Ana Sandy

Reza Arash

Teresita Fulvio

The processes controlling chemical fluxes to and from the oceans are essential to the understanding of marine and global geochemical cycles. However, their direct quantification is often impossible due to their spatial and temporal inaccessibility. Chemical tracers, such as elemental or isotope abundance ratios, can help to identify such processes and allow identification of imbalances in global geochemical cycles. In this context, the fluid-rock interactions occurring in hydrothermal systems at or near midoceanic ridges (MOR) were studied experimentally by reacting basalt with seawater at 250 • C and 290 • C while monitoring the Mg and Sr isotopic evolution of the fluid. The results indicate that seawater Sr was incorporated into anhydrite in the early stages, leading to a drop of fluid 87 Sr/ 86 Sr values towards the basaltic signature after basalt dissolution became the dominant process. This suggest that such fast intermediatetemperature reactions could partly explain previously identified discrepancies between MOR heat budget constraints and the marine 87 Sr/ 86 Sr budget. Furthermore, latestage anhydrite re-dissolution caused by fluid reduction and temperature decreases in our experiments represent a potential explanation for the low amounts of anhydrite found in altered oceanic basalt samples. Strong decreases in fluid δ 88/86 Sr values in experiments with crystalline basalt suggest that isotopically light Sr was preferentially released during non-stoichiometric dissolution. Furthermore, a slight preference of anhydrite for isotopically heavy Sr (ε

88/86

Anhydrite-Liquid = 0.033 ± 0.020 ‰) is indicated by the data, providing information about the effect of hydrothermal systems on the oceanic stable Sr cycle. The fluid δ 26/24 Mg mainly decreased during the experiments while Mg was removed by smectite precipitation, and mass balance indicates that isotopically heavy Mg was preferentially incorporated into the clays (ε

26/24

Smectite-Liquid ≈ 0.457 ± 0.072 ‰). The direction and magnitude of this fractionation is similar to previously estimated values, and the estimated influence of clay formation on Mg isotopic signatures in marine hydrothermal systems is small compared to carbonate precipitation. This is in accord with the relatively stable seawater δ 26/24 Mg during the Cenozoic rise in seawater Mg/Ca being caused by a change in the cycling of Mg-silicates as opposed to changes in the carbonate cycle [START_REF] Higgins | The Mg isotopic composition of Cenozoic seawater -evidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF], as well as recent changes in seawater δ 26/24 Mg being caused by a change in marine Mg-carbonate precipitation [START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF].

Towards the interpretation of rare earth element (REE) patterns in marine calcite, the fractionation between the REEs and Ca during the abiogenic precipitation of calcite at 25 • C and pH ∼ 6 was studied experimentally under steady-state conditions. These data suggest that the incorporation of REE 3+ ions into the calcite structure was likely charge balanced by incorporation of Na + under the experimental conditions, and that inferred partition coefficients for marine conditions can vary substantially depend--i-ing on the fluid composition. This indicates that careful analysis of the depositional conditions is necessary when REE concentrations in calcite are used as paleo proxies to infer past mixing or redox states of the oceans and input sources, which can be distinguished by their distinct REE patterns. Furthermore, the solubility of hydroxylbastnasite (REE(CO 3 )(OH)) was determined, indicating that this phase is less soluble than other known REE carbonates and that previous studies of REE co-precipitation with calcite were potentially affected by oversaturation with this phases.

Résumé

Connaitre les processus qui contrôlent les flux chimiques depuis et vers les océans est essentiel pour comprendre les cycles géochimiques marins et globaux. Cependant, la quantification directe de ces processus est souvent impossible en raison de leur inaccessibilité spatiale et temporelle. Les traceurs chimiques, tel que les rapports des concentrations élémentaires ou isotopiques, peuvent aider à identifier les processus en jeu et permettre de mettre en évidence des déséquilibres dans les cycles géochimiques globaux. Dans ce contexte, les interactions fluide-roche intervenant dans les systèmes hydrothermaux aux ou près des dorsales océaniques ont été étudiées expérimentalement en faisant réagir du basalte avec de l'eau de mer à 250 • C et 290 • C, tout en surveillant l'évolution isotopique du Mg et Sr dans le fluide. Les résultats indiquent l'incorporation du Sr dissout dans l'eau de mer dans l'anhydrite lors des premiers stades de la réaction, suivi par une baisse des valeurs 87 Sr/ 86 Sr des fluides vers la signature isotopique du basalte, une fois que la dissolution du basalte est devenue le processus dominant. Ces résultats suggèrent que les réactions rapides à températures moyennes pourraient expliquer en partie les divergences identifiées précédemment entre les contraintes du bilan thermique des dorsales océaniques et celles du bilan marin du 87 Sr/ 86 Sr. De plus, la ré-dissolution de l'anhydrite provoquée par la réduction et le refroidissement des fluides hydrothermaux dans les stades avancés de la réaction peuvent expliquer les faibles quantités d'anhydrite trouvée dans les échantillons de basalte océanique altérés. La forte diminution des valeurs de δ 88/86 Sr mesurées dans les expériences effectuées avec du basalte cristallin suggère que le Sr isotopiquement léger a été préférentiellement libéré lors d'une dissolution non-stoechiométrique. En outre, une légère affinité de l'anhydrite pour le Sr isotopiquement lourd (ε

88/86

Anhydrite-Liquid = 0.033 ± 0.020 ‰) est indiquée par les données analytiques, ce qui fournit des informations concernant l'effet des systèmes hydrothermaux sur le cycle océanique des isotopes stables du Sr. Le δ 26/24 Mg des fluides a diminué pendant les expériences principalement à cause de la précipitation du Mg dans les smectites, et le bilan de masse indique que le Mg isotopiquement lourd a été incorporé préférentiellement dans ces minéraux des argiles (ε

26/24

Smectite-Liquid ≈ 0.457 ± 0.072 ‰). L'intensité de ce fractionnement est similaire aux valeurs estimées précédemment et montre que l'influence de la formation des minéraux argileux sur la composition isotopique du Mg dans les systèmes hydrothermaux marins est faible par rapport à celle de la précipitation des carbonates. Ceci est en accord avec les δ 26/24 Mg relativement stables de l'eau de mer enregistrés pendant l'augmentation du rapport Mg/Ca en époque Cénozoïque, qui serait consécutif à une modification dans le cycle des silicates de Mg plutôt qu'à des changements dans le cycle du carbonate [START_REF] Higgins | The Mg isotopic composition of Cenozoic seawater -evidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF], et avec les changement récents en δ 26/24 Mg étant causés par un changement dans la précipitation des carbonates de Mg [START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF].

Concernant l'interprétation des spectres des terres rares dans les calcites marines, le fractionnement entre les terres rares et le Ca pendant la précipitation abiogénique de calcite à 25 • C et pH ∼ 6 a été étudié expérimentalement à l'état stationnaire. Ces données suggèrent que l'incorporation des ions REE 3+ dans la structure de la calcite est probablement équilibrée par l'incorporation de Na + et que les coefficients de partage déduits pour les conditions marines peuvent varier considérablement selon la composition du fluide. Une analyse minutieuse des conditions de dépôt est ainsi nécessaire quand les concentrations des terres rares dans la calcite sont utilisées comme des « paleo proxies » pour inférer les états de mélange ou rédox antérieurs des océans et des sources continentales. Enfin, l'étude de la solubilité de l'hydroxylbastnasite (REE(CO 3 )(OH)), conduite au cours de ce travail, indique que cette phase est moins soluble que les autres carbonates des terres rares connus, et que les études précédentes de co-précipitation des terres rares avec de la calcite étaient potentiellement affectées par la sursaturation par rapport à cette phase.

Preface

This thesis consists of four manuscripts that have been published in, or prepared for submission to peer-reviewed academic journals, as well as a general introduction to the topic (chapter 1) and general conclusions of this work (chapter 6).

Chapters 2 and 3 are in preparation for submission to international peer-reviewed journals. The two manuscripts are based on the same set of experiments which explored hydrothermal basalt-seawater interactions. Chapter 2 discusses the evolution of the Sr isotopic system, while chapter 3 examines the Mg isotopic system during such processes, and both studies discuss the implications for the use of these isotopes as tracers as well as for marine geochemical cycles. Supporting information for these two manuscripts is presented in appendices A and B. Both manuscripts are authored by M. Voigt, C. R. Pearce, A. Baldermann, and E. H. Oelkers with the following contributions: C. R. Pearce, Eric H. Oelkers and I conceived the studies and designed the experiments. I conducted the experiments and carried out chemical analysis of the fluid samples as well as SEM analyses of the solids. A. Baldermann analysed the solids by XRD and FTIR. I conducted the Sr and Mg isotopic analyses with help from C. R. Pearce. Furthermore, I carried out the data analysis, modelling and other calculations, and wrote the manuscripts with input from all authors.

A version of chapter 4 is published as "Voigt, M., Rodriguez-Blanco, J. D., [START_REF] Voigt | An experimental study of hydroxylbastnasite solubility in aqueous solutions at 25 •[END_REF] A version of chapter 5 is published as "Voigt, M., [START_REF] Voigt | The experimental determination of REE partition coefficients in the water-calcite system[END_REF]: The experimental determination of REE partition coefficients in the water-calcite system. Chemical Geology 462: 30-43. doi: 10.1016/j.chemgeo.2017. 04 . 024" and reprinted with permission. Copyright 2016 Elsevier. The supporting information for this manuscript is reproduced in appendix C. V. Mavromatis, E. H. Oelkers and I conceived the study, and I designed the experiments with input from V. Mavromatis. I conducted the experimental and analytical work as well as the data interpretation and wrote the manuscript. All authors contributed to revisions of the manuscript.

First of all, I would like to thank my supervisor Eric Oelkers for the support and advice throughout the last years. This work would not have been possible without his mentorship which allowed me to pursue fascinating new research topics on my own while making sure that I stayed on the right path.

I am also very grateful to Chris Pearce for introducing me to the world of isotope geochemistry and marine cycles, and for teaching me the ins and outs of stable isotope analyses during my stays in Southampton.

Furthermore, I would like to thank the scientists who provided materials and analytical support for this work: Liane Benning, Juan-Diego Rodriguez-Blanco and Beatriz Vallina who supplied me with hydroxylbastnasite, Deirdre Clark and Jan Přikryl for providing the famous Stapafell basalt, Andre Baldermann who carried out XRD and FTIR analyses, and Catherine Jeandel for supplying the seawater.

In addition, I thank the academic staff at the GET, namely Pascale Bénézeth, Mathieu Benoit, Vasileios Mavromatis, Franck Poitrasson, and Jacques Schott for their help and advice. I also owe many thanks to the technical staff, especially to Thierry Aigouy, Philippe Besson, Frederic Candaudap, Alain Castillo, Carole Causserand, Jérôme Chmeleff, Pascal Gisquet, Manuel Henry, Aurélie Marquet, Stephanie Mounic, Philippe de Parseval, Jonathan Prunier, and Michel Thibout at the GET as well as to Matt Cooper, Andy Milton, and Agnes Michalik at the NOC Southampton.

Of course, many thanks are due to the other graduate students and post-docs at the GET for their support and advice as well as numerous pétanque and Ariège sessions, including the "lunch group": Chris, Cristina, Franziska, Giuseppe, Anna, Fiorella, Vasileios, Nang, Nail, Chiara, Aurélia, Pedro, Janeet, Fausto, Hector, as well as the former members Andrea, Thomas, Aridane, Nik, and the various visitors. Chris, thanks for helping me to tinker with experiments in the lab, after lunch ping-pong practice, and planning the next trips to the Pyrenees on the relief map. I am equally grateful to the graduate students and post-docs in Southampton for supporting me in various ways, especially to David for help with isotope separations and making long clean lab sessions bearable.

List of Tables

General introduction 1.1 The role of the oceans in geochemical cycles

The oceans are an integral part of the global geochemical cycles. They cover most of the Earth's surface and are located at the interface between the continents, atmosphere, and oceanic crust, thus influencing the chemical transfer between those reservoirs. The concentrations of chemical elements in seawater is determined by a number of processes, the major processes controlling the cycles of the non-volatile elements being depicted in Figure 1.1. For many elements, continental weathering is the primary external input (e.g., [START_REF] Elderfield | Mid-ocean ridge hydrothermal fluxes and the chemical composition of the ocean[END_REF][START_REF] Bruland | Controls of trace metals in seawater[END_REF]: Elements are either dissolved into river-or groundwater on the continents and enter the oceans as a dissolved flux, or they are transported to the oceans by rivers or airflow in the form of particles. The particulate mass flux from the continents into the oceans is significantly higher than the dissolved mass flux [START_REF] Martin | Elemental mass-balance of material carried by major world rivers[END_REF][START_REF] Gaillardet | Global silicate weathering and CO 2 consumption rates deduced from the chemistry of large rivers[END_REF][START_REF] Viers | Chemical composition of suspended sediments in World Rivers: New insights from a new database[END_REF][START_REF] Jeandel | The influence of terrigenous particulate material dissolution on ocean chemistry and global element cycles[END_REF]. However, only some of the particulate material is dissolved into seawater, while the rest is removed from the water column by settling and burial, making it challenging to estimate their impact on the oceans [START_REF] Martin | The significance of the river input of chemical elements to the ocean[END_REF][START_REF] Jeandel | Ocean margins: the missing term in oceanic element budgets[END_REF][START_REF] Jeandel | The influence of terrigenous particulate material dissolution on ocean chemistry and global element cycles[END_REF]. Elements dissolved in the seawater can adsorb onto settling particulate material and thus be removed from the seawater in a process referred to as scavenging [START_REF] Balistrieri | Scavenging residence times of trace metals and surface chemistry of sinking particles in the deep ocean. Deep Sea Research Part A[END_REF][START_REF] Bruland | Controls of trace metals in seawater[END_REF]. Additionally, precipitation and sedimentation of carbonates is a significant sink for a number of elements including Ca, Mg, and Sr [START_REF] Wilkinson | Sedimentary carbonate record of calciummagnesium cycling[END_REF][START_REF] Krabbenhöft | Constraining the marine strontium budget with natural strontium isotope fractionations ( 87 Sr/ 86 Sr * , δ 88/86 Sr) of carbonates, hydrothermal solutions and river waters[END_REF]Pearce et al., 2015b). Hydrothermal systems at the ocean floor can act as both source and sink, depending on the element and the conditions [START_REF] Coogan | An internally consistent, probabilistic, determination of ridge-axis hydrothermal fluxes from basalt-hosted systems[END_REF].

Continental weathering

Scavenging, precipitation

Axial hydrothermal systems

Low temperature basalt alteration Sedimentation

REE incorporation into calcite

Mg and Sr isotope exchange in hydrothermal systems In many cases, the study of the processes that control the oceans' geochemical cycles is complicated by the location as well as the spatial-and time-scale at which they occur.

For example, the direct observation of reactions inside marine hydrothermal systems is not possible with currently available technologies. Even if direct studies are possible locally, integration from small scale studies to a representative global model is often challenging, for example the estimation of globally representative sediment transport to the oceans or marine hydrothermal fluxes [START_REF] Meybeck | Global occurrence of major elements in rivers[END_REF][START_REF] Coogan | An internally consistent, probabilistic, determination of ridge-axis hydrothermal fluxes from basalt-hosted systems[END_REF].

Furthermore, complications arise due to the large timescales that are necessary to achieve significant, detectable changes in element or isotope concentrations, and the assessment of the evolution of these system in the geologic past.

Chemical tracers have been developed to overcome these challenges: Reactions that cannot be directly observed can imprint their characteristic chemical signatures on rocks and fluids, which, if preserved, can provide information about these processes.

Although the number of the reactions that occur simultaneously in natural systems complicates the interpretation of the tracer signatures, their detailed analyses yields crucial information about many processes. In addition to tracing reactions and fluxes in oceanic systems, as described in this thesis, tracers are essential to many problems in Earth Sciences, including the determination of reservoirs in the Earth's lithosphere (e.g., [START_REF] Hurley | Radiogenic strontium-87 model of continent formation[END_REF][START_REF] Hart | A large-scale isotope anomaly in the Southern Hemisphere mantle[END_REF][START_REF] Hofmann | Sampling mantle heterogeneity through oceanic basalts: Isotopes and trace elements[END_REF], reconstruction of movements in pressure-temperature-time space (e.g., [START_REF] Hodges | Thermochronology in orogenic systems[END_REF], and monitoring of fluids in natural or artificial hydrological systems (e.g., [START_REF] Glynn | Geochemistry and the understanding of ground-water systems[END_REF][START_REF] Matter | Experimental evaluation of in situ CO 2 -water-rock reactions during CO 2 injection in basaltic rocks: Implica-tions for geological CO 2 sequestration[END_REF]. Laboratory experiments play a critical role in the interpretation of these tracer signatures in natural samples. By experimentally emulating a natural system (or parts of it) on a small scale, it is possible to (1) identify the mechanisms, e.g. mineral-fluid reactions, which potentially occur in nature, and (2) to quantify how the tracers are affected by different parameters in a controlled manner. In the context of this thesis, the behaviours of different elemental and isotopic tracers during water-rock interactions were studied experimentally: Chapters 2 and 3 aim to quantify stable Mg and Sr isotopic signatures as tracers of reactions in moderate-to high-temperature marine hydrothermal systems, and chapters 4 and 5 characterise how rare earth elements (REEs) behave in water-rock interactions with focus on the application to marine carbonate precipitation as a tracer of marine processes and continental inputs to the ocean (Figure 1.1). The following sections review the current knowledge about the functioning of these processes (sections §1.1.1 and §1.1.2), followed by a description of the physical relationships governing fractionation in those contexts (section §1.2).

Marine hydrothermal systems

Hydrothermal activity on the ocean floors is a manifestation of heat transfer from the cooling oceanic lithosphere to the oceans. A significant amount of the heat flux that is required to cool the magma and dissipate the heat of crystallisation at midocean ridges (MOR) cannot be explained by the observed heat flow at the ocean floors, and thus can be attributed to hydrothermal convection [START_REF] Stein | Constraints on hydrothermal heat flux through the oceanic lithosphere from global heat flow[END_REF]. Direct

evidence of this processes includes high-temperature hydrothermal venting at the ocean floor, which can reach temperatures exceeding 400 • C, as first observed on the East Pacific Rise [START_REF] Macdonald | Hydrothermal heat flux of the "black smoker" vents on the East Pacific Rise[END_REF] and identified for many oceanic ridges in the following years (e.g., [START_REF] Baker | On the global distribution of hydrothermal vent fields[END_REF]. Combining geophysical evidence with heat budget constraints, available alteration profiles of the oceanic crust, and hightemperature vent data has allowed construction of models of hydrothermal systems at the ridge axes ( and anhydrite during high-temperature reactions of seawater with basalt, while signi-ficant amounts of Si and Ca are released from the basalt (e.g., [START_REF] Mottl | Chemical exchange during hydrothermal alteration of basalt by seawater-I. Experimental results for major and minor components of seawater[END_REF][START_REF] Seyfried | Experimental seawater-basalt interaction at 300 • C, 500 bars, chemical exchange, secondary mineral formation and implications for the transport of heavy metals[END_REF][START_REF] Alt | Ophiolites and oceanic crust: new insights from field studies and the Ocean Drilling Program[END_REF][START_REF] Alt | Hydrothermal fluxes at mid-ocean ridges and on ridge flanks[END_REF][START_REF] Coogan | An internally consistent, probabilistic, determination of ridge-axis hydrothermal fluxes from basalt-hosted systems[END_REF].

Other elements such as Sr are affected by both precipitation into secondary minerals as well as the release from the wall rocks [START_REF] Davis | Imbalance in the oceanic strontium budget[END_REF]. Abundance ratios of two stable isotopes of the same element are convenient tracers of such complex interactions, as small differences in their properties can lead to fractionation that is characteristic of the processes involved. In the case of Sr, the radiogenic generation of 87 Sr by decay of 87 Rb is a further source of variations in 87 Sr/ 86 Sr ratios, because different Rb/Sr abundance ratios lead to the formation of reservoirs with different 87 Sr/ 86 Sr ratios over Earth's history [START_REF] Armstrong | A model for the evolution of strontium and lead isotopes in a dynamic Earth[END_REF]. Therefore, 87 Sr/ 86 Sr ratios are largely unaffected by isotopic fractionation (and are completely independent of mass-dependent isotopic fractionation if normalised to a constant 86 Sr/ 88 Sr ratio, which is commonly the case), but can be used to trace mixing of different sources.

Apart from identifying and quantifying water-rock interactions, these isotopic tracers can also be used to assess the influence of hydrothermal systems on marine element budgets, as the different sources and sinks often exhibit distinct isotopic signatures. Assuming that all current sources and sinks can be globally isotopically quantified, simple mass balance models indicate whether the isotopic composition of the oceans is currently at steady state. For example, currently available estimates of the stable Sr isotope budget indicate that this system is not at steady state [START_REF] Krabbenhöft | Constraining the marine strontium budget with natural strontium isotope fractionations ( 87 Sr/ 86 Sr * , δ 88/86 Sr) of carbonates, hydrothermal solutions and river waters[END_REF]Pearce et al., 2015b). Alternatively, it is possible to deduce if the nature and magnitude of the known fluxes to and from the oceans are consistent with the temporal isotopic change in the oceans. This requires reconstruction of past seawater isotopic compositions using a robust proxy. For example, Neogene seawater 87 Sr/ 86 Sr ratios can be reconstructed using foraminifers as proxies [START_REF] Hodell | Variation in the strontium isotopic composition of seawater (8 Ma to present) : Implications for chemical weathering rates and dissolved fluxes to the oceans[END_REF][START_REF] Mcarthur | Strontium isotope stratigraphy[END_REF], indicating that 87 Sr/ 86 Sr increased at a rate of ∼54 × 10 -6 /Ma during the last 2.5 Ma. Using this information and known fluxes from and to hightemperature hydrothermal systems as well as river input and benthic output fluxes, the marine radiogenic Sr budget can be constrained. However, imbalances arise in this budget [START_REF] Davis | Imbalance in the oceanic strontium budget[END_REF], suggesting that the nature and/or magnitude of the known fluxes is misrepresented. Different sources for the missing Sr in the budget have been proposed, including low-temperature alteration of oceanic basalts and different weathering fluxes [START_REF] Butterfield | Evidence for basaltic Sr in midocean ridge-flank hydrothermal systems and implications for the global oceanic Sr isotope balance[END_REF][START_REF] Vance | Variable Quaternary chemical weathering fluxes and imbalances in marine geochemical budgets[END_REF][START_REF] Allègre | The fundamental role of island arc weathering in the oceanic Sr isotope budget[END_REF]Jones et al., 2012a;[START_REF] Coogan | Alteration of ocean crust provides a strong temperature dependent feedback on the geological carbon cycle and is a primary driver of the Sr-isotopic composition of seawater[END_REF]. Another example are Mg isotopes, whose rather stable abundance ratios during the Cenozoic rise in seawater Mg/Ca ratios suggest a decline in the magnitude of Mg removed by hydrothermal systems and/or an increase in Mg/Ca of silicate weathering of the continents rather than a change in carbonate weathering or deposition [START_REF] Higgins | The Mg isotopic composition of Cenozoic seawater -evidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF]. Furthermore, data of [START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF] suggest that the seawater isotopic composition changed rapidly during the last ∼15 Ma, which can be explained by a decrease of Mg-carbonate formation.

However, such models of geochemical cycles, as well as the use of isotope fractionation to identify water-rock interactions critically depends on the knowledge of the sense and magnitude of isotopic fractionation caused by relevant processes. In this context, chapters 2 and 3 of this thesis present the results from a series of experiments in which basalt was reacted with seawater at temperatures of 250 • C and 290 • C. In these experiments, the evolution of the Sr and Mg isotopic composition of the liquid was followed by regular sampling, constraining isotopic signature of the fluid-rock interactions and marine hydrothermal systems.

