Triple Isotope Fractionation Exponents of Elements Measured by MC-ICP-MSAn Example of Mg Michael Tatzel,* ,†,⊥ Jochen Vogl, † Martin Rosner, ‡ Michael J. Henehan, § and Thomas Tü tken ∥ † Bundesanstalt fü r Materialforschung und -prü fung (BAM), Richard-Willstä tter Str. 11, 12489 Berlin, Germany ‡ IsoAnalysis UG, 10829 Berlin, Germany § GFZ German Research Centre for Geosciences, 14473 Potsdam, Germany ∥ Institute of Geosciences, Applied and Analytical Palaeontology, University of Mainz, 55128 Mainz, Germany * S Supporting Information ABSTRACT: In most chemical reactions, stable isotopes are fractionated in a mass-dependent manner, yielding correlated isotope ratios in elements with three or more stable isotopes. The proportionality between isotope ratios is set by the triple isotope fractionation exponent θ that can be determined precisely for, e.g., sulfur and oxygen by IRMS, but not for metal(loid) elements due to the lower precision of MC-ICP-MS analysis and smaller isotopic variations. Here, using Mg as a test case, we compute a complete metrologically robust uncertainty budget for apparent θ values and, with reference to this, present a new measurement approach that reduces uncertainty on θ values by 30%. This approach, namely, direct educt-product bracketing (sample−sample brack- eting), allows apparent θ values of metal(loid) isotopes to be determined precisely enough to distinguish slopes in three-isotope space. For the example of Mg, we assess appropriate quality control standards for interference-to-signal ratios and report apparent θ values of carbonate−seawater pairs. We determined apparent θ values for marine biogenic carbonates, where the foraminifera Globorotalia menardii yields 0.514 ± 0.005 (2 SD), the coral Porites, 0.515 ± 0.006 (2 SD), and two specimens of the giant clam Tridacna gigas, 0.508 ± 0.007 (2 SD) and 0.509 ± 0.006 (2 SD), documenting differences in the uptake pathway of Mg among marine calcifiers. The capability to measure apparent θ values more precisely adds a new dimension to metal(loid) δ values, with the potential to allow us to resolve different modes of fractionation in industrial and natural processes. I n most natural processes, stable isotopes are fractionated according to their relative mass difference or that of their isotopologues. In a few specific reactions, however, isotope abundances are shifted disproportionally to the relative mass differences of the isotopes or isotopologues. This effect is known as mass-independent isotope fractionation (MIF) and occurs, for instance, during chemical reactions in the gas phase of the sulfur cycle. 1 For elements with three or more stable isotopes such as O, Mg, Fe, Zn, and Mo, the mass-dependence of isotope fractionation can be visualized by correlations in “three-isotope plots”, i.e. x-y scatter plots of two linearized δ values. In this three-isotope space, mass-dependent isotope fractionation shifts materials along slopes that scale the two isotope ratios and that are known as the ‘mass fractionation exponent’ β 2 or ‘triple isotope fractionation exponent’ θ. 3 Fractionation laws predict minute but characteristic differences in the triple isotope fractionation exponents for equilibrium- and nonequilibrium mass-dependent stable isotope fractiona- tion mechanisms. 2 Thus, the three-isotope relationship discloses information on the mechanism of isotope fractiona- tion that cannot be obtained from δ values. For instance, high- precision isotope ratio mass spectrometry (IRMS) measure- ments allow resolution of differences in oxygen’s triple isotope composition, 4,5 facilitating a range of applications including the quantification of O 2 production by global photosynthesis, 6 the estimation of paleo-CO 2 concentrations from bioapatite, 3 the distinction of diagenetic alteration in silicates, and constraining paleo-hydrological conditions. 7,8 Recent progress in the theoretical and conceptual understanding of triple isotope fractionation 9, 10 has advanced the field, especially for applications of O and S isotope analysis by IRMS. The current state-of-the-art in metal(loid) isotope ratio analysis, however, limits the resolution of the small isotopic differences stemming from differences in triple isotope fractionation exponents. Indeed, within the metal isotope community for most elements it is often considered sufficient to analyze one isotope ratio and infer the others assuming scaling factors. 11 The ability to analytically resolve the triple isotope exponent in metal(loid)s could, however, as in the case of O and S, open up a whole range of potential discoveries. Received: June 13, 2019 Accepted: October 7, 2019 Published: October 7, 2019 Article pubs.acs.org/ac Cite This: Anal. Chem. 2019, 91, 14314-14322 © 2019 American Chemical Society 14314 DOI: 10.1021/acs.analchem.9b02699 Anal. Chem. 2019, 91, 14314−14322 Downloaded via UNIV MAINZ on November 24, 2019 at 14:50:53 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.