) 2555. V.A. Zonov and V.V. Serdyuk, article deposited at the All-Union Institute of Scientific and Technical Information (VINITI), Dept. No. 4830-72 (1972). A.B. Zdanovskii and V.V. Serdyuk, Russ. J. Phys. Chem. 47 (1973) 417. Z. Solc, A. Sostokova and M. Sedlackova, Sb. Ved. Praci, Vysoka Skola Chem.-Technol., Pardubice 28 (1972) 19. J.W. Mullin and A. Amatavivadhan, J. Appl. Chem. 17 (1967) 151. A.N. Campbell and B.G. Oliver, Can. J. Chem. 47 (1969) 2681. Ref. [13], p. 53. A. Seidell, in: Solubilities of Inorganic and Metal-Organic Compounds, Vol. 2, 4th ed., Ed. W.F. Linke (American Chemical Society, Washington, DC, 1965) pp. 286-287.
[22] J.W. Mellor, A Comprehensive Treatise on Inorganic and Theoretical Chemistry, Vol. 2, Suppl. 3 (London, 1956) p. 1961. [23] E.W. Washburn, Ed., International Critical Tables of Numerical Data Physics, Chemistry and Technology, Vol. 3 (McGraw-Hill, New York, 1928) p. 90. [24] R.J. Meyer, Ed., Gmelin's Handbuch der Anorganischen Chemie, 8th ed., No. 22 (Springer, New York, 1978) p. 999. [25] R.C. Weast, Ed., CRC Handbook of Chemistry and Physics, 60th ed. (CRC Press, Boca Raton, FL, 1979) p. D-255. [261 K. Chomjakow, S. Jaworowskaja and P. Schirokich, Z. Physik. Chem. A167 (1933) 35. [27] C. Drucker, Arkiv Kemi, Mineral. Geol. 22A (1946) No. 21. [28] C.M. Mason and J.B. Culvern, J. Am. Chem. Soc. 71 (1949) 2387. [29] L.N. Alymova, D.M. Korf and N.D. Lebedeva, Russ. J. lnorg. Chem. 11 (1966) 1288. [30] S. Palitzsch, Z. Physik. Chem. 138 (1928) 379. [31] A.A. Kazantsev, J. Chem. USSR 8 (1936) 1230. [32] A. Seidell, ref. [21], pp. 1014-1015. [33] Ref. [23], p. 235. [34] A.P. Rutskov, Izv. Fiz. Khim., Anal. Inst. Obshei Neorg. Khim. Akad. Nauk SSSR 17 (1949) 286. [35] Ref. [24], No. 21, p. 1767. [36] Ref. [25], pp. B-113, B-125.
791
LETTER TO THE EDITORS COMPARISON OF THEORY WITH EXPERIMENT IN CONVECTIONLESS GROWTH OF CRYSTALS FROM SOLUTION * Darrell G. SCHLOM ** Student Space Organization, California Institute of Technology, Pasadena, California 91125, USA
and
Paul J. SHLICHTA Jet Propulsion Laboratory California Institute of Technology, Pasadena, California 91109, USA Received 19 November 1984; .manuscript received in final form 25 March 1985
Wilcox's computer program for predicting the growth rates of crystals in convectionless supersaturated solution has been shown to
give good agreement with the best available experimental data. Slight modificationsin the original program were made to accommodatethe changeof diffusioncoefficientwith temperature. Several attempts have been made to measure the growth rates of crystals growing from solution under conditions of suppressed or minimized buoyant convection [1-4]. Of these experiments, those of Simon [1] appear to come the closest to convectionless conditions. Simon's experiment consisted of placing a 0.8 mm capillary tube, containing a NaC103 seed crystal in contact with solution saturated at 20°C, into a temperature bath set at a lower temperature, thereby initiating growth of the crystal. When the crystal grew upward into the solution, the resultant solute depletion near the interface caused a positive density gradient which initiated convection. In contrast, downward growth caused a negative density gradient ( d p / d z < 0) which was stable and inhibited convection. Simon measured growth rates after three or four days, when steady-state conditions had been established, and noted that the down-
* The publication of this paper was supported by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. ** Present address: Center for Materials Research, Stanford University, Stanford, California 94305, USA.