Rare Earth Elements in the seawater

Similar to isotopic tracers, the relative abundances of the individual rare earth elements can be used to trace chemical reactions, mixing processes and geochemical input fluxes. They show a similar chemical behaviour due to the similarity of their electron configuration, but their properties such as the ionic radii gradually change from the light to the heavy REEs, affecting their compatibility in crystal structures and their complexation in fluids (e.g., [START_REF] Hanson | Rare earth elements in petrogenetic studies of igneous systems[END_REF][START_REF] Elderfield | The oceanic chemistry of the rare-earth elements[END_REF]. Furthermore, some REEs can be present in valence states different from the common REE 3+ form (e.g., Ce 4+ , La 2+ ; [START_REF] Goldberg | Rare-earth distributions in the marine environment[END_REF]. Due to these properties, geochemical processes such as melting, crystallisation, dissolution, or precipitation lead to distinct REEs patterns (i.e.

relative REE concentrations) that are characteristic of the sources, environments, and processes involved, making the REEs powerful tracers (e.g., [START_REF] Hanson | Rare earth elements in petrogenetic studies of igneous systems[END_REF][START_REF] Elderfield | The rare earth elements in seawater[END_REF][START_REF] Mckenzie | Partial melt distributions from inversion of rare earth element concentrations[END_REF][START_REF] Sholkovitz | The aquatic chemistry of rare earth elements in rivers and estuaries[END_REF].

Unlike the Mg and Sr isotope ratios that are homogeneously distributed in the oceans [START_REF] Broecker | Tracers in the sea[END_REF][START_REF] Foster | Boron and magnesium isotopic composition of seawater[END_REF], current oceanic REEs patterns show spatial variability [START_REF] Elderfield | The rare earth elements in seawater[END_REF], indicating that their residence times can be shorter than the mixing time of the oceans of approximately 1000 years [START_REF] Broecker | Tracers in the sea[END_REF]. The input sources of dissolved REEs in the seawater are typically assumed to have shale-like REE patterns [START_REF] Elderfield | The oceanic chemistry of the rare-earth elements[END_REF]. Therefore, seawater REE patterns normalised to that of shale are characteristic of the processes removing REEs from the seawater. Dissolved REE concentrations in the seawater increase with depth in a similar way to nutrients which are taken up by phytoplankton and biogenic particles in surface waters (e.g., [START_REF] Elderfield | The oceanic chemistry of the rare-earth elements[END_REF][START_REF] Bruland | Controls of trace metals in seawater[END_REF].

However, as the REEs have no biological function, the removal of the REE is likely controlled by passive adsorption onto particles and incorporation into precipitating carbonates that can take up significant amounts of REE [START_REF] Schijf | YREE scavenging in seawater: A new look at an old model[END_REF]. Based on the comparison of vertical variations of seawater REE patterns with experimentally determined affinities of the REEs for different solids, [START_REF] Schijf | YREE scavenging in seawater: A new look at an old model[END_REF] deducted that REE scavenging in the deep oceans may be dominated by hydrated manganese oxides, while sorption onto the green macroalga Ulva lactuca and calcite potentially control REE concentrations in shallow seawater. Cerium can be easily oxidised to Ce 4+ in seawater, in which case formation of insoluble Ce-oxides leads to its removal from the seawater [START_REF] Elderfield | The oceanic chemistry of the rare-earth elements[END_REF], so that dissolved Ce concentrations are indicative of the redox state. Detailed analysis of the resulting negative Ce anomalies in oceanic REE patterns (Figure 1.3) indicates that rapid oxidative removal occurs in the surface waters and continues in the deep oceans over the mixing-time of the oceans [START_REF] Elderfield | The oceanic chemistry of the rare-earth elements[END_REF][START_REF] German | Dissolved rare earth elements in the Southern Ocean: Cerium oxidation and the influence of hydrography[END_REF]. Conversely, marine hydrothermal fluids exhibit a positive Eu anomaly (Figure 1.3 and Klinkhammer et al., 1994), suggesting strong reactions with plagioclase in the hydrothermal systems, as plagioclase can take up significant proportions of Eu 2+ [START_REF] Philpotts | Europium anomalies and the genesis of basalt[END_REF].

Hydrothermal fluid

Deep seawater Since the above-mentioned processes influence the REE patterns in characteristic ways at present, it is also possible to estimate their importance in the geological past if past seawater REE concentrations can be reconstructed. As carbonate minerals can incorporate significant amounts of REEs (e.g., [START_REF] Zhong | Partitioning of rare earth elements (REEs) between calcite and seawater solutions at 25 • C and 1 atm, and high dissolved REE concentrations[END_REF][START_REF] Stipp | Rare Earth element (REE) incorporation in natural calcite: upper limits for actinide uptake in a secondary phase[END_REF], carbonate mineral grains preserved in marine sediments can be used as paleo proxies for this purpose. In this context, biogenic and abiogenic marine carbonates have been used to study weathering cycles and changes in the oceanic redox conditions [START_REF] Liu | Cerium: a chemical tracer for paleo-oceanic redox conditions[END_REF][START_REF] German | Application of the Ce anomaly as a paleoredox indicator: The ground rules[END_REF][START_REF] Naqvi | Signatures of rare-earth elements in banded corals of Kalpeni atoll-Lakshadweep archipelago in response to monsoonal variations[END_REF][START_REF] Holser | Evaluation of the application of rare-earth elements to paleoceanography[END_REF][START_REF] Webb | Rare earth elements in Holocene reefal microbialites: a new shallow seawater proxy[END_REF][START_REF] Shields | Has the REE composition of seawater changed over geological time?[END_REF]. However, the interpretation of REE concentrations of ancient carbonates critically depends on the fractionation of the REEs during the mineral formation as well as on the preservation of these signatures over geological timescales. While the long-term retention of REE patterns in carbonates has to be evaluated using natural systems due to the long time scales [START_REF] Johannesson | Do Archean chemical sediments record ancient seawater rare earth element patterns?[END_REF][START_REF] Webb | Rare earth element geochemistry of scleractinian coral skeleton during meteoric diagenesis: a sequence through neomorphism of aragonite to calcite[END_REF], the behaviour of REEs during carbonate formation can be studied experimentally. Chapter 5 describes an experimental study of the fractionation of the REEs between aqueous fluid and solid during abiogenic calcite precipitation at different precipitation rates and aqueous solution compositions. As the concentration of REEs dissolved in aqueous solutions can be limited by the solubility of REE containing minerals, knowing the solubility of REE carbonate is a prerequisite for the accurate interpretation of REE fractionation during calcite precipitation experiments. Therefore, chapter 4 presents an experimental study of the solubility of hydroxylbastnasite (REE(CO 3 )(OH)) in aqueous solutions. These results allowed experiments to be designed avoiding the supersaturation with respect to this phase during the experiments described in chapter 5.

Fractionation in Earth Sciences

Both the behaviour of the REEs studied in chapter 5 and the evolution of the isotopic systems studied in chapters 2 and 3 are dominated by the fractionation of elements and isotopes between fluids and minerals. The following sections present a summary of the fundamental physical relationships describing fractionation at thermodynamic equilibrium (section §1.2.1) and during irreversible reactions (section §1.2.2). Furthermore, section §1.2.3 describes the particularities of isotopes in relationship to fractionation.

Thermodynamic equilibrium

Chemical fractionation occurs during the formation of a new phase from a mixture of different chemical components, such as precipitation of crystals from an aqueous solution or melt, or dissolution of solid solutions. The fractionation of a chemical species is usually described relative to another species using abundance ratios. If both species have the same valence state, it is common to describe fractionation via a chemical reaction

A α + B β --→ ←--A β + B α (1.1)
where X i designates the chemical species X in phase i. The corresponding thermodynamic equilibrium constant K D can be expressed as

K D = a β A /a β B a α A /a α B = c β A /c β B c α A /c α B D γ β A /γ β B γ α A /γ α B (1.2)
where a i X , c i X and γ i X stand for the activity, molar concentration, and activity coefficient of component X in phase i at equilibrium, respectively (e.g., [START_REF] Ganguly | Thermodynamics in earth and planetary sciences[END_REF]. The ratio of the molar concentrations D is often referred to as partition coefficient. If A and B are isotopes of the same element, this parameter is commonly called fractionation factor α (cf. section §1.2.3). Unfortunately, the nomenclature of the different ratios is not consistent in the scientific literature, and sometimes D is referred to as a distribution coefficient, and K D has been referred to as distribution or partition coefficient as well.

As the determination of the non-ideality of the solutions can be complex, simplification are often introduced that are valid only over certain conditions. For example, for the incorporation of trace elements into a solid solution, Henry's law can be applied, which states that a i X = k • c i X as c i X approach 0. An alternative, Raoult's law states that

a i X = c i X when c i X approach 1.
The relationship in equation (1.2) arises from the more fundamental thermodynamic equation

∆ R G = ∆ R G * + RT ln a β A /a β B a α A /a α B (1.3)
where ∆ R G designates the change of the Gibbs free energy during the reaction, ∆ R G *

the corresponding value at the chosen standard state, R the gas constant and T temperature. At equilibrium, ∆ R G = 0 and thus

ln K D = - ∆ R G * RT (1.4)
As the standard states are typically chosen to be at a constant composition, K D is independent of phase compositions, so that a generally valid value can be determined experimentally if the activity-composition relationships are known. By model inversion, the K D can then be used to determine unknowns in equation (1.2) for natural systems.

If the standard state is chosen to be at the temperature of interest,

ln K D = - ∆ R H * RT + ∆ R S * R (1.5)
where ∆ R H * and ∆ R S * are the enthalpy and entropy changes of the reaction at the standard state, respectively. If ∆ R H * and ∆ R S * are independent of temperature, this equation can reduce to

ln K D = a + b T (1.6)
where the parameters a and b are constant; this equation provides a good approximation for many exchange reactions over a considerable temperature range (e.g., [START_REF] Ganguly | Thermodynamics in earth and planetary sciences[END_REF]. The reason is that the temperature dependence of ∆ R H * and ∆ R S * is defined by the difference in heat capacities during the reaction, which is very small as reactants and products are the same phases. If the temperature dependency of the equilibrium constant according to equation (1.6) has been determined experimentally, measurement of K D in natural samples enables conclusions about the temperature of equilibration if this equilibrium is preserved over geologic time (see section §1.2.2), and similar expressions can be derived for the pressure dependency.

Kinetic aspects

Thermodynamic equilibrium, under which the relationships described in section §1.2.1 apply, is not always maintained in natural systems. In fact, the preservation of nonequilibrium states is of great use in Earth sciences. The extremely slow rates of most solid state diffusion processes at temperatures found at the Earth's surface and at shallow depths prevent the re-equilibration of the composition of many minerals even when environmental parameters change. This is exploited by geothermometers, geobarometers, geochronology, and paleo proxies. The strong temperature dependence of reaction rates was explained by Arrhenius (1889) as result of an activated complex:

Under the assumption that reaction rates R are proportional to the abundance of such an activated complex (n A ), which itself is in equilibrium with the reactant, the rate of a reaction can be described using

R ≡ dn R dt = k • n A = k • n R • K R-A (1.7)
with a rate constant k, the abundance of the reactant n R and the equilibrium constant K R-A . The temperature dependency of the equilibrium constant between the reactant and activated complex can be described using

K R-A = k exp E A RT (1.8)
where E A designates the activation energy required to form the activated complex and k is another constant, according to thermodynamics. Transition state theory, developed in the 1930s by Henry Eyring and co-workers (e.g., [START_REF] Eyring | The activated complex in chemical reactions[END_REF], explains how such relationships arise from statistical mechanics and allows the calculation of the various coefficients and the activation energy E A for simple reactions, but this remains challenging for complex reactions of relevance in Earth sciences.

Chemical kinetics not only play a role in the preservation of tracer signatures, but also in their generation. It is possible that the formation of a mineral occurred at steady state and sufficiently slow so that the thermodynamic condition of reversibility was met, or that thermodynamic equilibration was achieved at later time, which is often a valid assumption in magmatic and high-temperature metamorphic petrology (e.g., [START_REF] Lasaga | Kinetic theory in the Earth Sciences[END_REF][START_REF] Ganguly | Thermodynamics in earth and planetary sciences[END_REF]. In these cases, the mineral composition can be directly compared to experimentally determined equilibrium partition coefficients determine the formation or equilibration process and environmental conditions. However, the fractionation of elements or isotopes during the formation of minerals can deviate significantly from the equilibrium fractionation described in section §1.2.1 when net reaction rates are fast. For example, laboratory experiments suggest a rate-dependency of the fractionation of many elements, including Mg, Sr, Ba, Ni, Mn, Co, and Cd from Ca as well as of Ca and Mg isotopes during calcite precipitation [START_REF] Lorens | Sr, Cd, Mn and Co distribution coefficients in calcite as a function of calcite precipitation rate[END_REF][START_REF] Tesoriero | Solid solution partitioning of Sr 2+ , Ba 2+ , and Cd 2+ to calcite[END_REF][START_REF] Lakshtanov | Experimental study of nickel (II) interaction with calcite: Adsorption and coprecipitation[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF][START_REF] Gabitov | Crystal growth rate effect on Mg/Ca and Sr/Ca partitioning between calcite and fluid: An in situ approach[END_REF]. The reaction kinetics affecting the fractionation of elements and isotopes in such cases can be complex, as the rate law describing the exchange reaction depends on the exchange mechanism. Overall reaction such as reaction (1.1) can involve many elementary steps, making the determination of the appropriate rate law theoretically and experimentally challenging (e.g., [START_REF] Lasaga | Kinetic theory in the Earth Sciences[END_REF]. The composition of the various phases in a system and their change over time are then controlled by the slowest step in the overall reactions, unless multiple parallel reaction paths are possible. In the case of minerals precipitating from aqueous solutions, different reaction regimes can be identified (e.g., [START_REF] Depaolo | Surface kinetic model for isotopic and trace element fractionation during precipitation of calcite from aqueous solutions[END_REF]. If the net precipitation rate of the mineral is much slower than the rates of the individual reactions controlling the transport and exchange of elements in the system, thermodynamic equilibrium of fractionation is approached.

In many cases, solid state diffusion is slower than the precipitation rate. In this case, changing fluid composition or temperature conditions lead to variable incorporation of different components into the crystal structure and formation of a zoned crystal. The composition of the individual layers of the crystal can still represent thermodynamic equilibrium with the precipitating fluid at the time of their formation. However, when precipitation approaches rates at which surface reactions operate, those reactions control the fractionation of elements between liquid and solid, leading to deviations from equilibrium fractionation even if steady state conditions are maintained. It is also possible that diffusional transport in the aqueous solution affects precipitation, although this case is rather uncommon in nature.

In the following, potential effects of the precipitation rate on fractionation are illustrated with a set of simple rate laws. Actual rate laws can be far more complex, but such simple rate laws can successfully describe the rate dependence of fractionation seen in laboratory experiments in many cases, and can been interpreted as surface reaction control. In a simple case, formation of a binary solid solution might be described by the reactions HC aq + X aq --→ ←--HCX s (1.9) and TC aq + X aq --→ ←--TCX s (1.10)

where HC and TC designate a host and trace component of same valence state whose fractionation between the aqueous solution (aq) and solid (s) is of interest. The net rate for reaction (1.9), composed of the gross forward-and backward reaction rates R f and R b , may then take the form

R HC ≡ - dn HC aq dt = R HC f -R HC b = k HC f • c HC aq • c X aq -k HC b • c HCX aq (1.11)
where n is the molar amount and k are rate constants, and correspondingly for the trace component TC. This implies a reaction order of 1 and that rates are only dependent on the reactants of the respective reactions. It should be emphasised again that these assumptions are not generally valid, but can be used to demonstrate the potential effects of kinetics on fractionation. Under the assumption of steady state, the partition coefficient

D = c s HC /c s TC c aq HC /c aq TC = D f 1 + R b R b +Rp D f Deq -1 (1.12)
is obtained by mathematical manipulation, with the net precipitation rate R p = R f -R b and the two partition coefficients given by

D f = k TC f /k HC f (1.13)
and

D eq = k TC f /k HC f k TC b /k HC b (1.14)
A plot of D as function of R p /R b for arbitrary parameters (Figure 1.4) shows that D varies between the limits D eq and D f , and that the value of D eq is approached for R p R b . Therefore, D eq can be interpreted as the partition coefficient at thermody-namic equilibrium. At high net precipitation rates compared to R b , the value D f is approached. DePaolo (2011) used equation (1.12) to fit existing experimental data of Sr/Ca, Mn/Ca and 44 Ca/ 40 Ca fractionation into calcite as function of precipitation rate, and interpreted the rates as surface reaction controlled. As shown by [START_REF] Nielsen | Self-consistent ion-byion growth model for kinetic isotopic fractionation during calcite precipitation[END_REF], this equation may also be derived from an ion-by-ion model of crystal growth. Furthermore, [START_REF] Thien | A simple way to constrain the stoichiometry of secondary smectites upon aqueous glass alteration[END_REF] applied the equation to Cd/Ca and Co/Ca fractionation into calcite, and noted that this equation is essentially equivalent to the surface growth entrapment model of [START_REF] Watson | A conceptual model for near-surface kinetic controls on the traceelement and stable isotope composition of abiogenic calcite crystals[END_REF] under steady state conditions. However, such models contain a number of parameters which are not well constrained at the moment, such as R b and D f in equation (1.12), which is even more problematic for more complex models that include the feedback between fractionation and the rates themselves based on microscopic crystal growth processes (e.g., [START_REF] Nielsen | General model for calcite growth kinetics in the presence of impurity ions[END_REF]. Furthermore, these kinetic models of fractionation are strongly dependent on assumptions such as the form of the rate laws (e.g. equation (1.11)) which can be complex, especially if reactions are not exclusively controlled by surface reaction processes. Therefore, such reaction kinetic models provide a theoretical framework for the study of variations in partition coefficients, but prediction of these parameters under general conditions and the transfer to large scale natural systems remains challenging due to the complexity and variability of the reactions involved.

Isotopic ratios and fractionation

The description of fractionation at thermodynamic equilibrium (section §1.2.1) and its dependence on reaction rates (section §1.2.2) also applies for the fractionation of two isotopes of the same element. However, the magnitude of fractionation is considerably smaller for two isotopes because of their similar properties. In this context, the partition coefficient D defined in equation (1.2) is mainly called fractionation factor associated with the symbol α, or expressed as ε ≡ α -1 and given in units of per mil (‰).

Similarly, stable isotope ratios are most often expressed relative to a standard in the delta notation

δ i/j X ≡ i X/ j X Sample i X/ j X Standard -1 (1.15)
where i X designates the isotope with mass number i of element X. While isotopes show a very similar chemical behaviour, the sense and magnitude of this slight fractionation is characteristic of the processes involved, making them a popular class of tracers. However, the determination of differences in the abundance ratios can be challenging due to small degrees of fractionation. As most isotopic fractionation is related to the relative mass differences of the isotopes (see below), the fractionation is generally stronger for light elements. Mass spectrometers are the most common instrument used to quantify natural differences in isotope ratios arising from radioactive decay and stable isotope fractionation. Yet, only advancements in the thermal ionisation mass spectrometry (TIMS) and the development of the multi-collector inductively coupled mass spectrometer (MC-ICP-MS) over the last decades lead to the possibility to routinely measure the small differences in stable isotope ratios of heavy elements (e.g, [START_REF] Maréchal | Precise analysis of copper and zinc isotopic compositions by plasma-source mass spectrometry[END_REF][START_REF] Vanhaecke | Use of single-collector and multicollector ICP-mass spectrometry for isotopic analysis[END_REF][START_REF] Jakubowski | Inductively coupled plasma-and glow discharge plasma-sector field mass spectrometry Part I. Tutorial: fundamentals and instrumentation[END_REF].

As many elements have three or more isotopes, the relationship between the fractionation factors of the individual isotope pairs and properties of the isotopes is of considerable interest. Most fractionation found in nature is related to the mass differences of the isotopes, although mass-independent fractionation has been reported

for oxygen [START_REF] Clayton | A component of primitive nuclear composition in carbonaceous meteorites[END_REF] and sulfur [START_REF] Farquhar | Atmospheric influence of Earth's earliest sulfur cycle[END_REF]. Furthermore, the predominant mass-dependent effects can be explained by a combination of classical mechanical and quantum mechanical effects as shown by [START_REF] Bigeleisen | Calculation of equilibrium constants for isotopic exchange reactions[END_REF] and [START_REF] Urey | The thermodynamic properties of isotopic substances[END_REF]. While Bigeleisen, Urey, and co-workers showed that absolute fractionation factors for simple reactions can be calculated from spectroscopic data alone, this approach is challenging for reactions of relevance in Earth Sciences because of the complexity of the materials and reactions involved. However, it is possible to derive simple relationships between the fractionation factors of different isotopes of the same element from this theoretical framework. At equilibrium, no isotopic fractionation arises from classical mechanics, but quantum mechanical considerations predict that the fractionation factors in a three isotope system are related by

α 2/1 = α 3/1 β (1.16)
where α i/j is the fractionation factor between two isotopes and

β = 1 m 1 -1 m 2 1 m 1 -1 m 3 (1.17)
where m i is the atomic mass of isotope i (e.g., [START_REF] Matsuhisa | Mechanisms of hydrothermal crystallization of quartz at 250 C and 15 kbar[END_REF][START_REF] Weston | Anomalous or mass-independent isotope effects[END_REF][START_REF] Young | Kinetic and equilibrium massdependent isotope fractionation laws in nature and their geochemical and cosmochemical significance[END_REF]. For non-equilibrium fractionation, [START_REF] Bigeleisen | The relative reaction velocities of isotopic molecules[END_REF] discussed the a priori calculation of absolute fractionation factors based on transition state theory with the aim of predicting absolute reaction rates. Similarly to the equilibrium case, the estimation of absolute rates of general reactions as well as isotopic exchange is hindered by the complexity of the reactions. Nevertheless, for a three isotope system the theoretical framework of [START_REF] Bigeleisen | The relative reaction velocities of isotopic molecules[END_REF] can be used to derive a relationship between the relative forward reaction rate constants (k f ) of the kinetic fractionation. At high rates, α i/j = k i f /k j f (cf. section §1.2.2), for which an expression identical to equation (1.16) but with a different factor

β = ln m * 1 m * 2 ln m * 1 m * 3 (1.18)
can be derived [START_REF] Young | Kinetic and equilibrium massdependent isotope fractionation laws in nature and their geochemical and cosmochemical significance[END_REF]. Here, m * i can be the atomic masses of the isotopes, but generally depend on the bonding of the isotopes. For most fractionation observed in nature, the difference between the equilibrium and kinetic mass fractionation laws (equations (1.17) and (1.18)) is small. Assuming that m * i are the atomic masses, the difference between both fractionation laws for the three stable Mg isotopes ( 24 Mg, thermal systems. Chapter 5 characterises the fractionation of REEs and Ca during the precipitation of calcite from aqueous solutions using experimental data, and discusses the implications of these results for the use of REE concentrations in calcite as paleo proxies.

Equilibrium mass fractionation Kinetic mass fractionation

-3 -2 -1 0 1 2 δ 2524 Mg / ‰ -6 -4 -2 0 2 δ 2624 Mg / ‰ Figure 1
.5 -Variation of δ 26/24 Mg and δ 25/24 Mg according to the equilibrium and kinetic mass fractionation laws in relation to the DSM3 standard [START_REF] Galy | Magnesium isotope heterogeneity of the isotopic standard SRM980 and new reference materials for magnesium-isotope-ratio measurements[END_REF].

Introduction générale Version française

Les [START_REF] Martin | Elemental mass-balance of material carried by major world rivers[END_REF][START_REF] Gaillardet | Global silicate weathering and CO 2 consumption rates deduced from the chemistry of large rivers[END_REF][START_REF] Viers | Chemical composition of suspended sediments in World Rivers: New insights from a new database[END_REF][START_REF] Jeandel | The influence of terrigenous particulate material dissolution on ocean chemistry and global element cycles[END_REF]. Toutefois, seule une partie de ces particules est dissoute dans l'eau de mer ultérieurement, tandis que le reste est enlevé de la colonne d'eau par la sédimentation, rendant difficile l'estimation de leurs impacts sur les océans [START_REF] Martin | The significance of the river input of chemical elements to the ocean[END_REF][START_REF] Jeandel | Ocean margins: the missing term in oceanic element budgets[END_REF][START_REF] Jeandel | The influence of terrigenous particulate material dissolution on ocean chemistry and global element cycles[END_REF]. Les éléments dissous dans l'eau de mer peuvent être adsorbé sur des particules et ainsi être enlevé de l'eau de mer par un processus appelé « scavenging » [START_REF] Balistrieri | Scavenging residence times of trace metals and surface chemistry of sinking particles in the deep ocean. Deep Sea Research Part A[END_REF][START_REF] Bruland | Controls of trace metals in seawater[END_REF]. De plus, la précipitation et sédimentation des carbonates est un puit significatif pour nombre de ces éléments, dont le Ca, Mg et Sr [START_REF] Wilkinson | Sedimentary carbonate record of calciummagnesium cycling[END_REF][START_REF] Krabbenhöft | Constraining the marine strontium budget with natural strontium isotope fractionations ( 87 Sr/ 86 Sr * , δ 88/86 Sr) of carbonates, hydrothermal solutions and river waters[END_REF]Pearce et al., 2015b). Les systèmes hydrothermaux au fond de la mer peuvent agir comme source ou puit selon les éléments et les conditions [START_REF] Coogan | An internally consistent, probabilistic, determination of ridge-axis hydrothermal fluxes from basalt-hosted systems[END_REF] océaniques, comme décrits dans cette thèse, les traceurs sont essentiels pour répondre à de nombreux problèmes en sciences de la terre, comme l'identification de réservoirs dans la lithosphère terrestre (e.g., [START_REF] Hurley | Radiogenic strontium-87 model of continent formation[END_REF][START_REF] Hart | A large-scale isotope anomaly in the Southern Hemisphere mantle[END_REF][START_REF] Hofmann | Sampling mantle heterogeneity through oceanic basalts: Isotopes and trace elements[END_REF], la reconstruction des mouvements dans l'espace temps-pression-température (e.g., [START_REF] Hodges | Thermochronology in orogenic systems[END_REF] et la surveillance des fluides dans des systèmes hydrologiques naturels ou artificiels (e.g., [START_REF] Glynn | Geochemistry and the understanding of ground-water systems[END_REF][START_REF] Matter | Experimental evaluation of in situ CO 2 -water-rock reactions during CO 2 injection in basaltic rocks: Implica-tions for geological CO 2 sequestration[END_REF] Sr".

