First-principles calculation of iron and silicon isotope fractionation between Fe-bearing minerals at magmatic temperatures: The importance of second atomic neighbors

Highlights

• This DFT-based study provides new and self-consistent Fe and Si isotope fractionation factors for the main magmatic minerals present in the crust.

• Iron isotope fractionation factors between Fe²⁺-bearing minerals are not negligible even at magmatic temperatures.

• For a given temperature and oxidation state, the local cationic environment of Fe or Si is the main factor influencing the isotopic properties of silicate minerals.

• Fractional crystallization is a viable way to explain the heavy iron isotope signature of the most evolved lavas.

Abstract

In order to elucidate the processes involved in iron and silicon isotopes partitioning during magmatic differentiation, it is essential to know the precise value of equilibrium fractionation factors between the main minerals present in the evolving silicic melts. In this study, we performed first-principles calculations based on the density functional theory to determine the equilibrium iron and silicon isotopes fractionation factors between eleven relevant silicate or oxide minerals in the context of magmatic differentiation, namely: aegirine, hedenbergite, augite, diopside, enstatite, fayalite, hortonolite, Fe-rich and Fe-free forsterites, magnetite and ulvospinel. Results show that Fe²⁺-bearing silicate minerals display significant differences in iron isotope fractionation factors that cannot be neglected, even at high temperature (1000 °C). Various physical and chemical parameters control the iron isotopic fractionation of silicate minerals. However, the main parameter, after temperature and the iron oxidation state, is the nature and number of iron second neighbors (i.e. the local chemical composition around Fe atoms). This conclusion is also valid for silicon isotopes. In the investigated nesosilicates and inosilicates, silicon isotope reduced partition function ratios (also called β-factors) show no correlation with the average Si-O bond length, which remains almost constant, but Si β-factors are correlated with the local chemical composition of the minerals. Fractional crystallization is one of the mechanisms, which could explain the evolution of iron isotopic compositions during magmatic differentiation. Using the present theoretical set of equilibrium fractionation factors allows us to assess the impact of inter-mineral isotopic fractionations, and shows that pyroxene appears to be the main mineral phase driving the isotopic evolution to a heavier signature in the most evolved lavas.

Introduction

Silicon and iron represent, respectively, the second and fourth most abundant elements on Earth. Isotopic ratios of these elements are perfect candidates to become useful tracers of a variety of geological processes because of their ubiquitous nature. Despite the large mass difference between Fe isotopes (⁵⁴Fe, ⁵⁶Fe, ⁵⁷Fe, ⁵⁸Fe) and Si isotopes (²⁸Si, ²⁹Si, ³⁰Si), the magnitude of their high-temperature isotope fractionations is limited (e.g. Dauphas et al., 2012, Méheut et al., 2009, Savage et al., 2010, Teng et al., 2013, Williams, 2004, Zambardi et al., 2014). Iron is interesting because of its multiple oxidation states (Fe⁰, Fe²⁺ and Fe³⁺) that make it a perfect element to trace the redox conditions in igneous rocks such as the evolution of oxygen fugacity (fO₂) in the mantle associated with depth (Woodland and Koch, 2003, McCammon and Kopylova, 2004, Yaxley et al., 2012) or in the lavas during magmatic differentiation. In nature, silicon has two valence states (Si⁰, Si⁴⁺) (Poitrasson, 2017). Metallic silicon (Si⁰) can be found in metallic inclusions in meteorites, and most likely in the metallic cores of terrestrial planets (e.g. Wai and Wasson, 1969, Georg et al., 2007a, Georg et al., 2007b, Pack et al., 2011). In the magmatic differentiation context, Si can be considered as only tetravalent. Silicon concentration increases during magmatic differentiation whereas Fe concentration decreases. Therefore, silicon isotopes are more likely reflecting cumulative effect (Zambardi et al., 2014). Considering their contrasted behavior during magmatic differentiation, Si and Fe isotopes represent complementary approaches to constrain the mechanisms of isotopic fractionation involved in magmatic differentiation. Both isotopic systems were extensively studied in that context, either independently (Weyer et al., 2005, WILLIAMS et al., 2005, Poitrasson and Freydier, 2005, Shahar et al., 2008, Teng et al., 2008, Schuessler et al., 2009, Schoenberg et al., 2009, Williams et al., 2009, Lundstrom, 2009, Savage et al., 2011, Sossi et al., 2012, Dauphas et al., 2014; Foden et al., 2015, Nebel et al., 2015, Poitrasson and Zambardi, 2015, Sossi and O’Neill, 2017, Williams et al., 2018, Li et al., 2020) or together (Zambardi et al., 2014, Gajos et al., 2016). Nonetheless, the processes leading to heavy Fe and Si isotopic compositions in the most evolved lavas during magmatic differentiation are still debated. Fractional crystallization (e.g. Schuessler et al., 2009, Sossi et al., 2012, Telus et al., 2012, Foden et al., 2015, Du et al., 2017), partial melting (Williams et al., 2009), fluid exsolution processes (Poitrasson and Freydier, 2005), thermal diffusion (e.g., Lundstrom, 2009, Zambardi et al., 2014, Gajos et al., 2016) and sulfide saturation in the magma (Williams et al., 2018) were suggested to explain the Fe systematics observed among igneous rocks. As Shahar et al. (2008) pointed out, “In order to understand the meaning of small but significant differences in Fe isotope ratios among minerals representing differentiated planetary materials, the mechanisms of high-T Fe isotope fractionation must be quantified”.

