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Role of Temperature in the Spontaneous Precipitation of Calcium Sulfate Dihydrate Pavlos G. Klepetsanis,† Evangelos Dalas,‡ and Petros G. Koutsoukos*,§ Department of Pharmacy, University of Patras, University Campus, GR 265 00 Patras, Greece, Department of Chemistry, University of Patras, University Campus, GR 265 00 Patras, Greece, and Institute of Chemical Engineering and High Temperature Chemical Processes and Department of Chemical Engineering, University of Patras, University Campus, GR 265 00 Patras, Greece Received January 23, 1998. In Final Form: November 5, 1998 The spontaneous precipitation of calcium sulfate in supersaturated solutions over the temperature range between 25.0 and 80.0 °C was investigated by monitoring the solution specific conductivity during desupersaturation. From measurements of the induction times preceding the onset of precipitation the surface energy of the forming solid, identifield as gypsum, was found between ca. 12 and 25 mJ m-2 for the temperature range between 80.0 and 25.0 °C, respectively. Kinetics analysis showed that over 50 °C it is possible that anhydrous calcium sulfate is forming as a transient phase converting into the more stable calcium sulfate dihydrate. The linear dependence of the rates of precipitation on the relative solution supersaturation suggested a mechanism according to which the growth units are integrated into the active sites of the supercritical nuclei by surface diffusion. According to the morphological examination of the crystals it is possible that crystal growth occurs by the advancement of steps.
Introduction The formation of calcium sulfate scales is a welldocumented phenomenon encountered in a wide spectrum of industrial processes and applications including oil production by water-flooding, in particular for cases where incompatible waters are used,1 desalination of seawater by reverse osmosis,2 handling of geothermal brines for energy production,3 water distillation,4 phosphoric acid production by acidification of phosphorites with sulfuric acid,5 etc. Despite the fact that the system has been intensively investigated over the past three decades many aspects await reliable answers. A considerable amount of the published literature is concerned with batch, seeded growth studies,6-12 investigations in various hydrodynamic conditions,11-13 and spontaneous precipitation experiments.14-16 The solution chemistry of the aqueous †
Department of Pharmacy. Department of Chemistry. § Institute of Chemical Engineering and High Temperature Chemical Processes and Department of Chemical Engineering. ‡
(1) Cowan, J. C.; Weintritt, D. J. Water Formed Scale Deposits; Gulf Publ. Co.: Houston, TX, 1976; p 60. (2) Tsuge, H.; Sugino, Y.; Takeda, M.; Matsumura, T. Proceedings of the 9th Annual NSWIA Conference; Washington, DC, 1981. (3) Weismantel, G. Chem. Eng. 1973, 80, 40. (4) BETZ Handbook of Industrial Water Conditioning, 8th ed.; Betz Lab. Inc.: Trevose PA, 1982; pp 202-204. (5) Glater, J.; York, J. L.; Campbell, K. S. In Principles of Desalination; Spiegler K. S., Laird A. D. K., Eds.; Academic Press: New York, 1980; p 627. (6) Liu, S. T.; Nancollas, G. H. J. Cryst. Growth 1970, 6, 282. (7) Nancollas, G. H. Adv. Colloid Interface Sci. 1979, 10, 215. (8) Nancollas, G. H.; White, W.; Tsai, F.; Maslow, L. Corrosion 1979, 35, 304. (9) van Rosmalen, G. M.; Daudey, P. J.; Marchee´, W. G. J. J. Cryst. Growth 1981, 52, 801. (10) Gardner, G. L. J. Phys. Chem. 1978, 82, 864. (11) Meijer, J. A.; van Rosmalen, G. M. Desalination 1980, 34, 217. (12) Amjad, Z.; Hooley, K. J. Colloid Interface Sci. 1986, 111, 496. (13) Hasson, D.; Zahavi, J. Ind. Eng. Chem. Fundam. 1970, 9, 1. (14) Klepetsanis, P. G.; Koutsoukos, P. G. J. Cryst. Growth 1989, 98, 480. (15) Macek, J.; Zakarejsek S.; Radkovic, J.; Bole V. J. Cryst. Growth 1993, 132, 99. (16) So¨hnel, O.; Haldirova, M. Cryst. Res. Technol. 1984, 19, 477.