Introduction

Widespread hydrothermal activity at the mid-ocean ridges is well established (e.g., [START_REF] Stein | Constraints on hydrothermal heat flux through the oceanic lithosphere from global heat flow[END_REF][START_REF] Alt | Ophiolites and oceanic crust: new insights from field studies and the Ocean Drilling Program[END_REF][START_REF] Baker | On the global distribution of hydrothermal vent fields[END_REF][START_REF] German | Hydrothermal processes[END_REF]. Driven by the heat released from the mantle, seawater is heated while percolating through the oceanic crust, and, after its interaction with the basaltic crust, released again to the ocean (e.g., [START_REF] Sleep | Hydrothermal circulation, anhydrite precipitation, and thermal structure at ridge axes[END_REF][START_REF] Bickle | The structure and controls on fluid-rock interactions in ocean ridge hydrothermal systems: constraints from the Troodos ophiolite[END_REF][START_REF] Coogan | Reconciling temperatures of metamorphism, fluid fluxes, and heat transport in the upper crust at intermediate to fast spreading mid-ocean ridges[END_REF]. Fluids expelled near mid-ocean ridges, where new oceanic crust is created through submarine volcanic activity, can reach temperatures exceeding 400 • C, while further from active spreading centres, low-temperature hydrothermal fluids are released from the crust (e.g., [START_REF] Elderfield | Mid-ocean ridge hydrothermal fluxes and the chemical composition of the ocean[END_REF]. The significance of marine hydrothermal activity for marine geochemical cycles is widely described (e.g., [START_REF] Palmer | The strontium isotope budget of the modern ocean[END_REF][START_REF] Elderfield | Mid-ocean ridge hydrothermal fluxes and the chemical composition of the ocean[END_REF][START_REF] Davis | Imbalance in the oceanic strontium budget[END_REF][START_REF] Mottl | Partitioning of energy and mass fluxes between mid-ocean ridge axes and flanks at high and low temperature[END_REF][START_REF] Coogan | An internally consistent, probabilistic, determination of ridge-axis hydrothermal fluxes from basalt-hosted systems[END_REF][START_REF] German | Hydrothermal processes[END_REF]. Details of the chemical fluxes from these systems to the oceans, especially the partitioning of heat transfer, fluid flow and chemical fluxes between high-temperature, near axis, hydrothermal systems, and low-temperature, remain a subject of active debate (e.g., [START_REF] Davis | Imbalance in the oceanic strontium budget[END_REF][START_REF] Mottl | Partitioning of energy and mass fluxes between mid-ocean ridge axes and flanks at high and low temperature[END_REF][START_REF] Nielsen | Hydrothermal fluid fluxes calculated from the isotopic mass balance of thallium in the ocean crust[END_REF][START_REF] German | Hydrothermal processes[END_REF].

Strontium (Sr) is a particularly useful tracer of sources and sinks in marine geo-chemical cycles as the presence of both radiogenic and stable isotope systems enables different processes to be resolved [START_REF] Faure | The isotopic composition of strontium in oceanic and continental basalts: Application to the origin of igneous rocks[END_REF][START_REF] Krabbenhöft | Constraining the marine strontium budget with natural strontium isotope fractionations ( 87 Sr/ 86 Sr * , δ 88/86 Sr) of carbonates, hydrothermal solutions and river waters[END_REF]Pearce et al., 2015a). For example, the continental crust shows relatively high 87 Sr/ 86 Sr ratios (in this text, 87 Sr/ 86 Sr designates the traditional radiogenic Sr ratio corrected to a constant 86 Sr/ 88 Sr ratio of 0.1194; cf. [START_REF] Nier | The isotopic constitution of strontium, barium, bismuth, thallium and mercury[END_REF] compared to the unradiogenic mantle and oceanic crust due to the production of additional 87 Sr by decay of 87 Rb [START_REF] Armstrong | A model for the evolution of strontium and lead isotopes in a dynamic Earth[END_REF]. This enables the 87 Sr/ 86 Sr composition of seawater to be used to assess variations in Sr sources, as through their normalisation, reported radiogenic 87 Sr/ 86 Sr ratios are unaffected by isotopic fractionation during Sr removal [START_REF] Nier | The isotopic constitution of strontium, barium, bismuth, thallium and mercury[END_REF][START_REF] Faure | The isotopic composition of strontium in oceanic and continental basalts: Application to the origin of igneous rocks[END_REF]. The major sources of marine Sr are river and groundwater discharge from the continents, that provide radiogenic 87 Sr/ 86 Sr signatures to the oceans, and marine hydrothermal fluids that have unradiogenic 87 Sr/ 86 Sr compositions derived from the basaltic oceanic crust [START_REF] Davis | Imbalance in the oceanic strontium budget[END_REF][START_REF] Krabbenhöft | Constraining the marine strontium budget with natural strontium isotope fractionations ( 87 Sr/ 86 Sr * , δ 88/86 Sr) of carbonates, hydrothermal solutions and river waters[END_REF]Pearce et al., 2015a). It has been suggested that high-temperature hydrothermal circulation is not sufficient to balance the other input fluxes given the observed changes in oceanic 87 Sr/ 86 Sr [START_REF] Palmer | The strontium isotope budget of the modern ocean[END_REF][START_REF] Butterfield | Evidence for basaltic Sr in midocean ridge-flank hydrothermal systems and implications for the global oceanic Sr isotope balance[END_REF][START_REF] Davis | Imbalance in the oceanic strontium budget[END_REF]. Various explanations have been proposed to provide the missing unradiogenic 87 Sr/ 86 Sr flux, such as island arc weathering [START_REF] Allègre | The fundamental role of island arc weathering in the oceanic Sr isotope budget[END_REF], ridge-flank hydrothermal systems [START_REF] Butterfield | Evidence for basaltic Sr in midocean ridge-flank hydrothermal systems and implications for the global oceanic Sr isotope balance[END_REF], low-temperature alteration and carbonate precipitation [START_REF] Coogan | Alteration of ocean crust provides a strong temperature dependent feedback on the geological carbon cycle and is a primary driver of the Sr-isotopic composition of seawater[END_REF], temporal variability in continental weathering [START_REF] Vance | Variable Quaternary chemical weathering fluxes and imbalances in marine geochemical budgets[END_REF], and the dissolution of river derived basaltic particles (Jones et al., 2012a,b). There are, nevertheless, considerable uncertainties in the magnitude of these processes on the 87 Sr/ 86 Sr budget, so that there is still an on-going debate weighted input δ 88/86 Sr composition [START_REF] Krabbenhöft | Constraining the marine strontium budget with natural strontium isotope fractionations ( 87 Sr/ 86 Sr * , δ 88/86 Sr) of carbonates, hydrothermal solutions and river waters[END_REF]Pearce et al., 2015a).

This implies either an imbalance in the seawater δ 88/86 Sr (i.e. the modern system is not in steady state), and/or that the δ 88/86 Sr composition of oceanic sources and sinks, such as marine hydrothermal systems, is not well quantified at present. These persisting uncertainties and inconsistencies in both 87 Sr/ 86 Sr and δ 88/86 Sr marine budgets compels further assessment of the marine Sr sources and sinks. In this context, reactions occurring in seafloor hydrothermal systems are of critical importance. They are thought to represent the dominant source of unradiogenic 87 Sr/ 86 Sr to seawater, yet the size of the Sr flux to the oceans from high-and especially low-temperature systems remains poorly quantified [START_REF] Davis | Imbalance in the oceanic strontium budget[END_REF][START_REF] Coogan | Alteration of ocean crust provides a strong temperature dependent feedback on the geological carbon cycle and is a primary driver of the Sr-isotopic composition of seawater[END_REF]. Furthermore, the potential effects of Sr precipitation/removal in such systems on oceanic δ 88/86 Sr is currently poorly resolved (Pearce et al., 2015a).

The reactions leading to changes in the chemical composition of seawater during hydrothermal alteration have been extensively studied using experimental systems in the past (e.g., [START_REF] Bischoff | Seawater-basalt interaction at 200 • C and 500 bars: Implications for origin of sea-floor heavy-metal deposits and regulation of seawater chemistry[END_REF][START_REF] Seyfried | Hydrothermal transport of heavy metals by seawater: The role of seawater/basalt ratio[END_REF][START_REF] Mottl | Chemical exchange during hydrothermal alteration of basalt by seawater-I. Experimental results for major and minor components of seawater[END_REF][START_REF] Mottl | Chemical exchange during hydrothermal alteration of basalt by seawater-II. Experimental results for Fe, Mn, and sulfur species[END_REF][START_REF] Seyfried | Low temperature basalt alteration by sea water: an experimental study at 70 • C and 150 • C[END_REF][START_REF] Seyfried | Experimental seawater-basalt interaction at 300 • C, 500 bars, chemical exchange, secondary mineral formation and implications for the transport of heavy metals[END_REF][START_REF] Seyfried | Hydrothermal alteration of basalt by seawater under seawater-dominated conditions[END_REF][START_REF] Seewald | The effect of temperature on metal mobility in subseafloor hydrothermal systems: constraints from basalt alteration experiments[END_REF]. Experimental constraints on the extent of isotopic fractionation during such hydrothermal reactions are, however, sparse [START_REF] Berndt | Hydrothermal alteration processes at midocean ridges: Experimental and theoretical constraints from Ca and Sr exchange reactions and Sr isotopic ratios[END_REF][START_REF] James | An experimental study of alteration of oceanic crust and terrigenous sediments at moderate temperatures (51 to 350 • C): insights as to chemical processes in near-shore ridge-flank hydrothermal systems[END_REF]. This limits the interpretation of the behaviour of chemical tracers such as radiogenic 87 Sr/ 86 Sr ratios or δ 88/86 Sr in natural systems and introduces significant uncertainties in marine Sr mass balance models as described above. This study was designed to overcome some of these limitations

Methods

Experimental design

Basaltic glass and crystalline basalt (see section §2.2.2) were reacted with seawater in 400 mL Ti-autoclaves (Figure 2.1) at temperatures of 250 • C and 290 • C for durations of 53 and 92 days, respectively. Two experiments were conducted at each temperature using either the basaltic glass or the crystalline basalt as solid starting materials (Table 2.1). As the autoclaves were not pressurised before heating, the liquid-gas phase relations and pressure at the experimental temperature were constrained by the autoclave volume and reactant masses. Approximating the seawater as a H 2 O -NaCl solution with a molar NaCl fraction of 0.0106 (i.e. allocating all Cl -to NaCl), the thermodynamic equilibrium state of this H 2 O -NaCl system can be predicted using the relationships in [START_REF] Driesner | The system H 2 O-NaCl. Part II: Correlations for molar volume, enthalpy, and isobaric heat capacity from 0 to 1000 • C, 1 to 5000 bar, and 0 to 1 X NaCl[END_REF] and [START_REF] Driesner | The system H 2 O-NaCl. Part I: Correlation formulae for phase relations in temperature-pressure-composition space from 0 to 1000 • C, 0 to 5000 bar, and 0 to 1 X NaCl[END_REF]. Using the temperature, volume and mass constraints from the experiments, a major liquid phase and minor amounts of a low-NaCl vapour phase were predicted to coexist at both temperatures. Phase separation can also occur in marine hydrothermal systems under higher pressures and higher temperatures (Von [START_REF] Damm | Controls on the chemistry and temporal variability of seafloor hydrothermal fluids[END_REF], producing small amounts of a high-NaCl fluid together with a low-NaCl fluid. For our experiments, pressures of 39 and 73 bar were calculated for the 250 The autoclaves are rocked so that the solids are well mixed with the seawater, and the cooling apparatus attached to a valve allows fluid samples to be taken during the experimental run. At the beginning of each experiment, the reactors were filled with basalt and seawater so that the mass ratio of seawater to basalt was ∼ 10 (Table 2.1) consistent with previous experiments [START_REF] Seyfried | Low temperature basalt alteration by sea water: an experimental study at 70 • C and 150 • C[END_REF][START_REF] Seyfried | Experimental seawater-basalt interaction at 300 • C, 500 bars, chemical exchange, secondary mineral formation and implications for the transport of heavy metals[END_REF].

The absolute amounts of the reactants were lower for the 290 • C experiment to account for the greater thermal expansion at this temperature. Before sealing the reactors, the head space was flushed with N 2 to avoid oxidation reactions caused by uptake of O 2 from the gas phase. The experiments were started by placing the reactors into the furnaces, starting the rocking motion (∼1 cycle/min) and heating the furnaces to the desired temperature. The desired experimental temperature was reached within approximately 2 h in all experiments. The temperature inside the autoclave was continuously monitored with a type K thermocouple inserted into a thermowell in the closure of the reactors with an uncertainty of approximately ±2 • C.

Fluid samples were taken from the liquid in the autoclaves during all experiments using a valve with an attached water-cooled apparatus (Figure 2.1). The rocking motion was stopped prior to sampling and a Ti-frit located at the sampling outlet in the reactor (pore size 5 µm) prevented solids from leaving the autoclave. The liquid was filtered through a 0.45 µm cellulose acetate membrane at the outlet (replaced after each sampling) and collected in three separate polypropylene (PP) vials: The first ∼3 mL collected during each sampling were discarded to avoid cross-contamination from the sampling device (which was cleaned using dilute bi-distilled HNO 3 and ultrapure water before and after each sampling). Subsequently, a non-acidified sample (∼3 mL) was taken for pH measurements, followed by a ∼15 mL sample collected in a vial containing a known amount (∼0.45 g) of bi-distilled HNO 3 to avoid precipitation of solid phases due to the temperature change. The last sample was used for later compositional and isotopic analysis, and its vial was pre-cleaned by rinsing with ultrapure water, soaking in ∼1 mol/kg HCl and ultrapure water for at least 24 h, rinsing with ultrapure water again, and drying in a laminar flow hood in a clean room.

The experiments were terminated by quenching the reactors in water so that they attained the ambient temperature within approximately 30 minutes. After opening the reactors, the solid reaction products were separated from the liquid by vacuum filtration through a 0.45 µm cellulose acetate membrane, rinsed with ultrapure water, and dried at 50 • C.

Reactants

Two different types of basalt were used as reactants in the experiments: basaltic glass, and crystalline basalt (Figure 2.2a,b). Both rock types were collected from a basaltic dyke on Stapafell Mountain, SW Iceland, and have been previously described by Oelkers and Gíslason ( 2001) and [START_REF] Gudbrandsson | An experimental study of crystalline basalt dissolution from 2 pH 11 and temperatures from 5 to 75 • C[END_REF]. They have nearly identical chemical compositions (Table 2.2), which are similar to that of mid-ocean ridge basalt (MORB). Their Sr content and isotopic compositions were determined in this study, and correspond to typical basaltic values (Table 2.3). The crystalline basalt is composed of approximately 43 wt % plagioclase, 47 wt % pyroxene, 9 wt % olivine, while only minor amounts of olivine (approximately 3 wt %) are present in the basalt glass according to quantitative XRD analyses. Both materials were ground using a jaw crusher and an agate disc mill before the 40 to 80 µm size fraction was obtained by sieving. Ultra-fine particles were removed from these powders by repeated ultrasonic treatment in ultrapure water, followed by gravitational settling and decantation of the supernatant water. The resulting powder was dried at 60 • C. The specific surface areas of these powders were determined to be 0.07 and 0.4 m 2 /g for the basaltic glass and crystalline basalt, respectively, by the BET technique [START_REF] Brunauer | Adsorption of gases in multimolecular layers[END_REF]

Analytical methods

All liquid samples were analysed for their pH, elemental compositions and Sr isotopic composition. pH was measured using a Metrohm microelectrode at a temperature of 22 ± 1 • C. The electrode was calibrated with three NIST traceable pH buffer solutions (pH 4.0, 6.9 and 9.2) before each use, and the precision of these measurements is estimated to be ±0.07 pH units based on replicate analyses of buffers and samples.

Liquid samples from the 250 • C experiments were analysed for their Na, Mg, Si, K, Ca, Sr, and Fe contents using a ThermoFisher inductively coupled plasma atomic emission spectrometer (ICP-AES), and Al contents were determined by furnace atomic adsorption spectrometry (AAS) using a Perkin Elmer AAnalyst 600. Concentrations of Mg, Si, K, Ca, Sr, Fe and Al in the liquid samples from the experiments at 290 • C were determined by inductively coupled plasma mass spectrometry (ICP-MS) using an Agilent 7500ce with a known amount of In and Re added as internal standard. For these samples, Na contents were determined using a Perkin Elmer AAnalyst 400 flame AAS.

The seawater used as reactant was analysed by all of the above mentioned techniques, and the concentrations determined by the different techniques are in agreement with each other within the uncertainties. Aqueous SO 4 2and Cl -of all liquid samples were determined using a Dionex ICS 2000 ion chromatography (IC) system. All calibration standards were prepared from aqueous Merck Certipur solutions.

The 87 Sr/ 86 Sr and δ 88/86 Sr isotopic ratios of both solid and liquid samples were determined by thermal ionisation mass spectrometry (TIMS) using a ThermoFisher Triton at the National Oceanography Centre, Southampton following the sample preparation and analytical procedures described in Pearce et al. (2015a). For each sample, an unspiked and a spiked aliquot (containing an additional 84 Sr-87 Sr solution of known isotopic composition) were analysed, allowing correction for mass fraction during sample preparation and analysis. Radiogenic 87 Sr/ 86 Sr ratios were determined by correcting the data from the measurements of the unspiked sample for instrument mass fractionation assuming a 86 Sr / 88 Sr value of 0.1194 [START_REF] Nier | The isotopic constitution of strontium, barium, bismuth, thallium and mercury[END_REF] The two basalt powders used as reactants and the solid reaction products recovered from the reactors were analysed by scanning electron microscopy (SEM) using a Jeol JSM 6360LV equipped with an electron dispersive spectroscope (EDS). Powder X-ray diffraction (PXRD) patterns of the unreacted basalt powders and of the solids recovered from the reactors after the experiments were recorded on a PANalytical X'Pert PRO diffractometer (Co-Ka radiation) operated at 40 kV and 40 mA. This diffractometer is outfitted with a Scientific X'Celerator detector, 0.5°antiscattering and divergence slits, spinner stage, primary and secondary soller and automatic sample changer. The top loading technique was used for the preparation of the samples. The specimens were examined over the range 4°to 84°2Θ using a step size of 0.008°2Θ and a count time of 40 s per step. Phase identification was made using the PANalytical X'Pert HighScore

Plus software and a pdf-2 database. In addition, the mineralogies of the experimental solids and of two naturally-grown standards, namely the Garfield nontronite (Unites States) and ferrous saponite from the Saar-Nahe Basin (Germany), were studied by Fourier transform infra-red spectroscopy (FTIR) using a PerkinElmer Frontier FTIR spectrometer [START_REF] Baldermann | The Fe-Mg-saponite solid solution series a hydrothermal synthesis study[END_REF]. Standard KBr pellets were prepared by mixing 1 mg of sample with 200 mg KBr. Subsequently, mid-infrared (MIR) spectra were recorded in the range from 4000 to 650 cm -1 with a resolution of 2 cm -1 .

Thermodynamic calculations

The saturation states (Ω) of solid phases were calculated using PHREEQC [START_REF] Parkhurst | Description of input and examples for PHREEQC version 3 -A computer program for speciation, batch-reaction, onedimensional transport, and inverse geochemical calculations[END_REF] together with its Lawrence Livermore National Laboratory (LLNL)

database [START_REF] Johnson | Database thermo.com.V8.R6.230[END_REF] at the experimental temperature and saturated vapour pressure. The enthalpy of the aqueous MgSO 4 complex dissociation reaction was taken from the minteq.v4 database, as it is consistent with the results of [START_REF] Allison | MINTEQA2/PRODEFA2 -A geochemical assessment model for environmental systems: Version 3.0 User's Manual[END_REF]. In these calculations, the standard state for solid phases and H 2 O is the pure phase, while a hypothetical 1 mol/kg aqueous solution referenced to infinite dilution is chosen for unit activity (a) of aqueous species, both at the temperature and pressure of interest. The Livermore National Laboratory aqueous model [START_REF] Daveler | EQPT, a data file preprocessor for the EQ3/6 software package: User's guide and related documentation (version 7.0)[END_REF], which uses the extended Debye-Hückel equation [START_REF] Helgeson | Thermodynamics of hydrothermal systems at elevated temperatures and pressures[END_REF] was used to calculate activity coefficients (γ) of the aqueous species. As the redox state of the fluids was not specifically analysed, calculations were carried out assuming oxidising conditions (i.e. aqueous S is in the form of S 6+ ). The saturation index (SI) is defined as the base-10 logarithm of the saturation state Ω, which is the ratio of the ion activity product and the equilibrium constant of the precipitation reaction. Due to the quality of the thermodynamic database at temperatures of 200 to 300 • C and at seawater-like salinities, it seems reasonable to expect that the saturation indexes calculated for the reactive fluid samples collected in this study are somewhat uncertain. For anhydrite and quartz, minerals that contain few components the uncertainties associated with their calculated saturation indexes are likely no more than 0.2, in contrast, for feldspars and clay minerals, which have more complex hydrolysis reactions, such uncertainties likely exceed 1.

Uncertainties

Unless otherwise stated, uncertainties in this study represent the 95 % confidence interval (CI). The ± symbol is used to denote the half-width of the confidence interval (for normally distributed values, this corresponds to approximately 1.96 standard errors (SE)). Where possible, uncertainties were propagated through functions using linearisations. For non-algebraic or highly non-linear functions, Monte Carlo simulations were used to estimate the transformed probability distribution and the confidence interval is calculated from its quantiles.

Results

Evolution of the liquid composition during the experiments Magnesium, sulfate, calcium and potassium

The composition of the liquids sampled from the reactors changed significantly during the experiments (Figures 2.3 and 2.4, Table 2.4 on page 41). Magnesium and SO 4 2 -

were almost completely removed from the initial seawater within one week of reaction with basaltic glass at both studied temperatures. This removal was slower in the crystalline basalt experiments, so that near complete Mg removal was only achieved after three weeks at 250

Strontium

After dropping during the first 24 h, aqueous Sr concentrations followed the same trend observed for Ca, first decreasing then increasing during the rest of the experiment (Figure 2.5, Table 2.4 on page 41). In the basaltic glass experiments, the radiogenic 87 Sr/ 86 Sr isotope ratios decreased from the initial seawater value (0.709173) and attained values similar to that of the basaltic glass (0.703193) within one day. This process is slower in the crystalline basalt experiment at 290

Sodium and chloride

The sampling of reactor liquids lead to the formation of significant amounts of low-NaCl vapour during the late stages of the experiments. This process results in an enrichment of the solutes remaining in the liquid phase. As discussed in section §2.2.1;

approximating the phase relations as a binary H 2 O -NaCl system and using the thermodynamic data of [START_REF] Driesner | The system H 2 O-NaCl. Part II: Correlations for molar volume, enthalpy, and isobaric heat capacity from 0 to 1000 • C, 1 to 5000 bar, and 0 to 1 X NaCl[END_REF] and [START_REF] Driesner | The system H 2 O-NaCl. Part I: Correlation formulae for phase relations in temperature-pressure-composition space from 0 to 1000 • C, 0 to 5000 bar, and 0 to 1 X NaCl[END_REF], this process is predicted to show an exponential behaviour, with molar NaCl enrichments in the liquid below 5 % during early stages of the experiments, but enrichments of approximately 20 % for the end of the 290 The uptake of H 2 O by the vapour phase was accounted for in mass balance calculation using vapour masses calculated using the relationships of [START_REF] Driesner | The system H 2 O-NaCl. Part II: Correlations for molar volume, enthalpy, and isobaric heat capacity from 0 to 1000 • C, 1 to 5000 bar, and 0 to 1 X NaCl[END_REF] and [START_REF] Driesner | The system H 2 O-NaCl. Part I: Correlation formulae for phase relations in temperature-pressure-composition space from 0 to 1000 • C, 0 to 5000 bar, and 0 to 1 X NaCl[END_REF].

