Equilibrium mercury and lead isotope fractionation caused by nuclear volume effects in crystals

Abstract

To investigate equilibrium mercury (Hg) and lead (Pb) isotope fractionation caused by the nuclear volume effect (NVE) in crystals, the electron densities at nuclei (i.e., |Ψ(0)|2) for Hg- or Pb-bearing crystalline compounds were investigated by using the relativistic spin orbit zeroth-order regular approximation (ZORA) method with a three-dimensional periodic boundary condition based on the density functional theory (DFT). Many isotope fractionation factors of crystalline compounds are provided for the first time. Our results show, even at 1000 °C, NVE-driven Hg and Pb isotope fractionation are meaningfully large, i.e., range from 0.12‰ to 0.49‰ (202Hg/198Hg), from − 0.20‰ to 0.17‰ (208Pb/206Pb) and from − 0.08‰ to 0.06‰ (207Pb/206Pb) relative to Hg0 vapor and Pb0 vapor, respectively. Specifically, the fractionations range from − 0.06‰ to − 0.20‰ (208Pb/206Pb) and from − 0.02‰ to − 0.08‰ (207Pb/206Pb) for Pb2+-bearing species, from 0.10‰ to 0.17‰ (208Pb/206Pb) and from 0.04‰ to 0.06‰ (207Pb/206Pb) for Pb4+-bearing species in crystals. All calculated Hg-bearing species in crystals will enrich heavier isotope (202Hg) relative to Hg0 vapor. Meanwhile, Pb4+-bearing species enrich heavier Pb isotopes (208Pb and 207Pb) than Pb2+-bearing species in crystals, which the enrichment can be up to 0.37‰ (208Pb/206Pb) and 0.14‰ (207Pb/206Pb) at 1000 °C, due to their NVEs are in opposite directions. The NVE-driven MIFs of Hg isotopes, which are compared to the Hg202- Hg198 baseline, are up to − 0.158‰ ( $$\Delta {}_{{{\text{NV}}}}^{199} {\text{Hg}}$$ ), − 0.024‰ ( $$\Delta {}_{{{\text{NV}}}}^{200} {\text{Hg}}$$ ) and − 0.094‰ ( $$\Delta {}_{{{\text{NV}}}}^{201} {\text{Hg}}$$ ) relative to Hg0 vapor at 500 °C. For all studied Hg-bearing species in crystals, the MIFs of two odd-mass isotopes (i.e., $$\Delta {}_{{{\text{NV}}}}^{199} {\text{Hg}}$$ and $$\Delta {}_{{{\text{NV}}}}^{201} {\text{Hg}}$$ ) will be changed proportionally and their ratio (i.e., $$\Delta {}_{{{\text{NV}}}}^{199} {\text{Hg}}$$ / $$\Delta {}_{{{\text{NV}}}}^{201} {\text{Hg}}$$ ) will be a constant 1.67. The NVE can also cause mass-independent fractionations for 207Pb and 204Pb compared to the baseline of 208Pb and 206Pb. The largest NVE-driven MIFs are 0.043‰ ( $$\Delta {}_{{{\text{NV}}}}^{207} {\text{Pb}}$$ ) and − 0.040‰ ( $$\Delta {}_{{{\text{NV}}}}^{204} {\text{Pb}}$$ ) among all the studied species relative to Pb0 vapor at 500 °C. The magnitudes of odd-mass isotope MIF ( $$\Delta {}_{{{\text{NV}}}}^{207} {\text{Pb}}$$ ) and even-mass isotope MIF ( $$\Delta {}_{{{\text{NV}}}}^{204} {\text{Pb}}$$ ) are almost the same but with opposite signs, leading to the MIF ratio of them (i.e., $$\Delta {}_{{{\text{NV}}}}^{207} {\text{Pb}}$$ / $$\Delta {}_{{{\text{NV}}}}^{204} {\text{Pb}}$$ ) is − 1.08.