media in which the various calcium sulfate hydrates form is very important and needs to be carefully considered in order to quantify the mechanisms of the formation of the various calcium sulfate forms. Calcium sulfate may crystallize as gypsum (CaSO4‚2H2O, CSD), calcium sulfate hemihydrate (CaSO4‚1/2H2O, CSH) and anhydrite (CaSO4, CSA). The solubility of all calcium sulfate forms decreases with increasing temperature, a fact that is responsible for the formation of calcium sulfate scale on heat exchanger surfaces. The precipitation process includes both nucleation and crystal growth steps which are mechanistically different. The kinetics analysis is often complicated when the precipitation process is investigated under rapidly changing solution conditions. In the majority of the published work the key variable, the solution supersaturation, is rapidly changing especially during the initial stages of the precipitation of calcium sulfate. The operation of primary and secondary nucleation and crystal growth in the same experiment may complicate the interpretation of the results. In the present work we have monitored carefully the solution desupersaturation during the formation of calcium sulfate over a wide solution temperature range. Since the formation of this salt is not pH dependent,14 monitoring of the solution supersaturation was effected by measuring the specific conductance throughout the precipitation process. The kinetics results from the batch experiments done under carefully controlled conditions of temperature and solution supersaturation have been analyzed in an attempt to deduce the prevalent mechanism in the formation of calcium sulfate. The experimental temperatures were extended in regions (up to 80 °C) in which calcium sulfate forms other than CSD may form. Experimental Section The experiments reported in the present work were batch type, done in a glass reactor, volume totaling 0.600 dm3. The homogeneity of the solution with respect to all chemical components was ensured by magnetic stirring of the solutions at about 400 rpm. The temperature control (( 0.1 °C) was effected
10.1021/la9800912 CCC: $18.00 © 1999 American Chemical Society Published on Web 01/21/1999
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Figure 1. Schematic of the electronic circuitry of the electronic amplifier used for the measurement of very small changes of the solution specific conductivity. The symbols correspond to the electronic parts as follows: IC1,2,3, LM308; IC4, LM741H; R1 ) 100 kΩ, 1%; R2, R3 ) 50 kΩ, 1%; R4 ) R5 ) R6 ) R7 ) 4 kΩ, 1%; R8 ) R9 ) 100 Ω, 1%; R10 ) 100 kΩ, 1%; RF ) 100 Ω, 1%; VR1 ) 10 kΩ; VR2 ) 50 kΩ; C1 ) C2 ) 100 pF, 5%; C3 ) C4 ) C5 ) 1 nF, 5%; power supply (12 V. by circulating water from a thermostat through a jacket surrounding the reactor. Stock solutions of calcium nitrate and ammonium sulfate were prepared from the corresponding crystalline solids (Merck Puriss) using triply distilled water. The solutions, prior to their standardization, were filtered through membrane filters (0.2 µm, Millipore, Bedford, MA). The calcium stock solutions were standardized with photometric titrations with standard EDTA solutions (Merck, Titrisol) using murexide indicator and by atomic absorption spectrometry (Varian 1200). Ammonium sulfate stock solutions were standardized by titration with standard barium chloride solutions (Merck, Titrisol) and by ion chromatography (Metrohm IC 690). The supersaturated solutions were prepared directly in the thermostated reactor by simultaneously mixing equal volumes (0.250 dm3 each) of the calcium nitrate and ammonium sulfate solutions, through a Y-shaped glass tube. The mixing was done in less than 20 s, and maximum reproducibility was thus achieved. Immediately following mixing of the reagents and the establishment of the supersaturation the reactor was sealed with a Perspex lid bearing holes for the accommodation of a conductivity cell (Radiometer PP1042) and for sampling. The solution specific conductivity was measured with a conductivity meter (Radiometer, CDM 3). To enhance the output signal of the conductivity meter and be able consequently to measure changes in the solution specific conductivity as small as 1 µS cm-1, a special, low-cost amplifier was designed, and the corresponding electronic circuit is shown in Figure 1. A calibration line was made by measuring the specific conductivity and its relative differences in solutions titrated with standard calcium nitrate solutions both in the presence and in the absence of ammonium sulfate in order to avoid errors due to ion pair formation. Through linear regression of the calibration data, equations relating solution conductivity to solution concentration were established for all temperatures in which experiments were done.17,18 A typical (17) Smith, B. R.; Sweet, F. J. Coll. Interface Sci. 1971, 37, 612. (18) Christoffersen, M. R.; Christoffersen, J.; Weijnen, M. P. C.; van Rosmalen, G. M. J. Cryst. Growth 1982, 58, 585.
