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Influence of Mg2+ on the kinetics of calcite precipitation and calcite crystal morphology
Chemical Geology 163 Ž2000. 129–138 www.elsevier.comrlocaterchemgeo
Influence of Mg 2q on the kinetics of calcite precipitation and calcite crystal morphology Yuping Zhang ) , Richard A. Dawe
1
The Centre for Petroleum Studies, TH Huxley School, Imperial College, London, SW7 2BP, UK Received 21 July 1998; accepted 29 April 1999
Abstract The kinetics of calcite growth in the presence of Mg 2 has been studied by both a pH free drift method and by visual observation. Our experiments show that the calcite growth rate is reduced by the presence of Mg 2q. The higher the MgrCa ratio in the solution, the lower the growth rate in a CaCO 3 supersaturated solution. The inhibition of calcite growth by the presence of Mg 2q is caused by Mg 2q being incorporated into the original calcite seed surfaces and developing new crystal surfaces. The Mg 2q distribution on the calcite surfaces is not uniform as there is likely to be different Mg 2q densities on the newly developed surfaces than on the original surfaces of the calcite seeds. This causes the calcite crystal morphology to change. The significance of creating error in using the initial rate data rather than the equilibrium rate data for the prediction of the calcite precipitation kinetics is discussed. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Calcite precipitation; Mg 2q inhibition; Kinetics; Morphology; Marine calcite cements; Calcium carbonate
1. Introduction The kinetics of calcite precipitation is important in many hydrogeochemical environments and chemical engineering operations ŽMorse and Mackenzie, 1990.. Errors in the determination of calcite precipitation rates will clearly affect the predicted mass of precipitation in a given time interval, and will thus,
)
Corresponding author. Read Well Services, Offshore Technology Park, 1 Claymore Avenue, Aberdeen AB23 8GW, UK. E-mail: [email protected] 1 Present address: Petroleum Engineering, University of West Indies, St. Augustine, Trinidad, West Indies. E-mail: [email protected].
affect predictions of geological crystal growth and scaling within chemical plants. Many studies have shown that the calcite precipitation rate can be inhibited by the presence of Mg 2q ŽAkin and Lagerwerff, 1965; Mucci and Morse, 1983; Reeder and Grams, 1987; House and Howson, 1988; Morse and Mackenzie, 1990; Dromgoole and Walter, 1990; Paquette and Reeder, 1995; Paquette et al., 1996.. A possible reason is that Mg 2q ions can be incorporated into the calcite crystal lattices at Ca2q ion sites which then affect the morphology of the crystal and thence its growth. The rate reduction has been suggested to be approximately proportional to the concentration ratio of Mg 2q ions with Ca2q ions in the solution ŽMorse and Mackenzie, 1990.. The amount of Mg 2q being incorporated may be influenced by
0009-2541r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 5 4 1 Ž 9 9 . 0 0 0 9 7 - 2
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Y. Zhang, R.A. Dawe r Chemical Geology 163 (2000) 129–138
the local solution chemistry and the precipitation rate as well as temperature ŽKatz, 1973; Folk, 1974; Plummer and Mackenzie, 1974; Thorstenson and Plummer, 1977; Garrels and Wollast, 1978; Mucci, 1987; Howson et al., 1987; Morse and Mackenzie, 1990; Beck et al., 1992; Griffioen and Appelo, 1993; Hartley and Mucci, 1996.. However, the reported magnesium content of calcite precipitated in the laboratory from seawater is highly variable ŽGlover and Sippel, 1967; Kinsman and Holland, 1969; Berner, 1978; Garrels and Wollast, 1978; Mucci, 1987; Mucci and Morse, 1983.. Table 1 lists some examples of reported magnesium content in calcite precipitated from seawater from different studies. As we can see, the values obtained from most of the laboratory experiments are lower than those from natural calcite. In recent years, the studies have focused on the influence of crystal surface structure on the determination of the empirical partition coefficient for ‘‘foreign’’ ions incorporated into the calcite ŽDove and Hochella, 1993; Staudt et al., 1994; Paquette and Reeder, 1995; Paquette et al., 1996.. The path-dependent and non-equilibrium aspects of foreign ion incorporation during crystal growth have been considered as important factors in determining experimentally observed Mg 2q partition coefficients in calcite ŽPaquette and Reeder, 1995.. It has been clearly identified that the presence of Mg 2q modifies the morphology of calcite crystals ŽFolk, 1974; Gonzalez ´ et al., 1992; Paquette et al., 1996.. However, there does not appear to be a relationship between changes in crystal morphology and Mg 2q content on the crystal surfaces. These factors make the prediction of the calcite growth rate from currently available thermodynamic and kinetic data
complicated and liable to error. In this study we have examined the connection between the calcite seed morphology change and its growth kinetics in order to establish a proper experimental method to determine calcite growth rate in the presence of Mg 2q ion.
2. Experimental methods The experimental methods used in this study are a pH free drift method and a visual micromodel observation method. These have been used in our previous studies ŽDawe and Zhang, 1997 and Zhang and Dawe, 1998., so we shall only review them briefly here. 2.1. pH Free drift method When calcite precipitation occurs, the crystal growth rate can be determined from the calcium ion concentration change as a function of time, i.e., R m A yd w Ca2q x rdt
Ž 1. 2q x
where R m is the calcite growth rate, wCa is the concentration of calcium ions and t is time. In a closed system Ži.e., when there is no mass exchange between the solution and the environment., the solution pH change rate will depend only on the CaCO 3 precipitation rate ŽZhang and Dawe, 1998.. Therefore, the precipitation rate can be determined by measuring the rate of solution pH decrease ŽdpHrdt . which then can be converted to the calcium ion concentration changes as a function of time ŽdwCa2q xrdt . using the equations given in ŽZhang and Dawe, 1998.. In this earlier study, we demon-
Table 1 The magnesium content of calcite from seawater obtained from different studies Method 2y HCOy added drop by drop Ž08C. 3 q CO 3 pH-state at constant S R.G. calciteq CO 2 , then degas by diffusion pH-state at constant S 2y HCOy added Ž08C. 3 q CO 3 Natural magnesium calcite Ž161 samples.
Nuclei
Time to precipitate
S
MgCO 3 Žmol%.
Reference
glass dust reagent calcite reagent calcite reagent calcite glass dust
days 10–50 h ; 3 days 2–24 h minutes
; 50 5–7 NA 8–11 ) 200
0–1 7–10 9–10 8.1 " 1 14 12–15
Kinsman and Holland, 1969 Berner, 1975 Berner, 1978 Mucci and Morse, 1983 Glover and Sippel, 1967 Garrels and Wollast, 1978
Y. Zhang, R.A. Dawe r Chemical Geology 163 (2000) 129–138
strated that the calcite growth rate from supersaturated solutions without inhibitors can be described by, R m s k pm Ž S 0.5 y 1 .
n
Ž 2.
where k pm is the precipitation rate constant in molrm2 h kg, n is an apparent reaction order and S is the calcite supersaturation which is defined as: S s Ž Ca2q . Ž CO 32y . rK sp
Ž 3.
where K sp is the solubility product and Ž i . represents the activity of ith species. Sometimes the saturation index, SI Žs log S ., is preferred to represent the saturation level. When S s 1 or SI s 0, the water system is at equilibrium. As calcite crystals grow, the total surface area increases. This has been considered in the calcite growth rate calculations. If we assume that all the calcite crystal surfaces have the same activity for growth, the total calcite crystal surface area at time t should be A t s A i Ž Wi q Ž PPTt . 100 . rWi
2r3
Ž 4.
where A i and A t are the surface area of the calcite seeds at the beginning and at the time t, respectively; Wi is the initial seed weight in grkg H 2 O, and PPTt is the amount of CaCO 3 Ž M s 100 grmol. precipitate at the time t in molrkg. The crystal growth rate as a function of supersaturation can be obtained by plotting wdCCa 2q .rdt xrVA t against Ž St0.5 y 1., where V is the volume of the solution used in a experiment.