Different techniques can be used to determine isotope fractionation factors in silicate minerals, including: 1) conventional analysis of mineral separates involving mineralization followed by iron or silicon separation by anion exchange chromatography and MC-ICP-MS analyses, for both natural or synthetic samples (WILLIAMS et al., 2005, Savage et al., 2011, Sossi and O’Neill, 2017, Shahar et al., 2008); 2) In-situ laser ablation coupled to MC-ICP-MS techniques using nanosecond or femtosecond laser on natural samples (Sio et al., 2013, Oeser et al., 2014, Oeser et al., 2015, Collinet et al., 2017, Oeser et al., 2018); 3) For Fe isotopes, the vibrational properties of minerals can be determined by nuclear resonance inelastic X-ray scattering (NRIXS) from which reduced partition function ratios, called β-factors, are derived (Dauphas et al., 2012, Dauphas et al., 2014, Roskosz et al., 2015); 4) Also for iron, β-factors can be calculated from second-order Doppler (SOD) shift derived from Mössbauer spectroscopic measurements (Polyakov and Mineev, 2000, Polyakov et al., 2007, Polyakov, 2009, Polyakov and Soultanov, 2011); 5) Theoretical fractionation factors can also be determined from electronic structure calculations usually based on the density functional theory (Blanchard et al., 2009, Méheut et al., 2009, Huang et al., 2014, Méheut and Schauble, 2014, Wang et al., 2017). Concerning iron, only few fractionation factors are available for silicate minerals. Because olivine and most of pyroxenes are Fe²⁺-bearing minerals, the Fe isotope fractionation between them is often considered as negligible (Dauphas et al., 2014, Roskosz et al., 2015) or even inexistent (Beard and Johnson, 2004). However, some studies on natural samples highlight small but distinct isotopic signatures for olivine and coexisting clinopyroxene and orthopyroxene (Zhu et al., 2002, WILLIAMS et al., 2005). This effect was also proposed earlier from Mössbauer data by Polyakov and Mineev (2000). Besides temperature, iron oxidation state is described as one of the main parameters influencing the iron isotope fractionation with the coordination number of iron (Polyakov and Mineev, 2000, Dauphas et al., 2014, Sossi and O’Neill, 2017). Indeed, Fe³⁺-rich phases have stiffer bonds and therefore tend to concentrate heavy ⁵⁷Fe isotopes. This is the reason why most studies focused on the common Fe³⁺-bearing oxide of magmas, i.e., magnetite, in order to constrain the isotopic evolution during magmatic differentiation (Polyakov and Mineev, 2000, Polyakov et al., 2007, Shahar et al., 2008, Dauphas et al., 2012, Sossi and O’Neill, 2017). Our study provides the first ab-initio values of inter-mineral fractionation factors for iron isotopes in silicate minerals. Regarding Si isotopes, only few theoretical studies were performed on high-temperature silicate minerals (Grant, 1954, Huang et al., 2014, Méheut and Schauble, 2014, Qin et al., 2016). Grant (1954) suggested that polymerization was the key factor influencing Si isotopes among the differentiation path with enrichment of heavy isotopes with increasing polymerization. The study of Poitrasson and Zambardi (2015) on lunar and terrestrial rocks supported Grant’s hypothesis in displaying a clear relationship between increasing polymerization degree and increasing silicon isotope composition of lunar rocks. However, at the mineral scale, Méheut and Schauble (2014) displayed large isotopic fractionations between minerals having the same structure and silicon polymerization degree (kaolinite, lizardite). Silicon-Oxygen bond lengths (Huang et al., 2014) as well as the electronegativity of the cations Mg and Al (Méheut and Schauble, 2014) were also proposed to explain the difference in Si isotope signatures between minerals, but the effects of other cations have not been considered so far. Here, the influence of Ca, Fe, and Na on Si isotopes is tested through different silicate compositions.

The goal of the present study is to produce a consistent data set of iron and silicon β-factors representing the main Fe-bearing minerals of lavas. Four clinopyroxenes are investigated: aegirine, hedenbergite, augite and diopside as well as the most common orthopyroxene, i.e. enstatite. The olivine solid-solution is studied through four distinct compositions: fayalite, hortonolite and two forsterites (i.e. Fe-bearing and Fe-free forsterites). In addition, pure magnetite and ulvospinel were added to the study in order to model the fractionation factor between oxide and silicate minerals. This set of iron and silicon fractionation factors is obtained from first-principles quantum mechanical calculations. These data enable us to discuss the effect of different parameters (e.g. coordination number (CN), iron oxidation state, Fe-O and Si-O bond lengths, average or local chemical compositions) on the inter-mineral fractionation factors and to discuss the role of inter-silicate isotopic fractionation on the process of fractional crystallization that could explain the heavy Fe signatures of evolved lavas during magmatic differentiation.