ward convectionless growth was two orders of magnitude slower than upward growth at comparable supersaturations. The experiments of Nerad and Shlichta [2,3] also used downward unidirectional growth to stabilize the interface concentration gradient. These experiments, however, were macroscopic (4 × 75 mm cross section) and conducted in a special experiment cell designed to minimize horizontal thermal gradients. The experiments were monitored with a schlieren system which showed that, although convection was not entirely eliminated, it was reduced to velocities below 50 #m/s, which is at least an order of magnitude less than conventional earth-based experiments. Other experiments, such as those of Shiomi, Kuroda and Ogawa [4], were not monitored by schlieren and, in view of the non-inverted configuration and large diameter, were probably accompanied by considerable convection. Thus, in comparing these experimental results to theory, the agreement or disagreement with Simon's results is the most significant. Many theoretical models for convectionless solution growth have been proposed [5-10]. One of the most general, in terms of its assumptions, is the model proposed by Wilcox [11]. Wilcox's model
0022-0248/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
D.G. Schlorrg P.J. Shlichta / Convectionless growth of crystals from solution
792
Table 1 Parametric equations used in Wilcox's crystal growth program Diffusion coefficient Solubility Partial molar volume in solution Interface kinetics Concentration in solid
cm2/s m o l / c m3 cm3/mol cm4/mol • s m o l / c m3
D = Ad + BdT + GdC Ce = A~e exp( - E~ / T )
V = A,~ + BvT B =Bvc e x p ( - Eve~T)
Q = Ac~ +BcsT
C = concentration ( m o l / c m 3). T = temperature (K).
requires that the properties of the solution system, specific to each crystal, be represented in equation form with empirically derived coefficients. These equations are shown in table 1. In the present paper, we have used Wilcox's program to model the experiments of Simon and of Nerad and Shlichta and compared the results with the experimental data. The coefficients of fit to Wilcox's parametric equations for the diffusion coefficient, solubility, partial molar volume, and concentration in solid were determined by fitting his equations to the values given in the literature. For KDP the diffusion coefficient as a function of concentration and temperature was fit to the data in refs. [13-18]. The diffusion coefficient of sodium chlorate was assumed to have the same temperature dependence (B d) as KDP, and was fit to the data of Campbell and Oliver [19]. The solubility as a function of temperature was fit to the data given in refs. [20-31] for KDP and in refs. [32,33] for sodium
Table 2 Parametric equation fit coefficients for sodium chlorate and KDP Fit coefficients
NaCIO 3
KDP
A0 Bd Go Ace E~¢ Av Bv Bye Eve Ac~
- 4 . 1 4 × 1 0 -5 2.06x 10 -~ - 2 . 0 4 × 1 0 -3 0.0457 569 43.6 0 > 0.01 0 0.02339
- 5.29 × 10- 5 2.06 × 10- 7 - 1.36 × 10- a 0.418 1640 15.3 0.108 >0.1 0 0.01718 0
Bc~
0
chlorate. The molar volume of KDP as a function of temperature was determined from the solub~ty and density data of refs. [20-31] and the equation: PsolutionWKDP
V~olutio,= ] [ (MoI.Wt.)KDp Psolution( 1 __ W ) K D P ] - l
+
(Mol.Wt.)H2o
]
"
The partial molar volume was obtained by linearly extrapolating to zero weight fraction (WKDP = 0). The values obtained are in good agreement with Rutskov [34]. The partial molar volume of sodium chlorate, which was assumed to be independent of temperature and constant at concentrations near saturation, was obtained from ref. [35]. The concentration of solute in the solid crystal was obtained from ref. [36] for both crystals. The temperature dependence of the concentration in solid was taken to be zero (Bcs = 0) since the temperature excursions and the thermal expansion coefficient are small. Table 2 lists the resultant coefficients of fit used for Wilcox's program. Since the diffusion coefficient was assumed to be a function of temperature, the differential and finite difference equations given by Wilcox had to be adjusted to take this into account [12]: Specifically, his equations (1), (5), and (6) were changed to the following:
o (DBc)
Bc
-~y ~ -~y _ + Vcf By D(1
Bc
Bt '
+(1 -
+o (1 \
BC °c l a z f = 0-7'
(1) BC
(5)
793
D.G. Schlom, P.J. Shlichta / Convectionless growth of crystals from solution
At Cl = P1 + ( - ~ D ( 1
- Zt)2(P,+, - 2P I + P,_,)
at + 2-'~( 1 - Z/)(Vcf- D)(PI+I - PI-1) At + ~ G d (
1 _ Z t ) 2 ( p , + l _ p,_,)2.