Figure 2. Calibration curve for the correlation of the specific conductivity of the supersaturated solutions with the concentration of calcium in solution. (For each calibration point equimolar (total calcium):(total Sulfate) ) 1:1 solutions were used; 25 °C.) calibration curve is shown in Figure 2. The variation of the specific conductivity of the solution concomitant with the desupersaturation in a typical spontaneous precipitation experiment and the corresponding calcium concentration are also shown in the same figure. The time lapsed between the establishment of the solution supersaturation and the measurement of the first changes of the specific conductivity measured was defined as the induction time, τ, preceding the spontaneous precipitation of calcium sulfate. The precise determination of the induction time was done by the determination of the inflection point of the specific conductivity-time curve, plotting the derivative of the specific conductivity variation with time. In preliminary experiments it was established that the conductivity probe did not induce the precipitation of calcium sulfate. In these experiments, the
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Klepetsanis et al. Table 1. Equilibria Involved in the CaCl2-(NH4)2SO4-H2O System and the Corresponding Stability Constantsa equilibrium
log K25 (I f 0)
HSO4- ) H+ + SO42CaSO40 ) Ca2+ + SO42NH4SO4- ) NH4+ + SO42CaNO3+ ) Ca2+ + NO3H2O ) H+ + OHNH4+ ) H+ + NH3 CaSO4‚2H2O(s) ) Ca2+ + SO42- + 2H2O
1.99 2.31 1.11 0.06 13.99 9.24 -4.62
∆H (kcal/mol) 5.4 1.6 -6.0 -13.34 -12.45 0.3
a Martell, A. E.; Smith, R. M. Critical Stability Constants; Plenum Press: New York, 1981; Vol. 4.
Figure 3. Variation of the solution specific conductance (O) and of the number of particles (b) with time for the spontaneous precipitation of calcium sulfate in supersaturated solution (experiment no. 101). precipitation process was monitored turbidimetrically measuring light transmission. Moreover, in all experiments reported in the present work the total amount of crystals formed up to the end of each run did not affect the solution specific conductance measured.14 The rates reported were computed at the point of maximum slope of the conductivity-time plots for each experiment. The number of particles was found to reach a constant value, suggesting that, at this point, the number of active centers for crystal growth was constant. Typical plots, showing the constancy of the particle number as a function of the variation of the solution specific conductance during the spontaneous precipitation of calcium sulfate, are shown in Figure 3. During the course of precipitation samples were withdrawn for the measurements of the number and of the size distribution of the precipitating particles as well as for the verification of the validity of the calibration curve used for the measurement of calcium concentration in solution. Knowledge of the total calcium concentration and of the stoichiometry of the precipitating salt (Ca:SO4 ) 1:1) allowed for the calculation of the solution supersaturation with time during the precipitation process. The number and the particle size distributions were measured by a rotating laser scattering counter (Spectrex ILI 1000) connected with a computer for the data acquisition and subsequent analysis. Calcium analyses were done by ion chromatography and/or by spectrophotometric titrations. The solid phases were collected at the end of the precipitation process by filtration through membrane filters. Following drying at 40 °C overnight the solids were characterized by powder X-ray diffraction (Philips 1840/ 00) scanning electron microscopy (SEM, JEOL JSM 5200), infrared spectrometry (Perkin-Elmer 1760 FTIR), thermogravimetic analyses (DuPont 910), and specific surface area (SSA) measurements by a multiple point dynamic BET method.
