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1 Chapter 1Figure 1.1 E‐pH diagram reporting the stability of water at T = 25°C and P =...Figure 1.2 The E‐pH (Pourbaix) diagram for the Fe‐S‐H₂O system at 25°C at 1 ...Figure 1.3 Limit of equilibrium potential‐pO^2– graphs in molten alkali...Figure 1.4 Log fO₂ ‐ Ph diagrams for 290°C (left panel) and 145°C (right pan...Figure 1.5 (a) Ellingham diagram for the main components of the melt/slag (s...Figure 1.6 Common solid oxygen buffers used in petrology and geochemistry. T...Figure 1.7 Two‐redox potential fO₂‐fS₂ diagram. The conformation of stabilit...

2 Chapter 2Figure 2.1 Range of oxygen fugacity estimates for Solar Nebula, achondrites,...Figure 2.2 LogfO₂ (normalized to the FMQ buffer) calculated for mantle perid...Figure 2.3 (a) V/Sc and (B) calculated LogfO₂ (normalized to the FMQ buffer)...

3 Chapter 3Figure 3.1 Locations of samples compiled in this study as a function of tect...Figure 3.2 Distribution of fO₂ recorded by volcanics globally in different t...Figure 3.3 Distribution of fO₂ recorded by mantle lithologies (peridotites a...Figure 3.4 V/Yb ratios of ridge (gray “+” symbols, Gale et al., 2013), back‐...Figure 3.5 Progressive degassing of a C–O–H–S vapor in ridge, arc, and plume...Figure 3.6 Magmatic oxygen fugacity as recorded by volcanics for samples in ...Figure A1 Temperatures and values of fO₂ from the model of Ghiorso and Evans...Figure A2 XANES spectra of MORB glass VG3385 with spectra of mid‐ocean ridge...Figure A3 The measured experimental furnace fO₂ in log units relative to the...

4 Chapter 4Figure 4.1 Positions of redox buffers at 1 bar. From Frost, (1991) unless ot...Figure 4.2 Conceptual model of subduction zone cycling.Figure 4.3 Location of volcanic arcs and spreading ridges mentioned in the t...

5 Chapter 5Figure 5.1 (a) Solidus curves for peridotite in dry conditions (black line) ...Figure 5.2 Two depictions of the reduced and oxidized fluid realms for COH f...Figure 5.3 Illustration of the fO₂ levels at which HRM and CRM occur, relate...Figure 5.4 Illustration of pressure effects on the extent of redox fractiona...Figure 5.5 Ranges of redox states found in various geodynamic settings and i...Figure 5.6 Illustration of redox fronts that develop between lithosphere and...Figure 5.7 Comparison of likely widely applicable peridotite solidi in Phane...

6 Chapter 6Figure 6.1 (a) Oxidized/reduced iron (log‐form) for simple binaries at 1400°...Figure 6.2 (a) Comparison of Paul and Douglas (1965) data with those of Tang...Figure 6.3 (a) S^VI/S_tot from empirical formulations available in the literat...Figure 6.4 Mutual interaction of iron and sulfur redox couples in dry and hy...Figure 6.5 Patterns of sulfur release and their effect on melt sulfur distri...Figure 6.6 Covariation of sulfate and sulfide contents in andesitic to rhyol...Figure 6.7 (a) Covariation of sulfate and sulfide fractions in melt inclusio...Figure 6.8 (a) Plot of logK₁₅ vs logfO₂, showing the nearly negligible effec...Figure 6.9 (a) Melt sulfate/sulfide ratios vs. dissolved water contents from...

7 Chapter 7Figure 7.1 Histograms of measurements of the Fe²⁺/Fe^T ratio in global survey...Figure 7.2 A simple model of olivine‐liquid equilibria and FeO‐MgO systemati...Figure 7.3 PRIMELT3 outputs from calculation of primary magma parental to th...Figure 7.4 PRIMELT3 prediction for the Mg# of the liquidus olivine that firs...Figure 7.5 PRIMELT3 predictions for the Mg# of the liquidus olivine that fir...Figure 7.6 Predictions of the pMELTS model of oceanic crustal production for...Figure 7.7 rhyoliteMELTS calculations showing the fraction of original liqui...

8 Chapter 8Figure 8.1 Histogram of the log(abundance) of 78 elements (M; bin size 0.5) ...Figure 8.2 log(Fe³⁺/Fe²⁺) as a function of fO₂, relative to the quartz‐fayal...Figure 8.3 Fe³⁺/∑Fe as a function of fO₂, relative to the QFM buffer, predic...Figure 8.4 (a) log Fe₂O₃ (in wt%) of MORB glasses determined by Berry et al....

