M Stamm

Thomas Zambardi

Jérôme Chmeleff

Jacques Schott

Friedhelm Von Blanckenburg

Eric H Oelkers

The work is composed of six chapters.

Chapter 1 presents an extended general introduction to the thesis, addressing the aim and motivation of this study. Chapter 2 describes the theoretical background of the experiments, the materials and methods used during the experimental work. A general conclusion of the thesis is provided in Chapter 6, as well as, an outlook on future research possibilities in this field.

The main results of this thesis are described in Chapters 3, 4, and 5. These are included as three scientific manuscripts, which are either submitted or in preparation for submission to international peer-reviewed journals. These chapters are prepared so that they can be read individually, therefore some material is repeated within these chapters.

Extended Abstract

Silicon (Si) and Magnesium (Mg) are major elements in rock-forming minerals, biological systems and seawater. Characterizing the isotopic composition of these elements in inorganic and organic environments makes it possible to better constrain their geochemical cycle and to interpret the geologic record. The accurate interpretation of these natural isotopic signatures requires knowledge of the equilibrium isotope fractionation between Si or Mg bearing solids and the main inorganic and organic Si and Mg species present in natural waters. At present, these data are scarce and not reliable.

In this thesis laboratory experiments were performed at bulk chemical equilibrium to determine the equilibrium isotopic fractionation factor between Si or Mg bearing solids and aqueous solutions with various pH, temperature, and in the presence or absence of organic (catechol, citrate or EDTA) and inorganic ligands (sulphate) at 25° and 75°C.

The 'three-isotope method' was applied to unambiguously determine the equilibrium fractionation factor Δ eq of such two-component solid-solution system. The advantage of this method is that in the case where the two-component system does not reach full isotopic equilibrium, the isotopic composition at equilibrium can still be determined by extrapolation.

Additionally the three-isotope method provides information into isotope exchange rates, and thus insight into the mechanism of isotopic exchange. Fur this purpose, after attaining bulk chemical equilibrium the aqueous solutions were spiked with 29 Si or 25 Mg and then placed together with new amorphous SiO 2 or brucite powder to equilibrate isotopically. Isotopic measurements were performed on fluids and solids collected at selected times during the experiments with an MC-ICPMS.

Equilibrium fractionation factors between solids and distinct aqueous species were obtained by coupling the experimental results with the results of aqueous speciation calculations performed using PHREEQC. All experimental determined equilibrium fractionation factors were compared with results of corresponding ab initio calculations.

Among the noteworthy results of this thesis one should highlight the strong impact that can have Si and Mg complexation with some organic ligands on the isotopic composition of coexisting Si and Mg solids and aqueous species (i.e. Δ 30 Si Sicatechol-H 4 SiO 4 ° = -19.05± 0.49 ‰ and Δ 26 Mg Mg 2+ -MgEDTA 2-= 2.17 ± 0.19 ‰.). The results of this study can be used to model paleoclimate conditions and may provide a new insight into the isotopic records of sedimentary rocks, and biological systems.

Résumé

Le silicium (Si) et le magnésium (Mg) sont deux éléments majeurs abondants dans les minéraux, les systèmes biologiques, les eaux douces et les océans. La caractérisation de leurs compositions isotopiques dans la biosphère et les milieux terrestres inorganiques permet une meilleure compréhension de leurs cycles géochimiques et facilite l'interprétation de certains enregistrements géologiques. L'interprétation des signatures isotopiques naturelles requiert dès lors la connaissance précise des fractionnements isotopiques à l'équilibre survenant entre les principaux solides porteurs de silicium et magnésium et les principales espèces inorganiques et organiques de Si et Mg présentes dans les fluides naturels. A ce jour, ces données restent encore trop rares et peu fiables.

Les travaux de cette thèse s'appuient principalement sur des expériences de laboratoires conduites à l'équilibre chimique en vue de déterminer le fractionnement isotopique à l'équilibre entre des solides porteurs de Si ou Mg et des solutions aqueuses de différents pH, contenant ou non un ligand organique (catéchol, citrate ou EDTA) ou inorganique (sulfate) à des températures de 25 et 75°C.

La méthode des « trois isotopes » a été employée afin de déterminer sans ambiguïté le fractionnement à l'équilibre dans ces systèmes à deux composants « Δ eq fluide-solide ». Cette méthode présente comme avantage de pouvoir déterminer des compositions isotopiques par extrapolation, même si l'équilibre isotopique n'est pas atteint. Elle permet également de fournir des informations sur les vitesses d'échanges isotopiques et donc sur les mécanismes de l'échange isotopique lui-même. Dans ce but, après avoir atteint l'équilibre chimique entre silice amorphe et solution ou brucite et solution, un spike de 29 Si ou de 25 Mg a été ajouté à la solution aqueuse. Cette solution ensuite été mélangée à une nouvelle poudre de SiO 2 amorphe ou de brucite afin d'atteindre l'équilibre isotopique. Les mesures isotopiques ont été effectuées par MC-ICPMS sur les solutions et les solides, recueillis à des moments choisis au cours des différentes expériences.

Les fractionnements isotopiques à l'équilibre entre les solides et les espèces aqueuses et entre les différentes espèces aqueuses d'un même élément ont été obtenus en couplant les résultats expérimentaux avec les résultats des calculs de spéciation aqueuse effectués à l'aide du code géochimique PHREEQC. Tous les facteurs de fractionnement à l'équilibre entre solide et espèce aqueuse d'un élément ou entre deux espèces aqueuses d'un même élément ainsi obtenus ont été comparés aux résultats de calculs ab initio menés sur les mêmes systèmes. Parmi les résultats les plus remarquables, on retiendra l'impact très important que -iv-peut avoir la complexation du silicium et du magnésium avec certains ligand organiques sur la composition isotopiques de leurs espèces aqueuses et des solides en équilibre, avec, par exemple, Δ 30 Si Sicatechol-H 4 SiO 4 ° = -19.05± 0.49 ‰ et Δ 26 Mg Mg 2+ -MgEDTA 2-= 2.17 ± 0.19 ‰. Les résultats de cette étude, qui fournissent un éclairage nouveau sur des données isotopiques de roches sédimentaires et de systèmes biologiques, peuvent être utilisés afin de reconstituer certains paléo-environnements. corresponding technicians if needed. Measurements on the Neptune MC-ICP-MS and data evaluation were carried out by myself with assistance of Thomas Zambardi and Jérôme Chmeleff. Ab initio calculations were performed by Merlin Méheut. The manuscript was written by myself and the co-authors, notably Jacques Schott and Eric H. Oelkers, who also provided input on data interpretation.

Chapter 5 describes the content of the completed manuscript: "Determination of the equilibrium magnesium isotope fractionation factors between brucite and aqueous inorganic and organic species", authored by Franziska M. Stamm, Thomas Zambardi, Jerome Chmeleff, Jacques Schott, and Eric H. Oelkers, with the following contributions: The experimental work was performed by myself, with input of Jacques Schott. Analytical procedures were performed by myself with assistance of the corresponding technicians. Measurements on the Neptune MC-ICP-MS and data evaluation were carried out by myself with assistance of Thomas Zambardi and Jérôme Chmeleff. The manuscript was written by myself and the coauthors. Jacques Schott and Eric H. Oelkers provided input on data interpretation and helped finalize the manuscript.

The Appendix is composed of tables of the electronic supplement material of chapters 3,4, and 5.

vii

To Gisela, Hermann & Moritz

There are many people I would like to thank for their help and support during the past years.

First of all, I would like to thank my advisors Eric Oelkers and Jacques Schott for their support, inspiring discussions and guidance throughout my thesis. Thank you for your mentorship, the continuous encouragement, and making sure I stayed on the right path.

I would also like to thank the reviewers and jury members for taking the time to evaluate this thesis.

This I also want to thank current and former graduate students and post-docs of the GET, Simon Blotevogel, Laetitia Gal, Anna Harrison, Christian Grimm, Chiara Marieni, Helen McFarlane, Melody Premaillon, Giuseppe Saldi, Martin Voigt, Nail Zagretdenov, and many, many others for the time we spent together inside and outside of the lab. Special thanks go to Alisson Akerman, Sylvain Pinet and Leandre Ponthus for all their help and support.

x

During the past years, I was lucky to find great new friends. I would like to thank Fiorella, Hannah, Sebastian and Valeria for their motivation, and discovering Toulouse with me. I thank Marie and René for the lovely time we spent on IsoNose meetings, in Berlin and Toulouse. I also want to thank FX and Thomas for their constant motivation and help. I was lucky sharing fun coffee breaks, lunches and wonderful evenings together with Marianne and Irina.

I am fortunate to have fantastic friends, who accompanied me for many years. In particular I want to thank Iris, Hanna, Steffi, and Chrissi for their support, motivation, and distracting me by many fun skype conversations, discovering the Pyrenées, and the French cuisine together.

Thank you all for always being there.

I owe much gratitude to my parents Gisela and Hermann for their unconditional support and encouragement throughout the years. Thank you, for your advice, and for your confidence. I also thank the rest of my family, my sister Anna-Sophia and her husband Johannes, Eva, and my brothers Sebastian and Johannes. I would like to thank my niece Clara for bringing so much joy into our lives.

Finally, I warmly thank Moritz for his endless support, encouragement, patience and the ability to always make me laugh. Silicon (Si) and Magnesium (Mg) are among the most common elements in the Earth's crust, and thus play an important role in many geologic processes. Silicon and magnesium stable isotopes can therefore be used as reliable tracer for many (near-) surface processes, including weathering, mineral growth and precipitation, biological activity, and marine paleo conditions (e.g. [START_REF] Varela | Biological fractionation of silicon isotopes in Southern Ocean surface waters: BIOLOGICAL FRACTIONATION OF SILICON[END_REF][START_REF] Opfergelt | Plant silicon isotopic signature might reflect soil weathering degree[END_REF][START_REF] Wimpenny | The behaviour of magnesium and its isotopes during glacial weathering in an ancient shield terrain in West Greenland[END_REF]Opfergelt et al., 2012a;[START_REF] Pogge Von Strandmann | Lithium, magnesium and silicon isotope behaviour accompanying weathering in a basaltic soil and pore water profile in Iceland[END_REF]Tipper et al., 2012;[START_REF] Kasemann | Continental weathering following a Cryogenian glaciation: Evidence from calcium and magnesium isotopes[END_REF]Mavromatis et al., 2014;[START_REF] Saenger | Magnesium isotope fractionation in biogenic and abiogenic carbonates: implications for paleoenvironmental proxies[END_REF][START_REF] Fujii | Isotope fractionation of Si in protonation/deprotonation reaction of silicic acid: A new pH proxy[END_REF][START_REF] Gao | Magnesium isotope fractionation during dolostone weathering[END_REF]. Since the advent of multi-collector inductively coupled plasma mass spectrometry (MC-ICP-MS), the isotopic composition of Si and Mg could be determined for many terrestrial reservoirs, such as surface waters [START_REF] Brenot | Magnesium isotope systematics of the lithologically varied Moselle river basin, France[END_REF][START_REF] Georg | Stable silicon isotopes of groundwater, feldspars, and clay coatings in the Navajo Sandstone aquifer, Black Mesa, Arizona, USA[END_REF][START_REF] De La Rocha | The silicon isotopic composition of surface waters in the Atlantic and Indian sectors of the Southern Ocean[END_REF][START_REF] Ding | Silicon isotopic composition of dissolved silicon and suspended particulate matter in the Yellow River, China, with implications for the global silicon cycle[END_REF][START_REF] Grasse | The influence of water mass mixing on the dissolved Si isotope composition in the Eastern Equatorial Pacific[END_REF][START_REF] Pokrovsky | Silicon isotope variations in Central Siberian rivers during basalt weathering in permafrost-dominated larch forests[END_REF][START_REF] Frings | Silicate weathering in the Ganges alluvial plain[END_REF], soils [START_REF] Opfergelt | Magnesium retention on the soil exchange complex controlling Mg isotope variations in soils, soil solutions and vegetation in volcanic soils, Iceland[END_REF]Riotte et al., 2018a), biosphere, e.g. plants, foraminifera, sponges, diatoms [START_REF] Savin | Stable Isotope and Magnesium Geochemistry of Recent Planktonic Foraminifera from the South Pacific[END_REF][START_REF] Douthitt | The geochemistry of the stable isotopes of silicon[END_REF]Ding et al., 2008aDing et al., , 2008b;;[START_REF] Bolou-Bi | Experimental determination of magnesium isotope fractionation during higher plant growth[END_REF][START_REF] Pogge Von Strandmann | Lithium, magnesium and silicon isotope behaviour accompanying weathering in a basaltic soil and pore water profile in Iceland[END_REF]Opfergelt et al., 2012b;Riotte et al., 2018b), and minerals, sedimentary rocks, carbonates, cherts, and banded iron formations [START_REF] Douthitt | The geochemistry of the stable isotopes of silicon[END_REF]Ziegler et al., 2005aZiegler et al., , 2005b;;[START_REF] Georg | Stable silicon isotopes of groundwater, feldspars, and clay coatings in the Navajo Sandstone aquifer, Black Mesa, Arizona, USA[END_REF][START_REF] Hippler | Towards a better understanding of magnesium-isotope ratios from marine skeletal carbonates[END_REF][START_REF] Steinhoefel | Deciphering formation processes of banded iron formations from the Transvaal and the Hamersley successions by combined Si and Fe isotope analysis using UV femtosecond laser ablation[END_REF][START_REF] Van Den Boorn | Silicon isotope and trace element constraints on the origin of ∼3.5Ga cherts: Implications for Early Archaean marine environments[END_REF][START_REF] Savage | The silicon isotope composition of the upper continental crust[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF][START_REF] Wimpenny | Investigating the behaviour of Mg isotopes during the formation of clay minerals[END_REF][START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF]. Experimental studies have demonstrated that silicon and magnesium isotopic signatures in natural environments can evolve during mineral precipitation [START_REF] Li | Experimental study of silicon isotope dynamic fractionation and its application in geology[END_REF][START_REF] Basile-Doelsch | Another continental pool in the terrestrial silicon cycle[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF][START_REF] Geilert | Silicon isotope fractionation during abiotic silica precipitation at low temperatures: Inferences from flow-through experiments[END_REF][START_REF] Roerdink | Experimental constraints on kinetic and equilibrium silicon isotope fractionation during the formation of non-biogenic chert deposits[END_REF][START_REF] Oelze | The effect of Al on Si isotope fractionation investigated by silica precipitation experiments[END_REF], mineral growth, mineral dissolution [START_REF] Delvigne | Stratigraphic changes of Ge/Si, REE+Y and silicon isotopes as insights into the deposition of a Mesoarchaean banded iron formation[END_REF] or during adsorption of aqueous species onto solid surfaces [START_REF] Delstanche | Silicon isotopic fractionation during adsorption of aqueous monosilicic acid onto iron oxide[END_REF][START_REF] Oelze | Si stable isotope fractionation during adsorption and the competition between kinetic and equilibrium isotope fractionation: Implications for weathering systems[END_REF]. Isotopic fractionation during these mineral-solution reactions in nature can be influenced by diffusion and kinetic effects [START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF][START_REF] Geilert | Silicon isotope fractionation during abiotic silica precipitation at low temperatures: Inferences from flow-through experiments[END_REF][START_REF] Oelze | The effect of Al on Si isotope fractionation investigated by silica precipitation experiments[END_REF][START_REF] Roerdink | Experimental constraints on kinetic and equilibrium silicon isotope fractionation during the formation of non-biogenic chert deposits[END_REF][START_REF] Poitrasson | Silicon Isotope Geochemistry[END_REF]. However, the degree of Si and Mg isotope fractionation at isotopic equilibrium between minerals and coexisting fluids is scarcely known, so that the relative impact of kinetic versus equilibrium processes on the fractionation during fluid-mineral interaction cannot be assessed unambiguously.

List of Figures

In natural fluids Si and Mg can occur as different species, in addition to their major aqueous species silicic acid (H 4 SiO 4 ) and Mg(H 2 O) 6 2+ (Mg 2+ ). Additionally, a large number of organic and inorganic aqueous complexes can form with these elements. Aqueous speciation is known to have an important impact on isotopic fractionation factors, which has been demonstrated for elements such as boron, carbon, magnesium, mercury, transition metals and silicon [START_REF] Hemming | Boron isotopic composition and concentration in modern marine carbonates[END_REF][START_REF] Zhang | Abiologic silicon isotope fractionation between aqueous Si and Fe(III)-Si gel in simulated Archean seawater: Implications for Si isotope records in Precambrian sedimentary rocks[END_REF][START_REF] Zeebe | Stable boron isotope fractionation between dissolved B(OH) 3 and B(OH) 4[END_REF][START_REF] Klochko | Experimental measurement of boron isotope fractionation in seawater[END_REF][START_REF] Klochko | Re-evaluating boron speciation in biogenic calcite and aragonite using 11B MAS NMR[END_REF][START_REF] Asael | Fluid speciation controls of low temperature copper isotope fractionation applied to the Kupferschiefer and Timna ore deposits[END_REF][START_REF] Holloway | Ammonium in thermal waters of Yellowstone National Park: Processes affecting speciation and isotope fractionation[END_REF][START_REF] Jiskra | Solution Speciation Controls Mercury Isotope Fractionation of Hg(II) Sorption to Goethite[END_REF][START_REF] Ryan | Copper speciation and isotopic fractionation in plants: uptake and translocation mechanisms[END_REF][START_REF] Yin | Mercury speciation and mercury isotope fractionation during ore roasting process and their implication to source identification of downstream sediment in the Wanshan mercury mining area SW China[END_REF][START_REF] Fujii | Density functional theory estimation of isotope fractionation of Fe, Ni, Cu, and Zn among species relevant to geochemical and biological environments[END_REF][START_REF] Fujii | Isotope fractionation of Si in protonation/deprotonation reaction of silicic acid: A new pH proxy[END_REF][START_REF] Dupuis | Fractionation of silicon isotopes in liquids: The importance of configurational disorder[END_REF][START_REF] Noireaux | Crystallographic control on the boron isotope paleo-pH proxy[END_REF][START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF][START_REF] Balan | Theoretical isotopic fractionation between structural boron in carbonates and aqueous boric acid and borate ion[END_REF][START_REF] Mavromatis | Zinc isotope fractionation during the inorganic precipitation of calcite -Towards a new pH proxy[END_REF]. A critical factor to determining the equilibrium fractionation between a mineral and the coexisting aqueous fluid, is therefore the aqueous speciation of the system.

In the past, several experimental and theoretical ab initio studies were performed to determine Si and Mg equilibrium fractionation factors between solid and their coexisting aqueous solutions [START_REF] Rustad | Isotopic fractionation of Mg 2+ (aq), Ca 2+ (aq), and Fe 2+ (aq) with carbonate minerals[END_REF][START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF][START_REF] Schauble | First-principles estimates of equilibrium magnesium isotope fractionation in silicate, oxide, carbonate and hexaaquamagnesium(2+) crystals[END_REF][START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF][START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF][START_REF] Oelze | Si stable isotope fractionation during adsorption and the competition between kinetic and equilibrium isotope fractionation: Implications for weathering systems[END_REF][START_REF] Dupuis | Fractionation of silicon isotopes in liquids: The importance of configurational disorder[END_REF][START_REF] Fujii | Isotope fractionation of Si in protonation/deprotonation reaction of silicic acid: A new pH proxy[END_REF][START_REF] Pinilla | Equilibrium magnesium isotope fractionation between aqueous Mg2+ and carbonate minerals: Insights from path integral molecular dynamics[END_REF][START_REF] Roerdink | Experimental constraints on kinetic and equilibrium silicon isotope fractionation during the formation of non-biogenic chert deposits[END_REF]Zheng et al., 2016;[START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF][START_REF] Mavromatis | Effect of organic ligands on Mg partitioning and Mg isotope fractionation during low-temperature precipitation of calcite in the absence of growth rate effects[END_REF][START_REF] Colla | Computational prediction of Mg-isotope fractionation between aqueous [Mg(OH 2 ) 6 ] 2+ and brucite[END_REF][START_REF] Gao | Theoretical calculation of equilibrium Mg isotope fractionations between minerals and aqueous solutions[END_REF]. These studies give insight into the mechanisms of equilibrium isotopic exchange. This thesis builds upon these efforts through a systematic and carefully controlled experimental study.

This study investigates the effects of aqueous speciation, and the inorganic and organic complexation on the equilibrium isotope fractionation factors of Si and Mg in the amorphous silica (SiO 2 ) -aqueous solution and brucite (Mg(OH) 2 ) -aqueous solution system respectively. Constraining the equilibrium isotopic fractionation in these systems is crucial to understand the geochemical cycle of silicon and magnesium. Towards this goal, isotopic exchange experiments at bulk chemical equilibrium were performed between solids and fluids of different compositions and at different temperatures using the 'three-isotope method'. The experimentally determined equilibrium isotope fractionation factors are also compared to the results of corresponding ab inito calculations and the values obtained from previous experimental and theoretical studies. The results of this study aim to improve our ability to interpret the isotopic composition of Si and Mg in natural systems, and can be used to develop new tools to estimate past environmental conditions

1.1b. Introduction génerale (Version française)

Le silicium (Si) et le magnésium (Mg) sont parmi les éléments les plus abondants de la croute terrestre et ils jouent un rôle important dans de nombreux processus géologiques. Les isotopes stables de Si et de Mg peuvent donc être utilisés comme des traceurs fiables de nombreux processus se déroulant à la surface de la terre comme l'altération, la croissance et la précipitation des minéraux, l'activité biologique ou encore la chimie océanique à travers le temps (e.g. [START_REF] Varela | Biological fractionation of silicon isotopes in Southern Ocean surface waters: BIOLOGICAL FRACTIONATION OF SILICON[END_REF][START_REF] Opfergelt | Plant silicon isotopic signature might reflect soil weathering degree[END_REF][START_REF] Wimpenny | The behaviour of magnesium and its isotopes during glacial weathering in an ancient shield terrain in West Greenland[END_REF]Opfergelt et al., 2012a;[START_REF] Pogge Von Strandmann | Lithium, magnesium and silicon isotope behaviour accompanying weathering in a basaltic soil and pore water profile in Iceland[END_REF]Tipper et al., 2012;[START_REF] Kasemann | Continental weathering following a Cryogenian glaciation: Evidence from calcium and magnesium isotopes[END_REF]Mavromatis et al., 2014;[START_REF] Saenger | Magnesium isotope fractionation in biogenic and abiogenic carbonates: implications for paleoenvironmental proxies[END_REF][START_REF] Fujii | Isotope fractionation of Si in protonation/deprotonation reaction of silicic acid: A new pH proxy[END_REF][START_REF] Gao | Magnesium isotope fractionation during dolostone weathering[END_REF].

Depuis l'avènement de la spectrométrie de masse à plasma à couplage inductif multicollection (MC-ICP-MS), les compositions isotopiques de Si et Mg ont été déterminées dans de nombreux réservoirs terrestres tels que les eaux de surface [START_REF] Brenot | Magnesium isotope systematics of the lithologically varied Moselle river basin, France[END_REF][START_REF] Georg | Stable silicon isotopes of groundwater, feldspars, and clay coatings in the Navajo Sandstone aquifer, Black Mesa, Arizona, USA[END_REF][START_REF] De La Rocha | The silicon isotopic composition of surface waters in the Atlantic and Indian sectors of the Southern Ocean[END_REF][START_REF] Ding | Silicon isotopic composition of dissolved silicon and suspended particulate matter in the Yellow River, China, with implications for the global silicon cycle[END_REF][START_REF] Grasse | The influence of water mass mixing on the dissolved Si isotope composition in the Eastern Equatorial Pacific[END_REF][START_REF] Pokrovsky | Silicon isotope variations in Central Siberian rivers during basalt weathering in permafrost-dominated larch forests[END_REF][START_REF] Frings | Silicate weathering in the Ganges alluvial plain[END_REF], sols [START_REF] Opfergelt | Magnesium retention on the soil exchange complex controlling Mg isotope variations in soils, soil solutions and vegetation in volcanic soils, Iceland[END_REF]Riotte et al., 2018a), la biosphère, y compris plantes, foraminifères, éponges, diatomées [START_REF] Savin | Stable Isotope and Magnesium Geochemistry of Recent Planktonic Foraminifera from the South Pacific[END_REF][START_REF] Douthitt | The geochemistry of the stable isotopes of silicon[END_REF]Ding et al., 2008aDing et al., , 2008b;;[START_REF] Bolou-Bi | Experimental determination of magnesium isotope fractionation during higher plant growth[END_REF][START_REF] Pogge Von Strandmann | Lithium, magnesium and silicon isotope behaviour accompanying weathering in a basaltic soil and pore water profile in Iceland[END_REF]Opfergelt et al., 2012b;Riotte et al., 2018b), sans oublier, à l'état minéral, minéraux et roches profonds, roches sédimentaires, carbonates, cherts et formations de fer rubanées [START_REF] Douthitt | The geochemistry of the stable isotopes of silicon[END_REF]Ziegler et al., 2005aZiegler et al., , 2005b;;[START_REF] Georg | Stable silicon isotopes of groundwater, feldspars, and clay coatings in the Navajo Sandstone aquifer, Black Mesa, Arizona, USA[END_REF][START_REF] Hippler | Towards a better understanding of magnesium-isotope ratios from marine skeletal carbonates[END_REF][START_REF] Steinhoefel | Deciphering formation processes of banded iron formations from the Transvaal and the Hamersley successions by combined Si and Fe isotope analysis using UV femtosecond laser ablation[END_REF][START_REF] Van Den Boorn | Silicon isotope and trace element constraints on the origin of ∼3.5Ga cherts: Implications for Early Archaean marine environments[END_REF][START_REF] Savage | The silicon isotope composition of the upper continental crust[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF][START_REF] Wimpenny | Investigating the behaviour of Mg isotopes during the formation of clay minerals[END_REF][START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF]. Des études expérimentales ont démontré que les signatures isotopiques du silicium et du magnésium dans les milieux naturels peuvent évoluer au cours de la précipitation, de la croissance et de la dissolution des minéraux [START_REF] Li | Experimental study of silicon isotope dynamic fractionation and its application in geology[END_REF][START_REF] Basile-Doelsch | Another continental pool in the terrestrial silicon cycle[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF][START_REF] Geilert | Silicon isotope fractionation during abiotic silica precipitation at low temperatures: Inferences from flow-through experiments[END_REF][START_REF] Roerdink | Experimental constraints on kinetic and equilibrium silicon isotope fractionation during the formation of non-biogenic chert deposits[END_REF][START_REF] Oelze | The effect of Al on Si isotope fractionation investigated by silica precipitation experiments[END_REF] ou lors de l'adsorption d'espèces aqueuses sur des surfaces solides [START_REF] Delstanche | Silicon isotopic fractionation during adsorption of aqueous monosilicic acid onto iron oxide[END_REF][START_REF] Oelze | Si stable isotope fractionation during adsorption and the competition between kinetic and equilibrium isotope fractionation: Implications for weathering systems[END_REF]. Il a été montré que les fractionnements isotopiques naturels de ces éléments au cours des interactions solide-fluide peuvent être influencés par la diffusion et la cinétique des réactions [START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF][START_REF] Geilert | Silicon isotope fractionation during abiotic silica precipitation at low temperatures: Inferences from flow-through experiments[END_REF][START_REF] Oelze | The effect of Al on Si isotope fractionation investigated by silica precipitation experiments[END_REF][START_REF] Roerdink | Experimental constraints on kinetic and equilibrium silicon isotope fractionation during the formation of non-biogenic chert deposits[END_REF][START_REF] Poitrasson | Silicon Isotope Geochemistry[END_REF].

Cependant, les degrés de fractionnements isotopiques du Si et du Mg à l'équilibre entre les minéraux et les fluides à leur contact sont encore peu documentés, de sorte que l'impact des processus cinétiques sur ces fractionnements pendant les interactions fluide-minéral reste difficile à évaluer sans ambiguïté. [START_REF] Hemming | Boron isotopic composition and concentration in modern marine carbonates[END_REF][START_REF] Zhang | Abiologic silicon isotope fractionation between aqueous Si and Fe(III)-Si gel in simulated Archean seawater: Implications for Si isotope records in Precambrian sedimentary rocks[END_REF]Zhang et al., ., 2005;;[START_REF] Klochko | Experimental measurement of boron isotope fractionation in seawater[END_REF][START_REF] Klochko | Re-evaluating boron speciation in biogenic calcite and aragonite using 11B MAS NMR[END_REF][START_REF] Asael | Fluid speciation controls of low temperature copper isotope fractionation applied to the Kupferschiefer and Timna ore deposits[END_REF][START_REF] Holloway | Ammonium in thermal waters of Yellowstone National Park: Processes affecting speciation and isotope fractionation[END_REF][START_REF] Jiskra | Solution Speciation Controls Mercury Isotope Fractionation of Hg(II) Sorption to Goethite[END_REF][START_REF] Ryan | Copper speciation and isotopic fractionation in plants: uptake and translocation mechanisms[END_REF][START_REF] Yin | Mercury speciation and mercury isotope fractionation during ore roasting process and their implication to source identification of downstream sediment in the Wanshan mercury mining area SW China[END_REF][START_REF] Fujii | Density functional theory estimation of isotope fractionation of Fe, Ni, Cu, and Zn among species relevant to geochemical and biological environments[END_REF][START_REF] Fujii | Isotope fractionation of Si in protonation/deprotonation reaction of silicic acid: A new pH proxy[END_REF][START_REF] Dupuis | Fractionation of silicon isotopes in liquids: The importance of configurational disorder[END_REF][START_REF] Noireaux | Crystallographic control on the boron isotope paleo-pH proxy[END_REF][START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF][START_REF] Balan | Theoretical isotopic fractionation between structural boron in carbonates and aqueous boric acid and borate ion[END_REF]Mavromatis et al., 2018). Un facteur critique pour déterminer le fractionnement à l'équilibre entre un minéral et le fluide aqueux coexistant est donc la spéciation aqueuse du système.

Dans le passé, plusieurs études ab initio expérimentales et théoriques ont été effectuées pour déterminer les facteurs de fractionnement à l'équilibre du Si et du Mg entre le solide et ses solutions aqueuses coexistantes [START_REF] Rustad | Isotopic fractionation of Mg 2+ (aq), Ca 2+ (aq), and Fe 2+ (aq) with carbonate minerals[END_REF][START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF][START_REF] Schauble | First-principles estimates of equilibrium magnesium isotope fractionation in silicate, oxide, carbonate and hexaaquamagnesium(2+) crystals[END_REF][START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF][START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF][START_REF] Oelze | Si stable isotope fractionation during adsorption and the competition between kinetic and equilibrium isotope fractionation: Implications for weathering systems[END_REF][START_REF] Dupuis | Fractionation of silicon isotopes in liquids: The importance of configurational disorder[END_REF][START_REF] Fujii | Isotope fractionation of Si in protonation/deprotonation reaction of silicic acid: A new pH proxy[END_REF][START_REF] Pinilla | Equilibrium magnesium isotope fractionation between aqueous Mg2+ and carbonate minerals: Insights from path integral molecular dynamics[END_REF][START_REF] Roerdink | Experimental constraints on kinetic and equilibrium silicon isotope fractionation during the formation of non-biogenic chert deposits[END_REF]Zheng et al., 2016;[START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF][START_REF] Mavromatis | Effect of organic ligands on Mg partitioning and Mg isotope fractionation during low-temperature precipitation of calcite in the absence of growth rate effects[END_REF][START_REF] Colla | Computational prediction of Mg-isotope fractionation between aqueous [Mg(OH 2 ) 6 ] 2+ and brucite[END_REF][START_REF] Gao | Theoretical calculation of equilibrium Mg isotope fractionations between minerals and aqueous solutions[END_REF]. Ces études donnent un aperçu des mécanismes à l'origine des échanges isotopiques à l'équilibre. Ce travail de thèse s'appuie sur ces études pour améliorer notre connaissance de ces systèmes grâce à la mise en oeuvre d'une méthode expérimentale très rigoureuse pour déterminer les fractionnements isotopiques à l'équilibre.

Aqueous chemistry

The isotope exchange experiments in this study were performed in aqueous solutions at bulk chemical equilibrium with a solid phase and in the presence and absence of organic ligands.

The fundamental chemical relations used in this study are reviewed briefly in the following sections.

Chemical equilibrium

In nature, aqueous solutions and solids such as minerals and rocks are constantly interacting (e.g. through mineral dissolution or precipitation). These reactions will tend to evolve towards chemical equilibrium over time. In a simplified case, the general chemical reaction can be written (e.g. [START_REF] Garrels | Solutions, minerals, and equilibria, A Harper International student reprint[END_REF]:

+ ↔ + (1.1)
where B and C are the reactants, which form the products D and E, b, c, d and d are the moles of each reactant in the reaction. When the system reaches equilibrium, the ratio of the activities (a) of products and reactant are governed by the law of mass action given by:

= (1.2)
where K eq designates a thermodynamic equilibrium constant. At equilibrium the interaction between the reactants and products does not cease, however, the net reaction rate (r) is zero, as forward rate (r + ) and backward rate (r -) are equal (e.g. [START_REF] Aagaard | Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solutions; I, Theoretical considerations[END_REF][START_REF] Garrels | Solutions, minerals, and equilibria, A Harper International student reprint[END_REF][START_REF] Oelkers | General kinetic description of multioxide silicate mineral and glass dissolution[END_REF][START_REF] Oelkers | The temporal evolution of magnesium isotope fractionation during hydromagnesite dissolution, precipitation, and at equilibrium[END_REF][START_REF] Schott | The Link Between Mineral Dissolution/Precipitation Kinetics and Solution Chemistry[END_REF], i.e. = -= 0 (1.3) Equilibrium conditions can also be described in terms of the energies of the chemical reaction.

At equilibrium conditions at a distinct temperature and pressure the total free energy change ∆G is zero and thus the standard free energy change of the reaction (∆G ) can be related to the equilibrium constant by (e.g. [START_REF] Garrels | Solutions, minerals, and equilibria, A Harper International student reprint[END_REF][START_REF] White | Geochemistry[END_REF]:

∆! " # = -$% &' (1.4)
The experimental achievement of equilibrium is challenging as the reactions can slow as equilibrium is approached [START_REF] Schott | The Link Between Mineral Dissolution/Precipitation Kinetics and Solution Chemistry[END_REF] or the system can undergo slight changes during the experiment, which impacts the attainment of equilibrium. Therefore any experimental system has to be constantly monitored to ensure chemical equilibrium has been attained.

Speciation and complexation in aqueous solution

Metal ions in solution are usually represented as M n+ , as though they are bare ions suspended in a structureless medium, whereas they are complexes of water, similar to complexes of other ligands. The number of water molecules bound directly to the metal ion, its coordination number, is generally similar to the number of donor atoms found for the metal in solid state, for example in oxides. In solution there is an inner-sphere of water molecules bound directly to the metal ion, and an outer-sphere of more loosely held water molecules [START_REF] Martell | Metal Complexes in Aqueous Solutions[END_REF][START_REF] White | Geochemistry[END_REF]. Such metal ions in solution are called aquo ions. In aqueous solutions ions can associate with other ions, forming new species or complexes. Complex formation involves replacement of one or several water molecules coordinated to the metal ion by one or several ligands, which may replace either water molecules from the inner-sphere or water molecules from the outer-sphere [START_REF] Buffle | Complexation reactions in aquatic systems: an analytical approach[END_REF]Stumm, 1995). Outer sphere complexes result from electrostatic attraction between the ligand and the metal ion, but leave at least one water molecule between the metal and ligand, whereas in the inner sphere complex covalent bonds are formed between the metal and the ligand, such that no water molecules are present in between the ions. The rate of formation of a metal ion complex in aqueous solution is comparable to the rate at which water in the inner-sphere of this metal ion exchanges with water in the bulk solution [START_REF] Martell | Metal Complexes in Aqueous Solutions[END_REF][START_REF] Pokrovsky | Surface Chemistry and Dissolution Kinetics of Divalent Metal Carbonates[END_REF]. The mean lifetime of water molecules in the first coordination sphere varies considerably with the metal properties ranging from 2×10 -10 s (Rb + ) to 14.4 years (Rh 3+ ; [START_REF] Lincoln | Substitution reactions of solvated metal ions[END_REF].

Aqueous metal ions commonly complex to organic molecules. The principle is similar to the complexation of inorganic anions, however, organic compound often have more than one site, which can bind to the metal [START_REF] White | Geochemistry[END_REF]. Organic ligands, which have multiple positions to bind the same metal ion, can form multidendate complexes, also known as chelates. These chelates can form rings around the metal ions, and thus can function as metal carriers [START_REF] Buffle | Complexation reactions in aquatic systems: an analytical approach[END_REF]. Due to the multiple positions available to bind the ion, organic ligands are able to change the coordination of the binding metal [START_REF] Cella | 29Si NMR of five-and six-coordinate organosilicon complexes[END_REF][START_REF] Sjöberg | Equilibrium and structural studies of silicon(IV) and aluminium(III) in aqueous solution. 12. A potentiometric and 29 Si-NMR study of silicon tropolonates[END_REF]Kinrade et al., 2001Kinrade et al., , 2002;;[START_REF] Kinrade | Silicon-29 NMR studies of aqueous silicate solutions. 1. Chemical shifts and equilibria[END_REF][START_REF] Wang | Adsorption Behavior of Metasilicate on N-Methyl D-Glucamine Functional Groups and Associated Silicon Isotope Fractionation[END_REF].

Additionally, organic compounds are weak acids and have thus an affinity for protons in solution, therefore the complexation of a metal to an organic ligand is dependent on the pH of the solution [START_REF] White | Geochemistry[END_REF].

If a metal ion is complexed in aqueous solution the concentration of its "free ion" in water is reduced compared to the total concentration of the dissolved metal, which leads to an increase of the solubility of the minerals bearing this metal [START_REF] Bennett | The dissolution of quartz in dilute aqueous solutions of organic acids at 25°C[END_REF][START_REF] Bennett | Quartz dissolution in organic-rich aqueous systems[END_REF][START_REF] Bennett | Chemistry and Mechanisms of Low-Temperature Dissolution of Silicates by Organic Acids[END_REF][START_REF] Ganor | Organics in Water-Rock Interactions[END_REF][START_REF] Schott | The Link Between Mineral Dissolution/Precipitation Kinetics and Solution Chemistry[END_REF][START_REF] Appelo | Geochemistry, groundwater and pollution[END_REF][START_REF] White | Geochemistry[END_REF].

Principles of stable isotope fractionation

The present study investigates the equilibrium isotopic fractionation of Si and Mg among solids and aqueous solutions. A summary of the basic principles of stable isotopic fractionation are presented in the following sections.

Stable isotopes

Elements consist of atoms with positively charged protons, negatively charged electrons and neutrons, which have no charge. Protons and neutrons are present in the nucleus, which is surrounded by an electron cloud. In a given element the number of protons in the nucleus do not change, however the number of neutrons may vary. Atoms, which contain the same number of protons and electrons but differ in the number of neutrons are called isotopes. Two types of isotopes occur in nature: stable and unstable, i.e. radioactive, isotopes. Most natural elements have one or more stable isotopes. These have a permanent nuclear configuration, and do not undergo any spontaneous transformation in the form of radioactive decay or radiogenic growth.

Stable isotope fractionation

The isotopic composition of different materials, such as rocks, minerals, soils, plants, waters etc. can be compared by normalizing the measured isotopic ratios of these materials to an international reference standard. This standard is systematically analysed along with the samples. The isotopic fractionation between the samples and the standard are expressed using the δ notation:

( ) = * + ) , -. /0123 + ) , -. /405 0" -17 × 1000 [‰] (1.5)
where x E denotes the lightest isotope of the element E, and y E any heavier isotope of interest of element E.

Theoretically isotopes of a given element exhibit identical chemical properties, as they possess the same electron shell, however isotopes do exhibit different physicochemical properties, due to their mass difference and the resulting quantum mechanical effects. Atoms of the different isotopes of an element will react at different rates, even if they take part in the same reaction. Typically light isotopes or molecules react faster than heavier isotopes or molecules.

The isotopic fractionation factor of an element E between two substances A and B

(α = > ) can be expressed by following relation (e.g. [START_REF] Schauble | Applying Stable Isotope Fractionation Theory to New Systems[END_REF]:

@ A = + ) , -. A + ) ,
-.

(1.6)

Note that in terms of physical processes, α = > could reflect equilibrium or non-equilibrium partitioning of isotopes. For an isotope exchange reaction in which one atom is exchanged, α = > is equal to the reaction equilibrium constant. Because α = > is very close to unity (generally on the order of 1.00X), the relation 10 3 ln(1.00X) ≈ X allows to express the isotopic fractionation factor as the difference of the δ y E values of substances A and B:

10 B &'@ A ≈ ( D E -( D = ∆ E- (1.7)

Stable isotope fractionation processes

Isotopic fractionation can be distinguished into non-equilibrium, i.e. kinetic and equilibrium effects. Kinetic isotope fractionation depends on the different reaction rates of isotopes or isotopic molecules. It commonly occurs with incomplete exchange, unidirectional or fast reactions, such as diffusion, dissociation reactions, evaporation and biological processes [START_REF] Criss | Principles of stable isotope distribution[END_REF][START_REF] Schauble | Applying Stable Isotope Fractionation Theory to New Systems[END_REF][START_REF] Hoefs | Stable isotope geochemistry[END_REF][START_REF] White | Geochemistry[END_REF]. The fractionation associated to kinetic effects can be larger than those associated to equilibrium effects.