Results and Discussion In all experiments and over the temperature range (2580 °C) investigated in the present work CSD was the only calcium sulfate phase found, although thermodynamic calculations would predict the formation of CSA over temperatures exceeding 50 °C.13 It should be noted however that the phase identification was done following filtration of the aqueous media at room temperature, a fact which may have contributed decisively to the conversion of CSA eventually formed at the inital precipitation stages into CSD by hydration. The chemical nature of the solid precipitate was identified further by powder X-ray diffraction19 and infrared spectroscopy.20 TGA analyses of the precipitates yielded a weight loss of 20.9%, corresponding to CSD.19 The driving force for the formation of (19) Klepetsanis, P. G.; Koutsoukos, P. G. J.Colloid Interface Science, 1991, 143, 299. (20) Zussman, J. In Physical Methods in Determinative Mineralogy; Academic Press: London, 1977.
calcium sulfate dihydrate is the change in the Gibbs free energy ∆G for going from the supersaturated solution to equilibrium. The average per ion energy is given by
∆G ) -
2+ 2RT (Ca )(SO4 ) ln 2 K0sp
(1)
where ( ) denote activities, R and T are the gas constant and the absolute temperature, respectively, and K0sp is the thermodynamic solubility product of CSD. The ratio
Ω)
(Ca2+)(SO42-) K0sp
(2)
is the supersaturation ratio. The (relative) supersaturation is defined as
σ ) Ω1/2 - 1
(3)
It is obvious that the calculation of the solution supersaturation with respect to any calcium sulfate hydrate requires knowledge of the activities of all ions involved. The distribution and the activities of the ionic species in the supersaturated solutions were computed by taking into consideration the equilibria and the respective constants summarized in Table 1. In cases in which data for the thermodynamic constants were not available for all temperatures the constants were computed using enthalpies of formation. In addition to the equilibria shown in Table 1, the mass balance equations for total calcium, Cat, and total sulfate, St, along with the electroneutrality conditions were used and successive iterations were made for the ionic strength.21 The activity coefficients of the z-valent ions, γz were calculated from an extended Debye-Hu¨ckel equation22
log γz ) -
Az2I1/2 + bI 1 + BaI1/2
(4)
where I is the solution ionic strength, A and B are the Debye-Hu¨ckel constants,23 and a and b are constants characteristic for each ionic species. Values of a and b are summarized in Table 2. The temperature dependence of the equilibrium constants was taken into consideration for the calculations at temperatures other than 25 °C, using the enthalpy values and the van’t Hoff equation. For the solubility products of CSD and CSA the expression (21) Nancollas, G. H. Interactions in Electrolyte Solutions; Elsevier: Amsterdam, 1966; p 115. (22) Ball, J. W.; Nordstrom D. K. WATEQ 4F-Program for Calculation of Species Concentration in Seawater; USGS: Washington, DC, 1987. (23) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworths: London, 1959; p 145.
