Nuclear Volume Effects in Equilibrium Stable Isotope Fractionations of Hg, Tl and Pb Isotope Systems

Abstract:

Many evidences showed that heavy isotope systems could be significantly fractionated as the consequence of the nuclear volume effect (NVE) or so-called nuclear field shift effect. Here we investigate NVEs of Hg, Tl and Pb isotope systems by using quantum chemistry computational methods with careful evaluation on quantum relativistic effects via the Dirac’s formalism of full-electron wavefunction. Our results generally agree with previous studies but with noticeable differences in many cases. With the unique NVE driving force, equilibrium ²⁰²Hg/¹⁹⁸Hg and ²⁰⁵Tl/²⁰³Tl isotopes can be fractionated up to 3.94‰ and 2.78‰ at 0℃, respectively, showing potentially large equilibrium isotope fractionations can be expected for future studies of these two isotope systems. Moreover, the NVE causes large mass-independent fractionations (MIF) for odd-mass isotopes (e.g., ∆¹⁹⁹_NVHg and ∆²⁰¹_NVHg) and small MIFs for even-mass isotopes (e.g., ∆²⁰⁰_NVHg). For Pb isotope system, NVEs induce isotope fractionations up to 1.62‰ (²⁰⁷Pb/²⁰⁶Pb) and 4.06‰ (²⁰⁸Pb/²⁰⁶Pb) at 0℃. However, contributions from classical mass-dependent driving force are small, about 0.1-0.5‰ for ²⁰⁷Pb/²⁰⁶Pb and 0.2-0.9‰ for ²⁰⁸Pb/²⁰⁶Pb. We find that Pb⁴⁺-bearing species can be significantly enriched heavy isotopes than Pb²⁺-bearing species. Comparing to Pb⁰, Pb²⁺-bearing species even enrich lighter Pb isotopes. A very strange and interesting thing is that the beta value of Pb²⁺-bearing species can be smaller than the unity (1.000). Similar thing has been found on Tl⁺-bearing species. This is an impossible and unexplained situation if only based on classical mass-dependent isotope fractionation theory (e.g., Bigeleisen-Mayer equation). The consequence is that the different direction of beta values of Pb²⁺-bearing species will let the Pb isotope fractionation even larger when they fractionate with Pb⁴⁺-bearing species. Moreover, NVEs also cause mass-independent fractionation (MIF) of odd ²⁰⁷Pb isotopes (∆²⁰⁷_NVPb).