Equilibrium isotope fractionation, which is investigated in this study, requires that the system of interest is in chemical equilibrium [START_REF] Mills | The Kinetics of Isotopic Exchange between Carbon Dioxide, Bicarbonate Ion, Carbonate Ion and Water 1[END_REF][START_REF] Schauble | Applying Stable Isotope Fractionation Theory to New Systems[END_REF], and is caused by isotopic substitution, which arises mainly from vibrational motions of the molecules and atoms in the different phases of the system [START_REF] Urey | The thermodynamic properties of isotopic substances[END_REF]. An isotope exchange reaction can be written as follows (e.g. [START_REF] Hoefs | Stable isotope geochemistry[END_REF]:

E F + G ↔ E G + F (1.8)
where A and B denote the two substances in the system of interest, and the subscripts indicate that the phases A and B comprise either the light (1) or heavy (2) isotope. The fractionation factor α is related to the equilibrium constant K of the reaction as: @ = F/5 (1.9)

where n is the number of atoms exchange. Isotopic exchange reactions usually are written for the exchange of one atom. Therefore Eqn. 1.9 reduces to: @ = (1.10)

The isotopes in this equilibrium reaction will distribute, depending on their masses, to minimize the vibrational energy of the system. Heavier isotopes will decrease the vibrational energy, and the bond will become more stable.

In general the equilibrium stable isotope fractionation of an element has been known

to follow certain rules [START_REF] Bigeleisen | Calculation of Equilibrium Constants for Isotopic Exchange Reactions[END_REF][START_REF] Schauble | Applying Stable Isotope Fractionation Theory to New Systems[END_REF]. The three most important are:

1) Increasing temperature will lead to a decrease of the equilibrium isotopic fractionation in proportion of ~1/T 2 . Exceptions might occur when fractionation is very small or the element of interest is bonded to hydrogen.

2) The equilibrium isotopic fractionation of an element is largest, when the relative mass difference between its isotopes is large.

3) Equilibrium isotopic fractionation is affected by the atomic and molecular bonds of the element. Heavy isotopes will enrich in the compound where it will find the strongest bonds. This is due to the lower binding energy of light isotopes. The equilibrium isotopic fractionation is approximately proportional to the difference in the stiffness of the bonds. Shorter and stronger chemical bonds have the greater bond stiffness. This correlates with element properties, such as high oxidation states, presence of highly covalent bonds, transition elements and low coordination numbers.

For elements with three or more isotopes, the fractionation of the isotopes at equilibrium is typically proportional to their mass difference. This mass dependent process is usually described in a three-isotope plot as a linear curve, called the terrestrial fractionation line (TFL, [START_REF] Matsuhisa | Mechanisms of hydrothermal crystallization of quartz at 250°C and 15 kbar[END_REF]. Deviation from the TFL are described as mass-independent fractionation.

Influence of aqueous speciation on isotope fractionation

Aqueous solutions can contain several different species, depending on its composition. The speciation of an element in solution can have an important impact on the fractionation factor of this element. For many elements such as boron, carbon, magnesium, mercury, silicon and various transition metals it has been demonstrated that inorganic and organic speciation influences the isotopic fractionation [START_REF] Hemming | Boron isotopic composition and concentration in modern marine carbonates[END_REF][START_REF] Zhang | Abiologic silicon isotope fractionation between aqueous Si and Fe(III)-Si gel in simulated Archean seawater: Implications for Si isotope records in Precambrian sedimentary rocks[END_REF][START_REF] Zeebe | Stable boron isotope fractionation between dissolved B(OH) 3 and B(OH) 4[END_REF][START_REF] Klochko | Experimental measurement of boron isotope fractionation in seawater[END_REF][START_REF] Klochko | Re-evaluating boron speciation in biogenic calcite and aragonite using 11B MAS NMR[END_REF][START_REF] Asael | Fluid speciation controls of low temperature copper isotope fractionation applied to the Kupferschiefer and Timna ore deposits[END_REF][START_REF] Holloway | Ammonium in thermal waters of Yellowstone National Park: Processes affecting speciation and isotope fractionation[END_REF][START_REF] Jiskra | Solution Speciation Controls Mercury Isotope Fractionation of Hg(II) Sorption to Goethite[END_REF][START_REF] Ryan | Copper speciation and isotopic fractionation in plants: uptake and translocation mechanisms[END_REF][START_REF] Yin | Mercury speciation and mercury isotope fractionation during ore roasting process and their implication to source identification of downstream sediment in the Wanshan mercury mining area SW China[END_REF][START_REF] Fujii | Density functional theory estimation of isotope fractionation of Fe, Ni, Cu, and Zn among species relevant to geochemical and biological environments[END_REF][START_REF] Fujii | Isotope fractionation of Si in protonation/deprotonation reaction of silicic acid: A new pH proxy[END_REF][START_REF] Dupuis | Fractionation of silicon isotopes in liquids: The importance of configurational disorder[END_REF][START_REF] Noireaux | Crystallographic control on the boron isotope paleo-pH proxy[END_REF][START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF][START_REF] Balan | Theoretical isotopic fractionation between structural boron in carbonates and aqueous boric acid and borate ion[END_REF][START_REF] Mavromatis | Zinc isotope fractionation during the inorganic precipitation of calcite -Towards a new pH proxy[END_REF].

In natural fluids, elements often complex to organic ligands, which will also modify the distribution of the aqueous species of this element. Additionally some organic ligands are known to affect the coordination of the metal and thus strongly influence the isotope fractionation of the element. Few theoretical and experimental studies have shown the important influence of organics on the aqueous speciation of elements such as magnesium or iron (Domagal-Goldman and [START_REF] Domagal-Goldman | Density functional theory predictions of equilibrium isotope fractionation of iron due to redox changes and organic complexation[END_REF][START_REF] Klochko | Re-evaluating boron speciation in biogenic calcite and aragonite using 11B MAS NMR[END_REF][START_REF] Wiederhold | Iron Isotope Fractionation during Proton-Promoted, Ligand-Controlled, and Reductive Dissolution of Goethite[END_REF][START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF][START_REF] Mavromatis | Effect of organic ligands on Mg partitioning and Mg isotope fractionation during low-temperature precipitation of calcite in the absence of growth rate effects[END_REF][START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF]. Silicon takes part in nearly all geological processes, and therefore the study of its chemical behaviour and isotopic variations is crucial to understand these processes.

Silicon and magnesium isotopic systems

In nature, Si is generally bound to oxygen and does not take part in redox reactions. It is found usually in tetravalent oxidation state (4+) and forms numerous silicate minerals [START_REF] Poitrasson | Silicon Isotope Geochemistry[END_REF]. As an oxide (SiO 2 ), silicon mainly occurs as crystalline quartz and amorphous silica. Amorphous silica is found in cherts and plays an important role in biomineralization as it forms widespread biogenic minerals. SiO 2 solids are sparingly soluble [START_REF] Iler | The chemistry of silica: solubility, polymerization, colloid and surface properties, and biochemistry[END_REF][START_REF] Oelze | Silicon isotope fractionation at low temperatures in the presence of Aluminum: An experimental approach and application to different erent weathering regimes[END_REF]. The Si concentrations in natural waters remain mostly below 100 ppm. In natural solutions, Si commonly occurs as monosilicic acid, H 4 SiO 4 o . The dissolution reaction of SiO 2 in water can be described as (e.g. [START_REF] Iler | The chemistry of silica: solubility, polymerization, colloid and surface properties, and biochemistry[END_REF]: solubility, due to the following reactions (e.g. [START_REF] Iler | The chemistry of silica: solubility, polymerization, colloid and surface properties, and biochemistry[END_REF]:

IJKL G ) /#3M + 2 O G L → O Q JKL Q # (1.
O Q JKL Q # + LO → O B JKL Q + O G L (1.12)
and with further pH increase, H Q SiO Q will further dissociate in accord with: Dissolved Si in natural environments not only plays a role in the formation or dissolution of silicate or rock forming minerals, but H 4 SiO 4 o also plays an important role in the biological cycle and is used by many organisms [START_REF] Leng | The Potential use of Silicon Isotope Composition of Biogenic Silica as a Proxy for Environmental Change[END_REF]. Biogenic silicon functions as a structural element and is often included as opaline SiO 2 into plants, phytoplankton, zooplankton or sponges (e.g. [START_REF] Leng | The Potential use of Silicon Isotope Composition of Biogenic Silica as a Proxy for Environmental Change[END_REF][START_REF] Poitrasson | Silicon Isotope Geochemistry[END_REF]. In these natural environments, Si can complex with organic ligands. Studies have shown that this complexation could have an strong influence on the coordination of Si in solution [START_REF] Cella | 29Si NMR of five-and six-coordinate organosilicon complexes[END_REF][START_REF] Sjöberg | Equilibrium and structural studies of silicon(IV) and aluminium(III) in aqueous solution. 12. A potentiometric and 29 Si-NMR study of silicon tropolonates[END_REF]Kinrade et al., 2001Kinrade et al., , 2002;;[START_REF] Kinrade | Silicon-29 NMR studies of aqueous silicate solutions. 1. Chemical shifts and equilibria[END_REF][START_REF] Wang | Adsorption Behavior of Metasilicate on N-Methyl D-Glucamine Functional Groups and Associated Silicon Isotope Fractionation[END_REF].

O Q JKL Q # + 2 LO → O G JKL Q G + 2 O G L (1.13)
Due to its high abundance on Earth, and its importance for the geological and biochemical cycle, Si is a valuable tracer for near surface processes, such as biomineralization and weathering. Therefore the isotopic compositions of many Si reservoirs have been studied.

The first measurements of the isotopic compositions of Si in natural samples were performed in the 1950's by [START_REF] Reynolds | Natural variations in the isotopic constitution of silicon[END_REF], [START_REF] Allenby | Determination of the isotopic ratios of silicon in rocks[END_REF][START_REF] Tilles | Natural variations in isotopic abundances of silicon[END_REF]. After the moon landing, extensive work has been done on lunar samples an meteorites (e.g. [START_REF] Taylor | Oxygen and silicon isotope ratios of the Luna 20 soil[END_REF][START_REF] Yeh | 29Si/28Si and 30Si/28Si of Meteorites and Allende Inclusions[END_REF]. The two most important studies published on terrestrial samples are from [START_REF] Douthitt | The geochemistry of the stable isotopes of silicon[END_REF] and [START_REF] Ding | Silicon isotope geochemistry[END_REF]. As Si is always bound to oxygen in nature and not involved in redox reactions, only small Si isotope fractionations are expected. With the advent of multi-collector inductively coupled mass spectrometry (MC-ICP-MS) small variations in the Si isotope ratio could be determined [START_REF] Cardinal | Isotopic composition of silicon measured by multicollector plasma source mass spectrometry in dry plasma mode[END_REF].

Since then, many studies have been performed on various Si reservoirs, demonstrating that the Si fractionation is not as small as might have been expected.

Silicon isotope fractionation varies over a range of 12 ‰, with the lowest value of -6.02 ‰ reported by [START_REF] Wille | Silicon isotopic fractionation in marine sponges: A new model for understanding silicon isotopic variations in sponges[END_REF] for sponges and the highest value of +6.1 ‰ for rice grains reported by [START_REF] Ding | Silicon isotope study on rice plants from the Zhejiang province, China[END_REF]. Fig. 1.2 shows the distribution of the Si isotopic compositions of different terrestrial reservoirs. Extra-terrestrial materials (see [START_REF] Poitrasson | Silicon Isotope Geochemistry[END_REF], and references herein), igneous, and metamotphic rocks (e.g. [START_REF] Douthitt | The geochemistry of the stable isotopes of silicon[END_REF][START_REF] Ding | Silicon isotope geochemistry[END_REF]Ziegler et al., 2005aZiegler et al., , 2005b;;Zambardi, 2011 and references herein) are found to exhibit systematic and small 30 Si isotopic variations. Sedimentary rocks, such as shales and clastic metasediments exhibit a similar isotopic composition as igneous rocks (e.g. [START_REF] Savage | The silicon isotope composition of the upper continental crust[END_REF], as they normally derive Si from the physical disintegration of silicate minerals and rocks [START_REF] Georg | Geochemistry of stable silicon isotopes measured by high-resolution multi-collector inductively-coupled-plasma mass-spectrometry (HR-MC-ICP-MS)[END_REF]. In contrast, cherts and Banded Iron Formations (BIFs) show a much higher fractionation than the reservoirs described above (e.g. [START_REF] Heck | SIMS analyses of silicon and oxygen isotope ratios for quartz from Archean and Paleoproterozoic banded iron formations[END_REF][START_REF] Marin-Carbonne | Micrometer-scale chemical and isotopic criteria (O and Si) on the origin and history of Precambrian cherts: Implications for paleo-temperature reconstructions[END_REF][START_REF] Dal Corso | Pseudopotentials periodic table: From H to Pu[END_REF][START_REF] Poitrasson | Silicon Isotope Geochemistry[END_REF]. Soils depict a distinct negative Si isotope fractionation in comparison to igneous rocks, which is assumed to result from a kinetic fractionation process between clay minerals and natural waters [START_REF] Opfergelt | Variations of δ 30 Si and Ge/Si with weathering and biogenic input in tropical basaltic ash soils under monoculture[END_REF](Opfergelt et al., , 2012b[START_REF] Opfergelt | Iron and silicon isotope behaviour accompanying weathering in Icelandic soils, and the implications for iron export from peatlands[END_REF][START_REF] Poitrasson | Silicon Isotope Geochemistry[END_REF]. Silicon is strongly fractionated in biological environments. During the uptake of Si into plants, the light isotopes are preferred (e.g. [START_REF] Ding | Silicon isotope study on rice plants from the Zhejiang province, China[END_REF][START_REF] Sun | Silicon isotope fractionation in rice plants, an experimental study on rice growth under hydroponic conditions[END_REF][START_REF] Delvigne | Distinct silicon and germanium pathways in the soil-plant system: Evidence from banana and horsetail: distinct Si and Ge pathways in plants[END_REF][START_REF] Poitrasson | Silicon Isotope Geochemistry[END_REF]. However phytoliths can be enriched in heavy isotopes as shown by [START_REF] Ding | Silicon isotope study on rice plants from the Zhejiang province, China[END_REF]. This phenomenon was attributed to the evapotranspiration occurring in plants [START_REF] Ding | Silicon isotope study on rice plants from the Zhejiang province, China[END_REF](Ding et al., , 2008b;;[START_REF] Opfergelt | Plant silicon isotopic signature might reflect soil weathering degree[END_REF]. A wide range of isotopic fractionation is also exhibited by diatoms and sponges [START_REF] Douthitt | The geochemistry of the stable isotopes of silicon[END_REF][START_REF] De La Rocha | A first look at the distribution of the stable isotopes of silicon in natural waters[END_REF][START_REF] Ding | Silicon isotope geochemistry[END_REF][START_REF] Wischmeyer | Control mechanisms for the oceanic distribution of silicon isotopes[END_REF][START_REF] Wille | Silicon isotopic fractionation in marine sponges: A new model for understanding silicon isotopic variations in sponges[END_REF][START_REF] Hendry | Deep ocean nutrients during the Last Glacial Maximum deduced from sponge silicon isotopic compositions[END_REF][START_REF] Hendry | Silicon isotopes in Antarctic sponges: an interlaboratory comparison[END_REF][START_REF] Hendry | The relationship between silicon isotope fractionation in sponges and silicic acid concentration: Modern and core-top studies of biogenic opal[END_REF]. The process behind the incorporation of preferentially light isotopes is not yet understood.

Dissolved Si in natural waters, such as rivers and seawater, shows an enrichment in heavy isotopes [START_REF] De La Rocha | A first look at the distribution of the stable isotopes of silicon in natural waters[END_REF][START_REF] Varela | Biological fractionation of silicon isotopes in Southern Ocean surface waters: BIOLOGICAL FRACTIONATION OF SILICON[END_REF][START_REF] Cardinal | Relevance of silicon isotopes to Si-nutrient utilization and Si-source assessment in Antarctic waters: Silicon isotopes in arctic waters[END_REF][START_REF] Basile-Doelsch | Another continental pool in the terrestrial silicon cycle[END_REF][START_REF] Basile-Doelsch | Si stable isotopes in the Earth's surface: A review[END_REF][START_REF] Georg | New sample preparation techniques for the determination of Si isotopic compositions using MC-ICPMS[END_REF][START_REF] Reynolds | Silicon isotope fractionation during nutrient utilization in the North Pacific[END_REF][START_REF] Ding | Silicon isotopic composition of dissolved silicon and suspended particulate matter in the Yellow River, China, with implications for the global silicon cycle[END_REF]. During weathering or biomineralization, aqueous 28 Si(OH) 4 ° is preferentially consumed to form secondary minerals, which leads to the observed enrichment of 30 Si in the fluid.

The large variation of Si isotopic compositions reviewed above suggests that these compositions could be a useful tool to better understand many geological and biological processes. Knowing the mechanisms behind the Si isotope fractionation in nature might also help to quantify the Si geochemical cycle.

Magnesium isotopes

Magnesium (Mg), an alkaline earth metal, plays an important role in the oceans and in biological and hydrological systems. After oxygen, iron, and silicon, magnesium is the fourth most abundant element in the Earth [START_REF] Teng | Magnesium Isotope Geochemistry[END_REF] Magnesium is always found in a 2+, oxidation state and thus the range of its isotopic compositions in natural materials was believed to be small. However, Mg isotope fractionation varies over a range of ~7 ‰, as can be seen in Fig. 2.3 below. As silicon and other stable isotopes, magnesium fractionates at low temperatures.

Extra-terrestrial Mg reservoirs exhibit a small isotopic fractionation, from -0.61 ‰ in lunar [START_REF] Sedaghatpour | Magnesium isotopic composition of the Moon[END_REF] to 0 ‰ in chondritic samples [START_REF] Galy | Is there a CHUR for Mg? Presented at the Goldschmidt Abstract[END_REF].

Also the fractionation within the mantle and the oceanic crust are within 1 ‰ [START_REF] Teng | Magnesium Isotope Geochemistry[END_REF] .

The continental crust, however, is heterogeneous and Mg isotope compositions of rocks likely reflect their source compositions. The Mg isotopic signature of the upper continental crust is more heterogeneous than that of the deep continental crust and ranges from -1.64 ‰ [START_REF] Teng | Magnesium Isotope Geochemistry[END_REF] and citations herein) to 1.8 ‰ in weathered basalts [START_REF] Liu | Massive magnesium depletion and isotope fractionation in weathered basalts[END_REF]. The largest Mg isotopic fractionation is seen in carbonates. Due to the weaker bonding strength of Mg in carbonates compared to its aquo ion, these minerals tend to incorporate light Mg isotopes, whereas silicates, with a stronger Mg bonding strength, will tend to incorporate heavy Mg isotopes (e.g. [START_REF] Schauble | First-principles estimates of equilibrium magnesium isotope fractionation in silicate, oxide, carbonate and hexaaquamagnesium(2+) crystals[END_REF][START_REF] Teng | Magnesium Isotope Geochemistry[END_REF]. Mg also plays an important role during biological processes and exhibits a distinct isotopic fractionation in some bio materials (Fig. 2. [START_REF] Shahar | Hightemperature Si isotope fractionation between iron metal and silicate[END_REF]; it has therefore the potential for a reliable tracer of some biologic processes [START_REF] Teng | Magnesium Isotope Geochemistry[END_REF].

Magnesium isotopes are also known to fractionate substantially in the presence of organic ligands (e.g. [START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF][START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF][START_REF] Mavromatis | Effect of organic ligands on Mg partitioning and Mg isotope fractionation during low-temperature precipitation of calcite in the absence of growth rate effects[END_REF]. Magnesium is homogenously distributed in seawater due to its long residence time and has an average isotopic composition of -0.83 ‰ (e.g. [START_REF] Foster | Boron and magnesium isotopic composition of seawater: DATA BRIEF[END_REF][START_REF] Ling | Homogeneous magnesium isotopic composition of seawater: an excellent geostandard for Mg isotope analysis: Homogeneous magnesium isotopic composition of seawater[END_REF]. Corals and foraminifera are significantly lighter than ocean water, with average Mg isotopic compositions of -1 ‰ and -4.5 ‰, respectively [START_REF] Hoefs | Stable isotope geochemistry[END_REF]. This suggests that Mg isotopes might provide a tracer of biomineralization. The isotopic composition of rivers was extensively measured by Tipper et al. (2006), and are shown to be highly variable due to isotopic fractionation during water-rock interactions (e.g. Tipper et al., 2006;[START_REF] Wimpenny | The behaviour of magnesium and its isotopes during glacial weathering in an ancient shield terrain in West Greenland[END_REF]Mavromatis et al., 2014;[START_REF] Teng | Magnesium Isotope Geochemistry[END_REF].

As is the case for silicon understanding the Mg isotopic fractionation should enable the improved quantification of its geological and biogeochemical cycles.

Chapter 2

Materials and Methods

Theoretical Background

Three-isotope method

The experimental investigation of equilibrium isotope fractionation of Si and Mg in this thesis is based on the 'three-isotope method'. The three-isotope method was originally used to determine the equilibrium isotopic fractionation factors of oxygen between mineral and solution [START_REF] Matsuhisa | Mechanisms of hydrothermal crystallization of quartz at 250°C and 15 kbar[END_REF]Matthews et al., 1983aMatthews et al., , 1983bMatthews et al., , 1983c)). Over the past 10 years, this method was also successfully applied to non-traditional isotope systems, such as Mg and Fe [START_REF] Shahar | Equilibrium high-temperature Fe isotope fractionation between fayalite and magnetite: An experimental calibration[END_REF]Beard et al., 2010;[START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF][START_REF] Frierdich | Determination of the Fe(II)aq-magnetite equilibrium iron isotope fractionation factor using the three-isotope method and a multi-direction approach to equilibrium[END_REF][START_REF] Reddy | The effect of pH on stable iron isotope exchange and fractionation between aqueous Fe(II) and goethite[END_REF], as well as Si (Zheng et al., 2016). This approach is commonly used to evaluate the kinetics of isotopic exchange reactions between two components (Fig. 2.1; [START_REF] Cole | Rates and Mechanisms of Isotopic Exchange[END_REF][START_REF] Johnson | Isotopic fractionation between Fe(III) and Fe(II) in aqueous solutions[END_REF][START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF][START_REF] Wu | Stable iron isotope fractionation between aqueous Fe(II) and model Archean ocean Fe-Si coprecipitates and implications for iron isotope variations in the ancient rock record[END_REF]Zheng et al., 2016).

To apply this method to an element it has to have at least three stable isotopes [START_REF] Shahar | Equilibrium Fractionation of Non-traditional Stable Isotopes: an Experimental Perspective[END_REF] in measurable abundances. The three-isotope method is applied by performing experiments composed of a two-component system, a mineral phase A and an aqueous phase B. Their starting composition begins where both phases plot in a δ vs. δ diagram on the terrestrial fractionation line (TFL) as shown in Fig. 2.1. The TFL is the line where all natural samples plot and in which the isotopic compositions are related by massdependent fractionation. To apply the three-isotope method the aqueous phase of the experimental system is altered by the addition of an isotopic spike ( 29 Si or 25 Mg in the present study). The isotopic ratio of the spiked fluid is then distinctly offset from the TFL (t 0 of the liquid phase in Fig 2 .1). As the system undergoes isotopic exchange towards isotopic equilibrium, the isotopic compositions of the two components will gradually evolve over time (t 0 , t 1 , t 2 ,…). When the system reaches isotopic equilibrium, at 100% of isotopic exchange, the two components will plot on a secondary fractionation line (SFL) which has the same slope as the TFL, given the mass dependent behaviour of the isotopic fractionation.

The position of the SFL is defined by the isotopic mass balance of the system (see Fig. 2.1).

In many situations, especially at low temperature, the isotopic exchange is slow and equilibrium is rarely reached. The three-isotope method allows determination of the isotopic composition of the two components at 100% exchange.

The degree to which the system attains isotopic equilibrium can be determined using:

F = (δ -δ ) (δ -δ ) (2.1)
where F is the degree of isotopic exchange, and ranges from 0 to 1, δ t denotes the isotopic composition of either one of the components of the sample at any time, t, during the reaction, and δ i describes the initial and δ e the equilibrium isotopic composition of the component. Si. The isotopic composition of the two phases will evolve towards a value of 100% of isotopic exchange. The line connecting the two phases crosses the system average throughout the process, due to isotopic mass balance. At 100% exchange the two phases will plot on a SFL, parallel to the TFL The position of the SFL depends on the isotopic mass balance of the system. For many systems the isotopic exchange will be incomplete, and the isotopic composition at time t F of total exchange can be calculated by the extrapolation of the time series (t 0 to t n ). The extrapolated value will represent the equilibrium isotopic fractionation factor, if the isotopic exchange is occurring under equilibrium conditions.

In a two-component system δ e can be derived from the mass balance equation at equilibrium (Zheng et al., 2016), and calculated from:

δ = δ - × ∆ , (2.2)
where δ mean indicates the mean Si isotope composition of the system shown as system average in Fig 2 .1, and N A and N B denote the moles of Si in the two different Phases A and B. The ∆ eq,A-B of the system is not known, as it is the equilibrium value, which is derived from the three-isotope approach. The solution to Equation 2.2 is done iteratively. A first estimate of ∆ eq,A-B is made. The influence ∆ A-B has on the calculation is minimized due to the large isotopic contrast between the starting materials inflicted by the addition of the isotopic tracer, relative to ∆ eq,A-B (Zheng et al., 2016). The isotope fractionation factors can then be obtained by extrapolation of the isotopic compositions of the two components as a function of the degree of isotopic exchange (δ-F diagram) as shown in Fig. 2.2. As the reaction is progressing, the two phases approach a degree of isotopic exchange F=1, thus equilibrium. If F=1 is not reached the equilibrium values can be extrapolated, and the ∆ eq can be determined. = (1 -) (2.3) where k n is a rate constant and n the order of reaction, usually an integer from 0 to 3. Isotope exchange reactions mostly follow either a first-order (n=1) or second-order (n=2) rate law [START_REF] Criss | Kinetic theory of oxygen isotopic exchange between minerals and water[END_REF][START_REF] Huang | Kinetic studies on the isotopic exchange of calcium ion and calcium carbonate[END_REF][START_REF] Johnson | Isotopic fractionation between Fe(III) and Fe(II) in aqueous solutions[END_REF][START_REF] Welch | Kinetic and equilibrium Fe isotope fractionation between aqueous Fe(II) and Fe(III)[END_REF][START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF]Zheng et al., 2016). The integrated forms of these rates equations with F (t=0) = 0 can be written as:

! (1 -) = -# for n=1 (2.4) $ (# $) = % for n=2 (2.5)
The isotopic exchange rates can be determined using the first and second-order rate law by fixing the initial value of F at the intercept of t=0, so that the rate constant can be determined by regression of to obtain the best fit of the data [START_REF] Cole | Rates and Mechanisms of Isotopic Exchange[END_REF][START_REF] Johnson | Isotopic fractionation between Fe(III) and Fe(II) in aqueous solutions[END_REF][START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF].

Materials

Amorphous Silica (SiO 2 ,am)

The solid used for all Si experiments was a 100 mesh, Alpha Aeser ® silicic acid hydrate powder. To remove fine particles this material was sedimented in deionized (MQ ® ) water [START_REF] Pokrovski | Experimental study of the complexation of silicon and germanium with aqueous organic species: implications for germanium and silicon transport and Ge/Si ratio in natural waters[END_REF]. For this purpose, 40-85 g of amorphous SiO 2 was stirred with MQ ® -water in a 1 dm 3 glass beaker until it was suspended. It was then left to settle for 10 minutes, then decanted. This procedure was repeated until the supernatant became clear within the first 5 min. Subsequently, the recovered solid was dried in the oven at 60°C. Brucite immediately precipitates in accord with [START_REF] Lv | Controlled growth of three morphological structures of magnesium hydroxide nanoparticles by wet precipitation method[END_REF]:

MgCl % • 6H % O + 2 NH 1 → Mg(OH) % + 2 NH 3 Cl + 6H % O (2.6)
Nanoparticles, which are formed at the initial stage of the precipitation reaction serve as precipitation nuclei for the growth of larger brucite crystals, which grow by the aging of the reactive fluid. Therefore the reaction vessel was sealed and left at room temperature for three days after the addition of the aqueous MgCl 2 •6 H 2 O solution. The obtained brucite powder was filtered and washed with Milli-Q ® water to remove impurities, such as NH 4 Cl.

The powder was first dried at 135° C for 1 h, and, to assure it was anhydrous, fully dried at 60°C overnight. A hydrothermal treatment, as proposed by [START_REF] Henrist | Morphological study of magnesium hydroxide nanoparticles precipitated in dilute aqueous solution[END_REF], [START_REF] Lv | Controlled growth of three morphological structures of magnesium hydroxide nanoparticles by wet precipitation method[END_REF][START_REF] Estrada | Interaction between l -aspartate and the brucite [Mg(OH) 2 ]-water interface[END_REF] to improve brucite crystallinity, was not performed. Note, however, that the aqueous NH 3 solution used to create powder batch BD was heated briefly to 90°C during the synthesis, in an attempt to generate a higher degree of crystallinity of the grains. To verify that the powder obtained was brucite, it was analysed by X-ray Powder Diffraction (P-XRD, see Chapter 2.4. 1.5). The morphology of the samples was analysed using SEM and TEM. The specific surface areas of the powders were determined with the BET method. All synthesized brucite powders are listed in Table 2.2 below. Inorganic amorphous silica isotope exchange experiments were performed at pH 6.4 and 9.9 at 25°C, and at pH 5.8 and 9.1 at 75°. The aqueous solutions for these experiments were prepared as follows:

1) Aqueous solutions for experiments at pH ~6 were prepared using high purity deionized Milli-Q ® water (>18.2 Ω). During the first part of the 25° experiment, the pH had to be stabilized by the addition of minor quantities of 1 N HCl and 1.4 N NH 4 OH, which resulted in an ionic strength of 0.1M.

2) Aqueous solutions for Si experiments performed at pH 9.1 (75°C) and 9.9 (25°C)

were prepared as a NH 4 Cl -NH 4 OH pH-buffer, using suprapure NH 4 Cl salt and a 25 % NH 3 solution from Merck ® .

The aqueous solutions for the brucite isotope exchange experiments were prepared by: 1) Using high purity de-ionized Milli-Q ® water (>18.2 Ω) and bi-distilled HCl and an ionic strength of 0.15 M.

2) Two aqueous sodium sulphate solutions were then prepared at pH 9.5 and 10 by dissolving suprapur Merck ® sodium sulphate (Na 2 SO 4 ) powder into de-ionized (MQ ® ) water with bi-distilled HCl at an ionic strength of 0.14 M and 0.02 M for pH 9.5 and 10 respectively.

Aqueous organic solutions

The effect of organic complexation of aqueous Si and Mg on equilibrium mineral-fluid isotopic fractionation was determined for several organic ligands, which were selected because they are known to complex silicon or magnesium cations in solution. Organic silicon experiments were performed with:

Experimental design

Chemical equilibration of reactive fluids

All isotope exchange experiments were all performed under bulk chemical equilibrium but isotopic diseqilibrium conditions. To create aqueous solutions in equilibrium with the starting solids, 200 ml of all reactive inorganic and organic solutions were chemically Chemical equilibrium is achieved when the properties of a reacting system do not exhibit any observable change over time or a tendency to change. In a solid-aqueous solution system, this means that the rates of the forward and backward reaction, e.g. dissolutionprecipitation, are equal and there is no net exchange in concentration. This condition was assumed to be attained when both pH and concentration of the aqueous solutions remained constant over time at a given fixed temperature. When chemical equilibrium was attained, the aqueous solutions were filtered with 0.2 µm Merck ® Teflon syringe filters. The Mg and Si concentrations and the pH of these fluids were measured and reported in Table 2.5 and hereafter considered as the starting conditions of the isotopic exchange experiments.

Isotope exchange experiments

The chemical equilibrated solutions were enriched up to ~ 25‰ with either the 29 Si and 25 Mg isotope tracer for Si and Mg experiments, respectively. After spiking, the concentrations and pH were re-measured and adjusted if necessary by adding small quantities of HCl, NaOH or NH 4 OH to maintain these fluids as close as possible to the equilibrium conditions. The compositions of the starting spiked solutions are listed in Table 2.5. The isotopic exchange experiments consisted of a eight series of closed system experiments of different durations. Each experiment of each series was performed in 10 ml polypropylene reactors. Each series consisted of a number of individual experiments of selected durations but identical experimental conditions (e.g starting fluid composition, temperature, mass of solid). At selected times, the reactors were opened and all of the solids and fluids were collected and characterized. This allowed the determination of the fluid and solid composition at different isotopic exchange states. The amount of powder and aqueous solution used for each experiment series are listed in Table 2.6. To verify that no mass was lost during each closed system experiment, all reactors were weighted at the beginning and the end of each experiment. The sample tubes of experiments at 25°C were placed into an orbital shaker shown in Fig. 2.5 to be constantly mixed. The 75°C experiments were kept in a thermostatic bath and were hand shaken up to twice a day. 2.3.3.3). The speciation of the collected fluids were then calculated with PhreeqC (see Chapter 2.5), so that the fractionation factor between the different solution species, and the solid phase could be calculated. Centre (Toulouse, France). This technique enables surface structure imaging of the powder samples with up to a ~10 5 magnification [START_REF] Putnis | Introduction to mineral sciences[END_REF]. The sample was fixated on a carbon film, coated with platinum, and placed into the electron microscope under vacuum. The electron source is a Field Emission Gun (FEG) that produces a narrow electron beam of high and stable energy, enabling high resolution imaging. The amorphous silica and brucite samples were scanned with a 5 kV and 10 kV electron beam respectively. Two types of electrons are emitted back from the sample surface:

Analytical methods

1) The secondary electrons, which result from the collision of the incident electrons beam with the atoms of the sample. During this collision, they interact with the atomic structure of the sample, which impacts their energy. They are emitted at its surface in every direction. The collected electrons thus display different contrasts, which are used to image topography.

2) The backscattered electrons (BSE), which result from the initial electron beam hitting the sample surface and collected at a single high angle from this surface.

Their high energy is modulated by the level of absorption of the surface, which itself is dependent on its chemical composition.

The emitted electrons are collected and subsequently amplified. The collected electron signal changes the brightness of a cathode ray tube that scans the sample simultaneously with the electron probe. This enables a high magnification of the sample topography.

Specific detectors distinguish between the different emitted electrons. As a result, the sample can be shown either as a secondary electron (Fig. These three modes were used to characterize and image the structure, mainly of the amorphous silica powders, as SEM imaging could not provided sufficient resolution for these samples. The TEM permits, as well as the SEM described above, chemical analysis in form of X-ray spectroscopy.

Surface area

The specific surface areas of initial and final powders were determined with a Quantachrome Autosorb-1 MP using the multipoint BET method [START_REF] Brunauer | Adsorption of Gases in Multimolecular Layers[END_REF], and nitrogen (N) as the adsorbing gas. The sample surface was first cleaned from possible contaminants such as water and oils by heating the sample up to 100°C under vacuum; this treatment is also known as degassing. After this pre-treatment, the sample is brought to a constant temperature of 77.3°C in a thermostatic bath. Then, liquid nitrogen (-196 °C, at atmospheric pressure) is gradually introduced into the evacuated sample chamber. The nitrogen is adsorbed onto the sample surface and forms a monomolecular layer, covering the entire surface. Taking account of the density of nitrogen, the adsorbed mass of N, and the sample weight, one can calculate the surface area, based on the Brunauer, Emmett and Teller (BET) theory [START_REF] Brunauer | Adsorption of Gases in Multimolecular Layers[END_REF]. Subsequently, the system is degassed, and the desorption of gas from the powder can be determined. The uncertainty of the measurements collected in this thesis is estimated to be ± 10% with a reproducibility of ~2%.

Thermogravimetric analysis

Thermogravimetric analyses were performed with the Mettler Toledo ® ATG/DSC1 located at the National Polytechnic Institute in Toulouse, France to quantify the water content of the amorphous silica powder. These analyses were performed by placing a known mass of the powder samples into platinum crucibles and heating these at 10°C/min up to 1000°C. The mass difference of the sample before and after heating indicates the loss of water from the crystal lattice, and thus the total water content of the powder. It is expressed as weight loss in percent.

X-ray Powder Diffraction (P-XRD)

Synthesized brucite powders were analysed with a 2 nd Generation Bruker ® D2 Phaser, to determine the quality of the synthesized mineral. The brucite samples were irradiated with monochromatic X-rays. These were produced by accelerated electrons, generated in a cathode ray tube by a heated filament, with 30 kV onto a Copper (Cu) single-crystal. These X-rays have a characteristic CuKα 1 radiation of 1.54056Å, which are then filtered by a nickel (Ni) foil to produce monochromatic X-rays. These X-rays are then bundled onto the sample. Both the sample and detector are rotated so that the measurements covers a 2θ diffraction angle ranging from 2 -80°. According to Bragg's law, the interaction of the Xrays with the sample generates a material specific constructive interference and a diffracted ray pattern. As the samples have a random position in the diffractometer, all diffraction directions of the lattice are detected. These diffraction peaks can be converted into mineral specific lattice spacings (d-spacings), which allows mineral identification by their comparison with standard reference patterns (see representative brucite pattern in Annex I). Absorption Spectroscopy (F-AAS). The principle of these analyses were first described by [START_REF] Walsh | The application of atomic absorption spectra to chemical analysis[END_REF] and further developed by [START_REF] Russell | An atomic-absorption spectrophotometer and its application to the analysis of solutions[END_REF] and [START_REF] Box | A simple atomic absorption spectrophotometer[END_REF]. The solution sample is introduced as an aerosol into an air-acetylene-flame. The radiation from a hollow-cathode lamp, which emits the specific wavelength of Mg (285.21 nm) crosses through the flame. Some of the photons crossing the aerosol are absorbed by the Mg atoms of the sample present in the flame. The absorption is detected, measured and directly relates to the concentration. An intensity to concentration calibration curve is established by measuring standards solutions prepared in the same matrix as the samples.

Characterization of aqueous solutions

Aqueous Mg concentration measurements in this study were carried out for concentrations from 0.1 and 0.6 ppm using a Perkin Elemer AAnalyst 400. Calibration solutions were prepared using the sample matrix (2% HNO 3 , 0.05 M HCl, EDTA, sulphate, citrate) and to avoid interference was used a 1000 ppm Mg(NO₃)₂ Merck-Certipur ® standard solution diluted into aqueous 0.05mol/kg HNO 3 . Prior to measurements all samples were diluted. Therefore concentrations were close to the middle of the measurement concentration range (± 0.3 ppm). To minimize the effect of possible interference, a small quantity lanthanum oxide (30µL in 10 ml sample) was added to each sample and the standards prior to analysis. The limit of detection (LOD) and the limit of quantification (LOQ) were determined for each matrix to be 5 ppb and 1 ppb respectively. Measurements had an uncertainty of ±1%.

Atomic emission spectroscopy (AES)

The sodium content of samples containing Na were determined by flame atomic emission spectrophotometry (F-AES). The aqueous sample is introduced as a solution into a flame.

The electrons of the outer valence layer are excited towards a higher electronic state. When the electrons fall back to their fundamental state, photons are emitted at a characteristic wavelength (e.g. Na= 589.00 nm). The emission spectrum was measured by the atomic absorption spectrometer (Perkin Elemer AAnalyst 400) in the flame emission mode. As previously described (see AAS Chapter 2.4.2.2) a calibration curve is established allowing the determination of the Na concentration.

Sodium measurements were carried out at concentrations ranging from 0.5 to 6 ppm.

Sodium concentrations in purified samples were expected to be below the limit of quantification. Due to a high sample consumption (4 mL), samples needed to be diluted by a factor of 2.7 prior to analysis. The LOQ and LOD were determined at 0.06 ppm and 0.02 ppm respectively.

Colorimetry

Aqueous silicon concentrations in this thesis were determined by the application of the molybdate blue method [START_REF] Strickland | The Preparation and Properties of Silicomolybdic Acid. II. The Preparation and Properties of β-Silicomolybdic Acid[END_REF] following the procedure of [START_REF] Tréguer | Manuel d'analyses automatiques des sels nutritifs dans l'eau de mer[END_REF]. The principle of this method is the formation of a yellow β-molybdosilic acid (silicomolybdate), when ammonium molybdate is added to an acidic Si-rich solution. This reaction can be written as:

7 Si(OH) 3 + 12 H 9 Mo ; O %3 • 4 H % O + 126 H % O ↔ 7 H > Si(Mo > O ; ) 9 • 28 H % O (2.7)
Sulfuric acid is added to the molybdate solution as an acidifying agent, and oxalic acid is added to the sample solution to reduce possible phosphate interferences. Finally ascorbic acid is added to the sample solution to reduce the ammonium molybdate complex. This leads to a blue coloration of the solution. The absorbance of this color relative to a blank solution can be measured at 660 nm and is proportional to the dissolved Si concentration.

Standards of known concentrations were measured to establish a calibration curve.

Aqueous Si concentrations measurements were carried out at concentrations of 0.05 to 1 ppm, and from 0.1 to 10 ppm using a Bran & Luebbe technicon analyser III coupled to a Seal XY-2 autosampler and an auto analyser II mixing unit. The solution samples were introduced into the mixing unit at a flow rate of 0.32 ml/min.. The ammonium molybdate solution is mixed with this sample solution at a flow rate of ~0.8 ml/min. Subsequently oxalic acid and finally ascorbic acid are added at a flow rate of ~0.23 ml/min to the measuring solution. Calibration solutions were prepared by diluting a 1000 ppm Merck-Certipur ® Si standard solution with deionized MQ ® water. The sample solutions were likewise diluted with deionized MQ ® water so that their concentrations fell in the middle of the measurement range. At the beginning and end of each set of measurements a standard,

was measured to monitor for potential instrument drift. For measurements of Si concentrations between 0.05 and 1 ppm, a Mississippi 03 standard was used; for measurements of Si concentrations between 0.1 and 10 ppm a Miramichi 02 and later a Sangamon 03 standard were used. For the range of 0.05 to 1 ppm LOD was determined to be 0.004 ppm and the LOQ to be 0.013 ppm. The LOD and LOQ for measurements between 0.1 and 10 ppm were determined to be 0.01 ppm, and 0.04 ppm respectively. The long-term reproducibility of these measurements was within 3%.

