Insights from iron isotopes into magmatic differentiation and mantle heterogeneity of the Kerguelen Archipelago

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Iron geochemistry

Iron is of particular interest for geochemist due to the fact that it is a ubiquitous element with complex chemical behaviour. Iron is the most abundant redox-active metal in the entire Solar System and the fourth most abundant in the Earth’s crust. Iron is moder-ately volatile and a refractory element. Following the Goldschmidt’s classification, iron is a siderophile element. However, at high sulphide level iron is chalcophile and at high oxygen levels, iron becomes lithophile. The aptitude of iron to bind with both sulfur and oxygen explains the wide variety of minerals (silicates, oxides/hydroxydes, carbonates, sulphides) that contain iron on Earth. The most interesting characteristic of iron is how-ever its sensitivity to redox changes. Iron has three oxidation states, metallic iron (Fe0), ferrous iron (Fe2+) and ferric iron (Fe3+). The electronic configuration of F e0 is 3d6 4s2 whereas under oxidizing conditions Fe2+ and Fe3+ lose the two electrons of the outer 4s shell and display electronic configuration of 3d6 and 3d5, respectively. Consequently, iron contributes significantly to the electron transfer in numerous reactions in Earth.
In magmatic systems, iron is a major element in the magma and is stoichiometrically incorporated into mantle and crust minerals (e.g. olivines, pyroxenes, oxides such as magnetite). Iron abundance decreases with magmatic differentiation (increasing SiO2 content; Bowen (1928)), but remains present in amounts that have significant effects on melts (Mysen and Richet, 2019b) and mineral compositions. Iron, and more precisely the Fe3+/Fetot ratio, is also the most common proxy of oxygen fugacity (f O2) of the upper-mantle and basalts. At high temperature, the changes in the relative abundances of ferrous and ferric iron can be simply defined by the reaction : 2 Fe2+ + 1/2 O2 ! 2Fe3+ + O2.
The f O2 is commonly calculated from O2 buffered mineral reactions. The most common oxygen fugacity buffers are, in increasing order of oxidation, the Iron-Wurstite (IW), the Fayalite-Magnetite-Quartz (FMQ) and the Magnetite-Hematite (MH) buffer.

Iron stable isotopes

Iron has four natural stable isotopes 54Fe, 56Fe, 57Fe, 58Fe with respective mean abun-dances of 5.80, 91.72, 2.20 and 0.28 % and atomic masses of 53.9396105, 55.9349375, 56.9353940 and 57.9332756 a.m.u (atomic mass unit). In the literature, iron isotopic compositions are given alternatively as 56Fe or 57Fe. Measurement of 57Fe is more challenging because of its low abundance compared to 56Fe. However, the mass difference between 57Fe and 54Fe is greater than between 56Fe and 54Fe, as a consequence a larger range of fractionation (by 1:5 times) can be observed (Schauble, 2004).
Measurements of Fe isotopes There are two major challenges for Fe isotopes ac-curate analysis using Multi-Collector Inductively Coupled Plasma Mass Spectrometry (MC-ICP-MS) : 1) Resolving Fe isotopes from the different elemental and molecular iso-baric interferences (Table 1.1), 2) correcting for instrumental bias (matrix effects) in order to preserve the natural mass-dependent isotopic fractionation. Instrumental bias can be corrected using Ni isotopes spike associated to standard bracketing methods (e.g., Weyer et al., 2005) or daily regression method between ln57Fe/54Fe and ln61Fe/60Fe (Poitrasson and Freydier, 2005) assuming that Ni and Fe behave similarly to the matrix-induced mass-bias fluctuation. However, the use of Ni as a mass-bias monitor during analytical session is only valid if the 2 interference-free Ni isotopes can be collected simultaneously in the collector array (Johnson et al., 2020). Details of the mass-bias correction can be found in Poitrasson and Freydier (2005). Furthermore, ion-exchange chromatography is necessary before the introduction in the MC-ICP-MS in order to remove the isobars (i.e.54Cr, 58Ni) eventually present in the samples (see Chapter 5 and Poitrasson and Freydier (2005)) for details on the purification procedure) and prevent matrix effect.

