Mg/Ca Partitioning Between Aqueous Solution and Aragonite Mineral: A Molecular Dynamics Study

Mg/Ca Partitioning Between Aqueous Solution and Aragonite Mineral:A Molecular Dynamics Study

Sergio E. Ruiz-Hernandez,[a] Ricardo Grau-Crespo,*[a] Neyvis Almora-Barrios,[a]

Mari�tte Wolthers,[a, b] A. Rabdel Ruiz-Salvador,[c] Nestor Fernandez,[d] andNora H. de Leeuw*[a]

� 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eur. J. 2012, 18, 9828 – 98339828

DOI: 10.1002/chem.201200966

Introduction

The Mg content in coral fossils has been proposed before asa proxy for the reconstruction of past climates, based on cor-relations found between the Mg/Ca ratio and the sea surfacetemperature (SST) during biomineralization.[1] Magnesiumis always present in corals, with typical Mg/Ca ratios of �4 �10�3, well below the ratio of Mg/Ca =5.14 in seawater.[2] Thevariation found for the Mg/Ca ratio with SST is about fourtimes that of the Sr/Ca ratio, which is the most widely usedsignature in paleothermometry, thus promising higher reso-lution in climate change reconstructions.[1] However, doubtsremain regarding the reliability of the method due to thepoor reproducibility of the correlations[3] and uncertaintiesabout the location of Mg in the coral skeleton,[4] whichmainly consists of aragonite (CaCO3) and residual organicphases. It was initially thought that the Mg in corals occu-pies lattice positions in aragonite,[5] but recent X-ray absorp-tion fine structure (XAFS) data suggest that Mg is predomi-nantly hosted in a different phase, possibly of organicorigin.[4] Another possibility is that Mg accumulates at thearagonite surface. Coral skeletons contain two primaryultra-structural components: mm-sized aggregates of nano-

particulate CaCO3, often referred to as centres of calcifica-tion (COC), and fibrous aragonite within a skeletal organicmatrix, with intercalated organic macro-molecules.[6] TheCOC are formed first and subsequently overgrown by layersof fibrous aragonite during coral skeleton formation.[7]

Meibom et al.[8] have explained their observations of bandedMg micro-distribution in coral skeletons by either systematicdifferences in the amount of Mg in solid solution within ara-gonite and/or the preferential concentration of Mg at thesurfaces of individual aragonite fibres, as observed in mol-luscs[9] and foraminifera.[10] The higher Mg concentration inthe COC similarly could be explained by the presence ofsurface-adsorbed Mg in the COC, due to their higher sur-face to volume ratio.

To shed light on the likelihood of either of these latterscenarios (local domains in the bulk aragonite or surface en-richment) that are central to our understanding of the chem-ical basis of Mg/Ca paleothermometry, we have investigatedthe equilibrium partitioning of Mg between aqueous solu-tion and the bulk and surfaces of aragonite by using a combi-nation of molecular dynamics simulations and grand-canoni-cal statistical mechanics (see the Experimental Section). Weinclude in our model the effect of the difference betweenthe chemical potentials of Mg2+ and Ca2+ , which is kept thesame in the mineral as in solution, but we assume no inter-action between these two cations or with other ions in solu-tion. Of course, seawater is a complex phase including highconcentrations of Cl�, Na+ , SO4

2� and other ions, which cansignificantly affect the structure and dynamics of the hydra-tion shells of the cations of interest[11] and our results maytherefore be interpreted as referring to Mg- and Ca-bearingfresh water. However, this set-up allows us to identify, tothe exclusion of other factors, the effect of Ca/Mg ratios onthe uptake and location of Mg into the aragonite crystal andalso makes our predictions more easily verifiable by labora-tory-based experiments.

Results and Discussion

We first calculated the average energies of isolated Mg2+

and Ca2+ cations in water by using molecular dynamics(MD) at 300 K. The difference between the theoretical hy-dration energies is E ACHTUNGTRENNUNG[Mg2+]�E ACHTUNGTRENNUNG[Ca2+]=�344.5 kJ mol�1,

Abstract: We have calculated the con-centrations of Mg in the bulk and sur-faces of aragonite CaCO3 in equilibri-um with aqueous solution, based onmolecular dynamics simulations andgrand-canonical statistical mechanics.Mg is incorporated in the surfaces, inparticular in the (001) terraces, ratherthan in the bulk of aragonite particles.