Organic carbon measurements

Organic carbon was determined in aqueous solution samples containing organic ligands. The measurements were performed using a Shimadzu ® TOC-VCSN analyser, equipped with an ASI-V auto sampler and TOC-Control V software. The principle is based on a combustion catalytic oxidation method developed by Shimadzu ® . The sample is acidified to convert the carbonate and bicarbonate ions into dissolved carbon dioxide. The sample is then automatically injected with a syringe into a quartz tube filled with air and a platinum catalyst, which is then heated to 680°C. This transforms the dissolved organic carbon into CO 2 , which is transported to the infrared detector. The total organic carbon concentration (TOC) is obtained by comparison of infrared measurements to a calibration curve, which is established from a set of reference solutions under the same conditions as the sample measurements.

TOC measurements were carried out at carbon concentrations ranging from 2 to 30 ppm. The aqueous samples were to concentrated, they were diluted with MQ ® water in glass tubes prior to their analysis. Subsequently they were slightly acidified with bi-distilled HCl.

Quadrupole -ICP-MS

The element concentrations of the IAPSO and JDol-1 standard solutions after their cleaning by ion exchange chromatography (see Chapter 2.4.3.2) were measured on the Agilent ® 7500 quadrupole ICP-MS. The solution to be analysed is converted into a fine aerosol by a micro nebuliser and introduced under a constant argon gas flow into an argon plasma torch at temperatures between 5000 and 10000°K. The sample is then ionized. The ions are extracted via a high voltage anode through a set of two cones, which filter all the contaminants and create an ion beam. On their way to the detector, the ions and molecular species go through two filtering systems:

1) The collision/reaction cell: a closed space where ions of low kinetic energy and large molecules are stopped, deviated or broken by large ions (e.g. O, H or He) or react with these to form other species of higher mass, to be further measured. The latter function was not used during this thesis.

2) The quadrupole: this consists of four parallel rods (Fig 2.8). Opposite rods are charged with an adjustable high voltage, which is inverted for the normal pair of rods. The charged ions entering the system follow a spiral pathway, which depends on their mass to charge ratio and on the applied voltage. Hence, only the chosen mass/charge ratios are not deviated and can be measured afterwards. 15%, the concentrations determined for this element was discarded. The detection limit of the measurements was found to vary from 0.1 to 10 ppt, depending on the element analysed.

High Resolution -ICP-MS (HR-ICP-MS)

The isotope abundance in the spike solutions were determined by high resolution inductively coupled plasma mass spectrometry (HR-ICP-MS). The measurements were performed on a Thermo Sicentific ELEMENT-XR ® with a reversed Nier-Johnson geometry. The detailed functioning of an ICP-MS is described in detail in section 2.4.3.3.

The 29 Si and 25 Mg-spike solutions were diluted to concentrations between 0.05 and 2 ppm in 2% HNO 3 prior to the measurements. The magnesium and silicon samples were introduced with a free aspirating stable introduction system (SIS) and measured in medium resolution mode, with a mass resolution of ~4300. Silicon was additionally measured in high mass resolution mode (R ~9300). A 1 ppb Li tuning solution was used. The diluted spike solutions were introduced with Ar gas into the plasma. Blanks of 2% HNO 3 were measured for each measurement sequence. The intensities of the 3 stable isotopes with the masses 27. 9764, 28.9760, 29.9732, and 23.9845, 24.9853, 25.9821 for silicon and magnesium.

respectively, were measured. These were detected in either triple mode (Faraday and electron multiplier in analogue and pulse modes) for the magnesium spike solutions, or in analogue mode for the silicon spike solutions, with a secondary electron multiplier. The samples signals were corrected for a blank using the blank signals. The signal detected for the different isotopes directly depends on the concentration of the Si and Mg isotopes in the solution. The isotopic ratios could therefore be determined from the ratio of the blank corrected signal of the individual isotopes.

Isotopic Analysis

All samples for isotopic ratio determination needed to be purified to remove any potentially interfering elements prior to their analysis. These purification procedures are described in this section, along with the principles of the Multi Collector ICP-MS (MC-ICP-MS).

Silicon sample preparation and ion-exchange chromatography

Silicon bearing powders and aqueous solutions had to be purified prior to their analysis by MC-ICP-MS (see Chapter 2.4.3.3). For the amorphous SiO 2 powders, the sample purification is based on the alkaline fusion preparation protocol described in [START_REF] Zambardi | Precise Determination of Silicon Isotopes in Silicate Rock Reference Materials by MC-ICP-MS[END_REF]. This protocol calls for:

1) 1 to 5 mg of the powders were weighted into silver crucibles (XRF scientific, Montreal, Canada), together with ~200 mg Merck ® suprapure NaOH pellets. If the powders were in contact with organic solutions, a calcination was performed prior to the addition of the NaOH pellets. Therefore SiO 2 sample powder in the crucibles in a furnace at 500°C for 4h, similar to the approach for soils of [START_REF] Cornu | Evidence of titanium mobility in soil profiles, Manaus, central Amazonia[END_REF].

2) The crucibles were placed into a 720°C pre-heated furnace for 10 min.

3) After cooling to room temperature, the crucibles were placed into 30 cc Savillex® Teflon beakers filled with 20 ml Milli-Q® water to dissolve the fusion cake. . 4) After 24 hours, the resulting solutions were transferred to 60 cc polypropylene bottles and diluted with 20 ml Milli-Q ® water to obtain a 40 ml solution.

5) These solutions were then acidified to a pH of 1.5 using ~10 N HCl and placed on a heating plate at 50°C for 24 to 48 h to ensure that possible suspended material is completely and efficiently dissolved.

Aqueous samples of experiments run without the presence of organic ligands were prepared for Si isotope analysis by diluting the solutions -if needed -and subsequently acidifying them to pH ~2 using bi-distilled 3N HCl. Organic bearing fluid samples had to be carefully treated, as the presence of organic matter likely causes interferences during Si isotope measurements using the MC-ICP-MS. Therefore solutions containing organic ligands had to be processed to ensure complete removal of these organic compounds. For this standard methods such as the use of H 2 O 2 and UV-light were tested in a first attempt. These methods proved to be ineffective as confirmed by the organic carbon measurements. The following sample preparation protocol was therefore adopted to purify aqueous solutions containing organic ligands:

1) 5 ml of the organic bearing aqueous sample was evaporated to dryness in silver crucibles in a laminar flow box.

2) Calcination was performed by heating the SiO 2 and organic residue in the crucibles in a furnace at 500°C for 4h, similar to the approach of [START_REF] Cornu | Evidence of titanium mobility in soil profiles, Manaus, central Amazonia[END_REF] for soils.

3) Approximately ~200 mg of Merck ® NaOH pellets were added into the silver crucibles.

4) The fusion of the remaining SiO 2 powder was performed by placing the crucibles into a furnace at 720°C for 10 min.

5) The crucibles were cooled to room temperature, and subsequently placed in 30 cc Savillex® Teflon beakers filled with 15 ml Milli-Q® water to dissolve the amorphous SiO 2 powder.

6) The resulting solutions were transferred after 24 hours into 30 cc polypropylene bottles and diluted with Milli-Q ® water to 20 ml.

7) Samples were acidified to a pH of 1.5 using ~10 N aqueous HCl.

After sample preparation, the resulting solutions were purified by the cation-exchange chromatography protocol described by [START_REF] Zambardi | Precise Determination of Silicon Isotopes in Silicate Rock Reference Materials by MC-ICP-MS[END_REF]. In this method, 10 ml BioRad ® polypropylene columns were filled with 2 ml BioRad ® AG50W-12X (200-400 mesh) cationic resin. Before the samples were treated, the resin was cleaned and conditioned with 3 ml HCl and HNO 3 in following order: 3 N HCl, 6 N HCl, 7 N HNO 3 , 10 N HCl, 6 N HCl, and 3 N HCl [START_REF] Georg | New sample preparation techniques for the determination of Si isotopic compositions using MC-ICPMS[END_REF]. The resin was then flushed with Milli-Q ® , so that the pH before the sample was loaded was close to neutral. The sample solutions were loaded (0.5-2 ml, depending on the Si concentration). Si is not retained by the resin, as non ionic H 4 SiO 4 o largely dominates Si species in solution below pH 9, and was therefore directly collected. The columns were subsequently eluted twice with Milli-Q ® water to obtain a 6 ml sample solution. These sample solutions were then diluted to obtain 3 ppm of Si and acidified with 10 N bi-distilled HCl to obtain a 0.05 M HCl matrix. Silicon recovery after processing was determined by colorimetry to be between 90 to 100 %.

Magnesium sample preparation and ion chromatography

The magnesium bearing powders and aqueous solutions collected from the isotopic exchange experiments had also to be prepared and subsequently purified by ion exchange chromatography prior to their isotopic measurement with the Neptune ® MC-ICP-MS. The processing of the brucite powder consisted of:

1) ~1 mg of brucite powder and the JDo-1 standard were weighted and placed in Savillex ® beakers.

2) These powders were dissolved overnight in 2 ml of 15 N bi-distilled HNO 3 .

3) The resulting solutions were evaporated to dryness at 120°C, and the residues were re-dissolved in 5 ml 1N HNO 3 .

4) Mg concentrations of these latter solutions were determined using AAS.

5) Aliquots of the solutions containing 15 µg Mg were evaporated and re-dissolved in 2 ml 1M HNO 3 to be ready for column chemistry.

The Mg bearing aqueous solutions were prepared as follows:

1) Aliquots of the fluid samples (10-500 µl) and the IAPSO seawater standard containing 15 µg Mg were placed into Savillex ® beakers. In case of the presence of organic ligands ~0.5 ml H 2 O 2 was added and left to react for 3-6 hours.

2) Sample solutions were evaporated to dryness at 120°C.

3) The solid residues were re-dissolved in 2 ml of 1M HNO 3 to be ready for column chemistry.

The sample preparation follows the [START_REF] Teng | Investigation of magnesium isotope fractionation during basalt differentiation: Implications for a chondritic composition of the terrestrial mantle[END_REF] method. All the samples were processed in 10 ml Bio-Rad ® polypropylene (PP) columns filled with 1 ml Bio-Rad ® AG50W-X8 200-400 mesh cationic exchange resin. The resin was pre-cleaned with 1 N

HCl before filled into the columns. Once in the column, the resin was further cleaned with 10 ml of Milli-Q ® water, 20 ml of 4M HCl and finally once more with 10 ml of Milli-Q ® water. The resin was then conditioned with 10 times the resin volume of aqueous 1N HNO 3 .

2 ml of the prepared sample solutions were loaded onto the resin and the elements of interest (in this case only Mg) were eluted by the subsequent washing of the resin with 1 M HNO 3 .

Sodium is removed, and eluted within the first 10 ml after loading the sample. The Mg fraction was then collected in the following 20 ml of elution, and Ca was removed lastly from the resin, and then eluted within the next 30 ml [START_REF] Teng | Investigation of magnesium isotope fractionation during basalt differentiation: Implications for a chondritic composition of the terrestrial mantle[END_REF].

As ion exchange chromatography can significantly fractionate Mg isotopes [START_REF] Chang | Purification of Mg from low-Mg biogenic carbonates for isotope ratio determination using multiple collector ICP-MS[END_REF][START_REF] Teng | Investigation of magnesium isotope fractionation during basalt differentiation: Implications for a chondritic composition of the terrestrial mantle[END_REF], it is essential to obtain a Mg yield close to 100 %. A resin calibration was performed to ensure all the Mg was collected during column chromatography. Seven fractions of the two standards JDol-1 and IAPSO were collected starting from the last 2 ml of the sodium elution until the first 2 ml of the calcium elution.

These were subsequently analysed with the Agilent 7500 quadrupole ICP-MS (see Chapter 2.4.2.6) to determine the concentrations of all elements in solution. The elution curve for Mg in Fig. 2.9 shows no shift compared to the protocol of [START_REF] Teng | Investigation of magnesium isotope fractionation during basalt differentiation: Implications for a chondritic composition of the terrestrial mantle[END_REF], which indicates that Mg was eluted completely through the columns, validating the method used in this thesis. The isotopic compositions of the aqueous solutions and solid powders recovered from the isotopic exchange experiments were obtained using a Thermo Fisher Scientific Neptune ®

Multi-Collector Inductively Coupled Plasma Mass Spectrometer (MC-ICP-MS). The

Neptune ® MC-ICP-MS is a double focussing mass spectrometer, which is capable of preforming measurements with a highly accurate mass resolution using its multi collector mode [START_REF] Weyer | High precision Fe isotope measurements with high mass resolution MC-ICPMS[END_REF]. Its principle is based on the physical separation of isotopes in an ion beam by both an electrostatic analyser (ESA), which correspond to an energy filter, and a magnet that works as a mass filter. The ESA is placed before the magnet, as shown in Fig. 2.10 based on the Nier and Johnson geometry. All samples were prepared for analysis in weakly acidic aqueous solutions and converted into a fine aerosol in the nebulizer. The sample is subsequently introduced under a constant argon gas flow through the spray chamber into the torch. In the torch, an inductively coupled Argon plasma is generated at high temperatures (> 8000 K; [START_REF] Georg | New sample preparation techniques for the determination of Si isotopic compositions using MC-ICPMS[END_REF] in which the mixture of sample and gas is ionized. When the ions leave the torch, their energy will vary between 0.5 and 5 eV [START_REF] Georg | New sample preparation techniques for the determination of Si isotopic compositions using MC-ICPMS[END_REF]. The magnet alone could not be able to achieve a good isotope separation due to this energy variation. Therefore the ESA is placed before the magnet to deflect the ions as a function of their kinetic energy. This means that if the ion beam containing ions with different velocities reaches the ESA entrance only ions with the same kinetic energy will pass. Three entrance slits are located in front of the ESA enabling measurements in low, medium and high mass resolution. The ions leaving the ESA unit will be deflected by the magnet according to their mass to charge ratio. The isotopes thus will have an individual path according to their mass. The beam leaving the magnet, therefore contains various sub-beams, where each beam can be associated with a given isotope. The sub-beams are collected in 9 available Faraday cups. These generate an electrical signal, which can be detected by either a Faraday or SEM detector, allowing the determination of the relative isotopic abundances.

Silicon isotope measurements

Silicon isotope measurements were performed using the Thermo Scientific Neptune ® MC-ICP-MS located at the Observatoire Midi-Pyrénées / Laboratoire Géosciences Environnement Toulouse (GET), France, or that located at the GeoForschungsZentrum (GFZ) in Potsdam, Germany. Measurements were preformed in medium mass resolution mode with a total of 1.5 to 2 ppm Si in solution, under wet plasma (GET) and dry plasma (GFZ) conditions. For the wet plasma, the samples were introduced into the spectrometer via a ThermoFinnigan stable introduction system (SIS) with a double-pass cyclonic spray chamber. For dry plasma conditions at the GFZ, an Aridus desolvating unit was used.

Prior to any analysis, the signal sensitivity and intensity had to be verified and adjusted. Silicon isotope measurements can be influenced by polyatomic interferences from combinations of elements such as 12 C 16 O + , 14 N 2 , 14 N 15 N + , 14N 2 1 H + and 14 N 16 O + , as shown in The 'mass resolution' corresponds to the resolving power of the mass spectrometer. The mass resolution (R resolution ) is expressed by:

@ ABCDEFGHD = I ∆I (2.8)
where m is the mass of the isotope considered, measured in the middle of the plateau where no interferences occur, ∆m denotes the difference between the mass at 5% and 95% of the height of the peak. The mass resolution has to be at least 2000 to separate all three Si + ion beams from its interfering beams.

During measurements, an instrumental mass bias drift occurs, which can be attributed to isotopic fractionation generated by the instrument. It is generated by the vibrational excitation of the ions in the plasma and the ion beam due to interatomic collisions. This generally leads to a preferential expulsion of light isotopes, which results in an overestimation of the concentration of heavy isotopes during measurements (e.g., [START_REF] Zambardi | Recherche de marqueurs de processus de formation des planètes à travers les isotopes stables de masse moyenne[END_REF]. Most of the time, the instrumental mass bias is not constant, and its variations may depend on various parameters, such as matrix effects or the stability of the gas and sample flow. This can cause a mass bias drift. A first and effective approach to correct for the instrumental mass bias drift is the standard bracketing. This is based on the measurement of an isotopic standard solution, in the case of silicon, NBS-28, before and after each sample or a triple-sample set. This enables quantification of the isotopic fractionation of the sample from the average isotopic ratios of the standard over a period of time. The sample standard bracketing is, however, ineffective if the mass bias drift changes too fast and/or is non-linear. Such situations can occur, especially during the first 24h of a measurement session, a solution consists of combining sample standard bracketing with the addition of an internal standard. Therefore the samples and the external NBS-28 standard were doped with a multi-isotopic element with a mass close to that of the element of interest.

In the present study, the samples and standards for Si isotope analysis were doped with Magnesium. The 25 Mg-24 Mg ratios of these doped solutions were measured in a dynamic measurement mode. It is assumed that the mass bias drift will be the same for both magnesium and silicon isotopes. The application of this correction is widely used for silicon isotopes [START_REF] De La Rocha | Measurement of silicon stable isotope natural abundances via multicollector inductively coupled plasma mass spectrometry (MC-ICP-MS): SILICON STABLE ISOTOPE NATURAL ABUNDANCES[END_REF][START_REF] Cardinal | Isotopic composition of silicon measured by multicollector plasma source mass spectrometry in dry plasma mode[END_REF][START_REF] Engström | Chromatographic Purification for the Determination of Dissolved Silicon Isotopic Compositions in Natural Waters by High-Resolution Multicollector Inductively Coupled Plasma Mass Spectrometry[END_REF][START_REF] Zambardi | Precise Determination of Silicon Isotopes in Silicate Rock Reference Materials by MC-ICP-MS[END_REF]Zheng et al., 2016). Its principle is based on Russels's exponential law [START_REF] Russell | Ca isotope fractionation on the Earth and other solar system materials[END_REF], which can be applied to correct the mass bias drift during one run, given by:

@ H = J H × K L H L M N O (2.9)
where R i denotes the corrected isotopic ratio, and r i the measured isotopic ratio. M i is the mass of the isotope of interest, thus 29 Si or 30 Si, and M k is the mass of 28 Si . β indicates the fractionation coefficient calculated from the measurements fort magnesium, and considered to be identical to that of silicon [START_REF] Zambardi | Recherche de marqueurs de processus de formation des planètes à travers les isotopes stables de masse moyenne[END_REF]. The fractionation coefficient β can be derived from Eqn. 2.9, and can be written as:

P = ! (@ H /J H ) ! (L H /L M ) (2.10)
The fractionation coefficient for magnesium β Mg can thus be calculated with:

P RS = ! (@ H RS /J H RS ) ! (L H RS /L M RS ) (2.11)
Where @ H TU denotes the theoretical isotopic ratio of 25 Mg/ 24 Mg, which could be fixed at 0.126598 as the magnesium added to the samples and standards has a natural isotopic composition, and isotope distribution. J H TU denotes the measured 25 Mg/ 24 Mg ratio L TU in this case refers to the mass of 25 Mg, and M V TU to the mass of 24 Mg. As the mass bias drift of Mg is assumed to be identical to that of Si, the fractionation coefficient of Mg can be applied to Eqn. 2.9 as mass bias correction for Si:

@ H WH = J H WH × X L H WH L M WH Y O Z[
(2.12)

To ensure the accuracy and precision of isotopic analyses, the Si isotopic composition of the BHVO-2 reference material was measured during each measurement session. For the wet plasma conditions, this resulted in a long-term reproducibility of δ 30 Si= -0.26 ± 0.14 ‰, and δ 29 Si= -0.13 ± 0.09 ‰ (2 S.D, n=105). Dry plasma conditions at GFZ led to a long-term reproducibility δ 30 Si= -0.28 ± 0.09 ‰, and δ 30 Si= -0.14 ± 0.06 ‰ (n=18). The measured values of the Si isotope compositions of this standard obtained from both wet and dry plasma analysing conditions are plotted in Fig. 2.12. This figure also shows showing that the measured results obey the mass-dependent fractionation law within the average error.

The measured BHVO-2 values in this study are in close agreement with values reported in previous studies (e.g. [START_REF] Abraham | δ 30 Si and δ 29 Si Determinations on USGS BHVO-1 and BHVO-2 Reference Materials with a New Configuration on a Nu Plasma Multi-Collector ICP-MS[END_REF][START_REF] Zambardi | Precise Determination of Silicon Isotopes in Silicate Rock Reference Materials by MC-ICP-MS[END_REF][START_REF] Savage | The silicon isotope composition of the upper continental crust[END_REF][START_REF] Savage | High temperature silicon isotope geochemistry[END_REF]. The quality and purity of the sample preparation, and ion chromatography was verified by measuring the 28 Si signal of the procedural blank. This was found to be on average < 2% of the total signal and therefore considered negligible.

Magnesium isotope measurements

Magnesium isotope measurements were performed using the Thermo Scientific Neptune ® MC-ICP-MS located at the Observatoire Midi-Pyrénées / Laboratoire Géosciences Environnement Toulouse (GET), France. The samples were introduced into the plasma dissolved in 0.37N aqueous HNO 3 with the SIS coupled to a double-pass cyclonic spray chamber. The measurements were performed in low mass resolution mode at aqueous Mg concentrations of 600 ppb. Before starting the measurements, the signal sensitivity and intensity was verified and adjusted. As the Mg isotopic measurements are not affected by major interferences, the measurement position is chosen at the peak centre, as shown in Fig. Magnesium isotopic compositions in this study are given with respect to the DSM-3 standard [START_REF] Galy | Magnesium isotope heterogeneity of the isotopic standard SRM980 and new reference materials for magnesium-isotope-ratio measurements[END_REF]. Due to the limited access of the DSM-3 standard, the measurements were performed using the sample standard bracketing method described above, with respect to an in house MgNO 3 standard. The composition of the in house et al., 2008;[START_REF] Wombacher | Separation of Mg, Ca and Fe from geological reference materials for stable isotope ratio analyses by MC-ICP-MS and double-spike TIMS[END_REF][START_REF] Immenhauser | Magnesium-isotope fractionation during low-Mg calcite precipitation in a limestone cave -Field study and experiments[END_REF][START_REF] Wimpenny | The behaviour of magnesium and its isotopes during glacial weathering in an ancient shield terrain in West Greenland[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF]Mavromatis et al., , 2014aMavromatis et al., , 2014b[START_REF] Mavromatis | The effect of permafrost, vegetation, and lithology on Mg and Si isotope composition of the Yenisey River and its tributaries at the end of the spring flood[END_REF]. Repeated measurements of the MgNO 3 in house standard, gave a 2 S.D. of 0.07 ‰, and 0.12 ‰ for δ 25 Mg, and δ 26 Mg respectively. The 24 Mg signal of the procedural blank was measured to verify the quality and purity of the sample preparations, and ion chromatography methods. The blanks showed an average 24 Mg signal < 0.5% of the total signal and are therefore negligible.

2.13.

Analytical reproducibility

The accuracy of the isotopic measurement is not only validated by the measurement of blanks and standards, but also by the repeated measurements of the sampled aqueous solutions and solids. During the analysis, the Si samples were measured in blocks of 25 single measurements and the Mg samples in blocks of 30 single measurements. The average of these 25 or 30 measurements is then taken to be sample composition. Each sample was measured from 2 an 6 times to estimate the reproducibility of the measured isotopic ratio.

Starting materials were measured up to 9 times to further assess the uncertainties, as these starting materials need to be accurate to generate accurate extrapolations using the threeisotope method. In this thesis the standard error (SE) is used as the uncertainties of the isotopic measurements. The SE is given by:

\] = × \√ ! -1 (2.13)
where SD is the standard deviation of the n measurements, and t is the student t-correcting factor [START_REF] Platzner | Modern isotope ratio mass spectrometry, Chemical analysis[END_REF], which is an essential correction for measurements with less than 15 replicates.

Geochemical calculations with PHREEQC

Thermodynamic modelling

All geochemical calculations in this study were performed using the PHREEQC code (Parkhurst and [START_REF] Appelo | Geochemistry, groundwater and pollution[END_REF]. The standard state adopted is that of unit activity for pure minerals, solids and H 2 O. For aqueous species the standard state is unit activity of a hypothetical one molal solution extrapolated to infinite dilution at any given temperature and pressure. The activity coefficients of charged aqueous species were calculated using the Davies equation, whereas the activity coefficients of neutral species were assumed to be equal to one. In situ aqueous solution speciation and pH for experiments performed at 75°C

were computed from the measured Si and Mg concentration, the pH measured at room temperature, and the organic ligand concentration. Equilibrium constants for the dissolution reactions of amorphous SiO 2 and brucite were determined from the dissolution experiments performed during the chemical equilibration of initial reactive fluids (see Chapter 2.3.1).

This was done considering the following dissolution reactions:

For amorphous silica:

SiO % + 2 H % O ↔ H 3 SiO 3 ` (2.14)
and for brucite:

Mg(OH) % + 2 H ↔ Mg % + 2 H % O (2.15)
The law of mass action for the reactions (2.14) and (2.15) are given by: a Bb = c d e fgh e i c fgh j,kl c djh j (2.16) and:

a Bb = c Z[ jm (c d j h ) j c Z[(hd) j (c d m) j
(2.17)

where a Bb stands for an equilibrium constant and a i refers to the activity of the subscripted species or phase. Taking account of the standard state, in pure water Eqn. (2.16) reduces to: 2.18) and Eqn. (2.17) reduces to:

a Bb = n o e WHp e i (
a Bb = c Z[ jm (c d m) j (2.19)
The activities of the different species were first determined using by entering the results of the dissolution experiments at steady state into PHREEQC, and subsequently using these to calculate the equilibrium constants of theses reactions.

Si speciation calculations

Silicon speciation and pH at 75°C were calculated using the Livermore National Laboratory (llnl) database [START_REF] Johnson | Database thermo.com.V8.R6.230[END_REF]. The equilibrium constant for the dissolution of the amorphous SiO 2 powder in pure water was determined to be -2.80 and -2.38 at 25°C and 75°C respectively. The equilibrium constants for the Si aqueous species H 3 SiO 4 -and

H 2 SiO 4 2-
, and the polymeric species were used as included in the database, whereas the equilibrium constants of the catechol organic ligand complex were added, following [START_REF] Sillen | Stability Constants of Metal-Ion Complexes[END_REF], [START_REF] Sverjensky | Prediction of the thermodynamic properties of aqueous metal complexes to 1000°C and 5 kb[END_REF], and [START_REF] Pokrovski | Experimental study of the complexation of silicon and germanium with aqueous organic species: implications for germanium and silicon transport and Ge/Si ratio in natural waters[END_REF] as listed in Table 2.7. No thermodynamic data is available for the Si-glucamine complex.

Mg speciation calculations

Speciation calculations for the fluids collected from all the brucite isotope exchange experiments were performed using the core10 database [START_REF] Neveu | Aqueous geochemistry in icy world interiors: Equilibrium fluid, rock, and gas compositions, and fate of antifreezes and radionuclides[END_REF]. The equilibrium constant for the brucite dissolution reaction (2.15) was calculated from the measured fluid compositions of experiments run to pre-equilibrate the fluids used in the brucite isotope exchange experiment without organic ligands and then corrected in the database. Additionally, the equilibrium constants of aqueous citrate and EDTA complexes were added to the database to perform speciation calculations for solutions containing these organic ligands. The equilibrium constants added are listed in Table 2.8. , and the variation of the equilibrium isotope fractionation factors with temperature can be used to establish paleo-pH and temperature proxies. The application of the three-isotope method also provides insight into the rates of isotopic exchange. For the solid grain size used (∼20 nm), these rates match closely the measured bulk dissolution rates for amorphous silica for most of the isotope exchange process, suggesting the dominant isotope exchange mechanism in the experiments is detachment and reattachment of material at the amorphous silica surface.

Introduction

Silicon stable isotopes have been used as a tracer of a number of Earth (near-) surface processes, including weathering, biological activity, and marine paleo-temperature (e.g. De

La [START_REF] De La Rocha | Silicon-isotope composition of diatoms as an indicator of past oceanic change[END_REF][START_REF] Ding | Silicon isotope study on rice plants from the Zhejiang province, China[END_REF]Ziegler et al., 2005a;Opfergelt et al., 2006[START_REF] Opfergelt | Variations of δ 30 Si and Ge/Si with weathering and biogenic input in tropical basaltic ash soils under monoculture[END_REF]Opfergelt et al., , 2012[START_REF] Opfergelt | Iron and silicon isotope behaviour accompanying weathering in Icelandic soils, and the implications for iron export from peatlands[END_REF][START_REF] Georg | Silicon isotope variations accompanying basalt weathering in Iceland[END_REF][START_REF] De La Rocha | The silicon isotopic composition of surface waters in the Atlantic and Indian sectors of the Southern Ocean[END_REF][START_REF] Demarest | Fractionation of silicon isotopes during biogenic silica dissolution[END_REF][START_REF] Hendry | Silicon isotopes in Antarctic sponges: an interlaboratory comparison[END_REF][START_REF] Hendry | The relationship between silicon isotope fractionation in sponges and silicic acid concentration: Modern and core-top studies of biogenic opal[END_REF][START_REF] Pogge Von Strandmann | Lithium, magnesium and silicon isotope behaviour accompanying weathering in a basaltic soil and pore water profile in Iceland[END_REF][START_REF] Pokrovsky | Silicon isotope variations in Central Siberian rivers during basalt weathering in permafrost-dominated larch forests[END_REF][START_REF] Marin-Carbonne | The silicon and oxygen isotope compositions of Precambrian cherts: A record of oceanic paleo-temperatures?[END_REF][START_REF] Oelze | Si stable isotope fractionation during adsorption and the competition between kinetic and equilibrium isotope fractionation: Implications for weathering systems[END_REF][START_REF] Frings | Silicate weathering in the Ganges alluvial plain[END_REF][START_REF] He | Equilibrium and kinetic Si isotope fractionation factors and their implications for Si isotope distributions in the Earth's surface environments[END_REF].

The Si isotopic composition of many terrestrial reservoirs have been measured, including that of oceans, lakes, rivers and groundwaters (e.g. De La [START_REF] De La Rocha | A first look at the distribution of the stable isotopes of silicon in natural waters[END_REF][START_REF] De La Rocha | The silicon isotopic composition of surface waters in the Atlantic and Indian sectors of the Southern Ocean[END_REF][START_REF] Wischmeyer | Control mechanisms for the oceanic distribution of silicon isotopes[END_REF][START_REF] Reynolds | Silicon isotope fractionation during nutrient utilization in the North Pacific[END_REF][START_REF] Georg | Stable silicon isotopes of groundwater, feldspars, and clay coatings in the Navajo Sandstone aquifer, Black Mesa, Arizona, USA[END_REF][START_REF] Ding | Silicon isotopic composition of dissolved silicon and suspended particulate matter in the Yellow River, China, with implications for the global silicon cycle[END_REF][START_REF] Grasse | The influence of water mass mixing on the dissolved Si isotope composition in the Eastern Equatorial Pacific[END_REF][START_REF] Pokrovsky | Silicon isotope variations in Central Siberian rivers during basalt weathering in permafrost-dominated larch forests[END_REF][START_REF] Frings | Silicate weathering in the Ganges alluvial plain[END_REF], soils (Riotte et al., 2018a), and plants [START_REF] Douthitt | The geochemistry of the stable isotopes of silicon[END_REF]Ding et al., 2008aDing et al., , 2008b;;[START_REF] Pogge Von Strandmann | Lithium, magnesium and silicon isotope behaviour accompanying weathering in a basaltic soil and pore water profile in Iceland[END_REF]Opfergelt et al., 2012;Riotte et al., 2018b), and minerals, sedimentary rocks, cherts, and banded iron formations (e.g. [START_REF] Douthitt | The geochemistry of the stable isotopes of silicon[END_REF]Ziegler et al., 2005aZiegler et al., , 2005b;;[START_REF] Georg | Stable silicon isotopes of groundwater, feldspars, and clay coatings in the Navajo Sandstone aquifer, Black Mesa, Arizona, USA[END_REF][START_REF] Steinhoefel | Deciphering formation processes of banded iron formations from the Transvaal and the Hamersley successions by combined Si and Fe isotope analysis using UV femtosecond laser ablation[END_REF][START_REF] Van Den Boorn | Silicon isotope and trace element constraints on the origin of ∼3.5Ga cherts: Implications for Early Archaean marine environments[END_REF][START_REF] Savage | The silicon isotope composition of the upper continental crust[END_REF]. Constraining isotopic fractionation among these reservoirs is crucial to understanding the Si geochemical cycle.

Experimental studies have demonstrated that the Si isotopic signatures in natural environments can evolve during mineral precipitation [START_REF] Li | Experimental study of silicon isotope dynamic fractionation and its application in geology[END_REF][START_REF] Basile-Doelsch | Another continental pool in the terrestrial silicon cycle[END_REF][START_REF] Geilert | Silicon isotope fractionation during abiotic silica precipitation at low temperatures: Inferences from flow-through experiments[END_REF][START_REF] Roerdink | Experimental constraints on kinetic and equilibrium silicon isotope fractionation during the formation of non-biogenic chert deposits[END_REF][START_REF] Roerdink | Experimental constraints on kinetic and equilibrium silicon isotope fractionation during the formation of non-biogenic chert deposits[END_REF][START_REF] Oelze | The effect of Al on Si isotope fractionation investigated by silica precipitation experiments[END_REF], mineral dissolution [START_REF] Delvigne | Stratigraphic changes of Ge/Si, REE+Y and silicon isotopes as insights into the deposition of a Mesoarchaean banded iron formation[END_REF] or during adsorption of aqueous species [START_REF] Delstanche | Silicon isotopic fractionation during adsorption of aqueous monosilicic acid onto iron oxide[END_REF][START_REF] Oelze | Si stable isotope fractionation during adsorption and the competition between kinetic and equilibrium isotope fractionation: Implications for weathering systems[END_REF]. Silicon isotopic fractionation during such mineral-aqueous fluid reactions in nature have been considered to be influenced by kinetic isotope fractionation [START_REF] Geilert | Silicon isotope fractionation during abiotic silica precipitation at low temperatures: Inferences from flow-through experiments[END_REF][START_REF] Oelze | The effect of Al on Si isotope fractionation investigated by silica precipitation experiments[END_REF][START_REF] Roerdink | Experimental constraints on kinetic and equilibrium silicon isotope fractionation during the formation of non-biogenic chert deposits[END_REF][START_REF] Poitrasson | Silicon Isotope Geochemistry[END_REF]. However the degree of Si isotope fractionation at equilibrium is scarcely known, so that the relative impact of kinetic versus equilibrium processes on Si isotope fractionation during fluid-mineral interactions cannot be assessed unambiguously.

A critical factor to determine the equilibrium fractionation between a mineral and its coexisting aqueous fluid is the aqueous speciation of the system. The impact of aqueous speciation on the mineral/fluid fractionation factor has been demonstrated for elements such as boron, carbon, magnesium, mercury, transition metals and silicon [START_REF] Hemming | Boron isotopic composition and concentration in modern marine carbonates[END_REF][START_REF] Zhang | Abiologic silicon isotope fractionation between aqueous Si and Fe(III)-Si gel in simulated Archean seawater: Implications for Si isotope records in Precambrian sedimentary rocks[END_REF][START_REF] Zeebe | Stable boron isotope fractionation between dissolved B(OH) 3 and B(OH) 4[END_REF][START_REF] Klochko | Experimental measurement of boron isotope fractionation in seawater[END_REF][START_REF] Klochko | Re-evaluating boron speciation in biogenic calcite and aragonite using 11B MAS NMR[END_REF][START_REF] Asael | Fluid speciation controls of low temperature copper isotope fractionation applied to the Kupferschiefer and Timna ore deposits[END_REF][START_REF] Holloway | Ammonium in thermal waters of Yellowstone National Park: Processes affecting speciation and isotope fractionation[END_REF][START_REF] Jiskra | Solution Speciation Controls Mercury Isotope Fractionation of Hg(II) Sorption to Goethite[END_REF][START_REF] Ryan | Copper speciation and isotopic fractionation in plants: uptake and translocation mechanisms[END_REF][START_REF] Yin | Mercury speciation and mercury isotope fractionation during ore roasting process and their implication to source identification of downstream sediment in the Wanshan mercury mining area SW China[END_REF][START_REF] Fujii | Density functional theory estimation of isotope fractionation of Fe, Ni, Cu, and Zn among species relevant to geochemical and biological environments[END_REF][START_REF] Fujii | Isotope fractionation of Si in protonation/deprotonation reaction of silicic acid: A new pH proxy[END_REF][START_REF] Dupuis | Fractionation of silicon isotopes in liquids: The importance of configurational disorder[END_REF][START_REF] Noireaux | Crystallographic control on the boron isotope paleo-pH proxy[END_REF][START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF][START_REF] Balan | Theoretical isotopic fractionation between structural boron in carbonates and aqueous boric acid and borate ion[END_REF][START_REF] Mavromatis | Zinc isotope fractionation during the inorganic precipitation of calcite -Towards a new pH proxy[END_REF]. Dissolved silicon in aqueous environments can occur in various distinct species. Aqueous Si speciation depends on the solution pH and total dissolved Si concentration. In inorganic systems at ambient temperature, pH < 8.5 and m Si ≤ 10 - , form at the expense of silicic acid, whereas polymeric Si species become increasingly important in aqueous solutions supersaturated with respect to amorphous silica [START_REF] Dietzel | Dissolution of silicates and the stability of polysilicic acid[END_REF]. Figure 3.1 shows the aqueous speciation of Si in a solution containing 1.6×10 -3 M Si (corresponding to the equilibrium with amorphous silica at pH<9) as a function of pH for 25°C and 75°C, respectively. As the speciation of aqueous silicon changes with pH, equilibrium isotope fraction between this fluid and any Si bearing mineral will change accordingly [START_REF] Dupuis | Fractionation of silicon isotopes in liquids: The importance of configurational disorder[END_REF][START_REF] Fujii | Isotope fractionation of Si in protonation/deprotonation reaction of silicic acid: A new pH proxy[END_REF]. Several past studies have aimed to determine Si equilibrium fractionation factors between amorphous silica and its coexisting aqueous solutions [START_REF] Geilert | Silicon isotope fractionation during abiotic silica precipitation at low temperatures: Inferences from flow-through experiments[END_REF][START_REF] Oelze | Si stable isotope fractionation during adsorption and the competition between kinetic and equilibrium isotope fractionation: Implications for weathering systems[END_REF][START_REF] Roerdink | Experimental constraints on kinetic and equilibrium silicon isotope fractionation during the formation of non-biogenic chert deposits[END_REF]. Most reported an enrichment of the solid in light ( 28 Si)

isotopes, which could be explained by non-equilibrium fractionation during precipitation of amorphous silica from a supersaturated solution [START_REF] Dupuis | Fractionation of silicon isotopes in liquids: The importance of configurational disorder[END_REF]. The aim of this study is to expand on these past efforts, by determining experimentally the equilibrium fractionation factors between amorphous SiO 2 and the aqueous Si species as a function of pH over a range of 5.8 < pH < 10 at temperatures of 25°C and 75°C. To assure the attainment of isotopic equilibrium, the 'three-isotope method' was applied. The purpose of this paper is to report the results of this experimental study and provide new insights into how aqueous solution speciation and temperature can affect the Si equilibrium isotopic fractionation between amorphous silica and an aqueous solution.

Theoretical background

Geochemical calculations of amorphous silica dissolution rates

All geochemical calculations in this study were performed using the PHREEQC code (Parkhurst and Appelo, 2013) together with its llnl thermodynamic database. The standard state adopted in this study calls for unit activity of pure minerals, solids, and H 2 O. For aqueous species, the standard state is unit activity of a 1 molal solution extrapolated to infinite dilution. The activity coefficients of charged aqueous species were calculated using the Davies equation, whereas the activity coefficients of neutral species were assumed to be equal to one.

The experiments in the present study were begun by first equilibrating an initially Si free aqueous solution of known pH with amorphous silica. The dissolution reaction for amorphous silica is described by:

SiO , + 2 H O → H SiO (3.1)
The law of mass action for reaction (3.1) is given by:

= , (3.2)
where stands for an equilibrium constant and a i refers to the activity of the subscripted species or phase. Taking account of this standard state, in pure water ( = ! , where ! stands for the concentration of the subscripted species), Eqn. (3.2) reduces to:

= ! , (3.3)
where !

, stands for the concentration of H SiO in equilibrium with amorphous silica. The rates of amorphous silica dissolution (r) in a closed system and in the absence of specific inhibitors or catalysts can be described using [START_REF] Rimstidt | The kinetics of silica-water reactions[END_REF]: (3.6)

" = #! #$ = %/' () * -) , ! - (3
Noting that

: ; < : = < = ! . 1 >?
, where ! . 1 >? again denotes the concentration of dissolved silica in equilibrium with amorphous silica, the temporal evolution of dissolved silica concentration in the closed system is described by:

! = ! . 1 >? @1 -A ,B.: = < C (3.7)
Chapter 3. The experimental determination of equilibrium Si isotope fractionation factors -64-

Si isotope systematics

Silicon isotope compositions in this study are reported using the standard δ-notation in per mil (‰) relative to the international NBS-28 standard (NIST RM-8546), computed using: ) is defined as:

D E Si = F . Si E / Si1 GHIJ K . Si E / Si1 LM , K K -1N (
P QRJ S,TJU S E/ K = . Si E / Si K 1 QRJ S . Si E / Si K 1 TJU S (3.9)
The silicon isotopic fractionation between a solid and a coexisting aqueous phase can be also described using ∆ E Si QRJ S,TJU S , which is defined by: consistent with [START_REF] Zhang | Abiologic silicon isotope fractionation between aqueous Si and Fe(III)-Si gel in simulated Archean seawater: Implications for Si isotope records in Precambrian sedimentary rocks[END_REF]:

∆ E Si QRJ S,
10 Y 23P QRJ S,TJU S E/ K = Z.[ × 10 Y 23P QRJ S, E/ K 1 (3.12)
where x i refers to the mole fraction of the dissolved Si present in the subscripted aqueous species.