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The pH free drift experiments were conducted in a 250 ml multiple port and double-walled vessel which was connected to a recirculating constant temperature water bath kept at 258C. A schematic diagram of the pH-free drift equipment is shown in Fig. 1. The supersaturated calcium carbonate solutions were prepared by mixing equal volumes of CaCl 2 and NaHCO 3 solutions which were each twice the required final concentration. When Mg 2q was required, the appropriate amount of MgCl 2 was added to the CaCl 2 solutions to achieve the desired wMg 2q xrwCa2q x ratio. The desired pH was obtained by bubbling in CO 2 to lower the pH or N2 to increase the pH. Water from the water bath was circulated to the reaction vessel until the solution reached the experimental temperature Ž258C., and then the solution pH was measured. After the solution pH remained stable for 30 min, 0.08–0.2 g calcite seeds was added to the solution, and the vessel was then completely closed without a gas phase at the top of the vessel. The pH change accompanying the calcite growth was measured and recorded by an automatic titrator as a function of time immediately after the seed had been added to the CaCO 3 supersaturated solution. 2.2. The Õisual obserÕation method The CaCO 3 crystal growth rate can also be determined by measuring the change in a single crystal size over timed intervals ŽDawe and Zhang, 1997..
Fig. 1. Schematic diagram of the pH-free drift equipment.
Y. Zhang, R.A. Dawe r Chemical Geology 163 (2000) 129–138
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Fig. 2. The pattern of glass micromodel.
These calcite precipitation experiments were conducted in etched glass micromodels, which are twodimensional flowing systems with specially designed patterns etched onto a glass plate with a second flat glass sintered onto it. The details of how to make a glass micromodel are given by Dawe Ž1990. and Dawe and Grattoni Ž1998.. The pattern used in this study is one of parallel straight channels with different widths ŽFig. 2.. A schematic representation of the experimental system is given in Fig. 3. Calcite seeds were placed into a micromodel by injecting a seed suspended solution through the micromodel. A calcite supersaturated solution is then continuously injected through the micromodel. The changes in the crystal sizes during their growth were observed and recorded through a light microscope as a function of time. The crystal layer growth rate can be represented by: R L A d xrdt Ž 5. Ž . and is obtained by the same form of Eq. 2 with n s 2, i.e.: R L s k pl Ž S 0.5 y 1 .
2
Ž 6.
where R L is the crystal layer growth rate in mrs and d x is the layer increment of a crystal face in a time interval of d t, k pl is the rate constant of layer growth
rate in mrs. The mass rate R m can be converted into layer growth rate R L if the geometry of the crystals are known. For calcite crystals, the approximate conversion can be made if we assume that the calcite crystals are of cubic shape: Vc rc 1 rc R L Rm s s Ž 7. Sc M 3 M where Vc and Sc are the total volume and surface area of calcite crystals, rc is the density of calcite crystals in grcm3, M is molecular weight of calcite Ž100 grmol., R l in cmrh, so that the unit of R m will be molrm2 h kg. The CaCO 3 supersaturated solutions were made by injecting two solutions from two syringes fixed on a syringe injection pump. One solution contained twice the amount of the required calcium ion Žand magnesium ion. and the other twice the amount of carbonate alkalinity. The solution injection rate and the amount of calcite seeds were adjusted to a level at which the amount of lattice ions consumed for growth was much lower than that supplied Ž- 1%., so that the saturation inside the micromodel could be considered as constant. The solution pH at 258C was determined separately after mixing equal volumes of the two preheated solutions Ž258C. in a bottle with only one port which can be sealed by the pH electrode itself to avoid degassing. The saturation index was calculated using Solmineq88 ŽKharaka et al., 1988.. The chemicals used in all of our experiments were BDH AnalaR laboratory reagents. The calcite seeds were BDH AnalaR CaCO 3 powder which contain more than 99% of calcite as determined by X-ray diffraction analysis. It had a specific surface area of 5.88 m2rg determined by BET using a Coulter
Fig. 3. Schematic diagram of the micromodel experimental system.
Y. Zhang, R.A. Dawe r Chemical Geology 163 (2000) 129–138
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Omnisorp 100, a volumetric adsorption instrument, and nitrogen gas as adsorbate at liquid nitrogen temperatures. The pH electrode was calibrated by two NBS buffers at the beginning of each experiment. Electrode drift was examined at the end of each experiment using one pH buffer. The residual liquid junction caused by high ionic strength solutions was corrected using the Henderson equation ŽBates, 1964.. 3. Results and discussion Calcite growth rates for solutions with a range of wMg 2q xrwCa2q x ratios between 0 and 5 and with two different seed concentrations were determined by the pH free drift method. Table 2 summarises the solution compositions and the measured calcite growth rate interpreted by Eqs. Ž2. – Ž4.. As we can see from Table 2, the presence of Mg 2q reduces the calcite growth rate, and causes the reaction order n to increase and the rate constant k p to decrease. The rate reduction is proportional to the ratio of wMg 2q xrwCa2q x in the solution. The rate data obtained from the solutions containing Mg 2q cannot be interpreted by rate Eq. Ž2. very well as shown in Fig. 4. We can see from Fig. 4 that the initial precipitation rates are similar for all three water systems. However, for the water systems with Mg 2q present ŽNos. 5 and 6 in Table 2., the precipitation rates decrease as the supersaturation dropped and the apparent reaction order n increased with decreasing supersaturation. The reaction orders given in Table 2 are the average values over the whole time intervals. It is also interesting to note that the calcite growth rates are affected by the calcite seed concentration
Fig. 4. The measured calcite growth rate data plotted as a function of relative saturation Ž S 0.5 y1.. Curve Ž1., calcite growth rate in a supersaturated solution without Mg 2q; curves Ž2. and Ž3., the solution wMg 2q xrwCa2q x s1 and seed concentrations were 0.8 grl and 0.32 grl, respectively.
when a solution contains Mg 2q. The rate constants obtained at the lower calcite seed concentration were lower than those at the higher seed concentration Žcurve 3 of Fig. 4., whereas there was no significant influence of seed concentrations in a simple water systems without Mg 2q Žcomparing experiments Nos. 1 and 2 in Table 2.. Reddy and Gaillard Ž1981. studied the influence of calcite seed concentration on the calcite precipitation rate constant. They noticed that the rate constant is independent of the solidrsolution ratio when the calcite seed concentrations were above 0.3 grl, and it is higher at low seed concentrations. They suggested that this is because the contribution of surface nucleation andror secondary nucleation is relatively significant at low seed concentrations. The calcite seed concentration used in our experiments were 0.3–0.8 grl and the specific
Table 2 The effect of Mg 2q on calcite growth rates at 258C and different calcite seed concentrations No.
pH i
wMg 2q x Žmmolrkg.
