Strontium, Nickel, Cadmium, and Lead Substitution into Calcite

May 13, 2014 - Wettability alteration of calcite oil wells: Influence of smart water ions. Sanjay Prabhakar , Roderick Melnik. Scientific Reports 2017...
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Strontium, Nickel, Cadmium, and Lead Substitution into Calcite, Studied by Density Functional Theory M. P. Andersson,* H. Sakuma, and S. L. S. Stipp Nano-Science Center, Department of Chemistry, University of Copenhagen, Copenhagen 2100, Denmark ABSTRACT: We have used density functional theory to predict the ion exchange energies for divalent cations Ni2+, Sr2+, Cd2+, and Pb2+ into a calcite {10.4} surface in equilibrium with water. Exchange energies were calculated for substitution into the topmost surface layer, at the mineral−fluid interface, and into the second layer of the solid. This information can be used as an indicator for cation substitution in the bulk phase, such as for the uptake of toxic metals from the environment and the growth of secondary phases. In both the surface and in the second layer, Ni2+, Cd2+, and Pb2+ substitute exothermically and Sr2+ substitutes endothermically. Our results agree with published experimental data that demonstrate trace metal coprecipitation with calcite as a sink for Ni2+, Cd2+, and Pb2+, whereas Sr2+ has a distribution constant significantly smaller than 1. Ni2+ substitution is favored at the mineral−fluid interface compared with bulk substitution, which also agrees with experimental data. Our results predict that Ni2+, Cd2+, and Pb2+ form a stable solid solution with calcite. Successful prediction of the experimental results gives us confidence in our ability to predict the divalent cation preference for surfaces rather than for sites within the bulk crystal structure, which cannot be directly derived from experiment.

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INTRODUCTION Calcite, the rhombohedral polymorph of CaCO3, is a common mineral in the earth’s crust. It is present in soil, sediments, and rocks, and it readily forms as a secondary phase in the high-pH waters associated with the breakdown of concrete, such as would happen in an aging radioactive waste repository.1 Calcite frequently precipitates in soils and sediments when the solution concentration increases because of evaporation, forming a hard pan and also as “whitings” in warm marine environments.2−5 When calcite precipitates, divalent cations are taken up, whether the calcite is formed inorganically or biogenically, as a result of biological activity, such as in mollusc shells and the excrement of earthworms.6,7 Divalent cations, with atomic radii equivalent to or smaller than that of calcium, often substitute with little or no disruption to the atomic structure.8−11 The rhombohedral lattice can also tolerate a certain fraction of larger divalent cations before the orthogonal polymorph, aragonite, becomes the stable phase. Thus, calcite is a possible sequestering agent for divalent radionuclides and heavy metals, either through uptake during precipitation or as a result of the recrystallization of existing carbonate minerals in dynamic equilibrium with the solution phase. Thermodynamic and kinetic data are essential for risk assessment modeling and to predict the transport of contaminants, but for some conditions, including high temperature and pressure, obtaining data from experiments is difficult if not impossible. Computational approaches are invaluable for filling in missing data and for providing insight into the molecular-scale processes responsible for uptake and release. In particular, the stability of ions at the mineral−fluid interface can be different than in the bulk, and parameters such as temperature, ionic strength, solution composition including pH, and the presence of organic compounds affect the ability of © XXXX American Chemical Society

a mineral to sequester metal ions and to release them again when parameters change. Our aim was to gain a fundamental understanding of the behavior of four divalent ions that represent a range of size, charge, and electron configuration and that can be contaminants in environmental systems, either from a natural presence or as a result of anthropogenic activities. Nickel in high concentrations, such as in irrigated farming, causes painful skin allergies. Nickel from stainless steel reactors in nuclear power plants can become radioactive, and strontium90 is produced by fission.12 Cadmium and lead are toxic heavy metals often present in leachate from municipal waste facilities and in soils because of fertilizer residue accumulated from commercial products or from sewage sludge. We chose Ni2+, Sr2+, Cd2+, and Pb2+ for our molecular modeling study because of their range of size, charge, and electron configuration. Cadmium is the same size as calcium, and it becomes an ion by losing its 2s electrons so that it substitutes into calcite in a complete solid solution series with minimal deviation from Vegard’s law.13−15 Predicting cadmium substitution provides a baseline where solid experimental evidence for uptake into calcite exists for comparison. Nickel is smaller than calcium, but it also loses its s electrons and it is known to substitute into calcite to some extent.16,17 Strontium and lead are both larger than calcium, and when present in the solution in sufficient quantities, they inhibit calcite formation, favoring aragonite.18,19 We used density functional theory (DFT) to calculate the energies of Ni2+, Sr2+, Cd2+, and Pb2+ substitution into calcite {10.4} slabs, into the surface layer, and into the second layer of the slab, which then serves as an indicator for the substitution Received: March 2, 2014 Revised: May 2, 2014