Silica

Dissolved silica concentrations increased dramatically from the below detection quant-

Iron

The basaltic glass experiment at 250

Solid alteration products

The solids recovered after the experiments were substantially altered compared to the basalt used as starting materials. The SEM images from the 250 A separate experiment with basaltic glass at 250 • C that was terminated after only one day showed that both of these alteration minerals were already present after this period, although the honeycomb smectite structures were less developed at this stage.

The formation of smectite and anhydrite was confirmed by XRD (

Basaltic glass Crystalline basalt

Figure 2.7 -FTIR spectra of the basalts used as reactant in the experiment in comparison to those of the solid alteration products of the experiments with basaltic glass (left) and crystalline basalt (right) as well as those of Mg-saponite, Fe-saponite and nontronite [START_REF] Baldermann | The Fe-Mg-saponite solid solution series a hydrothermal synthesis study[END_REF]. Note the absence of the FeFeOH-stretch in the samples from this study as opposed to the nontronite sample used as standard, suggesting that trioctahedral smectite (saponite) is the predominant clay mineral formed in this study.

Discussion

Chemical exchange

The changes in the composition of the seawater during the experiments and the alteration mineral assemblage observed in this study are comparable to those seen in marine hydrothermal vent fluids (e.g., [START_REF] German | Hydrothermal processes[END_REF]. Consistent with previous experimental studies [START_REF] Seyfried | Experimental seawater-basalt interaction at 300 • C, 500 bars, chemical exchange, secondary mineral formation and implications for the transport of heavy metals[END_REF][START_REF] Seyfried | Hydrothermal alteration of basalt by seawater under seawater-dominated conditions[END_REF] (brucite) component [START_REF] Bischoff | Seawater-basalt interaction at 200 • C and 500 bars: Implications for origin of sea-floor heavy-metal deposits and regulation of seawater chemistry[END_REF][START_REF] Seyfried | Hydrothermal transport of heavy metals by seawater: The role of seawater/basalt ratio[END_REF][START_REF] Seyfried | Low temperature basalt alteration by sea water: an experimental study at 70 • C and 150 • C[END_REF][START_REF] Seyfried | Experimental seawater-basalt interaction at 300 • C, 500 bars, chemical exchange, secondary mineral formation and implications for the transport of heavy metals[END_REF][START_REF] Seyfried | Hydrothermal alteration of basalt by seawater under seawater-dominated conditions[END_REF]. The low pH can only be maintained as long as sufficient OH -can be removed from the liquid into clays along with Mg, as basalt hydrolysis consumes protons (e.g., [START_REF] Oelkers | The mechanism, rates and consequences of basaltic glass dissolution: I. An experimental study of the dissolution rates of basaltic glass as a function of aqueous Al, Si and oxalic acid concentration at 25 • C and pH= 3 and 11[END_REF] leading to an increase in pH [START_REF] Seyfried | Experimental seawater-basalt interaction at 300 • C, 500 bars, chemical exchange, secondary mineral formation and implications for the transport of heavy metals[END_REF]. As noted by [START_REF] Seyfried | Low temperature basalt alteration by sea water: an experimental study at 70 • C and 150 • C[END_REF], the absence of epidote, which is formed in natural systems, from experimental studies likely results from sluggish nucleation kinetics, and from lower pressures limiting the epidote stability. The sustained low pH observed in natural vent fluids even after the near complete Mg removal is likely a result of epidote formation which consumes OH -at higher temperatures [START_REF] Seewald | The effect of temperature on metal mobility in subseafloor hydrothermal systems: constraints from basalt alteration experiments[END_REF][START_REF] Seyfried | Phase equilibria constraints on the chemistry of hot spring fluids at mid-ocean ridges[END_REF] as well as the addition of magmatic H 2 S to the fluids [START_REF] German | Hydrothermal processes[END_REF].

Strontium isotopic exchange Initial stage (< 24 hours)

The most significant Sr isotopic exchange occurred during the first 24 h during most of the experiments conducted in this study. In all experiments, aqueous Sr concentrations decreased during these initial 24 hours as the 87 Sr/ 86 Sr ratio of the fluid decreased from the initial seawater towards that of the basalt (Figure 2.5 on page 38). Because these changes in 87 Sr/ 86 Sr reflect the mixing between different phases and not isotopic fractionation, both the release of Sr from the basalt and the removal of Sr into alteration phases are necessary to explain these observations.

The presence of anhydrite in the solids recovered after the experiments coupled with the decrease of SO 4 2during the first 24 h (Figure 2.3 on page 36) suggests that anhydrite is the main alteration mineral taking up Sr during this period; note Sr is readily incorporated into anhydrite [START_REF] Shikazono | The partitioning of strontium between anhydrite and aqueous solutions from 150 • to 250 •[END_REF]. This is consistent with positive anhydrite saturation indices calculated with PHREEQC for these experiments (Figure 2.9) and the observation of anhydrite precipitation when heating seawater to temperatures of 150 to 200 • C [START_REF] Bischoff | Hydrothermal chemistry of seawater from 25 • to 350 •[END_REF]. Assuming that anhydrite is the only solid phase removing aqueous Ca and SO The relative timing of basalt dissolution and anhydrite precipitation, and thus the evolution of the Sr isotopic system during the initial 24 h of each experiment were determined using an iterative mass balance model. ). This apparent fractionation when releasing Sr from the crystalline basalt is likely the result of the preferential dissolution of minerals having a stable Sr composition distinct from that of the bulk basalt. The effect of non-stoichiometric dissolution has also been suggested to explain stable Sr isotopic signatures in continental weathering environments [START_REF] Halicz | Strontium stable isotopes fractionate in the soil environments?[END_REF][START_REF] Wei | Seasonal changes in the radiogenic and stable strontium isotopic composition of Xijiang River water: Implications for chemical weathering[END_REF].

Model predictions are shown in Figures 2.10 and 2.11, and reveal a good fit to the boundary values (i.e. the symbols in Figure 2.10). This good fit indicates that the model design and assumptions described above are consistent with the isotopic data.

An initially fast anhydrite precipitation (compared to basalt dissolution) is predicted due to the oversaturation of seawater with respect to anhydrite at the experimental temperatures [START_REF] Bischoff | Hydrothermal chemistry of seawater from 25 • to 350 •[END_REF], leading to a drop in aqueous Sr concentrations while 87 Sr/ 86 Sr remains relatively constant. Subsequently, basalt dissolution becomes the dominant process and fluid 87 Sr/ 86 Sr decreases towards the basalt signature, which is promoted by the lower Sr content of the fluid. Finally, aqueous Sr concentrations eventually increase due to basalt dissolution while 87 Sr/ 86 Sr remain low, which is continued in the trends defined by the later samples (Figure 2.11). This result is similar to the proposed reaction path of [START_REF] Berndt | Hydrothermal alteration processes at midocean ridges: Experimental and theoretical constraints from Ca and Sr exchange reactions and Sr isotopic ratios[END_REF], and consistent with the trends inferred from anhydrite found in in ODP Hole 504B (Teagle et al., 1998b), while evidence for the last stage of fluid evolution was missing in these natural anhydrite samples. The best-fit values for D Sr range from 0.36 to 0.78, which is similar to the range of experimentally determined values of 0.27 to 0.73 [START_REF] Shikazono | The partitioning of strontium between anhydrite and aqueous solutions from 150 • to 250 •[END_REF]) and partition coefficients of 0.60 (2 SD = 0.28) derived from the TAG hydrothermal mound (Teagle et al., 1998a).

The model results suggest that changes in aqueous δ 88/86 Sr are caused by isotopic fractionation between the liquid and precipitating anhydrite, as well as by the nonstoichiometric dissolution of crystalline basalt. model can also explain the decrease in δ 88/86 Sr between 7 and 14 days of elapsed time during the crystalline basalt experiment at 250 • C resulting from anhydrite precipitation and basalt dissolution.

Strontium evolution at elapsed times > 24 hours

Following the initial period of coupled anhydrite precipitation and basalt dissolution, Sr concentrations in the fluid increase. However, aqueous 87 Sr/ 86 Sr also increases slightly during the later stages of all experiments (Figure 2.5 on page 38 and solid lines in Figure 2.11), which is inconsistent with continued basalt dissolution, as that would be expected to drive aqueous 87 Sr/ 86 Sr towards the lower basalt signature. Since this phenomenon also occurs in the basaltic glass experiments which likely has homogeneous 87 Sr/ 86 Sr, the dissolution of a primary mineral with elevated 87 Sr/ 86 Sr compared to the bulk basalt is unlikely to be the cause of this process. It seems likely, therefore, that the increase in 87 Sr/ 86 Sr is driven by the dissolution of previously precipitated alteration minerals that incorporated the higher 87 Sr/ 86 Sr ratios of the initial seawater. Note the degree of supersaturation with respect to anhydrite calculated with PHREEQC decreases during all experiments, and undersaturation is predicted for some later fluid

Implications for the marine Sr budget

The contribution of hydrothermal systems to the marine 87 Sr/ 86 Sr budget can be estimated by comparing the heat budget of mid-ocean ridges and the cooling oceanic lithosphere. Estimates of the latent heat of crystallisation and the required amount of cooling of newly created oceanic crust places upper limits on the heat transferred to the oceans through hydrothermal circulation at mid ocean-ridges. In combination with a known distribution of fluid temperatures, the corresponding hydrothermal water flux can be calculated [START_REF] Morton | A mid-ocean ridge thermal model: Constraints on the volume of axial hydrothermal heat flux[END_REF][START_REF] Palmer | The strontium isotope budget of the modern ocean[END_REF][START_REF] Elderfield | Mid-ocean ridge hydrothermal fluxes and the chemical composition of the ocean[END_REF][START_REF] Davis | Imbalance in the oceanic strontium budget[END_REF][START_REF] Mottl | Partitioning of energy and mass fluxes between mid-ocean ridge axes and flanks at high and low temperature[END_REF]. This, in turn, allows estimation of the 87 Sr/ 86 Sr by basalt dissolution. Therefore, if the anhydrite is re-dissolved at a later stage, the 87 Sr/ 86 Sr composition of the altered basalt may be relatively unchanged compared to the fresh basalt, such that the 87 Sr/ 86 Sr ratios of the recovered altered oceanic rocks (e.g., [START_REF] Staudigel | Large scale isotopic Sr, Nd and O isotopic anatomy of altered oceanic crust: DSDP/ODP sites 417/418[END_REF][START_REF] Alt | Ophiolites and oceanic crust: new insights from field studies and the Ocean Drilling Program[END_REF][START_REF] Harris | Channelling of hydrothermal fluids during the accretion and evolution of the upper oceanic crust: Sr isotope evidence from ODP Hole 1256D[END_REF] do not accurately reflect the degree of isotopic Sr exchange. There are various processes that might result in the re-dissolution of anhydrite. For example, in our experiments anhydrite re-dissolution is most likely caused by the release of reduced Fe 2+ (cf. section §2.4.2). Furthermore, increased SO 4 2in the quenched liquid compared to the final sample taken at experimental temperature (Table 2.4) indicates that anhydrite rapidly re-dissolves when it becomes undersaturated at lower temperatures; note the solubility of anhydrite is retrograde. In natural systems, re-dissolution might occur due to circulating low-temperature fluids at a later time [START_REF] Mottl | Chemical exchange during hydrothermal alteration of basalt by seawater-II. Experimental results for Fe, Mn, and sulfur species[END_REF]. Overrepresentation of basalt affected by such processes could explains imbalances in the Sr budget calculations that are based on MORB alteration profiles. This potentially limits the use of altered basalt compositions to infer the hydrothermal Sr flux to the oceans and provides a potential explanation for the Sr imbalances arising from models such as the marine Sr budget calculations of [START_REF] Davis | Imbalance in the oceanic strontium budget[END_REF] and the internally consistent model of global oceanic high-temperature hydrothermal chemical exchange of [START_REF] Coogan | An internally consistent, probabilistic, determination of ridge-axis hydrothermal fluxes from basalt-hosted systems[END_REF].

Similarly to the radiogenic 87 Sr/ 86 Sr imbalance in the marine budgets, several studies reported a disequilibrium between marine Sr input and output fluxes by analysing stable δ 88/86 Sr budgets [START_REF] Krabbenhöft | Constraining the marine strontium budget with natural strontium isotope fractionations ( 87 Sr/ 86 Sr * , δ 88/86 Sr) of carbonates, hydrothermal solutions and river waters[END_REF]Pearce et al., 2015a). In these studies, the estimated δ 88/86 Sr of the combined marine Sr inputs, dominated by rivers and hydrothermal systems, (∼ 0.3 ‰) is significantly higher than the carbonate sink (0.15 to 0.21 ‰), suggesting that seawater δ 88/86 Sr is currently not at steady state. However, Our experiments suggest that significantly lower fluid δ 88/86 Sr compositions may be reached in reactions with crystalline basalt, potentially due to the preferential dissolution of light minerals. Although there is no requirement for modern seawater δ 88/86 Sr to be at steady state (and indeed, glacial-interglacial weathering effects would imply that this is unlikely to be the case; [START_REF] Vance | Variable Quaternary chemical weathering fluxes and imbalances in marine geochemical budgets[END_REF], a lower integrated hydrothermal δ 88/86 Sr composition, or a larger net flux of this composition, would shift the combined marine input δ 88/86 Sr towards lower values, reducing the suggested imbalance between current input and output fluxes. Furthermore, as Sr is also precipitated into anhydrite during hydrothermal alteration, hydrothermal systems may also represent an important sink in the marine Sr cycle. As the anhydrite takes up Sr during the initial stages of hydrothermal alteration (section §2.4.2) and due to the small magnitude of isotopic fractionation, its δ 88/86 Sr is similar to that of seawater. Therefore, marine hydrothermal systems shift the flux-weighted δ 88/86 Sr towards higher values, further reducing the potential imbalance between sources and sinks. However, the global magnitude of this effect in comparison to the high magnitude of carbonate burial Sr flux [START_REF] Krabbenhöft | Constraining the marine strontium budget with natural strontium isotope fractionations ( 87 Sr/ 86 Sr * , δ 88/86 Sr) of carbonates, hydrothermal solutions and river waters[END_REF]Pearce et al., 2015a) is not well constrained at present.

Importantly, the possibility of hydrothermal fluid δ 88/86 Sr compositions being isotopically lighter than previously suggested provides new insights into the processes that govern marine Sr exchange, such as the fractionation during incorporation into anhydrite and non-stoichiometric basalt dissolution. Such processes and the resulting lower hydrothermal δ 88/86 Sr would also affect models of past seawater δ 88/86 Sr, and therefore put further constraints on past oceanic carbonate fluxes, as carbonate minerals such as calcite can take up significant amounts of Sr [START_REF] Vollstaedt | The Phanerozoic δ 88/86 Sr record of seawater: new constraints on past changes in oceanic carbonate fluxes[END_REF]. Furthermore, the magnitude of isotopic fractionation at equilibrium increases with decreasing temperature [START_REF] Bigeleisen | Calculation of equilibrium constants for isotopic exchange reactions[END_REF][START_REF] Urey | The thermodynamic properties of isotopic substances[END_REF], so that the magnitude of Sr isotopic fractionation between anhydrite and liquid may likely be higher in lower-temperature systems, unless equilibrium fractionation is cancelled out by kinetic isotope effects of the opposite sense.

Conclusion

Basaltic glass and crystalline basalt was reacted with seawater at temperatures of Given the rapid achievement of a near basaltic 87 Sr/ 86 Sr signature and significant Sr concentrations in the experiments at 250 • C, intermediate-temperature oceanic hydrothermal fluids could be the source of the 'missing basaltic Sr input' that has been postulated in marine radiogenic Sr budgets (e.g., [START_REF] Davis | Imbalance in the oceanic strontium budget[END_REF]. Furthermore, the inconsistency of observed MORB alteration with the marine Sr budget and the low amounts of anhydrite in ocean crust profiles (Teagle et al., 1998b) may be related to the re-dissolution of anhydrite, which is precipitated during hydrothermal alteration at a later stage due to the circulation of reduced or low-temperature fluids (as observed in our experiments). However, the significant uncertainties in the temperature distribution of the global hydrothermal water flux complicates the quantitative balancing of the marine Sr budget, which should also include other proposed low 87 Sr/ 86 Sr sources such as island arc weathering [START_REF] Allègre | The fundamental role of island arc weathering in the oceanic Sr isotope budget[END_REF], dissolution of riverine particulate materials (Jones et al., 2012a) and and low-temperature alteration and carbonate precipitation [START_REF] Coogan | Alteration of ocean crust provides a strong temperature dependent feedback on the geological carbon cycle and is a primary driver of the Sr-isotopic composition of seawater[END_REF]. Our experimental data also suggests that marine hydrothermal fluids with an isotopically light δ 88/86 Sr signature can be generated by fractionation of Sr during anhydrite precipitation or non-stoichiometric crystalline basalt dissolution. Such insights into the processes that potentially affect seawater δ 88/86 Sr highlight the need for detailed data on δ 88/86 Sr of the marine hydrothermal inputs information, which will help to further constrain models of the current and past marine Sr system [START_REF] Krabbenhöft | Constraining the marine strontium budget with natural strontium isotope fractionations ( 87 Sr/ 86 Sr * , δ 88/86 Sr) of carbonates, hydrothermal solutions and river waters[END_REF][START_REF] Vollstaedt | The Phanerozoic δ 88/86 Sr record of seawater: new constraints on past changes in oceanic carbonate fluxes[END_REF]Pearce et al., 2015a) and thus their relationship to changes in global processes such as plate tectonics, weathering, and climate.

Chapter 3

Isotopic fractionation during seawater-basalt interaction: Mg

A version of this chapter will be submitted for publication as "Voigt, M., Pearce, C. R., Baldermann, A., Oelkers, E. H.: Isotopic fractionation during seawater-basalt interaction:

Mg".

Introduction

The global marine Mg isotope budget is controlled by a combination of input and output fluxes from reservoirs of distinct Mg isotopic composition, and the fractionation of its three stable isotopes ( 24 Mg, 25 Mg and 26 Mg). Rivers, which transport Mg weathered from continental carbonate and silicate rocks, are the major source of Mg to the oceans, while seafloor hydrothermal systems and dolomite precipitation are the dominant marine Mg sinks (Tipper et al., 2006b;[START_REF] Higgins | The Mg isotopic composition of Cenozoic seawater -evidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF]. Paleo proxies such as marine evaporites or carbonate sediments suggest that the bulk Mg concentration in the seawater varied considerably over the Phanerozoic and is currently increasing [START_REF] Horita | Chemical evolution of seawater during the Phanerozoic: Implications from the record of marine evaporites[END_REF][START_REF] Fantle | Sr isotopes and pore fluid chemistry in carbonate sediment of the Ontong Java Plateau: Calcite recrystallization rates and evidence for a rapid rise in seawater Mg over the last 10 million years[END_REF][START_REF] Higgins | Records of Neogene seawater chemistry and diagenesis in deep-sea carbonate sediments and pore fluids[END_REF]. The current and past state of the Mg isotopic system is less clear, but foraminera from the past 40 Ma Ma indicate a rapid decrease in seawater δ 26/24 Mg over the past ∼15 Ma (Pogge von [START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF], while pelagic marine carbonates from the past 80 Ma suggest only small changes in seawater δ 26/24 Mg over this period [START_REF] Higgins | The Mg isotopic composition of Cenozoic seawater -evidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF].

However, the influence of the different fluxes on the isotope budget remain uncertain as the extent of isotopic fractionation occurring in marine hydrothermal systems is very poorly constrained at present [START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF][START_REF] Higgins | The Mg isotopic composition of Cenozoic seawater -evidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF]. Although basaltic rock dissolution in hydrothermal systems releases Mg to the fluid, it is coupled to Mg-rich clay precipitation. The net result of the coupled process is the almost quantitative removal of Mg from the seawater in high-temperature hydrothermal systems, as well as significant Mg removal at lower temperature conditions [START_REF] Mottl | Hydrothermal circulation through mid-ocean ridge flanks: Fluxes of heat and magnesium[END_REF][START_REF] Elderfield | Mid-ocean ridge hydrothermal fluxes and the chemical composition of the ocean[END_REF]. Consequently, there is a net transfer of Mg to the oceanic crust in such settings (e.g., [START_REF] Elderfield | Mid-ocean ridge hydrothermal fluxes and the chemical composition of the ocean[END_REF][START_REF] Coogan | An internally consistent, probabilistic, determination of ridge-axis hydrothermal fluxes from basalt-hosted systems[END_REF][START_REF] German | Hydrothermal processes[END_REF], and isotopic fractionation in the case of non-complete Mg removal (especially at lower temperatures) potentially affects the oceanic Mg isotope budget [START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF][START_REF] Higgins | The Mg isotopic composition of Cenozoic seawater -evidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF].

Although the number of studies of altered oceanic basalts to date are limited [START_REF] Teng | Magnesium isotope geochemistry[END_REF], current data suggests a wide range of Mg isotopic compositions can result from carbonate and smectite precipitation during low-temperature seawater alteration: A relatively strong fractionation of Mg isotopes is known to occur between fluids and Mgcontaining carbonate minerals, which preferentially take up light Mg isotopes [START_REF] Galy | Mg isotopic composition of carbonate: insight from speleothem formation[END_REF]Tipper et al., 2006b;[START_REF] Higgins | Constraining magnesium cycling in marine sediments using magnesium isotopes[END_REF][START_REF] Teng | Contrasting lithium and magnesium isotope fractionation during continental weathering[END_REF]Pearce et al., 2012;[START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF]; this is believed to be the main driver of past changes in seawater δ 26/24 Mg (Pogge von [START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF]. On the other hand, silicate alteration minerals such as clays show a smaller degree of isotopic fractionation, with most studies suggesting the preferential incorporation of heavy Mg isotopes into such minerals (Tipper et al., 2006a;[START_REF] Higgins | Constraining magnesium cycling in marine sediments using magnesium isotopes[END_REF][START_REF] Teng | Contrasting lithium and magnesium isotope fractionation during continental weathering[END_REF][START_REF] Wimpenny | Investigating the behaviour of Mg isotopes during the formation of clay minerals[END_REF]. There is also evidence for Mg fractionation in the opposite sense (i.e. the preferential incorporation of lighter Mg isotopes; cf. [START_REF] Pogge Von Strandmann | The influence of weathering processes on riverine magnesium isotopes in a basaltic terrain[END_REF][START_REF] Wimpenny | The behaviour of Li and Mg isotopes during primary phase dissolution and secondary mineral formation in basalt[END_REF], suggesting that the net Mg fractionation mechanism is highly dependent on the starting fluid composition and the specific alteration mineral.

Additionally, isotopic fractionation depends on the aqueous solution speciation, which can further complicate this issue [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF].

