(Ca,Sr)CO3 aqueous–solid solution systems: From atomistic simulations to thermodynamic modelling

The uptake of strontium in calcium carbonates is a topic of sustained interest in (radio)geochemistry. The available data on (Ca,Sr)CO3 aqueous–solid solution (Aq–SS) systems with the calcite (R3¯c) and aragonite (Pmcn) structures are reconciled using a stepwise approach from atomistic to thermodynamic modelling consisting of: (1) Quantum–mechanical and force-field calculations aimed at the prediction of standard thermodynamic properties of a hypothetical pure SrCO3(R3¯c) compound; (2) Force-field calculations on supercell structures of end members with defects of incoherent atoms in the cluster expansion framework, followed by Monte Carlo simulations of the excess SS mixing properties in both R3¯c and Pmcn structures; (3) Thermodynamic modelling of Aq–SS systems with SS phases of both structures using the Gibbs Energy Minimization (GEM) code in two scenarios: (i) aqueous solution in equilibrium with one SS phase of either Pmcn   or R3¯c structure; (ii) aqueous solution equilibrated with two SS phases having different structures. The (ii) case was investigated using two approaches: (A) The two SS introduced as separate phases, with the excess mixing in each phase described by an own Guggenheim polynomial and (B) End members of different structures combined into a single calcite–strontianite phase using the Darken’s Quadratic Formulation (DQF) mixing model.For the aragonite–strontianite SS system, a nearly symmetric solvus is predicted in good agreement with the available calorimetric and electrochemical data. The solubility data at low Sr concentrations are qualitatively reproduced with the DQF model. For the (Ca,Sr)CO3 SS with the calcite structure, a slightly asymmetric, moderately positive excess Gibbs free energy of mixing is predicted and shown to agree well with known equilibrium distribution coefficients for trace Sr in calcite and with the predicted solubility product of the hypothetical SrCO3(R3¯c) end member. Although each SS system with the calcite and aragonite structures shows a nearly symmetric moderate deviation from the ideal mixing, the GEM calculations of Aq–SS equilibria including two SS phases result in a broad, strongly asymmetric “miscibility gap” with maximum x = 0.003 mole fraction of Sr in calcite. These results are instructive because many polyvalent cations showing a strong uptake in calcite (e.g. actinides) are expected to form end member compounds with structures different from the host mineral. The combination of atomistic simulations with GEM thermodynamic modelling provides a new suite of computer-aided tools for modelling such geochemically complex systems. The accuracy of thermodynamic values predicted from atomistic simulations is shown to be comparable to that of the best experimental data.