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chemical potential, is equal for the first four water molecules, and significantly stronger than for subsequent layers, thereby clearly defining a monolayer of water as one water molecule per surface cation.22 Geometry optimizations were made using the gamma point. Single-point energies with a 2 × 2 × 1 Monkhorst Pack k-point mesh23 confirmed that gamma point adsorption energies for water converged within 0.01 eV. We also included empirical dispersion24 because this has been generally shown to increase the accuracy of adsorption energies predicted with DFT.25,26 All calculations for hydrated ions, free ions, and water were made in a cubic box with 12 Å sides, and we used the Martyna−Tuckerman correction27 to determine energies for isolated charged systems in a periodic plane wave calculation. The free energy of solvation for the calcite slabs with adsorbed water was calculated using COSMO-RS.28 We used DMol3 to generate the periodic COSMO surfaces and to calculate the corresponding vacuum energy. We performed geometry optimizations of the solvated surface as well as the vacuum surface using the PBE functional, the DNP basis set, and the medium quality for convergence criteria and cutoffs. Only the gamma point was used. The dielectric constant for the COSMO calculation was 10 000.0, corresponding to a perfect conductor, which is a requirement for the COSMO-RS treatment. The free energy of solvation for the slabs was calculated using COSMOtherm 29,30 and the DMOL3_PBE_C30_1301 parametrization. The binding energy of water molecules to the divalent cations in vacuum is calculated in a standard fashion:

of the trace components into bulk calcite. We chose to study behavior at the calcite surface as well as in the bulk because it is difficult to distinguish between these two sites in batch experiments that investigate cation uptake. If surface substitution is stronger than bulk substitution, then this means that the uptake of trace contaminants would be rapid but it would be less extensive than if substitution into the bulk is favored. Substitution site preference has implications for the contaminant front migration rate and the extent of desorption, i.e., remobilization and recontamination, that would be possible if system conditions were to change again. Both the rate of contaminant plume migration and the extent of desorption would influence contaminant behavior, in ways that thermodynamic and kinetic results from batch experiments cannot predict.

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COMPUTATIONAL DETAILS

All density functional theory calculations were made using the periodic plane wave method and the Quantum Espresso package.20 We used the Perdew−Burke−Ernzerhof (PBE) functional21 together with ultrasoft pseudopotentials taken from the pseudopotential library at the quantum espresso Website: Ca.pbe-nsp-van.UPF, C.pbe-rrkjus.UPF, O.pbe-rrkjus.UPF, H.pbe-rrkjus.UPF, Mg.pw91-np-van.UPF, Sr.pbe-nsp-van.UPF, Ba.pbe-nsp-van.UPF, Ni.pbe-nd-rrkjus.UPF, Cd.pbe-n-van.UPF, and Pb.pbe-nd-rrkjus.UPF. We used a kinetic energy cutoff of 25 Ry and a density cutoff of 250 Ry. These parameters were found to give converged adsorption energies for water on the calcite slab. All calculations involving nickel were spin polarized and a triplet state was found to be the most stable for the bare ion, the hydrated ion, and the slab calculations. The calcite {10.4} slabs were created using the lattice parameters of bulk calcite derived from X-ray diffraction, optimized using a kinetic energy cutoff of 35 Ry and a density cutoff of 350 Ry. The slabs were four molecular layers thick, with the simulation cell equal to 1 × 2 primitive unit cells (80 atoms). The lowest molecular layer in the slab was held fixed at bulk positions during the optimization to represent an essentially infinite solid. At least 15 Å of vacuum was present between the slabs to minimize the chance of interference. All slabs had a monolayer of water adsorbed, which amounts to one water molecule per surface cation. The optimized geometry for a water monolayer on pure calcite is shown in Figure 1. The differential adsorption energy, which can be viewed as a discretized version of the

E b = E(ion + 6 waters) − E( ion) − 6E(water)