Iron isotopes fractionation at high temperature

The improvement of iron isotopes analysis, in term of accuracy and precision, through time (see Johnson et al. (2020) for details) promoted the use of iron isotopes in high-temperature field. Iron isotope fractionation at high temperature is indeed small, in the order of 1 % or less, but significant (Fig 1.2). This section will focus on Fe isotopes fractionation occurring in the Earth’s mantle and crust and the processes associated. The effect of metasomatism on the iron isotopes signatures of mantle rocks, the influence of partial melting on peridotites and basalts Fe isotopes signatures as well as the evolution of Fe isotopes compositions of the lavas during magmatic differentiation will therefore be discussed as it is at the center of this phD thesis.

The Earth mantle and metasomatism

Investigation of iron isotopes compositions of the Earth mantle was carried on a variety of mantle rocks including lherzolites, harzurgites, dunites, wehrlites, pyroxenites and various metasomatised peridotites (e.g., Craddock et al., 2013; Huang et al., 2011; Macris et al., 2015; Poitrasson et al., 2013; Weyer and Ionov, 2007; Williams and Bizimis, 2014; Williams et al., 2005; Zhao et al., 2010, 2012, 2015). Mantle rocks display the largest 57Fe range at high temperature with values varying from -0.82 to 0.22 % (Fig. 1.2). However, most of the peridotites fall in a more limited 57Fe range between 0:16 and 0:2% (Johnson et al., 2020), indistinguishable from that of the chondrites -0.015 0.009 2SE (n = 146; Johnson et al. (2020)). Whereas most of the mantle rocks are indistinguishable in their 57Fe signature (Fig. 1.2), wehrlites display heavier iron isotopes composition of about 0:156 0:038 2SE (Weyer and Ionov, 2007; Zhao et al., 2012). However, the studied wehrlites were affected by melt percolation resulting in the generation of secondary clinopyroxene (Johnson et al., 2020). Pyroxenites tend also to be enriched in heavy iron isotopes (Williams and Bizimis, 2014) however there is a great variability of pyroxenite 57Fe in function of the localities they come from (e.g., Poitrasson et al., 2013; Williams and Bizimis, 2014).
The most negative 57Fe in the mantle were observed in several lherzolites and harzbur-gites that suffered from intermediate to high level of metasomatism (Poitrasson et al., 2013; Zhao et al., 2010). Mantle metasomatism can simply be defined as « composi-tional changes in the mantle wall-rock due to interaction with mantle fluids » (O’Reilly and Griffin, 2013). Mantle metasomatism is expected indeed to have strong effects on both chemical and isotopic composition of the mantle creating disequilibrium within the peridotites (Dauphas et al., 2017). This disequilibrium results in chemical reactions or chemical/isotopic diffusion of distinct elements between the melt and the mantle min-erals. Isotopic disequilibrium between minerals, such as Fe diffusion, can be preserved if the xenoliths are brought to the surface at short timescales after the metasomatism event, limiting the diffusive inter-mineral re-equilibration. The metasomatic overprinting of the initial Fe isotopes compositions of peridotites is variable and highly depends on the mantle source that generated the melt, the chemical and isotopic composition of the melt and the physico-chemical conditions of the partial melting that drive the mineral reaction (Johnson et al., 2020). Recent in-situ analysis on olivine using fs-LA-MC-ICP-MS demon-strated that chemical Fe-Mg diffusion results in significant iron isotope fractionation > 1 % in 57Fe (e.g., Collinet et al., 2017; Oeser et al., 2015, 2018). The light isotopes diffuse faster than the heavy isotopes, consequently it results in an enrichment in light isotopes in the direction of the diffusion. In the case of melt (or a fluid) percolation in the mantle, the mantle rocks would be enriched in light isotopes. Therefore, the negative 57Fe measured in the metasomatised peridotites may be interpreted as being caused by melt (or a fluid) percolation through the mantle generating Fe isotopes diffusion-driven fractionation (e.g., Poitrasson et al., 2013; Zhao et al., 2010).