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Table 2. Values for the Coefficients a and b (Eq 4) for the Species in the Ca(NO3)2-(NH4)2SO4 System ionic species
a
b
ionic species
a
b
Ca2+ SO42-
5.0 5.0
0.165 -0.040
NH4+ NH4SO4-
2.5 5.4
0.000 0.000
Table 4. Coefficients for the Calculation of the Solubility Product of Calcium Sulfate as a Function of Temperature solid
A1
A2
10-6A3
A4
A5
CSD CSA
182.532 164.814
-0.48932 -0.46478
-10.325 -10.764
-67441.7 -68807. 8
1156.21 1059.51
Table 3. Initial Conditions, Supersaturation, Induction Times, and Initial Rates for the Spontaneous Precipitation of Calcium Sulfate Dihydrate at Various Temperatures (Total Calcium, Cat ) Total Sulfate, St) expt no.
102Cat (M)
θ (°C)
τ (min)
∆G (kJ‚mol-1)
10-5R (M‚min-1)
101 102 103 104 105 106 111 112 113 114 115 121 122 123 124 131 132 133 134 135 141 142 143 144
5.0 4.75 4.25 4.0 3.75 3.5 3.4 3.3 3.2 3.1 3.0 3.2 3.0 2.80 2.75 2.5 2.4 2.3 2.25 2.1 2.35 2.25 2.1 2.0
25.0 25.0 25.0 25.0 25.0 25.0 38.4 38.4 38.4 38.4 38.4 50.0 50.0 50.0 50.0 65.0 65.0 65.0 65.0 65.0 80.0 80.0 80.0 80.0
32 39 45 52 89 105 26 24 54 81 106 11 35 49 95 8 21 29 42 163 14 16 37 204
-1.55 -1.47 -1.31 -1.22 -1.13 -1.02 -0.98 -0.94 -0.89 -0.84 -0.79 -0.95 -0.84 -0.74 -0.71 -0.70 -0.63 -0.56 -0.52 -0.41 -0.82 -0.75 -0.63 -0.54
6.8 5.9 2.1 1.9 1.0 0.5 6.0 5.1 4.5 2.4 2.1 2.0 1.2 0.9 0.7 2.4 1.9 1.7 1.3 0.8 12.1 7.2 2.0 1.3
Figure 4. Experimental conditions (Table 3, represented by rectangles) and the solubility isotherms of the three calcium sulfate hydrates: plot of solubility as a function of temperature.
of eq 5 was used for the calculation of the respective
ln K0s )
A2T A3 A5 A1 A4 ln T + + + 2 R 2R RT R 2RT
(5)
solubility products at various temperatures.24 The values for the constants Ai (i ) 1-5) are given in Table 4. The spontaneous precipitation of CSD was preceded by induction times which were inversely proportional to the solution supersaturation. The experimental conditions and the kinetics results obtained are summarized in Table 3. In general, the conditions of the working solutions were below the solubility isotherm of CSH with the exception of part of the set of experiments done at 80 °C, as shown in Figure 4. The dependence of the induction periods measured for various supersaturations and temperatures are shown in Figure 5. From the experimental methodology employed, it is obvious that the induction times, τ, measured include both the time needed for nucleation, τn, and the time, τg, required for the critical nucleus to grow to a size which would correspond to the extent of ion depletion needed by the conductivity probe to give an appropriate change in the specific conductance of the supersaturated solution,25 i.e.
τ ) τ n + τg
(6)
The strong dependence of the induction times on the solution supersaturation which was more pronounced at (24) Krishnam, R. U. G.; G. Atkinson, J. Chem. Eng. Data 1990, 35, 361. (25) Mullin, J. W. Crystallization, 2nd ed.; Butterworth-Heinemann: Oxford, U.K., 1992.
Figure 5. Plot of the induction times preceding the spontaneous precipitation of calcium sulfate dihydrate as a function of temperature and the solution supersaturation.
higher temperatures should be ascribed to the sensitivity of nucleation on both supersaturation and temperature. The dependence of the induction time on temperature and the solution supersaturation, assuming steady state, is given by eq 7, where C1 and C2 are constants. Constant
log τ )
C1 3
T log2 Ω
- C2
(7)
C1 is given by eq 8 as a function of the shape of the C,
C1 )
βγs3υ2 (2.303k)3ν2
(8)
forming nuclei, the molecular volume, υ, and the surface energy, γs, of the solid phase forming, where β is a shape factor (taken as 16π/3 here, assuming spherical shape for the nuclei forming), k is Boltzmann’s constant, and ν is
1538 Langmuir, Vol. 15, No. 4, 1999
Figure 6. Plots of the induction times measured at various temperatures as a function of the inverse of the square of the logarithm of the relative supersaturation: (O) 25 °C; (9) 38 °C; ([) 50 °C; (4) 65 °C; (×) 80 °C.
