A mechanistic model for calcite crystal growth using surface speciation

Geochimica et Cosmochimica Acta, Vol. 63, No. 2, pp. 217–225, 1999 Copyright © 1999 Elsevier Science Ltd Printed in the USA. All rights reserved 0016-7037/21801 $20.00 1 .00

Pergamon

PII S0016-7037(99)00026-5

A mechanistic model for calcite crystal growth using surface speciation ¨ . NILSSON,*,1 and J. STERNBECK2 O 1

Department of Geology and Geochemistry, Stockholm University, Stockholm, Sweden 2 Swedish Environmental Research Institute (IVL), Stockholm, Sweden (Received July 6, 1998, accepted in revised form January 8, 1999)

Abstract—A new mechanistic model for the crystal growth kinetics of calcite is presented, accounting for the presence of various surface complexes. Calcite crystal growth rates were determined with the constant composition method at Vc (calcite supersaturation) values of 1.5–9.8. In general the rate increases with Vc, 21 but variations in CO2 partial pressures and the (CO22 ) ratio also have a major effect on the crystal 3 )/(Ca growth rate. These effects are eliminated by assuming that calcite crystal growth proceeds through three reversible reactions, in which CaCO03(aq) and Ca21(aq) are incorporated at specific surface complexes. The model derived rates closely follow the experimental rates over the entire experimental range (r 5 0.996, n 5 23). The obtained rate constants indicate that CaCO03(aq) is '20 times more reactive than Ca21(aq) at the calcite-water interface. This agrees with the fact that dehydration of metal ions precedes crystal growth and, in analogy with other metal-ligand complexes, the CO22 ligand will increase the rate of water exchange 3 of Ca. This model is a modified version of a rhodochrosite crystal growth model (Sternbeck, 1997) which allows for the comparison of reaction mechanisms and rate constants. The rate constants for incorporation of CaCO03(aq) at the mineral surface are 55 to 270 times higher than for MnCO03(aq). This difference can not likely be explained by the water exchange rates, but may be due to the fact that ligand exchange mechanisms for Ca and Mn differ. Copyright © 1999 Elsevier Science Ltd Because the functional groups of mineral surfaces are dependent on solution composition, and thus may vary between different experiments in a dataset, mechanistic-rate laws of heterogeneous reactions should account for these changes. This may be accomplished by using surface speciation theory, which has greatly improved kinetic descriptions of the dissolution rate of, e.g., metal oxides and silicates (Stumm et al., 1987; Stumm and Wieland, 1990). Previous studies on the kinetics of calcite have often emphasized the importance and need of surface speciation (Morse, 1986; Chou et al., 1989; Brady et al., 1996), but the lack of reliable surface stability constants in combination with the limited knowledge of the calcite surface has prevented the use of the surface speciation theory. However, a study of the calcite-water interface using X-ray photoelectron spectroscopy (XPS) and low energy electron diffraction (LEED) suggested the occurrence of the surface complexes §CO3H (§ symbolises the mineral surface) and §CaOH (Stipp and Hochella, 1991). Based on these findings and pHzpc data for three carbonate minerals, Van Cappellen and coauthors (1993) presented a surface complexation model for the chemical structure and reactivity at the carbonate-water interface. This model postulated the formation of several different surface complexes as a result of reactions between the surface complexes §CO3H and §MeOH and the soluble species 0 Me21, H1, and CO2. It was shown that §CO2 3 , § MeHCO3 and 2 §MeCO3 dominated the mineral surface at pH values between 6 and 9 and at high Pco2. As Pco2 decreases the concentrations 1 of §MeHCO03 and §MeCO2 3 decreases in favour of §MeOH2 . Based on atomic force microscopy measurements, Stipp and coauthors (1994) presented a detailed drawing of the molecular structure of the calcite surface. In the light of this more recent finding, the charge that Van Cappellen and coauthors (1993) attributed to the surface complexes may be questioned. They assume that the surface cations have a residual charge of 11,

1. INTRODUCTION

Carbonate minerals are ubiquitous in surficial aquatic environments and play a central role in the regulation of pH and alkalinity. Calcite is also an efficient scavenger of trace elements such as Cd (Tesoriero and Pankow, 1996) and Mn (Boyle, 1983; Thomson et al., 1986). Being one of the most common minerals in marine sediments (Morse and Mackenzie, 1990) the trace element composition of calcite is frequently used to unravel past sedimentary and oceanographic conditions (e.g., Morse and Mackenzie, 1990; Lea and Boyle, 1991; Carpenter and Lohmann, 1992; Hastings and Emerson, 1996). However, a number of studies have shown that the incorporation of trace elements into calcite may be kinetically controlled (Lorens, 1981; Mucci and Morse, 1983; Tesoriero and Pankow, 1996). These findings emphasize the importance of understanding the reaction mechanisms at the mineral surface of calcite and other isomorphous carbonate minerals. Information on reaction mechanisms may be gained either by detailed kinetic studies or by surface sensitive spectroscopic methods. For calcite a number of experimental studies have been performed over a wide range of saturation states, ionic strengths, pH values and solution compositions including various metals and organic compounds (Morse, 1986; Dromgoole and Walter, 1990; Shiraki and Brantley, 1995). Two major categories of kinetic models have been used to describe the crystal growth and dissolution of calcite: affinity-based rate laws and mechanistic-rate laws. Affinity-based rate laws relate kinetics to the free energy of reaction (saturation state), while mechanistic-rate laws describe the rate as a function of one or several elementary reactions.

Author to whom correspondence ([email protected])

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which is only possible if three out of six bonds are dangling. According to the interpretation of Stipp and coauthors (1994), the residual charge of the cation at a flat terrace is rather 12/3, which results in §CaCO21.33 , §CaHCO20.33 . However, this 3 3 knowledge has not yet been used systematically to recalibrate the original model. In this paper we therefore use the more general charges as described by Van Cappellen and coauthors (1993). Recently it was shown that the crystal growth kinetics of rhodochrosite could be explained by using surface complexation (Sternbeck, 1997). In particular, the use of surface complexation explained the dependence of rhodochrosite crystal 21 growth kinetics on Pco2 and on the (CO22 ) ratio in the 3 )/(Mn solution. The objectives of the present research were to: (1) explain the kinetics of calcite crystal growth using a mechanistic model based on surface complexation, (2) compare the crystal growth rate of two isomorphous carbonate minerals (calcite and rhodochrosite) and (3) examine whether the difference in reaction rates and mechanisms between these minerals can be explained by variations in the water exchange rates between the two metals. 1.1. Background to Ligand Exchange Reactions for Ca21 and Mn21 Analogies between reactions at mineral surfaces and ligand exchange reactions in solution are very useful in studies of mineral-water interactions. It has previously been shown that dissolution rates of various minerals in an isomorphous series correlate with water exchange rates of the corresponding free metal ions (Casey and Westrich, 1992). This correlation is explained by similarities between metal coordination in solution and at the mineral surface. Rate constants for water exchange between the inner sphere of metal ions and the solvent have been measured for a number of metal ions. Water exchange rates depend on charge, size and the distribution of d electrons (Burgess, 1990). For ions with ionic radii larger than 100 pm, the water exchange rate has been described as diffusion controlled which give rates between 109 and 1010 s21 (Nielsen, 1984). The calcium ion has a radius of about 100 pm and no d electrons and thus a very fast rate of about 6 3 108 s21, the smaller manganese ion which has five 3d electrons has a slower exchange rate of about 3 3 107 s21 (Stumm and Morgan, 1996). Hydrated metal ions, Me, can react with soluble ligands, L, to form 1:1 complexes according to the general reaction (Lincoln and Merbach, 1995): m21 m(H2O)m1 1 L2 3 ML(H2O)n21 1 H2O, n

