Incorporation of Mg^{2+} in surface Ca^{2+} sites of aragonite: an ab initio study
 Jun Kawano^{1, 2}Email author,
 Hiroshi Sakuma^{3} and
 Takaya Nagai^{2}
DOI: 10.1186/s4064501500394
© Kawano et al.; licensee Springer. 2015
Received: 20 October 2014
Accepted: 17 March 2015
Published: 2 April 2015
Abstract
Firstprinciples calculations of Mg^{2+}containing aragonite surfaces are important because Mg^{2+} can affect the growth of calcium carbonate polymorphs. New calculations that incorporate Mg^{2+} substitution for Ca^{2+} in the aragonite {001} and {110} surfaces clarify the stability of Mg^{2+} near the aragonite surface and the structure of the Mg^{2+}containing aragonite surface. The results suggest that the Mg^{2+} substitution energy for Ca^{2+} at surface sites is lower than that in the bulk structure and that Mg^{2+} can be easily incorporated into the surface sites; however, when Mg^{2+} is substituted for Ca^{2+} in sites deeper than the second Ca^{2+} layer, the substitution energy approaches the value of the bulk structure. Furthermore, Mg^{2+} at the aragonite surface has a significant effect on the surface structure. In particular, CO_{3} groups rotate to achieve sixcoordinate geometry when Mg^{2+} is substituted for Ca^{2+} 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 Mg^{2+} and reduces the substitution energy. The structural rearrangements observed in this study of the aragonite surface induced by Mg^{2+} likely change the stability of aragonite and affect the polymorph selection of CaCO_{3}.
Keywords
Aragonite Impurity Surface structure Firstprinciples calculationBackground
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 firstprinciples calculations.
Many researchers have previously reported that alkalineearth 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, RuizHernandez 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 indepth 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 firstprinciples calculations, and the effect of Mg^{2+} on the formation of polymorphs was examined.
Methods
The optimized geometries and total energies of the surfaces were obtained using DFT with the Vienna ab initio simulation package (VASP) code (Kresse and Hafner 1993, 1994; Kresse and Furthmüller 1996a, b; Kresse and Joubert 1999) and the PerdewBurkeErnzerhof version of the generalized gradient approximation (GGAPBE) (Perdew et al. 1996). The energy cutoff of the planewave basis set was 900 eV, which was tested for energy convergence. The valence states for Ca, Mg, C, and O are 3s^{2}3p^{6}4s^{2}, 2p^{6}3s^{2}, 2s^{2}2p^{2}, and 2s^{2}2p^{4}, respectively, following previous DFT calculations for CaCO_{3} (Hossain et al. 2009) and MgCO_{3} (Hossain et al. 2010).
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 CO 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.
Results and discussion
Substitution energy of Mg^{2+} for Ca^{2+} near the aragonite surface
Estimated surface energies (J/m ^{ 2 } ) of the aragonite surfaces
Surface  This work  Akiyama et al.  de Leeuw and Parker  

DFT  DFT  Empirical potential  
Pure  Pure  Pure  Hydrated  
{001}  \( {\theta}_{{\mathrm{CO}}_3}=0.5 \)  0.49  0.58  0.85  0.90 
{010}  θ _{Ca} = 0.5  0.57  0.73  0.96  0.24 
{110}  θ _{Ca} = 0.5  0.49  0.64  0.88  0.56 
De Leeuw and Parker (1998) estimated the energies of pure and hydrated surfaces and found that hydration does not stabilize the carbonateterminated {001} surface and less so the calciumterminated {110} surface (Table 1). In contrast, the calciumterminated {010} surface was significantly stabilized by hydration. The surface energies calculated in this study show almost the same trend. Therefore, the substitution energies obtained for nonhydrated and hydrated {001} and {110} surfaces can be considered to have similar features. It is thus reasonable to analyze nonhydrated {001} and {110} surfaces to discuss the exchange energy in aqueous solutions, whereas Nada (2014) recently reported the importance of water layers on the calcite {104} surface.
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.
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 (RuizHernandez 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 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 sixcoordinate 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
Firstprinciples 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 sixcoordinate geometry, such as CaO_{6} octahedra in the calcite structure. Mg^{2+} generally assumes a preferential sixcoordinate geometry, even at the aragonite surface, indicating that it changes the surface stability of aragonite, which may affect the formation of CaCO_{3} polymorphs.
Abbreviations
 AFM:

atomic force microscopy
 DFT:

density functional theory
 GGAPBE:

generalized gradient approximationPerdewBurkeErnzerhof
 MD:

molecular dynamics
 VASP:

Vienna ab initio simulation package
Declarations
Acknowledgements
The authors would like to thank Y. Kimura, one of the session conveners of the 2013 JpGU annual meeting, for his recommendation for submission of the present study to PEPS. Thanks are also due to two anonymous reviewers and the editor for their constructive comments. This study was supported by a MEXT grant for the tenuretracking system and JSPS KAKENHI Grant Number 26870010.
Authors’ Affiliations
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