To better constrain the behaviour of Mg isotopes in marine hydrothermal systems, we performed a series of hydrothermal experiments reacting different types of basalt with seawater at 250 • C over several months. Unlike previous experimental studies of such systems (e.g., [START_REF] Bischoff | Seawater-basalt interaction at 200 • C and 500 bars: Implications for origin of sea-floor heavy-metal deposits and regulation of seawater chemistry[END_REF][START_REF] Seyfried | Hydrothermal transport of heavy metals by seawater: The role of seawater/basalt ratio[END_REF][START_REF] Mottl | Chemical exchange during hydrothermal alteration of basalt by seawater-I. Experimental results for major and minor components of seawater[END_REF][START_REF] Mottl | Chemical exchange during hydrothermal alteration of basalt by seawater-II. Experimental results for Fe, Mn, and sulfur species[END_REF][START_REF] Seyfried | Low temperature basalt alteration by sea water: an experimental study at 70 • C and 150 • C[END_REF][START_REF] Seyfried | Experimental seawater-basalt interaction at 300 • C, 500 bars, chemical exchange, secondary mineral formation and implications for the transport of heavy metals[END_REF][START_REF] Seyfried | Hydrothermal alteration of basalt by seawater under seawater-dominated conditions[END_REF][START_REF] Seewald | The effect of temperature on metal mobility in subseafloor hydrothermal systems: constraints from basalt alteration experiments[END_REF], the evolution of the aqueous Mg isotopic composition was followed by regular sampling, constraining the behaviour of Mg isotopes during the dissolution of basalt and the formation of secondary alteration minerals. These results were interpreted in the context of other constraints on basalt dissolution and anhydrite precipitation (reported separately in chapter 2), enabling direct comparison between the relative controls on the Mg and Sr composition of the fluids, and their associated implications for marine mass balance.

Methods

Experimental design

Efforts in this study focussed on seawater-basalt interaction experiments. The basalt used consisted of either basaltic glass or crystalline basalt powders (40 to 80 µm size fraction). These samples were originally collected from the Stapafell volcano, Iceland.

These powers were reacted with natural seawater collected from the equatorial Pacific at a depth of 350 m (EqPac cruise November 1992; [START_REF] Murray | JGOFS studies in the equatorial Pacific. Deep Sea Research Part II: Topical Studies in Oceanography[END_REF]. The composition of the glass and crystalline basalt samples (Table 2.2 on page 31), previously reported by [START_REF] Oelkers | The mechanism, rates and consequences of basaltic glass dissolution: I. An experimental study of the dissolution rates of basaltic glass as a function of aqueous Al, Si and oxalic acid concentration at 25 • C and pH= 3 and 11[END_REF] and [START_REF] Gudbrandsson | An experimental study of crystalline basalt dissolution from 2 pH 11 and temperatures from 5 to 75 • C[END_REF], respectively, is nearly identical to that of mid-ocean ridge basalt (MORB). The experiments were carried out in rocking Ti autoclaves at 250 • C and saturated vapour pressure for 53 days. The mass ratio of seawater to basaltic powder was ∼ 10 in all experiments. Fluid samples were retrieved from the reactor throughout the experiments using a sampling valve with an attached cooling apparatus. Further details on the experimental design used in this study are provided in section §2.2.1.

Analytical methods

The detailed analytical methods used to determine aqueous elemental concentrations and characterise the solid reactants are reported in section §2.2.3 (experiments at 250 • C). Aqueous Na, Mg, Si, K, Ca, Sr, and Fe concentrations were determined by inductively coupled plasma atomic emission spectrometer (ICP-AES), and Al contents were determined by furnace atomic adsorption spectrometry (AAS) using a Perkin Elmer AAnalyst 600. The phases in the unreacted basalt powders and of the solids recovered from the reactors were analysed by scanning electron microscopy (SEM), powder X-ray diffraction (PXRD) and Fourier transform infra-red spectroscopy (FTIR).

The Mg isotopic compositions of the basalts used as reactants and liquid samples of the experiments at 250 • C were determined by multiple collector inductively coupled plasma mass spectrometry (MC-ICP-MS) using a ThermoFisher Neptune at the National Oceanography Centre, Southampton. The solid samples were dissolved in a mixture of bi-distilled HNO 3 and HF at 130 • C, evaporated to dryness, and re-dissolved in bi-distilled HCl. Prior to analysis, Mg was purified using ion-exchange chromatography with a protocol adapted from Pogge von Strandmann et al. (2008,2012).

For this, a sample aliquot containing 2000 ng Mg was evaporated to dryness and redissolved in 200 µL of 0.8 mol/kg HNO 3 (the unit mol/kg designates molalities, i.e. the concentration of the solute per mass of H 2 O) before loading onto pre-cleaned Bio-Rad AG50W-X12 (200-400 mesh) resin equilibrated with 0.8 mol/kg HNO 3 in a Savillex 30 mL column to a height of 8.5 cm. Cations other than Mg were eluted using a total volume of 51 mL of 0.8 mol/kg HNO 3 , followed by the elution of Mg in 20 mL of 2 mol/kg HNO 3 . To ensure a 100 % yield, this elution protocol was tested using the IAPSO seawater standard, the DSM3 Mg standard [START_REF] Galy | Magnesium isotope heterogeneity of the isotopic standard SRM980 and new reference materials for magnesium-isotope-ratio measurements[END_REF] as well as the JB-3 basaltic rock standard from the Geological Survey of Japan. The column procedure was repeated 2-3 times to achieve a sufficient purity for Mg analyses, which was confirmed by measurement of Li, Na, Mg, Al, K, Ca, Ti V, Mg, Fe, Ni, Sr, Sn and Pb concentrations using a ThermoFisher X-Series ICP-MS. Despite the efficiency of this procedure, the observation of low Mg/Ca concentration ratios meant that complete removal of Ca was not achieved for two samples (BSW04-03 and BSW05-07), resulting in isobaric interferences during the MC-ICP-MS measurements; these analyses were corrected as described using the method described below.

Purified samples were introduced to the MC-ICP-MS in 3 % HNO 3 via a standard injection system (SIS). Thirty measurements with a combined integration time of 252 s were made per sample. The samples, containing approximately 600 ppb Mg, yielded et al., 2012;[START_REF] Teng | Magnesium isotope geochemistry[END_REF]. The magnitude of 2 standard deviations of the measurements made during this study varied from 0.07 to 0.24 ‰. The higher variability is reflected in the uncertainties propagated using the method described above.

Calcium interference in the two samples (BSW04-03 and BSW05-07) were corrected by assuming that the deviations of the measured δ 26/24 Mg and δ 25/24 Mg values from the mass dependent fractionation line [START_REF] Young | Kinetic and equilibrium massdependent isotope fractionation laws in nature and their geochemical and cosmochemical significance[END_REF] were caused by 48 Ca interference with the 24 Mg signal. This enabled the measured δ values to be corrected by back-tracking to the 'true' values that were consistent with mass dependent fractionation (Figure 3.1). The two affected samples were analysed by MC-ICP-MS after two and three repeats of the ion-exchange separation, which lead to an increasingly better, but not complete, removal of Ca. For both samples, these two individual analyses are consistent with the same corrected δ 26/24 Mg and δ 25/24 Mg. Furthermore, the analysis after three separation runs indicates a smaller amount of 48 Ca (Figure 3.1), consistent with the assumption that the deviations are caused by Ca interference. This also suggests that the interferences caused by 48 Ca, which were corrected for, are the dominant cause for the deviation from the mass dependent fractionation line as opposed to matrix effects. Propagation of uncertainties in this inversion was performed using Monte Carlo simulations, so that the uncertainties given for δ 26/24 Mg and δ 25/24 Mg of the two corrected samples include uncertainties of the interference correction.

Mass dependent fractionation 48 Ca interference correction BSW04-03

BSW05-07

Uncorrected, 2x purified Uncorrected, 3x purified Corrected

-8 -6 -4 -2 0 δ 2624 Mg / ‰ -7 -6 -5 -4 -3 -2 -1 0 δ 2524 Mg / ‰

Results

Evolution of the liquid composition

General chemical trends

The elemental composition of the seawater changed significantly during its reaction with basalt (see data for the 250 • C experiments in Table 2.4 on page 41 and section §2.3.1). The rate of change, as monitored by the temporal evolution of reaction fluid compositions, was higher for the experiment with basaltic glass in comparison to the one using crystalline basalt as the reactant. Magnesium was steadily removed from the liquid through basalt-seawater interaction and reached levels below the detection limit after 7 days in the basaltic glass experiment, while aqueous Ca concentrations increased during the experiments (Figure 3.2). Similarly to Mg, the SO 4 2initially present in the seawater was removed from the liquid over time. pH values did not decrease significantly in the basaltic glass experiment before they increased to approximately 9.5. In contrast, a pH of 3.7 was attained in the crystalline basalt experiment, before increasing to similar values as in the glassy basalt experiment (Figure 3.2). Significant concentrations of aqueous Fe (2.4 mmol/kg) were reached and sustained in the experiments with crystalline basalts while the liquids had acidic pH. Measurable quantities of aqueous silica were present in all experiments from the first sample (which was taken after ∼24 h), stabilising at ∼10 mmol/kg after decreasing from slightly higher values (20 mmol/kg).

Aqueous Na and Cl concentrations increased significantly at the end of the experiments: The last two samples of the experiment with basaltic glass has ∼ 17 % higher Cl -concentrations compared to seawater. This can be explained by the formation of low-NaCl vapour due to the removal of liquid by sampling from the autoclaves, leading to an enrichment of solutes that are not controlled by the precipitation of solid alteration phases (cf. section §2.3.1 for a detailed discussion). The reduced liquid volume due to this effect is taken into account in the mass balance calculations presented below, where estimates of the amount of low-NaCl vapour were determined using thermodynamic relationships for the H 2 O -NaCl system reported by [START_REF] Driesner | The system H 2 O-NaCl. Part II: Correlations for molar volume, enthalpy, and isobaric heat capacity from 0 to 1000 • C, 1 to 5000 bar, and 0 to 1 X NaCl[END_REF] and [START_REF] Driesner | The system H 2 O-NaCl. Part I: Correlation formulae for phase relations in temperature-pressure-composition space from 0 to 1000 • C, 0 to 5000 bar, and 0 to 1 X NaCl[END_REF]. To a lesser extent, uptake of H 2 O due to the formation of hydrated minerals leads to the same effect.

Magnesium isotopic composition

The basaltic glass used in this study has a δ 26/24 Mg composition of -0.28 ± 0.18 ‰, while the crystalline basalt shows a slightly lower value of -0.38 ± 0.18 ‰ (uncertainties listed here reflect the 95 % confidence interval, corresponding to ∼ 2 standard errors). These values are thus identical within uncertainty, and are in agreement with the value of -0.3 ‰ obtained by [START_REF] Wimpenny | The behaviour of Li and Mg isotopes during primary phase dissolution and secondary mineral formation in basalt[END_REF] for Stapafell basaltic glass.

The seawater used as reactant had a δ 26/24 Mg of -0.68 ± 0.18 ‰. This mean value is slightly higher than the value of -0.83 ‰ (2 SD of 0.09) recommended by [START_REF] Teng | Magnesium isotopic compositions of international geological reference materials[END_REF], which may reflect changes during storage and re-adjustment to seawater pH (cf. section §3.2.1), but both values are in agreement given the uncertainties. Starting from the initial seawater composition, the liquid evolved towards isotopically lighter (i.e. smaller δ 26/24 Mg values) compositions (Figure 3.2, Table 3.1). In the basaltic glass experiment δ 26/24 Mg decreased to -1.02 ± 0.19 ‰ during the first 24 h, then decreased further to -3.27 ± 0.87 ‰ between days 4 and 7 before aqueous Mg concentrations became too low for isotopic analysis. In the corresponding crystalline basalt experiment, aqueous Mg steadily decreased to a δ 26/24 Mg value of -1.11 ± 0.13 ‰ within the first 14 days. The next sample, taken after 21 days of total elapsed time had a δ 26/24 Mg of -0.79 ± 0.14 ‰, this value decreased again to -1.26 ± 0.41 ‰ at the end of the experiment (Figure 3.2).

Solid alteration products

The basalt powders used as reactants were significantly altered during the experiments. SEM images of the solids recovered from the reactors after the experiments were terminated (Figure 3.3) show that the basaltic grains are completely covered by a layer [START_REF] Fiore | Smectite formation in rhyolitic obsidian as inferred by microscopic (SEM-TEM-AEM) investigation[END_REF]. Furthermore, EDS data suggest that anhydrite was formed during all experiments. The formation of these two minerals is confirmed by XRD (Table 2.5 on page 48, Figure 2.6 on page 46), and the FTIR analyses allow the more specific identification of the clays as trioctahedral saponite (Figure 2.7 on page 47). Based on the position of the d 060 reflection in the XRD spectra [START_REF] Baldermann | The Fe-Mg-saponite solid solution series a hydrothermal synthesis study[END_REF], the ferrous saponite contains approximately 0.5 to 0.7 atoms per formula unit (a.p.f.u.) octahedral Fe in the experiment with crystalline basalt, and from 0.8 to almost 1 a.p.f.u. octahedral Fe in the basaltic glass experiment (Table 2.5 on page 48). Furthermore, XRD data suggest that a analcime/heulandite type zeolite was formed during the basaltic glass experiment.

Discussion

Alteration reactions

The initial stages (<24 h) of all experiments were dominated by the precipitation of anhydrite, which removed seawater SO 4 2and Ca from the fluid phase (see 250 • C experiments in section §2.4.2 for a detailed discussion). Subsequently, basalt dissolution, together with the ions dissolved in the seawater, led to the formation of the saponite and smectite-chlorite type alteration minerals that incorporated the aqueous Mg. Fluid pH was determined by the relative importance of two competing processes:

(1) The formation of Mg bearing hydrous minerals that took up seawater Mg as a Mg(OH) 2 component, decreasing the pH as seen in the beginning of the experiments with crystalline basalt (Figure 3.2), and (2) the leaching of Ca (and other cations) from the basalt causing pH and aqueous Ca concentrations to increase after Mg removal was near complete [START_REF] Bischoff | Seawater-basalt interaction at 200 • C and 500 bars: Implications for origin of sea-floor heavy-metal deposits and regulation of seawater chemistry[END_REF][START_REF] Seyfried | Hydrothermal transport of heavy metals by seawater: The role of seawater/basalt ratio[END_REF][START_REF] Seyfried | Low temperature basalt alteration by sea water: an experimental study at 70 • C and 150 • C[END_REF][START_REF] Seyfried | Experimental seawater-basalt interaction at 300 • C, 500 bars, chemical exchange, secondary mineral formation and implications for the transport of heavy metals[END_REF][START_REF] Seyfried | Hydrothermal alteration of basalt by seawater under seawater-dominated conditions[END_REF]. The low initial pH in the crystalline basalt experiments also explains the period of Fe enrichment in the liquid (released from basalt), after which it was incorporated into the clay minerals as indicated by the high octahedral Fe contents (cf. section §3.3.2) and the absence of secondary Fe hydroxide minerals. Furthermore, the correlation between the total mass of precipitated smectite and the estimated VI Fe tot of the smectite clays formed in experiments with basaltic glass and crystalline basalt (Table 2.5 on page 48) suggests that a Mg-rich smectite was initially precipitated, followed by increasing incorporation formation of a more Fe-rich smectite during subsequent mineral growth. As noted in section §2.4.1 and previous experimental studies [START_REF] Seyfried | Experimental seawater-basalt interaction at 300 • C, 500 bars, chemical exchange, secondary mineral formation and implications for the transport of heavy metals[END_REF], the absence of epidote as alteration phase, which is a difference to the alteration assemblage found in natural marine hydrothermal systems, is likely caused by sluggish reaction kinetics.

Magnesium isotope fractionation

The changes in aqueous δ 26/24 Mg during the experiments likely reflect the combined effects of isotopic fractionation during precipitation of the smectite-type alteration phases and the Mg release from basalt dissolution. Consequently, an assessment of the extent of isotope fractionation into the alteration products requires an estimate of the amount of Mg released from basalt dissolution and precipitated into the alteration phases during the experiments. Here, we estimate these values from mass balance using Mg, Ca and SO 4 2 -, assuming that Mg is only released from basalt dissolution and precipitated into a single alteration phase. It is assumed that no significant Mg is taken up by the low-NaCl vapour phase that is present at the end of the experiments, as the vapour pressure of Mg is significantly lower than that of Na (Lide, 2003), which is only present in traces in the vapour under the experimental conditions [START_REF] Driesner | The system H 2 O-NaCl. Part II: Correlations for molar volume, enthalpy, and isobaric heat capacity from 0 to 1000 • C, 1 to 5000 bar, and 0 to 1 X NaCl[END_REF][START_REF] Driesner | The system H 2 O-NaCl. Part I: Correlation formulae for phase relations in temperature-pressure-composition space from 0 to 1000 • C, 0 to 5000 bar, and 0 to 1 X NaCl[END_REF]. Furthermore, we assume that that the original basalt contains no significant SO 4 2 -, and that Ca and SO were estimated using the Steffen interpolation method [START_REF] Steffen | A simple method for monotonic interpolation in one dimension[END_REF] to establish a smooth trend while preserving the monotonicity.

Based on the mass balance constraints described above, the Mg isotopic evolution during the experiments was modelled using an incremental isotope mass balance model, allowing for isotopic fractionation during the precipitation of a single Mg-incorporating mineral (smectite) and during its simultaneous release due to basalt dissolution. A constant isotopic fractionation factor describing irreversible isotopic fractionation during smectite precipitation (i.e. the smectite does not react with the liquid after precipitation), defined as Saprolite-Fluid ≈ 0.4‰ for smectite-rich saprolite. The preferential enrichment of clays in heavy Mg suggested by our data is also in agreement with deep-sea pore-fluid data of [START_REF] Higgins | Constraining magnesium cycling in marine sediments using magnesium isotopes[END_REF], who observed δ 26/24 Mg of pore-fluids decreasing with depth at some of the studied sites, consistent with a Mg sink, likely clay minerals, isotopically enriched in heavy Mg relative to the pore-fluid. Similarly, silicate soil samples from the Southern Tibetan Plateau show higher δ 26/24 Mg compared to associated silicate rocks, which can be attributed to silicate rock weathering (Tipper et al., 2006a). Conversely, [START_REF] Pogge Von Strandmann | The influence of weathering processes on riverine magnesium isotopes in a basaltic terrain[END_REF] suggested the preferential uptake of light Mg into secondary minerals (such as talc and chlorite) for high pH fluids, but do not rule out the opposite trend at lower pH.

α

Differences in Mg isotope fractionation factors during clay mineral formation can

be explained by a number of parameters, including temperature, the exact nature of the mineral, reaction kinetics, and fluid speciation. For example, [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF] showed that the presence of organic complexes in seawater can have significant effects on Mg aqueous speciation in seawater and thus Mg isotopic fractionation during mineral precipitation. The speciation of aqueous Mg in our experiments, as calcu-lated with PHREEQC (Parkhurst and Appelo, 2013) using the Lawrence Livermore National Laboratory (LLNL) database [START_REF] Johnson | Database thermo.com.V8.R6.230[END_REF] and the MgSO 4(aq) dissociation enthalpy from the minteq.v4 database [START_REF] Allison | MINTEQA2/PRODEFA2 -A geochemical assessment model for environmental systems: Version 3.0 User's Manual[END_REF] at the experimental temperature (see section §2.2.4 for details), is dominated by the MgCl + complex, representing approximately 80 mol% of the total aqueous Mg in the initial seawater, while the Mg 2+ complex is estimated to have a relative constant abundance of 20 mol% (Figure 3.4e). The degree to which this influences the fractionation factors during our experiments is unclear. Note, however, that the significance of speciation differences are potentially greater at lower temperatures [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF], such that smectite precipitation from fluids with significantly different compositions could show a different behaviour.

Consequences for the marine Mg isotopic budget

Recent studies of the marine isotopic Mg budget suggest that carbonate formation and riverine inputs are major contributors to this system [START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF][START_REF] Higgins | The Mg isotopic composition of Cenozoic seawater -evidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF], and that decreasing seawater δ 26/24 Mg during the past ∼15 Ma were caused by decreasing carbonate precipitation [START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF]. However, the influence of Mg-clay formation in marine hydrothermal systems is poorly constrained at present. Irreversible fractionation during mineral formation in a closed system (as seen in our experimental study and in marine hydrothermal systems), implies that the effect of this process on the Mg isotopic composition of seawater decreases with increasing Mg removal by clays (see appendix §B.2), and is zero for complete Mg removal. Taking our best fit value of ε

26/24

Smecite-Liquid = 0.457 ± 0.072 ‰ from the model above, which attributes all isotopic effects to fractionation during smectite precipitation, the isotopic difference between seawater and clays during irreversible precipitation is approximately δ 26/24 Mg Clay -δ 26/24 Mg SW ≈ 0.42 ‰ for 10 % removal of Mg from seawater. This is slightly smaller than the value of 0.7 ‰ adopted by [START_REF] Higgins | The Mg isotopic composition of Cenozoic seawater -evidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF] in their marine Mg budget model for low-temperature hydrothermal alteration. On the other hand, Mg isotopic fractionation is likely more pronounced at lower temperatures (e.g., [START_REF] Teng | Magnesium isotope geochemistry[END_REF]. Given the small effect of this variable on the modelled δ 26/24 Mg in pelagic carbonates, this uncertainty likely does not have significant effects on the conclusions drawn from the marine δ 26/24 Mg model of [START_REF] Higgins | The Mg isotopic composition of Cenozoic seawater -evidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF], which concludes that the marine δ 26/24 Mg cycles is relatively insensitive to changes in the degree of marine clay formation compared to that of carbonate precipitation.

The impact of Mg isotopic fractionation during smectite formation in hightemperature marine hydrothermal systems on the marine Mg isotopic budget may be low, as Mg is almost quantitatively removed from the seawater during hydrothermal reactions (e.g., [START_REF] German | Hydrothermal processes[END_REF]. Using the results from the model above again, the isotopic difference between seawater and clays during irreversible precipitation is approximately δ 26/24 Mg Clay -δ 26/24 Mg SW ≈ 0.13 ‰ for an 80 % removal of Mg seawater (see appendix §B.2), which is assumed to be the lower limit of high temperature hydrothermal systems [START_REF] Mottl | Hydrothermal circulation through mid-ocean ridge flanks: Fluxes of heat and magnesium[END_REF]. Even considering a higher Mg flux at mid-ocean ridges compared to marine carbonate formation, the influence of the latter process on the Mg isotopic budget of the oceans is approximately an order of magnitude higher due to its larger isotopic fractionation factor of ε 26/24 Carbonate-Liquid ≈ -2 ‰ [START_REF] Higgins | The Mg isotopic composition of Cenozoic seawater -evidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF].

Conclusion

The evolution of aqueous δ 26/24 Mg was followed during basaltic glass and crystalline basalt -seawater interaction experiments at 250 • C and saturated vapour pressure. Smecite-Liquid determined in this study is in agreement with independent field and experimental evidence for similar silicate minerals (Tipper et al., 2006a;[START_REF] Higgins | Constraining magnesium cycling in marine sediments using magnesium isotopes[END_REF][START_REF] Teng | Contrasting lithium and magnesium isotope fractionation during continental weathering[END_REF][START_REF] Wimpenny | Investigating the behaviour of Mg isotopes during the formation of clay minerals[END_REF], and constrains the Mg isotopic signature of smectite precipitation at hydrothermal conditions. The observation that smectite preferentially incorporates isotopically heavy Mg, opposite of the trend seen for Mg in carbonates [START_REF] Galy | Mg isotopic composition of carbonate: insight from speleothem formation[END_REF]Tipper et al., 2006b;[START_REF] Higgins | Constraining magnesium cycling in marine sediments using magnesium isotopes[END_REF][START_REF] Teng | Contrasting lithium and magnesium isotope fractionation during continental weathering[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] highlights the utility of Mg isotopes in fluids as tracers of the formation of these different mineral types.

Furthermore, the magnitude of Mg fractionation observed during clay formation in this study is in good agreement with the previously estimated effects of Mg isotopic fractionation in low-temperature marine hydrothermal systems on the marine Mg budget; due to the small magnitude of fractionation compared to that observed during carbonate formation, potential changes in the global rates of marine clay formation are not expected to significantly influence the corresponding seawater δ 26/24 Mg [START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF][START_REF] Higgins | The Mg isotopic composition of Cenozoic seawater -evidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF].

Chapter 4

An experimental study of hydroxylbastnasite solubility in aqueous solutions at 25

Abstract

The mobility of rare earth elements (REE) in natural aqueous solutions is of increasing interest due to their application in numerous high-tech and renewable energy technologies (e.g., wind turbines, electric vehicles), as well as their role as tracers in the Earth Sciences. Basic thermodynamic data for water-rock interactions are, however, sparse and partially inconsistent, even for carbonate minerals of the bastnasite group (REE(CO 3 )(F, OH)), which currently represent the most exploited REE ore.