However, the total Mg content in thebulk and surface of aragonite particleswas found to be too small to account

for the measured Mg/Ca ratios incorals. We therefore argue that mostMg in corals is either highly metastablein the aragonite lattice, or is locatedoutside the aragonite phase of thecoral skeleton, and we discuss the im-plications of this finding for Mg/Ca pa-leothermometry.

Keywords: geochemistry · molecu-lar dynamics · paleothermometry ·statistical mechanics · surfacechemistry

[a] S. E. Ruiz-Hernandez, Dr. R. Grau-Crespo, Dr. N. Almora-Barrios,Dr. M. Wolthers, Prof. N. H. de LeeuwDepartment of Chemistry, University College London20 Gordon St. London WC1H 0AJ (United Kingdom)Fax: (+44) (0)20-7679-7463E-mail : [email protected]

[email protected]

[b] Dr. M. WolthersFaculty of Earth Sciences, Utrecht UniversityUtrecht (The Netherlands)

[c] Dr. A. R. Ruiz-SalvadorGroup of Materials Developed by DesignInstitute of Materials Research and EngineeringUniversity of HavanaHavana 1400 (Cuba)

[d] Prof. N. FernandezDepartment of Inorganic ChemistryFaculty of ChemistryUniversity of HavanaHavana 1400 (Cuba)

Supporting information for this article is available on the WWWunder http://dx.doi.org/10.1002/chem.201200966.

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which is in excellent agreement with the experimental value(�344 kJ mol�1).[12] The local geometry of the water shellaround the cations is also as expected: the radial distribu-tion functions (RDF) for the ions in water (Figure 1 b) clear-ly show that the first coordination sphere of water is closerto the cation for Mg2+ ACHTUNGTRENNUNG(2.0 �) than for Ca2+ ACHTUNGTRENNUNG(2.4 �). This isa consequence of the smaller radius of Mg2+ , which alsoleads to stronger interactions and lower coordinationnumber.

We can now consider the equilibrium between the solidphase and the ions in solution:

CaN CO3ð ÞNðbulkÞþMg2þaqð Þ Ð CaN�1Mg CO3ð ÞN bulkð ÞþCa2þ

aqð Þ ð1Þ

The calculated energetic cost for the direct reaction above isDe=64 kJ mol�1, indicating a high energetic preference forthe Mg ion to be in water instead of in the aragonite bulk.The equilibrium Mg content in the bulk, xeqACHTUNGTRENNUNG[bulk]�4�10�11,is obtained from the grand-canonical probabilities (see theExperimental Section, Eqs. (4) and (5)). The very low incor-poration of Mg in the aragonite bulk mineral at equilibriumis the result of two contributing factors: the small Mg2+

cation is very unstable in the nine-fold coordinated cationpositions of aragonite, and Mg2+ is also much more stable inwater than Ca2+ .

It is clear from the above that the incorporation of Mg inthe aragonite bulk is unlikely to account for the Mg/Ca ratioof �4�10�3 usually found in corals. We therefore considerthe incorporation of Mg at the aragonite surfaces. In thiscase, the simulation has to include explicitly the water mole-cules in contact with the solid surfaces (Figure 1 a). We havefocused on the surfaces with low Miller indices that are gen-erally expressed in the experimental morphology of aragon-ite crystals (Figure 2): (010), (110), (001) and (011).[13]

Table 1 shows that the incorporation of Mg at these surfaces,although still endothermic, is less energetically expensivethan for the bulk, as the flexibility of the surfaces enablesthe accommodation of the distortion produced by the inser-tion of the small Mg2+ cation. In addition, the Mg2+ cationat the surfaces can keep part of its favourable interactionwith interfacial water. However, there are clearly importantquantitative differences among the different surface orienta-tions.

Figure 1. a) Typical cell employed in the molecular dynamics simulationsof the surfaces (snapshot from simulation of the (001) surface) and theradial distribution functions (RDF) obtained by time-averaging of inter-ACHTUNGTRENNUNGatomic distances in molecular dynamics simulations, b) distances fromisolated Mg2+ and Ca2+ cations in aqueous solution to oxygen atoms inwater molecules (Ow) and c) distances from Mg2+ in lattice sites of twodifferent aragonite surfaces to oxygen atoms in water molecules.

Figure 2. The four aragonite surfaces considered in this work. The simula-tions cells were larger than shown here, and included water, as in Fig-ure 1a. Top views only show the outmost layers, with the surface cationsdrawn as larger spheres. Cas (surface) and Cass (subsurface) are the twotypes of cation sites considered for the (011) surface.