Oceanic crust and partial melting

Iron isotopes compositions of basaltic rocks were investigated in various studies (e.g., Gleeson et al., 2020; Konter et al., 2016; Nebel et al., 2013, 2018, 2019; Sossi et al., 2016; Sun et al., 2020; Teng et al., 2013). The majority of these studies focus on the composition of the oceanic crust by analysing mid-ocean ridge basalt (MORB) and ocean island basalt (OIB). Most basaltic rocks, independently of their geodynamical settings and origin, display heavier Fe isotopes composition than chondrites and mantle compositions (Fig. 1.2). Komatiites, that mainly erupted during Archean times and originated from high degree of melting, are the only basaltic rocks displaying 57Fe of 0:0015 0:014 % similar to the mantle value (Johnson et al., 2020). The similar iron isotopic composition of Komatiites and mantle rocks seems to indicate that Komatiites sampled the underlying mantle at the time of the formation. The iron isotope composition of MORB is generally homogeneous and the 57Fe is 0:100 0:02 % . Only enriched-MORB (E-MORB) type tends to display Fe heavier isotopes composition (Fig. 1.2 and Sossi et al. (2016)). The Fe isotope signatures of OIB tend to be slightly heavier than MORB (Fig. 1.2) and are more heterogenous even among samples from the same localities. The highest 57Fe values of basalt have been measured in Samoan OIB with a values of 0:45 0:05% (Konter et al., 2016) and in Galapagos Archipelago MORB with a value of 0:347 0:08% (Gleeson et al.,
2020). Two processes were inferred to be responsible for the general heavier Fe isotopes signature of basalts compared to the peridotites: 1) the variable degree of differentiation of the melt (Sossi et al., 2016) and 2) the degree of mantle partial melting (e.g., Dauphas et al., 2014; Foden et al., 2015; Gleeson et al., 2020; Nebel et al., 2019; Sossi et al., 2016; Weyer and Ionov, 2007; Williams and Bizimis, 2014) associated or not to isotopic heterogeneity of the mantle.
The variable degree of differentiation of the melt was investigated by Sossi et al. (2016), as most basalts do not reflect the composition of the initial parental magma due to early olivine crystallisation. Consequently, basalts 57Fe signature cannot be interpreted as a true signature of the mantle source as the heaviest signature observed can be caused by incorporation of light Fe isotopes in olivines. For this reason, Sossi et al. (2016) developed a correction for early olivine fractionation for basalt displaying MgO concentration < 8 Wt% in order to recover for the initial Fe isotopes signatures of the parental melt. By applying this correction to MORB (Sossi et al., 2016), and OIB (Gleeson et al., 2020; Nebel et al., 2019), some of the heaviest 57Fe basalt signature remained and partial melting processes were consequently explored in order to explain the heavy Fe isotope composition of the parental magma.
The impact of the degree of mantle partial melting on the variable 57Fe of basalts was investigated in various studies (e.g., Dauphas et al., 2014; Foden et al., 2015; Gleeson et al., 2020; Nebel et al., 2019; Sossi et al., 2016; Weyer and Ionov, 2007; Williams and Bizimis, 2014). Partial melting appears indeed as a favourable mean of fractionating significantly iron isotopes because of the difference of incompatibility between Fe2+ and Fe3+. Ferric iron is a moderately incompatible element with a K 0:4 whereas ferrous iron is compatible with a K 1 (Davis et al., 2013; Mallmann and O’Neill, 2009). Therefore, Fe3+ will partition in the melt at relatively low degree of partial melting. Significant iron isotopes fractionation is consequently expected as ferric iron form stronger bonds and concentrates 57Fe (Part 1.4.2). If most studies agree on the fact that partial melting has an impact on the Fe isotope signature of the basalts, its significance is still debated. It is still unclear whether partial melting can only explain partly the Fe isotope signature of the MORB (e.g., Dauphas et al., 2014) or if one (e.g., Sossi et al., 2016) or multiple stages of partial melting (e.g., Weyer and Ionov, 2007) are necessary to recreate the entire range of MORB signatures. The major difference between the different models elaborated in the literature are the fractionation factor between Fe3+ and Fe2+-minerals and melt. The iron isotopes composition of olivine and pyroxene are considered indeed as indistinguishable by some study (e.g., Beard and Johnson, 2004; Dauphas et al., 2014) whereas some display significant fractionation between them (e.g., Sossi et al., 2016; Williams and Bizimis, 2014): this has its importance as during partial melting clinopyroxene represents the major mineral phase that melts (Hirschmann et al., 1999). Moreover, the iron isotopes compositions of melts are also poorly constrained as the only available values are from synthetic glasses proxies analysed by NRIXS by Dauphas et al. (2014) and Prissel et al. (2018) for terrestrial and lunar glasses, respectively.
Concerning the heavy Fe isotopes signatures in both MORB and OIB, recent par-tial melting Monte-Carlo modelling from Gleeson et al. (2020) demonstrated that redox changes cannot be responsible for such iron isotopes signature in basalts and implies that an heavy-isotopes component (i.e. pyroxenite) is necessary in the mantle source material. The latter hypothesis supports the fact that Fe could be a viable proxy for the deter-mination of mantle heterogeneities as proposed by Williams and Bizimis (2014), Konter et al. (2016) and Nebel et al. (2019). The variability of 57Fe among the different OIB also supports the hypothesis that the upper-mantle has a heterogenous Fe isotope compo-sition. Ocean island basalt may indeed reflect more the variable Fe isotopes compositions of the different mantle regions than MORB as they sample deeper mantle sources and the plume regions are typically more heterogeneous in their chemical and isotopic composition (Hofmann, 2003).