Towards the improved quantification of the REE in natural and industrial systems,

Introduction

The rare earth elements (REE) are of particular interest due to their various applications in geosciences and high-technology components (e.g., [START_REF] Preinfalk | The industrial applications of rare earth elements[END_REF][START_REF] Binnemans | Recycling of rare earths: a critical review[END_REF][START_REF] Jordens | A review of the beneficiation of rare earth element bearing minerals[END_REF][START_REF] Mclellan | Sustainability of rare earths -an overview of the state of knowledge[END_REF]. Their use as tracers of geological processes arises from their relatively similar chemical behaviour but gradually decreasing ionic size from lanthanum to lutetium, leading to distinct REE concentration patterns of the REE in the different phases (e.g., [START_REF] Schnetzler | Partition coefficients of rare-earth elements between igneous matrix material and rock-forming mineral phenocrysts-II[END_REF]Lipin and McKay, 1989;[START_REF] Elderfield | The rare earth elements in rivers, estuaries, and coastal seas and their significance to the composition of ocean waters[END_REF]. If these signatures are preserved, they can help identify the provenance and nature of processes that lead to their formation (e.g., [START_REF] Elderfield | The rare earth elements in seawater[END_REF][START_REF] Mckenzie | Partial melt distributions from inversion of rare earth element concentrations[END_REF][START_REF] Taylor | The geochemical evolution of the continental-crust[END_REF]. Furthermore, the study of REE bearing minerals can help identify metamorphic or metasomatic processes in a variety of natural settings (e.g., [START_REF] Harlov | Fluid-mediated partial alteration in monazite: the role of coupled dissolution-reprecipitation in element redistribution and mass transfer[END_REF]Gysi et al., 2015). Apart from scientific applications, there is an increasing demand for REE as they can be exploited to create high strength permanent magnets, phosphors for electronic displays and various components in renewable energy technologies [START_REF] Jordens | A review of the beneficiation of rare earth element bearing minerals[END_REF]. Along with monazite, xenotime, and ion-adsorbed clays, the mineral bastnasite (REE(CO 3 )(F, OH)), first discovered in Sweden [START_REF] Hisinger | Analyser af några svenska mineralier. 2. Basiskt Fluor-Cerium från Bastnäs[END_REF], is one of the main ores exploited for the rare earths, with the majority currently mined in China [START_REF] Jordens | A review of the beneficiation of rare earth element bearing minerals[END_REF][START_REF] Wübbeke | Rare earth elements in China: Policies and narratives of reinventing an industry[END_REF][START_REF] Wang | Production forecast of China's rare earths based on the Generalized Weng model and policy recommendations[END_REF]. Major deposits of this carbonate mineral are found in association with carbonatites, peralkaline granites and syenites, veins/breccia, or, as in the case of the largest REE mine Bayan Obo (China), in sedimentary formations that underwent periods of magmatic, metamorphic and metasomatic overprint (Williams- [START_REF] Williams-Jones | A preliminary petrogenetic grid for REE fluorocarbonates and associated minerals[END_REF][START_REF] Migdisov | Hydrothermal transport and deposition of the rare earth elements by fluorine-bearing aqueous liquids[END_REF][START_REF] Smith | A review of the genesis of the world class Bayan Obo Fe-REE-Nb deposits, Inner Mongolia, China: Multistage processes and outstanding questions[END_REF]. Naturally occur-ring bastnasite is usually close in composition to its fluoro endmember (REE(CO 3 )F)

with low amounts of OH -present, causing interest in fluoride-bearing aqueous solutions [START_REF] Migdisov | An experimental study of the solubility and speciation of the Rare Earth Elements (III) in fluoride-and chloride-bearing aqueous solutions at temperatures up to 300 • C[END_REF]. Apart from this economic interest, the hydroxylbastnasite endmember (REE(CO 3 )(OH)), as well as other rare earth element hydroxides and carbonates, are of interest due to their potential for nuclear waste storage [START_REF] Rorif | Thermochemistry of selected trivalent lanthanide and americium compounds: orthorhombic and hexagonal hydroxycarbonates[END_REF]; the rare earths can be used as an analogue for long-lived actinides due to their similar electron configuration, motivating experiments aiming at predicting their behaviour (e.g., [START_REF] Runde | A study of solid-liquid phase equilibria of trivalent lanthanide and actinide ions in carbonate systems[END_REF][START_REF] Rorif | Thermochemistry of selected trivalent lanthanide and americium compounds: orthorhombic and hexagonal hydroxycarbonates[END_REF][START_REF] Stipp | Rare Earth element (REE) incorporation in natural calcite: upper limits for actinide uptake in a secondary phase[END_REF]. The REE can also form as fission products. As such, REE hydroxides or carbonates could form from the interaction of nuclear waste with natural waters, and thereby serve as potential host minerals for long-lived actinides [START_REF] Rorif | Thermochemistry of selected trivalent lanthanide and americium compounds: orthorhombic and hexagonal hydroxycarbonates[END_REF].

Despite its role in a plethora of processes, relatively few studies have assessed the stability of hydroxylbastnasite in presence of aqueous solutions. Although several studies have measured the solubility of the orthorhombic polymorph kozoite (REE(CO 3 )(OH); [START_REF] Meinrath | Solubility products of different Am (III) and Nd (III) carbonates[END_REF][START_REF] Runde | A study of solid-liquid phase equilibria of trivalent lanthanide and actinide ions in carbonate systems[END_REF][START_REF] Carroll | Precipitation of Nd-Ca carbonate solid solution at 25 • C. Geochimica et[END_REF][START_REF] Meinrath | Solid-liquid equilibria of Nd 3+ in carbonate solutions[END_REF] no study to date has directly measured hydroxylbastnasite solubility in aqueous solutions, and it is not clear which polymorph is thermodynamically stable at low temperature conditions. The thermodynamic properties of hydroxylbastnasite were inferred, however, from thermochemical data by [START_REF] Rorif | Thermochemistry of selected trivalent lanthanide and americium compounds: orthorhombic and hexagonal hydroxycarbonates[END_REF]. Towards the improved description of the behaviour of the rare earth elements in natural systems we have carried out a series of experiments at 25 • C to assess the solubility of the two REE(CO 3 )(OH) polymorphs hydroxylbastnasite and kozoite via dissolution and precipitation experiments in aqueous solutions and in presence of CO 2 .

This experimental data will enable comparison of the stability of both REE(CO 3 )(OH)

polymorphs. The purpose of this manuscript is to report the results of these experiments and use these to assess the stability of these minerals in low-temperature natural systems.

Methods

Synthesis of starting materials

Pure Nd-and La-hydroxylbastnasite, and Nd-kozoite crystals were synthesised hydrothermally as described by [START_REF] Vallina | The effect of heating rates on the morphology of crystalline neodymium carbonates[END_REF] to obtain minerals with pure end-member compositions. Briefly, aqueous solutions with a concentration of 50 mmol/kg of the desired REE-chloride were mixed with 50 mmol/kg Na 2 CO 3 solutions at ambient temperature, provoking the immediate precipitation of an amorphous rare earth element carbonate phase. This material was subsequently heated to 165 • C in titanium reactors placed in rocking furnaces or in Teflon-lined reactors that were manually shaken at regular intervals. This procedure was performed at saturated water-vapour pressure using slow heating rates where the final temperature was reached in approximately 100 min.

Synthesis was carried out at 165 • C to promote the formation of micrometric-sized crystals, because at higher temperatures the formation of spherulites (consisting of nanometric sized crystals) is promoted [START_REF] Vallina | The role of amorphous precursors in the crystallization of La and Nd carbonates[END_REF]. At 165 • C hydroxylbastnasite forms from kozoite by dissolution-recrystallisation, a relatively slow growth process (hours-days) compared to spherulitic growth (seconds-minutes). Synthesis products were quenched after 1 to 4 weeks, filtered through 0.22 µm membrane filters, washed with ultrapure water and isopropanol and dried at ambient temperature. Synthesis of both hydroxylbastnasite and kozoite, was possible by seeding the solutions with previously produced crystals of the selected mineral. The synthesis of hydroxylbastnasite and kozoite end-members with heavier REE was not possible using this method, presumably due to their distinct in ionic radii.

The crystalline products were analysed by X-ray diffraction (XRD) to verify the crystal structure and by scanning electron microscopy (SEM) to examine the size and shape of the individual crystals. Crystal size was > 5 µm (Figure 4.1), so that the influence of particle size on solubility is expected to be negligible. For all syntheses, the powder was found to be entirely composed of either hydroxylbastnasite or kozoite within the detection limit of approximately 0.1 % by comparison to the structural data of [START_REF] Ni | The atomic arrangement of bastnäsite-(Ce), Ce (CO 3 )F, and structural elements of synchysite-(Ce), röntgenite-(Ce), and parisite-(Ce)[END_REF] and [START_REF] Tahara | Crystal chemistry of RE(CO 3 )OH[END_REF], respectively (Figure 4.2).

Experimental design

All solubility experiments were performed at 25 ± 1 • C using reactors immersed in a thermostatically controlled water bath (Figure 4.

Analytical methods

The pH of all sampled fluids was measured in situ using a VWR double junction epoxy electrode. For each pH measurement, the solution was stirred until a stable potential was attained. Subsequently, stirring was stopped and the potential was recorded when it restabilised (generally this required less than 10 s). Stirring was stopped to avoid the build-up of stirring potentials in the low ionic-strength solutions; this method was found to yield reproducible results. The pH electrode was calibrated with three NIST traceable pH buffer solutions (pH 4.0, 6.9, 9.2, Fluka) before each use at the experimental temperature. Different ionic strengths of the pH buffers and experimental solutions can potentially lead to a measurement bias due to the different liquid junction potentials. However, no correction for this bias was applied, because its magnitude is likely smaller than the uncertainty of the the pH measurements [START_REF] Kadis | Evaluation of the residual liquid junction potential contribution to the uncertainty in pH measurement: A case study on low ionic strength natural waters[END_REF].

Aqueous rare earth element concentrations were determined by Inductively Coupled Plasma-Mass Spectrometry (ICP-MS) using a Thermo Scientific Element XR or Agilent 7500ce. Prior to analysis, samples were acidified to ∼0.37 mol/kg HNO 3 using bi-distilled acid, and known concentrations of In and Re were added as internal standards. Standards were prepared using NIST traceable PlasmaCal single element standards (SCP Science). Detection limits, determined by analysis of blanks that were subjected to the same experimental and analytical procedures as actual samples, are approximately 2 × 10 -11 mol/kg. Gaseous CO 2 concentrations were determined with a non-dispersive infra-red (NDIR) CO 2 gas analyser (model LI-820, LICOR Inc.). Solid experimental products were analysed by X-ray powder diffraction using a Co source and by SEM using a Quanta 3D FEG or Jeol JSM 6360LV equipped with an energydispersive X-ray spectrometer (EDS).

Thermodynamic modelling

Thermodynamic calculations of systems at equilibrium were performed using the PHREEQC software package [START_REF] Parkhurst | Description of input and examples for PHREEQC version 3 -A computer program for speciation, batch-reaction, onedimensional transport, and inverse geochemical calculations[END_REF] together with its Lawrence Livermore National Laboratory (LLNL) database [START_REF] Johnson | Database thermo.com.V8.R6.230[END_REF]. Standard state for solid phases and H 2 O is the pure phase, while a hypothetical 1 mol/kg aqueous solution referenced to infinite dilution is chosen for unit activity of aqueous species, both at the temperature and pressure of interest. The Livermore National Laboratory aqueous model [START_REF] Daveler | EQPT, a data file preprocessor for the EQ3/6 software package: User's guide and related documentation (version 7.0)[END_REF], which uses the extended Debye-Hückel equation of [START_REF] Helgeson | Thermodynamics of hydrothermal systems at elevated temperatures and pressures[END_REF] was used to calculate activity coefficients. Due to the low ionic strengths of all experimental fluids considered in this study, the choice of activity model does not significantly affect retrieved reaction quotients. We chose the [START_REF] Helgeson | Thermodynamics of hydrothermal systems at elevated temperatures and pressures[END_REF] activity model to insure all calculations were consistent with the LLNL database. Since the only aqueous REE complexes present in significant amounts in the experimental solutions are REECO 3 + and REE(CO 3 ) 2 -, the total (measured) REE concentration can be expressed as

c REE = c REE 3+ + c REECO3 + + c REE(CO3)2 -.
This allows the calculation of c REE 3+ , the activity a REE 3+ and thus the solubility products of the minerals of interest using the stability constants of the complexes and the activity model. The stability constants for the REECO 3 + and REE(CO 3 ) 2 -aqueous complexes were taken from [START_REF] Ohta | Rare earth element partitioning between Fe oxyhydroxide precipitates and aqueous NaCl solutions doped with NaHCO 3 : Determinations of rare earth element complexation constants with carbonate ions[END_REF] and listed in Table 4.1 with other equilibrium constants used in this study. To assess the uncertainty of PHREEQC calculations caused by uncertainty in input parameters, Monte Carlo type simulations were run using the IPhreeqc modules [START_REF] Charlton | Modules based on the geochemical model PHREEQC for use in scripting and programming languages[END_REF] in combination with Wolfram Mathematica.

Results

Evolution of aqueous solution compositions and solids

Experimental parameters as well as reactive aqueous solution compositions at steady state are listed in NdOHCO 3(HB) --→ ←--

Nd 3+ + OH -+ CO 3 2 --23.8 ± 0.1 This study LaOHCO 3(HB) --→ ←--La 3+ + OH -+ CO 3 2 --24.1 ± 0.3 This study NdOHCO 3(Kozoite) --→ ←--Nd 3+ + OH -+ CO 3 2 --22.3 ± 0.2
This study REE concentrations were attained after 6 to 33 days (Figure 4.4). A decrease of dissolution rates with increasing pH was observed, however the lack of information on the specific surface areas of the reacting solids, as well as large sampling intervals in some experiments prevent the quantification of mineral dissolution rates from these data.

The appearance of the minerals used in dissolution experiments remained unchanged under the SEM, and XRD patterns were identical before and after the experiments.

In experiments where the precipitation of hydroxylbastnasite or kozoite was induced, the addition of NaOH caused a rapid decrease of aqueous REE concentrations followed by the stabilisation of pH and REE concentrations (Figure 4.5). Analysis of the precipitated solids by XRD showed that kozoite precipitated from aqueous solutions having a pH below 7, even if hydroxylbastnasite was present in the reactor from the dissolution stage of the experiment. However, it was possible to precipitate hydroxylbastnasite at higher pH, as confirmed by the presence of only hydroxylbastnasite by XRD in the solid materials recovered from these experiments.

.3 ± 0.2 × 10 -4 0 1.08 ± 0.07 × 10 -3 0 2.1 ± 0.1 × 10 -3 -24.0 ± 0.2 C013A-05
Nd-HB 6.03 ± 0.09 3.8 ± 0.4 × 10 -6 9.67 ± 0.03 × 10 -4 0 0 9.87 ± 0.04 × 10 -4 -23.1 ± 0.3 C013B-05 Nd-HB 5.91 ± 0.09 2.3 ± 0.1 × 10 -6 9.70 ± 0.03 × 10 -4 0 0 9.83 ± 0.03 × 10 -4 -23.6 ± 0.3

C013A-11

Nd-HB 5.31 ± 0.09 3.6 ± 0.2 × 10 -5 9.67 ± 0.03 × 10 -4 1.005 ± 6.000 × 10 -4 0 1.174 ± 0.005 × 10 -3 -24.2 ± 0.3 C015 Nd-HB 7.16 ± 0.09 6.5 ± 0.3 × 10 -9 1.001 ± 0.004 × 10 -3 0 9.7 ± 0.2 × 10 -5 1.098 ± 0.004 × 10 -3 -23.86 ± 0.03 C029 Nd-HB 8.10 ± 0.04 1.38 ± 0.05 × 10 -9 1.00 ± 0.02 × 10 -3 0 1.05 ± 0.01 × 10 -3 2.1 ± 0.2 × 10 -3 -23.65 ± 0.02 C021-05 La-HB 5.78 ± 0.04 5.29 ± 0.06 × 10 -6 1.00 ± 0.02 × 10 -2 0 0 1.00 ± 0.02 × 10 -2 -23.8 ± 0.1 C021-15 La-HB 5.29 ± 0.04 3.98 ± 0.04 × 10 -5 1.00 ± 0.02 × 10 -2 1.02 ± 2.00 × 10 -4 0 1.02 ± 0.03 × 10 -2 -24.4 ± 0.1 C022 Nd-Kozoite 5.70 ± 0.04 3.17 ± 0.07 × 10 -4 8.9 ± 0.2 × 10 -3 1.01 ± 1.00

× 10 -3 0 1.09 ± 0.02 × 10 -2 -22.3 ± 0.1
Precipitation experiments

C013B-11

Nd-HB 7.10 ± 0.09 3.5 ± 0.2 × 10 -9 9.70 ± 0.03 × 10 -4 0 10.0 ± 0.2 × 10 -5 1.070 ± 3.000 × 10 -3 -24.12 ± 0.03

C013B-19

Nd-HB 8.22 ± 0.09 6.7 ± 0.3 × 10 -1 9.70 ± 0.03 × 10 -4 0 9.72 ± 0.06 × 10 -4 1.945 ± 7.000 × 10 -3 -23.98 ± 0.02 C014 Nd-Kozoite 5.65 ± 0.05 4.7 ± 0.5 × 10 -4 0 9.4 ± 0.2 × 10 -3 7.691 ± 0.009 × 10 -3 1.08 ± 2.00 × 10 -2 -22.3 ± 0.1 C019 Nd-Kozoite 5.68 ± 0.05 3.95 ± 0.03 × 10 -4 0 1.01 ± 0.02 × 10 -2 9.0 ± 0.1 × 10 -3 1.11 ± 3.00 × 10 -2 -22.3 ± 0.2 a These values refer to the concentration of salts added to create the reactive fluid used in the experiment.

Stoichiometry of dissolution

Since both hydroxylbastnasite and kozoite release hydroxyl ions during dissolution, the reactive fluid pH can be used to assess the stoichiometry of dissolution. This can be illustrated by calculating the pH of the experiments based on thermodynamic considerations (see section §4.2.4 for details) using the measured aqueous REE concentrations and initial reactive aqueous solution composition and assuming stoichiometric dissolution. The comparison of these calculated pH, which assume stoichiometric dissolution, with measured pH are shown in Figure 4.6. These results demonstrate that there is no systematic preferential release of REE ions compared to OH -from the minerals, consistent with stoichiometric dissolution. It can also be seen that the uncertainty of the calculated pH is higher at lower pH. This is caused by the increasing dependence of the pH on the mass of REE(CO 3 )(OH) dissolved (calculated using measured REE concentrations, which are subject to analytical uncertainties) with decreasing pH because of the lower absolute amount of OH -in the aqueous solution.

Solubility product calculations

Our experimental data of aqueous solutions in equilibrium with hydroxylbastnasite and kozoite (Table 4.2) allow the calculation of the solubility products (K SP ) of these minerals at 25 • C, defined by

K SP = a REE 3+ • a OH -• a CO3 2- (4.1)
where a i are the activities of the aqueous species i, corresponding to the dissolution reaction

REE(CO 3 )(OH) (s) --→ REE 3+ + OH -+ CO 3 2-. (4.2)
Calculation of activities were carried out in PHREEQC (see section §4.2.4 for details), and the resulting K SP of the individual experiments are listed in Table 4.2. The logarithms of the mean solubility products are -23.8 ± 0.1, -24.1 ± 0.3, and -22.3 ± 0.2 for Nd-hydroxylbastnasite, La-hydroxylbastnasite, and Nd-kozoite, respectively (cf.

Table 4.1). The values for hydroxylbastnasite are in close agreement with corresponding solubility products calculated from calorimetric data by [START_REF] Rorif | Thermochemistry of selected trivalent lanthanide and americium compounds: orthorhombic and hexagonal hydroxycarbonates[END_REF], which are -23.7 ± 0.6, -23.3 ± 0.6 for the Nd and La endmembers, respectively. The solubility product of Nd-kozoite, which was previously determined by [START_REF] Carroll | Precipitation of Nd-Ca carbonate solid solution at 25 • C. Geochimica et[END_REF] as -21.7 ± 0.3 (converted from the originally published dissolution reaction version using thermodynamic data described in section §4.2.4) is also close to that determined from our experiments. [START_REF] Runde | A study of solid-liquid phase equilibria of trivalent lanthanide and actinide ions in carbonate systems[END_REF] determined a value of log K SP = -19.94 ± 0.16 for orthorhombic NdOHCO 3 in 0.1 mol/kg ionic strength aqueous solution, which was converted to zero ionic strength by [START_REF] Rorif | Thermochemistry of selected trivalent lanthanide and americium compounds: orthorhombic and hexagonal hydroxycarbonates[END_REF], yielding a value of -21.4 ± 0.3.

Similarly, [START_REF] Rorif | Thermochemistry of selected trivalent lanthanide and americium compounds: orthorhombic and hexagonal hydroxycarbonates[END_REF] report log(K SP ) at zero ionic strength of -20.7 ± 0.2 and -21.6 ± 0.4, calculated from data reported by [START_REF] Meinrath | Solubility products of different Am (III) and Nd (III) carbonates[END_REF] and Meinrath and Takeishi (1993), respectively. These three values are slightly higher than that determined in this study. This difference might be caused by the lack of reversal of thermodynamic equilibrium in these past studies, which approached the solubility only from supersaturation. Comparison to the experimental data shows that they are in close agreement with the predicted shape of the solubility curve. It can also be seen that dissolution and precipitation experiments are consistent with each other and with thermodynamic equilibrium.

Discussion

The experimental data obtained for Nd-hydroxylbastnasite and Nd-kozoite indicate that the former is more stable at 25 • C because of its lower solubility product and therefore lower chemical potential. Furthermore, no significant difference was detec-ted between the solubilities of Nd-and La-hydroxylbastnasite. In the following two sections, we illustrate the stability of hydroxylbastnasite in natural aqueous solutions.

For this purpose, we compare the stability of hydroxylbastnasite with fluorobastnasite in presence of variable aqueous fluorine concentrations, and with monazite because of its widespread distribution in the continental crust [START_REF] Poitrasson | Experimental determination of synthetic NdPO 4 monazite end-member solubility in water from 21 • C to 300 • C: implications for rare earth element mobility in crustal fluids[END_REF].

Comparison to fluorobastnasite

Bastnasite found in nature is usually compositionally closer to the fluorobastnasite endmember (REEFCO 3 ) than to hydroxylbastnasite, making a comparison of their relative solubilities especially interesting. However, a direct comparison is not possible at the moment due to the lack of direct solubility measurements of fluorobastnasite in aqueous solutions. Nonetheless, an estimate is possible using thermochemical data obtained by Gysi and Williams-Jones (2015), who used results from differential scanning calorimetric experiments on natural bastnasite (Ce 0.50 La 0.25 Nd 0.20 Pr 0.05 CO 3 F) to calculate a Gibbs free energy of its formation at 25 • C and 1 bar of ∆ f G • = -1710 ± 12 kJ/mol for this mineral. Using the relationship ln

K SP = -∆ r G • diss RT = -∆ f G • REE 3+ (aq) + ∆ f G • CO3 2-(aq) + ∆ f G • F -(aq) -∆ f G • Bastnasite RT (4.3)
where R refers to the gas constant, and adopting the Gibbs free energies of formation for the aqueous species Ce 3+ , La 3+ , Nd 3+ , Pr 3+ , F -and CO 3 2from [START_REF] Oelkers | Summary of the apparent standard partial molal Gibbs free energies of formation of aqueous species, minerals, and gases at pressures 1 to 5000 bars and temperatures 25 to 1000 •[END_REF] as well as their estimated uncertainties of up to 600 kcal/mol in these parameters, a value of log K SP = -39 ± 2 is obtained for fluorobastnasite of this composition.

Even considering the uncertainties introduced by these calculations, and by the fact that the solubility product for fluorobastnasite was only determined for a mixed-REE mineral, this indicates that bastnasite is stabilised considerably if fluorine is present in the aqueous solution, as demonstrated by the calculated stability fields in Figure 4.8,

showing that the fluorine endmember is the more stable phase even if only extremely small quantities of aqueous F -are present. For the purpose of this calculation, it was assumed that the difference in solubility of the NdFCO 3 end-member compared to the one determined for the mixed-REE mineral by (Gysi et al., 2015) is negligible compared to the uncertainties introduced by the Gibbs free energies of formation for the aqueous species. This result is in agreement with the prevalence of fluorine-rich bastnasite in nature; hydroxylbastnasite, only forms in fluorine-poor systems [START_REF] Hsu | Synthesis and stability of bastnaesites in a part of the system (Ce,La)-F-H-C-O[END_REF][START_REF] Williams-Jones | A preliminary petrogenetic grid for REE fluorocarbonates and associated minerals[END_REF].