(1)

This definition means that the more negative the binding energy, the more strongly the water molecules attach to the ion. We show a comparison of the simulation results for internal energies with experimental free energies of solvation31 in Figure 2. The exchange reaction we have used to estimate the energy for ion substitution is

(calcite‐Ca) + Sr(H 2O)62 + → (calcite‐Sr) + Ca(H 2O)6 2 +

Figure 1. Atomic structure for the calcite {10.4} slab used in the simulations. (Reprinted with permission from Ref. 22; copyright (2014) American Chemical Society.) The top view (left) and side view (right) show the regular structure of a monolayer of water that hydrates the surface. Blue spheres represent the calcium ion, gray represents carbon, red represents oxygen, and white represents hydrogen.

(2)

Figure 2. Experimental free energy of solvation31 versus our DFTpredicted binding energies (Eq. 2) for the first solvation shell (six water molecules, octahedral coordination) of divalent cations Ba2+, Sr2+, Ca2+, Mg2+, Cd2+, Pb2+, and Ni2+ The straight line with a slope very close to 1 shows excellent agreement between predictions and experimental data. B

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where (calcite-Ca) is an unsubstituted calcite slab with a monolayer of water and (calcite-Sr) is a calcite slab with a monolayer of water and with a Ca2+ ion substituted for a Sr2+ ion. The reaction is analogous to the substitution of Ni2+, Cd2+, and Pb2+. The equilibrium distribution coefficient, D, can been written as

the solvated calcite slab and would cancel in the reaction energy for Eq. 2. Importantly, it also shows that for exchange reactions such as Eq. 2, there is actually no need to perform the implicit solvent calculation because this effect is canceled out anyway. All results in Tables 2 and 3 are therefore presented without the

[Sr 2 +]

( ) D= ( ) [Ca 2 +]

Table 2. Ion Exchange Energy and Distribution Coefficient for the Substitution of Sr2+, Ni2+, Cd2+, and Pb2+ into a Calcite {10.4} Slab, Equilibrated with a Monolayer of Water

solid

[Sr 2 +]

[Ca 2 +]

(3)

solution

which also serves as the equilibrium constant for Reaction 2, provided we assume that the calculated reaction energy is a good approximation of the reaction free energy. The similarity of the reactant and product side of Reaction 2 strongly suggests that entropic effects from translation, rotation, and vibration as well as zero-point energies ought to cancel. Using this approximation, our predicted distribution constants are independent of temperature and ionic strength. Thermodynamic equilibrium constants are not available in the literature, so all comparisons to experimental data later in the article are made with distribution constants which are operational, depend on the experimental conditions, and serve as a reasonable approximation for thermodynamic constants. It is worth mentioning that the concentration of foreign ions in our calculations is rather high because of the need to use a limited number of atoms and the periodicity of the simulation cell so that 1 out of 16 cations is substituted, which is 6%. Lattice strain effects are smaller for lower concentrations, which would only make the substitutions more favorable than the predictions here suggest.

ion

ion Ca2+ Sr2+ Ni2+ Cd2+ Pb2+

−95 −93 −97 −94 −94

12 −13 −44 −29

distribution constant (second layer)

0.012 7200 3.4 × 107 1.8 × 105

0.0078 190 5.2 × 107 1.2 × 105

solubility product of corresponding carbonate mineral 3.4 1.1 1.4 5.2 7.4

× × × × ×

10−9 10−10 10−7 10−12 10−14

ion concentration for saturation when [CO32−] = 5.8 × 10−5 M 5.8 1.9 2.4 8.9 1.3

× × × × ×

10−5 10−6 10−3 10−8 10−9

ion concentration required for 1% substitution into second layer of calcite [M]