9 Chapter 9Figure 9.1 XANES spectra from Cr²⁺ and Cr³⁺ standard glasses. There are seve...Figure 9.2 Adapted from Bell et al. (2017); illustrates how the crystallogra...Figure 9.3 Cr²⁺/∑Cr ratios plotted vs. experimental fO₂ from Roedder and Rey...Figure 9.4 Contains plots the XANES measured the Cr²⁺/∑Cr ratios from quench...Figure 9.5 Cr partitioning data compiled from several studies plotted vs. ex...Figure 9.6 XANES measured Cr²⁺/∑Cr values of a set of experimentally grown o...

10 Chapter 10Figure 10.1 Comparison between values of from O’Neill and Mavrogenes (2002...Figure 10.2 The relationship between S⁶⁺/∑S and Fe³⁺/∑Fe, estimated by combi...Figure 10.3 (a) Observed values of the sulfide capacity, , at 1400°C of sil...Figure 10.4 Comparison between measured values of the activity coefficient o...Figure 10.5 The oxygen contents as the component FeO in sulfide mattes coexi...Figure 10.6 The effect of pressure on the SCSS, comparing Equation 10.43 of ...Figure 10.7 SCSS for a binary compositional join between FeO‐free “matrix” a...Figure 10.8 The effect of H₂O on SCSS. Data from Moune et al. (2009) at 1045...Figure 10.9 Sulfur saturation in ocean floor basaltic (OFB) glasses from Jen...Figure 10.10 The difference between [S]_obs and the calculated SCSS from the ...Figure 10.11 Calculated atomic Ni/Fe (a) and Cu/Fe (b) in sulfide liquid in ...Figure 10.12 Comparison with the SCSS model of Smythe et al. (2017). (a) Cal...Figure 10.13 (a) Reproducibility of S analyses in basaltic glasses: a compar...Figure 10.14 Comparison of model [S]_SCSS with [S]_obs for Macquarie Island ba...Figure 10.15 Comparison between model [S]_SCSS and [S]_obs for two sets of gla...Figure 10.16 Olivine‐hosted melt inclusions from Le Voyer et al. (2017). (a)...Figure 10.17 Ni and Cu abundances in ocean floor basaltic (OFB) glasses vers...Figure 10.18 Calculated [S]_SCSS vs. [S]_obs for olivine‐hosted melt inclusion...Figure 10.19 (a) log₁₀ fS₂ and (b) log₁₀ fSO₂ calculated for 35 sulfide‐satu...

11 Chapter 11Figure 11.1 Isobaric calculations of H₂O and CO₂ contents in Basaltic melt a...Figure 11.2 Variation of the log fO₂ values as a function of the temperature...Figure 11.3 Experimentally determined S solubility data of basaltic melts as...Figure 11.4 Sulfur valence state at fO₂, expressed relative to FMQ. Figure m...Figure 11.5 Influence of oxygen fugacity on the partitioning of sulfur betwe...

12 Chapter 12Figure 12.1 Examples of iron concentration ([FeO] equivalent) in various ign...Figure 12.2 Variation of the Fe³⁺/Fe^TOT (Fe^TOT = Fe²⁺ + Fe³⁺) redox ratio as...Figure 12.3 Iron oxidation state in K₂O‐Al₂O₃‐SiO₂‐FeO melts at 1673 K in ai...Figure 12.4 Examples of compositional effects on the oxidation state of iron...Figure 12.5 Viscosity of (a) anorthite‐diopside (An‐Di) eutectic melt as a f...Figure 12.6 Viscosity of SiO₂, NaAlSi₃O₈ and NaFeSi₃O₈ melts.Figure 12.7 Isothermal viscosity as a function of the oxidation state of iro...Figure 12.8 Effects of the crystal (a) and water (b) contents on the viscosi...Figure 12.9 Viscosity, crystallinity, and oxidation state of andesite and ba...

13 Chapter 13Figure 13.1 Mössbauer spectra of an Fe‐bearing diopside glass prepared at 15...Figure 13.2 Example of Optical Absorption spectra of glasses containing diff...Figure 13.3 Optical absorption spectrum, in the range 4000–28500 cm^–1,...Figure 13.4 Optical Absorption spectrum of a V‐doped sodium aluminosilicate ...Figure 13.5 Energy scaled K‐edge XAS spectrum of vanadium in divanadium trio...Figure 13.6 XANES spectra of first‐ row multivalent transition metal oxides ...Figure 13.7 K‐edge XANES spectra of Mn (a) and Fe (b) crystalline compounds ...Figure 13.8 Cerium L_III‐edge XANES spectra for two Ce crystalline materials ...Figure 13.9 Schematic drawing of a lava, and XAS spectra at the Fe K‐edge an...Figure 13.10 Raman spectrum of an iron‐free pyroxene glass (CaO‐SiO₂‐Na₂O‐Mg...Figure 13.11 Raman spectra at room temperature for a series of iron‐pyroxene...Figure 13.12 a,b: Deconvolution of the 0.09 and 0.99 Raman spectra (based on ...Figure 13.13 Comparison of iron ratios analyzed by different techniques, wet...Figure 13.14 (a) Evolution of the normalized XANES spectra at the Fe K‐edge a...Figure 13.15 Fe³⁺/Fe_Tot redox as different temperatures, 412, 618, 710 °C fr...

