Prediction and Rationalization of Site Preference of Rare Earth Elements in Fluorapatite from Density Functional Theory

Fluorapatite (FAp, nominally Ca₁₀(PO₄)₆F₂) has been identified as an important host material for rare earth elements and yttrium (REY) in marine sediments. REY can be accommodated in either the larger 6+3 coordinated Ca1 site or the smaller 6+1 coordinated Ca2 site, yet little is known about the site preference of REY through the lanthanide series despite its importance for understanding REY enrichment processes in FAp. Theoretical investigations based on density functional theory (DFT) predict that all REY intrinsically prefer the smaller and more ionic Ca2 site. The Ca2 site preference is less pronounced when the excess of positive charge resulting from the REY³⁺ for Ca²⁺ substitution is compensated by a coupled Na⁺ for Ca²⁺ substitution, instead of the energetically more favorable Si⁴⁺ for P⁵⁺ coupled substitution. The site preference varies quadratically with the ionic radius of REY and linearly with the sum of the first and second ionization energies. The quadratic shape of the site preference is similar to the shape of the Onuma diagrams, which suggests that the local effective elastic constant of the site controls the site preference rather than the nominal size of the site. Despite being smaller, the Ca2 site has a lower effective elastic constant and is, therefore, more flexible than the Ca1 site for accommodating larger and smaller trivalent REY cations. Concentration-dependent computations show that REY clustering is thermodynamically favorable except for Yb and Lu.