predicted uptake process

1.3 5.3 × 10−5 1.9 × 10−10 8.3 × 10−8

precipitation incorporation incorporation precipitation

implicit solvent. This makes our results more generally applicable and our method could potentially be used for other surfaces using any planewave code. From Table 2, it is apparent that the stability of Sr2+ in calcite differs significantly from the stability of the other ions. Sr2+ substitution for Ca2+ is endothermic, +11 kJ/mol in the surface layer and +12 kJ/mol in the second layer, meaning that the uptake of Sr requires the presence of defects in the crystal structure such as offsets in atomic rows. Ni2+ substitution, on the other hand, is exothermic, −22 kJ/mol in the surface layer and −13 kJ/mol in the second layer. This means that sorption on and in calcite is favored, consistent with the distribution coefficient presented by Lakshtanov and colleagues.17 Nickel, which is smaller than Sr2+, can be included in the atomic structure by a slight displacement of the atoms from their ideal sites. Cd2+ substitution is very exothermic, −43 kJ/mol in the surface layer and −44 kJ/mol in the second layer, implying that calcite can take up large amounts of Cd2+, simply replacing Ca2+, again consistent with experimental data. 13,14 Pb 2+ substitution is also exothermic: −30 kJ/mol in the surface layer and −29 kJ/mol in the second layer. The exothermic substitution energies are consistent with a strong interaction between Pb2+ and calcite.32 Using our calculated energy of substitution for the second layer, we can estimate the distribution coefficient for uptake into the calcite bulk to be 0.0079 for Sr2+, 190 for Ni2+, 5.2 × 107 for Cd2+, and 1.2 × 105 for Pb2+. If entropy effects are included, then the inclusion of a small number of foreign ions increases the configurational entropy so that our distribution constants based on electronic energies are only minimum values. The experimental Sr2+ distribution constant depends on the precipitation rate but is on the order of 0.1,8,33,34 which

Table 1. Free Energy of Solvation for the Clean and Substituted Calcite Slab, Equilibrated with a Monolayer of Water ΔGsolv (kJ/mol)

11 −22 −43 −30

distribution constant (first layer)

Table 3. Predicted Concentrations for 1% Uptake for Sr2+, Ni2+, Cd2+, and Pb2+ into Calcite Compared to the Solubility Product of the Corresponding Carbonate Mineral

RESULTS AND DISCUSSION Figure 2 confirms that the formation energy of the first hydration shell, octahedrally coordinated with six water molecules, is a good model for full ion hydration for Ni2+, Cd2+, and Pb2+ as well as Mg2+, Ca2+, Sr2+, and Ba2+22 and that exchange energies calculated using Eq. 2 are meaningful. It also demonstrates that our method is valid for both ultrasoft pseudopotentials and projector augmented wave pseudopotentials. The formation energy is directly proportional to the hydration free energy of the ion, with a slope close to 1. This implies that for any two divalent ions, the difference in formation energy for the first hydration layer serves as an excellent approximation for the difference in free energy of hydration, without the need to calculate any entropic contributions such as those from vibrations. Furthermore, the free energy of solvation for calcite slabs hydrated with a monolayer of water and substituted with Ni2+, Sr2+, Cd2+, and Pb2+differs very little from the solvation energy of the hydrated, unsubstituted slabs (Table 1). These results add credibility to our approach, where we include only the first hydration shell on the free ions and a monolayer of water on calcite to predict the ion substitution energies at the surface. This confirms our assumption that any effects from further hydration have only a minor influence on the total energy of

none Sr2+ Ni2+ Cd2+ Pb2+

second layer (kJ/mol)

Sr2+ Ni2+ Cd2+ Pb2+

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ion substituted into top layer of calcite {10.4}

first layer (kJ/mol)

C

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lead carbonate are considerably lower than for calcite so precipitation could present another mechanism for removing these contaminants. We assumed that the water phase was in equilibrium with the solid and thus saturated with respect to calcite at a concentration of [Ca2+] = [CO32−] = 5.8 × 10−5 M. Using these concentrations and the distribution constants from Table 2, we predicted what contaminant ion concentrations would be necessary to substitute 1% of the Ca2+ ions with the substituting ions in the second layer of calcite (Table 3). We compared these concentrations to the saturation concentration derived from the solubility products for the corresponding carbonate minerals (Table 3). The concentrations used here for Ca2+ and CO32− correspond to high pH but in fact it is only the ratio of the cations that matter in comparing the two processes. This makes our prediction, for which the removal process dominates, pH-independent, provided the solution is saturated with calcite. The low Sr2+ distribution constant means that Sr2+ is more likely to precipitate as strontianite, SrCO3, rather than being taken up by calcite. Ni2+ and Cd2+ are predicted to be incorporated into calcite at ion concentrations for which the solution is still well undersaturated with respect to the Ni2+ and Cd2+ phases, gaspeite (NiCO3), and otavite (CdCO3), which agrees with experiments.14,16,17 The solubility of PbCO3 is so low that despite the predicted stability of Pb2+ in calcite, cerussite (PbCO3) would form as a secondary phase in a saturation state lower than before calcite would form. Such a precipitate has indeed been observed experimentally.15,19 Predicting the best process for removing each contaminant would allow us to tailor the remediation methods through understanding the systems. We have used DFT calculations for calcite {10.4} slabs, hydrated with a monolayer of water, to predict ion substitution energies for Ni2+, Sr2+, Cd2+, and Pb2+ into the first and second layers of the slabs. Our results agree well with reported experimental data. They predict that Sr2+ substitution for Ca2+ is endothermic and not sensitive to position at the surface or in the bulk. Ni2+, Cd2+, and Pb2+ substitution for Ca2+ is exothermic. Cd2+ binds equally well on the surface and in the bulk whereas Ni2+ binds significantly more strongly in the surface than within the solid. By comparing experimental and predicted distribution constants, we predict that experiments with Cd2+ performed at room temperature are far from equilibrium with respect to Cd2+ incorporation into calcite. The thermodynamic substitution energies predicted by DFT strongly suggest that at elevated temperatures, much more Cd2+ can be incorporated where kinetic barriers are more easily overcome.