Three-isotope method

Equilibrium fractionation factors in the present study were generated using the 'threeisotope method'. The three-isotope method was originally used to determine the equilibrium isotopic fractionation factors of oxygen between mineral and co-existing aqueous solutions [START_REF] Matsuhisa | Mechanisms of hydrothermal crystallization of quartz at 250°C and 15 kbar[END_REF]Matthews et al., 1983aMatthews et al., , 1983bMatthews et al., , 1983c)). Over the past 10 years, this method was also successfully applied to non-traditional isotopic systems, such as Mg and Fe [START_REF] Shahar | Equilibrium high-temperature Fe isotope fractionation between fayalite and magnetite: An experimental calibration[END_REF]Beard et al., 2010;[START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF][START_REF] Frierdich | Determination of the Fe(II)aq-magnetite equilibrium iron isotope fractionation factor using the three-isotope method and a multi-direction approach to equilibrium[END_REF][START_REF] Reddy | The effect of pH on stable iron isotope exchange and fractionation between aqueous Fe(II) and goethite[END_REF], as well as Si (Zheng et al., 2016). This approach is commonly used to evaluate the kinetics of isotopic exchange reactions between two components [START_REF] Cole | Rates and Mechanisms of Isotopic Exchange[END_REF][START_REF] Johnson | Isotopic fractionation between Fe(III) and Fe(II) in aqueous solutions[END_REF][START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF][START_REF] Wu | Stable iron isotope fractionation between aqueous Fe(II) and model Archean ocean Fe-Si coprecipitates and implications for iron isotope variations in the ancient rock record[END_REF]Zheng et al., 2016). Before exchange, one component (Phase A, typically the solid) exhibits a "natural" isotopic composition and plots on a δ vs. δ diagram, such as Fig. 3.2, on a primary fractionation line, also known as the terrestrial fractionation line (TFL). This line follows a mass-dependent relation where δ 30 Si ≈ 1.93 x δ 29 Si [START_REF] Young | Kinetic and equilibrium mass-dependent isotope fractionation laws in nature and their geochemical and cosmochemical significance[END_REF]Zheng et al., 2016). The second component (Phase B, typically the fluid) is enriched in one isotope (for example, 29 Si in the present study) and thus has a distinct and known offset from the TFL. As the system undergoes isotopic exchange, the isotopic compositions of the two components will gradually evolve over time (t) towards isotopic equilibrium. Once the isotopic exchange is complete and isotopic equilibrium has been attained, the isotopic compositions of the two phases will fall on a secondary fractionation line (SFL) parallel to the TFL. The position of the SFL is defined by the isotopic mass balance of the system (see Fig. 3.2).

For many systems, isotopic exchange is slow and therefore often incomplete. The three-isotope method, nevertheless, allows validation of the attainment of isotopic equilibrium. The degree to which the system has attained isotopic equilibrium can be quantified using the degree of isotope exchange (F), defined by:

] = .D B -D 1 .D -D 1 (3.13)
where δ t denotes the isotopic composition of either one of the phases at any time, t, during the isotope exchange reaction, and δ i and δ e describe the initial and equilibrium isotopic composition of this phase. The parameter F ranges from 0 to 1 as isotopic equilibrium is attained. In a two-component system δ e can be derived from the mass balance constraints (Zheng et al., 2016), and calculated from

D = D H G^-4 _ QRJ S _ QRJ S + _ TJU S 6 × ∆ QRJ S,TJU S, (3.14)
where δ mean in this study stands for the mass averaged Si isotope composition of the system, ∆ QRJ S,TJU S, designates the equilibrium isotope fractionation between the solid and fluid phases, and N solid and N fluid denote the number of moles of Si in the solid and fluid phase, respectively. If the ∆ QRJ S,TJU S, of the system is not known, it can be obtained from an iterative fit of experimental data (Zheng et al., 2016).

Kinetics of isotopic exchange

The three-isotope method not only allows determination of the equilibrium fractionation factors of a solid-fluid system, but also allows determination of the kinetics of isotopic exchange. Following the approach of [START_REF] Cole | Rates and Mechanisms of Isotopic Exchange[END_REF] and [START_REF] Johnson | Isotopic fractionation between Fe(III) and Fe(II) in aqueous solutions[END_REF] isotope exchange rates can be quantified using

-#.1 -]1 #$ = ) ^.1 -]1 ^ (3.15)
where k n stands for the rate constant of reaction order n, where this reaction order is usually an integer from 0 to 3. Isotope exchange reactions typically follow either a first-order (n=1)

or second-order (n=2) rate law [START_REF] Criss | Kinetic theory of oxygen isotopic exchange between minerals and water[END_REF][START_REF] Huang | Kinetic studies on the isotopic exchange of calcium ion and calcium carbonate[END_REF][START_REF] Johnson | Isotopic fractionation between Fe(III) and Fe(II) in aqueous solutions[END_REF][START_REF] Welch | Kinetic and equilibrium Fe isotope fractionation between aqueous Fe(II) and Fe(III)[END_REF][START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF]Zheng et al., 2016). The integrated form of this rate equation can be written as either

ln .1 -F1 = -k d t for n=1 (2.16) f .d,f1 = k t for n=2 (2.17)
Isotope exchange rate constants can be quantified by fitting the experimental value of F to Eqn. (3.16) for the first order rate constant or Eqn. (3.17) for the second order rate constant [START_REF] Cole | Rates and Mechanisms of Isotopic Exchange[END_REF][START_REF] Johnson | Isotopic fractionation between Fe(III) and Fe(II) in aqueous solutions[END_REF][START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF].

Methods

Experimental approach

Starting powder -amorphous silica

All experiments in the present study were performed in series using Alpha Aeser ® 100 mesh hydrated silicic acid powder. This powder was cleaned prior to each experimental series by sedimentation in >18.2 Ω de-ionized water (Milli-Q ® ) to remove ultrafine particles [START_REF] Pokrovski | Experimental study of the complexation of silicon and germanium with aqueous organic species: implications for germanium and silicon transport and Ge/Si ratio in natural waters[END_REF]. In each case, from 40 to 75 g of the powder was suspended by stirring in a 1dm 3 glass beaker. The powder was sedimented for 10 minutes and then decanted. This operation was repeated until the supernatant became clear within the first 5 min. Subsequently the powder was oven dried at 60°C. To avoid hydration of the powder while it cooled to room temperature, it was placed into a desiccator. Autosorb-1MP using the nitrogen multipoint BET method [START_REF] Brunauer | Adsorption of Gases in Multimolecular Layers[END_REF]. The average surface area of the initial amorphous silica powders is 196.3 m 2 /g, and ranged from 175 m 2 /g to 215 m 2 /g with an estimated uncertainty of ± 10%.

Initial aqueous solutions

The initial aqueous solutions used in the experiments were prepared at pH ~6 and ~10 for the 25°C experiments and at pH ~6 and ~9 for the 75°C experiments; experiments run with these fluids are labelled SibA, SicB, SigA, and SikB, respectively. The pH of the fluids were selected so that it would be possible to quantify the effect of the aqueous H 3 SiO 4 -species on equilibrium fractionation factors at these two temperatures. These solutions were prepared using high purity de-ionized Milli-Q ® water (>18.2 Ω), and reagent grade HCl, NH 4 OH and NH 4 Cl. The compositions of these initial solutions are provided in Table 3.1.

Characterization of the aqueous solutions

The aqueous solution pH was regularly monitored during the experiments with a Metrohm ® 913 pH Meter connected to a standard glass microelectrode. This electrode was calibrated using certified Orion Thermo Scientific ® buffers. The uncertainty in the measurements was determined to be 0.05, equal to 2 standard deviations of ~40 repeated measurements of the pH=4.01 calibration standard. For experiments at 75°C, the pH was measured at 25°C and later calculated to this higher temperature with PHREEQC.

Aqueous silicon concentrations were determined by the molybdate blue method [START_REF] Truesdale | Manuel d'analyse des sels nuritifs dans l'eau de mer: Utilisation de L'autoanalyzer II technicon (r)[END_REF]) using a Bran & Luebbe ® analyser-III colorimeter coupled to a Seal XY-2 autosampler and a Technicon analyser II mixing unit. The measurements were conducted over the 0.1 to 10 ppm concentration range. The long-term reproducibility of these measurements was determined to be within 3% and the quantification limit was 0.04 ppm.

Experiment design: Step 1 Equilibration of reactive fluids

Experiments in this study were conducted in four distinct series. Each series began by equilibrating 200 ml of an initial aqueous fluid of selected composition with 3 g of prewashed amorphous SiO 2 powder in closed polypropylene bottles (see Table 3.1). Once closed, these bottles were placed in shaking thermostatic baths at either ~25°C or ~75°C.

The aqueous fluids in the bottles were sampled 8 times at regular intervals during the 19 to 65 days of this equilibration stage. The pH was measured immediately after each sampling at room temperature. The samples collected from the 75°C experiments were then diluted to prevent precipitation. Aqueous Si concentrations were determined by colorimetry on all samples. Chemical equilibrium was assumed to be attained when both pH and the Si concentration of the aqueous solutions attained constant values within uncertainty.

This initial stage was stopped once these constant values were reached. The fluids were then filtered with Teflon syringe filters (Merck ® 0.2 µm). Fluids recovered from the 75°C experiments were kept in the thermostatic bath until subsequently used in the isotopic exchange experiments described below. The four chemical equilibrated fluids were enriched with a 29 Si isotope tracer to obtain δ 29 Si = ~ 23‰ (see Table 3.2). The added 29 Si isotope tracer was prepared by dissolving Eursio-top ® 29 SiO 2 powder, having an initial composition of 0.21% 28 Si, 99.76% 29 Si, and 0.03% 30 Si in de-ionized water. After the addition of this spike to the equilibrated fluids, the Si concentration and pH were measured. For experiments at pH ~ 6 the fluid pH was adjusted, if necessary, by adding a small quantity of HCl or NH 4 OH to assure these initial fluids were as close to equilibrium with amorphous silica as possible. Each series of exchange experiments consisted of a suite of 8 closed system experiments of selected durations. This approach was selected so that both the solids and fluids could be collected and analysed after distinct experiment durations. The overall duration of each experimental series were selected so that degree of isotopic exchange would approach 1 at the end of each series; these overall durations are provided in Table 3.2. Each individual experiment was performed in 10 ml polypropylene reactors. Into each reactor was added ~ 0.15 g of amorphous SiO 2 powder with a known Si isotope composition and 5 ml of the prepared 29 Si enriched fluid. The 25°C experiments were placed into an orbital shaker to be constantly mixed. The 75°C experiments were placed into a thermostatic bath and hand shaken once or twice a day. To verify that no leakage occurred during any experiment, all reactors were weighted both at the beginning and the end of each experiment. At pre-chosen time intervals, the reactors were centrifuged for 20 min at 4500 rpm and then opened. The supernatant was separated from the powder and filtered using Merck ® 0.2 µm Teflon syringe filters. The pH was measured immediately after sampling, and fluids recovered from the 75°C experiments were diluted just after measuring pH. The recovered powder was washed and filtered with de-ionized water, oven-dried at 40°C, and stored for further analysis. × m, where n denotes the number of measurements performed and t denotes the Student t-factor [START_REF] Platzner | Modern isotope ratio mass spectrometry, Chemical analysis[END_REF]. δ eq represents the equilibrium isotopic composition of 29

Si and F denotes the degree of isotopic exchange. a denotes the spiked initial solution.

Si isotope analysis

Silicon isotope compositions were measured in the fluid and solid samples collected from all isotope exchange experiments, as well as the initial washed SiO 2 powders, the spiked initial fluid and the non-spiked chemical equilibrated fluids. Aqueous samples were prepared by first acidifying the solutions using bi-distilled 3N HCl to pH ~2. Amorphous silica powders were processed using the alkali fusion method described by [START_REF] Zambardi | Precise Determination of Silicon Isotopes in Silicate Rock Reference Materials by MC-ICP-MS[END_REF]. From 2 to 5 mg of the solids were weighted into silver crucibles (XRF scientific, Montreal, Canada) together with a ~200 mg Merck ® NaOH pellet. The crucibles were capped and placed into a furnace heated at 720°C for 10 min. They were subsequently cooled to room temperature and placed into 30 cm 3 Savillex ® Teflon beakers filled with 20 ml Milli-Q ® water for 24 hours to dissolve the fusion cake. The resulting fluids were then transferred to 60 cm 3 polypropylene bottles and diluted to 40 ml by adding Milli-Q ® water.

These 40 ml samples were then acidified using ~10 N bi-distilled HCl to obtain a pH of 1.5.

All prepared Si-bearing fluids generated from either the solid or fluid samples were purified by cation-exchange chromatography using the Bio-Rad ® AG50W-12X cationic resin [START_REF] Georg | New sample preparation techniques for the determination of Si isotopic compositions using MC-ICPMS[END_REF][START_REF] Zambardi | Precise Determination of Silicon Isotopes in Silicate Rock Reference Materials by MC-ICP-MS[END_REF]. The detailed cleaning procedure of the resin is described in [START_REF] Zambardi | Precise Determination of Silicon Isotopes in Silicate Rock Reference Materials by MC-ICP-MS[END_REF]. From 0.5 to 2 ml of prepared fluids containing up to 70 µg Si were loaded, directly collected, and eluted twice with deionized MQ ® water to obtain 6 ml samples. These were then diluted and acidified to obtain a 3 ppm solution with a total 0.05 M HCl concentration. Silicon recovery after processing was determined to be between 90 to 100 %. The 28 Si signal of the procedural blank, processed in the same way, was found to be less than < 2% and was thus considered as negligible.

Silicon isotope ratios were determined using a Thermo Scientific Neptune ® MC-ICP-MS either at the Observatoire Midi Pyrenées / Laboratorie Géosciences Environnement Toulouse (GET), France, or the GeoForschungsZentrum (GFZ) in Potsdam, Germany.

Measurements were performed in medium resolution under either wet plasma (GET) or dry plasma (GFZ) conditions. The wet plasma samples were introduced with a Thermo SIS system with a double-pass cyclonic spray chamber. An ESI ApexHF desolvator (having sample path made of Perfluoroalkoxy alkane, PFA) and fitted with a PFA nebulizer was used for dry plasma conditions at the GFZ [START_REF] Schuessler | Testing the limits of micro-scale analyses of Si stable isotopes by femtosecond laser ablation multicollector inductively coupled plasma mass spectrometry with application to rock weathering[END_REF]. The instrumental mass bias drift was corrected using the sample standard bracketing technique relative to NBS-28 (NIST SRM 8546), combined with Mg doping as an internal standard in all measured samples and standards. Measurements of 25 Mg/ 24 Mg ratios were performed in the dynamic mode, alternating between Si and Mg isotopes. Russell's exponential law [START_REF] Russell | Ca isotope fractionation on the Earth and other solar system materials[END_REF] was then used to correct for the mass bias drift. The accuracy and precision of the isotopic analysis were validated by repeated measurement of the BHVO-2 reference material. They yielded a long-term reproducibility of δ 30 Si= -0.26 ± 0.13 ‰ for the GET analyses (2 S.D, n=59) and δ 30 Si= -0.28 ± 0.09 ‰ for the GFZ analyses (2 S.D, n=18), which are in close agreement with data from previous studies (e.g. [START_REF] Abraham | δ 30 Si and δ 29 Si Determinations on USGS BHVO-1 and BHVO-2 Reference Materials with a New Configuration on a Nu Plasma Multi-Collector ICP-MS[END_REF][START_REF] Zambardi | Precise Determination of Silicon Isotopes in Silicate Rock Reference Materials by MC-ICP-MS[END_REF][START_REF] Savage | The silicon isotope composition of the upper continental crust[END_REF][START_REF] Savage | High temperature silicon isotope geochemistry[END_REF]. 3.

Results

Attainment of fluid-amorphous SiO 2 equilibrium during the fluid equilibration

The Si concentration of the pH 6 initial fluids at both 25° and 75°, and the pH 9.1 fluid at 75°C systematically increase to a constant maximum value. In contrast, the dissolved Si concentrations of the pH 10 and 25°C experiment first maximizes then decreases to a final constant value. The constant final Si concentrations were within 10 % of those calculated to be in equilibrium of amorphous SiO 2 using PHREEQC. The curve drawn through these measured Si concentrations correspond to a fit of these data to Eqn. (3.7); the rate constants obtained by this regression are provided in Table 3.3. Ostwald ripening affecting the silica grains during the runs. Overall the post-experiment solids, however, appear to have been essentially unchanged by these isotope exchange experiments.

Chemical and isotopic evolution of the isotope exchange experiments

The temporal evolution of the pH, the bulk Si composition of the fluids, and the isotopic Si

Silicon isotope fractionation factors

The equilibrium Si fractionation factors, ∆ eq 30 SiSiO 2 ,am-fluid, at the conditions of the four experimental series considered in this study were generated with the aid of Fig. 3.6 as described in section 3.2.3. The value of ∆ eq 30 SiSiO 2 ,am-fluid was estimated from the extrapolation to F = 1 of the solid lines drawn though the isotopic data shown in these figures. This fit was aided by the fact that these isotopic exchange reactions approached close to isotopic equilibrium in each experimental series. A close correspondence can be seen between the isotopic data and these fits. The values of ∆ eq 30 SiSiO 2 ,am-fluid obtained from these fits are provided in Table 3.4 and vary with temperature and pH. Note that as mentioned above, the final few measurements of the experimental series performed at pH 9.9 and 25°C, and pH 9.1 and 75°C were excluded from the fit due to pH drift; their exclusion affected negligibly the retrieved values of ∆ eq 30 SiSiO

Discussion

Silicon isotope fractionation between amorphous silica and aqueous solution

The equilibrium isotopic fractionation factors between amorphous silica (SiO 2 0.32 H 2 O) and aqueous solutions determined in this study at 25°C and pH 6.4 is ∆ eq 30 SiSiO 2 ,am-fluid= 0.45 ± 0.20 ‰. This value is identical, within uncertainty with those of Roerdink et al. The results of the present study, performed using the three-isotope method, which thereby verifies the attainment of isotopic equilibrium in the amorphous silica -aqueous solution system validates the results of these former studies. The three-isotope method was also adopted by Zheng et al. (2016) to assess the Si equilibrium fractionation factor between a Fe(III)-Si gel and an aqueous solution at pH 8.

These authors report an equilibrium fractionation factor, ∆ eq 30 SiSiO 2 ,am-fluid of -2.3 ± 0.23 ‰.

The differences between this result and those reported in the present study are likely attributable to the substantial presence of Fe(III) in the solid phase (X Fe(III) /X Si = 0.5).

Many studies have shown that the absolute values of isotopic fractionation decreases as temperature increases (e.g. [START_REF] Urey | The thermodynamic properties of isotopic substances[END_REF][START_REF] Bigeleisen | Chemistry of Isotopes: Isotope chemistry has opened new areas of chemical physics, geochemistry, and molecular biology[END_REF][START_REF] Schauble | Applying Stable Isotope Fractionation Theory to New Systems[END_REF][START_REF] Shahar | Hightemperature Si isotope fractionation between iron metal and silicate[END_REF][START_REF] Huang | First-principles calculations of equilibrium silicon isotope fractionation among mantle minerals[END_REF]. Such is also the case in the present study. At pH ~6 the ∆ eq 30 SiSiO 2 ,am-fluid decreases from 0.45 ± 0.20 ‰ to 0.07 ± 0.06 ‰ as temperature increases from 25 to 75 °C. Similarly, the ∆ eq 30 SiSiO 2 ,am-fluid decreases from 1.63 ± 0.23 ‰ to 1.06 ± 0.13 ‰ at pH between 9.1 and 9.9.

Isotope fractionation among Si aqueous species

The 2015) study, however, took a different approach to determine this equilibrium fractionation factor than that of the present study. Their method relied on the purification of a Na 2 SiO 4 solution at pH 9.4 by column chromatography using an anionic resin. The two dominant Si aqueous species were collected in different elutions.

These elutions were then measured for their Si isotopic compositions. This approach allows running experiments at much lower Si concentrations than those of the present study since there is no need for the solutions to be in equilibrium with a solid Si-bearing phase. Note that at amorphous silica-aqueous fluid equilibrium at pH >9 there is a possibility of the formation of minor amounts of polynuclear Si bearing aqueous species [START_REF] Dietzel | Dissolution of silicates and the stability of polysilicic acid[END_REF] that could affect the measured equilibrium isotopic fractionation between amorphous silica and its coexisting aqueous fluid. The method used by Fuji et al. ( 2015) however, does not verify that isotopic equilibrium is attained. Additionally, undefined fractionation may have occurred during the column separation by sorption of Si on the anionic resin (Fuji et al., 2015).

Kinetics of Si isotope exchange

The first part of each experimental series began by dissolving amorphous SiO 2 to equilibrium with an aqueous solution. The dissolution rates of these experiments were retrieved by fitting these data to the transition state rate equations (3.4) to (3.7). The rates, reported in Table 3.3, range from 3.13 x 10 -12 to 1.24 x 10 -10 mol/m 2 /s; these rates increase with increasing temperature and increasing pH. The rates are similar to the dissolution rates of quartz obtained at corresponding temperature and pH conditions by [START_REF] Brady | Controls on silicate dissolution rates in neutral and basic pH solutions at 25°C[END_REF], [START_REF] Berger | Dissolution rate of quartz in lead and sodium electrolyte solutions between 25 and 300°C: Effect of the nature of surface complexes and reaction affinity[END_REF][START_REF] Icenhower | The dissolution kinetics of amorphous silica into sodium chloride solutions: effects of temperature and ionic strength[END_REF][START_REF] Icenhower | The dissolution kinetics of amorphous silica into sodium chloride solutions: effects of temperature and ionic strength[END_REF]; these past reported values ranged from 10 -12 to 10 -13 mol/m²/s. Our values are also similar to the amorphous silica and the phytoliths dissolution rates at 25°C and pH 5 of 10 -12 and 3×10 -12 mol/m²/s reported by [START_REF] Plettnick | Kinetics and mechanisms of dissolution of silica at room temperature and pressure[END_REF] and [START_REF] Fraysse | Surface properties, solubility and dissolution kinetics of bamboo phytoliths[END_REF], respectively. In contrast, our rates are substantially slower than that of amorphous silica nanoparticles at 25°C and pH 7 reported by [START_REF] Diedrich | The Dissolution rates of SiO 2 nanoparticles as a function of particle size[END_REF].

The rates of isotopic equilibration provide some insight into the process controlling isotopic equilibration. The variation of the degree of isotopic exchange (F) is plotted at a function of time in Fig 3 .7. The curves through the data points in this figure were generated using the first order rate equation (Eqn. 3.16), to be consistent with the bulk dissolution rate equation. The rate constants used for these calculations were obtained from the dissolution of the amorphous silica during the first stage of each experimental series. It can be seen in this figure that the curves are close to, but somewhat lower than the F values during the first exchange rates tend to slow down relative to that estimated using the corresponding bulk amorphous silica dissolution rates as the systems approach isotopic equilibrium. This behaviour suggests that the dominant rate-controlling mechanism of isotope equilibration in the present study over the first 10 to 20 days is the detachment and reattachment of material to the amorphous silica surface. If this is the case, it would imply that Si transport within the amorphous silica grains in this study is relatively fast compared to the rate of detachment and attachment of SiO 2 at the surface for the bulk of the isotopic exchange process. This faster rate is likely due to the relatively small grain size of the amorphous SiO 2 used in the experiments; the average grain size of these particles was 21 ± 5 nm. Based on the unit cell dimension of quartz, which is ~ 5Å [START_REF] Danielsson | A low-temperature apparatus for singlecrystal diffractometry. The unit-cell dimension of α-quartz in the temperature range 86-298 K[END_REF], it is likely that these grains are no more than ~40 unit cells across. In addition, the presence of water in the amorphous silica structure may facilitate the diffusive transport of Si into and out of these grains. Only after isotopic exchange has attained 80 to 90% of their equilibrium values do these exchange rates slow compared to bulk amorphous silica dissolution rates. This may indicate that the final equilibration of the isotope exchange reaction is becoming transport-limited near the end of each experimental series. Nevertheless, all experimental series performed in this study approached isotopic equilibrium within the 55 to 360 days of each experimental series. If the rapid rate of the total Si isotopic equilibration as observed here is also the case in natural ambient temperature systems, the preservation of original Si isotopic signatures in natural fine grained amorphous SiO 2 materials may be rare. substantially smaller than that of boron [START_REF] Zeebe | Stable boron isotope fractionation between dissolved B(OH) 3 and B(OH) 4[END_REF][START_REF] Klochko | Experimental measurement of boron isotope fractionation in seawater[END_REF][START_REF] Noireaux | Crystallographic control on the boron isotope paleo-pH proxy[END_REF], as the Si does not change its coordination in inorganic systems, it has the advantage of a simpler and better-defined aqueous and solid speciation, potentially making it a more precise tool for constraining paleo-pH values. Note, however, that the experiments presented in this study suggest that small (∼20 nm) amorphous silica grains can rapidly equilibrate with its co-existing aqueous fluid in the laboratory. As such further work should be made on the kinetics of isotopic exchange as a function solid grain size, to assess the degree to which the Si isotope signatures of precipitated amorphous SiO 2 are preserved over geologic timeframes. The data obtained in this study not only show a distinct Si isotopic fractionation depending on solution pH, but also on solution temperature. The equilibrium Si isotope fractionation factor between amorphous SiO 2 and H 4 SiO 4 ° at 75°C is significantly lower than that at ambient temperature. Si isotopic fraction becomes more important at lower temperatures. In Fig. 3.9, the equilibrium isotope fractionation factors of the present study at neutral pH are extrapolated to 0 °C, showing that a fractionation of ~0.9 ‰ can be expected at this temperature. This conclusion is supported by the ab initio calculations of [START_REF] Dupuis | Fractionation of silicon isotopes in liquids: The importance of configurational disorder[END_REF] shown in Fig. 3.9, exhibiting a much stronger fractionation factor between quartz and H 4 SiO 4 ° as temperature decreases. This relatively large low temperature fractionation factor might explain the low δ 30 Si signatures found in Banded Iron Formations (BIFS, Chakrabarti et al., 2012) or the δ 30 Si variation of Archean cherts [START_REF] Marin-Carbonne | Micrometer-scale chemical and isotopic criteria (O and Si) on the origin and history of Precambrian cherts: Implications for paleo-temperature reconstructions[END_REF].

Can Si fractionation be used as a paleo pH and temperature proxy?

Conclusion

The results presented in this study confirm the significance of aqueous silica speciation on equilibrium isotope fractionation between fluids and Si-bearing solids. The equilibrium fractionation factor between amorphous SiO 2 and its co-existing aqueous solution ∆ eq 30 SiSiO 2 ,am-fluid at 25°C is 0.45 ± 0.20 ‰ at pH 6 and 1.63 ± 0.23 ‰ at pH 9.9. Using these values and the distribution of the species in the aqueous solution, an equilibrium isotope fractionation value between H It follows that the Si isotopic compositions of precipitated minerals may provide insight into the temperature of their formation.

This study also further validates the use of the three-isotope method as an effective means to determine both the rates of isotope exchange and equilibrium isotope fractionation factors. Such equilibrium fractionation factors facilitate greatly the interpretation of natural isotope signatures. Moreover the rates of isotope exchange rates determined by this approach may provide new insight into both the mechanism of isotope exchange and the conditions at which mineral isotopic signatures are best preserved in natural systems.

Chapter 4 Extreme silicon isotope fractionation between silicic acid and aqueous organosilicon complexes: Implication for silica biomineralization

A version of this chapter will be submitted for publication as: "Franziska M. The results of this study indicate that the complexation of Si by those organic ligands, which change the coordination of aqueous Si, can lead to extreme equilibrium Si isotope fractionation between aqueous fluids and solid phases. Such results can therefore be used to improve our ability to interpret the Si isotope compositions of natural solids, and in particular those associated with marine silica biomineralization processes (e.g. sponge spicules).

Introduction

Silicon (Si) is a major element in the Earth's crust and thus in biological systems. There are various biogenic uses of Si. In marine environments, Si is used by phytoplankton, zooplankton and sponges in the form of opal to form frustules, tests or spicules (e.g. De La [START_REF] De La Rocha | Silicon-isotope composition of diatoms as an indicator of past oceanic change[END_REF][START_REF] Kubicki | Molecular orbital modeling of aqueous organosilicon complexes: implications for silica biomineralization[END_REF][START_REF] Hendry | Silicon isotopes in Antarctic sponges: an interlaboratory comparison[END_REF][START_REF] Poitrasson | Silicon Isotope Geochemistry[END_REF], in plants Si occurs mostly as phytoliths, which are responsible for structural stability and defensive mechanisms (e.g. [START_REF] Kubicki | Molecular orbital modeling of aqueous organosilicon complexes: implications for silica biomineralization[END_REF][START_REF] Ding | Silicon isotope study on rice plants from the Zhejiang province, China[END_REF][START_REF] Sun | Silicon isotope fractionation in rice plants, an experimental study on rice growth under hydroponic conditions[END_REF][START_REF] Delvigne | Distinct silicon and germanium pathways in the soil-plant system: Evidence from banana and horsetail: distinct Si and Ge pathways in plants[END_REF][START_REF] Poitrasson | Silicon Isotope Geochemistry[END_REF]. In higher organisms, such as animals or humans Si is used for bone or tissue formation (e.g. [START_REF] Birchall | The essentiality of silicon in biology[END_REF][START_REF] Jugdaohsingh | Silicon and boron differ in their localization and loading in bone[END_REF]. The fractionation of Si during such biomineralization processes can be significant with δ 30 Si reported values ranging between +3 and -6.5 ‰ [START_REF] Poitrasson | Silicon Isotope Geochemistry[END_REF]. In general, biogenic solid phases prefer the uptake of light Si isotopes [START_REF] De La Rocha | Silicon-isotope composition of diatoms as an indicator of past oceanic change[END_REF][START_REF] Wischmeyer | Control mechanisms for the oceanic distribution of silicon isotopes[END_REF][START_REF] Ding | Silicon isotope study on rice plants from the Zhejiang province, China[END_REF][START_REF] Basile-Doelsch | Another continental pool in the terrestrial silicon cycle[END_REF][START_REF] Basile-Doelsch | Si stable isotopes in the Earth's surface: A review[END_REF]Opfergelt et al., 2006;[START_REF] Sun | Silicon isotope fractionation in rice plants, an experimental study on rice growth under hydroponic conditions[END_REF][START_REF] Wille | Silicon isotopic fractionation in marine sponges: A new model for understanding silicon isotopic variations in sponges[END_REF][START_REF] Hendry | Silicon isotopes in Antarctic sponges: an interlaboratory comparison[END_REF][START_REF] Hendry | The relationship between silicon isotope fractionation in sponges and silicic acid concentration: Modern and core-top studies of biogenic opal[END_REF][START_REF] Poitrasson | Silicon Isotope Geochemistry[END_REF]. In marine environments, the strongest Si isotopic fractionation of -6.02 ‰ has been observed in sponges [START_REF] Wille | Silicon isotopic fractionation in marine sponges: A new model for understanding silicon isotopic variations in sponges[END_REF]. The processes and mechanisms controlling these observed fractionations are not yet fully understood (Kinrade et al., 2002;[START_REF] Kubicki | Molecular orbital modeling of aqueous organosilicon complexes: implications for silica biomineralization[END_REF][START_REF] Poitrasson | Silicon Isotope Geochemistry[END_REF].

Dissolved Si can form strong aqueous complexes with a number of organic ligands including polyols, saccharides, phenols, pyridine and tropolones [START_REF] Rosenheim | Über innerkomplexe Brenzcatechinate vierwertiger Elemente[END_REF][START_REF] Weiss | Wasserbeständige, kationische Siliciumkomplexe mit 1-Hydroxypyridin-N-oxyd[END_REF][START_REF] Cella | 29Si NMR of five-and six-coordinate organosilicon complexes[END_REF][START_REF] Sjöberg | Equilibrium and structural studies of silicon(IV) and aluminium(III) in aqueous solution. 12. A potentiometric and 29 Si-NMR study of silicon tropolonates[END_REF][START_REF] Sedeh | Equilibrium and Structural Studies of Silicon(IV) and Aluminium(III) in Aqueous Solution. 30. Aqueous Complexation between Silicic Acid and Some ortho-Di-and Triphenolic Compounds[END_REF][START_REF] Sedeh | Equilibrium and structural studies of silicon(IV) and aluminum(III) in aqueous solution. 31. Aqueous complexation between silicic acid and the catecholamines dopamine and L-DOPA[END_REF][START_REF] Pokrovski | Experimental study of the complexation of silicon and germanium with aqueous organic species: implications for germanium and silicon transport and Ge/Si ratio in natural waters[END_REF][START_REF] Kinrade | Stable Five-and Six-Coordinated Silicate Anions in Aqueous Solution[END_REF]Kinrade et al., 2001aKinrade et al., , 2001bKinrade et al., , 2002;;[START_REF] Kinrade | Silicon-29 NMR studies of aqueous silicate solutions. 1. Chemical shifts and equilibria[END_REF][START_REF] Benner | Hydrogen-Bonded Sugar-Alcohol Trimers as Hexadentate Silicon Chelators in Aqueous Solution[END_REF][START_REF] Kinrade | Complexes of pentaoxo and hexaoxo silicon with furanoidic vicinal cis-diols in aqueous solutionAs presented at the Second Silicon in Agriculture Conference[END_REF][START_REF] Kubicki | Molecular orbital modeling of aqueous organosilicon complexes: implications for silica biomineralization[END_REF][START_REF] Peloquin | Recent advances in hexacoordinate silicon with pyridine-containing ligands: Chemistry and emerging applications[END_REF][START_REF] Wang | Adsorption Behavior of Metasilicate on N-Methyl D-Glucamine Functional Groups and Associated Silicon Isotope Fractionation[END_REF]. Such complex formation alters the coordination environment of aqueous Si and thus has an impact on its aqueous-mineral fractionation factor, as has been demonstrated for a large number of stable isotopes [START_REF] Wiederhold | Iron Isotope Fractionation during Proton-Promoted, Ligand-Controlled, and Reductive Dissolution of Goethite[END_REF][START_REF] Domagal-Goldman | Density functional theory predictions of equilibrium isotope fractionation of iron due to redox changes and organic complexation[END_REF][START_REF] Klochko | Re-evaluating boron speciation in biogenic calcite and aragonite using 11B MAS NMR[END_REF][START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF][START_REF] Pokrovsky | Germanium isotope fractionation during Ge adsorption on goethite and its coprecipitation with Fe oxy(hydr)oxides[END_REF][START_REF] Noireaux | Crystallographic control on the boron isotope paleo-pH proxy[END_REF][START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF][START_REF] Saldi | Boron isotopic fractionation during adsorption by calcite -Implication for the seawater pH proxy[END_REF].

Past studies based on Nuclear Magnetic Resonance (NMR) have shown that Si, which usually occurs as the four-coordinated silicic acid (H 4 SiO 4 o

) complex in aqueous solution can form five-and six-coordinated complexes in the presence of organic ligands such as phenols and polyols [START_REF] Cella | 29Si NMR of five-and six-coordinate organosilicon complexes[END_REF][START_REF] Sjöberg | Equilibrium and structural studies of silicon(IV) and aluminium(III) in aqueous solution. 12. A potentiometric and 29 Si-NMR study of silicon tropolonates[END_REF]Kinrade et al., 2001b, Chapter 4. Extreme Si isotope fractionation between silicic acid and organosilicon complexes -95-2002; [START_REF] Kinrade | Silicon-29 NMR studies of aqueous silicate solutions. 1. Chemical shifts and equilibria[END_REF][START_REF] Wang | Adsorption Behavior of Metasilicate on N-Methyl D-Glucamine Functional Groups and Associated Silicon Isotope Fractionation[END_REF]. Furthermore, the direct evidence of a six-coordinated organosilicon compound formed in-vivo has been provided by the 29 Si nuclear resonance study of the fresh water diatom Navicula pelliculosa (Kinrade et al., 2002). Such coordination changes can significantly alter Si isotope fractionation during fluid-(bio)mineral interaction as suggested by [START_REF] Kubicki | Molecular orbital modeling of aqueous organosilicon complexes: implications for silica biomineralization[END_REF]. The objective of this study is to investigate the effect of aqueous organic Si complexation on equilibrium Si isotope fractionation in water-rock systems. This study used catechol (C 6 H 4 (OH) 2 ) as a representative aqueous organic ligand because it readily binds to Si [START_REF] Rosenheim | Über innerkomplexe Brenzcatechinate vierwertiger Elemente[END_REF][START_REF] Barnum | Catechol complexes with silicon[END_REF][START_REF] Pokrovski | Experimental study of the complexation of silicon and germanium with aqueous organic species: implications for germanium and silicon transport and Ge/Si ratio in natural waters[END_REF][START_REF] Gulley-Stahl | Surface Complexation of Catechol to Metal Oxides: An ATR-FTIR, Adsorption, and Dissolution Study[END_REF] and changes the usual 4 coordinated aqueous Si to a hexacoordinated complex with a 6-membered ring structure (Fig. 4. 1;[START_REF] Rosenheim | Über innerkomplexe Brenzcatechinate vierwertiger Elemente[END_REF][START_REF] Sjöberg | Equilibrium and structural studies of silicon(IV) and aluminium(III) in aqueous solution. 12. A potentiometric and 29 Si-NMR study of silicon tropolonates[END_REF][START_REF] Sedeh | Equilibrium and Structural Studies of Silicon(IV) and Aluminium(III) in Aqueous Solution. 30. Aqueous Complexation between Silicic Acid and Some ortho-Di-and Triphenolic Compounds[END_REF][START_REF] Sedeh | Equilibrium and structural studies of silicon(IV) and aluminum(III) in aqueous solution. 31. Aqueous complexation between silicic acid and the catecholamines dopamine and L-DOPA[END_REF][START_REF] Kinrade | Stable Five-and Six-Coordinated Silicate Anions in Aqueous Solution[END_REF]. To determine the equilibrium fractionation factor, this study used the 'three-isotope method'. Experiments were performed at pH ~8.8 and 25°C, with aqueous catechol concentrations of 0.05 M and 0.08 M. The results of these experimental efforts are compared with further ab initio calculations performed in this study. The purpose of this paper is to report the results of this combined experimental and theoretical study and to provide a new insights into the effects of aqueous organic complexations on Si isotope equilibrium fractionation in the biosphere and hydrosphere.

Experimental methods

Starting materials

All experiments were performed using Alpha Aeser ® 100 mesh hydrated silicic acid powder.

Ultrafine particles were removed from this powder by sedimentation following the procedure of [START_REF] Pokrovski | Experimental study of the complexation of silicon and germanium with aqueous organic species: implications for germanium and silicon transport and Ge/Si ratio in natural waters[END_REF]. Fifty grams of the powder was suspended in The average grain size of the recovered silicic acid powder was 23 ± 10 nm as determined using TEM images and the ImageJ software package [START_REF] Schindelin | Fiji: an open-source platform for biological-image analysis[END_REF]. This uncertainty is 2 standard deviation from a mean of 78 measurements. The water content of the powder was determined to be 7.86 % by thermogravimetric analysis using a Mettler Toledo ® ATG/DSC1. This is consistent with the chemical formula SiO 2 0.28 H 2 O. The surface area of the cleaned amorphous SiO 2 powder was determined to be 195.6 m 2 /g with an estimated uncertainty of ± 10% using a Quantachrome Autosorb-1MP, together with the nitrogen multipoint BET method [START_REF] Brunauer | Adsorption of Gases in Multimolecular Layers[END_REF].

Two

Experimental design

The three-isotope method was used in the present study to determine the equilibrium isotopic fractionation factor between amorphous SiO 2 and the selected aqueous catechol solutions. This method permits evaluation of the degree of isotopic exchange between the solid and its coexisting aqueous solution after adding a 29 Si tracer to the aqueous phase. A detailed description of this method is given by previous studies [START_REF] Matsuhisa | Mechanisms of hydrothermal crystallization of quartz at 250°C and 15 kbar[END_REF]Matthews et al., 1983aMatthews et al., , 1983bMatthews et al., , 1983c;;[START_REF] Shahar | Equilibrium high-temperature Fe isotope fractionation between fayalite and magnetite: An experimental calibration[END_REF]Beard et al., 2010;[START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF][START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF][START_REF] Frierdich | Determination of the Fe(II)aq-magnetite equilibrium iron isotope fractionation factor using the three-isotope method and a multi-direction approach to equilibrium[END_REF][START_REF] Reddy | The effect of pH on stable iron isotope exchange and fractionation between aqueous Fe(II) and goethite[END_REF]Zheng et al., 2016;[START_REF] Stamm | The experimental determination of equilibrium Si isotope fractionation factors among H 4 SiO 4 o , H 3 SiO 4 and amorphous silica (SiO 2 •0.32 H 2 O) at 25 ° and 75 °C using the three-isotope method[END_REF].

All experiments performed in this study were conducted at bulk chemical equilibrium but isotopic disequilibrium conditions to minimize the potential effect of kinetics on the isotopic fractionation. The experiments were performed within experimental series consisting of two steps.

