Incorporation of Mg2+ in surface Ca2+ sites of aragonite: an ab initio study

First-principles calculations of Mg2+-containing aragonite surfaces are important because Mg2+ can affect the growth of calcium carbonate polymorphs. New calculations that incorporate Mg2+ substitution for Ca2+ in the aragonite {001} and {110} surfaces clarify the stability of Mg2+ near the aragonite surface and the structure of the Mg2+-containing aragonite surface. The results suggest that the Mg2+ substitution energy for Ca2+ at surface sites is lower than that in the bulk structure and that Mg2+ can be easily incorporated into the surface sites; however, when Mg2+ is substituted for Ca2+ in sites deeper than the second Ca2+ layer, the substitution energy approaches the value of the bulk structure. Furthermore, Mg2+ at the aragonite surface has a significant effect on the surface structure. In particular, CO3 groups rotate to achieve six-coordinate geometry when Mg2+ is substituted for Ca2+ in the top layer of the {001} surface or even in the deeper layers of the {110} surface. The rotation may relax the atomic structure around Mg2+ and reduces the substitution energy. The structural rearrangements observed in this study of the aragonite surface induced by Mg2+ likely change the stability of aragonite and affect the polymorph selection of CaCO3.


Background
The formation of calcium carbonate (CaCO 3 ) polymorphs, calcite, aragonite, and vaterite has been extensively investigated due to their importance in geological and biological environments. To account for the formation of a particular polymorph, the role of impurities has been proposed as the controlling factors in many studies (e.g., Kitano 1962;Davis et al. 2000); however, the mechanism for the incorporation of impurities during crystal growth is poorly understood. In this study, we focus on the incorporation of Mg 2+ in the aragonite surface and analyze its behavior using first-principles calculations.
Many researchers have previously reported that alkaline-earth cations other than Ca 2+ affect the growth kinetics of CaCO 3 (e.g., De Yoreo and Vekilov 2003; Astilleros et al. 2010;Nielsen et al. 2013). In particular, Mg 2+ has been considered important to the formation of CaCO 3 polymorphs. For example, Kitano (1962) indicated that the addition of Mg 2+ to a solution promoted the metastable formation of aragonite. Recently, detailed atomic force microscopy (AFM) observations of the growth surface of calcite suggested that Mg 2+ inhibits the crystal growth of calcite by blocking the propagation of kink sites (Nielsen et al. 2013) or by increasing the mineral solubility (Davis et al. 2000). To analyze this phenomenon on calcite surfaces at the atomic level, atomistic simulations were also conducted using static lattice energy minimization (Titiloye et al. 1998), molecular dynamics (MD) (de Leeuw and Parker 2001), and electronic structure calculations based on density functional theory (DFT) (Sakuma et al. 2014).
However, there are relatively few studies focusing on the aragonite surface. To discuss the mechanism for the formation of CaCO 3 polymorphs, not only should the atomic behavior on the calcite surface be understood but also that on the aragonite surface. Moreover, the Mg content in coral fossils comprising aragonite has been used to reconstruct the past climatic record (e.g., Mitsuguchi et al. 1996); however, the location of Mg 2+ in the coral skeleton is strongly debated (Finch and Allison 2008). Therefore, understanding the mechanism for the incorporation of Mg 2+ into the aragonite surface is important not only for the mineral and material sciences but also for the biological and environmental sciences. Divalent cations smaller than Ca 2+ , such as Mg 2+ , do not generally enter the aragonite structure, whereas larger cations, such as Ba 2+ , cannot be incorporated in the calcite structure. However, the structure near a crystal surface differs from the bulk crystal because of its flexibility. Thus, a crystal surface can incorporate ions that are unstable in the bulk structure and play an important role during the formation and subsequent crystal growth of calcium carbonate polymorphs. We investigated the substitution of Mg 2+ ions at the Ca 2+ sites of aragonite surfaces. Mg 2+ is unstable in ninefold coordination in aragonite and does not readily enter into the bulk aragonite structure; however, Mg 2+ is expected to be substitutable for Ca 2+ at sites near the surface. Recently, Ruiz-Hernandez et al. (2012) performed MD calculations regarding Mg 2+ substitution at the aragonite surface. However, they analyzed only the Mg 2+ substitution into Ca 2+ sites at the top surface. To discuss the incorporation of an ion into a specific surface, the ion substitution energy for Ca 2+ sites should be estimated at the top surface and deeper. Furthermore, the substitution of Mg 2+ for Ca 2+ may change the surface structure. This could affect the stability relations among polymorphs, as surface energy differences among polymorphs have been proposed to account for their stability field (Navrotsky 2004;Kawano et al. 2009). Hence, an in-depth analysis of these surface structures and their incorporation of ions is important; however, details regarding the surface structural changes when a Mg 2+ ion is incorporated at the surface are presently lacking. Therefore, in this study, the stability of Mg 2+ near the aragonite surface and the structure of Mg 2+ -containing aragonite surface were investigated using first-principles calculations, and the effect of Mg 2+ on the formation of polymorphs was examined.