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Magmatic differentiation

While the Fe isotopes compositions of basalts from different geodynamical settings vary moderately from Earth’s mantle composition, the Fe isotopes compositions of highly dif-ferentiated igneous rocks are considerably heavier, with 57Fe up to 0:9% (Fig 1.3). The figure (1.3) compiles the 57Fe composition of various igneous and volcanic magmatic series from distinct tectonic settings and localities. A general trend emerges from figure 1.3 with a general increase in 57Fe with increasing degree of differentiation (increasing SiO2 content). Above 60 Wt% of SiO2, the mean 57Fe for both plutonic and volcanic rocks is 0:3% (n=360; Johnson et al. (2020)). In the case of volcanic series such as Kilauea Iki (Teng et al., 2008) and Red Hill (Sossi et al., 2012), the increase in 57Fe is observable at lower SiO2 content. The processes involved in the enrichment in heavy iron isotopes of the most evolved igneous rocks are still debated. Different processes were proposed such as :
1. Fluid exsolution. The heavy 57Fe of granites and rhyolites measured by Poitrasson and Freydier (2005) and Heimann et al. (2008) were assessed to be due to exsolution of a fluid from highly evolved melts during late magmatic stages. An aqueous fluid rich in chlorine can indeed be exsolved from the evolved magmas resulting in the mobilization of elements such as Zn, Cu, Mo or Fe. These fluids enriched in light Fe isotopes would drive the Fe isotopes compositions of the residual magma to heavier values. However, subsequent studies displayed arguments against the potential ef-fect of fluid exsolution on the 57Fe of evolved rocks : i) The A-type granite, that displays heavy Fe isotopes compositions, are among the most anhydrous (Sossi et al., 2012; Telus et al., 2012), ii) The study of Zn and Li isotopes, both elements being very mobile in chlorine-rich fluids, in evolved magmatic rocks display no significant isotopes fractionation (Schuessler et al., 2009; Telus et al., 2012), except for some pegmatites (Telus et al., 2012). Therefore, fluid exsolution is not expected to play a major role on Fe isotopes fractionation during magmatic differentiation.
2. Diffusion-driven processes. Lundstrom (2009), Zambardi et al. (2014) and Gajos et al. (2016) proposed thermal diffusion as the one of the processes driving the Fe isotopes composition to heavier value in the evolved igneous rocks based on the fact that thermal gradient could control Fe isotope fractionation in magmas (Huang et al., 2009; Richter et al., 2003). However, Telus et al. (2012) measured Zn isotopes as well as other isotopic systems supposed to behave similarly as Fe in case of thermal diffusion, and no correlations were observed. Another scenario proposed by Zhao et al. (2015) to explain the A-type granites 57Fe, is based on diffusion between a silica-rich and a Fe-rich immiscible melt. The potential effect of diffusion between minerals and melt were also proposed as great 57Fe variations were shown in olivines (e.g., Collinet et al., 2017; Oeser et al., 2015, 2018; Sio et al., 2013; Teng et al., 2008) and illmenite (Tian et al., 2020). Wu et al. (2018) also evidenced significant iron isotopes fractionation in an adjacent gabbro and granite profile in Dabie Orogen, showing that large isotopic fractionation can be produced in igneous rocks by kinetic diffusion at least on a decimeter scale. However, if Fe-Mg inter-diffusion plays a role on the isotopic signature of some magmatic series studied (e.g., Teng et al., 2008; Wu et al., 2018), it is unlikely to play a role on large granitic intrusion.