(1)

where n is the number of water molecules in the inner sphere (nCa 5 8, Carugo and coauthors, 1993, and nMn 5 6, Burgess, 1990). In general the replacement of inner sphere water molecules by a monodendate or bidendate ligand is a reaction that increases the exchange rate of the remaining water molecules in the metal complex (Margerum et al., 1978; Burgess, 1990; Lincoln and Merbach, 1995; Phillips et al., 1997a,b; Casey et al., 1998). It has been proposed that the carbonate ligand increases the reactivity of various metal ions (Sternbeck, 1997;

King, 1998) and that MeCO03 complexes can be important in the crystal growth of carbonate minerals. This labilization effect has also been invoked to explain ancient dolomite crystal growth in the oceans, where the formation of strong aqueous complexes, such as MgSO04, may be a key factor in the understanding of the dolomite problem (Brady et al., 1996). The incorporation of dissolved species at mineral surfaces resembles ligand exchange (Eqn. 1), which implies that the reaction pathways involved in ligand exchange can be used to explain reactions leading to crystal growth. For ligand exchange different reaction pathways are possible depending on the importance of bond formation or bond breaking in forming the complex. If the ligand enters the inner coordination sphere before a water molecule leaves, the metal ion has an associative character. On the other hand, if a water molecule leaves the inner sphere before the ligand enters, the metal ion has a dissociative character. In between are intermediate reactions, dissociative and associative. There are no sharp boundaries and the reaction pathway can be anything between the two endmembers (Burgess, 1990). The charge of the incoming ligand is of less importance in dissociative pathways than in associative pathways (Burgess, 1990). Surface sites may be thought of as analogies to incoming ligands. Ligand exchange proceeds via a dissociative pathway for Ca21 and an associative pathway for Mn21 (Burgess, 1990; Lincoln and Merbach, 1995; Rotzinger, 1997). However, mechanistic and kinetic studies of Ca21 are rare (Lincoln and Merbach, 1995). 2. MATERIALS AND METHODS

2.1. Materials The seed material in all experiments was calcium carbonate (Merck no 1.02066) precipitated guaranteed reagent. The powder was shown to be pure crystalline calcite by XRD analysis. The specific seed surface area was determined to 0.348 6 0.004 m2 g21 with the BET method, using N2 gas adsorption. Both experimental and titrant solutions were prepared from pure analysis quality chemicals (NaHCO3, Na2CO3, CaCl2 and NaCl) and freshly deionized water (Easy Pure system, resistivity of 18 MV cm21). Before each experiment the electrode was calibrated with NBS buffer solutions (pH 4.01, 7.41 and 9.18) at the same temperature as in the experiment. Gas mixtures (N2/CO2) were obtained commercially with a CO2 partial pressure (Pco2) at a relative accuracy of 2%.

2.2. Experimental Procedure Crystal growth experiments were conducted in a 1000 ml cylindrical vessel filled with 800 ml solution. The solution was stirred with a propeller at 500 rpm and temperature was held at 25°C 6 0.1°C by the use of a thermostated water bath. All glassware and plastic were washed with a dilute HCl solution (12 h) and rinsed three times with deionized water and air dried prior to use. A constant composition method was used to study the crystal growth of calcite seeds from the experimental solution, see Sternbeck (1997) for further details. The concept for this technique is that the supersaturation of the solution remains constant throughout the whole experiment. The titrands in the experiments were 0.30 M Na2CO3 and 0.30 M CaCl2. To keep near constant ionic strength in the solution, 70 mM NaCl was used as a background electrolyte in all experiments. The Pco2 was held constant by bubbling gas of known CO2 content, 310 ppm and 1540 ppm CO2, first through water to saturate the gas with water vapour, and then through the reaction solution. The true partial pressures were about 3% lower since the gas mixtures were saturated with water. The experimental solution was prepared immediately before each experiment in order to avoid any homogenous precipitation of calcite. When the pH of the solution was constant it was assumed that

Calcite crystal growth using surface speciation

219

Table 1. Thermodynamic constants. Reaction

log K (25°C, 1 atm)

CO2(g) N CO*2(aq) 1 CO*2(aq) N HCO2 3 1 H HCO3 N CO22 1 H1 3 1 Ca21 1 HCO2 3 N CaHCO3 0 Ca21 1 CO22 N CaCO 3 3 Ca21 1 Cl2 N CaCl1 21 22 Ca 1 CO3 N CaCO3(s) Na1 1 CO22 N NaCO2 3 3 0 Na1 1 HCO2 3 N NaHCO3 H2O N OH2 1 H1

21.468 26.352 210.329 1.106 3.224 20.23 8.48 1.27 20.25 214.0

equilibrium between the gas and the solution was established. It is very important to reach equilibrium before introducing crystal seeds since any changes in uptake or loss of Pco2 will affect pH and thereby the titration rate. Equilibration times lasted about five hours for the lower pressure (310 ppm) and about one hour for the higher pressure (1540 ppm). When equilibrium was reached the carbonate burette was used to blank titrate the solution to assure that the system was stable before initiating crystal growth. This procedure did not raise pH more than 0.01 units in any run. Precipitation was initiated by introduction of calcite seeds (61 mg– 405 mg) to the supersaturated solution. The concentrations of calcite surface area in solution (m2 dm23) were sufficiently low so as not to affect the solution composition. Titrands were added automatically in response to production of H1 ions so that the measured pH was held constant (within 0.01 pH units). The rate was determined during the first 30 to 80 minutes once the rate of titrand addition became linear. Studies with scanning force microscopy (SFM) have indicated that a change from surface nucleation to spiral growth occurs after one to two hours of growth, leading to decreasing rates with time (Dove and Hochella, 1993). No such changes could be observed in this study, although the experiments lasted for two and up to six hours. Two different experiments were performed in duplicate and differed by less than 5%. In the experiments total Ca21 concentration ranged from 0.65 mM to 30.0 mM and the alkalinity ranged from 1.12 meq l21 to 6.00 meq l21. This gave pH values in the range of 7.60 to 8.84. Calcite supersatura21 tion ranged from 1.53 to 9.80 and the (CO22 ) ratio was in the 3 )/(Ca range of 2.6 3 1024 to 4.3 3 1021.