compares well with our predicted value, if we consider that with entropy included our distribution constant would be higher than 0.0079. One must keep in mind that an order of magnitude change in a distribution constant corresponds to only ∼6 kJ/mol in free energy difference at room temperature. The predicted minimum distribution constant of 190 for Ni2+ helps explain why Ni2+ is taken up by calcite to such a high degree.16,17 In addition, there is an 8 kJ/mol difference between energy at the surface and in the second layer, so uptake is favored upon surface incorporation. The experimental distribution coefficient for nickel is about 3,17 which is 1.5 orders of magnitude lower than our predicted distribution constant. This could be an effect of slow dehydration kinetics. Ni2+ hydrates strongly at room temperature and its dehydration rate could be the rate-limiting step for ion uptake by the mineral. A similar situation is found for the precipitation of magnesite, which requires the dehydration of Mg2+, which is about the same size at Ni2+, before the rhombohedral carbonate can form. This requires temperatures of about 80 °C before the dehydration rate of the Mg2+ ion is high enough.35 Ni2+ is even more strongly hydrated than Mg2+,31 so if the dehydration rate depends on the bond strength in the first hydration layer, then the discrepancy between the calculated and experimental distribution constants could be explained. The strong preference predicted for Ni2+ in the calcite surface and bulk, rather than in solution, means that the migration behavior of Ni2+ in soil or degraded concrete, which contains fine-grained calcite, is not the same as in soil with coarse-grained calcite. Our results also indicate that Ni2+ uptake by calcite would be considerably favored at higher temperatures, such as are expected in a radioactive waste repository. Higher temperature favors more rapid dehydration, so kinetic barriers are more easily overcome. The hydration energies of the contaminant cations influence the kinetics but they do not control eventual partitioning. If water is moving away from a compromised repository, then higher temperature would favor sorption on calcite surfaces, removal from solution, and eventual incorporation. As depleted fluids moved further into the far field, where the temperature would be lower, the uptake rate and extent would be lower but the fluid concentration would also be lower. Cadmium has an apparent distribution coefficient in calcite of 20,36 which is far lower than our predicted value of 5.2 × 107. The distribution coefficient for Cd2+ is higher than for Ni in experiments and in our predictions but for both uptake at the surface and in the bulk, the predictions are too high. The hydration energy for Cd2+ (−1755 kJ/mol)31 is fairly close to that of Mg2+ (−1830 kJ/mol)31 and certainly lower than for Ca2+ (−1505 kJ/mol),31 which suggests that, as for Ni2+, the dehydration kinetics could at least partially account for the large discrepancy between the measured and calculated distribution coefficients, in particular, for experiments performed at room temperature. If solid-state diffusion is a limiting factor for Cd2+ incorporation into the bulk of calcite,14 then this would also delay the time it takes to reach equilibrium. Our calculations suggest that most experimental studies for Cd2+ interaction have been performed far from equilibrium. Pb2+ interacts with calcite primarily through the precipitation of secondary phases,15,19 which we discuss below. In our calculations, the only process taken into account is ion substitution into calcite. In order to put our results into a larger context, other processes should be considered such as secondary phase formation. The solubilites of cadmium and