3. Partial melting. The effect of partial melting of the lower crust was also investi-gated in order to understand the heavy Fe isotopes compositions of evolved igneous rocks (e.g., Foden et al., 2015; Xia et al., 2017; Xu et al., 2017). Partial melting of the lower crust appears indeed as a viable mechanism to re-create the high 57Fe signatures of the S-type granites generated under reduced conditions (Foden et al., 2015), of the migmatites from Dabie Orogen (Xu et al., 2017) and of Hair rhyolite (Xia et al., 2017).
4. Fractional crystallization. Fractional crystallization (FC) is considered to be the main driver behind the chemical differentiation of magmatic rocks. Many stud-ies invoked that fractionation crystallization could also be responsible of isotopic fractionation during magmatic differentiation (e.g., Schuessler et al., 2009; Sossi et al., 2012; Williams et al., 2018). Removal of isotopically light Fe2+-rich minerals (olivine, orthopyroxene, clinopyroxene, illmenite, ulvospinel) from the magma dur-ing FC should indeed drive the melt to heavier isotopic compositions. Some studies (Shahar et al., 2008; Zambardi et al., 2014) inferred that crystallisation of mag-netite, in a system open to oxygen, should drive the Fe isotopes values of the more evolved rocks to low 57Fe if fractional crystallization was the only process involved in iron isotope fractionation during magmatic differentiation. On the other side, Dauphas et al. (2014) model, using their set of equilibrium fractionation factors between olivine and melt and magnetite and melt obtained by NRIXS, shows that FC could explain the heavy Fe isotopes compositions in the silicic magmatic rocks above 68 Wt% SiO2. This was also supported by the model produced by Foden et al. (2015), going a step further by predicting variations in 57Fe in lavas with lower SiO2 content, as observed in different magmatic suites (e.g., Sossi et al., 2012; Teng et al., 2008). As for partial melting modelling (Part 1.4.3.2), the choice of equilibrium fractionation factors between mineral and melt used in FC modelling is essential to precisely determine if FC could explain entirely or partly the iron isotopes evolution during magmatic differentiation.
The evolution of the 57Fe during FC were also inferred to be coupled with f O2 evolution of the melt (Sossi et al., 2012). The two magmatic suites of Red Hill volcanoes studied by Sossi et al. (2012), clearly demonstrated two types of 57Fe variations for a system open and closed in oxygen. In a system open to oxygen, the
57Fe as well as the concentration of Fe3+ increase in the last stage of differentiation due to the removal of Fe2+ generated by olivines and pyroxenes cristallisation in the early stage of magmatic differentiation. In the case of a system closed to oxygen, the concentration of Fe3+ is finite. Therefore, the 57Fe will increase, as in an open system to oxygen, until the crystallisation of Fe3+-bearing minerals (e.g. magnetite) that will trigger the 57Fe to lower values in the most evolved lavas (Sossi et al., 2012).

Table of contents :