Al k T Žmeqrkg.
wCa2q x Žmmolrkg.
SI
kp n R m s k p Ž S 0.5 y 1. n
Seed Žgrl.
1 2 3 4 5 6 7 8
7.68 7.75 7.81 7.79 7.81 7.87 7.74 7.82
0 0 1.0 2.8 5.5 5.1 25 27
10.9 10.6 10.9 11.6 11.1 11.4 11.3 11.5
5.40 5.52 5.31 5.61 5.57 5.60 5.59 5.76
0.733 0.795 0.847 0.875 0.851 0.936 0.758 0.825
0.820 0.850 0.519 0.611 0.133 0.262 0.010 0.008
0.32 0.80 0.32 0.80 0.32 0.80 0.32 0.80
1.86 1.87 3.03 3.00 4.29 3.24 6.52 6.07
Y. Zhang, R.A. Dawe r Chemical Geology 163 (2000) 129–138
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Table 3 The calcite growth rate at different ratios of wMg 2q xrwCa2q x at 258C a No.
pH
wCa2q x Žmmolrkg.
wHCOy x 3 Žmmolrkg.
wMg 2q xr wCa2q x
SI
RL Ž mrs = 10 10 .
kp Ž mrs = 10 10 .
1 2 3 4
8.05 8.01 8.05 8.05
2.52 2.52 2.52 2.60
5.09 5.09 5.09 5.03
0 0.1 0.5 1.0
0.75 0.71 0.74 0.76
1.47 0.673 0.695 0.395
0.769 0.421 0.378 0.201
a
NaCl s 0.09 molrkg, ionic strength was 0.1 eqrkg.
surface area of calcite seeds was much higher than that used by Reddy and Gaillard Ž5.9 and 1.0 m2rg, respectively.. Therefore, the rate constants obtained from our pH free drift method should not be influenced by surface nucleation. Our low rate constants obtained at the lower seed concentration with Mg 2q present imply that there is a relationship between the rate constant and the crystal size. This is because the lower the seed concentration the larger the final crystal size will be when a free drift method is used for solutions with the same supersaturation. The study by Mucci and Morse Ž1983. suggested that the higher the wMg 2q xrwCa2q x ratio in the solution, the more Mg 2q is incorporated into the calcite crystals and the calcite growth rate will be lower. This indicates that the reduction in calcite growth rate is proportional to the amount of Mg 2q incorporated into the calcite crystal surface. If calcite growth rates decrease with increasing crystal size as the result of the presence of Mg 2q, the average Mg 2q density on the crystal surfaces Žthe numbers of Mg 2q ions on one unit of surface area. must be gradually increasing as the crystal size is increasing.
Fig. 5. Calcite crystals obtained from Ž1. a supersaturated solution without Mg 2q ; Ž2 . wMg 2q xr wCa 2q x s 0.5, 258C, Ž3 . wMg 2q xrwCa2q x s 0.5, 408C.
To understand why the calcite growth rate is affected by the presence of Mg 2q and calcite seed concentration, we observed the process of calcite crystal growth inside a glass micromodel under a microscope and measured the crystal geometric size change as a function of time. The results show that the calcite layer growth rates decrease with increasing ratios of wMg 2q xrwCa2q x ŽTable 3.. We also observed that the seed crystal morphology gradually changed from the original rhomobohedral to other morphologies as shown in Fig. 5. New faces were developed from the edges Žcrystal No. 2 of Fig. 5. or the corners Žcrystal No. 3 of Fig. 5. of the original surfaces of calcite seeds. To explain a crystal morphology change, a simple crystal model is used here. In this crystal model, the surfaces of a crystal are classified into three groups, F Žflat., S Žstepped. and K Žkinked. surfaces ŽHartman, 1973; Markov, 1995. as shown in Fig. 6. The K and S surfaces can be considered as full of kinks and steps, respectively. It is obvious that the highest growth rate will be achieved at the K surface, then the S surface, and finally by the F surface. Therefore, the K and S surfaces are normally absent from equilibrium crystal morphologies ŽHartman, 1973..
Fig. 6. A schematic representation of a crystal illustrating F Žflat., S Žstepped. and K Žkinked. surfaces depending on whether they are parallel to two or one most dense rows of atoms, or are not parallel to any of the most dense rows of atoms, respectively.
Y. Zhang, R.A. Dawe r Chemical Geology 163 (2000) 129–138
Our experimental results show that new faces started to appear on the edges of rhomobohedral calcite crystal when Mg 2q was present in the solution. Similar morphological changes as the result of the presence of Mg 2q have been observed by Paquette et al. Ž1996.. The pictures presented in their paper show the initial stage of new surfaces developing at the corners and edges of calcite seed 10144 faces. Paquette and Reeder Ž1995. suggest that there are geometrically different types of surface sites on the original surfaces of the calcite seeds. Mg 2q has a higher affinity for some of these sites and it is adsorption or perhaps dehydration during incorporation that preferentially slows down growth in specific directions, for example towards the edges and corners as identified by Fig. 1 of Paquette et al. Ž1996.. As a consequence of inhibition by Mg 2q, new crystal faces will be developed, and these faces are dominated by the type of surface sites for which Mg 2q has a higher affinity, eventually creating the morphology changes. If the faces developed on the edges and corners are the S and K faces, one may want to know what can cause the growth rate to slow down on those surfaces with a high density of kink sites. One possibility is that the Mg 2q density on the newly developed surfaces is higher than that on the original surfaces of the calcite seeds. As a high Mg 2q density gives a lower growth rate, the relative growth rate on the F face can be higher than those on the other two faces and eventually disappear. The experimental results from Reeder and Grams Ž1987. and Paquette and Reeder Ž1995. support our hypotheses. They studied the relationship between the crystal surface structure and foreign cations incorporated into calcite, and measured the Mg 2q density on different surfaces of magnesium calcite by EPMA Želectron probe microanalysis. and SXRFMA ŽX-ray fluorescence microanalysis.. They found there was a differential partitioning of Mg 2q incorporation on different faces, and this difference can be a factor of 3–4 under their experimental conditions. As the crystal morphology is gradually changing from low-Mg-content face dominant to high-Mgcontent face dominant, the average Mg 2q density on the entire calcite surface area will gradually increase, and the overall calcite growth rate on the calcite crystal surfaces at a constant supersaturation and
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ratio of wMg 2q xrwCa2q x will gradually decrease. As the slower growing faces become more dominant, they make an increasing contribution to the overall measured growth rate. Then, as the result of the crystal morphology gradually changing, a lower rate constant and a higher empirical reaction order will appear in the rate equation when a free drift experimental method is used. As a stable rate constant may only be obtained when the crystal seeds have reached their stable morphology, the calcite growth rate and reaction order determined under this stage will only then truly represent the calcite growth kinetics. These are the values that should be used in any calculation of calcite precipitation under natural conditions. The crystal seed morphology change caused by the presence of Mg 2q can be a slow process. As we can see, the crystal No. 2 in Fig. 5 has not reached its stable morphology at a such large size Ž50–70 mm. because the F faces have not disappeared completely. We can expect that the final morphology of crystal No. 2 could be a pyramidal shape as shown in Fig. 7. Some recent experiments were aimed to check the kinetic model of calcium carbonate scaling by flowing a CaCO 3 supersaturated solution through a steel tube ŽZhang et al., 1999.. Thus, the picture of crystals from SEM shows us a type of stable morphology of calcite precipitate with Mg 2q in the solution at wMg 2q xrwCa2q x ratio of 0.5 ŽFig. 8.. The precipitation started from heterogeneous nucleation sites on metal surface and calcium carbonate scale formed as a consequence. In this case, the morphology of the precipitate is similar to our expected final morphology of No. 2 in Fig. 5. It is very rare that a crystal will grow to such a large size as we were able to in our visual observation experiments during the typical calcite mass deposit experiments as reported in the literature. For example, Mucci and Morse Ž1983. carried out some
Fig. 7. The calcite crystal morphology at the beginning Ža., middle Žb. and final Žc. stages of the morphology change as the result of present of Mg 2q in a solution.