(6)
"~ E
0.6
~¢ O
0.4
"J
0.2
4(az) 2 ~ ITH CI~LH S N E RI A D
An important variable in Wilcox's model is the interface kinetics parameter. If this is set at or above 0.1 for K D P (or above 0.01 for sodium chlorate), the rate-limiting step of solution growth is bulk diffusion of the solute through the solution; therefore, higher values for the interface kinetics parameter do not affect growth rate predictions. For lower interface kinetics coefficient values, the rate-limiting step becomes incorporation of the solute into the crystal. Substantial reductions in predicted growth rate result if very low values are used, .but these values are not considered realistic. '.*{: Wilcox's model was applied to the growth of sodium chlorate and compared to Simon's results. Fig. 1 shows Simon's observed growth rates compared with the predicted growth rate after 80 h at the constant final temperature. It will be noted that the predicted growth rate levels off after about 50 h, corresponding to Simon's "steady-state conditions". Wilcox's model was also applied to potassium dihydrogen phosphate (KDP) and compared to the results of Nerad and Shlichta. In these experiments, only the total amount of growth on the seed crystal was measured. Fig. 2 shows A ¢o O
10
x
8
o -.. E o
6 4
.< •:
O
2 o
r
i
I
I
I
I
I
0.0
10
20 TIME
4
30
&
I 40
A I 50
(hours)
Fig. 2. Comparisonof theoreticalpredictionwith data of Nerad andShlichta [3].
Nerad and Shlichta's observed growth compared to the prediction of Wilcox's model. Since Wilcox's model only applies to growth on a single face of a crystal, it could not be applied to the results o~ Shiomi, Kuroda and Ogawa. The predictions of Wilcox's model are in remarkably good agreement with the experimental results of Simon, i f one assumes a reasonable (>/0.01) value for the interface kinetics parameter. The data of Nerad and Shlichta are 30 to 90% higher than the predictions of the Wilcox model for Bye >/0.1. This is consistent with the observation of occasional low-level convection in these experiments. These comparisons indicate that the Wilcox model can be used to make reliable order-of-magnitude predictions of growth rates in the absence of convection. This model is currently being used to predict growth rates for a forthcoming "Getaway Special" solution growth experiment being prepared by the Caltech Student Space Organization for a future Space Shuttle flight.
References
I 5
J
I 10
[
I 15
SIMON I 20
o TEMPERATURE
(°C)
Fig. 1. Comparisonof theoreticalpredictionwith data of Simon [1].
[1] B. Simon, J. Crystal Growth 43 (1978) 640. [2] P.J. Shlichta, Crystal Growth in a Spaceflight Environment: MPS 770-100, Final Report (Jet PropulsionLaboratory, California Institute of Technology,December 1984). [3] B.A. Nerad and P.J. Shliehta, J. Crystal Growth, to be published. [4] Y. Shiomi,T. Kuroda and T. Ogawa, J. Crystal Growth 50 (1980) 397. [5] H.T. Minden, J. Crystal Growth 6 (1970) 228.