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The (010) and (110) are non-polar surfaces terminated byboth cations and oxygen anions from the carbonate groups(Figure 2). They are the most prominent surfaces in the ex-perimental morphology, forming the long lateral faces of theacicular shape of aragonite particles.[13] There is only onetype of surface cation site at each surface, which in bothcases is coordinated to six oxygen anions (compared withnine in the bulk). However, the distribution of interatomicdistances around the cation sites is different for the two sur-faces, leading to Mg being more stable in the (110) than inthe (010) surface by 17 kJ mol�1.

The (011) surface is another non-polar surface that is typi-cally expressed in the experimental morphology of aragon-ite, forming the small base and top faces of the acicular par-ticles. Here, we can distinguish two types of cation sites thatare accessible to water, labelled Cas (surface site) and Cass

(subsurface site) in Figure 2. Both are in seven-fold coordi-nation to carbonate oxygen anions, but the Cass site is locat-ed deeper into the bulk. By calculating substitution energiesfrom our MD simulations, we found that the subsurface siteCass is less stable for Mg substitution by 44 kJ mol�1.

Finally, the (001) Ca-terminated surface is a dipolar sur-face that is stabilised by a reconstruction involving the for-mation of cation vacancies, as shown in Figure 2. A promi-nent feature of this surface is that the cation surface sitesare only four-coordinated and stand proud of the surface.Hence, not only should this site be capable of adaptingbetter to a cation with a different size, but it will also bemore exposed to the interaction with water molecules,which is favourable for Mg2+ . This observation explains whythe substitution energy for the (001) sites is so low (only2.6 kJ mol�1). The calculation of the equilibrium Mg concen-tration for this surface thus required a special procedure in-volving higher-order grand-canonical probabilities (see theSupporting Information). The estimated concentration is�6 %, which is the highest Mg content among the surfacesinvestigated here. The effect of the interaction with water inthe stabilisation of Mg at this surface is illustrated in Fig-ure 1 c: the coordination with water of surface Mg2+ ions ismuch higher when they are substituted in the (001) surface

than when they are in the (110) surface, which is the secondmost favourable surface for Mg2+ incorporation.

The preferential incorporation of Mg into the (001) sur-face can be expected to retard the growth of this surface,relative to Mg-free conditions, on the basis of the Cabrera–Vermilyea model, according to which impurities “pin” sur-face steps, retarding their movement and therefore the sur-face growth.[14] The morphology of a crystal is determinedby a complex interplay of many effects, including the rela-tive surface stabilities and the interaction with the solventand other ions. Previous theoretical work has shown that thearagonite (001) surface is not stable enough to appear signif-icantly in the equilibrium morphology of pure aragonite.[15]

The fact that this surface is actually observed experimental-ly, even if in smaller proportion than other, more stable sur-faces, could be explained by the Mg growth-retarding effectshown here. Thus, our present results allow us to reconcileprevious theoretical results with experimental observations.

The above estimations of the Mg composition of differentsurfaces can be extended to the equilibrium with other com-positions in aqueous solution (inset of Figure 3). The surfacesite Mg occupancies increase with the concentration (activi-ty) of Mg2+ relative to Ca2+ in aqueous solution. The lineartrend in the logarithmic plot for the (010), (011) and (110)surfaces corresponds to the dilute limit and can be obtainedanalytically from our grand-canonical formulation by takingthe limit of very low Mg concentrations. The (001) surfacedoes not follow the same behaviour because it accepts moreMg impurities, and exhibits saturation due to the straincaused by these higher impurity concentrations (see theSupporting Information for the calculation details).

Since Mg can be incorporated much more easily at thesurfaces than in bulk aragonite, and different surfaces ac-commodate different amounts of Mg under the same condi-tions, we can expect that the equilibrium Mg content of ara-gonite particles depends strongly on particle size and mor-phology. As a function of the particle volume V, the effec-

Table 1. Parameters characterising the equilibrium exchange of Ca2+ andMg2+ ions between aragonite (bulk and surfaces) and aqueous solution.The substitution energy De is defined by Equation (1). The probabilities(Pn,m) and equilibrium Mg concentrations (x) were calculated at T=

300 K considering an aqueous solution with Ca/Mg ratio typical of sea-ACHTUNGTRENNUNGwater, by using Eqs. (3)–(5) in the Experimental Section.