Step 1: Equilibration of the reactive aqueous solutions with amorphous SiO 2

Two experimental series were conducted in this study. One with an aqueous 0.05 mol/kg catechol solution and the other with a 0.08 mol/kg catechol solution as described above.

Each solution (200 mL) was first equilibrated with 3 g of washed amorphous SiO 2 powder in a closed polypropylene bottle. The closed bottles were placed in a constantly shaking thermostatic bath at 25°C. The aqueous solutions were regularly sampled over 10 days. The short equilibration period was chosen as catechol decomposes or reacts with ammonia over time in solution [START_REF] Rosenheim | Über innerkomplexe Brenzcatechinate vierwertiger Elemente[END_REF][START_REF] Barnum | Reaction of catechol with colloidal silica and silicic acid in aqueous ammonia[END_REF][START_REF] Pillar | Heterogeneous Oxidation of Catechol[END_REF][START_REF] Pillar | Catechol Oxidation by Ozone and Hydroxyl Radicals at the Air-Water Interface[END_REF]. The pH and concentration of the solutions were measured immediately after each sampling. Aqueous Si concentration of each sample was determined by colorimetry. When both the measured pH and Si concentrations of the sampled solutions attained a constant value, chemical equilibrium was assumed to be attained. These equilibrated solutions were then filtered with Teflon syringe filters (Merck ® 0.2 µm).

Step 2: Isotopic exchange experiments

To employ the three-isotope method, the chemical equilibrated solutions were enriched with a 29 Si isotope tracer solution having an initial composition of 0.21% 28 Si, 99.76% 29 Si, and 0.03% 30 Si, to obtain starting reactive fluids having a δ 29 Si ∼23‰ (see Table 4.1). To ensure that these solutions were still at equilibrium with amorphous SiO 2 after adding the spike, the powder with a known Si isotope composition was placed in 10 ml polypropylene reactors together with 10 ml of the prepared 29 Si enriched aqueous catechol solution. The reactors were wrapped in aluminium foil, to avoid light, and placed in an orbital shaker to be constantly mixed at 25 °C. To verify that the reactors were indeed closed, they were weighted at the beginning and end of each experiment. The experiments were terminated at pre-chosen times. Once an experiment was complete, the reactor was centrifuged for 20 min at 4500 rpm. The supernatant was then separated from the powder and filtered with Merck ® 0.2 µm Teflon syringe filters. The pH and Si concentrations of the recovered aqueous solutions were measured immediately after sampling. These solutions were then immediately prepared for column chromatography to avoid any isotopic fractionation during decomposition of the organic ligand. The powders were washed and filtered with de-ionized Milli-Q ® water, oven dried at 40°C, then stored prior to Si isotopic analysis. [START_REF] Platzner | Modern isotope ratio mass spectrometry, Chemical analysis[END_REF]. δ eq represents the equilibrium isotopic composition of 29

Si and F denotes the degree of isotopic exchange. a denotes the spiked initial solution.

Analytical methods

Characterization of aqueous solutions

The pH of all aqueous solutions was determined using a Metrohm ® 913 pH Meter connected to a standard glass microelectrode. Electrode calibration was performed using certified Orion Thermo Scientific ® buffers. The uncertainty of the measurements was determined to be 0.05, and set equal to 2 standard deviations by repeated measurements (n=40) of the pH=4.01 calibration standard.

Aqueous silicon concentrations were determined by the molybdate blue method [START_REF] Truesdale | Manuel d'analyse des sels nuritifs dans l'eau de mer: Utilisation de L'autoanalyzer II technicon (r)[END_REF] To determine their isotopic compositions, amorphous SiO 2 powders were prepared by an initial calcination of 1-5 mg of the reacted powder at 500°C [START_REF] Cornu | Evidence of titanium mobility in soil profiles, Manaus, central Amazonia[END_REF] and then using the alkali fusion method of [START_REF] Zambardi | Precise Determination of Silicon Isotopes in Silicate Rock Reference Materials by MC-ICP-MS[END_REF], as described in detail by [START_REF] Stamm | The experimental determination of equilibrium Si isotope fractionation factors among H 4 SiO 4 o , H 3 SiO 4 and amorphous silica (SiO 2 •0.32 H 2 O) at 25 ° and 75 °C using the three-isotope method[END_REF]. The sampled aqueous solutions were prepared by a combination of calcination at 500°C, similar to the approach of [START_REF] Cornu | Evidence of titanium mobility in soil profiles, Manaus, central Amazonia[END_REF] for soils, and the modified alkali fusion method of [START_REF] Zambardi | Precise Determination of Silicon Isotopes in Silicate Rock Reference Materials by MC-ICP-MS[END_REF]. Five ml of aqueous solution was evaporated in silver crucibles (XRF scientific, Montreal, Canada). The remaining Si and organic residue was then calcined by heating the crucibles in a furnace at 500°C for 4h, destroying all remaining organic residue thus leaving only the Si of the solution behind. After cooling, ~200 mg of Merck ® NaOH pellets were weighted into these crucibles. The crucibles were capped and placed into a furnace heated at 720°C for 10 min.

After cooling to room temperature the crucibles were placed into 30 ml Savillex ® Teflon beakers filled with 15 ml Milli-Q ® water to dissolve the amorphous SiO 2 powder. The resulting aqueous solutions were transferred after 24 hours into 30 mL polypropylene bottles and diluted with Milli-Q ® water to 20 ml and subsequently acidified with ~10 N bi-distilled HCl to a pH of 1.5.

All samples were purified prior to Si isotope analysis by cation exchange chromatography using 2 ml of Bio-Rad ® AG50W-12X cationic resin filled into 10 ml Bio-Rad ® polypropylene columns. The resin was initially cleaned as described in [START_REF] Georg | New sample preparation techniques for the determination of Si isotopic compositions using MC-ICPMS[END_REF]. After cleaning, 2 ml of the samples were loaded on to the column, directly collected, and eluted twice with 2 ml Milli-Q ® water. The collected fluids were then diluted and acidified to obtain a 3 ppm solution and a total HCl concentration of 0.05 mol/kg. The overall Si recovery was determined to be between 90 and 100 %. The 28 Si signal of the procedural blank was found to be less than < 3% of the total signal and thus considered negligible.

Silicon isotope ratios were determined using the Thermo Scientific Neptune ® MC-ICP-MS located at the Laboratore Géosciences Environnement Toulouse (GET), France.

Measurements were performed under wet plasma conditions in medium resolution. A

Thermo SIS system was used together with a double-pass cyclonic spray chamber to inject the samples into the spectrometer. Instrumental mass bias drift was corrected using samplestandard bracketing combined with Mg addition as an internal standard. Measurements of [START_REF] Russell | Ca isotope fractionation on the Earth and other solar system materials[END_REF] was used to further correct for the mass bias drift.

To ensure the accuracy and precision of the isotopic analysis, the BHVO-2 reference material was repeatedly measured during each run. The reproducibility of δ 30 Si= -0.25 ± 0.16 ‰, and δ 29 Si= -0.13 ± 0.08 ‰ (2 S.D, n=48) was determined, which is in close agreement with measured BHVO-2 values of previous studies (e.g. [START_REF] Abraham | δ 30 Si and δ 29 Si Determinations on USGS BHVO-1 and BHVO-2 Reference Materials with a New Configuration on a Nu Plasma Multi-Collector ICP-MS[END_REF][START_REF] Zambardi | Precise Determination of Silicon Isotopes in Silicate Rock Reference Materials by MC-ICP-MS[END_REF][START_REF] Savage | The silicon isotope composition of the upper continental crust[END_REF][START_REF] Savage | High temperature silicon isotope geochemistry[END_REF].

Speciation calculations

All aqueous speciation calculations in this study were performed using the PHREEQC code (Parkhurst and Appelo, 2013) together with its llnl thermodynamic database, with some minor modifications. First the equilibrium constant for the amorphous SiO 2 dissolution reaction reported by [START_REF] Stamm | The experimental determination of equilibrium Si isotope fractionation factors among H 4 SiO 4 o , H 3 SiO 4 and amorphous silica (SiO 2 •0.32 H 2 O) at 25 ° and 75 °C using the three-isotope method[END_REF] was included in the llnl database; those values were obtained on the same amorphous SiO 2 powder as used in the present study. Second, the dissociation constants of aqueous catechol from [START_REF] Sillen | Stability Constants of Metal-Ion Complexes[END_REF] and the formation constant of the Si-catechol complex from [START_REF] Pokrovski | Experimental study of the complexation of silicon and germanium with aqueous organic species: implications for germanium and silicon transport and Ge/Si ratio in natural waters[END_REF] summarized in Table 4.2 were added to the used llnl database. The equilibrium fractionation factor between the solution and amorphous silica depends on the Si speciation of the solution, and the individual fractionation factors, . 3 &3C ,'( /,-, of each i Si aqueous species with respect to amorphous silica. Therefore, the Si isotopic fractionation factor between the solution and amorphous silica can be expressed as [START_REF] Zhang | Abiologic silicon isotope fractionation between aqueous Si and Fe(III)-Si gel in simulated Archean seawater: Implications for Si isotope records in Precambrian sedimentary rocks[END_REF]:

10 @ AB. /0*12304 &3C ,'( /,- = E F 3 × 3 10 @ AB. 3 &3C ,'( /,- (4.5)
where x i refers to the mole fraction of the subscripted Si aqueous species present in solution.

Ab initio calculations

In this work, we are interested in the equilibrium fractionation of Si isotopes between Sicatechol complexes and amorphous silica or H 4 SiO 4 . To model the Si-catechol complex, we considered the crystalline structure of Li 2 [Si(cat) 3 ] 3.5 dme (cat = catecholate dianion, dme = dimethoxy ethane CH 3 -O-CH 2 -CH 2 -O-CH 3 ) synthesized and characterized by [START_REF] Hahn | Catecholate Complexes of Silicon: Synthesis and Molecular and Crystal Structures of [Si(cat)2].cntdot.2THF and Li2[Si(cat)3].cntdot.3.5dme (cat = Catecholate Dianion)[END_REF]. The modeling of amorphous silica is a difficult task because its structure is not defined. Instead, we considered the cases of SiO 2 -quartz and of dissolved H 4 SiO 4 , which can be seen as two compositional end-members of amorphous silica.

The equilibrium fractionation of silicon isotopes between two phases is obtained by combining the β-factors of both phases. The β-factor corresponds to the isotopic fractionation factor between the phase A and a perfect gas of Si atoms. This quantity can be computed, within the harmonic approximation, from the vibrational frequencies of the phase of interest [START_REF] Bigeleisen | Calculation of Equilibrium Constants for Isotopic Exchange Reactions[END_REF]. All the details regarding the calculation of the βfactor of quartz and of dissolved H 4 SiO 4 in the harmonic approximation are given in [START_REF] Méheut | Equilibrium isotopic fractionation in the kaolinite, quartz ,water system: Prediction from first-principles density-functional theory[END_REF] and [START_REF] Dupuis | Fractionation of silicon isotopes in liquids: The importance of configurational disorder[END_REF], respectively. The β-factor of the Si catecholate model is computed from its phonon frequencies at the Γ-point, center of the Brillouin zone (according to equation ( 5) of [START_REF] Dupuis | Fractionation of silicon isotopes in liquids: The importance of configurational disorder[END_REF]. The phonon frequencies are computed from first-principles using density functional theory (DFT) [START_REF] Hohenberg | Inhomogeneous Electron Gas[END_REF][START_REF] Kohn | Self-Consistent Equations Including Exchange and Correlation Effects[END_REF]. The calculation was based on the exchange-correlation functional of Perdew, Burke and Ernzerhof (PBE) [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF], a plane-wave basis set, and atomic pseudopotentials as implemented in the Quantum Espresso package. The pseudopotentials used for Si, O and H are described in the electronic annexes of [START_REF] Méheut | Equilibrium isotopic fractionation in the kaolinite, quartz ,water system: Prediction from first-principles density-functional theory[END_REF]. The pseudopotential used for Li is taken from the PSlibrary (Dal Corso, 2014).

The pseudopotental used for C is described in [START_REF] Füger | Oxygen isotope fractionation during smithsonite formation from aqueous solutions[END_REF]. Electronic wave-functions are expanded in plane-waves up to an energy cutoff ε cut = 80 Ry and the charge density cutoff is set to 4 ε cut . The electronic structure calculation is performed at the Γ-point of the first Brillouin zone. Phonon frequencies are computed using linear response theory [START_REF] Baroni | Phonons and related crystal properties from density-functional perturbation theory[END_REF] with the Quantum Espresso package [START_REF] Giannozzi | QUANTUM ESPRESSO: a modular and opensource software project for quantum simulations of materials[END_REF].

Results

Attainment of equilibrium between the fluid and amorphous SiO 2

The initial aqueous Si-free solutions with 0.05, and 0.08 mol/kg catechol were first The aqueous solutions show a steady increase and their concentrations begin to stabilize at a constant value after 10 days of equilibration. The aqueous Si concentration of the 0.05 mol/kg catechol solution reaches equilibrium as confirmed with PHREEQC calculations. The final equilibrium concentration of the 0.08 mol/kg catechol solution is ~8 % higher than the corresponding value calculated using PHREEQC, which lies within the error of the calculation; this measured value was thus adopted as the equilibrium Si concentration of this fluid. Note that the presence of aqueous catechol increases substantially the concentration of aqueous Si in equilibrium with amorphous SiO 2 (Fig. 4.3). Assuming that the activity of dissolved silica is equal to the aqueous silica concentration G &3C , the rates of the amorphous silica dissolution (r) in a closed system can be calculated using [START_REF] Rimstidt | The kinetics of silica-water reactions[END_REF]:

H = IJ K ,LM IN = O/P RS T -S G &3C U (4.6)
where S and M refer to the interfacial surface area and mass of solution normalized to 1 kg of water and k + and k -designates amorphous silica dissolution and precipitation constants, respectively. The temporal evolution of dissolved silica concentration in the closed system can be described by [START_REF] Rimstidt | The kinetics of silica-water reactions[END_REF][START_REF] Stamm | The experimental determination of equilibrium Si isotope fractionation factors among H 4 SiO 4 o , H 3 SiO 4 and amorphous silica (SiO 2 •0.32 H 2 O) at 25 ° and 75 °C using the three-isotope method[END_REF]: Representative SEM and TEM images of the amorphous SiO 2 collected from the longest duration experiment in the presence of 0.08 ml/kg catechol were obtained, and are provided in Fig. 2C andD. These solids appear close to identical to the pre-treated amorphous SiO 2

C K = C K WX R1 -e Z.\ ] U (4.7) Noting that ^_ ] ^ ] = G K WX ,
prior to the experiments. The grain sizes of the reacted powders were determined to be 21 ± 9 nm (n=100, 2 S.D.), which is identical to that of the initial cleaned powder. The water content, however, was lower; it was reduced from an initial value of 7.86 % to 6.54 % consistent with the chemical formula SiO Equilibrium Si fractionation factors, ∆ eq 30 Si Si aq -SiO 2 ,am , were calculated iteratively as described in detail in [START_REF] Stamm | The experimental determination of equilibrium Si isotope fractionation factors among H 4 SiO 4 o , H 3 SiO 4 and amorphous silica (SiO 2 •0.32 H 2 O) at 25 ° and 75 °C using the three-isotope method[END_REF]. In brief the equilibrium isotopic composition of amorphous silica (δ 30 Si SiO 2 ,am ) and the solution (δ 30 Si aq ) were obtained from a plot of measured δ 30 Si Si aq and δ 30 Si SiO 2 ,am as a function of the degree of isotopic exchange F and linear extrapolation of δ 30 Si values to 100% isotope exchange (F=1). F was calculated using Si Si aq -SiO 2 ,am retrieved by this analysis are provided in Table 4.4. As mentioned above, the isotopic measurements of the fluid and solid recovered from the longest duration experiment of the 0.08 mol/kg catechol series was excluded due to a significant decrease in its aqueous Si concentration. This exclusion, however, did not significantly affect the retrieved values of ∆ eq 30 Si Si aq -SiO 2 ,am .

Values of ∆ eq 30 Si Si aq -SiO 2 ,am generated from the experiments performed in this study from the experimental series run in the 0.05 mol/kg catechol solutions was -16.45 ± 1.75 ‰ and that obtained from the experiments run on the presence of 0.08 mol/kg catechol was -18.60 ± 3.44 ‰. This isotope fractionation is dramatically higher than that determined with the same amorphous SiO 2 powder in the absence of catechol at pH 6.4 reported by [START_REF] Stamm | The experimental determination of equilibrium Si isotope fractionation factors among H 4 SiO 4 o , H 3 SiO 4 and amorphous silica (SiO 2 •0.32 H 2 O) at 25 ° and 75 °C using the three-isotope method[END_REF]. That study reported an equilibrium fractionation factor between an organic-ligand free aqueous solution and amorphous SiO 2 of -0.45 ± 0.22 ‰ (see Table 4.4).

The extreme variation of ∆ eq 30 Si Si aq -SiO 2 ,am can be attributed to the complexation of Si to aqueous catechol in solution taking account of the distribution of the aqueous species, calculated with PHREEQC and listed in Table 4.4. The major aqueous species is represented by the Si catecholate complex (Si-Cat) with 86 % and 91 % for the 0.05 mol/kg and the 0.08 mol/kg catechol experiment, respectively. Note that the H 3 SiO 4 -species in solution represents less than 5 % of total Si speciation, which lies within the error of the calculation and is therefore considered as negligible. Therefore the Si catecholate and H 4 SiO 4 o species will be assumed to be 100 % of total Si-speciation in solution. Using Eqn. (4.5) the equilibrium isotopic fractionation factor between the Si catecholate complex and amorphous SiO 2 (∆ +f @g Si hiZ K ,'( ) can be calculated for both experimental solutions and are shown in Tab. 4. Moreover, knowing the fractionation between H 4 SiO 4 0 and amorphous silica [START_REF] Stamm | The experimental determination of equilibrium Si isotope fractionation factors among H 4 SiO 4 o , H 3 SiO 4 and amorphous silica (SiO 2 •0.32 H 2 O) at 25 ° and 75 °C using the three-isotope method[END_REF], it is possible to determine the equilibrium fractionation factor between Si catecholate and H 4 SiO 4 o (∆ +f @g Si hiZ j k K k l).

The experimentally derived equilibrium fractionation factors result in two distinct isotopic fractionation factors: ∆ +f @g Si hiZ K ,'( of -19.50 ± 0.97 ‰ and a ∆ +f @g Si hiZ j k K k l of -19.05 ± 0.49 ‰.

Ab initio calculations performed in this study predict that isotopic fractionation between Si catecholate and quartz ∆ +f @g Si hiZ mnioZp can expected to be -21.03 ‰ at 25 °C.

Based on the theoretical value of the fractionation factor between quartz and H 4 SiO 4 0 generated at 25°C by [START_REF] Dupuis | Fractionation of silicon isotopes in liquids: The importance of configurational disorder[END_REF], ∆ +f @g Si q k C k l mnioZp -2.10 ‰ the fractionation factor between Si catecholate and H 4 SiO 4 o ∆ +f @g Si hiZ j k K k l at 25 °C is calculated to be -18.91 ‰ at 25°C, and thus slightly heavier than ∆ +f @g Si hiZ mnioZp . This value is in excellent agreement with that determined experimentally in the present study.

Isotope exchange kinetics

The rate with which isotopic equilibrium is attained helps constraining the mechanism of the isotope exchange process. Fig. 4.7 shows the temporal evolution of the degree of isotopic exchange (F) in the absence of organic ligand [START_REF] Stamm | The experimental determination of equilibrium Si isotope fractionation factors among H 4 SiO 4 o , H 3 SiO 4 and amorphous silica (SiO 2 •0.32 H 2 O) at 25 ° and 75 °C using the three-isotope method[END_REF], and of in the presence of aqueous catechol. The curves in this figure are generated assuming a first order rate law [START_REF] Cole | Rates and Mechanisms of Isotopic Exchange[END_REF][START_REF] Johnson | Isotopic fractionation between Fe(III) and Fe(II) in aqueous solutions[END_REF][START_REF] Stamm | The experimental determination of equilibrium Si isotope fractionation factors among H 4 SiO 4 o , H 3 SiO 4 and amorphous silica (SiO 2 •0.32 H 2 O) at 25 ° and 75 °C using the three-isotope method[END_REF] and using the rate constants retrieved form the silica equilibration experiments and provided in Table 4.3. It can be seen that the isotope exchange of the catechol experiments is rapid during the first 1.5 days. After this time the exchange reaction rate slows noticeable. The solutions reached only ∼60 to 70 % of isotopic equilibrium over the 7 days of the isotopic exchange experimental series which is significantly less than the degree of isotopic exchange attained in the absence of organic ligand over the same period of time (∼82%).

Discussion

Silicon isotope fractionation in the presence of catechol

The equilibrium fractionation factor ∆ eq 30 Si Si aq -SiO 2 ,am determined in this study in the presence of 0.05 mol/kg and 0.08 mol/kg catechol exhibits a much stronger fractionation of -16.45 ± 1.74 ‰ and -18.60 ± 3.44 ‰, respectively, than that determined in catechol-free solution by Stamm et al. 2019 (∆ eq 30 Si Si aq -SiO 2 ,am = -0.45 ‰). The solid is enriched in the heavier isotopes in both studies but to a much greater extent in the presence of catechol. The strong isotopic fractionation observed in our experiments can be attributed to the formation of organosilicon complexes. Aqueous catechol complexes strongly with Si [START_REF] Barnum | Catechol complexes with silicon[END_REF][START_REF] Barnum | Reaction of catechol with colloidal silica and silicic acid in aqueous ammonia[END_REF][START_REF] Cella | 29Si NMR of five-and six-coordinate organosilicon complexes[END_REF][START_REF] Pokrovski | Experimental study of the complexation of silicon and germanium with aqueous organic species: implications for germanium and silicon transport and Ge/Si ratio in natural waters[END_REF][START_REF] Gulley-Stahl | Surface Complexation of Catechol to Metal Oxides: An ATR-FTIR, Adsorption, and Dissolution Study[END_REF] and this complexation leads to a Si coordination change [START_REF] Cella | 29Si NMR of five-and six-coordinate organosilicon complexes[END_REF][START_REF] Boudin | Reactivity of dianionic hexacoordinated silicon complexes toward nucleophiles: a new route to organosilanes from silica[END_REF][START_REF] Kinrade | Stable Five-and Six-Coordinated Silicate Anions in Aqueous Solution[END_REF]Kinrade et al., 2001aKinrade et al., , 2001b;;[START_REF] Benner | Hydrogen-Bonded Sugar-Alcohol Trimers as Hexadentate Silicon Chelators in Aqueous Solution[END_REF][START_REF] Kubicki | Molecular orbital modeling of aqueous organosilicon complexes: implications for silica biomineralization[END_REF]. In the present case, the complexation of silicon with catechol leads to a six-fold coordination of the Si atom bonded to thee catechol molecules. This coordination change is responsible for the strong equilibrium Si fractionation observed in this study.

Our experimental results and ab initio calculations are in close agreement. The equilibrium fractionation factor between the Si-catecholate complex and quartz at 25°C was calculated to be ~ -21 ‰. The experimental ∆ eq 30 Si SiCat-SiO 2 ,am determined in this study is equal to -19.50 ± 0.97 ‰. This result matches that generated from our ab initio calculations within uncertainty. A similar close agreement between experimental results and ab initio calculations were found for the equilibrium fractionation factor between Si-catecholate and silicic acid, with experimental and theoretical ∆ eq 30 Si SiCat-H 4 SiO 4 ° values of -19.05 ± 0.49 ‰ and -18.9 ‰, respectively These close agreements validate our interpretation that the presence of aqueous catechol is responsible for the large equilibrium isotopic fractionation observed in this study. Note that the amount of catechol used in our experimental study is far higher than that typically found in nature. Yet even a small concentration of catechol or any organic ligand forming with Si organosilicon complexes containing hexaoxo-or pentaoxosilicon sites can have a significant effect on the equilibrium fractionation factors between aqueous Si and co-existing solid phases.

Si isotope exchange kinetics in the presence of catechol

Our isotope exchange experiments began by first equilibrating amorphous SiO 2 with aqueous solutions containing either 0.05 or 0.08 mol/kg catechol. The temporal variation of Si concentration in the aqueous fluids during this equilibration step yields amorphous silica dissolution rates in these systems. The rates obtained from these equilibration steps are 9.72 x 10 -11 to 1.65 x 10 -10 mol/m 2 /s, and increase with increasing catechol concentration (see Table 3). These rates are slightly faster than those obtained for amorphous SiO 2 dissolution in aqueous organic-ligand free solutions at pH 6.4 in [START_REF] Stamm | The experimental determination of equilibrium Si isotope fractionation factors among H 4 SiO 4 o , H 3 SiO 4 and amorphous silica (SiO 2 •0.32 H 2 O) at 25 ° and 75 °C using the three-isotope method[END_REF] using the identical amorphous silica powder. The rates obtained in this study in the presence of aqueous catechol are also faster than those reported for different amorphous silica powders obtained in organic-ligand free solutions by [START_REF] Brady | Controls on silicate dissolution rates in neutral and basic pH solutions at 25°C[END_REF], [START_REF] Plettnick | Kinetics and mechanisms of dissolution of silica at room temperature and pressure[END_REF][START_REF] Fraysse | Surface properties, solubility and dissolution kinetics of bamboo phytoliths[END_REF]. The presence of aqueous organic ligands, such as catechol, have been reported to enhance silicate mineral dissolution rates in a number of studies [START_REF] Bennett | The dissolution of quartz in dilute aqueous solutions of organic acids at 25°C[END_REF][START_REF] Bennett | Quartz dissolution in organic-rich aqueous systems[END_REF][START_REF] Bennett | Chemistry and Mechanisms of Low-Temperature Dissolution of Silicates by Organic Acids[END_REF][START_REF] Ganor | Organics in Water-Rock Interactions[END_REF][START_REF] Schott | The Link Between Mineral Dissolution/Precipitation Kinetics and Solution Chemistry[END_REF].

The application of the three-isotope method allows evaluation of the kinetics of isotopic exchange and hence can provide insight into the mechanism driving isotopic equilibration. The rates of isotopic equilibration in this study were generated following the approach of [START_REF] Cole | Rates and Mechanisms of Isotopic Exchange[END_REF] and [START_REF] Johnson | Isotopic fractionation between Fe(III) and Fe(II) in aqueous solutions[END_REF] using:

-I 1 -d IN = S 4 1 -d 4 (4.9)
where k is the rate constant and n the order of reaction. Typically isotope exchange rates follow either a first-order (n=1) or a second-order (n=2) rate law [START_REF] Criss | Kinetic theory of oxygen isotopic exchange between minerals and water[END_REF][START_REF] Huang | Kinetic studies on the isotopic exchange of calcium ion and calcium carbonate[END_REF][START_REF] Johnson | Isotopic fractionation between Fe(III) and Fe(II) in aqueous solutions[END_REF][START_REF] Welch | Kinetic and equilibrium Fe isotope fractionation between aqueous Fe(II) and Fe(III)[END_REF][START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF]Zheng et al., 2016).

The integrated form of Eqn. (4.7) can thus be written as

ln 1 -F = -k v t for n=1 (4.10) x v x = k , t for n=2 (4.11)
In the present study the first order rate equation (Eqn. 4. 4.6). This suggests that within the first 1.5 days the rate controlling mechanism is the detachment and reattachment of material to the amorphous silica surface, whereas, for longer times, the rate controlling mechanism is the Si transport within the amorphous silica grain. Silicon is an essential element in biological processes. It is an important structural component for plants, phytoplankton, zooplankton and sponges [START_REF] Poitrasson | Silicon Isotope Geochemistry[END_REF]. Various sea sponges and microorganisms, such as diatoms and radiolarian, secrete skeletal structures in silica via dissolved Si uptake [START_REF] Hendry | Silicon isotopes in Antarctic sponges: an interlaboratory comparison[END_REF]. Species-dependent silicon isotope fractionation ranging from -0.5 to -2 ‰ has been reported for marine diatoms [START_REF] Sutton | Species-dependent silicon isotope fractionation by marine diatoms[END_REF] whereas fractionation up to -6.5 ‰ between sponges spicules and co-existing fluids have been measured [START_REF] Douthitt | The geochemistry of the stable isotopes of silicon[END_REF][START_REF] Wischmeyer | Control mechanisms for the oceanic distribution of silicon isotopes[END_REF][START_REF] Wille | Silicon isotopic fractionation in marine sponges: A new model for understanding silicon isotopic variations in sponges[END_REF][START_REF] Hendry | Deep ocean nutrients during the Last Glacial Maximum deduced from sponge silicon isotopic compositions[END_REF][START_REF] Hendry | Silicon isotopes in Antarctic sponges: an interlaboratory comparison[END_REF][START_REF] Hendry | The relationship between silicon isotope fractionation in sponges and silicic acid concentration: Modern and core-top studies of biogenic opal[END_REF]. H 4 SiO 4 o is taken up by the sponge through a sodium transporter, and is subsequently precipitated via a central organic filament [START_REF] Hendry | Silicon isotopes in Antarctic sponges: an interlaboratory comparison[END_REF]. The biomineralization occurs with the help of the enzyme silicatein [START_REF] Perry | Silicification: The Processes by Which Organisms Capture and Mineralize Silica[END_REF][START_REF] Uriz | Siliceous spicules and skeleton frameworks in sponges: Origin, diversity, ultrastructural patterns, and biological functions[END_REF][START_REF] Müller | The unique skeleton of siliceous sponges (Porifera; Hexactinellida and Demospongiae) that evolved first from the Urmetazoa during the Proterozoic: a review[END_REF]. This enzyme is considered by some studies to form five coordinated intermediates (Kinrade et al., 2002, Zhou et al., 1999). The important fractionation reported in sponge spicules therefore could be explained by the change in coordination of Si due to the enzyme silicatein, which then would lead to the preferential incorporation of light Si isotopes into the spicules.

Like sponges and diatoms, plants preferentially incorporate light Si isotopes into their structure during the incorporation of Si from the soil solutions [START_REF] Ding | Silicon isotope study on rice plants from the Zhejiang province, China[END_REF][START_REF] Sun | Silicon isotope fractionation in rice plants, an experimental study on rice growth under hydroponic conditions[END_REF][START_REF] Delvigne | Distinct silicon and germanium pathways in the soil-plant system: Evidence from banana and horsetail: distinct Si and Ge pathways in plants[END_REF][START_REF] Opfergelt | Silicon isotopes and continental weathering processes: Assessing controls on Si transfer to the ocean[END_REF][START_REF] Sun | Effects of growth and dissolution on the fractionation of silicon isotopes by estuarine diatoms[END_REF].

However, the biochemistry of Si in plants is not well known, and only a few Si transporters in plants have been yet identified [START_REF] Poitrasson | Silicon Isotope Geochemistry[END_REF]. [START_REF] Kubicki | Molecular orbital modeling of aqueous organosilicon complexes: implications for silica biomineralization[END_REF] advocated that the Si transport may not occur as H 4 SiO 4 o through plant, but as hypercoordinated organosilicon complexes formed by silicon with phenols or carbohydrates molecules containing at least four adjacent hydroxyl groups. The results presented in this study suggest that such hypercoordinated organosilicon complexes would lead to a strong negative fractionation between the fluid phase and Si incorporated in the plant structure.

As aqueous Si complexion can readily alter the fractionation of this metal into solids, and as aqueous ligands are abundant in various organisms, it seems reasonable to conclude that much insight could be gained into the biomineralizaion process if it were possible to interpret quantitatively the Si isotopic signals in biomaterials. Such will only be the case if we are able to quantify in detail the degree to which some aqueous Si-organic compounds alter equilibrium fractionation factors. The results in this study show that both rigorous experiments and detailed ab initio calculations can aid in this effort.

Conclusion

The results of this study demonstrate that the formation of organosilicon complexes containing hexaoxo-silicon sites rather than the four-coordinated Si centres typical of aqueous silica species can have an important influence on the equilibrium isotope fractionation between fluids and Si-bearing solids. Indeed it was shown in the present study that the equilibrium fractionation factor between quartz (amorphous silica) and the Sicatechol complex is about 20 ‰ lighter than the equilibrium factor between quartz (amorphous silica) and silicic acid. These values are in close agreement with the results of ab initio calculation performed in this study demonstrating the robustness of both type of Si isotopes quantifications. Note that the Si isotope composition of organosilicon complexes containing pentaoxo-silicon is likely to be also much lighter, by about 10 ‰ than that of H 4 SiO 4 °. Such results demonstrate that the presence of aqueous organic ligands in natural systems can play an important role on the Si isotopes fractionation and thus might explain the strong negative fractionation found in biological systems.

Chapter 5 Determination of the equilibrium magnesium isotope fractionation factors between brucite and aqueous Mg inorganic and organic species

A version of this chapter will be submitted for publication as: "Franziska M. Stamm, Thomas Zambardi, Jérôme Chmeleff, Jacques Schott, Eric H. Oelkers: Determination of the equilibrium magnesium isotope fractionation factors between brucite and aqueous inorganic and organic species"

Introduction

Magnesium is a key element in continental weathering, in hydrological systems, such as the carbonate precipitation in oceans, in diagenetic reactions, as well as in biochemical processes [START_REF] Brenot | Magnesium isotope systematics of the lithologically varied Moselle river basin, France[END_REF][START_REF] Pogge Von Strandmann | Lithium, magnesium and uranium isotope behaviour in the estuarine environment of basaltic islands[END_REF][START_REF] Hippler | Towards a better understanding of magnesium-isotope ratios from marine skeletal carbonates[END_REF][START_REF] Foster | Boron and magnesium isotopic composition of seawater: DATA BRIEF[END_REF][START_REF] Immenhauser | Magnesium-isotope fractionation during low-Mg calcite precipitation in a limestone cave -Field study and experiments[END_REF][START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF][START_REF] Wimpenny | The behaviour of magnesium and its isotopes during glacial weathering in an ancient shield terrain in West Greenland[END_REF]Opfergelt et al., 2012;[START_REF] Pogge Von Strandmann | Lithium, magnesium and silicon isotope behaviour accompanying weathering in a basaltic soil and pore water profile in Iceland[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF][START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF][START_REF] Liu | Massive magnesium depletion and isotope fractionation in weathered basalts[END_REF][START_REF] Kasemann | Continental weathering following a Cryogenian glaciation: Evidence from calcium and magnesium isotopes[END_REF]Mavromatis et al., 2014a;[START_REF] Opfergelt | Magnesium retention on the soil exchange complex controlling Mg isotope variations in soils, soil solutions and vegetation in volcanic soils, Iceland[END_REF][START_REF] Wimpenny | Investigating the behaviour of Mg isotopes during the formation of clay minerals[END_REF][START_REF] Gao | Magnesium isotope fractionation during dolostone weathering[END_REF][START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF][START_REF] Oelkers | The temporal evolution of magnesium isotope fractionation during hydromagnesite dissolution, precipitation, and at equilibrium[END_REF]. The behaviour of Mg isotopes during these processes could be applied to understand the Mg geochemical cycle and to precisely reconstruct paleoclimate conditions.

Numerous studies have been aimed at quantifying Mg fractionation during the formation of various minerals including calcite, dolomite, magnesite or brucite [START_REF] Immenhauser | Magnesium-isotope fractionation during low-Mg calcite precipitation in a limestone cave -Field study and experiments[END_REF][START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF][START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF]Mavromatis et al., , 2014a)). These studies showed that these carbonate minerals and brucite preferentially incorporate light Mg isotopes, whereas epsomite and clay minerals are likely to incorporate heavy Mg isotopes (Tipper et al., 2006a;[START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF]Tipper et al., 2012aTipper et al., , 2012b;;Opfergelt et al., 2012). In biological environments, plant roots can be enriched in heavy Mg isotopes, whereas the upper parts of the plants are isotopically lighter [START_REF] Bolou-Bi | Effects of biogeochemical processes on magnesium isotope variations in a forested catchment in the Vosges Mountains (France)[END_REF]. These differences can stem from the different bonding environments of Mg, in most cases the bond lengths between magnesium and oxygen ions [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF]. Mg isotopic signatures can also be significantly affected by reaction kinetics during solidsolution interactions (i.e. transport to and from the reacting interface, dissolution or precipitation), such as shown by [START_REF] Schott | The Link Between Mineral Dissolution/Precipitation Kinetics and Solution Chemistry[END_REF], [START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF], and [START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF]. Another reason for the differences in Mg fractionation in mineral-aqueous solutions systems is the Mg aqueous speciation in the aqueous fluid [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF][START_REF] Mavromatis | Effect of organic ligands on Mg partitioning and Mg isotope fractionation during low-temperature precipitation of calcite in the absence of growth rate effects[END_REF]. The influence of aqueous speciation on isotopic fractionation has already been demonstrated not only for magnesium but also for boron, carbon, mercury, silicon and several transition metals [START_REF] Hemming | Boron isotopic composition and concentration in modern marine carbonates[END_REF][START_REF] Zhang | Abiologic silicon isotope fractionation between aqueous Si and Fe(III)-Si gel in simulated Archean seawater: Implications for Si isotope records in Precambrian sedimentary rocks[END_REF][START_REF] Zeebe | Stable boron isotope fractionation between dissolved B(OH) 3 and B(OH) 4[END_REF][START_REF] Klochko | Experimental measurement of boron isotope fractionation in seawater[END_REF][START_REF] Klochko | Re-evaluating boron speciation in biogenic calcite and aragonite using 11B MAS NMR[END_REF][START_REF] Asael | Fluid speciation controls of low temperature copper isotope fractionation applied to the Kupferschiefer and Timna ore deposits[END_REF][START_REF] Holloway | Ammonium in thermal waters of Yellowstone National Park: Processes affecting speciation and isotope fractionation[END_REF][START_REF] Jiskra | Solution Speciation Controls Mercury Isotope Fractionation of Hg(II) Sorption to Goethite[END_REF][START_REF] Ryan | Copper speciation and isotopic fractionation in plants: uptake and translocation mechanisms[END_REF][START_REF] Yin | Mercury speciation and mercury isotope fractionation during ore roasting process and their implication to source identification of downstream sediment in the Wanshan mercury mining area SW China[END_REF][START_REF] Fujii | Density functional theory estimation of isotope fractionation of Fe, Ni, Cu, and Zn among species relevant to geochemical and biological environments[END_REF][START_REF] Fujii | Isotope fractionation of Si in protonation/deprotonation reaction of silicic acid: A new pH proxy[END_REF][START_REF] Dupuis | Fractionation of silicon isotopes in liquids: The importance of configurational disorder[END_REF][START_REF] Noireaux | Crystallographic control on the boron isotope paleo-pH proxy[END_REF][START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF][START_REF] Balan | Theoretical isotopic fractionation between structural boron in carbonates and aqueous boric acid and borate ion[END_REF][START_REF] Mavromatis | Zinc isotope fractionation during the inorganic precipitation of calcite -Towards a new pH proxy[END_REF]. The influence of the bonding environment of the metal and the reaction kinetics on the equilibrium fractionation factor in mineral-solution reaction is yet not fully understood.

Several past studies have aimed to experimentally and theoretically determine the Mg equilibrium fractionation factor between minerals and the coexisting aqueous solutions [START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF][START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF][START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF][START_REF] Mavromatis | Effect of organic ligands on Mg partitioning and Mg isotope fractionation during low-temperature precipitation of calcite in the absence of growth rate effects[END_REF][START_REF] Colla | Computational prediction of Mg-isotope fractionation between aqueous [Mg(OH 2 ) 6 ] 2+ and brucite[END_REF][START_REF] Gao | Theoretical calculation of equilibrium Mg isotope fractionations between minerals and aqueous solutions[END_REF]. The studies of [START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF], [START_REF] Colla | Computational prediction of Mg-isotope fractionation between aqueous [Mg(OH 2 ) 6 ] 2+ and brucite[END_REF] and [START_REF] Gao | Theoretical calculation of equilibrium Mg isotope fractionations between minerals and aqueous solutions[END_REF] focussed on the fractionation between brucite and its co-existing aqueous solution. Brucite, also used in this study, is an important secondary mineral, which occurs in a wide range of geological settings (e.g. [START_REF] Hostetler | Brucite in alpine serpentinites[END_REF][START_REF] Alabaster | An occurrence of brucite at Merehead Quarry, Cranmore, Somerset[END_REF][START_REF] Brown | Petrologic and stable isotope constraints on the source and evolution of skarn-forming fluids at Pine Creek, California[END_REF][START_REF] Bach | Unraveling the sequence of serpentinization reactions: petrography, mineral chemistry, and petrophysics of serpentinites from MAR 15°N (ODP Leg 209, Site 1274[END_REF][START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF]. It has a structure similar to phyllosilicates and is therefore believed to be a suitable proxy for studying Mg isotopic fractionation during the weathering and alteration of Mg silicate rocks [START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF]. Brucite also occurs in the skeletons of corals, diatoms and algae [START_REF] Weber | Brucite in the Caleareous Alga Goniolithon[END_REF][START_REF] Nothdurft | Brucite microbialites in living coral skeletons: Indicators of extreme microenvironments in shallow-marine settings[END_REF][START_REF] Buster | Magnesium content within the skeletal architecture of the coral Montastraea faveolata: locations of brucite precipitation and implications to finescale data fluctuations[END_REF][START_REF] Tesson | Brucite formation mediated by the diatom Phaeodactylum tricornutum[END_REF] where it is involved in biomineralization processes.