Prior to calculation of the aragonite surface, the structural parameters of aragonite were simulated. The calculated lattice parameters are a = 5.022 Å, b = 8.042 Å, and c = 5.816 Å, whereas the experimental values are a = 4.962 Å, b = 7.969 Å, and c = 5.743 Å (Balmain et al. 1999). The calculated C-O bond lengths are 1.291 to 1.301 Å, which are comparable to previous experimentally and theoretically obtained values (Balmain et al. 1999;Akiyama et al. 2011).
Aragonite surfaces were simulated as repeated slabs. The unit supercell contained 80 atoms and 4 or 5 Ca and CO 3 layers of the unit (2 × 1) surface structure with a 15 Å thick vacuum layer. The macroscopic dipole was removed, and the neutrality of the supercell was ensured by the two equivalent surfaces on opposite sides of the slab. To calculate the substitution energy, the total energy of the slab was simulated by relaxing the atoms except those on the bottom layer. In the calculation, the supercell parameters were fixed using the calculated aragonite unit cell parameters, because Mg ions are not supposed to be substituted into the bulk Ca sites but only into surface sites; hence, substitution does not affect the lattice constants. Optimization was performed with a convergence threshold of 5.0 × 10 −6 eV/atom for the maximum energy change and 0.05 eV/Å for the maximum force. The atomic structures of the slab were drawn with the VESTA software (Momma and Izumi 2008). CaCO 3 crystals generally grow in an aqueous solution with H 2 O molecules just above the surface; however, the presence of the vacuum layer above the surface was considered here. The validity of this setting will be discussed in the next section. In the calculation, the positions of all the slab atoms were relaxed, and the surface energies E surf were obtained by dividing the difference between the total energy of the slab E slab and that of the bulk crystal E bulk , including the same number of atoms, by the total area of the calculated surface A, which includes the top and bottom surfaces:

Results and discussion
The results suggest that the {001} and {110} surfaces are slightly more stable than the {010} surface, which is consistent with previous DFT and empirical potential calculations (Akiyama et al. 2011;De Leeuw and Parker 1998). Therefore, we focused on the {001} and {110} aragonite surfaces and analyzed the substitution energy of Mg 2+ for Ca 2+ . The structures considered in this study are shown in Figure 1. In the first Ca layer of the {001} surface, there are two types of Ca sites because the coverage of CO 3 ions is 0.5 in the most stable structure of this surface. The site labeled A in Figure 1 (denoted as site A hereafter) is the site above which no CO 3 groups are located, whereas the site labeled B in the same figure (site B) is similar to the site in the bulk with respect to the arrangement of surrounding CO 3 2− ions, except for the lack of one CO 3 2− . In contrast, there are two Ca layers in the {110} surface with different depths between the CO 3 layers.
