A general moment NRIXS approach to the determination of equilibrium Fe isotopic fractionation factors: Application to goethite and jarosite

Abstract

The equilibrium Fe isotopic fractionation factors of goethite and jarosite have considerable importance for interpreting Fe isotope variations in low temperature aqueous systems on Earth and possibly Mars in the context of future sample return missions. We measured the β-factors of goethite FeO(OH), potassium-jarosite KFe_3(SO_4)_2(OH)_6, and hydronium-jarosite (H_3O)Fe_3(SO_4)_2(OH)_6, by Nuclear Resonant Inelastic X-ray Scattering (NRIXS, also known as Nuclear Resonance Vibrational Spectroscopy – NRVS or Nuclear Inelastic Scattering – NIS) at the Advanced Photon Source. These measurements were made on synthetic minerals enriched in ^(57)Fe. A new method (i.e., the general moment approach) is presented to calculate β-factors from the moments of the NRIXS spectrum S(E). The first term in the moment expansion controls iron isotopic fractionation at high temperature and corresponds to the mean force constant of the iron bonds, a quantity that is readily measured and often reported in NRIXS studies. The mean force constants of goethite, potassium-jarosite, and hydronium-jarosite are 314 ± 14, 264 ± 12, and 310 ± 14 N/m, respectively (uncertainties include statistical and systematic errors). The general moment approach gives ^(56)Fe/^(54)Fe β-factors of 9.7, 8.3, and 9.5‰ at 22 °C for these minerals. The β-factor of goethite measured by NRIXS is larger than that estimated by combining results from laboratory exchange experiments and calculations based on electronic structure theory. Similar issues have been identified previously for other pairs of mineral–aqueous species, which could reflect inadequacies of approaches based on electronic structure theory to calculate absolute β-factors (differences in β-factors between aqueous species may be more accurate) or failure of laboratory experiments to measure mineral–fluid equilibrium isotopic fractionation at low temperature. We apply the force constant approach to published NRIXS data and report 1000 × ln β for important Fe-bearing phases of geological and biochemical relevance such as myoglobin, cytochrome f, pyroxene, metal, troilite, chalcopyrite, hematite, and magnetite.

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