2.3. Chemical Analyses Alkalinity was determined immediately on 0.4 mm filtered samples of solution taken before and after the experiments. Alkalinity was evaluated on a Gran plot (precision 6 0.5%). The HCl used in the titration of alkalinity was adjusted with NaCl to 70 mM ionic strength and the H1 concentration was determined by calibration against a NaHCO3 solution. Alkalinity before and after an experiment mostly differed by less than 2%. Calcium concentration was determined colorimetrically by EDTA titration using calconcarboxylic acid as indicator (modified from Rump and Krist, 1992) with a relative standard deviation of 0.4% (n 5 10). There was no need to check the calcium concentration after every run since the amount of calcium and carbonate added were exactly the same throughout the experiment.

Plummer and Busenberg Plummer and Busenberg Plummer and Busenberg Plummer and Busenberg Plummer and Busenberg Ruaya (1988) Plummer and Busenberg Nordstrom et al., (1990) Nordstrom et al., (1990) Nordstrom et al., (1990)

Vc 5

(1982) (1982) (1982) (1982) (1982) (1982)

IAP Kc

(2)

where IAP is the ion activity product (Ca ) 3 (CO ) in solution. Kc is the solubility product of calcite (Plummer and Busenberg, 1982). The speciation of the calcite surface was performed with the model for carbonate minerals proposed by Van Cappellen and coauthors (1993), see Introduction in this paper. All constants used were taken from Van Cappellen and coauthors (1993). Input parameters for these calculations were Pco2, surface area (m2 dm23), ionic strength, pH and concentration of free Ca21. The values of the three latter parameters were obtained from the solution speciation. The surface speciation was calculated for each experimental run and included seven surface complexes. To get a general view of the calculated surface densities and the variation between the experiments, the maximum and minimum values for each complex are given in Table 2. The dominating species were in 2 all runs §CaOH1 2 and §CO3 . The surface complex with the largest variation between the experiments was §CaCO2 3. 21

22 3

3. RESULTS

The chemical composition of each experiment and the experimentally determined rates are presented in Table 3. The experimental conditions in this study were systematically varied in two ways: 21 (1) the (CO22 ) ratio was varied under constant Pco2 3 )/(Ca and Vc and; 21 (2) the Pco2 was varied for constant Vc and (CO22 ) 3 )/(Ca ratio. In this section an affinity-based rate model will be evaluated and compared to a proposed model based on actual chemical reactions. The latter involves surface complexes. Affinitybased rate laws have frequently been used to describe both calcite dissolution (e.g., Sjo¨berg, 1976) and precipitation (e.g., Mucci and Morse, 1983). The rate law is described as:

Table 2 Calculated maximum and minimum surface densities in the experiments.

2.4. Speciation Calculations Solution speciation was calculated using Pco2 (corrected for water content), alkalinity, and total soluble Ca, Na and Cl. Measured pH values were avoided in the calculations due to the liquid junction error (see e.g. Plummer and Busenberg, 1982). Ionic strength and activity coefficients were found by iteration and expressions for activity coefficients were taken from Plummer and Busenberg (1982). The thermodynamic constants used in the calculations are given in Table 1. The degree of calcite supersaturation, Vc, can be expressed by the relationship:

Source

Surface complex [CaOH1 2 [CO2 3 [CO3Ca1 [CaHCO03 [CaCO2 3 [CO3H0 [CaOH0

Max value (mol m22)

Min value (mol m22)

7.89 3 1026 7.97 3 1026 31.6 3 1027 11.2 3 1027 10.5 3 1027 10.7 3 1029 24.0 3 10210

6.53 3 1026 5.14 3 1026 3.38 3 1027 2.99 3 1027 4.55 3 1028 1.09 3 1029 2.46 3 10210

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Table 3. Experimental conditions for calcite crystal growth experiments (25°C, 1 atm). Experiments are presented in increasing crystal growth order. Exp. No

PCO2 ppm

Catot mM

Alk meq 121

(Ca21) 3 103

(CO22 3 ) 3 106

(CaCO03 3 106

(CO23)2/(Ca21)

Vc

pHcalc

pHexp

Rate mmol hr21 m22

7 14 2 4 10 1 6 5 8 3 11 13 12 9 23 15 18 20 21 19 22 16 17

1540 1540 1540 1540 1540 1540 1540 1540 1540 1540 1540 1540 1540 1540 310 310 310 310 310 310 310 310 310

8.00 1.90 10.0 18.0 1.60 2.00 7.00 7.00 5.10 30.0 1.15 7.23 2.27 3.80 1.55 2.50 6.95 7.00 5.10 7.15 11.7 0.65 2.30

1.25 2.70 1.50 1.40 4.00 4.00 2.50 2.50 3.10 1.75 6.00 2.97 4.94 4.25 1.30 1.40 1.12 1.18 1.47 1.42 1.38 4.90 2.85

2.97 0.743 3.64 6.11 0.617 0.767 2.60 2.60 1.92 9.32 0.432 2.66 0.857 1.43 0.615 0.980 2.61 2.62 1.94 2.67 4.17 0.238 0.877

1.71 8.51 2.36 1.85 18.2 18.0 6.61 6.61 10.3 2.46 39.7 9.14 26.7 19.4 9.14 10.17 5.96 6.55 10.27 9.13 7.79 102 36.9

8.49 10.6 14.3 18.9 18.8 23.2 28.8 28.8 33.2 38.4 28.7 40.7 38.4 46.2 9.42 16.7 26.0 28.8 33.4 40.7 54.4 40.8 54.3

5.74 3 1024 1.15 3 1022 6.48 3 1024 3.02 3 1024 2.96 3 1022 2.35 3 1022 2.55 3 1023 2.55 3 1023 5.40 3 1023 2.64 3 1024 9.20 3 1022 3.43 3 1023 3.12 3 1022 1.36 3 1022 1.48 3 1022 1.04 3 1022 2.29 3 1023 2.50 3 1023 5.29 3 1023 3.42 3 1023 1.87 3 1023 4.30 3 1021 4.21 3 1022