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hand, under laboratory conditions the average Mg 2q partition onto the pure calcite seeds increases during the morphology transfer. When the growth rates are measured at the different stages of the morphology change, different growth rate constants will be obtained. We believe that once the crystal morphology reaches its equilibrium state, the crystal growth rate will become constant and the amount of Mg 2q incorporated at this stage will be uniform. Thus, the calcite growth rate constant in the presence of Mg 2q Žor other inhibitors. cannot be determined by a pHfree-drift method. This is because the total surface area of the crystal will have changed and the newly formed crystal morphology will depend on the water compositions and experimental conditions. The rate constant of calcite growth with Mg 2q incorporation cannot be obtained with confidence with uncertain calcite surface areas. However, it can be determined more accurately using a steady state method such as our visual observation method.
Fig. 8. Calcite crystals obtained from a supersaturated solution with wMg 2q xrwCa2q x s 0.5, 708C, saturation index s 0.6, started from a heterogeneous nucleation on a steel surface.
4. Conclusion precipitation experiments and, in order to avoid significant surface area variations during the calcite growth rate measurements, limited the amount of overgrowth precipitation to less than 10% of the initial seed weight. It is obvious that the growth rate determined at this initial stage of calcite seed morphology change will be higher than that when the morphology changes are complete. If the Mg 2q partition coefficient is determined at the early stage of the morphology change, the value will be lower than that at the equilibrium conditions. This may be one of the reasons why the Mg 2q partition coefficient in naturally occurring marine calcite cements is reported to be much higher Žaverage 12 mol% MgCO 3 . than that obtained under controlled laboratory conditions from natural or artificial seawater on pure calcite seeds at 258C Žaverage 8 mol% MgCO 3 .. The natural conditions allow the reactions between the natural waters and natural calcite surfaces to occur over a geological time scale so that the stable crystal morphology may have been achieved. On the other
Ž1. The inhibition of calcite growth by the presence of Mg 2q is caused by the Mg 2q being non-uniformly incorporated into the calcite crystal surface and developing new crystal surfaces which have a higher Mg 2q density and lower growth rate than that on the original calcite seed surfaces. These slower growing faces dominate the morphology of the growing crystals. This can be the reason why marine calcites have a higher Mg 2q content than that obtained by seeded experiments under the same environmental conditions. Ž2. The calcite growth rate constant in the presence of Mg 2q may not be determined accurately by a pH-free-drift method using pure calcite seeds, because a stable morphology of the crystals may not be established at the initial stage of the crystal growth. Even if the crystals are allowed to reach their stable morphology, the surface area will have changed significantly. However, it can be determined accurately using a steady state method such as our visual observation method.
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Acknowledgements The authors are grateful to Harry Shaw and Carlos Grattoni of Imperial College for helpful discussion and advice. The authors thank the referees who thoroughly reviewed this paper and gave many valuable suggestions. This work was financially supported by the EU Joule III QC-Scale project. [SB] References Akin, G.W., Lagerwerff, J.V., 1965. Calcium carbonate equilibria in aqueous solutions open to the air: II. Enhanced solubility of CaCO 3 in the presence of Mg 2q and SO42y. Geochim. Cosmochim. Acta 29, 353–360. Bates, R.G., 1964. Determination of pH — Theory and Practice, Wiley, 123–124. Beck, J.W., Berndt, M.E., Seyfried, W.E., 1992. Application of isotopic doping techniques to evaluation of reaction kinetics and fluidrmineral distribution coefficients: an experimental study of calcite at elevated temperatures and pressures. Chemical Geology 97, 125–144. Berner, R.A., 1975. The role of magnesium in the crystal growth of calcite and aragonite from seawater. Geochim. Cosmochim. Acta 39, 489–504. Berner, R.A., 1978. Equilibrium, kinetics, and the precipitation of magnesium calcite from seawater. Am. J. Sci. 278, 1475–1477. Dawe, R.A., 1990. Reservoir Physics at the Pore Scale, Seventyfive Years of Progress in Oil Field Science and Technology. Balkema, Rotterdam, 177–194. Dawe, R.A., Grattoni, C.A., 1998. The visualisation of the pore scale physics of hydrocarbon recovery from reservoirs. First Break 16, 371–386. Dawe, R.A., Zhang, Y., 1997. Kinetics of calcium carbonate scaling — observations from glass micromodels. J. Pet. Sci. Eng. 18, 179–187. Dove, P.M., Hochella, M.F., 1993. Calcite precipitation mechanisms and inhibition by orthophosphate: in situ observations by scanning force microscopy. Geochim. Cosmochim. Acta 57, 705–714. Dromgoole, E.L., Walter, L.M., 1990. Inhibition of calcite growth rates by Mn2q in CaCl 2 solutions at 10, 25, and 508C. Geochim. Cosmochim. Acta 54, 2991–3000. Folk, R.L., 1974. The natural history of crystalline calcium carbonate: Effect of magnesium content and salinity. J. Sediment. Petrol. 44, 43–53. Garrels, R.M., Wollast, R., 1978. Discussion of: equilibrium criteria for two-component solids reacting with fixed composition in an aqueous phase example: the magnesium calcites. Am. J. Sci. 278, 1469–1474. Glover, E.D., Sippel, R.F., 1967. Synthesis of magnesium calcites. Geochim. Cosmochim. Acta 31, 603–614. Gonzalez, L.A., Carpenter, S.J., Lohmann, K.C., 1992. Inorganic ´ calcite morphology: roles of fluid chemistry and fluid flow. J. Sediment. Petrol. 62, 382–399.