De    1987; Rodriguez-Cruz et al. 1999;Bock et al. 2006). Therefore, to substitute into a surface Ca 2+ site, a Mg atom must be released from the hydration shell. In this study, a six-coordinated complex was assumed for the divalent cations in the hydration shells, and the cohesive energies of the primary hydration shells of Ca 2+ and Mg 2+ ions were calculated using the DFT method as references. The calculated and experimental Gibbs free energies for hydration (Marcus 1991) have an excellent 1:1 correspondence, as shown in Figure 2. Following the discussion by Sakuma et al. (2014), such correspondence suggests that the relative binding enthalpy of the first hydration shell with six water molecules can describe the relative free energies of divalent cations in water.
Using these results, the energy ΔE of the Mg 2+ substitution in surface Ca 2+ sites of aragonite can be expressed as follows: ð2Þ where E surface(Ca) and E surface(Mg) represent the total energies of the aragonite slab with and without Mg, and E hydration shell(Ca) and E hydration shell(Mg) are the energies of the hydration shells of Ca 2+ and Mg 2+ with 6H 2 O, respectively. The calculated cohesive energy of the primary hydration shell of Mg 2+ with 6H 2 O is approximately −13.8 eV (1,330 kJ/mol) and that for Ca 2+ is −10.8 eV (1,030 kJ/mol), which indicates that the hydration shell of the smaller cation is more stable than that of the larger cation.
For Mg 2+ substitution in Ca 2+ sites of the bulk aragonite structure, the substitution energy obtained from Equation 2 using the energy of the bulk instead of the energy of the slab was calculated as 93.1 kJ/mol. However, the substitution energy for the surface site is much smaller than that for the bulk. Whether Mg ions will actually substitute for Ca depends on the chemical potential difference including entropy, while the entropy of an ion in aqueous solutions is difficult to estimate. Therefore, the negative or positive sign of the substitution energy ΔE does not directly mean that Mg ions enter the crystal or not. However, these energies can provide information regarding the relative stability of Mg in the site around the surface. The results of the present calculations suggest that Mg 2+ can substitute more easily at surface sites than in the bulk aragonite structure. Figure 3 shows the Mg 2+ substitution energy ΔE for a Ca 2+ site as a function of depth for the interface of the {001} and {110} surfaces.  We first discuss the {001} surface ( Figure 3a). When Mg 2+ substitutes into site A in the first Ca layer, above which no CO 3 groups are located, the substitution energy is almost zero and Mg 2+ is easily incorporated into site A, which agrees with the MD calculations (Ruiz-Hernandez et al. 2012). The substitution energy increases when Mg 2+ is substituted into the B site but is still much lower than that when it enters the Ca site in the bulk aragonite structure. However, for substitution within the deeper layers, the substitution energies increase significantly and reach almost that of the bulk aragonite structure. Thus, Mg 2+ readily attaches to the first layer of the {001} surface but less so within the deeper layers.
In the {110} surface, the substitution energy of Mg 2+ into the first Ca layer is almost the same as that for the B site in the {001} surface, and it rapidly increases with substitution in the deeper layers ( Figure 3b). However, for this surface, even the energy for the substitution at Ca sites in the fifth layer is smaller than that for the bulk. This suggests that for {110} faces, a slightly higher energy would be required for Mg 2+ ions to enter the Ca site of the top layer, whereas Mg 2+ ions would enter the deeper layers more easily than the {001} face.

Structure of aragonite surfaces with Mg 2+ ions at the Ca 2+ sites
The structures of aragonite surfaces that contain Mg 2+ ions were examined next. In the aragonite {001} surface, the CO 3 2− ions are arranged parallel to the surface; therefore, the flexibility of the movement and rotation of ions initially seem higher than those on the other surfaces. Figure 4b shows the relaxed structure of the {001} surface containing Mg 2+ ions in B sites of the first Ca layer, where Mg 2+ is surrounded by CO 3 ions. Figure 4 shows that the CO 3 groups move from the original positions and rotate 30°in the same direction. Notably, not only the CO 3 2− ions above the Mg 2+ ions, which exist on the surface, but also the CO 3 groups below Mg 2+ , which make up the second CO 3 layer, rotate in the same manner. The arrangement of CO 3 ions around a Mg atom resembles the structure of calcite. To clarify this, the arrangement of the CO 3 groups around the Mg ions is shown in Figure 5. This figure shows that CO 3 groups around a Mg 2+ ion move and rotate to assume sixcoordinate geometry, which is the arrangement of the MgO 6 octahedron in the calcite structure.