1.53 1.91 2.59 3.40 3.40 4.18 5.18 5.18 5.99 6.92 5.18 7.35 6.92 8.34 1.70 3.01 4.69 5.19 6.02 7.35 9.80 7.35 9.79

7.603 7.952 7.674 7.621 8.118 8.116 7.898 7.898 7.995 7.683 8.287 7.968 8.201 8.131 8.316 8.339 8.223 8.244 8.341 8.316 8.281 8.840 8.619

7.615 7.97 7.68 7.63 8.14 8.13 7.915 7.92 8.01 7.68 8.31 7.98 8.22 8.145 8.35 8.36 8.25 8.28 8.375 8.325 8.29 8.87 8.64

0.376 1.40 2.46 4.25 5.46 7.94 8.46 8.61 11.7 12.1 13.1 13.2 16.8 18.5 0.829 3.73 6.53 7.58 10.5 11.5 16.2 17.3 22.3

R 5 k(Vc 2 1)n

(3)

where R is the experimental reaction rate (mmol hr21m22), k is the rate constant, n is the order of reaction and Vc is the degree of thermodynamic supersaturation of the solution with respect to calcite. In Figure 1 the experimental precipitation rates have been fitted to Eqn. 3. Calculated regression parameters for k and n are given in Table 4. Obviously, both k and n vary with Pco2 and n is not an integer. Many studies have been performed to determine the reaction order of calcium carbonate reactions. Values in a wide range have been reported for various experimental conditions and the reaction order is seldom unity (e.g., Mucci and Morse, 1983; Zhong and Mucci, 1989; Dromgoole and Walter, 1990; Shiraki and Brantley, 1995), which could be expected if the equation would have a mechanistic significance (Inskeep and Bloom, 1985). The scatter of experimental calcite crystal growth rates in Figure 1 is not random. In general the rate of crystal growth

increases with supersaturation but variations in Pco2 and the 21 (CO22 ) ratio have a major effect on the crystal growth 3 )/(Ca rate. At fixed values of Vc, rates increase with increasing Pco2 21 and with increasing (CO22 ) ratio. These dependencies 3 )/(Ca can also be found in other experimental data sets for calcite (Dromgoole and Walter, 1990; Winter and Burton, 1992; Zuddas and Mucci, 1994; Lebron and Sua´rez, 1998), and has also been described for rhodochrosite (Sternbeck, 1997). It appears that calcite crystal growth rates depend on the 21 same parameters, Pco2 and the (CO22 ) ratio, as does 3 )/(Ca the speciation of the calcite surface (Van Cappellen et al., 1993). Therefore, a calcite crystal growth model that includes surface speciation can probably improve the knowledge of the factors controlling calcite kinetics. 3.1. The Use of Surface Complexation Theory Based on a surface complexation model for carbonate minerals (Van Cappellen et al., 1993) a mechanistic model for the kinetics of rhodochrosite crystal growth was recently proposed (Sternbeck, 1997). This mechanistic model eliminated the rate 21 dependence on the Pco2 and the (CO22 ) ratio by as3 )/(Mn suming that crystal growth proceeded by adsorption of MnCO03 at the dehydrated surface complexes §MnHCO03 and §MnCO2 3 . It is here tested if this model can be used to describe calcite crystal growth. Since crystal growth requires equivalent adsorption on dehydrated carbonate and dehydrated metal sites,

Table 4. Rate constants for Eqn. 3. PCO2 (ppm) Fig. 1. Calcite precipitation rates (mmol hr21m22 ) as a function of supersaturation and Pco2. Lines represent best fit to Eqn. 3 for Pco2 310 ppm, 1540 ppm and all data.

310 1540 All data

k (mmol hr21 m22)

n

r

1.37 6 0.14 1.18 6 0.11 1.23 6 0.09

1.21 6 0.06 1.41 6 0.07 1.33 6 0.05

0.986 0.975 0.975

Calcite crystal growth using surface speciation Table 5. Rate constants for Eqn. 6. Rate constant k1 k2 k3 k4

Table 6. Rate constants for Eqn. 8.

Value and std. error

Rel std. error

1.56 6 1.56 3 108 M21 hr21 5.50 6 0.77 3 108 M21 hr21 21.03 6 2.54 3 103 hr21 3.98 6 0.83 3 103 hr hr-1

100% 14% 246% 21%

k1

0 N [CaCO2 [CaCO2 3 1 CaCO3 3 1 6H2O

(4)

k3

k2

[CaHCO03 1 CaCO03 N [CaHCO03 1 6H2O

Rate constant k1 k2 k3 k4 k5 k6

adsorption on those sites that are in minority should be the rate determining step(s). In this study it is therefore likely that adsorption on §CaHCO03 and §CaCO2 3 are involved in the rate determining step (Table 2). These two surface carbonate complexes were also those active in the rhodochrosite model suggesting that calcite crystal growth may be described by these two reversible reactions:

(5)

k4

where k1, and k2 are rate constants for forward reactions and k3 and k4 are rate constants for backward reactions. The forward reaction describes crystal growth and the backward describes dissolution by hydrolysis. It is assumed that Ca21 is eightcoordinated to water (Carugo et al., 1993) and CaCO03 thus coordinates to six water molecules in the inner sphere. The surface complexes occurring on the right and left hand side, in Eqn. 4 and 5, are not the same. The surface complexes on the left hand side escape into the bulk lattice following incorporation of CaCO03. The surface complexes on the right hand side are converted to soluble CaCO03 following hydrolysis. The net rate of calcite crystal growth, forward reactions minus backward reactions, will be described as: R 5 k1 3 (CaCO03) 3 {[CaCO2 3} 1 k23 (CaCO03) 3 {[CaHCO03} 2 0 k3 3 {[CaCO2 3 } 2 k4 3 {[CaHCO3}

221

(6)

where activity in solution is denoted ( ), and the density of a surface complex on the mineral surface is denoted { } (mol m22). Using the experimentally determined rates, solution activities and surface densities, the rate constants k1 to k4 are calculated by multiple linear regression using proportional weighting (Table 5). When calculated rates are plotted versus experimental rates the correlation coefficient, r, equals 0.957, the slope is 0.81 and the intercept is 0.07 mmol hr21 m22. If the model exactly could predict experimental rates over the whole experimental domain, these values should read 1, 1 and 0, respectively. This model underestimates calcite crystal growth rates and for both statistical and mechanistical (i.e. wrong sign on k3) arguments this model fails in a true description of calcite kinetics. However, it is not obvious that a model describing rhodochrosite kinetics should be directly applicable to calcite because there are important chemical differences between Ca21 and Mn21. Because ions generally release most of their hydrated water before incorporation into the crystal lattice, one