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Griffioen, J., Appelo, C.A.J., 1993. Nature and extent of carbonate precipitation during aquifer thermal energy storage. Applied Geochemistry 8, 161–176. Hartley, G., Mucci, A., 1996. The influence of pCO 2 on the partitioning of magnesium in calcite overgrowths precipitated from artificial seawater at 258C and 1 atm total pressure. Geochim. Cosmochim. Acta 60, 315–324. Hartman, P., 1973. Crystal Growth: An Introduction. In: Hartman, P. ŽEd.., Amsterdam North-Holland Publ. ŽNorth-Holland series in Crystal Growth, Vol. 1.. House, W.A., Howson, M.R., 1988. Crystallisation kinetics of calcite in the presence of magnesium ions. J. Chem. Soc. Faraday, Trans. 1 84, 2723–2734. Howson, M.R., Pethybridge, A.D., House, W.A., 1987. Synthesis and distribution coefficient of low-magnesium calcites. Chemical Geology 64, 79–87. Katz, A., 1973. The interaction of magnesium with calcite during crystal growth at 25–908C and one atmosphere. Geochim. Cosmochim. Acta 37, 1563–1586. Kharaka, Y.K., Gunter, W.D., et al., 1988. Solmineq88: a computer program for geochemical modelling of water–rock interactions. U.S. Geological Survey, Water-Resources Investigations Report, CA, 88–4221. Kinsman, K.J.J., Holland, H.D., 1969. The co-precipitation of cations with CaCO 3 : IV. The co-precipitation of Sr 2q with aragonite between 16 and 968C. Geochim. Cosmochim. Acta 33, 1–17. Markov, I.V., 1995. Crystal Growth for Beginners — Fundamentals of Nucleation, Crystal Growth and Epitaxy. World Scientific. Morse, J.W., Mackenzie, F.T., 1990. Geochemistry of Sedimentary Carbonates. Elsevier. Mucci, A., 1987. Influence of temperature on the composition of magnesian calcite overgrowths precipitated from seawater. Geochim. Cosmochim. Acta 51, 1977–1984. Mucci, A., Morse, J.W., 1983. The incorporation of Mg 2q and Sr 2q into calcite overgrowths: influences of growth rate and solution composition. Geochim. Cosmochim. Acta 47, 217– 233. Paquette, J., Reeder, R.J., 1995. Relationship between surface structure, growth mechanism and trace element incorporation in calcite. Geochim. Cosmochim. Acta 59, 735–749. Paquette, J., Vali, H., Mucci, A., 1996. TEM study of Pt–C replicas of calcite overgrowths precipitated from electrolyte solutions. Geochim. Cosmochim. Acta 60, 4689–4699. Plummer, L.N., Mackenzie, F.T., 1974. Predicting mineral solubility from rate data: application to the dissolution of magnesium calcites. Am. J. Sci. 274, 61–83. Reddy, M.M., Gaillard, W.D., 1981. Kinetics of calcium carbonate Žcalcite.-seeded crystallisation: influence of solidrsolution ratio on the reaction rate constant. J. Colloid Interface Sci. 80, 171–177. Reeder, R.J., Grams, J.C., 1987. Sector zoning in calcite cement crystals: implications for trace element distributions in carbonates. Geochim. Cosmochim. Acta 51, 187–194. Staudt, W.J., Reeder, R.J., Schoonen, M.A.A., 1994. Surface structural controls on compositional zoning of SO42y and
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SeO42y in synthetic calcite single crystals. Geochim. Cosmochim. Acta 58, 2087–2098. Thorstenson, D.C., Plummer, L.N., 1977. Equilibrium criteria for two-component solids reacting with fixed composition in an aqueous phase — example: the magnesium calcites. Am. J. Sci. 277, 1203–1223. Zhang, Y., Dawe, R.A., 1998. The kinetics of carbonate scaling in
high salinity water systems. Applied Geochemistry 13, 177– 184. Zhang, Y., Shaw, H., Farquhar, R., Dawe, R.A., 1999. The kinetics of carbonate scaling — application for the prediction of downhole carbonate scaling. SPE Oilfield Scale Symposium, Aberdeen, 27–28 January.
Influence of Mg 2q on the kinetics of calcite precipitation and calcite crystal morphology Yuping Zhang ) , Richard A. Dawe
1
The Centre for Petroleum Studies, TH Huxley School, Imperial College, London, SW7 2BP, UK Received 21 July 1998; accepted 29 April 1999
Abstract The kinetics of calcite growth in the presence of Mg 2 has been studied by both a pH free drift method and by visual observation. Our experiments show that the calcite growth rate is reduced by the presence of Mg 2q. The higher the MgrCa ratio in the solution, the lower the growth rate in a CaCO 3 supersaturated solution. The inhibition of calcite growth by the presence of Mg 2q is caused by Mg 2q being incorporated into the original calcite seed surfaces and developing new crystal surfaces. The Mg 2q distribution on the calcite surfaces is not uniform as there is likely to be different Mg 2q densities on the newly developed surfaces than on the original surfaces of the calcite seeds. This causes the calcite crystal morphology to change. The significance of creating error in using the initial rate data rather than the equilibrium rate data for the prediction of the calcite precipitation kinetics is discussed. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Calcite precipitation; Mg 2q inhibition; Kinetics; Morphology; Marine calcite cements; Calcium carbonate
1. Introduction The kinetics of calcite precipitation is important in many hydrogeochemical environments and chemical engineering operations ŽMorse and Mackenzie, 1990.. Errors in the determination of calcite precipitation rates will clearly affect the predicted mass of precipitation in a given time interval, and will thus,
)
Corresponding author. Read Well Services, Offshore Technology Park, 1 Claymore Avenue, Aberdeen AB23 8GW, UK. E-mail: [email protected] 1 Present address: Petroleum Engineering, University of West Indies, St. Augustine, Trinidad, West Indies. E-mail: [email protected].
affect predictions of geological crystal growth and scaling within chemical plants. Many studies have shown that the calcite precipitation rate can be inhibited by the presence of Mg 2q ŽAkin and Lagerwerff, 1965; Mucci and Morse, 1983; Reeder and Grams, 1987; House and Howson, 1988; Morse and Mackenzie, 1990; Dromgoole and Walter, 1990; Paquette and Reeder, 1995; Paquette et al., 1996.. A possible reason is that Mg 2q ions can be incorporated into the calcite crystal lattices at Ca2q ion sites which then affect the morphology of the crystal and thence its growth. The rate reduction has been suggested to be approximately proportional to the concentration ratio of Mg 2q ions with Ca2q ions in the solution ŽMorse and Mackenzie, 1990.. The amount of Mg 2q being incorporated may be influenced by
0009-2541r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 5 4 1 Ž 9 9 . 0 0 0 9 7 - 2
130
Y. Zhang, R.A. Dawe r Chemical Geology 163 (2000) 129–138
the local solution chemistry and the precipitation rate as well as temperature ŽKatz, 1973; Folk, 1974; Plummer and Mackenzie, 1974; Thorstenson and Plummer, 1977; Garrels and Wollast, 1978; Mucci, 1987; Howson et al., 1987; Morse and Mackenzie, 1990; Beck et al., 1992; Griffioen and Appelo, 1993; Hartley and Mucci, 1996.. However, the reported magnesium content of calcite precipitated in the laboratory from seawater is highly variable ŽGlover and Sippel, 1967; Kinsman and Holland, 1969; Berner, 1978; Garrels and Wollast, 1978; Mucci, 1987; Mucci and Morse, 1983.. Table 1 lists some examples of reported magnesium content in calcite precipitated from seawater from different studies. As we can see, the values obtained from most of the laboratory experiments are lower than those from natural calcite. In recent years, the studies have focused on the influence of crystal surface structure on the determination of the empirical partition coefficient for ‘‘foreign’’ ions incorporated into the calcite ŽDove and Hochella, 1993; Staudt et al., 1994; Paquette and Reeder, 1995; Paquette et al., 1996.. The path-dependent and non-equilibrium aspects of foreign ion incorporation during crystal growth have been considered as important factors in determining experimentally observed Mg 2q partition coefficients in calcite ŽPaquette and Reeder, 1995.. It has been clearly identified that the presence of Mg 2q modifies the morphology of calcite crystals ŽFolk, 1974; Gonzalez ´ et al., 1992; Paquette et al., 1996.. However, there does not appear to be a relationship between changes in crystal morphology and Mg 2q content on the crystal surfaces. These factors make the prediction of the calcite growth rate from currently available thermodynamic and kinetic data
complicated and liable to error. In this study we have examined the connection between the calcite seed morphology change and its growth kinetics in order to establish a proper experimental method to determine calcite growth rate in the presence of Mg 2q ion.