1 Introduction 
1.1 General introduction (English version)
1.2 Introduction générale (French version)
1.3 Stable isotopes fractionation
1.3.1 Generalities
1.3.2 Gibbs free energy and equilibrium constant
1.3.3 Partition function
1.3.4 The fractionation factor
1.3.5 The factor
1.3.6 Calculation of the -factor
1.3.7 Determination of experimental isotope fractionation factor
1.4 Iron isotopes systematics
1.4.1 Iron geochemistry
1.4.2 Iron stable isotopes
1.4.3 Iron isotopes fractionation at high temperature
1.5 Silicon isotopes systematics
1.5.1 Silicon geochemistry
1.5.2 Silicon stable isotopes
1.5.3 Silicon isotopes fractionation at high temperature
2 Methods for first-principles calculations of minerals and melts 
2.1 Theoretical analysis of the electronic structure
2.1.1 The Schrödinger equation
2.1.2 Density Functional Theory
2.2 DFT calculation of solids characteristics
2.2.1 Description of a crystal : structure optimization
2.2.2 Bloch theorem and plane waves
2.2.3 Reciprocal lattice parameters and the Brillouin zone
2.2.4 Pseudopotentials
2.2.5 Magnetism
2.2.6 Electronic density of states
2.2.7 Vibrational frequencies
2.2.8 Quantum Espresso
2.3 Ab-initio molecular dynamics
2.3.1 Ergodicity principle
2.3.2 Born – Oppenheimer Molecular Dynamics
2.3.3 Verlet algorithm
2.3.4 Thermodynamic particle ensemble
2.3.5 Thermostats
2.3.6 VASP
2.3.7 Physical properties investigated
3 First-principles calculation of iron and silicon isotope fractionation between Fe-bearing minerals at magmatic temperatures: The importance of second atomic neighbors 
3.1 Abstract
3.2 Introduction
3.3 Methodology
3.3.1 Calculation of equilibrium isotope fractionation factors
3.3.2 Modeling approach
3.4 Results
3.4.1 Structural properties
3.4.2 Reduced partition function ratios of iron and silicon
3.5 Discussion
3.5.1 Parameters controlling Fe isotope fractionation in minerals
3.5.2 Parameters controlling Si isotope fractionation in minerals
3.5.3 Comparison with previous data
3.5.4 Geochemical implications on magmatic differentiation
3.6 Conclusion
3.7 Acknowledgements
4 Iron and silicon isotope fractionation in silicate melts using first-principles molecular dynamics. 
4.1 Abstract
4.2 Introduction
4.3 Methodology
4.3.1 Modelling approach
4.3.2 Calculation of equilibrium isotope fractionation factors
4.3.3 The “snapshot” method
4.3.4 The “VAF” method
4.4 Results
4.4.1 Structural melt properties
4.4.2 Reduced partition function ratios of iron and silicon.
4.5 Discussion
4.5.1 Iron and silicon environment in the silicate melts.
4.5.2 « Snapshot” vs “VAF” method.
4.5.3 Iron isotope fractionation in melts.
4.5.4 Silicon isotope fractionation in melts.
4.5.5 Applications
4.6 Conclusion
4.7 Acknowledgement
5 Insights from iron isotopes into magmatic differentiation and mantle heterogeneity of the Kerguelen Archipelago 
5.1 Abstract
5.2 Introduction
5.3 Geological setting
5.4 Sample description
5.5 Methods
5.5.1 Petrological studies
5.5.2 Mass spectrometry
5.5.3 Fe3+/Fetot determination
5.6 Results
5.6.1 Mineralogy
5.6.2 Compositional evolution of the oxides
5.6.3 Compositional evolution of pyroxenes and amphibole
5.6.4 Iron isotope compositions
5.6.5 Ferric-ferrous iron ratios
5.7 Discussion
5.7.1 Petrologic evolution
5.7.2 Mantle heterogeneity
5.7.3 Magmatic differentiation: impact of fractional crystallization
5.8 Conclusion
5.9 Acknowledgements
6 In situ iron isotopes fs-LA-MC-ICP-MS analyses in magmatic context
6.1 Introduction
6.2 Generalities
6.2.1 Principle of laser
6.2.2 Laser ablation and ICP-MS: limitations
6.2.3 Advantages of femtosecond vs nanosecond laser
6.2.4 Essentials parameters during lasers ablation
6.3 Iron isotopes measurements using fs-La-MC-ICP-MS
6.3.1 Femtosecond laser ablation – MC-ICP-MS
6.3.2 Reference materials
6.3.3 Samples
6.3.4 Mass-bias correction and uncertainties calculation
6.4 Results
6.4.1 References materials
6.4.2 Olivines profiles
6.5 Discussion
6.5.1 Precision and spatial resolution
6.5.2 Kerguelen Olivine isotopic profiles
6.6 Conclusion
6.7 Acknowledgement
7 Conclusions and perspectives 
7.1 General conclusions (English Version)
7.2 Conclusion générale (French Version)
7.3 Perspectives
7.3.1 First-Principles calculations
7.3.2 Characterization of mantle heterogeneities
7.3.3 fs-LA-MC-ICP-MS measurements

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