14 Chapter 14Figure 14.1 Generic example of the temperature dependence of the β‐fact...Figure 14.2 Relative departure (numbers on the curves) from Equation 14.8 in...Figure 14.3 Iron β‐factors (^56/54Fe) at 298 K as a function of the iron...Figure 14.4 Temperature dependence of iron β‐factors (^56/54Fe) for mine...Figure 14.5 Iron β‐factors (^56/54Fe) at 298 K as a function of the aver...Figure 14.6 XANES centroid energy (left) and mean force constant of iron mea...

15 Chapter 15Figure 15.1 After Sossi and O’Neill (2017). Dependence of the calculated for...Figure 15.2 Iron‐oxygen force constants in spinel group minerals (after Rosk...Figure 15.3 After Dauphas et al. (2014). Mean force constants of Fe‐O bonds ...Figure 15.4 After Liu et al. (2017). Force constants (N/m) of iron bonds in ...Figure 15.5 After Fujii et al. 2014. Temperature dependence of the 10³lnβ^56/...Figure 15.6 Melting models from Sossi & O’Neill (2017) (see Equations 15.21–...Figure 15.7 After Sossi and O’Neill (2017). Iron isotope composition of mafi...Figure 15.8 After Foden et al. (2018). δ⁵⁷Fe_(IRMM‐14) vs. Slab Thermal...Figure 15.9 After Heimann et al. 2008. An early compilation of iron isotope ...Figure 15.10 δ⁵⁷Fe of whole rocks against their Mg#, characterizing the chan...Figure 15.11 After Du et al. 2017. Compilation of Fe isotope mineral composi...Figure 15.12 After Debret et al. (2016). Increase in δ⁵⁶Fe and decrease of F...

16 Chapter 16Figure 16.1 A periodic stable showing traditional and selected non‐tradition...Figure 16.2 The temperature dependent of ln β or isotopic enrichment factor,...Figure 16.3 A Rayleigh fractionation model summarizing the key experimental ...Figure 16.4 Temperature dependence of ln β between different Zn‐S and Zn‐C s...Figure 16.5 The effect of and temperature log fO₂ on the speciation of Cu wi...

17 Chapter 17Figure 17.1 (a) Schematic illustration of lattice strain parameters D ₀, r ₀,...Figure 17.2 Relative oxygen fugacity conditions (in log units relative to FM...Figure 17.3 Mineral/melt partitioning of transition metals as a function of ...Figure 17.4 Comparison of Cr olivine(Fo₁₀₀)/melt partitioning coefficients o...Figure 17.5 Zircon/melt partition coefficients for REE elements determined e...Figure 17.6 Mineral/melt partitioning of redox‐sensitive rare earth elements...Figure 17.7 Mineral/melt partitioning of U as a function of oxygen fugacity ...Figure 17.8 Mineral/melt partitioning of siderophile elements (Mo, W, and Re...

18 Chapter 18Fig. S1 Summary of commonly applied oxygen fugacity buffers and their positi...Fig. 18.1 Graphical representation of the magnetite–ilmenite oxybarometer/th...Fig. 18.2 Estimated proportions of V³⁺, V⁴⁺, and V⁵⁺ in a ferrobasaltic melt...Fig. 18.3 Results of titanomagnetite‐melt vanadium partitioning experiments ...Fig. 18.4 (a) Iron solubility in rhyolite melts as a function of alumina sat...Fig. 18.5 Performance of FeTiMM on experimental samples. Oxygen fugacities (...Fig. 18.6 (a) Comparison of fO₂ values (reported in log units relative to th...Fig. 18.7 The principle of the equilibrium test between magnetite and melt p...

19 Chapter 19Figure 19.1 (a) Plot of ionic radius (data from Shannon, 1976) vs. ionic cha...Figure 19.2 Ionic radii for six‐fold coordinated REE³⁺. (Radius values from ...Figure 19.3 (a) Mineral/melt REE partition coefficients for plagioclase (Plg...Figure 19.4 Experimental data from Drake (1975) show that the partitioning o...Figure 19.5 Eu²⁺/(Eu²⁺ + Eu³⁺) redox fraction as determined by XANES vs. oxy...Figure 19.6 Dependence of the Ce⁴⁺/Ce_tot redox ratio on alkali content, and ...Figure 19.7 Parallel (VV) and cross‐polarized (VH) Raman spectra (normalized...Figure 19.8 X‐Ray Absorption Spectroscopy data at the Eu L_III‐edge (left) an...Figure 19.9 (a) XAS spectra, normalized at the Fe K‐edge, collected for the ...