The experimental values obtained by [START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF] show that brucite in the presence of ligand-free solution preferentially incorporates light Mg isotopes resulting in a ∆ eq 26 Mg brucite-solution of -0.17 ± 0.07 ‰. This result, however, is inconsistent with the ab inito calculations reported by [START_REF] Colla | Computational prediction of Mg-isotope fractionation between aqueous [Mg(OH 2 ) 6 ] 2+ and brucite[END_REF] and [START_REF] Gao | Theoretical calculation of equilibrium Mg isotope fractionations between minerals and aqueous solutions[END_REF], who proposed a fractionation factor ∆ eq 26 Mg brucite-solution of 2.7 and 3.3 ‰, respectively. Additionally, [START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF] reported a fractionation factor between brucite and EDTA, ∆ eq 26 Mg brucite-MgEDTA 2- ≥ 2.0 ‰. This value is in good agreement with the ab initio calculations reported by [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF]. This study also reported the Mg isotope fractionation factors among aqueous Mg 2+ species and numerous aqueous inorganic and organic complexes including Mg(citrate) - , MgSO 4 o , MgHCO 3 + , MgCO 3 °.

The aim of this study is to experimentally determine the equilibrium Mg isotope fractionation factors between brucite and aqueous Mg in the presence and absence of inorganic and organic ligands at 25°C. The 'three isotope method' was adopted in this study to determine unambiguously these fractionation factors at equilibrium. This paper reports the results of the experimental study, which are compared with corresponding results generated from existing computational models. Taken together, these results will provide new insight into how aqueous solution speciation can affect the Mg equilibrium isotopic fractionation among minerals and aqueous solutions.

Methods

Starting materials

Brucite synthesis

The experiments in this study were performed using microcrystalline brucite (Mg(OH) 2 ).

This brucite was synthesized by the wet precipitation method of [START_REF] Henrist | Morphological study of magnesium hydroxide nanoparticles precipitated in dilute aqueous solution[END_REF], [START_REF] Lv | Controlled growth of three morphological structures of magnesium hydroxide nanoparticles by wet precipitation method[END_REF][START_REF] Estrada | Interaction between l -aspartate and the brucite [Mg(OH) 2 ]-water interface[END_REF]. Consistent with this method, 100 ml of an aqueous 2M MgCl 2 •6 H 2 O solution was prepared and added dropwise at a rate of 2.5 ml/min using a Metrohm ® 702 SM Titrino titrator, into 200 ml of a constantly stirred 45°C suprapur Merck ® 25% NH 3 solution. Brucite nanoparticles form immediately and serve as precipitation nuclei for the growth of larger brucite crystals. The larger crystals form by the aging of the solidsolution suspension. The reaction vessel was thereby sealed and left at room temperature.

After three days the precipitated brucite powder was filtered, washed with Milli-Q ® water and subsequently dried at 135° C for 1 h. The resulting solids were then allowed to further dry overnight at 60°C. A hydrothermal treatment, as proposed by [START_REF] Henrist | Morphological study of magnesium hydroxide nanoparticles precipitated in dilute aqueous solution[END_REF], [START_REF] Lv | Controlled growth of three morphological structures of magnesium hydroxide nanoparticles by wet precipitation method[END_REF][START_REF] Estrada | Interaction between l -aspartate and the brucite [Mg(OH) 2 ]-water interface[END_REF] to improve brucite crystallinity, was not performed. The dried powder was analysed by X-ray diffraction using a 2 nd Generation Bruker ® D2 Phaser, to determine the purity of the precipitated phase. The morphology of these solids were analysed using a MEB JEOL JSM-7800F Prime electron microscope (SEM) at the Raimond Castaing Microcharacterization Centre (Toulouse, France). Images of two representative synthesized brucite powders are shown in Fig. 5.1 A and B. The specific surface areas of these powders were determined using a Quantachrome Autosorb-1MP together with the nitrogen multipoint BET method [START_REF] Brunauer | Adsorption of Gases in Multimolecular Layers[END_REF] within an estimated uncertainty of ± 10%. Details of the synthesized brucite powders used in this study are listed in Table 5.1.

Characterization of sampled experimental solutionss

Aqueous solution samples were collected from all experiments. The pH of these samples was measured using a Metrohm ® 913 pH Meter connected to a standard glass microelectrode with a 2 SD uncertainty of 0.05. The magnesium concentrations of these samples were determined by Flame Atomic Absorption Spectroscopy (F-AAS). These analyses were performed for concentrations from 0.1 to 0.6 ppm Mg using a Perkin Elemer AAnalyst 400. Analytic standards were prepared using an identical matrix to that of the experimental series analysed to avoid interference during measurements. The limit of detection (LOD) and the limit of quantification (LOQ) of these measurements were determined for each matrix to be 5 ppb and 1 ppb, respectively. These measurements had an uncertainty of ±1%.

solutions were re-measured, and the collected solutions used in the second step of each experimental series for the isotopic exchange experiments (see Table 5.3). 5.3). In addition the pH of these solutions were adjusted with bi-distilled HCl or suprapur NaOH solution if necessary.

Step 2 of each experimental series were performed as 8 individual batch reactor experiments, which ran for as long as 263 to 522 days depending on the series. For each individual experiment, a known quantity of synthesized brucite powder was placed in 10 ml polypropylene reactors together with the prepared 25 Mg enriched solutions. The masses of solution and solid in each reactor are provided in Table 5. were washed with de-ionized Milli-Q ® water and oven dried at 40°C, and later analysed for Mg isotope composition.

Data reporting and Mg isotope analysis

The isotopic compositions of the magnesium bearing powders and the experimental solutions collected from the isotope exchange experiments, the initial chemical equilibrated solutions, and the spiked initial solutions were measured using a Thermo Scientific Neptune ® MC-ICP-MS at the Obersvatoire Midi-Pyrénées / Laboratoie Géosciences Environnement Toulouse (GET), France.

The obtained Mg isotopic compositions of 26 Mg and 25 Mg in the samples are expressed with the standard δ-notation in per mil (‰) relative to the international DSM-3 standard following the relation:

Mg = ( / ) ( / )
-1 × 1000

(5.1)

and

! Mg = ( " / ) ( " / )
-1 × 1000

(5.

2)

The Mg fractionation factor between an aqueous solution and a solid (# $%&'()*&+'( / ,

) is defined as: ( 5.3) or as ∆ Mg $%&'()*&+'( , which is expressed by: ∆ Mg $%&'()$%&+-'%. = Mg $%&'( -Mg $%&+-'%.

(5.4)

Note that as # $%&'()$%&+-'%.

/ , ≈ 1, ∆ Mg $%&'()$%&+-'%. is approximately related to

# $%&'()$%&+-'%.
/ , by:

∆ Mg $%&'()$%&+-'%. ≈ 10 : ;<# $%&'()$%&+-'%. / , .

(5.5)

The samples were prepared for MC-ICP-MS measurements using an approach similar to that of [START_REF] Teng | Investigation of magnesium isotope fractionation during basalt differentiation: Implications for a chondritic composition of the terrestrial mantle[END_REF], [START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF], 2014a, 2014b).

One mg of sampled brucite or JDo-1 dolomitic carbonate standard powder were dissolved into 2 ml 15 N bi-distilled HNO 3 , and subsequently evaporated to dryness at 120°C. This residual was then re-dissolved into 5 ml 1 N HNO 3 . The Mg concentration of these solution were determined using F-AAS. Aliquots containing 15 µg Mg were once again evaporated and re-dissolved into 2 ml 1 N HNO 3 . For the experimental solutions and the IAPSO seawater standard, aliquots containing 15µg Mg were evaporated to dryness, then redissolved into 2 ml 1 N HNO 3 . For solutions containing organic ligands (i.e. citrate or EDTA) ~0.5 ml of 30 % H 2 O 2 was added to the solutions and left to react between 3-6 hours prior to evaporation to remove these species.

All samples were purified by cation exchange chromatography using 1 ml Bio-Rad ® AG50W-12X 200-400 mesh cationic resin. The resin was originally cleaned and the samples were eluted as described by [START_REF] Teng | Investigation of magnesium isotope fractionation during basalt differentiation: Implications for a chondritic composition of the terrestrial mantle[END_REF]. As Mg isotopes could be significantly fractionated during ion exchange [START_REF] Chang | Purification of Mg from low-Mg biogenic carbonates for isotope ratio determination using multiple collector ICP-MS[END_REF][START_REF] Teng | Investigation of magnesium isotope fractionation during basalt differentiation: Implications for a chondritic composition of the terrestrial mantle[END_REF], it was necessary to obtain close to 100% Mg yields from the column chemistry; Mg yields were determined by F-AAS to be ~97 %. The average 24 Mg signal of the procedural blank was found to be less than < 0.5% of the total 24 Mg signal and were therefore considered negligible.

Magnesium isotope ratio measurements were performed in low resolution at aqueous Mg concentrations of 600 ppb. A Thermo SIS system was used together with a double-pass cyclonic spray chamber to introduce the samples, after their dissolution into 0.37N aqueous HNO 3 into the plasma. The instrumental mass bias drift was corrected using the samplestandard bracketing technique. An in house MgNO 3 standard was used for the samplestandard bracketing due to limited access to the DSM-3 standard. The isotopic composition of this in house standard was determined to be δ 25 Mg = 0.16 ± 0.08 ‰ and δ 26 Mg = 0.32 ± 0.14 ‰ by repeated measurements (n=61) relative to DSM-3. The Mg isotope composition of the measured samples were then corrected with these values to generate isotopic compositions of the samples relative to the DSM-3 standard [START_REF] Galy | Magnesium isotope heterogeneity of the isotopic standard SRM980 and new reference materials for magnesium-isotope-ratio measurements[END_REF].

The experimental solution samples containing EDTA and sulphate were treated as described above, in contrast to the studies of [START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF][START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF]. The impact of these dissolved species on the measurements was evaluated by doping the bracketing standard with aqueous citrate, EDTA and sulphate in the concentrations used in the experiments. The maximum deviation measured from the in-house standard was of 0.02 ‰, and 0.03 ‰ for δ 25 Mg, and δ 26 Mg respectively. The impact of aqueous citrate, EDTA, and sulphate on the measured Mg isotope compositions are thus considered to be negligible.

During each analytical session, the JDol-1 standard and the IAPSO seawater standard were repeatedly measured to monitor the accuracy and precision of the measurements. The measured composition of these standards over the long-term was δ 25 Mg = -1.21 ± 0.08 ‰ and δ 26 Mg = -2.32 ± 0.15 ‰ for the JDo-1 standard, and δ 25 Mg = -0.45 ± 0.11 ‰, and δ 26 Mg = -0.86 ± 0.20 ‰ for the IAPSO seawater standard. These are in close agreement with previously reported values (e.g. [START_REF] Pogge Von Strandmann | Lithium, magnesium and uranium isotope behaviour in the estuarine environment of basaltic islands[END_REF][START_REF] Wombacher | Separation of Mg, Ca and Fe from geological reference materials for stable isotope ratio analyses by MC-ICP-MS and double-spike TIMS[END_REF][START_REF] Immenhauser | Magnesium-isotope fractionation during low-Mg calcite precipitation in a limestone cave -Field study and experiments[END_REF][START_REF] Wimpenny | The behaviour of magnesium and its isotopes during glacial weathering in an ancient shield terrain in West Greenland[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF]Mavromatis et al., , 2014aMavromatis et al., , 2014b[START_REF] Mavromatis | The effect of permafrost, vegetation, and lithology on Mg and Si isotope composition of the Yenisey River and its tributaries at the end of the spring flood[END_REF].

Geochemical and speciation calculations with PHREEQC

Geochemical and speciation calculations in the present study were performed using the PHREEQC code (Parkhurst and Appelo, 2013) together with its core10 thermodynamic database after adding the equilibrium constants for aqueous sulphate, citrate and EDTA bearing species to this database listed in Table A of the electronic supplement (Annex III).

The adopted standard state is that of unit activity for pure minerals, solids and H 2 O. The standard state for the aqueous species is unit activity of a 1 molal solution extrapolated to infinite dilution at any given temperature and pressure. The activity coefficients of neutral species were assumed to be equal to one, whereas the activity coefficients of charged aqueous species were calculated using the Davies equation. The dissolution of brucite can be described by:

Mg(OH) + 2 H A ↔ Mg A + 2 H O (5.6)
for which law of mass action is given by:

C DE = F GH I (F J K )
F GH(KJ) (F J I) (5.7) where C DE stands for an equilibrium constant and a i refers to the activity of the subscripted species or phase. Taking account of the standard state in pure water and for pure brucite, Eqn. (5.7) reduces to:

C DE = L I (L M I ) (5.8)
To be consistent with the solids used in this study, the equilibrium constant (Table A of the electronic supplement; Annex III) used for brucite solubility in geochemical calculations was determined from Eqn. (5.8) and PHREEQC using the measured equilibrium Mg concentration and pH of aqueous samples collected in the first-step equilibration of the ligand-free experimental series after the solutions attained steady-state conditions (Table B of the electronic supplement Annex III).

The proportion and identity of Mg-bearing aqueous species present in the solution phase has a significant effect on the mineral-solution equilibrium Mg isotope fractionation factor. The mineral-solution Mg fractionation factor corresponds to the weighted average of the individual isotope fractionation factors of all the Mg bearing species in the solution in accord with [START_REF] Zhang | Abiologic silicon isotope fractionation between aqueous Si and Fe(III)-Si gel in simulated Archean seawater: Implications for Si isotope records in Precambrian sedimentary rocks[END_REF]: (5.9)

where x i refers to the mole fraction of the total Mg in the solution that is present in the subscripted aqueous species and , # $%&'()' N/ , corresponds to the fractionation factor between the solid and the it Mg bearing aqueous species.

Results

Equilibrium between solution and brucite

Prior to performing isotope exchange experiments, the initial Mg-free solutions were equilibrated with synthesized brucite powder. The evolution of the aqueous Mg concentration over the 35-60 days of equilibration of each experimental series is shown in The experimental solutions during this first equilibration step exhibit a steady Mg concentration increase before stabilising within 20 days. Supposing that reaction (5.6) is an elementary reaction, the rate of the brucite dissolution (r) at a given constant pH is given by: 5.10) where S and M refer to the brucite-aqueous solution interfacial surface area and mass of solution, and k + and k -designates brucite dissolution and precipitation rate constants, respectively. Assuming that the activity of aqueous magnesium is equal to the dissolved aqueous Mg concentration, the temporal evolution of dissolved Mg concentration in a closed system can be described using: 5.11) where X ) _ = `a b X ) , S ( ) Z stands for the concentration of aqueous Mg in equilibrium with brucite, and t denotes the elapsed time since the beginning of the experiment. The curves drawn through the measured Mg concentrations shown in Fig. 5.2 were calculated using Eqn. (5.11). The rate constants for the brucite dissolution reactions generated from these curves are provided in Table 5.4. Brucite far from equilibrium dissolution rates determined in this study in the absence of organic and inorganic ligands are similar to those determined by [START_REF] Pokrovsky | Experimental study of brucite dissolution and precipitation in aqueous solutions: surface speciation and chemical affinity control[END_REF] who reported values ranging from 6×10 -9 mol/m 2 /s at pH 9.5 to 10 -10 mol/m 2 /s at pH 12. [START_REF] Platzner | Modern isotope ratio mass spectrometry, Chemical analysis[END_REF]. δ eq represents the equilibrium isotopic composition of 25 Mg and F denotes the degree of isotopic exchange.

Q = RS RT = U/V WX A -X ) S Y (
S = S ( ) Z W1 -[ )-.] ^Y (

Determination of magnesium equilibrium isotope fractionation factors

Equilibrium fractionation factors, ∆ eq 26 Mg brucite-solution, were determined using the threeisotope method as described in previous studies (e.g. [START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF][START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF]Zheng et al., 2016;[START_REF] Stamm | The experimental determination of equilibrium Si isotope fractionation factors among H 4 SiO 4 o , H 3 SiO 4 and amorphous silica (SiO 2 •0.32 H 2 O) at 25 ° and 75 °C using the three-isotope method[END_REF]. In accord with this method, the measured δ 26 Mg aq and δ 26 Mg brucite values are plotted as a function of the degree of isotopic exchange (F). The degree of isotopic exchange was calculated using:

c = (d 5 )d 2 ) (d )d 2 )
(5.12) where δ t denotes the isotopic composition of either one of the phases at any time t during the reaction, and δ i and δ e describe the initial and equilibrium isotopic composition of this phase. F increases from 0 to 1 as isotopic equilibrium is attained. A more detailed description of the determination of F can be found in previous studies [START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF]Zheng et al., 2016;[START_REF] Stamm | The experimental determination of equilibrium Si isotope fractionation factors among H 4 SiO 4 o , H 3 SiO 4 and amorphous silica (SiO 2 •0.32 H 2 O) at 25 ° and 75 °C using the three-isotope method[END_REF]. As isotopic exchange of this two-phase system is incomplete in the experimental series performed in this study, these compositions can be extrapolated to 100 % isotopic exchange (F=1). The δ-F plots for all experiments performed in this study are shown in Fig. 5.4 and the resulting ∆ eq 26 Mg brucite-solution generated from the extrapolation are listed in Table 5.6.

The equilibrium Mg isotope fractionation factors between brucite and aqueous solution at 25°C in the absence of either aqueous organic ligands or aqueous sulphate, ∆ eq 26 Mg brucite-solution was determined to be -0.62 ± 0.72 ‰ and -0.09 ± 0.21 ‰ for powder to solution ratio of 0.02 (series BB, Fig. The ∆ eq 26 Mg between Mg 2+ and Mg(EDTA) 2-exhibits a significant positive fractionation of 2.08 ± 0.21 ‰.

Isotope exchange kinetics

The kinetics of isotopic exchange can be also quantified using the 'three-isotope method'.

The rate with which isotopic equilibrium is attained helps define the mechanism of the isotopic equilibration. The degree of isotopic exchange (F) is plotted as a function of time in Fig. 5.5. The isotopic exchange rates of the experiments in this study were determined using [START_REF] Cole | Rates and Mechanisms of Isotopic Exchange[END_REF][START_REF] Johnson | Isotopic fractionation between Fe(III) and Fe(II) in aqueous solutions[END_REF]:

)((e)f) (- = X . (1 -c) .
( 5.13) where k is the rate constant and n the order of reaction. Isotope exchange rates follow either a first-order (n=1) or a second-order (n=2) rate law [START_REF] Criss | Kinetic theory of oxygen isotopic exchange between minerals and water[END_REF][START_REF] Huang | Kinetic studies on the isotopic exchange of calcium ion and calcium carbonate[END_REF][START_REF] Johnson | Isotopic fractionation between Fe(III) and Fe(II) in aqueous solutions[END_REF][START_REF] Welch | Kinetic and equilibrium Fe isotope fractionation between aqueous Fe(II) and Fe(III)[END_REF][START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF]Zheng et al., 2016). A firstorder reaction was assumed to be consistent with both Eqn. (5.11) and the brucite dissolution rates measured in the present study. The integrated form of Eqn. (5.13) can for a first order reaction be written as:

ln(1 -c) = -X e T.

(5.14) An example of the temporal evolution of the degree of ion exchange for the ligand free experiment (BABE) and the experiment in the presence of EDTA (BE EDTA) are shown in Fig 5.5. In both cases an initial fast isotope exchange rate is followed, after few days, by a much slower exchange rate in agreement with Eqn. (5.14), the first order rate law. Note that the isotope exchange rate constant derived from Eqn. (5.14) is 2.92×10 -11 mol/m 2 /s for the inorganic system but 4.54 ×10 -13 mol/m 2 /s in the presence of EDTA. Values of the initial and first-order rate constants ('bulk' rate constants) for isotope exchange are listed in Table 5. 5.4) performed as the first stage of each experimental series. Dashed lines are generated assuming first order rate law, using the bulk isotopic rate constants shown in Table 5.7

It can be seen that F calculated values using bulk brucite dissolution rates (doted lines) are much higher than the corresponding measured F values (they predict attainment of isotope equilibrium in about 15 days) but that the bulk dissolution rate constants provide a reasonable fit of F values (dashed lines) for reaction times ≥ 20 days.

Discussion

Magnesium isotope fractionation between brucite and Mg 2+

The average value at 25°C of the equilibrium Mg isotope fractionation factor between brucite and aqueous solution in the absence of aqueous organic and inorganic ligands is ∆ eq 26 Mg brucite-solution = -0.36 ± 0.38‰. This value corresponds to the equilibrium isotope fractionation between brucite and aqueous Mg 2+ , as 96% of dissolved Mg in these experiments is present as Mg 2+ (see [START_REF] Catti | Static compression and H disorder in brucite, Mg(OH)2, to 11 GPa: a powder neutron diffraction study[END_REF][START_REF] Chakoumakos | Low-Temperature Structure and Dynamics of Brucite[END_REF] The Mg isotope exchange experiments performed in this present study show that the Mg equilibrium isotope fractionation between a mineral and its co-existing aqueous solution is highly depending on Mg speciation in the aqueous phase. The results also show, that there are still significant disagreements between ab initio calculations and experimental determinations of equilibrium Mg isotope fractionation factors. Understanding and resolving these differences is crucial to precisely determine the Mg isotope fractionation in the presence of various inorganic and organic ligands and to accurately interpret the Mg isotopic signatures of minerals formed in natural environments.

Mg isotope exchange kinetics

The rates of isotopic equilibration determined in this study, as illustrated by Fig. 5.6, provide some insight into the processes controlling isotope exchange between brucite and solution. The dashed lines drawn through the data points in Fig 5 .6, showing the variation of the degree of isotopic exchange (F) as a function of time, were calculated using the first order rate equation for isotope exchange (Eqn. 5.14), whereas the dotted curves were generated using the rate constants for brucite dissolution (Eq. 5.11). Within the first 5 to 10 days of each experimental series the, measured temporal evolution of the F values are consistent with the measured bulk brucite dissolution rates. This correspondence suggests that the rate of Mg isotopic exchange over this time period is controlled by the attachment and detachment of material at the brucite surface / fluid interface. Over these first 5 to 10 days, the degree of isotope exchange F for the experimental series run in the absence of aqueous ligands, and with aqueous citrate and sulphate reached values ranging from 0.15 to 0.8 depending on the nature of the ligand and the solid to solution ratio. After this fast initial isotopic exchange, the rate slows considerably, by about 2-3 orders of magnitude (Table 5.7). This suggests that the isotopic exchange during the later part of the experimental series is limited by a slower process, perhaps the slower transport of Mg within the solid.

Almost all experimental series performed in this study did not attain isotopic equilibrium within the series duration. The only exception is the experimental series performed in the presence of aqueous EDTA, which reaches Mg isotope equilibrium within 131 days. The rates of isotopic exchange, possibly catalysed by EDTA complexation at brucite surface, are close to the brucite dissolution rate (Table 5.7). This and the 53% decrease of brucite specific area measured after 131 days of reaction strongly suggest a large degree of brucite recrystallization during the isotope exchange reaction.

Implications for natural systems

The fractionation factors obtained in this study show that the equilibrium Mg isotopic signatures of minerals depend on aqueous solution speciation. Many studies have shown that fluids originating from silicate weathering have a heavier Mg composition than their source rocks; surface waters tend to preferentially drain the light Mg isotopes from the source rocks (e.g. Tipper et al., 2006;[START_REF] Brenot | Magnesium isotope systematics of the lithologically varied Moselle river basin, France[END_REF]Opfergelt et al., 2012). In the present study, however, results demonstrate that the Mg in aqueous solutions in the absence of organic ligands preferentially retains light Mg isotopes when precipitating brucite. Other Mg bearing minerals, however, could preferentially incorporate light Mg. For example, dolomite appears to preferentially incorporate light Mg; Li et al. (2012) and [START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF] reported that Mg in dolomite is 2.5 to 3.5 ‰ lighter than its coexisting fluid. Indeed, [START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF] noted that isotope fractionation depends on both the aqueous bonding environment and the identity of the mineral precipitating in the system.

In the presence of organic and inorganic ligands, the equilibrium Mg isotopic fractionation between brucite and aqueous solutions depends strongly on aqueous speciation.

Organically bound Mg in Mg-EDTA species exhibits a equilibrium Mg isotopic fractionation factor of > 2 ‰, suggesting that the water in organic-rich environments such as soils will tend to preferentially remove light Mg [START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF]. This observation can therefore explain the preferential uptake of heavy Mg isotopes into plants, as aqueous organic Mg complexes are generally neutral or negatively charged, so unavailable for plant uptake [START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF]. Such enrichment can be seen in nature as well as in laboratory experiments (e.g. [START_REF] Bolou-Bi | Experimental determination of magnesium isotope fractionation during higher plant growth[END_REF][START_REF] Opfergelt | Magnesium retention on the soil exchange complex controlling Mg isotope variations in soils, soil solutions and vegetation in volcanic soils, Iceland[END_REF].

Conclusion

The results of this study show that the aqueous speciation of Mg can have an significant influence on its equilibrium isotope fractionation. In the absence of organic or inorganic ligands ∆ eq 26 Mg brucite-solution is slightly negative with a fractionation of -0.36 ± 0.38 ‰. This value contrasts with past theoretical studies, which suggested that brucite should be enriched in heavy 26 Mg isotopes compared with this solution. Depending on the ligand present in the aqueous phase the equilibrium fractionation factor ∆ eq 26 Mg brucite-solution can change. For example in the presence of aqueous EDTA, ∆ eq 26 Mg brucite-solution was found to be 2.43 ± 0.20 ‰. This value is in close agreement with previous experimental and theoretical studies.

Results obtained for citrate and sulphate bearing solutions, however, exhibit equilibrium Mg fractionation factors between -0.07 ± 0.21 and -0.17 ± 0.10 ‰ in the presence of citrate and an average equilibrium fractionation factor of 0.18 ± 0.21 ‰ in the presence of sulphate.

These results differ significantly with the corresponding results of previously reported ab initio calculations.

The findings of this study demonstrate that the presence of organic ligands in natural systems can influence equilibrium Mg isotopic fractionation factors between minerals and aqueous solutions. As such the Mg isotope concentrations of precipitated minerals, could potentially be used as tracer to characterize the environment in which a mineral has formed.

Note, however, that the results of this study differ significantly from those previously reported from ab initio calculations, suggesting that these need to be revised or further validated before they can be used with confidence as isotopic tracers of natural processes.

Chapter 6

Conclusions and outlook

General conclusions and outlook (English version)

This thesis determined the effects of aqueous speciation, notably the role of aqueous inorganic and organic complexation on the equilibrium fractionation factors of Si and Mg in the amorphous SiO 2 -aqueous solution and brucite (Mg(OH) 2 )-aqueous solution systems.

Isotopic exchange experiments at bulk chemical equilibrium were performed using the threeisotope method and compared to corresponding ab initio calculations. In addition to providing verified equilibrium fractionation factors, this method provides the rates of isotope exchange.

Evaluation of these rates provides insight into the mechanism and the conditions at which mineral isotopic signatures are generated and preserved in nature.

Towards the quantitative application of Si isotopic signatures as a tracer for weathering, pH and marine paleo-temperature, the first part of this thesis determined the equilibrium Si isotope fractionation factors between amorphous silica (SiO 2 0.32 H 2 O) and inorganic aqueous fluids at pH ranging from 5.8 to 9.9 at 25° and 75°C. Experimental results

show that at 25 °C, the equilibrium fractionation factor between amorphous silica and the aqueous fluid, Δ eq 30 Si solid-fluid , increases from 0.45 ± 0.20 ‰ at pH 6.4 to 1.63 ± 0.23 ‰ at pH 9.9. These fractionation factors decrease with increasing temperature, and are equal to 0.07 ± 0.06 ‰ at pH 5.8 and 1.06 ± 0.13 ‰ at pH 9.1 at 75 °C. The value obtained for pH < 7 and 25°C is in good agreement with the experimental values obtained by [START_REF] Roerdink | Experimental constraints on kinetic and equilibrium silicon isotope fractionation during the formation of non-biogenic chert deposits[END_REF] and [START_REF] Oelze | The effect of Al on Si isotope fractionation investigated by silica precipitation experiments[END_REF], and the decrease of isotopic fractionation with increasing temperature follows the relationship suggested in previous theoretical and experimental studies (e.g. [START_REF] Urey | The thermodynamic properties of isotopic substances[END_REF][START_REF] Bigeleisen | Chemistry of Isotopes: Isotope chemistry has opened new areas of chemical physics, geochemistry, and molecular biology[END_REF][START_REF] Schauble | Applying Stable Isotope Fractionation Theory to New Systems[END_REF][START_REF] Shahar | Hightemperature Si isotope fractionation between iron metal and silicate[END_REF][START_REF] Huang | First-principles calculations of equilibrium silicon isotope fractionation among mantle minerals[END_REF]. Taking into account the pH dependence of aqueous Si speciation calculated with PHREEQC, the equilibrium Si isotope fractionation factors between the two major aqueous species H (2015), showing that either experimental or theoretical calculations can be used to accurately model natural processes. The results obtained in the first part of this thesis indicate that Si isotopic signatures can potentially be used as paleo pH proxies in alkaline environments, and furthermore can provide insight into the temperature of mineral precipitation. The rate of isotopic exchange in these inorganic Si systems match closely the measured bulk dissolution rates of amorphous SiO 2 , indicating that the dominant mechanism for isotopic exchange in this system is the detachment and reattachment of material at the amorphous SiO 2 surface, and not the transport within the solid. This latter observation suggests that the original Si isotope compositions incorporated in minerals could potentially be altered over time through fluidmineral interaction even when the system is at bulk chemical equilibrium.

In natural biogenic environments, dissolved Si can form strong aqueous complexes with various organic ligands. These complexes can change Si coordination from the usual four-coordinated aqueous silicic acid (H 4 SiO 4 o

) complex to a five-or six-coordinated aqueous Si complex if organic ligands are present. Such a change in aqueous complexation could change considerably mineral-fluid isotope fractionation. This possibility was evaluated in the second part of this thesis, where the equilibrium isotope fractional factors among amorphous silica and catechol (C 6 H 4 (OH) 2 ) bearing aqueous solutions were measured using the threeisotope method. It was shown that the equilibrium Si isotope fractionation factor between the Si-catechol complex and amorphous silica is about 20 ‰ lighter than the corresponding equilibrium Si isotope fractionation factor between silicic acid and amorphous silica.

Measured equilibrium Si isotope fractionation factors were found to be in very close agreement with corresponding values obtained by ab initio calculations. Taken together, the results of this study demonstrate that the presence of aqueous organic ligands can have an important impact on the Si isotopic fractionation and might explain the strong negative fractionation found in naturally formed biological Si, such as sponges or diatoms.

The third part of this thesis measured the equilibrium Mg isotope fractionation factors between brucite and Mg bearing aqueous solutions in the absence/ presence of selected organic and inorganic ligands, notably citrate, EDTA (ethylenediaminetetraacetic acid), and sulphate. The isotopic fractionation factor determined in this study between brucite and solution, in the absence of inorganic and organic ligands, is in good agreement with the experimental data of [START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF] and theoretical calculations conducted recently in our laboratory. Similar to the results in the amorphous silica-aqueous fluid studies summarized above, the aqueous speciation of Mg was found to have an important influence on equilibrium Mg isotope fractionation. In the presence of aqueous EDTA, the equilibrium Mg isotope fractionation factor between brucite and solution, Δ eq 26 Mg brucite-solution , was found to be 2.43 ± 0.20 ‰, showing that brucite incorporates heavy Mg on the presence of this aqueous ligand. This is in close agreement with previous experimental and theoretical studies. Measured equilibrium Mg isotope fractionation factors determined in the presence of aqueous citrate and aqueous sulphate exhibit smaller equilibrium Mg isotopic fractionation factors ranging from -0.07 ± 0.21 to -0.17 ± 0.10 ‰ and 0.20 ± 0.05 to 0.15 ± 0.41 ‰, respectively. These values differ somewhat from previously reported ab initio calculations, suggesting that these need to be revised or further validated before they can be used with confidence. These findings show that the presence of organic ligands and inorganic carbonate and hydrogen carbonate ligands, in natural systems have a significant impact on the equilibrium Mg isotopic fractionation factors between minerals and aqueous solutions. As such the Mg isotope concentrations of precipitated minerals might prove to be a useful tracer to characterize the environment in which a mineral has formed.

As with all these, this thesis both provides new insights but also opens the door to new future research projects. Results of this thesis show that the equilibrium isotope fractionation is highly dependent on the aqueous speciation. Therefore the aqueous composition can significantly influence the isotopic signatures of minerals and solutions in natural systems.

Notably, in biological environments, the presence of aqueous organic ligands can alter significantly the isotopic signatures of precipitated minerals. Organic (or inorganic) ligands have two possible routes for impacting the isotopic composition of the solid, either by altering the isotopic composition of the free metal ion incorporated in the solid, or by participating directly in the incorporation of the metal into the solid phase in the form of an organometallic complex. In the latter case organic ligands drive the uptake and incorporation of Si and Mg into organisms such as sponges, diatoms, plants. In some instances, the biotic fluid within the organism provides the chemical drive to concentrate metals from solution to help make the skeletons or shells. An exciting new research direction would be to determine which inorganic and organic ligands take part in these biological and natural processes. The degree of isotopic fraction might aid in such studies. For example, as shown for Si in this thesis, organic ligands can change the coordination of Si in solution and therefore result in distinct Si isotope fractionation. Knowing the principles of isotopic fractionation in the presence of the organic and inorganic ligands it might also be possible to develop new isotopic tools to better constrain the biogeochemical cycles of Si and Mg, and the behaviour of these elements in natural processes.

This thesis additionally provides insight into the mechanisms of isotopic exchange,

showing that the rate of isotopic exchange depends strongly on the system of interest, and its geometry, which can be controlled either by chemical reaction at the solid-liquid interface or by transport within the solid. A possible future research project could be focussed on identifying the rate of isotopic exchange for different mineral-solution systems to develop a general understanding of both the mechanism of isotope exchange as well as the degree to which mineral isotopic signatures are preserved over geological timescales.

Conclusion générale et perspectives (Version française)

Cette thèse a permis de déterminer les effets de la spéciation aqueuse, notamment la formation et [START_REF] Oelze | The effect of Al on Si isotope fractionation investigated by silica precipitation experiments[END_REF] tandis que la diminution du fractionnement isotopique avec l'augmentation de la température suit la relation suggérée dans des études théoriques et expérimentales antérieures (par exemple, [START_REF] Urey | The thermodynamic properties of isotopic substances[END_REF][START_REF] Bigeleisen | Chemistry of Isotopes: Isotope chemistry has opened new areas of chemical physics, geochemistry, and molecular biology[END_REF][START_REF] Schauble | Applying Stable Isotope Fractionation Theory to New Systems[END_REF][START_REF] Shahar | Hightemperature Si isotope fractionation between iron metal and silicate[END_REF][START_REF] Huang | First-principles calculations of equilibrium silicon isotope fractionation among mantle minerals[END_REF]. En tenant compte de la distribution en fonction du pH des espèces aqueuses de Si calculée avec PHREEQC, nous avons déterminé le facteur de fractionnement isotopique de Si à l'équilibre entre les deux espèces aqueuses majeures

Bibliography

Annex I: Electronic supplement of chapter 3

1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 1 .

 1111111111 Geochemical calculations of amorphous silica dissolution rates ...................... 3.2.2. Si isotope systematics ......................................................................................... 3.2.3. Three-isotope method ......................................................................................... 3.2.4. Kinetics of isotopic exchange ............................................................................. Experimental approach ...................................................................................... 3.3.1.1. Starting powder -amorphous silica ........................................................... 3.3.1.2. Initial aqueous solutions ............................................................................ 3.3.1.3. Characterization of the aqueous solutions ................................................. 3.3.1.4. Experiment design: Step 1 Equilibration of reactive fluids ...................... 3.3.1.5. Experiment design: Step 2 Isotopic exchange experiments ...................... -xiv-3.3.2. Si isotope analysis .............................................................................................. Attainment of fluid-amorphous SiO 2 equilibrium during the fluid equilibration75 3.4.2. Results of Isotope exchange experiments ........................................................... 3.4.2.1. Observations on the solid phases .............................................................. 3.4.2.2 Chemical and isotopic evolution of the isotope exchange experiments ..... 3.4.3. Silicon isotope fractionation factors .................................................................. 3.4.4. Isotope exchange kinetics ................................................................................... Silicon isotope fractionation between amorphous silica and aqueous solution 3.5.2. Isotope fractionation among Si aqueous species ............................................... 3.5.3. Kinetics of Si isotope exchange .......................................................................... 3.5.4. Can Si fractionation be used as a paleo pH and temperature proxy? ............... Introduction ................................................................................................................. 4.2. Experimental methods ................................................................................................ 4.2.1. Starting materials ............................................................................................... 4.2.2. Experimental design ........................................................................................... 4.2.2.1. Step 1: Equilibration of the reactive aqueous solutions with amorphous SiO 2 ........................................................................................................................ 4.2.2.2. Step 2: Isotopic exchange experiments ..................................................... 4.2.3. Analytical methods ........................................................................................... 4.2.3.1. Characterization of aqueous solutions ..................................................... 4.2.3.2. Data reporting and Si isotope analysis .................................................... -xv-4.3.3. Speciation calculations .................................................................................... Attainment of equilibrium between the fluid and amorphous SiO 2 .................. 4.5.2. Results of isotope exchange experiments ......................................................... 4.5.3. Experimental and theoretical silicon isotope fractionation factors ................. 4.5.4. Isotope exchange kinetics ................................................................................. Silicon isotope fractionation in the presence of catechol ................................ 4.6.2. Si isotope exchange kinetics in the presence of catechol ................................. 4.6.3. Implications for biomineralization ................................................................... Starting materials ............................................................................................. 5.2.1.1. Brucite synthesis ..................................................................................... 5.2.1.2. Initial reactive aqueous solutions ............................................................ 5.2.1.3. Characterization of sampled experimental fluids .................................... 5.2.2. Experimental design ......................................................................................... 5.2.2.1. Step 1: Equilibration of initial aqueous solutions with Mg(OH) 2 ........... 5.2.2.2. Step 2: Isotopic exchange experiments ................................................... 5.2.3. Data reporting and Mg isotope analysis .......................................................... 5.2.4. Geochemical and speciation calculations with PHREEQC ............................. 5.3. Results ........................................................................................................................ Equilibrium between fluid and brucite .............................................................. 5.3.2 Results of isotope exchange experiments .......................................................... 5.3.3. Determination of magnesium equilibrium isotope fractionation factors ......... 5.3.4. Isotope exchange kinetics ................................................................................. Magnesium isotope fractionation between brucite and Mg 2+ .......................... 5.4.2. Magnesium isotope fractionation between Mg 2+ and aqueous Mg organic and inorganic complexes ................................................................................................... 5.4.3. Mg isotope exchange kinetics ........................................................................... 5.4.3. Implications for natural systems ...................................................................... 5.5. Conclusion ..............................................................................................................supplement of chapter 3 ................................................................ Annex II: Electronic supplement of chapter 4 .............................................................. Annex III: Electronic supplement of chapter 5 ............................................................

Figure 1 . 1 -Figure 1 . 2 -Figure 1 . 3 -Figure 2 . 1 -Figure 2 . 2 -Figure 2 . 3 -Figure 2 . 4 -Figure 2 . 5 -Figure 2 . 6 -Figure 2 . 7 -Figure 2 . 8 -Figure 2 . 9 -Figure 2 .Figure 2 .Figure 2 .Figure 2 .Figure 2 .Figure 3 . 1 -Figure 3 . 2 -Figure 3 . 3 -Figure 3 . 4 -Figure 3 . 5 -Figure 3 . 6 -Figure 3 . 7 -Figure 3 . 8 -Figure 3 . 9 -Figure 4 . 1 -Figure 4 . 2 -Figure 4 . 3 -Figure 4 . 5 -Figure 4 . 6 -Figure 4 . 7 -Figure 5 . 1 -Figure 5 . 2 -Figure 5 . 3 -Figure 5 . 4 -

 1112132122232425262728292222231323334353637383941424345464751525354 Figure 1.1 -pH dependence of the solubility of SiO 2 solids at 25°C. ..................................... 14 Figure 1.2 -Si isotopic compositions in various major reservoirs relative to bulk silicate Earth (BSE) shown in grey (modified from Zambardi, 2011 and Poitrasson, 2017) ........................ 16 Figure 1.3 -Mg isotopic compositions in major terrestrial reservoirs relative to the average Mg isotopic composition of the mantle, i.e., bulk Earth shown in grey (modified from Teng, 2017).. ....................................................................................................................................... 18 Figure 2.1 -Concept of the three isotope method modified after Li et al. (2011) .................. 22 Figure 2.2 -Illustrative example of the extrapolation to obtain the fractionation factor between phase B and phase A. ................................................................................................. 23 Figure 2.3 -Sketch of the experimental brucite synthesis method. ........................................ 25 Figure 2.4 -Dissolution curves of amorphous Silica (A) and brucite (B) obtained during the preparation of aqueous solutions for the isotope exchange experiments. ................................ 30 Figure 2.5 -Orbital shaker ...................................................................................................... 32 Figure 2.6 -A. The MEB JEOL JSM-7800F Prime scanning electron microscope used in this thesis. B. The secondary electron image of Brucite. C. The secondary electron image of amorphous silica. ...................................................................................................................... 34 Figure 2.7 -A. The JEOL JEM-ARM200F Cold FEG Transmission electron microscope used in this thesis. B. A sample holder with small Cu grill C. A diffraction contrast image of SiO 2 powder. ..................................................................................................................................... 36 Figure 2.8 -The four parallel rods of the quadrupole ............................................................. 41 Figure 2.9 -Elution profile of the Mg, demonstrating that all Mg is collected during column chromatography. ....................................................................................................................... 46 Figure 2.10 -Schematic design of the Neptune MC-ICP-MS (after ThermoScientific and Weyer and Schwieters, 2003) ................................................................................................... 47 Figure 2.11 -Peak scan for Si isotopes in medium mass resolution with representative interferences ............................................................................................................................. 48 Figure 2.12 -All BHVO-2 Si isotope compositions measured in this study, values are related to the mass-dependent fractionation law within uncertainty. ................................................... 51 Figure 2.13 -Mass scan for Mg isotopes in medium mass resolution. ................................... 52 Figure 2.14 -All Mg isotope standard measurements of IAPSO (blue) and JDol (grey) performed in this thesis ............................................................................................................ 53

Figure 5 . 5 -

 55 Figure 5.5 -Representative plots of the experiment without inorganic or organic ligands (BABE) and the experiment performed with aqueous EDTA in solution .............................