Comparison to monazite

Monazite (REEPO 4 ) is another common rare earth element mineral, which is of interest because of its applications in geosciences (e.g. geochronology, geothermometry) as well as due to its use as an ore mineral (e.g., [START_REF] Poitrasson | Experimental determination of synthetic NdPO 4 monazite end-member solubility in water from 21 • C to 300 • C: implications for rare earth element mobility in crustal fluids[END_REF]. The solubility of synthetic NdPO 4 has been determined as log K SP = -26.02 (interpolated for 25 • C) by [START_REF] Poitrasson | Experimental determination of synthetic NdPO 4 monazite end-member solubility in water from 21 • C to 300 • C: implications for rare earth element mobility in crustal fluids[END_REF], allowing a direct comparison to hydroxylbastnasite. The boundary between the stability fields of the two minerals in equilibrium with aqueous solutions of variable CO 2 and phosphorus contents at neutral pH is shown in Figure 4.9, illustrating the potential effect of different CO 2 partial pressures in natural systems.

It was found that phosphate-REE complexes are only present in negligible quantities under these conditions, as inferred from stability constants of from [START_REF] Millero | Stability constants for the formation of rare earth-inorganic complexes as a function of ionic strength[END_REF] and [START_REF] Haas | Rare earth elements in hydrothermal systems: Estimates of standard partial molal thermodynamic properties of aqueous complexes of the rare earth elements at high pressures and temperatures[END_REF]. Although precise data of phosphorus concentrations found in nature are sparse, estimates of lake water P concentrations [START_REF] Hudson | Phosphate concentrations in lakes[END_REF] indicate that monazite is the more stable phase in these waters in equilibrium with atmospheric CO 2 levels. Similar to fluorobastnasite, it can be concluded that hydroxylbastnasite is only thermodynamically more stable in phosphorous-poor conditions or at extremely high CO 2 partial pressures.

-4 -3 -2 -1 0 log(pCO 2 ) -12 -11 -10 -9 -8 -7 -6
-5 log(P / mol/kg) Lake waters [START_REF] Hudson | Phosphate concentrations in lakes[END_REF] Figure 4.9 -Plot of the aqueous P concentrations in equilibrium with Ndhydroxylbastnasite and Nd-monazite (solid line) in aqueous solutions at 25 • C and pH 7 as a function of p CO2 . The dashed lines represent the uncertainties (one standard deviation), calculated from the uncertainties in the thermodynamic properties of the minerals. See text for the details of the model calculations. The blue rectangle shows the approximate range of phosphorous concentrations in natural lake waters [START_REF] Hudson | Phosphate concentrations in lakes[END_REF] and atmospheric CO 2 concentrations.

Conclusions

Dissolution and precipitation experiments of synthetic hydroxylbastnasite and kozoite (hexagonal and orthorhombic REE(CO 3 )(OH), respectively) were performed in aqueous solutions at 25 • C to assess the solubility of these minerals. For Nd-kozoite, the solubility product was determined to be log K SP = -22.3 ± 0.2, which is in good agreement with data obtained previously using a similar methodology [START_REF] Meinrath | Solubility products of different Am (III) and Nd (III) carbonates[END_REF][START_REF] Runde | A study of solid-liquid phase equilibria of trivalent lanthanide and actinide ions in carbonate systems[END_REF][START_REF] Carroll | Precipitation of Nd-Ca carbonate solid solution at 25 • C. Geochimica et[END_REF][START_REF] Meinrath | Solid-liquid equilibria of Nd 3+ in carbonate solutions[END_REF]. Our experiments showed that hydroxylbastnasite is thermodynamically stable compared to kozoite in aqueous solutions under these conditions, and the solubility product of the Nd endmember is equal to log K SP = -23.8 ± 0.1. To our knowledge, this is the first direct determination of hydroxylbastnasite solubility in aqueous solutions, and our K SP is consistent with the value calculated from calorimetric data by [START_REF] Rorif | Thermochemistry of selected trivalent lanthanide and americium compounds: orthorhombic and hexagonal hydroxycarbonates[END_REF].

Furthermore, it was found that the solubility of La-hydroxylbastnasite does not differ significantly from the Nd endmember within the precision achieved in this study.

Comparison of the solubility of hydroxylbastnasite with that of fluorobastnasite (inferred from calorimetric data of Gysi and Williams-Jones ( 2015)) shows that the fluorine endmember is stable even if only small quantities of fluorine are present in aqueous solution. This explains the prevalence of fluorine-rich bastnasite in natural environments, whereas hydroxylbastnasite only forms in fluorine-devoid systems [START_REF] Hsu | Synthesis and stability of bastnaesites in a part of the system (Ce,La)-F-H-C-O[END_REF][START_REF] Williams-Jones | A preliminary petrogenetic grid for REE fluorocarbonates and associated minerals[END_REF]. Similarly, it can be seen from comparison to monazite [START_REF] Poitrasson | Experimental determination of synthetic NdPO 4 monazite end-member solubility in water from 21 • C to 300 • C: implications for rare earth element mobility in crustal fluids[END_REF] hydroxylbastnasite is only stable if phosphorous concentrations are lower than commonly found in nature or if the CO 2 partial pressure is extremely high.

Although our results expand the dataset of thermodynamic stabilities of rare earth element minerals in aqueous solutions at 25 • C and provide robust values for their solubility products, there is still a lack of solubility measurements of bastnasite at higher temperatures as well as equivalent data for fluorobastnasite at 25 • C. Difficulties in K SP measurements at high temperature is partly due to the lack of reliable data for the stabilities of the various aqueous complexes that REE form with carbonate and hydroxyl ions, which are relatively small at 25 • C, but could play a major role at higher temperature [START_REF] Haas | Rare earth elements in hydrothermal systems: Estimates of standard partial molal thermodynamic properties of aqueous complexes of the rare earth elements at high pressures and temperatures[END_REF]. Furthermore, there is no available data on the dissolution and precipitation kinetics of these REE-carbonate minerals in aqueous solutions. Together with the thermodynamic stabilities determined here, such kinetic data could provide valuable information to assess the conditions of formation and preservation of natural REE mineral deposits, and help to model the fate of actinides that are released from nuclear waste storage sites. natural waters including seawater. Such variations are likely the origin for the large differences of D REE values reported in the literature based on experimental and field evidence.

Introduction

The rare earth elements (REEs) are of particular interest in geoscience due to their use as chemical tracers of natural processes (e.g., [START_REF] Schnetzler | Partition coefficients of rare-earth elements between igneous matrix material and rock-forming mineral phenocrysts-II[END_REF][START_REF] Elderfield | The rare earth elements in rivers, estuaries, and coastal seas and their significance to the composition of ocean waters[END_REF][START_REF] Johannesson | Rare earth elements as geochemical tracers of regional groundwater mixing[END_REF]. As a result of their systematic electron configuration, they exhibit a relatively similar chemical behaviour. Their gradually varying ionic size, however, leads to distinct REE concentration patterns stemming from their aqueous complexation and their varying ability to incorporate into and/or adsorb onto solid phases (e.g, [START_REF] Schnetzler | Partition coefficients of rare-earth elements between igneous matrix material and rock-forming mineral phenocrysts-II[END_REF][START_REF] Elderfield | The oceanic chemistry of the rare-earth elements[END_REF]Lipin and McKay, 1989;[START_REF] Elderfield | The rare earth elements in rivers, estuaries, and coastal seas and their significance to the composition of ocean waters[END_REF][START_REF] Köhler | Experimental studies of REE fractionation during water-mineral interactions: REE release rates during apatite dissolution from pH 2.8 to 9.2[END_REF]. Due to their ability to incorporate REE and their widespread distribution in sedimentary rocks, the REE content of biogenic (e.g., [START_REF] Palmer | Rare earth elements in foraminifera tests[END_REF][START_REF] Sholkovitz | The incorporation of rare earth elements in modern coral[END_REF][START_REF] Webb | Rare earth elements in Holocene reefal microbialites: a new shallow seawater proxy[END_REF][START_REF] Nothdurft | Rare earth element geochemistry of Late Devonian reefal carbonates, Canning Basin, Western Australia: confirmation of a seawater REE proxy in ancient limestones[END_REF][START_REF] Azmy | Biogenic and abiogenic low-Mg calcite (bLMC and aLMC): Evaluation of seawater-REE composition, water masses and carbonate diagenesis[END_REF] and abiogenic carbonates [START_REF] Parekh | Distribution of trace elements between carbonate and non-carbonate phases of limestone[END_REF] have been used as paleo proxies for past seawater compositions, its redox state, and its input sources. For example, the REE contents of carbonate minerals have been used to trace fluxes from and to the continents and oceanic crust [START_REF] Elderfield | The oceanic chemistry of the rare-earth elements[END_REF]. [START_REF] Webb | Rare earth elements in Holocene reefal microbialites: a new shallow seawater proxy[END_REF] demonstrated that ancient marine REE concentrations can be reconstructed using the REE compositions preserved in sedimentary rocks. Such information could provide insight into the sources of chemical inputs to the oceans over Earth's history.

The quantification of past ocean water composition using REE patterns in carbonate minerals requires accurate partitioning factors for the aqueous REE-carbonate mineral systems. For this reason, a number of past studies have been aimed at the experimental determination of REE partitioning factors between fluids and co-existing carbonate minerals. Experimentally determined partition coefficients for REEs co-precipitation with calcite have been reported by [START_REF] Terakado | The coprecipitation of rare-earth elements with calcite and aragonite[END_REF], [START_REF] Zhong | Partitioning of rare earth elements (REEs) between calcite and seawater solutions at 25 • C and 1 atm, and high dissolved REE concentrations[END_REF], [START_REF] Tanaka | REE abundances in ancient seawater inferred from marine limestone and experimental REE partition coefficients between calcite and aqueous solution[END_REF] and [START_REF] Toyama | Experimental study of rare earth element partitioning between calcite and sodium chloride solution at room temperature and pressure[END_REF].

Other studies addressed the partitioning behaviour of europium into calcite, as Eu is considered an analogue for long-lived trivalent actinides, which are of interested in nuclear waste disposal [START_REF] Yeghicheyan | Etude expérimentale du partage des terres rares entre carbonates de calcium et solutions aqueuses: Influence de la cinétique de cristallisation et de la spéciation des terres rares en solution[END_REF][START_REF] Lakshtanov | Experimental study of europium (III) coprecipitation with calcite[END_REF][START_REF] Curti | Solid solutions of trace Eu(III) in calcite: Thermodynamic evaluation of experimental data over a wide range of pH and pCO 2[END_REF]. REE partition coefficients have also been inferred from the composition of reefal microbialities [START_REF] Webb | Rare earth elements in Holocene reefal microbialites: a new shallow seawater proxy[END_REF], reefal Mg-calcites [START_REF] Scherer | Rare-earth element distribution in Holocene and Pleistocene corals and their redistribution during diagenesis[END_REF], and foraminifers [START_REF] Palmer | Rare earth elements in foraminifera tests[END_REF] compared to that of their co-existing ocean waters.

While there is a general agreement that REEs are preferentially incorporated into calcite compared to the aqueous solution from which they precipitate, there is considerable disagreement between the magnitudes of this partitioning process (cf. section §5.2.1).

Similarly, there are significant uncertainties about the differences between the partitioning coefficients of individual REEs. This study was motivated to help resolve these discrepancies through detailed experimental work. Most notably, experiments were performed in this study at fluid concentrations below the hydroxylbastnasite (REE(CO 3 )(OH)) solubility limit (Voigt et al., 2016, chapter 4) to avoid the interpretative ambiguities of previous studies. By varying aqueous REE concentrations, calcite supersaturation, and precipitation rate, we studied the relationships between calcite precipitation rates and REE partitioning coefficients, as well as effects of changing the concentrations of individual aqueous REEs on calcite growth rates. Results were modelled using thermodynamically based, charge balanced exchange reactions to facilitate their application to a broader range of aqueous solutions.

Theoretical background

Thermodynamic description of the partitioning of REEs between calcite and co-existing fluids

The partitioning of REE into calcite is commonly described using the [START_REF] Henderson | The fractional precipitation of barium and radium chromates[END_REF] partition coefficient D REE , defined as

D REE ≡ n Calcite REE /n Calcite Ca n Fluid REE /n Fluid Ca (5.1)
where n stands for the molar amount of the subscripted element in the superscripted phase. Previous experimentally determined partition coefficients were obtained using various fluid compositions and calcite precipitation rates. Such factors, however, likely influence significantly the partitioning behaviour. For example, [START_REF] Terakado | The coprecipitation of rare-earth elements with calcite and aragonite[END_REF] suggested that this partitioning is influenced by aqueous REE complexation.

Tanaka and Kawabe ( 2006) used a modified partition coefficient D REE ω to address this issue. This modified partition function, taking account of aqueous REE speciation, is defined by:

D REE ω = n Calcite REE /n Calcite Ca n Fluid REECO3 + /n Fluid Ca (5.2)
Note the difference between equations (5.1) and (5.2) is that the latter is written in terms of the molar amounts of the REECO 3 + aqueous species, whereas the former is written in terms of the molar amounts of the total aqueous REE.

The partition coefficients D REE and D REE ω , as defined in equations (5.1) and (5.2)

are not consistent with charged balanced exchange reactions, and thus could vary as function of the aqueous phase composition. Due to the charge difference between Ca 2+

and REE 3+ , the formulation of a charge balanced exchange reaction requires knowledge of the reactions dominating this exchange. While there is clear spectroscopic evidence for the incorporation of the REEs into the Ca 2+ site in calcite [START_REF] Elzinga | EXAFS study of rare-earth element coordination in calcite[END_REF][START_REF] Withers | Broad distribution of crystal-field environments for Nd 3+ in calcite[END_REF], different reactions for this exchange have been proposed.

Some studies suggested that in NaCl dominated aqueous fluids, charge balance is main-tained by co-incorporation of Na + into the calcite structure [START_REF] Zhong | Partitioning of rare earth elements (REEs) between calcite and seawater solutions at 25 • C and 1 atm, and high dissolved REE concentrations[END_REF][START_REF] Yeghicheyan | Etude expérimentale du partage des terres rares entre carbonates de calcium et solutions aqueuses: Influence de la cinétique de cristallisation et de la spéciation des terres rares en solution[END_REF]. An exchange reaction consistent with this observation and the aqueous REE 3+ species is given by Ca

2 (CO 3 ) 2 + REE 3+ + Na + --→ ←--NaREE(CO 3 ) 2 + 2 Ca 2+ (5.3)
where NaREE(CO 3 ) 2 corresponds to a solid Na-REE endmember and Ca 2 (CO 3 ) 2 represents the pure calcite endmember. The law of mass action for reaction (5.3) is given by

K NaREE(CO3)2 D = a NaREE(CO3)2 (a Ca 2+ ) 2 a Ca2(CO3)2 a REE 3+ a Na + (5.4)
where a i denotes the activity of the subscripted component or species. K

NaREE(CO3)2 D
refers to the equilibrium constant of this reaction (see section §5.2.2 for the choice of standard states). The similar ionic sizes of Ca 2+ and Na + favour this reaction, and there is spectroscopic evidence supporting this model [START_REF] Fernandes | Site-selective time-resolved laser fluorescence spectroscopy of Eu 3+ in calcite[END_REF][START_REF] Schmidt | Untersuchungen zum Einbaumechanismus von Actiniden und Lanthaniden in Calcium-haltige Sekundärphasen[END_REF]. It should be noted that exchange reactions such as reaction (5.3), can also be expressed using other aqueous REE species such as REECO 3 + or REE(CO 3 ) 2 -.

Another possible charged balanced REE exchange reaction is

Ca 3 (CO 3 ) 3 + 2 REE 3+ --→ ←--REE 2 X(CO 3 ) 3 + 3 Ca 2+ . (5.5)
This reaction is based on the presence of a vacancy, X, in the calcite lattice and was proposed by [START_REF] Lakshtanov | Experimental study of europium (III) coprecipitation with calcite[END_REF]. These authors found this model to be consistent with the results of their co-precipitation experiments. The law of mass action for reaction (5.5) is given by:

K REE2X(CO3)3 D = a REE2X(CO3)3 (a Ca 2+ ) 3 a Ca3(CO3)3 (a REE 3+ ) 2 .
(5.6) [START_REF] Curti | Solid solutions of trace Eu(III) in calcite: Thermodynamic evaluation of experimental data over a wide range of pH and pCO 2[END_REF]

Thermodynamic modelling

All thermodynamic calculations in this study were performed using the PHREEQC software package [START_REF] Parkhurst | Description of input and examples for PHREEQC version 3 -A computer program for speciation, batch-reaction, onedimensional transport, and inverse geochemical calculations[END_REF] and the IPhreeqc modules [START_REF] Charlton | Modules based on the geochemical model PHREEQC for use in scripting and programming languages[END_REF], coupled with Wolfram Mathematica. The standard state for solid phases and H 2 O is the pure phase, while a hypothetical 1 mol/kg aqueous solution referenced to infinite dilution is chosen for unit activity (a) of aqueous species, both at the temperature and pressure of interest. The Livermore National Laboratory aqueous model [START_REF] Daveler | EQPT, a data file preprocessor for the EQ3/6 software package: User's guide and related documentation (version 7.0)[END_REF], which uses the extended Debye-Hückel equation [START_REF] Helgeson | Thermodynamics of hydrothermal systems at elevated temperatures and pressures[END_REF] was used to calculate activity coefficients (γ) of aqueous species. The Lawrence Livermore National Laboratory (LLNL) database [START_REF] Johnson | Database thermo.com.V8.R6.230[END_REF] was used with the modifications and additions explained below. Solubility products (K SP ) of calcite and hydroxylbastnasite were taken from [START_REF] Plummer | The solubilities of calcite, aragonite and vaterite in CO 2 -H 2 O solutions between 0 and 90 • C, and an evaluation of the aqueous model for the system CaCO 3 -CO 2 -H 2 O[END_REF] and Voigt et al. (2016, chapter 4), respectively. Stability constants for the CO 2 solubility and aqueous complexes in the CO 2 -H 2 O -Ca system were taken from [START_REF] Plummer | The solubilities of calcite, aragonite and vaterite in CO 2 -H 2 O solutions between 0 and 90 • C, and an evaluation of the aqueous model for the system CaCO 3 -CO 2 -H 2 O[END_REF]. The stability constants for the REE complexes relevant at the experimental conditions (i.e. REECO 3 + , REE(CO 3 ) 2 -and REEHCO 3 2+ )

were taken from [START_REF] Luo | Carbonate complexation of yttrium and the rare earth elements in natural waters[END_REF]. The activities of the solid components, such as a NaREE(CO3)2 , are calculated assuming ideal solid solutions (i.e. the activity coefficients γ for solid components are equal to one, cf. appendix §C.1).

Methods

Experimental design

The co-precipitation of REE with calcite was conducted using the "constant addition technique", inspired by experiments reported in previous studies [START_REF] Zhong | Partitioning of rare earth elements (REEs) between calcite and seawater solutions at 25 • C and 1 atm, and high dissolved REE concentrations[END_REF][START_REF] Tesoriero | Solid solution partitioning of Sr 2+ , Ba 2+ , and Cd 2+ to calcite[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF][START_REF] Gautier | Hydromagnesite solubility product and growth kinetics in aqueous solution from 25 to 75 • C[END_REF][START_REF] Mavromatis | Characterization of boron incorporation and speciation in calcite and aragonite from co-precipitation experiments under controlled pH, temperature and precipitation rate[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]. This technique allows the co-precipitation of calcite with trace elements at selected rates and at constant reactive fluid compositions. Precipitation took place in 1 L polypropylene (PP) reactors, which were placed on an orbital shaker (Figure 5.1). The fluid in these reactors was held at a constant temperature of 25.0 ± 0.5 • C using purpose-built heating coils connected to a thermostatically controlled water bath. Preliminary experiments showed that mixing the calcite-fluid mixtures using orbital shaking at 250 rpm keeps the calcite powder in suspension while avoiding precipitation on the reactor walls.

At the beginning of each experiment, the reactors were filled with 80 to 400 g of an aqueous solution containing 0.1 or 0.15 mol/kg NaCl, which was in equilibrium with calcite at the experimental conditions. To achieve calcite equilibrium, aqueous NaCl (VWR AnalR Normapur) solutions were equilibrated with ∼4 g of Merck EMSURE calcite powder (having diameters of approximately 3 to 15 µm) while continuously bubbling pure CO 2 (> 99.9 % purity, supplied by Air Products) through this fluid at ambient pressure for at least 5 h at 25 Electron Microscopy (SEM) using a Jeol JSM 6360LV, by powder X-ray diffraction (XRD) together with a Bruker D8 Phaser with a Cu source and a X-ray wavelength of 0.154060 nm (analyses were performed within approximately 1 month after the end of the experiments), and their specific surface area was determined by the BET technique [START_REF] Brunauer | Adsorption of gases in multimolecular layers[END_REF] using krypton and 11 measured adsorption points.

Uncertainties and statistical criteria

The uncertainties of quantities reported in this study, designated by the ± symbol, refer to one standard deviation (σ). Where possible, the propagation of these uncertainties was performed using common algebraic relationships. For highly non-linear functions (e.g. PHREEQC calculations), propagation of uncertainties was performed using Monte Carlo type simulations. In the case of model fits, an effective variance technique [START_REF] Orear | Least squares when both variables have uncertainties[END_REF] was used, which gives the parameter estimates and their standard errors based on the uncertainties of all input parameters. The reduced chi-squared statistic (χ 2 red ), the sum of squared errors, weighted by the variance of the observations and divided by the number of degrees of freedom, is given for model fits as a measure of the goodness of fit accounting for the uncertainties in the observations. A χ 2 red close to unity indicates that the squared errors are consistent with the uncertainties while χ 2 red 1 suggests a poor model fit [START_REF] Bevington | Data Reduction and Error Analysis[END_REF]. Correlations among different parameters are examined using Spearman's rank correlation coefficient ρ, which describes how well the relationship between two parameters can be described by a monotonic function (ρ = 1 or ρ = -1 for perfect positive or inverse correlations, and ρ = 0 for no correlation).

Results

Characteristics of the solids

Scanning electron microscope (SEM) images of the initial calcite seeds and the calcite recovered from representative experiments are shown in Figure 5.2. Examination of the solids recovered from the reactors after the experiments suggests that minor crystal aggregation occurred during the experiments, which is consistent with numerous previous calcite precipitation studies (e.g., [START_REF] Wachi | Effect of gas-liquid mass transfer on crystal size distribution during the batch precipitation of calcium carbonate[END_REF][START_REF] Tai | Nucleation, agglomeration and crystal morphology of calcium carbonate[END_REF][START_REF] Collier | Growth and aggregation rates for calcite and calcium oxalate monohydrate[END_REF][START_REF] Andreassen | Growth and aggregation phenomena in precipitation of calcium carbonate[END_REF]. Furthermore, the SEM images show that the surface roughness increased during crystal growth, which is also reflected in the higher BET specific surface areas of the products with a mean value of 0.46 m 2 /g (see Table 5.1) compared to the initial value of 0.24 m 2 /g. SEM observations did not reveal any difference in the morphology of the precipitated materials as a function of fluid REE concentration, precipitation rate, or the identity of the REE in the aqueous phase. The XRD patterns of the recovered solids, shown in Figure 5.3, are similar to that of the original seed material, and no evidence of aragonite or hydroxylbastnasite was detected (within the detection limit of ∼ 1 wt %). According to thermodynamic calculations, the mineral hydroxylbastnasite (REE(CO 3 )(OH)) is the REE mineral with the lowest solubility at the experimental conditions. Although the solubility product of hydroxylbastnasite has only been reported for the La-and Nd-endmembers (log(K SP ) of -23.8 ± 0.1 and -24.1 ± 0.3, respectively (Voigt et al., 2016, chapter 4)), the solubilities of heavy-REE minerals are likely to be systematically higher (Voigt et al., 2016, chapter 4). Thermodynamic calculations suggest that the reactive aqueous solutions are undersaturated with respect to hydroxylbastnasite at La concentrations below approximately 2 × 10 -8 mol/kg, which is the case for all of our reactive fluids except for CP16 (see ion is incorporated per ∼ 7000 Ca 2+ ions in the calcite. This is consistent with the experimentally determined upper limit for Eu 3+ uptake of [START_REF] Stipp | Rare Earth element (REE) incorporation in natural calcite: upper limits for actinide uptake in a secondary phase[END_REF], which suggests that one Eu 3+ can be incorporated for every ∼ 900 Ca 2+ ions.