2. Experimental methods The experimental methods used in this study are a pH free drift method and a visual micromodel observation method. These have been used in our previous studies ŽDawe and Zhang, 1997 and Zhang and Dawe, 1998., so we shall only review them briefly here. 2.1. pH Free drift method When calcite precipitation occurs, the crystal growth rate can be determined from the calcium ion concentration change as a function of time, i.e., R m A yd w Ca2q x rdt
Ž 1. 2q x
where R m is the calcite growth rate, wCa is the concentration of calcium ions and t is time. In a closed system Ži.e., when there is no mass exchange between the solution and the environment., the solution pH change rate will depend only on the CaCO 3 precipitation rate ŽZhang and Dawe, 1998.. Therefore, the precipitation rate can be determined by measuring the rate of solution pH decrease ŽdpHrdt . which then can be converted to the calcium ion concentration changes as a function of time ŽdwCa2q xrdt . using the equations given in ŽZhang and Dawe, 1998.. In this earlier study, we demon-
Table 1 The magnesium content of calcite from seawater obtained from different studies Method 2y HCOy added drop by drop Ž08C. 3 q CO 3 pH-state at constant S R.G. calciteq CO 2 , then degas by diffusion pH-state at constant S 2y HCOy added Ž08C. 3 q CO 3 Natural magnesium calcite Ž161 samples.
Nuclei
Time to precipitate
S
MgCO 3 Žmol%.
Reference
glass dust reagent calcite reagent calcite reagent calcite glass dust
days 10–50 h ; 3 days 2–24 h minutes
; 50 5–7 NA 8–11 ) 200
0–1 7–10 9–10 8.1 " 1 14 12–15
Kinsman and Holland, 1969 Berner, 1975 Berner, 1978 Mucci and Morse, 1983 Glover and Sippel, 1967 Garrels and Wollast, 1978
Y. Zhang, R.A. Dawe r Chemical Geology 163 (2000) 129–138
strated that the calcite growth rate from supersaturated solutions without inhibitors can be described by, R m s k pm Ž S 0.5 y 1 .
n
Ž 2.
where k pm is the precipitation rate constant in molrm2 h kg, n is an apparent reaction order and S is the calcite supersaturation which is defined as: S s Ž Ca2q . Ž CO 32y . rK sp
Ž 3.
where K sp is the solubility product and Ž i . represents the activity of ith species. Sometimes the saturation index, SI Žs log S ., is preferred to represent the saturation level. When S s 1 or SI s 0, the water system is at equilibrium. As calcite crystals grow, the total surface area increases. This has been considered in the calcite growth rate calculations. If we assume that all the calcite crystal surfaces have the same activity for growth, the total calcite crystal surface area at time t should be A t s A i Ž Wi q Ž PPTt . 100 . rWi
2r3
Ž 4.
where A i and A t are the surface area of the calcite seeds at the beginning and at the time t, respectively; Wi is the initial seed weight in grkg H 2 O, and PPTt is the amount of CaCO 3 Ž M s 100 grmol. precipitate at the time t in molrkg. The crystal growth rate as a function of supersaturation can be obtained by plotting wdCCa 2q .rdt xrVA t against Ž St0.5 y 1., where V is the volume of the solution used in a experiment.
131
The pH free drift experiments were conducted in a 250 ml multiple port and double-walled vessel which was connected to a recirculating constant temperature water bath kept at 258C. A schematic diagram of the pH-free drift equipment is shown in Fig. 1. The supersaturated calcium carbonate solutions were prepared by mixing equal volumes of CaCl 2 and NaHCO 3 solutions which were each twice the required final concentration. When Mg 2q was required, the appropriate amount of MgCl 2 was added to the CaCl 2 solutions to achieve the desired wMg 2q xrwCa2q x ratio. The desired pH was obtained by bubbling in CO 2 to lower the pH or N2 to increase the pH. Water from the water bath was circulated to the reaction vessel until the solution reached the experimental temperature Ž258C., and then the solution pH was measured. After the solution pH remained stable for 30 min, 0.08–0.2 g calcite seeds was added to the solution, and the vessel was then completely closed without a gas phase at the top of the vessel. The pH change accompanying the calcite growth was measured and recorded by an automatic titrator as a function of time immediately after the seed had been added to the CaCO 3 supersaturated solution. 2.2. The Õisual obserÕation method The CaCO 3 crystal growth rate can also be determined by measuring the change in a single crystal size over timed intervals ŽDawe and Zhang, 1997..
Fig. 1. Schematic diagram of the pH-free drift equipment.
Y. Zhang, R.A. Dawe r Chemical Geology 163 (2000) 129–138
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Fig. 2. The pattern of glass micromodel.
These calcite precipitation experiments were conducted in etched glass micromodels, which are twodimensional flowing systems with specially designed patterns etched onto a glass plate with a second flat glass sintered onto it. The details of how to make a glass micromodel are given by Dawe Ž1990. and Dawe and Grattoni Ž1998.. The pattern used in this study is one of parallel straight channels with different widths ŽFig. 2.. A schematic representation of the experimental system is given in Fig. 3. Calcite seeds were placed into a micromodel by injecting a seed suspended solution through the micromodel. A calcite supersaturated solution is then continuously injected through the micromodel. The changes in the crystal sizes during their growth were observed and recorded through a light microscope as a function of time. The crystal layer growth rate can be represented by: R L A d xrdt Ž 5. Ž . and is obtained by the same form of Eq. 2 with n s 2, i.e.: R L s k pl Ž S 0.5 y 1 .
