Abstract
The nuclear volume effects (NVEs) of Hg, Tl and Pb isotope systems are investigated with careful evaluation on quantum relativistic effects via the Dirac’s formalism of full-electron wave function. Equilibrium 202Hg/198Hg, 205Tl/203Tl, 207Pb/206Pb and 208Pb/206Pb isotope fractionations are found can be up to 3.61‰, 2.54‰, 1.48‰ and 3.72‰ at room temperature, respectively, larger than fractionations predicted by classical mass-dependent isotope fractionations theory. Moreover, the NVE can cause mass-independent fractionations (MIF) for odd-mass isotopes and even-mass isotopes. The plot of vs. for Hg-bearing species falls into a straight line with the slope of 1.66, which is close to previous experimental results. For the first time, Pb4+-bearing species are found can enrich heavier Pb isotopes than Pb2+-bearing species to a surprising extent, e.g., the enrichment can be up to 4.34‰ in terms of 208Pb/206Pb at room temperature, due to their NVEs are in opposite directions. In contrast, fractionations among Pb2+-bearing species are trivial. Therefore, the large Pb fractionation changes provide a potential new tracer for redox conditions in young and closed geologic systems. The magnitudes of NVE-driven even-mass MIFs of Pb isotopes (i.e., ) and odd-mass MIFs (i.e., ) are almost the same but with opposite signs.
Highlights
Toshiyuki Fujii and his co-workers have made tremendous efforts on experimental evaluations of NVEs for isotope systems, including Ti, Sn, Zr, Ni, Zn, Gd, Nd, Cr, Sr, Te and Cd etc.[15,16,17,18,19,20,21,22,23,24,25,26,27,28,29] they performed quantum chemistry calculations for a few isotope systems, such as Zn20,21, Ni18, Tl30 and Pb31
There are a few different computational methods used to investigate quantum relatistic effects associated with the NVE, e.g., Schauble[4,32] used the DIRAC and ABINIT software package, Abe et al.[5,6,7] used a four-component relativistic atomic program package-GRASP2K, Fujii et al.[18,20,21,30,31] used a software provided by Tokyo University (UTchem)
Equilibrium stable isotope fractionations of Hg, Tl, and Pb-bearing species are shown in Figures 1, 2, and 3 and Tables 1, 2, and 3 relative to Hg0, Tl0, and Pb0 in terms of 1000·lnβ, including conventional mass-dependent (1000·lnβ MD) and nuclear volume effect fractionation factors (1000·lnβ NV)
Summary
Toshiyuki Fujii and his co-workers have made tremendous efforts on experimental evaluations of NVEs for isotope systems, including Ti, Sn, Zr, Ni, Zn, Gd, Nd, Cr, Sr, Te and Cd etc.[15,16,17,18,19,20,21,22,23,24,25,26,27,28,29] they performed quantum chemistry calculations for a few isotope systems, such as Zn20,21, Ni18, Tl30 and Pb31. There are a few different computational methods used to investigate quantum relatistic effects associated with the NVE, e.g., Schauble[4,32] used the DIRAC and ABINIT software package, Abe et al.[5,6,7] used a four-component relativistic atomic program package-GRASP2K, Fujii et al.[18,20,21,30,31] used a software provided by Tokyo University (UTchem). Nemoto et al.[36] found a two-component realtivistic method (the finite-order Douglas-Kroll-Hess method with infinite-order spin-orbit interactions for the one-electron term and atomic-mean-field spin-same-orbit interaction for the two-electron term, i.e., IODKH-IOSO-MFSO) with almost equivalent accuracy but 30 times faster than the previous four-component method by DIRAC software package They predicted the IODKH-IOSO-MFSO method could compute larger system for future NVE calculation. Large fractionations (up to ca. 4‰ at room temperature) between Pb4+- and Pb2+-bearing species are found for the first time
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