Value and std. error

Rel std. error

2.83 6 0.61 3 108 M21 hr21 3.13 6 0.41 3 108 M21 hr21 3.81 6 1.48 3 103 hr21 2.51 6 0.71 3 103 hr21 1.35 6 0.13 3 107 M21 hr21 8.73 6 1.56 3 102 hr21

22% 13% 39% 28% 10% 18%

possible rate limiting step in precipitation is the release of the hydrated layer around the cation (Nielsen, 1984). When Eqn. 6 was shown to describe rhodochrosite crystal growth it was proposed that MnCO03 should be more readily incorporated in the lattice than free Mn21 ions. The argument is that Mn21 has a relatively slow rate of water exchange whereas water exchange usually is much more rapid if one or more water molecules are substituted for by other ligands, as in MnCO03 (Margerum et al., 1978; Lincoln and Merbach, 1995). The water exchange rate of Ca21 is about 20 times faster than that of Mn21 (Stumm and Morgan, 1996) and it is possible that the more labile Ca21 can adsorb and dehydrate on the calcite surface. In addition to CaCO03, it is thus possible that Ca21 is directly incorporated at the mineral surface. It could be anticipated that Ca21 is incorporated at either §CaCO2 3 , §CaHCO03 or at both, but only incorporation at §CaCO2 3 gave a good fit to experimental data. This is probably a result of stronger electrostatic attraction between Ca21 and the more negatively charged §CaCO2 3 as compared to the uncharged §CaHCO03. In reality however, the latter surface site may actually be slightly negative (see Introduction). The proposed backward term to this reaction is not obvious since this reaction could be detachment of Ca21 from either 21 §CO3Ca1 or §CaOH1 leaves the surface complex 2 . When Ca 1 §CO3Ca only one Ca-O bond must be broken because Ca21 is already partly hydrated. Detachment of §CaOH21 from the calcite surface, where calcium has five bonds to carbonate oxygens and one bond to water (see Fig. 3 in Stipp et al., 1994), implies that five Ca-O bond must be broken. Both reactions were evaluated but only the reaction involving §CO3Ca1 gave a good fit to data. More work under dissolution conditions is required to further clarify the backward reaction of this mechanism. Conclusively, in addition to reactions 4 and 5, the following reaction contributes to calcite crystal growth: k5

21 N [CaCO2 [ CO3Ca1 1 8H2O. 3 1 Ca

(7)

k6

The net rate of calcite crystal growth can be represented by the equation: R 5 k1 3 (CaCO03) 3 {[CaCO2 3} 1 k2 3 (CaCO03)3 {[CaHCO03} 2 k3 3 {[CaCO2 3}2 k4 3 {[CaHCO03} 1 k5 3 (Ca21) 3 {[CaCO2 3} k63 {[ CO3 Ca1}

(8)

The crystal growth rates calculated using Eqn. 8 and rate constants obtained by multiple linear regression (Table 6) are

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Fig. 2. Experimental calcite precipitation rates (mmol hr21 m22) as a function of calculated calcite precipitation rates (mmol hr21 m22). Line represent best fit to Eqn. 8 for all data. The correlation coefficient r is 0.996, the slope is 0.978 and the intercept 0.014 mmol hr21 m22. Recalling that the lowest rate in this experimental dataset is 0.38 mmol hr21 m22 (range 0.38 –22), this intercept must be considered as very low.

plotted against experimental crystal growth rates in Fig. 2. The agreement between calculated and experimentally determined rates must be considered as very good. The relative deviations as a function of the experimental rate is shown in Fig. 3. 4. DISCUSSION

The crystal growth kinetics of calcite is explained with a model where CaCO03 (strictly CaCO3(H2O)06) and Ca21 (strictly Ca(H2O)21 8 ) in the bulk solution adsorb to specific surface complexes at the crystal surface. Other mechanistical models describing calcite kinetics have explained the reaction mechanism with reversible reactions between the bulk solid phase and dissolved species (e.g., Plummer et al., 1978; Chou et al., 1989). The use of surface complexes in calcite kinetics have previously been used by Arakaki and Mucci (1995), who described both dissolution and crystal growth by the use of the surface complexation model of Van Cappellen and coauthors (1993). However, in their model, reactions involving surface complexes are mixed with a reaction involving the bulk solid. The model proposed here is, to our knowledge, the first successful attempt to mechanistically model calcite crystal growth solely from surface speciation. Predicted rates show agreement

Fig. 4. The relative errors of the calculated rates (Eqn. 8 and Eqn. 3) vs. experimental (CO3)/(Ca21) ratios.

within a factor 1.2 with experimental crystal growth rates over the entire experimental range (0.38 –22 mmol hr21 m22). In comparison to affinity based models (Eqn. 3) this model has a better fit to the experimental data (Fig. 4) and it also strongly eliminated the dependence of the crystal growth rate on the 21 (CO22 ) ratio in solution, or pH, as well as on Pco2. 3 )/(Ca The calcite surface chemistry model of Van Cappellen and coauthors (1993) can be criticised for not being calibrated against actual surface charge data and that some of the proposed surface complexes have not been described elsewhere. However, Van Cappellen and coauthors (1993) have tried to quantify the effect of adsorption of CO2(g) on mineral surfaces, and regardless of the precision of their model it is reasonable to assume that the number of carbonate surface sites at the mineral surface are proportional to Pco2. In fact, several studies show a rate dependence on Pco2 for both calcite crystal growth (Dromgoole and Walter, 1990; Winter and Burton, 1992; Zuddas and Mucci, 1994; Lebron and Sua´rez, 1998) and calcite dissolution (Plummer et al., 1978; Sjo¨berg, 1978; Chou et al., 1989). By the use of our model the dependence of Pco2 on the carbonate mineral kinetics can be explained as follows. An increase in Pco2 leads to an increased adsorption of CO2 on the mineral surface which generates higher densities of the surface complexes §CaHCO03 and §CaCO2 3 . These surface complexes are involved in the rate limiting steps during crystal growth and dissolution (Eqn. 4, 5 and 7). Therefore, an increase in Pco2 will enhance both the calcite growth and dissolution rate. 4.1. Rate Constants

Fig. 3. The relative errors of the calculated rates (Eqn. 8) vs. experimental rates (mmol hr21 m22).