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address

H.S.: Functional Geomaterials Group, National Institute for Materials Science, Japan. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank members of the NanoGeoScience group for discussion and particularly George Redden for carefully reading the manuscript. Funding was provided through the W-EOR D

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(20) Gianozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Coccocioni, M.; Dabo, I.; Dal Corso, A.; de Gironcoli, S.; Fabris, S.; Fratesi, G.; Gebauer, R.; Gerstmann, U.; Gougoussis, C.; Kokalj, A.; Lazzeri, M.; Martin-Samos, L.; Marzari, N.; Mauri, F.; Mazzarello, R.; Paolini, S.; Pasquarello, A.; Paulatto, L.; Sbraccia, C.; Scandolo, S.; Sclauzero, G.; Seitsonen, A. P.; Smogunov, A.; Umari, P.; Wentzcowitch, R. M. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter 2009, 21, 395502. (21) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (22) Sakuma, H.; Andersson, M. P.; Bechgaard, K.; Stipp, S. L. S. Surface Tension Alteration on Calcite, Induced by Ion Substitution. J. Phys. Chem. C 2014, 118, 3078−3087. (23) Monkhorst, H. J.; Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B: Condens. Matter 1976, 13, 5188−5192. (24) Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 2006, 27, 1787−1799. (25) Tongying, P.; Tantirungrotechai, Y. A performance study of density functional theory with empirical dispersion corrections and spin-component scaled second-order Moller-Plesset perturbation theory on adsorbate-zeolite interactions. J. Mol. Struct.: THEOCHEM 2010, 945, 85−88. (26) Andersson, M. P.; Stipp, S. L. S. Sensitivity Analysis of Cluster Models for Calculating Adsorption Energies for Organic Molecules on Mineral Surfaces. J. Phys. Chem. C 2011, 115, 10044−10055. (27) Martyna, G. J.; Tuckerman, M. E. A reciprocal space based method for treating long range interactions in ab initio and force-fieldbased calculations in clusters. J. Chem. Phys. 1999, 110, 2810−2821. (28) Klamt, A.; Jonas, V.; Burger, T.; Lohrenz, J. C. W. Refinement and parametrization of COSMO-RS. J. Phys. Chem. A 1998, 102, 5074−5085. (29) Eckert, F.; Klamt, A. Fast solvent screening via quantum chemistry: COSMO-RS approach. AIChE J. 2002, 48, 369−385. (30) Eckert, F.; Klamt, A. COSMOtherm, version C3.0, release 13.01; COSMOlogic GmbH & Co. KG: Leverkusen, Germany, 2013. (31) Marcus, Y. Thermodynamics of Solvation of Ions 0.5. Gibbs Free-Energy of Hydration at 298.15 K. J. Chem. Soc., Faraday Trans. 1991, 87, 2995−2999. (32) Rouff, A. A.; Elzinga, E. J.; Reeder, R. J.; Fisher, N. S. X-ray absorption spectroscopic evidence for the formation of Pb(II) innersphere adsorption complexes and precipitates at the calcite-water interface. Environ. Sci. Technol. 2004, 38, 1700−1707. (33) Nehrke, G.; Reichart, G. J.; Van Cappellen, P.; Meile, C.; Bijma, J. Dependence of calcite growth rate and Sr partitioning on solution stoichiometry: Non-Kossel crystal growth. Geochim. Cosmochim. Acta 2007, 71, 2240−2249. (34) Tang, J. W.; Kohler, S. J.; Dietzel, M. Sr2+/Ca2+ and Ca-44/ Ca-40 fractionation during inorganic calcite formation: I. Sr incorporation. Geochim. Cosmochim. Acta 2008, 72, 3718−3732. (35) Saldi, G. D.; Jordan, G.; Schott, J.; Oelkers, E. H. Magnesite growth rates as a function of temperature and saturation state. Geochim. Cosmochim. Acta 2009, 73, 5646−5657. (36) Kitano, Y.; Kanamori, N.; Fujiyoshi, R. Distribution of Cadmium Between Calcium-Carbonate and Solution 0.1. Ca(HCO3)2 + Cd2+ + Bipyridine - Carbonate System. Geochem. J. 1978, 12, 137−145.

project by Maersk Oil Research and Technology Centre for studies on calcite surface properties. The computing resources were provided by the Danish Center for Scientific Computing (DCSC), which has since changed its name to the Danish eInfrastructure Cooperation (DeIC).

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