Figure 7. Variation of surface energies determined from nucleation kinetics data as a function of temeperature: (O) data from ref 28; (9) present work.
the number of ions in the calcium sulfate crystals (ν ) 2). Plots according to eq 7 are shown in Figure 6. As may be seen, at all temperatures except for 65 °C, a single straight line was obtained for each set of experiments. At 65 °C the plot consisted of two linear parts with a change in the slope at about Ω )1.51. The steeper part may be ascribed to homogeneous precipitation while the other part to primarily heterogeneous.26,27 From the slopes of the straight lines, the surface energies were computed for each temperature, and as may be seen in Figure 7, their values are in good agreement with literature values obtained from measurements of rates of precipitation and of induction times from calcium sulfate nucleation experiments,28,29 while the extension of the temperature range to 80 °C showed a decrease of the surface energies with temperature as expected.30 In our experiments, variation of the stirrer speeds between 100 and 400 rpm did not show any effect in the measured rates of CSD precipitation suggesting that the process was not mass transport controlled. Moreover, if mass transport were the rate-determining mechanism for (26) So¨hnel, O.; Mullin, J. W.; Jones, A. G. Ind. Eng. Chem. Res. 1988, 27, 1721. (27) So¨hnel, O.; Garside, J. Precipitation; Butterworth-Heinemann: Oxford, U.K., 1992; pp 66-70. (28) Keller, D. M.; Massey, R. E.; Hileman, O. E., Jr. Can. J. Chem. 1978, 56, 831. (29) Linnikov, O. O. Russ. J. Appl. Chem. 1995, 68, 1023. (30) Adamson, A. W. Physical Chemistry of Surfaces, 5th ed.; J. Wiley: New York, 1995.
Klepetsanis et al.
Figure 8. Plot of the rate of calcium sulfate precipitation, RP, as a function of the solution supersaturation, σ: (b) 25.0 °C; (O) 38.5 °C; ( ) 50.0 °C; (4) 65.0 °C; (×) 80 °C.
Figure 9. Typical powder X-ray diffraction spectrum of calcium sulfate dihydrate obtained by spontaneous precipitation
Figure 10. Plot of the logarithm of the rate constants determined from the kinetics of precipitation of calcium sulfate over the temperature range between 25 and 80.0 °C as a function of the inverse of the absolute temperature.
the formation of CSD, the overall rate measured should be
rate ≡ RP )
DvC∞σ δ
(9)
where Dv is the diffusion coefficient (ca. 1 × 10-9 m2 s-1), C∞ is the CSD solubility (4.9 × 10-3 mol dm-3), and δ is the diffusion layer thickness. The rates measured at the corresponding supersaturations (Table 3) would correspond to diffusion layer thickness values about 10 mm (assuming a specific surface area for the growing crystals of 1 m2 g-1, value measured at the end of the crystallization
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Figure 11. Scanning electron micrographs of gypsum crystals precipitated spontaneously in aqueous supersaturated solution: (a) 25 °C; (b) 65 °C; (c-f) 80 °C.