Furthermore, the {110} surface seems to have less flexibility than the {001} surface because the CO 3 groups are arranged perpendicular to the {110} surface. However,  even in this case, the CO 3 groups move and rotate to achieve six-coordinate geometry, as shown in Figure 6. Moreover, for the {110} surface, when Mg 2+ substitutes at a Ca site, not only in the first but also in the fifth Ca layer, the CO 3 groups also rotate to achieve six-coordinate geometry but do not form MgO 6 octahedra ( Figure 7). This is opposite to the {001} surface, wherein the CO 3 groups do not move to accommodate the Mg substitution into the Ca sites near the {001} surface, except in the top layer. This is probably because atoms can move easily perpendicular to the surface, but less easily when parallel to it because the size of the surface is fixed, even though the layer thickness is not fixed. Therefore, contrary to the first expectation, it is easier for CO 3 groups to rotate in the {110} surface where atoms easily move parallel to the CO 3 groups. In contrast, in the {001} surface, atoms do not readily move in the long direction parallel to the CO 3 groups, because the size of this plane is fixed.
The differences between the {001} and {110} surfaces lead to differences in the substitution energies; when Mg 2+ ions substitute in the deeper Ca layers, the atomic arrangement near the {110} surface is more relaxed than that near the {001} surface. Hence, the substitution energies for {110} are lower than those for the {001} surface. The energy gained by the rotation of CO 3 is estimated to be around 20 eV, by comparison of the substitution energy for the deep layers of the {110} surface and the value for the substitution in the bulk where CO 3 groups are not rotated.
The results suggest that the CO 3 groups near the surface easily move and rotate relative to their original positions. Moreover, Mg 2+ ions strongly prefer six-coordinate geometry. Therefore, the presence of Mg 2+ affects the surface stability of aragonite, and it may further affect the  structure of the small clusters that appear during the early formation of CaCO 3 , which has more flexibility than the surface, both of which affect the polymorph selection of CaCO 3 .

Conclusions
First-principles calculations were performed for Mg 2+containing aragonite surfaces. The results suggest that the substitution energy of Mg 2+ for Ca 2+ at the surface is lower than the substitution energy of Mg 2+ for Ca 2+ in the bulk structure. However, for the {001} surface, when Mg 2+ substitutes for Ca 2+ deeper than the second Ca layer, the substitution energy is almost the same as that for substitution in the bulk aragonite structure. In contrast, for the {110} surface, even when Mg 2+ ion substitutes into deeper layers, the substitution energy is still lower than the substitution energy in the bulk aragonite structure. Thus, Mg 2+ ions easily attach onto the {001} surface with lower energy; however, it should be difficult for these ions to move to deeper layers. In contrast, for the {110} surface, a relatively higher energy is required for Mg 2+ ions to substitute for Ca 2+ at the top surface sites, whereas they enter more easily to deeper layers than the {001} face. This is probably because the atomic structure of this surface is more relaxed, and the CO 3 groups move and rotate from their original positions even when Mg 2+ ions are in deeper layers. In contrast, for the {001} surface, the CO 3 groups do not move when Mg 2+ substitutes for Ca 2+ , except in the top layer sites where CO 3 groups easily move and rotate to achieve six-coordinate geometry, such as CaO 6 octahedra in the calcite structure. Mg 2+ generally assumes a preferential six-coordinate geometry, even at the aragonite surface, indicating that it changes the surface stability of aragonite, which may affect the formation of CaCO 3 polymorphs.