Equilibrium fractionation of REE isotopes in nature: Insights from NRIXS and DFT+U studies of Eu and Dy phonon density of states

Abstract

Rare Earth Elements (REEs) are commonly utilized in Earth and environmental sciences to study a variety of geological processes due to their distinct patterns and radioactive-radiogenic decay systems (¹⁴⁷Sm-¹⁴³Nd, ¹⁴⁶Sm-¹⁴²Nd, ¹³⁸La-¹³⁸Ce). Advances in analytical techniques now enable the use of REE stable isotopic fractionations to clarify lingering ambiguities in REE systematics. In this study, we employed Nuclear Resonant Inelastic X-ray Scattering (NRIXS) to study the phonon density of states of ¹⁵¹Eu and ¹⁶¹Dy in several pure compounds, as well as in synthetic basalt and andesite glasses, and rhyolite glasses produced under various redox conditions, to determine equilibrium isotopic fractionation factors for the REEs. We additionally utilized Density Functional Theory with a Hubbard U correction (DFT+U) to calculate these factors. Our findings indicate that the directionally averaged mean force constant of Dy³⁺ is ∼270 N/m across various compounds, while those of Eu²⁺ and Eu³⁺ are ∼83 and 214 N/m, respectively, in geologically relevant glasses and other pure compounds. These force constants were then used to estimate those of all REEs using scaling arguments. The results suggest that equilibrium isotopic fractionation should be limited for REEs in igneous rocks, allowing for the interpretation of REE isotopic fractionation in these rocks and minerals as a result of kinetic effects. This could facilitate understanding the role of diffusion in igneous rocks and ore formation. Additionally, our results imply that significant Eu isotopic fractionation could exist in hydrothermal fluids, which could aid in understanding the formation of ore deposits and REE cycling in the oceans.