DeACHTUNGTRENNUNG[kJ mol�1]P0 P1,m P2,m xeq

Bulk 64.0 �1 1.1 � 10�8 – 4 � 10�11

010 38.2 �1 1.8 � 10�5 – 1 � 10�6

110 21.1 0.975 0.025 – 1 � 10�3

011 23.767.3

0.996 0.0041.2 � 10�10

– 2 � 10�4

001 2.6 0.033 0.967 2.9� 10�4

3.8� 10�3

1.4� 10�5

6 � 10�2

Figure 3. Effective Mg concentration of aragonite particles (bulk and sur-face) as a function of particle size for two typical aragonite morphologies.In the inset, the fraction of sites occupied by Mg at each aragonite sur-face in equilibrium with aqueous solution, as a function of the relative ac-tivities of the cations in solution (at T=300 K).

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tive Mg concentration has a constant bulk contribution anda surface contribution that decreases with increasing V:

xeq total½ � ¼ xeq bulk½ � þ xffiffiffiffi

V3p ð2Þ

in which the coefficient x depends on the morphology (butnot the volume) of the particle, and on the impurity contentof the surfaces expressed in the particular morphology. To il-lustrate this dependence, we consider two typical acicularmorphologies (Figure 3): one has a flat termination, exhibit-ing the Mg-rich (001) surface, whereas the other is terminat-ed by (011) surfaces. The dominant lateral surfaces were the(110) and (010) in both cases, following experimental obser-vations.

It is clear that the surface contribution dominates the ef-fective Mg concentration in the particle at any relevant par-ticle size. Particles exhibiting the (001) surface always havearound one order of magnitude more Mg than those withthe same volume but terminating in (011) surfaces. Further-more, for any reasonable size of the aragonite nanoparticlesthe effective Mg concentration at equilibrium is still wellbelow the overall values typically found in corals. One possi-ble explanation is that Mg incorporates in a metastable wayinto the aragonite particles, due to kinetic factors duringparticle growth, for example through a labilising effect onthe Mg hydration shell by background electrolytes in solu-tion.[4] If the strong hydration layer surrounding Mg cationsin solution is disturbed by the presence of other ions, Mgmay become more easily available for incorporation into thearagonite surface. However, as our bulk calculations haveshown that Mg incorporation in the aragonite lattice is ener-getically not favourable either, we would expect this effectto lead to even less, rather than more, Mg in the aragonitecrystal.

Alternatively, if cation transport in the fluid near thegrowing aragonite is too slow compared with the growthrate, the fluid adjacent to the crystal may locally adopta higher Mg/Ca ratio, leading to more Mg incorporation.However, this kind of mechanism is unlikely to account forthe observed substitution level, as this would require a hugelocal modification of the Mg/Ca ratio in the fluid. Anotherexplanation is that most of the Mg content in corals is notincorporated in the aragonite phase of the skeleton, but ishosted in a different phase, as suggested recently by Finchand Allison[4] based on an XAFS investigation of Mg incorals. Our theoretical results tend to support this latter sce-nario.

Finally, impurities at the surface may become entrappedin a growing crystal,[16] which may be another route for Mgto become incorporated into the aragonite mineral. Howev-er, calculations of the incorporation of Mg and other impuri-ty ions at growth steps on the calcite surface have shownthat an increasing mismatch between the impurity layer andthe pure lattice will make crystal growth an increasingly en-dothermic process.[17] We therefore consider that surface en-trapment will not be enough to explain the discrepancy be-

tween Mg content in coral and the Ca/Mg ratio found in so-lution in its growth environment.

Conclusion

Our combined molecular dynamics and statistical mechanicsstudy predicts that most of the Mg in aragonite is confinedto the particle surface, in particular to the (001) surface. It istherefore expected that the Mg content of aragonite parti-cles from corals will depend strongly on particle size andmorphology, which complicates the interpretation of theorigin of the correlation between coral Mg content and tem-perature. Furthermore, the overall Mg content of aragoniteparticles (including bulk and surface) in equilibrium withour simple model of seawater is well below the value typi-cally measured for corals, thus suggesting either metastableincorporation into aragonite, or more likely, incorporationinto a completely different phase. If the latter is the case,the Mg concentration in corals is a function of phase distri-bution, which can be affected by several uncontrollable fac-tors, effectively randomising any dependence with tempera-ture. Taken together with other experimental evidence, ourresults suggest that the Mg/Ca ratio in coral fossils is unlike-ly to constitute a reliable record of past temperatures at thesea surface.

