<i>Ab Initio</i> Approach to the Temperature-Dependent Coupled Substitution of Rare Earth Elements (REE) into Fluorapatite using Halide (F, Cl), Monazite, Bastnäsite, and Aqueous REE Sources

Rare earth elements are crucial for developing alternative energy sources, such as batteries, for current and future applications. Mineral exploration and processing rely on thermodynamic models, which require accurate properties for all of the involved minerals and solutes. Modeling REE deportment in geological and engineered systems is challenging due to their tendency to occur in trace amounts in ore minerals, hindering direct experimental determination of key thermodynamic properties. This study uses quantum-mechanical calculations and literature values of standard thermodynamic entities to determine incorporation mechanisms and energies for different reference and host phases using solid and aqueous environments. This approach can be transferred to a wide range of applications. This study investigates the coupled substitution of light rare-earth elements (lanthanum to gadolinium) and Na+ for two Ca2+ sites in fluorapatite. With fluoride source phases, incorporation enthalpies become more negative with increasing temperature, while Gibbs free energies become more positive. When using enthalpies and Gibbs free energies of formation for chloride reference phases, which are more soluble than the fluorides, in combination with the quantum-mechanical data of the fluorides, the incorporation energies are more positive. To eliminate dependence on the anion in the reference phases and to understand the thermodynamics between host/incorporated solid and aqueous cations (REEaq3+, Na/Cuaq+, and Ca2+), dissolution energies of the reference phases are added. This procedure enables the calculation of bulk REE/Ca equilibrium ratios in fluorapatite as a function of aqueous REE3+, Na+, and Ca2+ activities via equilibrium constants.