Figure 5 . 6 -

 56 Figure 5.6 -The temporal evolution of the degree of isotopic exchange F during the six experimental series run this study. .........................................................................................

Figure 1 . 1 -

 11 Figure 1.1 -pH dependence of the solubility of SiO2 solids at 25°C. Red curve represents the aqueous Si concentration in equilibrium with quartz and the blue curve with amorphous silica (modified after Oelze, 2015)

Figure 1 . 2 -

 12 Figure 1.2 -Si isotopic compositions in various major reservoirs relative to bulk silicate Earth (BSE) shown in grey (modified from Zambardi, 2011 and Poitrasson, 2017). Data acquired from Zambardi (2011) and Poitrasson (2017) and references therein, Wille (2010) was added for Si isotope composition in sponges.

Figure 1 . 3 -

 13 Figure 1.3 -Mg isotopic compositions in major terrestrial reservoirs relative to the average Mg isotopic composition of the mantle, i.e., bulk Earth shown in grey (modified from[START_REF] Teng | Magnesium Isotope Geochemistry[END_REF]. Data acquired fromYoung and Galy (2004) and[START_REF] Teng | Magnesium Isotope Geochemistry[END_REF] and the references therein.

Figure 2 . 1 -

 21 Figure 2.1 -Concept of the three isotope method modified after[START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF]. The solid (Phase A) has a natural isotopic composition and plots on the mass-dependent fractionation line. The solution (Phase B) shows a distinct offset of the TFL, due to spiking of either 25 Mg or 29 Si. The isotopic composition of the two phases will evolve towards a value of 100% of isotopic exchange. The line connecting the two phases crosses the system average throughout the process, due to isotopic mass balance. At 100% exchange the two phases will plot on a SFL, parallel to the TFL The position of the SFL depends on the isotopic mass balance of the system. For many systems the isotopic exchange will be incomplete, and the isotopic composition at time t F of total exchange can be calculated by the extrapolation of the time series (t 0 to t n ). The extrapolated value will represent the equilibrium isotopic fractionation factor, if the isotopic exchange is occurring under equilibrium conditions.

Figure 2 . 2 -

 22 Figure 2.2 -Illustrative example of the extrapolation to obtain the fractionation factor between phase B and phase A.As the reaction is progressing, the two phases approach a degree of isotopic exchange F=1, thus equilibrium. If F=1 is not reached the equilibrium values can be extrapolated, and the ∆ eq can be determined.

Figure 2 . 3 -

 23 Figure 2.3 -Sketch of the experimental brucite synthesis method.

  equilibrated with ~3g of either amorphous SiO 2 or synthesized brucite powder in highdensity polyethylene (HDPE) Nalgene ® bottles. These were placed into either a 25°C or 75°C thermostatic shaking bath. The aqueous solutions were sampled at regular intervals over 70 days. The pH was immediately measured (see Chapter 2.4.2.1), and adjusted with reagent grade HCl, NaOH, or NH 3 if needed. The aqueous Si and Mg concentrations of the sampled solutions were determined by colorimetry (see Chapter 2.4.2.4) and atomic absorption spectrometry (AAS, see Chapter 2.4.2.2), respectively, to assess when chemical equilibrium was reached. The results of these measurements are shown in Fig. 2.4.

Figure 2 . 4 -

 24 Figure 2.4 -Dissolution curves of amorphous Silica (A) and brucite (B) obtained during the preparation of aqueous solutions for the isotope exchange experiments.

Figure 2 . 5 -

 25 Figure 2.5 -Orbital shaker used to constantly mix the isotopic exchange experiments at 25°C

1 .

 1 Scanning electron microscopy (SEM)Representative experimental powders were imaged using the MEB JEOL JSM-7800F Prime electron microscope (Fig.2.6 A) located at the Raimond Castaing Microcharacterization

  photons. These have characteristic wavelengths and energies, according to the elemental composition of the sample. The obtained photons yield the energy-dispersive X-ray spectra (EDS), which is used for the non quantitative chemical identification, to confirm the purity of the powders.

Figure 2 . 6 - 3 )

 263 Figure 2.6 -A. The MEB JEOL JSM-7800F Prime scanning electron microscope used in this thesis. B. The secondary electron image of Brucite. C. The secondary electron image of amorphous silica.

Figure 2 . 7 -

 27 Figure 2.7 -A. The JEOL JEM-ARM200F Cold FEG Transmission electron microscope used in this thesis. B. A sample holder with small Cu grill C. A diffraction contrast image of SiO 2 powder.

Figure 2 . 8 -

 28 Figure 2.8 -The four parallel rods of the quadrupole

Figure 2 .

 2 Figure 2.9 -Elution profile of the Mg, demonstrating that all Mg is collected during column chromatography.

Figure 2 .

 2 Figure 2.10 -Schematic design of the Neptune MC-ICP-MS (after ThermoScientific and Weyer[START_REF] Weyer | High precision Fe isotope measurements with high mass resolution MC-ICPMS[END_REF]

Fig 2 .

 2 Fig 2.11. It is crucial, therefore, to tune the spectrometer so that that it samples the plateau where only the three Si isotopes are present (Fig 2.10).

Figure 2 .

 2 Figure 2.11 -Peak scan for Si isotopes in medium mass resolution with representative interferences. The green arrow indicates the Si plateau, where Si isotopes can be measured without interferences (modified after[START_REF] Bouman | Stable isotope ratio measurements using the Finnigan NEPTUNE multicollector ICP-MS[END_REF]

Figure 2 .

 2 Figure 2.12 -All BHVO-2 Si isotope compositions measured in this study, values are related to the mass-dependent fractionation law within uncertainty. The red line marks the Si mass-dependent isotopic fractionation line. Average uncertainty on the measurements is shown in bottom right corner.

Figure 2 .

 2 Figure 2.13 -Mass scan for Mg isotopes in medium mass resolution. The vertical line represents the peak centre and thus the mass position where measurements were carried out (modified after Sikdar and Rai, 2017).

MgNO 3

 3 standard was determined by repeated measurements (n=61) relative to DSM-3, with an isotopic composition of δ 25 Mg = 0.16 ± 0.08 ‰ and δ 26 Mg = 0.32 ± 0.14 ‰. The measured Mg samples were then corrected with these values to generate isotopic compositions of sampled fluids relative to the DSM-3 standard established by Galy et al. (2003). The long-term reproducibility of the isotopic analyses was assessed by repeated analysis of the JDol-1 dolomitic carbonate standard, and the IAPSO seawater standard during each analytical session. The values obtained (Fig. 2.14) were δ 25 Mg of -1.21 ± 0.08 ‰, and δ 26 Mg of -2.32 ± 0.15 ‰, and δ 25 Mg -0.45 ± 0.11 ‰, and δ 26 Mg -0.86 ± 0.20 ‰, respectively. These are in close agreement with corresponding measurements reported by previous studies (e.g. Pogge von Strandmann

Figure 2 .

 2 Figure 2.14 -All Mg isotope standard measurements of IAPSO (blue) and JDol (grey) performed in this thesis. Values obey the mass-dependent fractionation law within uncertainties (shown within the symbols). Red line marks the Mg mass-dependent isotopic fractionation line.

Figure 3 . 1 -

 31 Figure 3.1 -Distribution of aqueous Si species in equilibrium with amorphous silica as a function of pH, for A. 25°C and B. 75°C.

  Zheng et al. (2016) measured Si isotopic fractionation at chemical equilibrium between a Fe(III)-bearing silica gel and artificial Archean seawater; they reported a 25°C equilibrium fractionation factor, Δ 30 Si gel-fluid of ~ -3.5 ‰.[START_REF] Dupuis | Fractionation of silicon isotopes in liquids: The importance of configurational disorder[END_REF] used first-principle methods to calculate the and kaolinite and its co-existing aqueous solution. These calculations predict a ∆ 30 Si mineral- solution at neutral pH of 2.1 ± 0.2‰ and 0.4 ± 0.2‰, for the quartz-aqueous solution and kaolinite-aqueous solution system, respectively. Additionally these authors reported the 25°C equilibrium fractionation factor of -1.6 ± 0.3‰, between the H 3 SiO 4 -and H 4 SiO 4 0 aqueous silicon species. Similarly,[START_REF] Fujii | Isotope fractionation of Si in protonation/deprotonation reaction of silicic acid: A new pH proxy[END_REF] experimentally and theoretically determined the equilibrium fractionation factor between the two aqueous species H determined values of -3.5 ‰ (experimental) and -3 ‰ (ab initio calculations) are somewhat inconsistent with those calculated by[START_REF] Dupuis | Fractionation of silicon isotopes in liquids: The importance of configurational disorder[END_REF].

  .4) S and M refer to the interfacial surface area and mass of solution normalized and k + and k - designates amorphous silica dissolution and precipitation rate constants, respectively. Note ! in Eqn (4) has units of mol/kg H 2 O. Rearranging Eqn.(3.4) and integrating it between times t= 0 and t gives , and ! .8 1 denotes ! at time zero. When starting from a zero concentration of H SiO 9 in solution, Eqn.(3.5) reduces to

  atomic ratio of the Si with mass x, which denotes either 29 Si or30 Si, to that of28 Si in the sample of interest. The Si isotopic fractionation factor between a solid and an aqueous fluid (P QRJ S,TJU S E/ K

  TJU S = D E Si QRJ S -D E Si TJU S (3.10) Note that ∆ E Si QRJ S,TJU S is approximately related to P QRJ S,between the solid and the aqueous fluid depends on the proportion of the different species present in this fluid and their individual fractionation factors with the solid P QRJ S, E/ K

Figure 3 . 2 -

 32 Figure 3.2 -Schematic diagram of the three-isotope method applied to Si, after Li et al.(2011) and Zheng et al. (2016). At time (t) zero, and in the absence of isotopic exchange (shown in %) Phase A plots as the isotopically "normal" component on the terrestrial fractionation line (TFL). At t0 Phase B shows a distinct offset from the TFL as it is enriched in 29Si. The isotopic composition of phases A and B gradually evolve towards 100% isotopic exchange. The lines connecting the two phases at a given time always cross the system average as required by isotope mass balance. When isotopic exchange is complete, the two phases plot on a secondary fractionation line, whose position is dictated by the isotopic mass balance of the system.

  Representative scanning electron microscope (SEM) and transmission electron microscope (TEM) images of the resulting powders are shown in Fig. 3.3 A and B. These images were acquired using a MEB JEOL JSM-7800F Prime electron microscope and a JEOL JEM-ARM200F Cold FEG transmission electron microscope at the Raimond Castaing Microcharacterization Centre (Toulouse, France), respectively. The TEM images were used to measure average grain size with the ImageJ software package (Schindelin et al., 2012); the average measured grain size was ~21 ± 5 nm (2SD, n=100). Energy dispersive spectroscopy (EDS) analyses indicate the powder contained pure Si without other metals present. Thermogravimetric analyses, performed with a Mettler Toledo ® ATG/DSC1, showed that the powders also contained ~8.7 % H 2 O, which is consistent with the chemical formula SiO 2 0.32 H 2 O. The specific surface areas of the cleaned amorphous silica were determined with a Quantachrome

Figure 3 . 3 -

 33 Figure 3.3 -Representative images of amorphous SiO2 powders. A) SEM image of the initial powder showing agglomerates of amorphous SiO2 grains. B) TEM image of the initial powder showing rounded ~ 21 nm SiO2 grains. C) Representative SEM image of reacted amorphous silica powder. D) TEM image of reacted amorphous silica recovered from the longest duration experiment performed at T ~25°C, pH ~6.

  Each experimental series began by equilibrating the initial Si-free fluids with the pre-treated amorphous SiO 2 . The temporal evolution of dissolved Si concentration and pH in these fluids are provided in Table A of the electronic supplement (Annex I); the Si concentrations are also shown in Fig. 4.

Figure 3 . 4 -

 34 Figure 3.4 -Temporal evolution of dissolved Si concentration during the equilibration of the initial reactive fluids with amorphous silica during the first stage of each experimental series. The dashed lines represent a fit of the data using Eqn. 7 with values of rate constant k'-listed in Table3.

  compositions fluids and solids during the second stage of all experimental series are provided in Fig.3.5. The pH of the fluids remained close to constant during the experimental series other than during series run at pH 9.1 and 75°C, where the pH decreased. This decrease could be due to a loss of NH 4 OH through evaporation over time from the reactors.Note that pH variations at alkaline conditions will alter the relative importance of the H 3 SiO 4 -versus H 4 SiO 4 0 species in solution. As such the isotopic compositions of the final fluids of the high pH series were not considered in the determination of equilibrium fractionation factors given below. The dissolved Si concentrations remained close to constant during the pH ~6 experiments, but tended to decrease with time during the higher temperature experiments; this decrease is consistent with the observed decrease in pH, which tends to decrease amorphous silica solubility. The δ 29 Si values of the fluids and solids mirror one another; in each case, the δ 29 Si value of the 29 Si enriched fluid phase decreases rapidly at the beginning of each experimental series, while the δ 29 Si value in the corresponding solid increases. Note that δ 29 Si of the solids increase far less than the δ 29 Si decreases in the fluid phase due to the relative masses of Si in these phases.

Figure 3 . 5 -

 35 Figure 3.5 -Plots of pH, Si concentrations and isotopic compositions of solid and fluid phases as a function of time during the second stage of each experimental series. The 2 S.D. uncertainties of data points are denoted by the error bars. Initial values are represented by dashed lines with their 2 S.D. error envelope shaded in grey. A) pH= 6.4 at 25 °C, B) pH= 9.9 at 25 °C, C) 5.8 at 75 °C, and D) 9.1 at 75 °C.

Figure 3 . 6 -

 36 Figure 3.6 -Plots of the isotopic composition of the solid and fluid phases as a function of the degree of isotope exchange during the second stage of each experimental series. A) pH= 6.4 at 25 °C , B) pH= 9.9 at 25 °C, C) 5.8 at 75 °C, and D) 9.1 at 75 °C. Excluded data from the fit are shown by grey symbols -see text.

  am-fluid of 0.0 ± 1.1 ‰ at 20 °C and 0.5 ± 0.6‰ at 35 °C for this system. Note that these former values were obtained at a pH of 8.5 from amorphous silica precipitation experiments using a surface kinetic model to correct for the effect of precipitation kinetics. Oelze et al. (2014) proposed a ∆ eq 30 SiSiO 2 ,am-fluid of -0.3 ‰ from experiments measuring the adsorption of silica onto gibbsite, and Oelze et al. (2015) proposed a ∆ eq 30 SiSiO 2 ,am-fluid of around 0 ‰ based on amorphous silica precipitation experiments in the presence and absence of Al.

Fujii

  et al. (2015) proposed the use of Si isotope fractionation as a proxy of seawater paleo-pH due to the pH-dependent concentration of the H 3 SiO 4 -and H 4 SiO 4 ° species and the consequent variation of solid-aqueous fluid fractionation factors with pH. Seawater however has a pH of ~8 and thus mainly H 4 SiO 4 ° will be present. As such, Si isotopes may be more useful for determining pH in more alkaline environments. Numerous such environments can be found in nature, for example alkaline lakes (e.g. Mono lake, California USA) or in mafic/ultramafic rocks. The results of this study confirm the possibility of using Si isotopic signatures in precipitated minerals as pH proxies of natural waters and provides the equilibrium Si isotope fractionation factors between amorphous SiO 2 , the dominant SiO 2 phase precipitating at ambient conditions with its coexisting aqueous solution at different pH. The variation of amorphous SiO 2 -aqueous fluid fractionation factors determined as a function of pH at 25° and 75°C using the equilibrium fractionation factors from this study are provided in Fig 3.8. Although the variation of this fractionation factor with pH is

Figure 3 . 8 -

 38 Figure 3.8 -Si equilibrium fractionation factors between amorphous silica and the fluid at 25°C and 75°C as a function of pH calculated using the Si equilibrium fractionation factors derived in the present study together with the aqueous speciation of Si shown in Fig 3.1. The curves in this figure are dashed at elevated pH as this calculation does not take into account polyatomic Si aqueous complexes, which may become important at these conditions.

Figure 3 . 9 -

 39 Figure 3.9 -Si equilibrium fractionation factors between quartz (Dupuis et al., 2015) and amorphous silica and H4SiO4o (this study) as a function of temperature. Red dotted describes extrapolated values.

Figure 4 . 1 -

 41 Figure 4.1 -Si coordination of H 4 SiO 4 o aqueous species and when it complexes to catechol

>18. 2 Ω

 2 de-ionized Milli-Q ® , water by stirring in a 1dm 3 glass beaker. The solid was sedimented and then decanted. This was repeated until the supernatant became clear within the first 5 min. The powder was subsequently oven dried, and placed into a desiccator while cooling. Scanning electron microscope (SEM) and transmission electron microscope (TEM) images, shown in Fig. 4.2 A and B, were acquired using a MEB JEOL JSM-7800F Prime electron microscope and a JEOL JEM-ARM200F Cold FEG transmission electron microscope, respectively.

Figure 4 . 2 -

 42 Figure 4.2 -Representative images of amorphous SiO2 powders. A. SEM image of starting powder showing agglomerates of SiO2 grains. B. TEM image of starting powder showing rounded ~ 21 nm SiO2 grains. C. Representative SEM image of reacted silicon powder. D. TEM image with 40 000x magnification of powder reacted at T ~25°C, pH ~6.

  pH and Si concentrations of this spiked solution were measured. The isotope exchange experiments in this study were conducted in series. Each series consisted of 8 individual closed system experiments and lasted 7 days. The short duration of the experiments avoids the decomposition of the aqueous catechol. Moreover by performing individual closed system experiments solids and fluids could be collected and analysed after a selected experiment duration. For the individual experiments, ~0.30 g of pre-washed amorphous SiO 2

  using a Bran & Luebbe ® analyser-III colorimeter coupled to a Seal XY-2 autosampler and a Technicon analyser II mixing unit. The measurements ranged from 0.1 to 10 ppm, with a long-term reproducibility within 3% and a quantification limit of 0.04 ppm.4.2.3.2. Data reporting and Si isotope analysisSilicon isotope compositions were measured on all aqueous solutions and powders sampled from the isotope exchange experiments, as well as the initial powder, the non-spiked chemical equilibrated solutions, and the spiked initial solutions. The silicon isotope compositions in this study are expressed as the standard δ-notation in per mil (‰) relative to the international NBS-28 standard (NIST RM-8546) in accord with: x denotes the mass of Si, either 29 Si or 30 Si, and Si % / Si &'()*+ ,refers to the molar ratio of the Si with mass x to that of mass 28 in the sample.The fractionation factor between an aqueous solution and a solid (. that ∆ Si /0*35 >*135 is approximately related to . /0*12304 /0

  equilibrated with pre-washed amorphous SiO 2 prior to running the isotope exchange experiments. The evolution of the aqueous solution Si concentration and pH over the 10 days of this equilibration stage and the calculated equilibrium Si concentrations with PHREEQC are provided in Table A of the electronic supplement (Annex II). The temporal evolution of these aqueous Si concentrations are also shown in Fig. 4.3.

Figure 4 . 3 -

 43 Figure 4.3 -Dissolved Si concentration during the 7 day equilibration of the experimental solutions containing 0.05 mol/kg and 0.08 mol/kg catechol, compared to a solution without organic ligands at pH 6 (data from Stamm et al., 2019). Dashed lines represent the equilibrium concentration calculated for 0.05 mol/kg and 0.08 mol/kg catechol experiments with PHREEQC.

  where C K WX represents the concentration of dissolved silica in equilibrium with amorphous silica and S `through these measured Si concentrations were calculated by fitting the measured Si concentration to Eqn. (4.7). The rate constants for the amorphous silica dissolution reactions are provided in Table4.3.

  2 0.18 H 2 O. The measured BET surface areas of the final reacted powders (e.g. the powders recovered from the longest reacted individual closed reactors in each series) are 10-15 % lower than that of the pre-experiment powders and were equal to 174.7 m 2 /g and 165.6 m 2 /g for the 0.05 and 0.08 mol/kg catechol solution respectively. These changes could result from some minor Ostwald ripening of the amorphous silica grains during the experiments, however the experimental solids appear to be unchanged during the isotope exchange experiments under SEM. The temporal evolution of the pH, Si concentration, and the Si isotopic compositions of the aqueous solutions and solids during 7 days of isotopic exchange are shown in Fig. 4.4. The pH of the aqueous 0.05 mol/kg catechol solution remained constant during the experiments. The pH of the aqueous 0.08 mol/kg catechol experiments decreased at the beginning of the experimental series, but remained constant thereafter. The aqueous Si concentration in 0.05 mol/kg catechol series remained constant, whereas in the 0.08 mol/kg catechol series it first decreased, but then stabilised after 1 day. Due to a decrease in dissolved Si concentration of more than 10%, the composition of the aqueous solution collected from the longest duration experiment of the 0.08 mol/kg catechol experiment series was not considered in the retrieval of equilibrium isotope fractionation factors described below. In both experimental series the δ 29 Si values of the fluids and solids (Tab. 4.1) mirror one another. The δ 29 Si value of the 29 Si enriched solutions decreases rapidly in the first 3 h of the experiment experimental series and the corresponding δ 29 Si value of the solids increased. The same trend is exhibited by the δ 30 Si values.

Figure 4 . 4 -

 44 Figure 4.4 -Plots of pH, Si concentrations and isotopic compositions of solids and solutions over time during the isotopic exchange experiments. The 2 S.D. uncertainties of data points are denoted by the error bars. Initial values are represented by dashed lines with their 2 S.D. error envelope. A: 0.05 M catechol experiment, B. 0.08 M catechol experiment

  denotes δ 29 Si of the fluid at any time t during the reaction, and δ i and δ e describe the initial and equilibrium δ 29 Si value of the fluid, respectively; δ e was deduced iteratively from mass balance considerations. The δ-F plots for δ 30 Si are shown in Fig. 4.5. A close correspondence can be observed between the experimental δ 30 Si values and the extrapolation straight-lines forced to the points of the starting materials. It can be seen that at the end of the longest runs about 70 an 60 % of equilibrium fractionation was reached in 0.05 mol/kg and 0.08 mol/kg catechol solutions (Fig.4.5 B and C), respectively. The values of ∆ eq 30

Figure 4 . 5 -

 45 Figure 4.5 -Plots the isotopic composition of the solids and solutions as a function of the degree of isotope exchange (F) during the isotope exchange experiments. A. pH= 6.4 at 25 °C (modified after Stamm et al., 2019), B: 0.05 M catechol experiment, C. 0.08 M catechol experiment.

  Fig. 4.6 shows the calculated Si isotopic fractionation factors between Si catecholate and quartz, and Si catecholate and H 4 SiO 4 o as a function of temperature, which are fitted with the polynomial functions of 1/T shown in Table4.5.

Figure 4 . 6 -

 46 Figure 4.6 -Results of ab initio calculations, showing the evolution of the fractionation factor between Si catecholate and quartz, and Si catecholate and silicic acid as a function of temperature. Experimental data of this study are shown by the star and circle symbols.

Figure 4 . 7 -

 47 Figure 4.7 -The temporal evolution of the degree of isotopic exchange of the organic experiments of this study and experiments without organic ligands of Stamm et al. (2019). Dashed lines are generated assuming a first order rate law (Eqn. 4.10), using the dissolution rate constants from the amorphous silica dissolution experiments.

  10) was applied to calculate F values as this rate law is consistent with the dissolution rate of the amorphous SiO 2 determined above. Values of F generated as a function of time from Eqn. (4.10) using amorphous silica rate constants derived from Eqn. (4.7) are compared with experimental F values of this study in Fig. 4.7. It can be seen in this figure that during the first 1.5 days of reaction F values derived from amorphous silica dissolution rate are close to the measured F values. Over this period of time isotope exchange experiments attained up to 55 % of their final equilibrium value. After 1.5 days the isotopic exchange rate slows significantly (Table

Figure 5 . 1 -

 51 Figure 5.1 -Representative images of synthesized brucite powders. A. SEM image of the initial powder BB showing agglomerates brucite grains and fine brucite platelets . B. SEM image of the initial powder BE showing fine brucite platelets C. Representative SEM image of reacted brucite powder of the sulphate experiment. D. Representative SEM image of reacted brucite powder of the EDTA experiment.

3 . 2 µm

 32 The reactors were sealed and placed into a constantly mixing orbital shaker. Closed system conditions were verified by weighing the reactors at the beginning and end of each experiment. At pre-chosen time intervals, an individual experiment was stopped. The reactors were centrifuged for 20 min at 4500 rpm and the supernatant was separated from the powder and filtered with Merck® 0.Teflon syringe filters. The pH of the solutions were measured immediately after sampling. The remaining sample was acidified with 10 µl 15 N HNO 3 and subsequently analysed for Mg concentration and isotopic composition. The recovered brucite powders

Fig. 5 .

 5 Fig. 5.2 and listed in Table B of the electronic supplement (Annex III).

Figure 5 . 2 -

 52 Figure 5.2 -Temporal evolution of dissolved Mg concentration during the equilibration of the initial reactive solutions during the first step of each experimental series. The dashed lines represent a fit of the data using Eqn. 11 with values of rate constant k' -listed in Table 5.4.

Fig. 5 .

 5 1 C and D. The appearance of these solids is significantly different than that of the initial synthesized brucite. The initial synthesized brucite consists mainly of thin platelet structures (Fig.5.1 A and B) with small rounded grains, whereas the reacted brucite powder (Fig.5.1 C and D) exhibits mainly small rounded grains. The measured BET surface areas of the reacted powder, provided in Table5.5, are within 10 % of their initial values, with the exception of the brucite recovered from the longest experiment of series BB, run without organic ligands, which exhibited a surface area increase of 24%, and the brucite recovered from the longest exchange experiment of series BE EDTA, run in the presence of aqueous EDTA, which exhibited a surface area decrease of 53 %. The evolution of the pH, aqueous Mg concentrations, and the Mg isotopic compositions of the solutions and solids during all isotopic exchange experiments are shown in Fig. 5.3. The pH of the isotope exchange experiments exhibits some variation, notably for the experiments run in the presence of aqueous citrate, sulphate, and EDTA. These pH variations have a measurable impact on the dissolved Mg concentration in the experimental aqueous solutions. If the aqueous Mg concentration of a reactive solution during an isotope exchange experiment differed by more than 10 % from its original value, the experiment was not considered in the determination of the equilibrium fractionation factors retrieved below. The experimental runs in the presence of citrate show an increase in the aqueous Mg concentration, which stabilizes in the longest duration experiments (Fig. 5.3 C). Therefore the equilibrium fractionation factor was determined using: i) all measured isotopic data and, ii) only the data from long duration runs exhibiting constant aqueous Mg concentration. Note that after an initial increase in the pH and aqueous Mg concentration, the conditions of the experiments run in the presence of aqueous EDTA remained constant and were considered as equilibrium conditions (Fig. 5.3 F).

Figure 5 . 3 -

 53 Figure 5.3 -Plots of pH, Mg concentrations and isotopic compositions of solid phase and solutions as a function of time during the second stage of each experimental series. The 2 S.D. uncertainties of data points are denoted by the error bars. Initial values are represented by dashed lines with their 2 S.D. error envelope (grey shades). A. No inorganic or organic ligand (BB) , B: No inorganic or organic ligand (BABE) C. Mg citrate experiment (BBC), and D. Mg sulphate experiment (BCS), E. Mg sulphate experiment (BDS), F. Mg EDTA experiment (BE-EDTA).

  5.4A) and 0.1 (series BABE, Fig 4B), respectively. Two equilibrium Mg isotope fractionation factors for experiments containing aqueous citrate were determined, ∆ eq 26 Mg brucite-solution = -0.07± 0.21 ‰ and -0.17± 0.10 ‰ for a fraction of Mg(citrate) -in solution of 0.51 and 0.44, respectively (Fig. 5.4 C and D).

Figure 5 . 4 -

 54 Figure 5.4 -Plots of the isotopic composition of the solid phase and solutions as a function of the degree of isotope exchange during the second stage of each experimental series. A. No inorganic or organic ligand (BB) , B: No inorganic or organic ligand (BABE) C. Mg citrate experiment using all isotopic data (BBC), D. Mg citrate experiment using only the two solutions of longest duration (BBC * ), E. Mg sulphate experiment (BCS), F. Mg sulphate experiment (BDS), G. Mg EDTA experiment (BE-EDTA). Excluded data from the fit are shown by grey symbols -see section 5.3.2.

Figure 5 . 5 -

 55 Figure 5.5 -Representative plots of the experiment without inorganic or organic ligands (BABE) and the experiment performed with aqueous EDTA in solution. The blue dotted lines denote the are used to determine the rate of the initial or surface exchange (grey area). The bulk isotope exchange rates are derived using the red dashed lines.

  7 and compared to the values of brucite dissolution rate derived in the present study from Eqn. (5.11). It can be seen that the values of the initial rate constant for Mg isotope exchange are comparable (within one order of magnitude) to the bulk brucite dissolution rate constants generated during the first step of each experimental series. The longer-term rates, however are about 3 to 4 orders of magnitude slower than their corresponding bulk brucite dissolution rate constants except in the presence of EDTA. These results are shown in Figure 5.6 where the measured and calculated variation of the degree of isotopic exchange F are shown as a function of time.

Figure 5 . 6 -

 56 Figure 5.6 -The temporal evolution of the degree of isotopic exchange F during the six experimental series run this study. Dotted lines are generated assuming a first order rate law (Eqn. 5.14), using the dissolution rate constants from the brucite dissolution rate experiments (Table5.4) performed as the first stage of each experimental series. Dashed lines are generated assuming first order rate law, using the bulk isotopic rate constants shown in Table5.7

Chapter 6 .

 6 Conclusions and outlook-160-Another important tool to model past and present natural processes are ab initio calculations. Therefore the accuracy of such calculation has to be verified. During this thesis it has been shown for the Si-catecholate system that ab initio calculations can accurately predict the equilibrium fractionation factor of this system or between silicic acid and its deprotonated form. However, experimental and theoretical results of the equilibrium isotope fractionation factors can also significantly differ from each other, as has been demonstrated in this thesis for the case of Mg. The cause of the differences are poorly understood, but might be caused by the difficulty of precisely modelling the structure of the weak complexes Mg forms with many inorganic and organic ligands. As such, one should be cautious applying the results of ab initio calculations to natural systems without validation. These observed discrepancies between experimental data and theoretical predictions should be addressed in future studies.Ideally an extensive database of equilibrium isotopic fractionation factors among Si and Mg minerals and aqueous fluids, taking account of both experimental results and ab initio calculations, can be developed allowing the extensive use of mineral isotopic signals to interpret natural geochemical systems.

  de complexes aqueux inorganiques et organiques, sur les facteurs de fractionnement à l'équilibre du silicium et du magnésium dans les systèmes silice amorphe (SiO 2 (s))solution et brucite (Mg(OH) 2 ) -solution. Les expériences d'échange isotopique ont été réalisées à l'équilibre chimique en utilisant la «méthode des trois isotopes» et les résultats ont été comparés à ceux de calculs ab initio correspondants aux mêmes systèmes. En plus de fournir des facteurs de fractionnement isotopique à l'équilibre, cette méthode permet de déterminer les vitesses d'échange isotopique et ainsi de mieux comprendre les mécanismes d'acquisition des signatures isotopiques des solides dans la nature et les conditions de leur préservation. Afin d'appliquer quantitativement les signatures isotopiques de Si comme traceurs de l'altération continentale ou du pH et de la température passés des océans, la première partie de cette thèse a été consacrée à la détermination des facteurs de fractionnement isotopique de Si à l'équilibre entre la silice amorphe (SiO 2 0.32 H 2 O) et des fluides aqueux inorganiques à pH variable de 5.8 à 9.9 à 25 et 75 °C. Les résultats expérimentaux montrent qu'à 25 °C, le facteur de fractionnement isotopique à l'équilibre entre silice amorphe et fluide aqueux, Δ eq 30 Si solide-fluide , augmente de 0.45 ± 0.20 ‰ à pH 6.4 à 1.13 ± 0.23 ‰ à pH 9.9. Avec l'augmentation de la température à 75 °C, ces facteurs de fractionnement diminuent jusqu'à 0.07 ± 0.6 ‰ à pH= 5.8 et 1.06 ± 0.13 ‰ à pH= 9.1. La valeur obtenue pour un pH < 7 et 25 °C est en bon accord avec les valeurs expérimentales obtenues par Roerdink et al. (2015)

  13 ‰ et à -2.21 ± 0.05 ‰. Ces valeurs sont comparables aux résultats des calculs ab initio rapportés par[START_REF] Dupuis | Fractionation of silicon isotopes in liquids: The importance of configurational disorder[END_REF], montrant que des calculs expérimentaux ou théoriques peuvent être utilisés pour modéliser avec précision les processus naturels de fractionnement isotopique du silicium. Les résultats obtenus dans la première partie de cette thèse indiquent que les signatures isotopiques de Si peuvent potentiellement être utilisées comme indicateurs de paléo pH dans des environnements alcalins et peuvent en outre donner une idée de la température de formation de solides siliceux. La vitesse d'échange isotopique dans les systèmes inorganique SiO 2 (am) -solution correspond à la vitesse de dissolution de la silice amorphe, ce qui montre que le mécanisme dominant d'échange isotopique dans ce système est l'attachement/ détachement de matière à l'interface solideliquide et non pas le transport au sein du solide. Cette dernière observation suggère que les signaux isotopiques originaux du Si de la silice amorphe pourraient éventuellement être modifiés au fil du temps par le biais d'une interaction fluide-solide, même à l'équilibre chimique entre solution et silice amorphe.Dans les environnements biogéniques naturels, la silice dissoute peut se complexer avec nombre de ligands organiques. La coordinence du silicium dissous peut ainsi passer de 4 à 5 ou 6 en présence de certains ligands organiques. De tels changements de coordinence sont susceptibles de considérablement modifier le fractionnement isotopique de Si lors des interactions solide-fluide. Cette possibilité a été évaluée dans la seconde partie de cette thèse en mesurant à l'aide de la méthode des trois isotopes les facteurs de fractionnement isotopiques à l'équilibre entre silice amorphe et solutions aqueuses contenant du catéchol (C 6 H 4 (OH) 2 ). Il a été montré que le facteur de fractionnement isotopique de Si à l'équilibre entre le complexe aqueux Si-catéchol et la silice amorphe est environ 20 ‰ plus négatif que le facteur de fractionnement isotopique de Si à l'équilibre entre l'acide silicique et la silice amorphe. Les facteurs de fractionnement isotopique de Si mesurés à l'équilibre sont en très bon accord avec les valeurs correspondantes obtenues par calculs ab initio. Ces résultats montrent que la présence de ligands organiques aqueux peut avoir un impact considérable sur le fractionnement isotopique du silicium et pourrait expliquer les signatures isotopiques fortement négatives de Si observées dans des biomatériaux naturels comme , les éponges ou les diatomées.La troisième partie de cette thèse est dédiée à la mesure des facteurs de fractionnement isotopique du magnésium à l'équilibre entre la brucite et des solutions aqueuses contenant du Mg en présence ou non de ligands organiques et inorganiques sélectionnés, notamment le citrate, l'EDTA (acide éthylènediaminetétraacétique) et le sulfate. Le facteur de fractionnement isotopique déterminé dans cette étude entre brucite et solution, en l'absence de ligands inorganiques et organiques, est en bon accord avec les données expérimentalesde Li et al. (2014) et les calculs théoriques conduits récemment dans notre laboratoire. Les résultats obtenus en présence de ligands présentent des similitudes avec ceux des échanges isotopiques entre fluide aqueux et silice amorphe rapportés ci-dessus. Il s'est avéré notamment que la spéciation aqueuse de Mg pouvait avoir une influence importante sur le fractionnement isotopique de Mg à l'équilibre. En présence d'EDTA, nous avons mesuré un facteur de fractionnement isotopique de Mg à l'équilibre entre la brucite et la solution, Δ eq 26 Mg brucite- solution , égal à 2.43 ± 0.20 ‰, ce qui montre que la brucite incorpore préférentiellement les isotopes lourds du Mg en présence de ce ligand. Ceci est en accord avec les études expérimentales et théoriques existantes. Les facteurs de fractionnement isotopiques de Mg mesurés à l'équilibre en présence de citrate et de sulfate aqueux présentent des valeurs nettement plus faibles, respectivement égales à -0.04 ± 0.19 ‰ et 0.41 ± 0.14 ‰. Ces valeurs diffèrent quelque peu de celles déduites des calculs ab initio récemment publiées, ce qui suggère que ces calculs doivent être révisés ou davantage validés avant de pouvoir être utilisés avec confiance. Ces résultats montrent que la présence dans les systèmes naturels de certains ligands organiques, comme celle des ligands inorganiques carbonate et hydrogénocarbonate, peut avoir un impact significatif sur les facteurs de fractionnement isotopique du Mg à l'équilibre entre les minéraux porteurs de magnésium et les solutions aqueuses. La composition isotopique de Mg dans les minéraux magnésiens pourrait ainsi s'avérer être un traceur utile pour caractériser les environnements dans lesquels se sont formés ces minéraux. Cette thèse fournit de nouvelles connaissances mais ouvre aussi la porte à de nouveaux projets de recherche. Nos résultats montrent que le fractionnement isotopique à l'équilibre peut fortement dépendre de la spéciation aqueuse de l'élément étudié. Par conséquent, la composition chimique aqueuse, notamment la présence de nombreux ligands, peut influencer de manière significative les signatures isotopiques des solides et des solutions dans les systèmes naturels. Dans les environnements biologiques, notamment, la présence de ligands organiques aqueux peut altérer de manière significative les signatures isotopiques des solides précipités. Les ligands organiques (ou inorganiques) ont deux voies possibles pour impacter la composition isotopique du solide, soit en altérant la composition isotopique de l'ion métallique libre incorporé dans le solide, soit en participant directement à l'incorporation du métal dans la phase solide sous forme de complexe organométallique. Dans ce dernier cas, les ligands organiques peuvent conduire le piégeage et l'incorporation d'éléments comme Si et Mg dans des organismes tels que les éponges, les diatomées et les plantes. Dans certains cas, le fluide biotique au sein de l'organisme fournit le vecteur chimique nécessaire pour concentrer les métaux de la solution afin d'aider à la fabrication des squelettes ou des coquilles. Une nouvelle direction de recherche prometteuse serait de déterminer quels sont les ligands inorganiques et organiques participant à ces processus biologiques naturels. La mise en oeuvre des isotopes stables non traditionnels pourrait faciliter de telles études. Par exemple, comme on l'a montré pour Si dans cette thèse, les ligands organiques peuvent modifier la coordination des métaux en solution et entraîner ainsi une composition isotopique distincte du métal. Connaissant les principes de fractionnement isotopique en présence des ligands organiques et inorganiques, il pourrait également être possible de développer de nouveaux outils isotopiques pour mieux contraindre les cycles biogéochimiques du silicium et du magnésium ainsi que le comportement de ces éléments dans les processus naturels. Cette thèse fournit en outre un aperçu sur les mécanismes d'échange isotopique, montrant que la vitesse d'échange isotopique dépend fortement du système étudié et de sa géométrie, pouvant être contrôlée soit par réaction chimique à l'interface solide-liquide soit par transport au sein du solide. Un futur projet de recherche pourrait être centré sur la quantification des vitesses d'échange isotopique pour différents systèmes solide-solution afin de mieux caractériser les mécanisme d'échange isotopique ainsi que le degré de préservation des signatures isotopiques des solides à l'échelle des temps géologiques. Les calculs ab initio sont un autre outil important pour modéliser les processus naturels passés et présents. Par conséquent, il est nécessaire de pouvoir vérifier la précision de ces calculs. Au cours de cette thèse, on a montré que les calculs ab initio pouvaient prédire avec précision le facteur de fractionnement à l'équilibre pour le système SiO 2 -catecholate ou entre l'acide silicique et sa forme déprotonée. Cependant, les résultats des calculs expérimentaux et théoriques des facteurs de fractionnement isotopiques à l'équilibre peuvent également diverger comme nous l'avons montré dans le cas de Mg. L'origine de ces différences est encore mal connue mais elle peut résider dans la difficulté à modéliser précisément la structure des complexes assez faibles que forme le magnésium avec nombre de ligands inorganiques et organiques. Il convient donc de faire preuve de prudence en appliquant sans les valider les résultats des calculs ab initio à des systèmes naturels. Des études devront être conduites dans le futur afin de résoudre les divergences observées entre les données expérimentales et les prédictions théoriques. Idéalement, une base de données exhaustive des facteurs de fractionnement isotopique à l'équilibre entre solides et espèces aqueuses de Si et de Mg, tenant compte des résultats expérimentaux et des calculs ab initio, pourrait être développée, permettant ainsi l'utilisation extensive des signatures isotopiques des solides pour interpréter les systèmes géochimiques naturels.

  work was funded by the European Union through the IsoNose People Programme and I am very grateful to be part of this network.

