New Estimates of the Free Energy of Calcite/Water Interfaces for Evaluating the Equilibrium Shape and Nucleation Mechanisms

Abstract

This paper deals with several properties of calcite crystals. First, the solvated surface energies at 0 K of the {101̅ 4}, {101̅ 0}, {112̅ 0}, {011̅ 8}, {011̅ 2}, {0001}, and {213̅ 4} forms were determined by means of the COSMIC method. We find that the presence of water reduces by ∼7−14% the dry surface energy at 0 K, in a homogeneous way. The solvated and dry equilibrium shapes at 0 K result to be nearly homothetic: in both cases the {101̅ 4}, {101̅ 0}, {011̅ 2}, and {0001} forms are present. In a second part of the paper, the free energy at 300 K of the most widely studied {101̅ 4}/water interface has been determined (γ (101̅ 4)/w 300 K = 0.412 ± 0.020 J/m 2 ) by combining simple thermodynamic relations and contact angle measurements. Some considerations on the free energy of other interfaces:{101̅ 0}, {112̅ 0}, {011̅ 8}, {011̅ 2}, {0001}, and {213̅ 4} are also proposed. We show that our results are consistent with thermodynamic constraints and fit quite well the known dependence of the solubility of calcite on grain size experimentally determined. Furthermore, as a side result and for the first time, on the basis of our estimate of γ (101̅ 4)/w 300 K and calculated (101̅ 4) solvated surface energy, the latter affected by the limits of the COSMIC method, a rough estimate of the vibrational energy and entropy (γ (101̅ 4)/w 300 K,vib ) and configurational entropy (γ (101̅ 4)/w 300 K,config ) of the (101̅ 4)/water interface is obtained: (γ (101̅ 4)/w 300 K,vib + γ (101̅ 4)/w 300 K,config ) = −0.066 ± 0.038 J/m 2 . Finally, by applying the classical nucleation theory and our estimate of γ (101̅ 4)/w 300 K we calculated the activation energy for homogeneous and heterogeneous nucleation at room temperature. We found extremely high values for such thermodynamical quantity, suggesting that the direct formation of calcite should be prevented. This strongly supports the view that calcite formation should proceed throughout the early formation of an amorphous calcium carbonate phase (ACC).

Nucleation of metastable aragonite CaCO 3 in seawater

“…The use of H 2 O adsorbates is a reasonable approximation for hydrated surface energies under pH values corresponding to neutral and ocean water (pH = 8.1). We attain γ hydrated =γ dry ratios ranging from 50% to 70%, consistent with calorimetry studies on oxides (8) and to previous computational studies on CaCO 3 surfaces using COSMIC (COnductor-like Screening MOdel) solvation models (36).…”

“…The solvated surface is modeled by adsorption of explicit water molecules on the cation sites, which physically captures the thermodynamic effect of water hydration (34). The dominant facets of the aragonite nucleus are predicted to be the (001), (011), (010), and (110) forms, and for calcite the ð1014Þ and ð1010Þ forms, consistent with experimental morphologies and other calculations in the literature (35,36). We determine the hydrated surface energy of a pristine calcite nucleus to be 0.…”

A thermodynamic adsorption/entrapment model for selenium(IV) coprecipitation with calcite

“…In order to do this, there are several 685 key parameters that go into determining the solvent accessible surface, including the radii of the ions. In 686 a recent work the same solvation model has been used to estimate the interfacial energy between 687 calcite and water (Bruno et al, 2013 were run using 2--D periodic boundary conditions within the two region approach, in which the region 698 nearest the surface is fully relaxed while the underlying region is held fixed at the bulk geometry to 699 recreate the potential on the surface region. A thickness of 4 layers of calcite for each region was found 700 to be sufficient to yield converged surface energies.…”

A new calculation strategy to analyze the vibrational free energy of a slab and calculate the vibrational contribution of the surface free energy

“…Questa è la versione dell'autore dell'opera: BRUNO M., PRENCIPE M. (2013) Summary: We developed a new calculation strategy for determining the vibrational contribution of each layer or atom forming a slab, where the latter is a two-dimensional periodic structure of given thickness, generated by separating the bulk structure along the hkl plane of interest and used to simulate the crystal surfaces. By means of this new calculation methodology, it is now possible to estimate how the surface free energy of a crystal face changes with temperature by only taking into account the entropic contribution due to the vibrational motion of atoms in the slab.…”