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 b-factors of goethite FeO(OH), potassium-jarosite KFe 3 (SO 4 ) 2 (OH) 6 , and hydronium-jarosite (H 3 O)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 b-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 b-factors of 9.7, 8.3, and 9.5& at 22°C for these minerals. The b-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 b-factors (differences in b-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 Â ln b for important Fe-bearing phases of geological and biochemical relevance such as myoglobin, cytochrome f, pyroxene, metal, troilite, chalcopyrite, hematite, and magnetite.

Spinel–olivine–pyroxene equilibrium iron isotopic fractionation and applications to natural peridotites

“…The partial PDOS, g(E) is itself derived from the measured phonon excitation probability density function S(E) using a Fourier-Log inversion. More recently, Dauphas et al (2012) and Hu et al (2013) showed that β-factors could be calculated directly from S(E), through the mean force constant, ‫,〉ܨ〈‬ of the bonds holding iron in position. At the high temperatures relevant to igneous and metamorphic geochemistry, the fractionation between 56 Fe and 54 Fe takes the form:…”

“…For the calculation of β-factors at temperatures below ~300 °C, higher order moments of S(E) are needed (Eq. 3; Dauphas et al, 2012, Hu et al, 2013 and those terms are also compiled in Table A1.…”

“…Additional complications also arise when a distribution of hyperfine field parameters is caused by changes of chemical or magnetic nature, which is the case in some spinel minerals. For example the β-factors for magnetite proposed by Polyakov and Mineev (2000) were later proven to be inaccurate when NRIXS and new Mössbauer data were made available Mineev et al, 2007;Dauphas et al, 2012).…”

“…In this study, the synchrotron technique of nuclear resonant inelastic X-ray scattering (NRIXS) is used to derive β-factors of iron isotopes by measuring the force constant of iron bonds Sturhahn et al 1995;Dauphas et al, 2012Dauphas et al, , 2014. Monocrystals of different compositions, (Mg, Fe)(Al, Cr, Fe)2O4 and redox states are explored.…”

Isotope Fractionation Processes of Selected Elements

“…Equilibrium Fe isotope fractionations for mineral-mineral and mineral-fluid systems have been determined by 3 different approaches: (i) calculations of β-factors based on density functional theory (DFT) (Schauble et al 2001;Anbar et al 2005;Blanchard et al 2009;Rustad and Dixon 2009;Rustad et al 2010) and (ii) calculations based on Mössbauer spectroscopy and inelastic nuclear resonant X-ray scattering measurements (Polyakov 2007;Polyakov and Soultanov 2011;Dauphas et al 2012) and (iii) isotope exchange experiments (Skulan et al 2002;Welch et al 2003;Shahar et al 2008;Beard et al 2010;Saunier et al 2011;Wu et al 2011;Frierdich et al 2014).…”