In this section the factors controlling the rate constants will be discussed. This knowledge may help to predict and understand incorporation of foreign substances (e.g., cations) in calcite and the role of solution speciation. Both Ca21 and CaCO03 are adsorbed on the same surface complex, §CaCO2 3 , which enables a comparison of the rate constants. According to the values of k1 and k5 (Table 6), the incorporation of CaCO03 is 21 times more rapid than Ca21. The reaction of a ligand (e.g., CO22 3 ) with a hydrated metal ion changes the Me-OH2 bond distances in the inner sphere which weakens the bonds to the hydrating water. This phenomenon has been reported for copper-carbonate complexes (Schosseler et al., 1997) but to our knowledge not yet for carbonate complexes with Ca or other metals. As a result the rate of exchange of water molecules between the inner sphere and bulk solution is enhanced. This

Calcite crystal growth using surface speciation

should increase the rate of metal incorporation at the mineral surface, because dehydration of the adsorbing species must precede crystal growth. Therefore, the higher value of k1 than k5 may be due to a higher water exchange rate. In comparison to studies on other metal complexes, a 20 fold increase in water exchange rate as a result of complexation with a bidendate ligand is reasonable (Margerum et al., 1978; Burgess, 1990; Phillips et al., 1997a,b; Lincoln and Merbach, 1995). For instance the complexation of Al31 with the bidendate oxalate ligand increased the rate of water exchange by a factor '102 (Phillips et al., 1997b) and the complexation of Co21 with the bidendate malonate ligand increased the rate of water exchange about 11 times (Margerum et al., 1978). Because of the uncertainties associated with our calculations, including the value of the surface complex constants, the value of this increase in lability due to carbonate complexation must be considered as an approximation. The effect on the calcite crystal growth rate from other possible complexes in solution like CaCl1, 2 CaHCO1 3 or NaCO3 has been neglected here due to their lower stability in comparison to CaCO03 (see Table 1). 4.2. Comparison of the Calcite and Rhodochrosite Models Calcite kinetics is very fast in comparison to other carbonate minerals such as rhodochrosite and magnesite, but comparable to witherite (Chou et al., 1989; Sternbeck, 1997). Due to slow kinetics, rhodochrosite crystal growth rates were only measured at V values equal to or larger than 8. At V 5 8, calcite crystal growth was 3,700 times more rapid than rhodochrosite. By extrapolating the affinity based equations for crystal growth (Eqn. 3) to V 5 1.5 and 3.0, growth of calcite is about 10,000 and 6,000 times faster than rhodochrosite, respectively. The solubility products differ only by a factor ;70 –100, and the activity of MeCO03 at equal V differs thus 15–21 times. Thus, at equal V the number of CaCO03 molecules in solution are 15–21 times more common than MnCO03 molecules so the difference in crystal growth rates is probably related to different kinetic properties of MnCO03 and CaCO03. Neither can the additional reaction involving free Ca21 (Eqn. 7) explain this difference in behaviour because the contribution of this reaction to the total calcite crystal growth rate is not of this magnitude. A possible explanation of this large variation in growth rates is that differences in the water exchange rates of the adsorbed species produce different rates of incorporation into the crystal lattice. Previous studies have shown that rate coefficients for dissolution of some metal silicates correlate with the water exchange rates of these metals in solution (Casey and Westrich, 1992), and that the rate of ligand promoted dissolution correlates with the water exchange rates of the corresponding metalligand complexes in solution (Ludwig et al., 1996). A similar correlation should also be applicable under conditions where precipitation reactions dominate. In precipitation reactions, bonds must be broken between the dissolved metal and its ligands (including water), whereas in dissolution processes, bonds must be broken between the solid mineral and the leaving ion. Because mechanistic rate constants (k1 to k4) for calcite and rhodochrosite are available, it is investigated if the rate constants vary predictably with the water exchange rates of the main adsorbing species, which in this case is MeCO03.

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The k1 and k2 values are 55 to 270 times higher for calcite than for rhodochrosite (see Sternbeck, 1997). If rate constants were linearly related to water exchange rates, then it would appear that the rate of water exchange in CaCO03 should be 55–270 times more rapid than in MnCO03. Water exchange rates for CaCO03 and MnCO03 are not known, but as mentioned earlier the rate of water exchange for Ca21 is about 20 times more rapid than for Mn21. Ligand promoted enhancement of water exchange rates are more pronounced for metal ions with lower exchange rates (Lincoln and Merbach, 1995), suggesting that water exchange in CaCO03 should be less than 20 times more rapid than in MnCO03. This disagrees with the observed increased reactivity of CaCO03 relative to MnCO03. Three possible explanations that all may contribute to this observation are suggested: (1) The rate constants are not linearly proportional to the water exchange rates. (2) There are uncertainties associated with the calculations of the rate constants, i.e. specific surface areas, site densities, and surface complex stability constants. (3) The experimental conditions were not exactly the same in the two studies. In the calcite study the (Me21)/ (MeCO03) ratio varies between 6 and 323 and in the rhodochrosite study it varies between 7 and 119. Thus, experimental conditions were not equally suitable for detecting a possible rate dependence on Me21. The first statement is probably the major contributor to the observed contradictions, as will be shown in the following. For calcite the values of k1 and k2 are almost equal which indicate that CaCO03 is incorporated at equal rates to the surface com0 plexes §CaCO2 3 and §CaHCO3, i.e. independent of the charge. This independence suggest a dissociative reaction pathway (Burgess, 1990), see Introduction. In fact, ligand exchange reactions for Ca21 are generally of dissociative character (Burgess, 1990). In contrast, for rhodochrosite k1 is 4.4 times larger than k2 which means that incorporation of MnCO03 is more rapid at the more negatively charged surface complex 0 §MnCO2 3 than at the surface complex §MnHCO3. This dependence on the charge of the incoming ligands suggests an associative pathway, which is reasonable since Mn21 generally is described as a metal with associative character (Lincoln and Merbach, 1995; Rotzinger, 1997). The incoming ligand 0 (§MnCO2 3 or §MnHCO3) must enter the inner sphere before water molecules in the inner sphere leave, and then the charge of the ligand is more important to the reaction pathway (Burgess, 1990). The rates of ligand exchange for metal ions with associative character are not necessarily related to rates of water exchange (Lincoln and Merbach, 1995). Conclusively, we suggest that the large difference in rate constants of crystal growth (k1 and k2) for rhodochrosite relative to calcite is due to different character of ligand exchange reactions for Mn21 and Ca21, but also to the lower rates of water exchange for Mn21. The influence of the character of the reaction mechanism can also be found in the dissolution constants. According to the dissolution rate constants, k3, k4 and k6 (Table 6), carbonateligand complexation at surface Ca groups promotes dissolution of calcite relative to hydrated Ca groups, since k3 and k4 are about three times higher than k6. The detachment of CaCO03 is 1.5 times more rapid from the §CaCO2 3 surface site than §CaHCO03, but the difference is not statistically significant. The difference appears to be even more pronounced for rhodochro-