2
Ž 6.
where R L is the crystal layer growth rate in mrs and d x is the layer increment of a crystal face in a time interval of d t, k pl is the rate constant of layer growth
rate in mrs. The mass rate R m can be converted into layer growth rate R L if the geometry of the crystals are known. For calcite crystals, the approximate conversion can be made if we assume that the calcite crystals are of cubic shape: Vc rc 1 rc R L Rm s s Ž 7. Sc M 3 M where Vc and Sc are the total volume and surface area of calcite crystals, rc is the density of calcite crystals in grcm3, M is molecular weight of calcite Ž100 grmol., R l in cmrh, so that the unit of R m will be molrm2 h kg. The CaCO 3 supersaturated solutions were made by injecting two solutions from two syringes fixed on a syringe injection pump. One solution contained twice the amount of the required calcium ion Žand magnesium ion. and the other twice the amount of carbonate alkalinity. The solution injection rate and the amount of calcite seeds were adjusted to a level at which the amount of lattice ions consumed for growth was much lower than that supplied Ž- 1%., so that the saturation inside the micromodel could be considered as constant. The solution pH at 258C was determined separately after mixing equal volumes of the two preheated solutions Ž258C. in a bottle with only one port which can be sealed by the pH electrode itself to avoid degassing. The saturation index was calculated using Solmineq88 ŽKharaka et al., 1988.. The chemicals used in all of our experiments were BDH AnalaR laboratory reagents. The calcite seeds were BDH AnalaR CaCO 3 powder which contain more than 99% of calcite as determined by X-ray diffraction analysis. It had a specific surface area of 5.88 m2rg determined by BET using a Coulter
Fig. 3. Schematic diagram of the micromodel experimental system.
Y. Zhang, R.A. Dawe r Chemical Geology 163 (2000) 129–138
133
Omnisorp 100, a volumetric adsorption instrument, and nitrogen gas as adsorbate at liquid nitrogen temperatures. The pH electrode was calibrated by two NBS buffers at the beginning of each experiment. Electrode drift was examined at the end of each experiment using one pH buffer. The residual liquid junction caused by high ionic strength solutions was corrected using the Henderson equation ŽBates, 1964.. 3. Results and discussion Calcite growth rates for solutions with a range of wMg 2q xrwCa2q x ratios between 0 and 5 and with two different seed concentrations were determined by the pH free drift method. Table 2 summarises the solution compositions and the measured calcite growth rate interpreted by Eqs. Ž2. – Ž4.. As we can see from Table 2, the presence of Mg 2q reduces the calcite growth rate, and causes the reaction order n to increase and the rate constant k p to decrease. The rate reduction is proportional to the ratio of wMg 2q xrwCa2q x in the solution. The rate data obtained from the solutions containing Mg 2q cannot be interpreted by rate Eq. Ž2. very well as shown in Fig. 4. We can see from Fig. 4 that the initial precipitation rates are similar for all three water systems. However, for the water systems with Mg 2q present ŽNos. 5 and 6 in Table 2., the precipitation rates decrease as the supersaturation dropped and the apparent reaction order n increased with decreasing supersaturation. The reaction orders given in Table 2 are the average values over the whole time intervals. It is also interesting to note that the calcite growth rates are affected by the calcite seed concentration
Fig. 4. The measured calcite growth rate data plotted as a function of relative saturation Ž S 0.5 y1.. Curve Ž1., calcite growth rate in a supersaturated solution without Mg 2q; curves Ž2. and Ž3., the solution wMg 2q xrwCa2q x s1 and seed concentrations were 0.8 grl and 0.32 grl, respectively.
when a solution contains Mg 2q. The rate constants obtained at the lower calcite seed concentration were lower than those at the higher seed concentration Žcurve 3 of Fig. 4., whereas there was no significant influence of seed concentrations in a simple water systems without Mg 2q Žcomparing experiments Nos. 1 and 2 in Table 2.. Reddy and Gaillard Ž1981. studied the influence of calcite seed concentration on the calcite precipitation rate constant. They noticed that the rate constant is independent of the solidrsolution ratio when the calcite seed concentrations were above 0.3 grl, and it is higher at low seed concentrations. They suggested that this is because the contribution of surface nucleation andror secondary nucleation is relatively significant at low seed concentrations. The calcite seed concentration used in our experiments were 0.3–0.8 grl and the specific
Table 2 The effect of Mg 2q on calcite growth rates at 258C and different calcite seed concentrations No.
pH i
wMg 2q x Žmmolrkg.
Al k T Žmeqrkg.
wCa2q x Žmmolrkg.
SI
kp n R m s k p Ž S 0.5 y 1. n
Seed Žgrl.
1 2 3 4 5 6 7 8
7.68 7.75 7.81 7.79 7.81 7.87 7.74 7.82
0 0 1.0 2.8 5.5 5.1 25 27
10.9 10.6 10.9 11.6 11.1 11.4 11.3 11.5
5.40 5.52 5.31 5.61 5.57 5.60 5.59 5.76
0.733 0.795 0.847 0.875 0.851 0.936 0.758 0.825
0.820 0.850 0.519 0.611 0.133 0.262 0.010 0.008
0.32 0.80 0.32 0.80 0.32 0.80 0.32 0.80
1.86 1.87 3.03 3.00 4.29 3.24 6.52 6.07
Y. Zhang, R.A. Dawe r Chemical Geology 163 (2000) 129–138
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Table 3 The calcite growth rate at different ratios of wMg 2q xrwCa2q x at 258C a No.
pH
wCa2q x Žmmolrkg.
wHCOy x 3 Žmmolrkg.
wMg 2q xr wCa2q x
SI
RL Ž mrs = 10 10 .
kp Ž mrs = 10 10 .
1 2 3 4
8.05 8.01 8.05 8.05
2.52 2.52 2.52 2.60
5.09 5.09 5.09 5.03
0 0.1 0.5 1.0
0.75 0.71 0.74 0.76
1.47 0.673 0.695 0.395
0.769 0.421 0.378 0.201
a
NaCl s 0.09 molrkg, ionic strength was 0.1 eqrkg.
surface area of calcite seeds was much higher than that used by Reddy and Gaillard Ž5.9 and 1.0 m2rg, respectively.. Therefore, the rate constants obtained from our pH free drift method should not be influenced by surface nucleation. Our low rate constants obtained at the lower seed concentration with Mg 2q present imply that there is a relationship between the rate constant and the crystal size. This is because the lower the seed concentration the larger the final crystal size will be when a free drift method is used for solutions with the same supersaturation. The study by Mucci and Morse Ž1983. suggested that the higher the wMg 2q xrwCa2q x ratio in the solution, the more Mg 2q is incorporated into the calcite crystals and the calcite growth rate will be lower. This indicates that the reduction in calcite growth rate is proportional to the amount of Mg 2q incorporated into the calcite crystal surface. If calcite growth rates decrease with increasing crystal size as the result of the presence of Mg 2q, the average Mg 2q density on the crystal surfaces Žthe numbers of Mg 2q ions on one unit of surface area. must be gradually increasing as the crystal size is increasing.
Fig. 5. Calcite crystals obtained from Ž1. a supersaturated solution without Mg 2q ; Ž2 . wMg 2q xr wCa 2q x s 0.5, 258C, Ž3 . wMg 2q xrwCa2q x s 0.5, 408C.
To understand why the calcite growth rate is affected by the presence of Mg 2q and calcite seed concentration, we observed the process of calcite crystal growth inside a glass micromodel under a microscope and measured the crystal geometric size change as a function of time. The results show that the calcite layer growth rates decrease with increasing ratios of wMg 2q xrwCa2q x ŽTable 3.. We also observed that the seed crystal morphology gradually changed from the original rhomobohedral to other morphologies as shown in Fig. 5. New faces were developed from the edges Žcrystal No. 2 of Fig. 5. or the corners Žcrystal No. 3 of Fig. 5. of the original surfaces of calcite seeds. To explain a crystal morphology change, a simple crystal model is used here. In this crystal model, the surfaces of a crystal are classified into three groups, F Žflat., S Žstepped. and K Žkinked. surfaces ŽHartman, 1973; Markov, 1995. as shown in Fig. 6. The K and S surfaces can be considered as full of kinks and steps, respectively. It is obvious that the highest growth rate will be achieved at the K surface, then the S surface, and finally by the F surface. Therefore, the K and S surfaces are normally absent from equilibrium crystal morphologies ŽHartman, 1973..
