Iron stable isotopes

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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