¨ . Nilsson and J. Sternbeck O

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site, a factor of 16, but especially the value of k4 is very uncertain for rhodochrosite (see Sternbeck, 1997). Apparently, the associative/dissociative character of the metal ions is an important factor in carbonate kinetics because it determines the importance of the charge of the surface complexes. This model should also be applicable on other 1:1 carbonate minerals like magnesite, siderite or smithsonite. In these cases, ligand exchange reactions for Mg21, Fe21 or Zn21, respectively, are dissociative (Burgess, 1990; Rotzinger, 1997) and the kinetics of these carbonate minerals, relative to calcite, may be predicted by water exchange rates of the main adsorbing species. Depending on the water exchange rate of the metal ion and possible metal-ligand complexes, various adsorbing species at the active sites are possible, e.g., Me21, MeCO03, MeHCO1 3 . Complexes with other ligands such as MgSO4 have also been shown to be important, e.g. in the case of dolomite (Brady et al., 1996). For metal ions with an associative character, like Mn, the reaction pathway for carbonate crystal growth implies a more differentiated mechanism with more rapid reactions occurring at the more negatively charged surface sites. Because the relative surface density of the active 0 surfaces complexes, §MeCO2 3 and §MeHCO3, are dependent on pH and Pco2, it is likely that the kinetics for metal carbonates with an associative character are more sensitive to changes in pH and Pco2. Finally, the presented model is an attempt to explain the carbonate kinetics with reaction mechanisms at the mineralaqueous solution interface. The results show that there are mechanistic similarities between mineral crystal growth and ligand exchange reactions in solution. Further support for the mechanisms presented could possibly be given from ab initio calculations and experiments with other strong ligands. 5. CONCLUSIONS

From laboratory experiments we have succeeded in mechanistically modelling calcite crystal growth with surface speciation. Over a wide range of rates, our model shows agreement within a factor 1.2 with experimental crystal growth rates. At a given supersaturation, the rate increased with increasing Pco2 21 and (CO22 ) ratio. This is due to CO2 adsorption which 3 )/(Ca results in an increased number of carbonate active sites at the mineral surface. Because these sites are involved in the rate limiting steps, both crystal growth and dissolution rates are enhanced with increasing Pco2. The species in solution that adsorb to the active sites are proposed to be the partly dehydrated CaCO03 as well as Ca21. The rate constants indicate that CaCO03 is '20 times more reactive than Ca21 at the calciteaqueous solution interface. This increased reactivity probably reflects an increased water exchange rate of similar magnitude, due to ligand promoted destabilisation of inner sphere water molecules. It has also been possible to compare calcite and rhodochrosite crystal growth rates under similar chemical and physical conditions. There is a major difference between the two crystal growth mechanisms. In the calcite model, there is incorporation of Ca21 and CaCO03 at the mineral surface whereas in the rhodochrosite model, only MnCO03 is incorporated. Although the water exchange rate of the metal ions predicts the relative magnitude of crystal growth kinetics, it is not the only factor

that determines the growth rate of a particular carbonate mineral. By comparing the rate constants it is suggested that the calcite reaction mechanism is of a dissociative character and the rhodochrosite mechanism is of an associative character. This agrees with the character of ligand exchange reactions of Ca21 and Mn21 in solution. Acknowledgments—We thank Rolf Hallberg, for valuable comments on the manuscript, Hele´ne Strandh for fruitful discussions and Roger Herbert for improving the English. We also thank Patrick Brady and two anonymous reviewers for constructive reviews of the manuscript. Especially one anonymous reviewer is appreciated for important comments on the charge of surface complexes. This study was supported by the Swedish Nuclear and Waste Management Co (SKB), which is gratefully appreciated. NOTES The term mechanistic is sometimes used to describe different physical crystal growth mechanisms. In this paper, however, the term mechanistic refers to elementary reactions. REFERENCES Arakaki T. and Mucci A. (1995) A continuous and mechanistic representation of calcite reaction-controlled kinetics in dilute solutions at 25°C and 1 atm total pressure. Aquatic Geochemistry 1, 105–130. Boyle E. A. (1983) Manganese carbonate overgrowths on foraminifera tests. Geochim. Cosmochim. Acta 47, 1815–1819. Brady P. V., Krumhansl J. L., and Papenguth H. W. (1996) Surface complexation clues to dolomite growth. Geochim. Cosmochim. Acta 60, 727–731. Burgess J. (1990) Metal ions in solution. Ellis Horwood. Carpenter S. J. and Lohmann K. C. (1992) Sr/Mg ratios of modern marine calcite: Empirical indicators of ocean chemistry and precipitation rate. Geochim. Cosmochim. Acta 56, 1837–1849. Carugo O., Djinovic K., and Rizzi M. (1993) Comparison of the co-ordinative behaviour of calcium (II) and magnesium (II) from crystallographic data. J. Chem. Soc. Dalton Trans. 1993, 2127–2135. Casey W. H. and Westrich H. R. (1992) Control of dissolution rates of orthosilicate minerals by divalent metal-oxygen bonds. Nature 355, 157–159. Casey W. H., Phillips B. L., Nordin J. P., and Sullivan D. J. (1998) The rates of exchange of water molecules from Al(III)-methylmalonate complexes: The effect of chelate ring size. Geochim. Cosmochim. Acta 62, 2789 –2797. Chou L., Garrels R. M., and Wollast R. (1989) Comparative study of the kinetics and mechanism of dissolution of carbonate minerals. Chemical Geology 78, 269 –282. Dove P. M. and Hochella M. F., Jr. (1993) Calcite precipitation mechanisms and inhibition by orthophosphate: In situ observations by scanning force microscopy. Geochim. Cosmochim. Acta 57, 705– 714. Dromgoole E. L. and Walter L. M. (1990) Inhibition of calcite growth rates by Mn21 in CaCl2 solutions at 10, 25 and 50oC. Geochim. Cosmochim. Acta 54, 2991–3000. Hastings D. W. and Emerson S. R. (1996) Vanadium in foraminiferal calcite as a tracer for changes in the areal extent of reducing sediments. Paleoceanography 11, 665– 678. Inskeep W. P. and Bloom P. R. (1985) An evaluation of rate equations for calcite precipitation kinetics at Pco2 less than 0.01 atm and pH greater than 8. Geochim. Cosmochim. Acta 49, 2165–2180. King D. W. (1998) Role of carbonate speciation on the oxidation rate of Fe(II) in aquatic systems. Environ. Sci. Technol. 32, 2997–3003. Lea D. W. and Boyle E. A. (1991) Barium in planktonic foraminifera. Geochim. Cosmochim. Acta 55, 3321–3331. Lebron I. and Sua´rez D. L. (1998) Kinetics and mechanisms of precipitation of calcite as affected by Pco2 and organic ligands at 25oC. Geochim. Cosmochim. Acta 62, 405– 416. Lincoln S. F. and Merbach A. E. (1995) Substitution reactions of solvated metal ions. Advances in Inorganic Chemistry 42, 1– 88. Lorens R. B. (1981) Sr, Cd, Co distribution coefficients in calcite as a