Fig. 6. A schematic representation of a crystal illustrating F Žflat., S Žstepped. and K Žkinked. surfaces depending on whether they are parallel to two or one most dense rows of atoms, or are not parallel to any of the most dense rows of atoms, respectively.
Y. Zhang, R.A. Dawe r Chemical Geology 163 (2000) 129–138
Our experimental results show that new faces started to appear on the edges of rhomobohedral calcite crystal when Mg 2q was present in the solution. Similar morphological changes as the result of the presence of Mg 2q have been observed by Paquette et al. Ž1996.. The pictures presented in their paper show the initial stage of new surfaces developing at the corners and edges of calcite seed 10144 faces. Paquette and Reeder Ž1995. suggest that there are geometrically different types of surface sites on the original surfaces of the calcite seeds. Mg 2q has a higher affinity for some of these sites and it is adsorption or perhaps dehydration during incorporation that preferentially slows down growth in specific directions, for example towards the edges and corners as identified by Fig. 1 of Paquette et al. Ž1996.. As a consequence of inhibition by Mg 2q, new crystal faces will be developed, and these faces are dominated by the type of surface sites for which Mg 2q has a higher affinity, eventually creating the morphology changes. If the faces developed on the edges and corners are the S and K faces, one may want to know what can cause the growth rate to slow down on those surfaces with a high density of kink sites. One possibility is that the Mg 2q density on the newly developed surfaces is higher than that on the original surfaces of the calcite seeds. As a high Mg 2q density gives a lower growth rate, the relative growth rate on the F face can be higher than those on the other two faces and eventually disappear. The experimental results from Reeder and Grams Ž1987. and Paquette and Reeder Ž1995. support our hypotheses. They studied the relationship between the crystal surface structure and foreign cations incorporated into calcite, and measured the Mg 2q density on different surfaces of magnesium calcite by EPMA Želectron probe microanalysis. and SXRFMA ŽX-ray fluorescence microanalysis.. They found there was a differential partitioning of Mg 2q incorporation on different faces, and this difference can be a factor of 3–4 under their experimental conditions. As the crystal morphology is gradually changing from low-Mg-content face dominant to high-Mgcontent face dominant, the average Mg 2q density on the entire calcite surface area will gradually increase, and the overall calcite growth rate on the calcite crystal surfaces at a constant supersaturation and
135
ratio of wMg 2q xrwCa2q x will gradually decrease. As the slower growing faces become more dominant, they make an increasing contribution to the overall measured growth rate. Then, as the result of the crystal morphology gradually changing, a lower rate constant and a higher empirical reaction order will appear in the rate equation when a free drift experimental method is used. As a stable rate constant may only be obtained when the crystal seeds have reached their stable morphology, the calcite growth rate and reaction order determined under this stage will only then truly represent the calcite growth kinetics. These are the values that should be used in any calculation of calcite precipitation under natural conditions. The crystal seed morphology change caused by the presence of Mg 2q can be a slow process. As we can see, the crystal No. 2 in Fig. 5 has not reached its stable morphology at a such large size Ž50–70 mm. because the F faces have not disappeared completely. We can expect that the final morphology of crystal No. 2 could be a pyramidal shape as shown in Fig. 7. Some recent experiments were aimed to check the kinetic model of calcium carbonate scaling by flowing a CaCO 3 supersaturated solution through a steel tube ŽZhang et al., 1999.. Thus, the picture of crystals from SEM shows us a type of stable morphology of calcite precipitate with Mg 2q in the solution at wMg 2q xrwCa2q x ratio of 0.5 ŽFig. 8.. The precipitation started from heterogeneous nucleation sites on metal surface and calcium carbonate scale formed as a consequence. In this case, the morphology of the precipitate is similar to our expected final morphology of No. 2 in Fig. 5. It is very rare that a crystal will grow to such a large size as we were able to in our visual observation experiments during the typical calcite mass deposit experiments as reported in the literature. For example, Mucci and Morse Ž1983. carried out some
Fig. 7. The calcite crystal morphology at the beginning Ža., middle Žb. and final Žc. stages of the morphology change as the result of present of Mg 2q in a solution.
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hand, under laboratory conditions the average Mg 2q partition onto the pure calcite seeds increases during the morphology transfer. When the growth rates are measured at the different stages of the morphology change, different growth rate constants will be obtained. We believe that once the crystal morphology reaches its equilibrium state, the crystal growth rate will become constant and the amount of Mg 2q incorporated at this stage will be uniform. Thus, the calcite growth rate constant in the presence of Mg 2q Žor other inhibitors. cannot be determined by a pHfree-drift method. This is because the total surface area of the crystal will have changed and the newly formed crystal morphology will depend on the water compositions and experimental conditions. The rate constant of calcite growth with Mg 2q incorporation cannot be obtained with confidence with uncertain calcite surface areas. However, it can be determined more accurately using a steady state method such as our visual observation method.
Fig. 8. Calcite crystals obtained from a supersaturated solution with wMg 2q xrwCa2q x s 0.5, 708C, saturation index s 0.6, started from a heterogeneous nucleation on a steel surface.
4. Conclusion precipitation experiments and, in order to avoid significant surface area variations during the calcite growth rate measurements, limited the amount of overgrowth precipitation to less than 10% of the initial seed weight. It is obvious that the growth rate determined at this initial stage of calcite seed morphology change will be higher than that when the morphology changes are complete. If the Mg 2q partition coefficient is determined at the early stage of the morphology change, the value will be lower than that at the equilibrium conditions. This may be one of the reasons why the Mg 2q partition coefficient in naturally occurring marine calcite cements is reported to be much higher Žaverage 12 mol% MgCO 3 . than that obtained under controlled laboratory conditions from natural or artificial seawater on pure calcite seeds at 258C Žaverage 8 mol% MgCO 3 .. The natural conditions allow the reactions between the natural waters and natural calcite surfaces to occur over a geological time scale so that the stable crystal morphology may have been achieved. On the other
Ž1. The inhibition of calcite growth by the presence of Mg 2q is caused by the Mg 2q being non-uniformly incorporated into the calcite crystal surface and developing new crystal surfaces which have a higher Mg 2q density and lower growth rate than that on the original calcite seed surfaces. These slower growing faces dominate the morphology of the growing crystals. This can be the reason why marine calcites have a higher Mg 2q content than that obtained by seeded experiments under the same environmental conditions. Ž2. The calcite growth rate constant in the presence of Mg 2q may not be determined accurately by a pH-free-drift method using pure calcite seeds, because a stable morphology of the crystals may not be established at the initial stage of the crystal growth. Even if the crystals are allowed to reach their stable morphology, the surface area will have changed significantly. However, it can be determined accurately using a steady state method such as our visual observation method.
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