The nuclear volume component of equilibrium field shift isotope fractionations in europium and other lanthanide elements is estimated using Mössbauer spectroscopy and electronic structure calculations. This effect goes in the opposite direction from equilibrium mass-dependent fractionation, and in the case of europium is predicted to dominate over mass dependent fractionation for most materials. Including both effects, Eu²⁺-bearing species will have approximately 0.4–1‰ higher ¹⁵³Eu/¹⁵¹Eu than Eu³⁺-bearing species at 298 K (25°C), and about 0.3‰ higher ¹⁵³Eu/¹⁵¹Eu at 973 K (700°C). Field shift fractionation mainly depends on oxidation state; differences in coordination structure without changes in oxidation state appear to have much weaker associated fractionations. Nuclear volume isotope fractionation will become even more dominant over mass dependent fractionation at higher temperatures because nuclear volume effects scale with 1/T (K), vs. 1/T² for mass-dependent fractionation. Fractionation favoring high ¹⁵³Eu/¹⁵¹Eu in minerals that preferentially incorporate Eu²⁺, such as plagioclase, is consistent with recent measurements on igneous rocks showing low ¹⁵³Eu/¹⁵¹Eu in samples with large negative europium anomalies (Lee and Tanaka, 2021). The present results agree with the recent conclusion that equilibrium fractionation cannot explain cosmochemical REE fractionations in primitive meteoritical materials (Hu et al., 2021), because the net fractionation is too small (~0.2‰ or less) at temperatures >1200 K where vapor-phase REE species are relevant.

The field shift effect will also tend to drive ¹⁴²Ce/^xxxCe ratios higher in reduced species (+2 > +3 > +4), for instance by 0.4‰ for ¹⁴²Ce/¹⁴⁰Ce in Ce³⁺ vs. Ce⁴⁺ at 298 K, approximately canceling the mass-dependent fractionation. The nuclear volume component of fractionation in cerium isotope pairs not involving ¹⁴²Ce will be smaller (<0.1‰) because the other nuclei have very similar volumes. As a result, mass-dependent fractionation will drive ¹³⁸Ce/¹⁴⁰Ce and ¹³⁶Ce/¹⁴⁰Ce lower in Ce⁴⁺ species while ¹⁴²Ce/¹⁴⁰Ce hardly fractionates at equilibrium. This will yield an atypical mass vs. fractionation pattern in redox pairs.

During the early Paleogene (59–50 Ma), several short-term global warming events, known as hyperthermal events, occurred. Negative carbon isotope (δ¹³C) excursions are a typical proxy for detecting hyperthermal events. During the recovery from hyperthermal events, δ¹³C values returned toward pre-event levels via scavenging lighter C isotopes from the ocean and sequestrating them within sediments. The biological pump plays a key role in this process. Barium (Ba) is a nutrient-type element primarily transported in the water column by barite formed in microenvironments associated with the decomposition of organic matter, and the Ba-stable isotope ratio is a proxy of biological productivity. In this study, the δ^138/134Ba values of bulk sediment samples from Ocean Drilling Program Site 738C in the southern part of the Kerguelen–Heard Plateau were analyzed. Although the samples predominantly comprised calcareous chalk corresponding to the latest Paleocene to early Eocene (56–52 Ma), the Ba isotope ratios of the bulk samples reflected a barite mixture with slight carbonate. Three negative δ^138/134Ba shifts were detected, corresponding to the global super-warming event “Paleocene–Eocene Thermal Maximum” at 56 Ma and to two hyperthermal events, known as ETM2 and I1. The changes in δ^138/134Ba and δ¹³C values during PETM were comparable to those reported from the South Atlantic Ocean. Although commonly recognized, the scale of δ^138/134Ba changes was smaller in the modest hyperthermal events (ETM2 and I1). Ba stable isotope ratios are a highly effective and powerful tool to reveal the response of the surficial system of Earth during hyperthermal events.