Calcite crystal growth using surface speciation function of calcite precipitation rate. Geochim. Cosmochim. Acta 45, 553–561. Ludwig C., Devidal J.-L., and Casey W. H. (1996) The effect of functional groups on the ligand-promoted dissolution of NiO and other oxide minerals. Geochim. Cosmochim. Acta 60, 213–224. Margerum D. W., Cayley G. R., Weatherburn D. C., and Pagenkopf G. K. (1978) Kinetics and mechanisms of complex formation and ligand exchange. Amer. Chem. Soc. Monogr. 174, 1–220. Morse J. W. (1986) The surface chemistry of calcium carbonate minerals in natural waters: An overview. Marine Chemistry 20, 91–112. Morse J. W. and Mackenzie F. T. (1990) Geochemistry of sedimentary carbonates. Elsevier. Mucci A. and Morse J. W. (1983) The incorporation of Mg21 and Sr21 into calcite overgrowths: Influences of growth rate and solution composition. Geochim. Cosmochim. Acta 47, 217–233. Nielsen A. E. (1984) Electrolyte crystal growth mechanisms. J. Crystal Growth 67, 289 –310. Nordstrom D. K., Plummer L. N., Langmuir D., Busenberg E., Jones B. F., and Parkhurst D. L. (1990) Revised chemical equilibrium data for major water-mineral reactions and their limitations. In Chemical modelling of aqueous systems II (eds. D. C. Melchior, R. L. Bassett), Chap. 32, pp. 398 – 413. ACS Symposium Series 416. Phillips B. L., Casey W. H., and Neugebauer Crawford S. (1997a) Solvent exchange in AlFx(H2O)6-x3-x (aq) complexes: Ligand-directed labilization of water as an analogue for ligand-induced dissolution of oxide minerals. Geochim. Cosmochim. Acta 61, 3041– 3049. Phillips B. L., Neugebauer Crawford S., and Casey W. H. (1997b) Rate of water exchange between Al(C2O4)(H2O)1 4 (aq) complexes and aqueous solutions determined by 17O-NMR spectroscopy. Geochim. Cosmochim. Acta 61, 4965– 4973. Plummer L. N., Wigley T. M., and Parkhurst D. L. (1978) The kinetics of calcite dissolution in CO2-water systems at 5o to 60oC and 0.0 to 1.0 atm CO2. Am. J. Sci. 278, 179 –216. Plummer L. N. and Busenberg E. (1982) The solubilities of calcite, aragonite and vaterite in CO2-H2O solutions between 0 and 90°C, and an evaluation of the aqueous model for the system CaCO3-CO2H2O. Geochim. Cosmochim. Acta 46, 1011–1040. Rotzinger F. P. (1997) Mechanism of water exchange for the di- and trivalent metal hexaaqua ions of the first transition series. J. Am. Chem. Soc., 119, 5230 –5238. Ruaya J. R. (1988) Estimation of instability constants of metal chloride complexes in hydrothermal solutions up to 300°C. Geochim. Cosmochim. Acta 52, 1983–1996. Rump H. H. and Krist H. (1992) Laboratory manual for the examination of water, waste water and soil. VCH Verlagsgesellschaft mbH. Schosseler P. M., Wehrli B., and Schweiger A. (1997) Complexation of copper (II) with carbonate ligand in aqueous solution: A CW and pulse EPR study. Inorg. Chem. 36, 4490 – 4499.

225

Shiraki R. and Brantley S. L. (1995) Kinetics of near-equilibrium calcite precipitation at 100°C: An evaluation of elementary reactionbased and affinity-based rate laws. Geochim. Cosmochim. Acta 59, 1457–1471. Sjo¨berg E. L. (1976) A fundamental equation for calcite dissolution kinetics. Geochim. Cosmochim. Acta 40, 441– 447. Sjo¨berg E. L. (1978) Kinetics and mechanism of calcite dissolution in aqueous solutions at low temperatures. Stockholm Contrib. Geol. 32, 1–96. Sternbeck J. (1997) Kinetics of rhodochrosite crystal growth at 25oC: The role of surface speciation. Geochim. Cosmochim. Acta 61, 785–793. Stipp S. L. and Hochella M. F., Jr. (1991) Structure and bonding environments at the calcite surface as observed with X-ray photoelectron spectroscopy (XPS) and low energy electron diffraction (LEED). Geochim. Cosmochim. Acta 55, 1723–1736. Stipp S. L. S., Eggleston C. M., and Nielsen B. S. (1994) Calcite surface structure observed at microtopographic and molecular scales with atomic force microscopy (AFM). Geochim. Cosmochim. Acta 58, 3023–3033. Stumm W. and Morgan J. J. (1996) Aquatic Chemistry. John Wiley & Sons. Stumm W. and Wieland E. (1990) Dissolution of oxide and silicate minerals: rates depend on surface speciation. In Aquatic Chemical Kinetics (ed. W. Stumm), Chap. 13, pp. 367– 400. Wiley-Interscience. Stumm W., Wehrli B., and Wieland E. (1987) Surface complexation and its impacts on geochemical kinetics. Croatica Chemica Acta 60, 429 – 456. Tesoriero A. J. and Pankow J. F. (1996) Solid solution partitioning of Sr21, Ba21 and Cd21 to calcite. Geochim. Cosmochim. Acta 60, 1053–1063. Thomson J., Higgs N. C., Jarvis I., Hydes D. J., Colley S., and Wilson T. R. S. (1986) The behaviour of manganese in Atlantic carbonate sediments. Geochim. Cosmochim. Acta 50, 1807–1818. Van Cappellen P., Charlet L., Stumm W., and Wersin P. (1993) A surface complexation model of the carbonate mineral aqueous solution interface. Geochim. Cosmochim. Acta 57, 3505–3518. Winter D. J. and Burton. E. A. (1992) Experimental investigations of aCa/aCO3 ratio on the kinetics of calcite precipitation: implications for the rate equation and trace element incorporation. GSA Abstr. Prog., A37. Zhong S. and Mucci A. (1989) Calcite and aragonite precipitation from seawater solutions of various salinities: Precipitation rates and overgrowth composition. Chemical Geology 78, 283–299. Zuddas P. and Mucci M. (1994) Kinetics of calcite precipitation from seawater: I. A classical chemical description for strong electrolyte solutions. Geochim. Cosmochim. Acta 58, 4353– 4362.