experiments). This value is unrealistic, supporting further a surface diffusion controlled mechanism.31 According to this mechanism the rate-determining step is the integration of the growth units in the active sites of the growing supercritical nuclei. For aqueous solutions the overall rate, RP, depends linearly on the solution supersaturation:32
RP ) kPσ
(10)
Here kP is the rate constant. Plots according to eq 10 are shown in Figure 8. It should be noted that the kinetics analysis was done on the basis of the mineral phase found after the collection of the precipitate from the reactor which in all cases was identified as CSD. Typical powder X-ray diffractogram obtained from precipitates is shown in Figure 9. From the kinetics plot it may be seen that a discontinuity was found for the apparent rate constant between temperatures 38.5 and 50.0 °C. From the solubility isotherms of the calcium sulfate system shown in Figure 4, it may be seen that at this temperature CSA (31) Liu, Y.; Nancollas, G. H. J. Cryst. Growth 1996, 165, 116. (32) Bennema, P. J. Crystal Growth 1967, 1, 278.
is more stable. Since the rate constants (represented by the slopes of the straight lines) for the kinetics of precipitation measured increased from 25.0 to 38.5 °C and again from 50.0 to 80.0 °C, it may be concluded that a different mineral, CSA, precipitates at these temperatures. That this intermediate phase was not identified is probably due to the fact that the analysis by XRD was done following drying at room temperature at which conversion to the more stable CSD is very likely. It should be noticed that CSH may convert into CSD in the solid state in the presence of air humidity alone.33 The variation of the apparent rate constants with temperature is shown in Figure 10. With application of an Arrhenius formalism, two values were calculated for the respective activation energies of the mineral phases precipitating: 46 and 67 kJ mol-1. Both values should be considered rather as temperature coefficients, but their magnitudes corroborated further the surface diffusion controlled mechanism for the spontaneous formation of the mineral phase in (33) Semenovich, I. S. Kinetics of Phase Transitions of Calcium Sulfate Hydrates under Conditions of Phosphoric Acid Wet Process Production. Ph.D. Thesis, Research Institute of Fertilizers and Insectofungicides (NIUI F NPO “Minudobreniya”), Moscow, 1992.
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supersaturated calcium sulfate solutions over the temperature range between 25.0 and 80.0 °C. Both values are in very good agreement with activation energies reported in the literature for the precipitation in brines34 and in synthetic supersaturated solutions.6,17 The first-order dependence of the measured rates of precipitation on the relative supersaturation is consistent with the prediction of the Burton, Cabrera, and Frank spiral growth theory35 a mechanism inferred by Christoffersen.18 Further studies however involving the use of scanning force microscopy failed to verify the observation of spirals in calcium sulfate dihydrate crystals, even at very low supersaturations, and it was shown that the growth takes place by the advancement of elementary steps.36,37 Examination of the morphology of the precipitated gypsum crystals by SEM showed the formation of characteristic prismatic habits shown in Figure 11. The (34) Kushnir, J. Geochim. Cosmochim. Acta 1980, 44, 1471. (35) Burton, W. K.; Cabrera, N.; Frank, F. C. Philos. Trans. R. Soc. London 1951, A243, 299. (36) Bosbach, D.; Rammensee, W. Geochim. Cosmochim. Acta 1994, 58, 843. (37) Hall, C.; Cullen, D. C. AIChE J. 1996, 42, 232.
Klepetsanis et al.
edge of the crystals, as may be seen in the micrograph Figure 11e consisted of layers. On the surface of the top layer, advancing steps could be noticed (Figure 11f) thus supporting the previous reports concerning crystal growth of gypsum by advancing steps. In conclusion, the spontaneous precipitation of calcium sulfate dihydrate over the temperature range between 25.0 and 80.0 °C was found to be a surface diffusion controlled process in which the rates of precipitation varied linearly with the solution supersaturation. The estimate of the apparent activation energy supported further this conclusion. The measurements were done by monitoring the changes of the specific conductivity of the supersaturated solutions during the solid formation process. From the kinetics data and particularly from the dependence of the induction times preceding the onset of precipitation on the solution supersaturation, the surface energies of the solid phases forming were of the order of magnitude anticipated for sparingly soluble salts and they decreased with increasing temperature. LA9800912
