[Introduction]
   Formation process of calcium carbonate polymorphs, calcite, aragonite and vaterite has been extensively investigated because of its importance in both geological and biological environments. In order to account for the formation of a particular polymorph, impurity effect has been proposed as controlling phenomena by many researchers, however incorporation mechanism of these impurities during crystal growth is poorly understood.
   Here, we focused on the effect of alkaline earth cations (M²⁺) other than Ca²⁺ as the impurities. In general, smaller divalent cations than Ca²⁺, like Mg²⁺, cannot form solid solution with aragonite, while larger cations like Ba²⁺ cannot be incorporated into the structure of calcite. However, the structure of a crystal surface or small cluster as an initial stage of crystal growth can be different from the bulk crystal because of its flexibility, and it can play an important role as the site for incorporation of ions which is unstable in the bulk structure and in the subsequent crystal growth. Therefore, in the present study, the stability of alkaline earth cation (1) on the surface and (2) in the cluster forming in an early stage of nucleation was investigated by the first-principles calculations based on the density functional theory, and the impurity effects on the formation of polymorphs were discussed.

[Mg²⁺ at a surface]
   Recently, it has been pointed out that the surface energy difference among polymorphs could determine their stability field [1], so that it becomes more important to analyze in detail their surface structures and the incorporation process of ions and molecules into the surfaces. Here we focused on the case in which Mg²⁺ ion substitutes for Ca²⁺ site of aragonite (001) surface as an impurity. While Mg²⁺ is unstable in the nine-fold cation positions of aragonite and can hardly be incorporated into the bulk aragonite crystal, it is expected to be substituted for Ca²⁺ site at the surface. Our simulation results show that Mg²⁺ can be incorporated into the Ca²⁺ sites at the surface with lower substitution energy than that in the bulk. Furthermore, Mg²⁺ on the aragonite surface considerably affects the surface structure, especially on the arrangement of CO₃ groups, indicating that the presence of Mg²⁺ can change the surface stability of aragonite.
 
[Mg²⁺ in a cluster]
   According to the concept of prenucleation cluster (e.g. Gebauer et al. [2]), stable small clusters of calcium carbonate form even in an undersaturated solution and play an important role for the formation of polymorphs. Tribello et al. [3] showed by using molecular dynamics simulations that, at an early stage of calcium carbonate growth, isolated ions disappear very quickly and charged clusters are rarely observed. It means that, Ca²⁺/CO₃^2- pair forms first, and then larger clusters appear as the aggregation of these pairs.
   Therefore, in order to understand the effect of impurities like Mg²⁺ on an early stage of CaCO₃ growth, we should discuss the incorporation process of these ions during the formation of Ca²⁺/CO₃^2- pairs and their aggregation. In the present study, we calculated energies of (i) primary hydration shells of M²⁺, (ii) M²⁺/CO₃^2- pairs, and (iii) clusters including two M²⁺/CO₃^2- pairs, and determined the stable arrangement of these clusters by the first-principles calculations.
   The calculation results show that Mg²⁺ is easier to be incorporated into a small cluster and prefers to be at the center of the cluster, while the hydration energy of Mg²⁺ is higher than that of other divalent cations. This indicates that Mg²⁺ is difficult to be released from hydration shell, however, once released, it is easy to be incorporated into the clusters. Considering that thermal energy is needed to release Mg²⁺ ion from hydration shell, the effect of Mg²⁺ is expected to be more striking with increasing temperature.

[1] A. Navrotsky, PNAS 101 (2004) 12096, [2] D. Gebauer et al., Science 322 (2008) 1819, [3] G.A. Tribello et al., J. Phys. Chem.B 113 (2009) 11680.

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