Experimental Section

Structural models : For the bulk simulations, a 4 � 4� 4 supercell of thecrystallographic unit cell of aragonite was employed. The equilibrium cellparameters for the bulk were obtained by molecular dynamics simula-tions at constant pressure and temperature. The surfaces were represent-ed using periodic two-dimensional slabs separated by gaps of �20 �filled with water molecules at the density of liquid water (Figure 1a). Thewidth of the slab is slightly different for each surface orientation, inorder to keep the surface symmetry, but it was always chosen to be atleast 15 �, which we have checked to be thick enough to guarantee a neg-ligible interaction between the two sides of the slab. In all cases, the later-al periodicity of the slab model was chosen in such a way that single im-purities were separated from their images by three non-substituted cationsites in each direction parallel to the surface.

Evaluation of interatomic potential energies : Our calculations of the po-tential energies of the surface systems are based on the Born model ofsolids,[18] in which ions are assumed to interact through long-range Cou-lomb forces and additional short-range forces given by simple parametricfunctions, which represent electron-mediated interactions, for example,Pauli repulsions and van der Waals dispersion attractions between neigh-bouring electron-charge clouds. The electronic polarizability of the ionsis also accounted for, using the model by Dick and Overhauser,[19] inwhich each polarizable ion is represented by a core and a massless shell,which are connected by a spring. The potential parameters were takenfrom previous work by de Leeuw and Parker[17, 20] and are summarised inthe Supporting Information.

Molecular dynamics simulations : The molecular dynamics simulationswere performed using the DL POLY2 code.[21] All surface simulationswere performed at constant volume (cell parameters obtained from con-stant pressure calculations in the bulk) and temperature (300 K). Thetotal simulation time for each job was 160 ps, including 60 ps of equilibra-tion. The convergence of the results with respect to all the precision pa-

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rameters and the stability of the system evolution during the equilibriumphase were carefully tested.

Statistical mechanics : The partitioning of the Mg2+ and Ca2+ cations be-tween aragonite and seawater as a function of temperature and seawatercomposition was modelled using a grand-canonical supercell formal-ism.[22] The states of the cations in the bulk, surfaces and seawater aretreated in separate simulations, which are made consistent with eachother by the use of common chemical potentials of the involved species.The difference between the chemical potentials of Mg2+ and Ca2+ is cal-culated from the energies (E) and the activities (a) of the ions in aqueoussolution:

Dm ¼ E Mg2þaqð Þ

h i

� E Ca2þaqð Þ

h i

þ RT lna Mg2þ

aqð Þ

h i

a Ca2þaqð Þ

h i ð3Þ

in which R is the gas constant. The energies of the ions are calculatedfrom molecular dynamics simulations using the same interatomic poten-tials as for the solid phase. The logarithmic term, including the activities,accounts for the difference in the translational entropy of the ions inwater. The activities of the ions are proportional to their concentrationsthrough the so-called activity coefficients, which for the ions in seawaterare g ACHTUNGTRENNUNG[Mg2+(aq)]= 0.215 and g ACHTUNGTRENNUNG[Ca2+(aq)] =0.201.[23] The concentrations ofthe ions in seawater are in a typical ratio c ACHTUNGTRENNUNG[Mg2+(aq)]/c ACHTUNGTRENNUNG[Ca2+(aq)] =

5.14,[2] which is the value used in our calculations, unless otherwisestated. The composition of the solid (bulk or surfaces) is then modelledby an ensemble of configurations of supercells with a fixed number N ofcation sites and a variable number n of Mg2+ cations (the number ofCa2+ cations is then N�n). For each composition, the probability of themth configuration with n substitutions is given by a Boltzmann exponen-tial:

Pn;m ¼Wn;m

Xexp

En;m � E0 � nDm

RT

� �

ð4Þ

in which En,m and Wn,m are the energy and the degeneracy (number ofequivalent ionic arrangements) of the configuration, E0 is the energy ofthe unsubstituted (Ca-only) structure, and X is the grand-canonical con-figurational partition function. In this way, the equilibrium concentrationof impurities (per site) in the bulk or surface can be obtained as:

xeq ¼1N

X

n

nX

m

Pn;m ð5Þ

At low dopant concentrations, which is generally the case for Mg substi-tutions in aragonite, the terms with n=0 and n=1 are dominant andhigher-order terms can be excluded. However, for the (001) surface,which can accommodate more Mg2+ cations, it was necessary to includeterms up to n=2. Further details are given in the Supporting Informa-tion.

Acknowledgements

We acknowledge the EU (grant MRTNCT-2006–035488), University ofHavana, the Cuban Environmental Agency, the Netherlands Organisa-

tion for Scientific Research (NWO), the Darwin Centre for Biogeoscien-ces and the Royal Society for funding.

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