Special thanks go to

Jérôme Chmeleff for his advice and patience in teaching me, together with Thomas Zambardi everything I know about the Neptune. I also want to thank Merlin Méheut for many interesting discussions and sharing his knowledge about ab initio calculations. I am thankful to the academic staff at the GET, especially Pascale Bénézeth, Sebastian Fabre, Vasileios Mavromatis for their help and support. Additionally, I owe many thanks to the technical staff, who supported me during my lab work. Special appreciation is directed to Philippe Besson, Frederic Candaudap, Alain Castillo, Carole Causserand, Pascal Gisquet, Manuel Henry, Aurélie Marquet, Stephanie Mounic at the GET, Gwénaëlle Guittier from the Laboratoire de Génie Chimique, Philippe De Parseval, and Teresa Hungria from the Centre de MicroCaractérisation Raimond Castaing Toulouse. During my PhD I had the opportunity to spend time and learn in other great laboratories. I would like to express my gratitude to Wafa Abouchami, Julien Bouchez, Jérôme Gillardet and Xu Zhang for welcoming and helping me during my stay at the IPG in Paris. Many thanks to Josefine Buhk, Friedhelm von Blanckenburg, Daniel Frick, Jan Schüssler and Maja Tesmer from the GFZ in Potsdam for their support and help during my secondment.

Table 4 .

 4 6 -Isotopic exchange rates, calculated after 1.5 days of isotopic exchange. ........... 115

Table 5 . 1 -

 51 Synthesized brucite powders used in this study .................................................. 124

Table 5 . 2 -

 52 Initial aqueous solutions prepared for chemical equilibration of brucite. ........... 126

Table 5 . 3 -

 53 Mg concentrations and pH of solutions after chemical equilibration, and after adding the isotopic spike ........................................................................................................ 128

Table 5 .

 5 4 -Equilibrium Mg concentrations in solutions and dissolution rate constants and rates obtained from chemical equilibration. ........................................................................... 133

Table 5 .

 5 5 -Overview of the results of the isotopic exchange experiments performed in this study ....................................................................................................................................... 135

Table 5 .

 5 6 -Average aqueous Mg-speciation during the second stage of each experimental series run in this study ............................................................................................................ 144

Table 5 . 7

 57

-Rate constants obtained in this study. ................................................................. 152

  Dans les fluides naturels, Si et Mg peuvent apparaître sous forme de différentes espèces parallèlement à celles qui dominent généralement leur spéciation aqueuse, l'acide silicique (H 4 SiO 4 ) et l'ion Mg 2+ . En particulier, nombre de ligands organiques et inorganiques peuvent former des complexes aqueux avec ces deux éléments. On sait que des fractionnements isotopiques importants peuvent se produire entre les différentes espèces aqueuses d'un même élément présentes en solution. De tels fractionnements ont été mis en évidence pour des éléments la tels que le bore, le carbone, le magnésium, le mercure, les métaux de transition, le silicium

Table 2 .

 2 1 -Summary of the properties of the washed amorphous SiO 2 powders used in this study: S BET represents the specific BET surface area of the powders. The water content (m H2O ) and the resulting chemical formula of the powder taking account of this water content are provided.

	batch batch	m start	m end	∆m	S BET	m H2O	chemical
	n°	name	[g]	[g]	[g]	[m 2 /g]	[wt %]	formula
	1	Sib	44.82	23.37	21.45	214.7	8.93	SiO 2 • 0.33 H 2 O
	2	Sic	62.37	31.05	31.32	195.0	9.15	SiO 2 • 0.34 H 2 O
	3	Sid	82.17	25.40	56.77	189.8	8.67	SiO 2 • 0.32 H 2 O
	4	Sig	50.59	32.57	18.02	195.6	7.87	SiO 2 • 0.28 H 2 O
	5	Sik	73.59	13.73	59.86	179.80	8.86	SiO 2 • 0.32 H 2 O
	2.2.2. Brucite synthesis
	For magnesium experiments, microcrystalline brucite (Mg(OH) 2 ) powder was synthesized
	by the wet precipitation method previously described by Henrist et al. (2003), Lv et al.
	(2004), and Estrada et al. (2015). In detail, 100 ml of an aqueous 2M MgCl 2 solution was
	prepared from reagent grade MgCl 2 •6H 2 O powder from VWRChemicals ® and deionized
	Milli-Q ® water. This aqueous MgCl 2 •6H 2 O solution was added using a Metrohm ® 702 SM
	Titrino titration device at 2.5 ml/min dropwise into 200 ml suprapur Merck ® 25% NH 3
	solution, which was constantly stirred and heated to 45°C. This experimental protocol is
	summarized in Fig. 2.3.

Table 2 .2 -Characteristics

 2

				of the synthesized brucite
	powders used in this study.
	batch batch T precipitation m obtained	S BET
	n°	name	[°C]	[g]	[m 2 /g]
	1	BB	48.0	10.58	30.54
	2	BC	45.0	7.94	39.4
	3	BD	48.1	7.19	29.23
	4	BE	53.1	8.27	35.53
	2.2.3. Aqueous Solutions
	2.2.3.1. Inorganic solutions

Table 2 . 3 -

 23 Summary of the initial aqueous solutions of each experimental series performed in the present study2) Ethylenediaminetetraacetic acid (EDTA): Titriplex III Merck ® 0.1 N EDTA solution for titration with the chemical formula C 10 H 14 N 2 Na 2 O 8 •2 H 2 O was used to perform Mg-EDTA experiments. The compositions of all aqueous solutions used in the experiments performed in this study are listed in table 2.3. The aqueous isotopic spike solutions used in this study (see Chapter 2.1.1) were prepared using Eursio-top ® SiO 2 and MgO powder isotopically enriched in 29 Si and 25 Mg, respectively. The 29 Si isotope tracer was prepared by dissolving 40.6 mg of the 29 SiO 2 enriched powder, having an initial composition of 0.21% 28 Si, 99.76% 29 Si, and 0.03%

	2.2.4. Isotopic spike solutions

30

Si into 500 ml of de-ionized water. The pH was then adjusted to 10 using a 2 mol/kg ammonia solution. This solution was then filtered with a 0.22 µm Millipore ® Teflon syringe-filter and its concentration was measured with colorimetry (see Chapter 2.3.2.4). Both spike solutions were analysed by High Resolution -ICP-MS (see Chapter 2.3.2.5), to determine the isotope ratios of the spikes. The spike ratios in solution and the properties of spike solutions are listed in Table

2

.4.

The 25 Mg enriched spike solution was prepared by dissolving 50.7 mg 25 MgO enriched powder, with a initial composition of 2.4% 24 Mg, 96.4 % 25 Mg, and 1.2% 26 Mg into a 500 ml 1N HCl solution prepared from MQ ® water and bi-distilled HCl. After its complete dissolution, the solution was filtered with 0.22 µm Millipore ® Teflon syringe-filter and the pH was adjusted with 4 mol/kg NaOH to 8.8. The concentration of Mg in this fluid was determined by AAS (see Chapter 2.4.2.2).

Table 2 . 4 -

 24 Properties of the spiked 25 Mg-and 29 Si-aqueous solutions.

	solution	pH	Concentration 24 Mg or 28 Si 25 Mg or 29 Si 26 Mg or 30 Si
			[ppm]	[%]	[%]	[%]
	29 SiO 2	9.8	25.5	0.21	99.76	0.03
	25 MgO	8.8	40.8	2.43	96.47	1.10

Table 2 . 5 -

 25 Measured concentrations and pH of chemical equilibrated, and spiked solutions used in the isotope equilibration experiments performed in this thesis. Note that concentrations and pH did not significantly change due to the addition of the spike, therefore equilibrium conditions are maintained within uncertainty of the analyses.

	Experiment Temperature chem. equil. solution	spiked solution
	ID	[°C]	pH	Conc.	pH	Conc.
				[ppm]		[ppm]
	Solutions for amorphous silica isotope exchange experiments
	SibA	25	6.2	44.40	6.1	47.96
	SicB	25	10.1	116.24	9.9	115.42
	Sig75A	75	5.8	117.36	5.2	122.27
	Sik75B	75	9.3	282.22	9.2	287.16
	SigC0.05 M	25	8.9	343.23	8.9	344.64
	SigC0.08 M	25	8.9	612.07	8.9	599.30
	SidG	25	10.0	115.68	10.0	114.13
	Solutions for the brucite isotope exchange experiments
	BB	25	9.4	2018.99	9.0	2084.04
	BABE	25	9.4	2019.89	9.4	2002.65
	BB-Citrate	25	10.1	147.97	10.2	146.05
	BCS	25	9.4	1724.00	9.5	1703.29
	BDS	25	9.9	274.16	9.9	271.01
	BE-Edta	25	12.5	1626.09	12.4	1715.05

Table 2 . 6 -

 26 Average amount of powder and solution used for each set of isotopic exchange experiment

	Experiment Temperature m powder	V solution	powder:solution ratio
	ID	[°C]	[g]	[ml]
	amorphous silica isotope exchange experiments
	SibA	25	0.15	5.03	1:33
	SicB	25	0.15	5.01	1:34
	Sig75A	75	0.15	4.01	1:26
	Sik75B	75	0.15	5.04	1:33
	SigC0.05 M	25	0.30	9.94	1:33
	SigC0.08 M	25	0.30	9.98	1:33
	SidG	25	0.31	9.89	1:32
		brucite isotope exchange experiments
	BB	25	0.10	5.02	1:50
	BABE	25	0.49	5.03	1:10
	BB-Citrate	25	0.10	5.02	1:49
	BCS	25	0.19	3.04	1:16
	BDS	25	0.51	5.04	1:10
	BE-Edta	25	0.50	5.00	1:10

  meter, and that calculated from the electrode voltage was 0.006. This lies within the error of the measurement, therefore it is considered as negligible.Experimental solutions from the T ≈ 75°C experiments cooled during sampling and thus had to be measured at lower temperatures. The sample temperature was thus determined simultaneously with the pH. Values of pH were automatically corrected for the measured temperature by the pH meter. These pH values could later be recalculated with PHREEQC

	2.4.2.1. pH measurements Solution pH was measured with a Metrohm ® 913 pH Meter connected to a glass microelectrode (pH= 0-14 / T= 0-80°C) containing a 3M KCl electrolyte solution. Electrode 2.4.2.2. Atomic absorption spectroscopy (AAS) calibration was performed using Orion Thermo Scientific (see Chapter 2.4) for T=75°C. Aqueous magnesium concentrations were measured by Flame Atomic

® buffers with certified values of 4.01, 7.00, and 10.01 at 25°C. The pH 4.01 buffer was repeatedly measured (n=39) over 5 months to assure measurement quality. The average deviation between the value indicated by the pH

Table 2 . 7 -

 27 Equilibrium constant added to the PHREEQC llnl database

	Reaction			log K	Source
	SiO 2 + 2 H 2 O ↔ H 4 SiO 4 o	-2.80	this study
	SiO 2 + 2 H 2 O ↔ HSiO 3	-	-9.95	Sverjensky (1997)
	SiO 2 + 2 H 2 O ↔ H 2 SiO 4 2-+ 2 H +	-22.96	Sverjensky (1997)
	H 2 Cat o ↔ HCat -+ H +		-9.45	Sillen & Martell (1971)
	H 2 Cat o ↔ HCat 2-+ 2 H +	-22.45	Sillen & Martell (1971)
	SiO 2 + 3 H 2 Cat ↔ SiCat 3	--+ 2 H + + 2 H 2 O	-12.00	Pokrovski & Schott (1998)

Table 2 . 8 -

 28 Equilibrium constants added for speciation calculation to the core10 database.

		Reaction		log K	Source
	Mg(OH) 2 + 2H + = 2 H 2 O + Mg 2+	17.209	this study
		Sulphate
	SO 4	2-+ Mg 2+ ↔ MgSO 4		2.41	McCollom & Shock (1997)
		Citrate
	Citrate 3-+ H + ↔ HCitrate 2-		6.40	Bénézeth et al. (1997)
	HCitrate 2-+ H + ↔ H 2 Citrate -		4.76	Bénézeth et al. (1997)
	H 2 Citrate -+ H + ↔ H 3 Citrate 2-		3.13	Bénézeth et al. (1997)
	Mg 2+ + Citrate 3-↔ Mg(Citrate) -		5.00	Covingron & Danish (2009)
	Mg 2+ + HCitrate 2-↔ MgHCitrate	2.59	Covingron & Danish (2009)
	Mg 2+ + H 2 Citrate -↔ MgH 2 Citrate +	1.00	Covingron & Danish (2009)
	Mg 2+ + 2Citrate 3-↔ Mg(Citrate) 2	4-	5.49	Covingron & Danish (2009)
		EDTA
	EDTA 4-+ H + ↔ HEDTA 3-		10.95	Carini & Martell (1953)
	EDTA 4-+ 2 H + ↔ H 2 EDTA 2-		17.22	Carini & Martell (1953)
	EDTA 4-+ 3 H + ↔ H 3 EDTA -		20.37	Hummel (2005)
	EDTA 4-+ 4 H + ↔ H 4 EDTA		22.60	Hummel (2005)
	EDTA 4-+ 5 H + ↔ H 5 EDTA +		23.90	Hummel (2005)
	Mg 2+ EDTA 4-↔ MgEDTA 2-		10.45	Gautier (2013)
	Mg 2+ EDTA 4-+ H + ↔ MgHEDTA -	20.87	Hummel (2005)
	Na + + EDTA 4-↔ NaEDTA 3-		2.70	Felmy & Mason (2003)

The experimental determination of equilibrium Si isotope fractionation factors among H 4 SiO 4 o , H 3 SiO 4 -and amorphous silica (SiO 2 •0.32 H 2 O) AT 25 and 75 °C using the three isotope method

				o ) in most
	natural aqueous fluids at pH <8.5, but forms H 3 SiO 4	-, H 2 SiO 4 2-, and polymeric Si species in
	more alkaline fluids. In this study isotope exchange experiments were performed at bulk
	chemical equilibrium between amorphous silica (SiO 2 •0.32 H 2 O) and inorganic aqueous
	fluids at pH ranging from 5.8 to 9.9 at 25° and 75°C with experiments running as long as
	375 days. The 'three isotope method' was used to quantify the equilibrium Si isotope
	fractionation, ∆ eq	30 Si, between amorphous silica and aqueous Si; this equilibrium
	fractionation factor was found to be 0.45 ± 0.20 ‰ at pH=6.4 and 25 o C, and 0.07 ± 0.06 ‰
	at pH=5.8 and 75°C. At more basic pH, equilibrium fractionation factors between solid and
	aqueous solution are higher, 1.63 ± 0.23 ‰ at pH=9.9 and 25 o C, and 1.06 ± 0.13 ‰ at
	pH=9.1 and 75°C. Taking account of the distribution of the aqueous Si species, an
	equilibrium fractionation factor between H 3 SiO 4	-and H 4 SiO 4	o of -2.34 ± 0.13 ‰ and -
	2.21± 0.05 ‰ for 25 and 75°C was determined, respectively. The distinct equilibrium
	isotope fractionation factors of H 3 SiO 4	-and H 4 SiO 4	o
				4 SiO 4	o , H 3 SiO 4	-and
	amorphous silica (SiO 2• 0.32 H 2 O) AT 25 and 75 °C using the three isotope method.
	Geochimica et Cosmochimica Acta 255, 49-6. DOI: 10.1016/j.gca.2019.03.035" Copyright
	2019 Elsevier.

A version of this chapter is published as: "Franziska M. Stamm, Thomas Zambardi, Jérôme Chmeleff, Jacques Schott, Friedhelm von Blanckenburg, Eric H. Oelkers: The experimental determination of equilibrium Si isotope fractionation factors among H

Table 3 . 1 -

 31 Summary of the initial conditions of the first stage of each experimental series performed in the present study. Quantity in grams of fluids and solids used are denoted as m

	initial sol and m SiO 2 ,am .

Table 3 . 2

 32

-Overview of the results of the isotopic exchange experiments performed in this study. Uncertainties of the isotopic measurements are expressed as 2 SD (Standard Deviation) and 2 SE (Standard Error). The 2 SE is computed following the relation: gh = gi j.k,l1

Table 3 . 3 -

 33 Concentration of aqueous Si in equilibrium with amorphous silica and dissolution rate constants obtained from the first stage of the four experimental series run in this study.

	Exp.	Si-conc. equilibrium	k' -	k +
		[mmol]	[1/s]	[mol/(m²*s)]
	SibA	1.6	1.36 x 10 -6	3.13 x10 -12
	SicB	4.2	4.63 x 10 -6	2.85 x10 -11
	Sig75A	4.2	4.05 x 10 -6	2.47 x10 -11
	Sik75B	9.2	9.26 x 10 -6	1.24 x10 -10
	3.4.2. Results of Isotope exchange experiments
	3.4.2.1. Observations on the solid phases
	SEM and TEM images of amorphous SiO 2 collected from the longest duration experiment
	run of each experimental series were obtained; representative images are provided in Fig.
	3.3 C and D. These images show that these final solids contain only amorphous SiO 2 , and
	are identical in appearance to the pre-experiment, pre-treated solids.
	A summary of the various measured characteristics of the solids collected after the
	longest duration experiment of each series is provided in Table B of the electronic
	supplement (Annex I). The measured grain sizes of the collected final solids were 20 ± 1 nm
	(n=85, 2 S.D.), which are identical, within uncertainty, to the corresponding pre-treated
	solids. The water content of these final solids was measured at 8.4% by TGA, which is
	identical within uncertainty to that of the original pre-treated solids. Measured BET surface
	areas of the final reacted powders are somewhat lower than those of the original pre-treated
	solids; the largest decreases were those of the final pH 6.4, 25°C experiment and the final

pH 9.1, 75°C experiment, which exhibited a decrease of ~35%. This could result from

Table 3

 3

	2 ,am-fluid. The ∆ eq	30 SiSiO 2 ,am-fluid

30 SiSiO 2 ,am-fluid variation with pH can be attributed to the dependence of aqueous Si speciation on pH. The speciation of Si in the reactive fluids of each series is provided in

Table 3 . 4 -

 34 Average aqueous Si-speciation during the second stage of each experimental series run in this study together with the resulting isotopic fractionation factors between solid and solution, solid and the H

	.
	-	4
	3 SiO
	species, and between H
	-	4
	3 SiO

Table 3 . 5

 35 Initial isotopic exchange rates, calculated from the first 10 days of isotope exchange based on a first order rate law. Included in this table are values of k exch , where k exch =k 1 C Si,eq /(S/M), where C Si,eq refers to the total aqueous Si concentration in the fluid, k exch are directly comparable to k + in Table3.3.

			initial exchange
	Exp.	Si-conc.	k exch	k exch
		[mmol]	[1/s]	[mol/(m²*s)]
	SibA	9.0	2.36 x 10 -6	6.64 x10 -13
	SicB	20.3	3.08 x 10 -6	2.71 x10 -12
	Sig75A	16.5	6.50 x 10 -6	3.63 x10 -12
	Sik75B	42.7	1.40 x 10 -5	2.20 x10 -11

  aqueous solutions, one containing 0.05 mol/kg and the other 0.08 mol/kg catechol were prepared by dissolving Merck ® pyrocatechol (C 6 H 4 (OH) 2 ) in a NH 4 Cl -NH 3 pH-buffer solution. The buffer solution was prepared from de-ionized Milli-Q ® water, suprapur Merck ® NH 4 Cl salt and Merck ® 25 % NH 3 solution. In total concentrations of 0.1 mol/kg NH 4 Cl and 0.36 mol/kg NH 3 were used to prepare these buffer solutions.

Table 4 .

 4 1 -Overview of the results of the isotopic exchange experiments performed in this study. Uncertainties of the isotopic measurements are expressed as 2 SD (Standard Deviation) and 2 SE (Standard Error). The 2 SE is computed following the relation:

	× , where n denotes the number of measurements
	=

Table 4 . 2 -

 42 Summary of dissociation constants added to the PHREEQC llnl database and their reference

	Reaction	log K	Source
	SiO 2 + 2 H 2 O ↔ H 4 SiO 4 o	-2.80	Stamm et al. (2019)
	H 2 Cat o ↔ HCat -+ H +	-9.45	Sillen & Martell (1971)
	H 2 Cat o ↔ HCat 2-+ 2 H +	-22.45	Sillen & Martell (1971)
	SiO 2 + 3 H 2 Cat ↔ SiCat 3 --+ 2 H + + 2 H 2 O	-12.00	Pokrovski & Schott (1998)

Table 4 .

 4 3 -Equilibrium silicon concentrations in solutions and dissolution rate constants obtained from chemical equilibration of amorphous SiO 2 with solutions containing catechol.

	Exp.	Si-conc. equilibrium	k' -	k +	Source
		[mmol]	[1/s]	[mol/(m²*s)]
	SibA	1.58	1.36 x 10 -6 3.13 x10 -12	Stamm et al. (2019)
	SigC0.05	12.22	6.94 x 10 -6 9.72 x10 -11	this study
	SigC0.08	21.75	5.21 x 10 -6 1.65 x10 -10	this study

Table 4 . 4 -

 44 Average aqueous Si-speciation of the isotope exchange experiments together with the resulting isotopic fractionation factors between catechol bearing solution and the solid, Si catecholate and amorphous SiO

2 , and between Si catecholate and H

4 SiO 4 ° (H4).

Table 4 . 5 -

 45 Fits of 1000 ln α 30 Si Si catecholate-

	silica based on ax 2 +bx 3 , with x=10 3 /T
	Silica	T	a	b
		[°C]
	quartz 0-1100 -3.01	0.34
	H 4 SiO 4 0-1100 -2.96	0.38

Table 4 .

 4

	6 -Isotopic exchange rate constants, calculated after
	1.5 days of isotopic exchange.
	Exp.	Si-conc.	k exch	k exch
		[mmol]	[1/s]	[mol/(s*m²)]
	SibA	9.0	2.36 x 10 -6 6.64 x10 -13
	SigC0.05	11.1	7.02 x 10 -7 1.32 x10 -12
	SigC0.08	19.4	4.77 x 10 -7 1.56 x10 -12

Table 5 . 1 -

 51 Synthesized brucite powders used in this study.

	Note that the aqueous NH 3 solution used to create powder batch BD was heated briefly to 90°C during the synthesis,
	in an attempt to generate a higher degree of crystallinity of
	the grains.
	batch batch T precipitation	m	S BET
	n°	name	[°C]	[g]	[m 2 /g]
	1	BB	48.0	10.58	30.54
	2	BC	45.0	7.94	39.4
	3	BD	48.1	7.19	29.23
	4	BE	53.1	8.27	35.53

  5.2.1.2. Initial reactive aqueous solutionsThe experiments of this study were performed in six distinct series; each series was conducted using a distinct initial aqueous solution. The compositions of these initial aqueous solutions are listed in Table.5.2. All initial aqueous solutions were prepared at pH between 9.5 and 10.5 at 25°C from de-ionized Milli-Q ® water (>18.2 Ω), bi-distilled HCl, suprapur Merck ® Na 2 SO 4 , reagent grade Merck ® tri-sodium citrate dehydrate and Titriplex III Merck ® 0.1 N Na 2 EDTA solution. According to their composition and the initial brucite powder used, the experimental series were named BB and BABE for the inorganic experiments, BBC for the aqueous citrate bearing experiments, BCS and BDS for the aqueous sulphate bearing experiments with ~35 and 65 % MgSO 4 complexation in solution, and BE-EDTA for the aqueous EDTA bearing experiments.

Table 5 . 2 -

 52 Initial aqueous solutions prepared for chemical equilibration of brucite.

Table 5 . 3 -

 53 Mg concentrations and pH of solutions after chemical equilibration, and after adding the isotopic spike, and the average amount of powder and solution used in the isotope exchange experiments.5.2.2.2. Step 2: Isotopic exchange experimentsPrior to beginning the isotopic exchange experiments, the chemical equilibrated solutions collected from step 1 were enriched with a 25 Mg isotope tracer with a initial composition of 2.4% 24 Mg, 96.4% 25 Mg, and 1.2 % 26 Mg, to obtain a total δ 25 Mg of ~ 20 ‰ (see Eqn. 5.2 and Table5.4). Due to the addition of this spike solution, the Mg concentrations of the experimental solutions were lowered. Consequently a small amount of MgCl 2 •6 H 2 O was added to these solutions to re-attain equilibrium Mg concentrations (see Table

Table 5 .4 -Equilibrium

 5 Mg concentrations in solutions and dissolution rate constants obtained from chemical equilibration of synthesized brucite with solutions with and without inorganic and organic ligands.Representative SEM images of the brucite powders collected from the longest duration Mg isotope exchange experiments are provided in

	Exp.	pH	C (Mg)eq	k' -	k +
			[mmol]	[1/s]	[mol/(m²s)]
	BB/BABE 9.3	83.9	9.26 x 10 -6	3.87 x 10 -9
	BBC	10.2	6.0	5.79 x 10 -6	1.87 x 10 -10
	BCS	9.5	71.5	1.16 x 10 -5	4.70 x 10 -9
	BDS	10.0	10.3	1.74 x 10 -5	1.08 x 10 -9
	BE EDTA 12.5	75.7	2.89 x 10 -6	2.32 x 10 -9

Table 5 . 5 -

 55 Overview of the results of the isotopic exchange experiments performed in this study. a denotes the spiked initial solution. Uncertainties of the isotopic measurements are expressed as 2 SD (Standard Deviation) and 2 SE (Standard Error). The 2 SE is computed following the relation: SE=SD/√((n-1) )×t, where n denotes the number of measurements performed and t denotes the Student t-factor

Table 5 . 6 -

 56 Average aqueous Mg-speciation during the second stage of each experimental series run in this study together with the resulting isotopic fractionation factors between brucite and solution, brucite and the Mg 2+ species, and between Mg 2+ and the different solutions species Mg (citrate) -) of the fractionation factors between brucite and the Mg aqueous complexes investigated in this study are listed in Table5.6. The equilibrium fractionation factors between Mg 2+ and the Mg aqueous complexes derived from these values and the equilibrium fractionation factor between brucite and Mg 2+ are also reported in

	denoted as i.
	4 o , and Mg(EDTA) 2-
	, MgSO

Table 5 .

 5 6. The equilibrium fractionation factor between aqueous Mg 2+ and Mg(citrate) -

	∆ eq	26 Mg Mg 2+ -Mg(citrate) -was determined to be in the range between -0.14 ± 0.22 and -0.29 ±
	0.21 ‰ and that between Mg 2+ and MgSO 4	o ranges between 0.72 ± 0.23 and 0.14 ± 0.21 ‰.

Table 5 .

 5 [START_REF] Schuessler | Testing the limits of micro-scale analyses of Si stable isotopes by femtosecond laser ablation multicollector inductively coupled plasma mass spectrometry with application to rock weathering[END_REF]. This value is identical, within uncertainty, to that reported at 20 °C by[START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF] based on brucite recrystallization and synthesis experiments performed at brucite-aqueous solution chemical equilibrium using the three isotope method, ∆ eq 26 Mg brucite-solution = -0.17 ± 0.07 ‰. The results of the present study and those reported byLi and co-workers (2014) indicate that light Mg is preferentially

	incorporated in brucite crystal lattice at temperatures from 20° to 40°C. This slight
	enrichment of the solid in light Mg isotopes can be attributed to the slightly shorter average
	Mg-O bond length in the octahedral Mg aquo ion (2.08/2.09 Å; Schott et al., 2016)
	compared to the corresponding average bond length in brucite octahedrons (2.100-2.093 Å;

  . In contrast,[START_REF] Wimpenny | Investigating the behaviour of Mg isotopes during the formation of clay minerals[END_REF] reported a ∆ eq 26 Mg brucite-Mg 2+ ≈ 0.5 ‰ at 80°C based on brucite synthesis experiments similar to those of[START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF], which reflects the incorporation of heavy Mg into the brucite structure.[START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF] suggested, that this implies a reverse fractionation from positive to negative with decreasing temperature. As this type of behaviour was only previously observed for O, H, and C isotopes, it seems likely that the difference in the direction of Mg isotope fractionation with temperature could be due to kinetic factors, which might occur during the quenching of the experiment from 80°C to ambient temperature[START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF]. in the present and other ambient temperature experimental studies and 0.58 ± 0.16 ‰ at 20°C. PHREEQC speciation calculations show that in the solution equilibrated with epsomite 81 % of dissolved Mg is present as MgSO 4 o and only 19% as Mg 2+ . Using the values of ∆ eq 26 Mg Mg 2+ -MgSO 4 o= -2.62 ‰ and + 0.43 ‰ reported by Schott et al. (2016) and in this study, respectively, values of ∆ eq 26 Mg epsomite-Mg 2+ equal to + 2.7 and 0.3 ‰, respectively, can be calculated at 20°C. The strong fractionation between epsomite and Mg 2+ implied by the MgSO 4 ° reduced partition function ratio reported by Schott et al. (2016) is unlikely because it is not consistent with the similar Mg-O bond lengths of the Mg aquo ion (2.08/2.09 Å) and epsomite (2.09 Å; Baur, 1964). In contrast, the weak fractionation between epsomite and Mg 2+ (0.3 ‰) found in this study is consistent with these structural considerations. It should be noted that the value of the reduced partition function ratio reported by Schott et al. (2016) was based on a calculated optimized structure of MgSO 4 ° in which the sulphate ligand replaces a water molecule of the first coordination sphere in the Mg aquo ion, thus forming an inner-sphere complex with magnesium. The measured isotopic fractionation between sulphate-rich solutions and brucite and epsomite rather suggests that sulphate ions mostly form outer-sphere complexes with magnesium where sulphate replaces a water molecule of the second coordination sphere of the Mg aquo MgEDTA 2-than in Mg 2+ , as Mg 2+ is relatively enriched in heavy 26 Mg. This fractionation factor is consistent with the relative Mg-O bond lengths, with average Mg-O bond length inthe aqueous Mg-EDTA complex equal to 2.17 Å[START_REF] Pozhidaev | Crystal structure of disodium magnesium ethylenediaminetetraacetate tetrahydrate[END_REF] and thus longer than the Mg-O bond length in brucite (2.08/2.09 Å;[START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF].

	The fractionation factors between brucite and aqueous Mg 2+ determined by ab initio calculations suggest an enrichment of heavy Mg isotopes incorporated into brucite. The values of ∆ eq 2+ ) and/or double solvent separated ion pairs, which generate weaker Mg isotope fractionation. These results are in qualitative agreement with the detail dielectric relaxation spectroscopy investigation of aqueous solutions of MgSO 4 showing, for example, that in an aqueous 0.1 M MgSO 4 solution, the Mg-SO 4 inner-sphere complexes account for only 20% of the MgSO 4 (aq) ion pairing (Buchner et al., 2004). Such uncertainties may also affect the structure of the Mg-citrate aqueous complexes and explained the observed difference between the calculated and measured value of ∆ eq 26 Mg Mg 2+ -Mg(citrate) -. Isotopic exchange experiments performed in the presence of aqueous EDTA yield a value of ∆ eq 26 Mg brucite-EDTA equal to + 2.43 ± 0.20 ‰ at 25°C. This value is in close agreement with corresponding results of Li et al. (2014), who reported a Mg isotope fractionation factor between brucite and aqueous EDTA at 22°C ≥ + 2.0 ‰. Taking account of the results reported above on the equilibrium isotope fractionation factor between Mg 2+ and MgEDTA 2-, ∆ eq 26 Mg Mg 2+ -MgEDTA 2-was determined to be 2.08 ± 0.21 ‰. This value is similar to the results of DFT calculations reported by Schott et al. (2016) who suggested 26 Mg ion (Mg(H 2 O) 18 ∆ eq 26 Mg Mg 2+ -MgEDTA 2-= + 1.7 ‰. This result implies that Mg forms weaker bonds in

brucite-Mg 2+ at 25°C recommended by

[START_REF] Colla | Computational prediction of Mg-isotope fractionation between aqueous [Mg(OH 2 ) 6 ] 2+ and brucite[END_REF]

and

[START_REF] Gao | Theoretical calculation of equilibrium Mg isotope fractionations between minerals and aqueous solutions[END_REF]

are equal to +3.14 ‰ and + 2.7/2.9 ‰, respectively. The large discrepancy between the values obtained

Table 5 . 7 -

 57 Rate constants obtained in this study. Dissolution rate constants were calculated from the brucite dissolution experiments. Initial and bulk isotopic exchange rate constants were extracted using the first order rate law Eqn. 5.14.

  were determined to be -2.34 ± 0.13 ‰, and -2.21± 0.05 ‰, respectively. These values are comparable with the results of ab initio calculations reported byDupuis et al.

					3 SiO 4	-
	and H 4 SiO 4	o , Δ eq 30 Si H 3 SiO 4	--H 4 SiO 4	o , were determined. Retrieved Δ eq	30 Si H 3 SiO 4 --H 4 SiO 4 o at 25 °
	and 75 °C

Table A :

 A Temporal evolution of dissolved Si concentration and pH during equilibration of the initial Si-free reactive fluids with the pre-treated amorphous silica.

	Exp.	Temperature	Time	pH	Si-conc.	Si-conc.
		[°C]	[d]		[ppm]	[mmol/kg]
	SibA:
		25	0	8.7	0.0	0.0
		25	1	5.5	2.7	0.1
		25	4	6.6	14.8	0.5
		25	7	6.0	23.1	0.8
		25	13	6.8	32.8	1.2
		25	19	6.6	39.0	1.4
		25	27	6.7	44.2	1.6
		25	37	6.4	46.7	1.7
		25	47	6.2	44.4	1.6
	SicB:
		25	0	10.2	0.0	0.0
		25	1	10.2	58.2	2.1
		25	4	10.2	104.1	3.7
		25	8	10.2	115.0	4.1
		25	16	10.2	154.3	5.5
		25	26	10.1	141.1	5.0
		25	50	10.2	114.7	4.1
		25	66	10.1	118.7	4.2
	Sig75A:
		75	0	5.9	0.0	0.0
		75	1	6.4	41.1	1.5
		75	4	6.5	87.7	3.1
		75	19	5.8	108.0	3.9
		75	23	5.7	107.1	3.8
		75	29	5.8	115.1	4.1
		75	33	5.7	114.9	4.1
		75	41	5.7	116.7	4.2
		75	69	5.7	117.4	4.2
	Sik75B:
		75	0	9.25	0.00	0.0
		75	1	10.02	148.7	5.3
		75	3	9.4	236.2	8.4
		75	8	9.9	231.4	8.2
		75	14	9.3	264.2	9.4
		75	22	9.3	257.9	9.2
		75	37	9.3	257.4	9.2

Table B :

 B Summary of the measured characteristics of the reacted solids collected after the longest duration experiment for the experiments at 25°C and pH 5.8 at 75°C. Longest reacted powder available at time of analysis at pH 9.1 and 75°C after 33 days.

	sample	Temp. run time	S BET	grain size m H2O chemical formula
		[°C]	[d]	[m 2 /g]	[nm]	[wt %]
	SibA 8	25	351	137.1	20.86	9.4	SiO 2 • 0.33 H 2 O
	SicB 8	25	385	164.1	20.69	8.6	SiO 2 • 0.34 H 2 O
	Sig75A 8	75	55	171.7	19.60	8.1	SiO 2 • 0.28 H 2 O
	Sik75B 6	75	33	119.0	n.a.	7.5	SiO 2 • 0.32 H 2 O

Table 3.2 -continued

Mg/ 24 Mg ratios were performed in the dynamic mode. The Russell's exponential law

Table 5.5 -continued

Acknowledgements

Kinetics of isotopic exchange reactions

The three-isotope method not only allows the determination of the equilibrium fractionation factors of a solid-solution system, it also allows determination of the kinetics of isotopic exchange. The isotope exchange rates can be quantified using (Cole and Chakrabarty, 2001;Johnson et al., 2002): Chapter 2. Materials and Methods -24--(1 -)

at the Laboratoire Géosciences Enviornement Toulouse / Centre National de la

List of Tables

 Table 2.
Abstract

The accurate interpretation of Si isotope signatures in natural systems requires knowledge of the equilibrium isotope fractionation between Si bearing solids and the dominant Si-bearing aqueous species. Aqueous silicon speciation is dominated by silicic acid (H 4 SiO 4

Isotope exchange kinetics

The rate of attainment of isotopic equilibrium provides insight into the mechanism of isotope exchange. The temporal evolutions of the degree of isotope exchange, F, for the four experimental series in this study are shown in Fig 3 .7. It can be seen that isotope exchange is relatively rapid during the first 10 days of each experimental series. After 10 days, the exchange reaction slows as the system begins to attain isotopic equilibrium. The curves in this figure were generated using the first order rate law, Eqn. (3.16), to be consistent with the amorphous SiO 2 rate expression provided by Eqn. (3.3) to (3.7). The rate constants used to generate these curves were those retrieved from the amorphous silica dissolution rate experiments run at the beginning of each series -see above and Table 3.3. It can be seen that the initial isotopic exchange rates shown in Table 3.5 are similar toif not faster than-those of the bulk amorphous silica dissolution rates obtained from the first stage of each experimental series. As isotopic equilibrium is approached, these isotope exchange rates become slow relative to that calculated from the bulk amorphous silica dissolution rates.

Experimental design

The three-isotope method [START_REF] Matsuhisa | Mechanisms of hydrothermal crystallization of quartz at 250°C and 15 kbar[END_REF] was used in this study to determine the equilibrium isotopic fractionation factor between brucite and aqueous solutions. This method allows determination of the degree of isotopic exchange between brucite and the aqueous solution as it evolves over time. Isotopic disequilibria in the mineral-solution system is provoked by enriching the solution with 25 Mg. The system will strive to isotopic equilibrium over time. As isotopic exchange is slow and equilibrium is not reached during the experiments, the three-isotope method allows the extrapolation of the degree of isotopic change so that the isotopic composition of the two components at 100% exchange (e.g.

isotopic equilibrium) can be determined. A detailed description of this method is given by previous studies [START_REF] Matsuhisa | Mechanisms of hydrothermal crystallization of quartz at 250°C and 15 kbar[END_REF]Matthews et al., 1983aMatthews et al., , 1983bMatthews et al., , 1983c;;[START_REF] Shahar | Equilibrium high-temperature Fe isotope fractionation between fayalite and magnetite: An experimental calibration[END_REF]Beard et al., 2010;[START_REF] Li | Exchange and fractionation of Mg isotopes between epsomite and saturated MgSO4 solution[END_REF][START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF][START_REF] Frierdich | Determination of the Fe(II)aq-magnetite equilibrium iron isotope fractionation factor using the three-isotope method and a multi-direction approach to equilibrium[END_REF][START_REF] Reddy | The effect of pH on stable iron isotope exchange and fractionation between aqueous Fe(II) and goethite[END_REF]Zheng et al., 2016;[START_REF] Stamm | The experimental determination of equilibrium Si isotope fractionation factors among H 4 SiO 4 o , H 3 SiO 4 and amorphous silica (SiO 2 •0.32 H 2 O) at 25 ° and 75 °C using the three-isotope method[END_REF]. The application of the three-isotope method in this study was performed at conditions of bulk chemical equilibrium but isotopic disequilibrium.

As such each experimental series consisted of two parts. The first part was the chemical equilibration of the water-brucite system. The equilibrated solution collected at the end of this first step was then enriched in heavy Mg and used in the second step, a isotope equilibration step performed with fresh brucite powder. These two steps are described in detail below.

Step 1: Equilibration of initial aqueous solutions with Mg(OH) 2

Six experimental series were performed in this study. Each series began by equilibrating 200 mL of an initial aqueous solution with 3 g of synthesized brucite powder in closedsystem polypropylene reactors. The composition of these initial aqueous solutions are provided in Table 5.2. To ensure constant temperature, the reactors were placed in a continuously shaking thermostatic bath at 25°C. The reactor solutions were regularly sampled over the 35 to 57 days duration of this first equilibration step. The solution pH was immediately measured after sampling. Part of each solution sample was acidified with 10 µl 10 N bi-distilled HCl to avoid any Mg precipitation during storage prior to their further analysis. The aqueous Mg concentrations of these solutions were determined with F-AAS.

Once the pH and Mg concentration of the experimental aqueous solutions were constant over time chemical equilibrium was assumed to have been attained. The solutions were then filtered with Merck ® 0.2 µm Teflon syringe filters. The pH and Mg concentrations of the the ab initio calculations remains unclear [START_REF] Gao | Theoretical calculation of equilibrium Mg isotope fractionations between minerals and aqueous solutions[END_REF]. It may originate in uncertainties associated with quantum chemistry calculations, for example [START_REF] Colla | Computational prediction of Mg-isotope fractionation between aqueous [Mg(OH 2 ) 6 ] 2+ and brucite[END_REF] only a small degree of isotope fractionation between brucite and Mg 2+ (aq) might be expected. This is consistent with preliminary ab initio calculations performed for this study, which suggest an equilibrium fractionation factor between brucite and aqueous Mg 2+ of 0.8 ± 0.2 ‰ at 25 °C (pers. comm. Merlin Méheut). This is significantly smaller than the values recommended by [START_REF] Colla | Computational prediction of Mg-isotope fractionation between aqueous [Mg(OH 2 ) 6 ] 2+ and brucite[END_REF] and [START_REF] Gao | Theoretical calculation of equilibrium Mg isotope fractionations between minerals and aqueous solutions[END_REF], and closest to being consistent to the value suggested by [START_REF] Wimpenny | Investigating the behaviour of Mg isotopes during the formation of clay minerals[END_REF].

Magnesium isotope fractionation between Mg 2+ and aqueous Mg organic and inorganic complexes

The values of ∆ eq 26 Mg Mg 2+ -Mg(citrate) -determined in this study are -0.14 ± 0.22 ‰ and -0.29 ± 0.21 ‰. These values are significantly smaller than that derived by [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF] from DFT calculations, who suggested that ∆ eq 26 Mg Mg 2+ -Mg(citrate) -= -3 ‰. Although the values determined in this study are significantly smaller than the theoretically calculated values of [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF], they do suggest an enrichment of Mg 2+ in 24 Mg isotopes, consistent with shorter Mg-O bonds in aqueous Mg citrate compared to the Mg aquo ion [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF].

The average value of the equilibrium isotope fractionation factor between aqueous Annex III: Electronic supplement of chapter 5