794 [6] [7] [8] [9] [10] [11] [12] [13]
[14] [15]
[16] [17] [18] [19] [20] [21]
D.G. Schlom, P.J. Shlichta / Convectionless growth of crystals from solution R. Ghez, J. Crystal Growth 19 (1973) 153. R. Ghez and J.S. Lew, J. Crystal Growth 20 (1973) 273. H. Mi~ler-Krumbhaar, J. Chem. Phys. 63 (1975) 5131. R. Ghez, Intern. J. Heat Mass Transfer 23 (1980) 425. M.B. Small and J.F. Barnes, J. Crystal Growth 5 (1969) 9. W.R. Wilcox, J. Crystal Growth 56 (1982) 690. W.R. Wilcox, private communication; W.R. Wilcox, J. Crystal Growth 68 (1984) 71. W.A. Roth and K. Scheel, Eds., Landolt-BOrnstein Physikalisch-chemische Tabellen, Band 2, Tei154 (Springer, Berlin, 1969) p. 624. J.D. Hatfield, O.W. Edwards and R.L. Dunn, J. Phys. Chem. 70 (1966) 2555. V.A. Zonov and V.V. Serdyuk, article deposited at the All-Union Institute of Scientific and Technical Information (VINITI), Dept. No. 4830-72 (1972). A.B. Zdanovskii and V.V. Serdyuk, Russ. J. Phys. Chem. 47 (1973) 417. Z. Solc, A. Sostokova and M. Sedlackova, Sb. Ved. Praci, Vysoka Skola Chem.-Technol., Pardubice 28 (1972) 19. J.W. Mullin and A. Amatavivadhan, J. Appl. Chem. 17 (1967) 151. A.N. Campbell and B.G. Oliver, Can. J. Chem. 47 (1969) 2681. Ref. [13], p. 53. A. Seidell, in: Solubilities of Inorganic and Metal-Organic Compounds, Vol. 2, 4th ed., Ed. W.F. Linke (American Chemical Society, Washington, DC, 1965) pp. 286-287.
[22] J.W. Mellor, A Comprehensive Treatise on Inorganic and Theoretical Chemistry, Vol. 2, Suppl. 3 (London, 1956) p. 1961. [23] E.W. Washburn, Ed., International Critical Tables of Numerical Data Physics, Chemistry and Technology, Vol. 3 (McGraw-Hill, New York, 1928) p. 90. [24] R.J. Meyer, Ed., Gmelin's Handbuch der Anorganischen Chemie, 8th ed., No. 22 (Springer, New York, 1978) p. 999. [25] R.C. Weast, Ed., CRC Handbook of Chemistry and Physics, 60th ed. (CRC Press, Boca Raton, FL, 1979) p. D-255. [261 K. Chomjakow, S. Jaworowskaja and P. Schirokich, Z. Physik. Chem. A167 (1933) 35. [27] C. Drucker, Arkiv Kemi, Mineral. Geol. 22A (1946) No. 21. [28] C.M. Mason and J.B. Culvern, J. Am. Chem. Soc. 71 (1949) 2387. [29] L.N. Alymova, D.M. Korf and N.D. Lebedeva, Russ. J. lnorg. Chem. 11 (1966) 1288. [30] S. Palitzsch, Z. Physik. Chem. 138 (1928) 379. [31] A.A. Kazantsev, J. Chem. USSR 8 (1936) 1230. [32] A. Seidell, ref. [21], pp. 1014-1015. [33] Ref. [23], p. 235. [34] A.P. Rutskov, Izv. Fiz. Khim., Anal. Inst. Obshei Neorg. Khim. Akad. Nauk SSSR 17 (1949) 286. [35] Ref. [24], No. 21, p. 1767. [36] Ref. [25], pp. B-113, B-125.