Attainment of steady-state reactive fluid compositions and retrieved precipitation rates

The term steady-state in this study is defined by reactive fluids that exhibited no change in pH, Ca concentration, and alkalinity within analytical uncertainty for at least 48 hours during an experiment. An example of the attainment of steady state is shown in Figure 5.4. It can also be seen that the fluid phase REE concentration in this example was relatively constant after 16 hours. To estimate the uncertainty associated with the variation of these parameters, 3-5 reactive fluid samples were taken during each experiment after steady-state was attained, and the mean values and standard deviations of these reactive fluid compositions are reported in show an excellent agreement, and the mean value of both, averaged over the individual fluid samples taken during steady-state for each experiment, is provided in Table 5.2. The calculated precipitation rates ranged from 10 -7.0 to 10 -8.3 mol/m 2 /s, spanning approximately one order of magnitude (Table 5.2).

REE partition coefficients between aqueous solution and calcite

The aqueous REE concentrations, but both partition coefficients are of similar magnitude at lower concentrations. This partition coefficient is also negatively correlated with the calcite saturation state Ω (defined as Ω ≡ (a Ca 2+ a CO3 2-)/K Calcite SP ) in our dataset (ρ = -0.84), as shown in Figure 5.5b. This observation may be due to the inhibition of calcite growth rates by the presence of aqueous REE (see section §5.5.4), leading to higher supersaturation with respect to calcite in the experiments with increasing REE concentration. Due to the magnitude of this effect, it dominates Ω in our dataset, leading to the covariation of c REE and Ω (ρ = 0.90).

-9.0 -8.5 -8.0 -7.5 -7.0 -6.5 -6.0 log(c REE / mol/kg) The symbols labelled as 'La+Yb' are experiments spiked with both La and Yb, and the REE named in parentheses is the one plotted using the corresponding symbol.

Discussion

REEs exchange reactions in the aqueous fluid and calcite system

The partitioning of the REEs between aqueous solutions and calcite as a function of the precipitation rate and REE concentration cannot be described by a single partition coefficient (D REE ). Therefore, we adopt thermodynamic models to calculate the equilibrium distribution coefficients (K D ) for the different possible exchange mechan- [START_REF] Zhong | Partitioning of rare earth elements (REEs) between calcite and seawater solutions at 25 • C and 1 atm, and high dissolved REE concentrations[END_REF][START_REF] Yeghicheyan | Etude expérimentale du partage des terres rares entre carbonates de calcium et solutions aqueuses: Influence de la cinétique de cristallisation et de la spéciation des terres rares en solution[END_REF] reaction (5.3) was adopted to describe our experimental observations. Note also that the similar sizes of the Ca 2+ and Na + favour the incorporation of Na into calcite, as the energy required for the lattice deformation during this process is related to the size difference between the host lattice site and the foreign ion [START_REF] Blundy | Prediction of crystal-melt partition coefficients from elastic moduli[END_REF]. This approach is similar to that of [START_REF] Curti | Solid solutions of trace Eu(III) in calcite: Thermodynamic evaluation of experimental data over a wide range of pH and pCO 2[END_REF]. These authors assumed, however, that their experiments were in thermodynamic equilibrium with the REE bearing solid endmember, whereas we assume equilibrium only with the exchange reactions described in section §5. As noted by [START_REF] Curti | Solid solutions of trace Eu(III) in calcite: Thermodynamic evaluation of experimental data over a wide range of pH and pCO 2[END_REF], the results of [START_REF] Lakshtanov | Experimental study of europium (III) coprecipitation with calcite[END_REF], which were obtained for Eu under similar conditions as our experimental results, are incompatible with the presence of a vacancy in calcite, but consistent with exchange reactions involving either NaREE(CO 3 ) 2 or H(REE)(CO 3 ) 2 . The K D for these two models fit to the Eu co-precipitation data of [START_REF] Lakshtanov | Experimental study of europium (III) coprecipitation with calcite[END_REF] are also provided in Table 5.3, suggesting a similar goodness for both model fits. high saturation states at low c REE without significantly increasing the ionic strength and calcite precipitation rates to levels where precipitation kinetics likely affect the partitioning behaviour prohibited this approach in our study. However, assuming the validity of the exchange reaction involving NaREE(CO 3 ) 2 , the behaviour of D REE as function of fluid composition can be predicted using the relationship:

D REE =K NaREE(CO3)2 D • a Na + c Ca 2 (a Ca 2+ ) 2 • γ REECO3 + γ REE(CO3)2 -γ REEHCO3 2+ γ REE 3+ K 2   a CO3 2-γ REEHCO3 2+ γ REE(CO3)2 -γ REE 3+ K 2 K REECO3 + +γ REECO3 + γ REEHCO3 2+ K 2 γ REE(CO3)2 -+ a CO3 2- 2 γ REE 3+ K REE(CO3)2 - + a CO3 2-a H + γ REECO3 + γ REE(CO3)2 -γ REE 3+ K REEHCO3 2+   (5.7)
where γ i represents the activity coefficients of the subscripted aqueous species, which are derived from combining equations (5.1) and ( 5

Differences between the partitioning behaviour of the individual REEs

It can be seen in Table 5.3 that the K NaREE(CO3)2 D obtained from the regression of experimental data vary among La, Yb and Eu. As shown by [START_REF] Blundy | Prediction of crystal-melt partition coefficients from elastic moduli[END_REF], lattice strain induced in the solid by differences in the ionic size of foreign ions and their host site has a major influence on partition coefficients. Adopting their model, the following expression is obtained describing the dependence of the REE partition coefficients on the size difference between the radius of the host lattice site (r 0 ) and the foreign ions (r REE , r Na ), as well as the elastic response of that site (E):

K NaREE(CO3)2 D = K 0 D exp    -4πN A (2E) 1 2 r 3+ 0 (r REE + r Na -2r 0 ) 2 + 1 3 (r REE + r Na -2r 0 ) 3 2 RT    (5.8)
where R stands for the ideal gas constant, N A designates the Avogadro constant and T refers to the temperature in kelvin. Because of the charge-balanced exchange of two Ca 2+ ions for Na + + REE 3+ in the K

NaREE(CO3)2 D
model, the sum of the radii differences between r REE , r Na and r 0 have to be considered, and the factor of 2 for the elastic response is introduced to facilitate comparison with the elastic modulus based on a single CaCO 3 unit. In this model, K 0 D corresponds to the strain-compensated partition coefficient for an ion with radius r 0 . The curve shown in Figure 5.6 was obtained using the K NaREE(CO3)2 D values listed in Table 5.3 (an uncertainty of 0.1 was assigned to K NaEu(CO3)2 D to account for experimental and analytical interlaboratory differences) using the effective ionic radii of octahedrally coordinated REE reported by [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF]. The best fit parameters are r 0 = 111.7 ± 0.1 pm, E = 81 ± 5 GPa and log K 0 D = 3.84 ± 0.04. The value of r 0 is slightly smaller than the effective ionic radius of octahedrally coordinated Ca 2+ , 112 pm, which is consistent with the observations of [START_REF] Blundy | Prediction of crystal-melt partition coefficients from elastic moduli[END_REF], who noted that r 0 decreases with the increasing charge of the foreign ion. Furthermore, the site elastic modulus (E) retrieved here is in good agreement with the aggregate elastic modulus for calcite of approximately 76 GPa [START_REF] Chen | Elasticity of single-crystal calcite and rhodochrosite by Brillouin spectroscopy[END_REF], validating our lattice strain model parameters. The red circles show experimental results from our experiments (La, Yb) and those of Lakshtanov and Stipp (2004) (Eu). The blue curve depicts the best fit to the lattice strain model of [START_REF] Blundy | Prediction of crystal-melt partition coefficients from elastic moduli[END_REF].

Variation of REE partitioning as function of precipitation rate

No correlation between the precipitation rate and

D REE or K NaREE(CO3)2 D
is evident in our experimental dataset (Figure 5.7). The variability in D REE can be largely attributed to the fact that D REE is a strong function of aqueous fluid composition (cf. section §5.5.1). While [START_REF] Zhong | Partitioning of rare earth elements (REEs) between calcite and seawater solutions at 25 • C and 1 atm, and high dissolved REE concentrations[END_REF] and [START_REF] Lakshtanov | Experimental study of europium (III) coprecipitation with calcite[END_REF] did not detect a correlation between the calcite precipitation rate and the partition coefficient for rates ranging from approximately log(R/(mol/m 2 /s)) = -9.4 to -6.7, [START_REF] Yeghicheyan | Etude expérimentale du partage des terres rares entre carbonates de calcium et solutions aqueuses: Influence de la cinétique de cristallisation et de la spéciation des terres rares en solution[END_REF] observed decreasing D Eu with increasing growth rates. The high precipitation rates observed by [START_REF] Yeghicheyan | Etude expérimentale du partage des terres rares entre carbonates de calcium et solutions aqueuses: Influence de la cinétique de cristallisation et de la spéciation des terres rares en solution[END_REF], ranging from log(R/(mol/m 2 /s)) = -7.2 up to -4.9, could explain the relationship seen in their data, as the precipitation kinetics could influence REE partitioning at faster growth rates. Since the precipitation rates of authigenic marine limestone are usually below 10 -7 mol/m 2 /s [START_REF] Luff | Simulation of long-term feedbacks from authigenic carbonate crust formation at cold vent sites[END_REF][START_REF] Karaca | Controls on authigenic carbonate precipitation at cold seeps along the convergent margin off Costa Rica[END_REF], the independence of the partitioning behaviour seen in our experiments and in data of [START_REF] Zhong | Partitioning of rare earth elements (REEs) between calcite and seawater solutions at 25 • C and 1 atm, and high dissolved REE concentrations[END_REF] and [START_REF] Lakshtanov | Experimental study of europium (III) coprecipitation with calcite[END_REF] is likely to be a closer representation of the natural conditions during marine authigenic calcite formation. Nevertheless, [START_REF] Böhm | Carbon isotope records from extant Caribbean and South Pacific sponges: Evolution of δ 13 C in surface water DIC[END_REF] and [START_REF] Fallon | Carbon isotope constraints on vertical mixing and air-sea CO 2 exchange[END_REF] reported that the molar growth rate of marine biogenic calcite ranges from approximately 0.5 to 1.5 mm/year, which is equal to ∼10 -7.1 to 10 -6.6 mol/m 2 /s assuming that the surface area available for growth is twice that of the macroscopic living surface [START_REF] Gussone | Calcium isotope fractionation in calcite and aragonite[END_REF]. These estimates are at the upper end of the values considered in this study, suggesting that growth rate effects on REE partitioning could play a role in the case of fast biogenic calcite precipitation.

The observation that the partitioning is independent from the precipitation rate for growth rates below ∼10 -7 mol/m 2 /s is consistent with findings for Sr and Ba co-precipitation with calcite [START_REF] Lorens | Sr, Cd, Mn and Co distribution coefficients in calcite as a function of calcite precipitation rate[END_REF][START_REF] Tesoriero | Solid solution partitioning of Sr 2+ , Ba 2+ , and Cd 2+ to calcite[END_REF][START_REF] Gabitov | Crystal growth rate effect on Mg/Ca and Sr/Ca partitioning between calcite and fluid: An in situ approach[END_REF] indicating that kinetic effects are only present at growth rates above ∼10 -6.5 mol/m 2 /s for these elements. This is conceptually consistent with kinetic models which predict that equilibrium precipitation is approached below a threshold where where R 0 stands for the calcite precipitation rate in absence of REEs, n designates an empirical reaction order and k represents a rate constant. Regression of the rates measured in the absence of REEs in this study are found to be consistent with n = 0.95 ± 0.68 and log(k/(mol/m 2 /s)) = -6.38 ± 0.52 (see Figure 5.8). The blue curve shows the best fit to the empirical rate law [START_REF] Morse | Dissolution kinetics of calcium carbonate in sea water; VI, The near-equilibrium dissolution kinetics of calcium carbonate-rich deep sea sediments[END_REF].

Assuming that an exchange reaction such as (5.3) is the predominant process, aqueous Ca 2+ ions can compete with aqueous REEs for adsorption onto the calcite surface sites during its growth. This suggests a competitive Langmuir adsorption mechanism, comparable to that used to describe the incorporation of Mg and Mn into calcite (Dromgoole and Walter, 1990a;[START_REF] Lin | Effect of Mg 2+ on the kinetics of calcite crystal growth[END_REF]. Similar to the derivation of [START_REF] Lin | Effect of Mg 2+ on the kinetics of calcite crystal growth[END_REF], by assuming a correlation between the calcite growth rate and the concentration of surface sites occupied by Ca 2+ , one obtains

R 0 -R R = k * c REE a Ca 2+ b (5.10)
where k * and b represent empirical constants. The total aqueous REE concentration c REE is used in this expression as it is not known which aqueous REE complexes dominate the rate controlling effect. Note a linear correlation with b = 1 is inconsistent with the growth inhibition seen in our experiments. A best fit for this model to our experimental data yields log k * = 8.6 ± 1.5 and b = 1.20 ± 0.26 with a χ 2 red of 0.24 (see Figure 5.9). The strong effect of aqueous REE on calcite precipitation rates even at the low aqueous REE concentrations present in our experiments is consistent with findings of [START_REF] Zhong | Partitioning of rare earth elements (REEs) between calcite and seawater solutions at 25 • C and 1 atm, and high dissolved REE concentrations[END_REF], who observed an inhibitory effect of aqueous REE concentrations below 1 µmol/kg. Similarly, [START_REF] Akagi | Inhibiting effects of lanthanum ion on calcite formation from CaCl 2 -NaHCO 3 solutions at 25 •[END_REF] reported an inhibition of calcite precipitation rates at molar REE/Ca ratios of 10 -4 . The magnitude of the inhibition caused by the presence of aqueous REEs is much higher compared to other elements: [START_REF] Lin | Effect of Mg 2+ on the kinetics of calcite crystal growth[END_REF] found log k * = 0.5 for Mg, and data of Dromgoole and Walter (1990a) are consistent with log k * ≈ 2.7 for Mn. Consideration of the partition coefficients of these elements, which are log D Mg ≈ -1.7 [START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF] and log D Mg ≈ -1 (Dromgoole and Walter, 1990b), respectively, suggests a relationship between the inhibitory effect on calcite precipitation rates and the magnitude of trace element incorporation. This is consistent with the microscopic crystal growth model proposed by [START_REF] Nielsen | General model for calcite growth kinetics in the presence of impurity ions[END_REF], where the incorporation of trace elements into minerals can lead to these ions acting as active growth site (kink) blockers, which was also proposed for the growth of calcite in the presence of Sr 2+ [START_REF] Wasylenki | Nanoscale effects of strontium on calcite growth: An in situ AFM study in the absence of vital effects[END_REF].

-7.0 -6.5 -6.0 -5.5 -5.0 -4.5 log(∑c REE /a Ca 2+ ) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 log((ℛ 0 -ℛ )/ℛ ) Figure 5.9 -Plot illustrating the inhibitory effect of the REEs on calcite growth assuming a correlation between the Ca 2 + surface site concentration and the growth rate, implying a linear relationship between the logarithms of (R 0 -R) R and c REE /a Ca 2+ . The blue line shows a best fit equation of this model.

REE partitioning in seawater

A major application of REE fractionation between calcite and aqueous fluids is in marine environments. For this purpose, the results of this study can be related to seawater compositions using the NaREE(CO 3 ) 2 model described above. Note this application requires that this exchange reaction dominates at seawater conditions as it does at pH 6 and p CO2 of 1 atm. This assumption is supported by spectroscopic evidence from experiments at pH 8 (Marques [START_REF] Fernandes | Site-selective time-resolved laser fluorescence spectroscopy of Eu 3+ in calcite[END_REF][START_REF] Schmidt | Untersuchungen zum Einbaumechanismus von Actiniden und Lanthaniden in Calcium-haltige Sekundärphasen[END_REF] and the observation of a correlation between D Na and aqueous REE concentrations by [START_REF] Zhong | Partitioning of rare earth elements (REEs) between calcite and seawater solutions at 25 • C and 1 atm, and high dissolved REE concentrations[END_REF]; each of these observations is consistent with the incorporation of REEs from seawater into calcite as NaREE(CO 3 ) 2 . Relating our experimental data, obtained at pH ∼ 6, to marine conditions has the advantage of avoiding the solubility minimum of phases such as hydroxylbastnasite at pH 8.2 (Voigt et al., 2016, chapter 4). and the best fit to the lattice strain model for a seawater matrix [START_REF] Millero | The composition of standard seawater and the definition of the reference-composition salinity scale[END_REF], to experimental data of [START_REF] Zhong | Partitioning of rare earth elements (REEs) between calcite and seawater solutions at 25 • C and 1 atm, and high dissolved REE concentrations[END_REF], [START_REF] Tanaka | REE abundances in ancient seawater inferred from marine limestone and experimental REE partition coefficients between calcite and aqueous solution[END_REF] and [START_REF] Toyama | Experimental study of rare earth element partitioning between calcite and sodium chloride solution at room temperature and pressure[END_REF]. (b) Comparison of the same calculated D to partition coefficients calculated from natural samples: Reefal microbialities [START_REF] Webb | Rare earth elements in Holocene reefal microbialites: a new shallow seawater proxy[END_REF], reefal Mg-calcites [START_REF] Scherer | Rare-earth element distribution in Holocene and Pleistocene corals and their redistribution during diagenesis[END_REF], and foraminifers [START_REF] Palmer | Rare earth elements in foraminifera tests[END_REF]. The dashed curves show the best of our K NaREE(CO3)2 D model, but using REECO 3 + and REE(CO 3 ) 2 -in the exchange reaction instead of REE 3 + . and the best fit to the lattice strain model determined by us. The present day seawater composition is taken from [START_REF] Millero | The composition of standard seawater and the definition of the reference-composition salinity scale[END_REF], the pore water composition is represented by the chemistry of the most extremely altered composition reported by [START_REF] Sholkovitz | Interstitial water chemistry of the Santa Barbara Basin sediments[END_REF] [START_REF] Tanaka | REE abundances in ancient seawater inferred from marine limestone and experimental REE partition coefficients between calcite and aqueous solution[END_REF] for seawater conditions from their co-precipitation results (Figure 5.10a). However, their partition coefficients are approximately one order of magnitude higher than those obtained from our experiments. One possible explanation for this difference is the (1996) for Eu at fast growth rates (cf. Figure 5.7). Our calculated partition coefficients can also be compared to those derived from natural samples (Figure 5.10b). Partitioning coefficients inferred from reefal microbialities [START_REF] Webb | Rare earth elements in Holocene reefal microbialites: a new shallow seawater proxy[END_REF], reefal

Mg-calcites [START_REF] Scherer | Rare-earth element distribution in Holocene and Pleistocene corals and their redistribution during diagenesis[END_REF], and foraminifers [START_REF] Palmer | Rare earth elements in foraminifera tests[END_REF] are slightly lower than our calculated values for the light-medium REEs, and the concave pattern is less prominent in these field studies.

One possibility for the differences in reported for REE partitioning between seawater and calcite is the variability of seawater compositions, which affects this partitioning, as illustrated in Figure 5.11. As calcite formed in marine sediments is influenced by pore water chemistry, which can be markedly different from that of seawater, this change can also influence the partition coefficients. This is demonstrated by calculating D REE for the pore water composition taken from the most extremely altered pore water composition (G1, greatest depth) reported by [START_REF] Sholkovitz | Interstitial water chemistry of the Santa Barbara Basin sediments[END_REF] for Santa Barbara Basin sediments (Figure 5.11, Table 5.4). Compared to seawater, these waters are characterised by lower sulphate, Ca and Mg contents along with significantly higher alkalinity, ammonia and phosphate concentrations. It can be seen that the REE partition coefficients are predicted to decrease significantly with the modification of the seawater compositions in the pores. In addition there is a change in the shape of the partition coefficients as a function of the REE, highlighting the potential influence of pore fluid compositions on these coefficients. Changes in the seawater chemistry during the Earth's history would only lead to minor changes in the D REE calculated using our model. Taking seawater Mg, Ca, and SO 4 concentrations (30, 25 and 10 mmol/kg, respectively) estimated for the Cretaceous by [START_REF] Horita | Chemical evolution of seawater during the Phanerozoic: Implications from the record of marine evaporites[END_REF], and assuming its equilibrium with an atmospheric p CO2 of 1000 ppm [START_REF] Royer | CO 2 -forced climate thresholds during the Phanerozoic[END_REF] and therefore a lower seawater pH, D REE are predicted to be only slightly higher than in present-day seawater (Figure 5.11,

D REE = x 1 c Ca c Ca 0.45 + 10 5 x 2 a CO3 2-+ 10 10 x 3 a CO3 2- 2 (5.11)
where c i designates the aqueous concentrations of component i and x j stand for the coefficients shown in and the best fit to the lattice strain model determined by us for variations in seawater compositions based on [START_REF] Millero | The composition of standard seawater and the definition of the reference-composition salinity scale[END_REF], which is shown by the red curve. The blue curve demonstrates the effect of the pore water chemistry, represented by the chemistry of the most extremely altered composition reported by [START_REF] Sholkovitz | Interstitial water chemistry of the Santa Barbara Basin sediments[END_REF], while the green curve illustrates partition coefficients calculated for Cretaceous seawater Mg, Ca and SO 4 concentrations estimated by [START_REF] Horita | Chemical evolution of seawater during the Phanerozoic: Implications from the record of marine evaporites[END_REF] in equilibrium with a p CO2 of 1000 ppm.

Note again that while these partitioning behaviour predictions are based on the NaREE(CO 3 ) 2 partitioning reaction (5.3), it is likely that other exchange reactions dominate REE incorporation into calcite in cases where low Na concentrations are present in the fluid, leading to a distinct partitioning behaviour. This likely precludes the direct application of this model to processes such as the speleothem formation from cave waters, which typically contain low sodium concentrations compared to our experiments and seawater. Furthermore, the experimental results of [START_REF] Yeghicheyan | Etude expérimentale du partage des terres rares entre carbonates de calcium et solutions aqueuses: Influence de la cinétique de cristallisation et de la spéciation des terres rares en solution[END_REF] suggest an influence of the precipitation rate on partition coefficients at fast growth rates, which may be present in speleothem formation and is not accounted for by our models.

Conclusions

Analysis of the aqueous solution compositions of the experiments performed in this study confirm that REE are preferentially fractionated into calcite, and the partition coefficients correlate with reactive fluid D REE as well as its saturation state with respect to calcite. Data interpretation, together with independent spectroscopic evidence [START_REF] Fernandes | Site-selective time-resolved laser fluorescence spectroscopy of Eu 3+ in calcite[END_REF][START_REF] Schmidt | Untersuchungen zum Einbaumechanismus von Actiniden und Lanthaniden in Calcium-haltige Sekundärphasen[END_REF] suggests that the incorporation of REE 3+ ions into the calcite structure at near to neutral pH and the presence of aqueous NaCl is accompanied by the incorporation of Na + . As the REE speciation in our experimental fluids is similar to that of seawater, it is likely that this coupled exchange is predominant during the precipitation of marine limestone from seawater. Partitioning coefficients calculated based on our exchange model for a typical present-day seawater chemistry show a concave pattern as a function of the REE, with a log D La of 2.8, a maximum for log D Gd of 3.6, and decreasing partitioning coefficients towards log D Lu of 2.2. Note, however that these parameters depend strongly the aqueous chemistry, so that equation (5.11) and coefficients in Table 5.4 should be used to estimate REE partition coefficients between calcite and seawater-like aqueous solutions. This dependence of REE partitioning on the fluid composition possibly explains the large variability seen in D REE inferred from previous experimental studies and from natural calcite. the marine radiogenic Sr budget that arise from heat-budget and crustal alteration standpoints (e.g., [START_REF] Davis | Imbalance in the oceanic strontium budget[END_REF], complementing other proposed resolutions such as island arc weathering [START_REF] Allègre | The fundamental role of island arc weathering in the oceanic Sr isotope budget[END_REF], basaltic riverine particulate material dissolution (Jones et al., 2012a), and low-temperature alteration and carbonate precipitation [START_REF] Coogan | Alteration of ocean crust provides a strong temperature dependent feedback on the geological carbon cycle and is a primary driver of the Sr-isotopic composition of seawater[END_REF]. Furthermore, the significant decrease of fluid δ 88/86 Sr in some of our experiments suggest that the isotopic signature of marine hydrothermal activity could be lower than previously estimated [START_REF] Krabbenhöft | Constraining the marine strontium budget with natural strontium isotope fractionations ( 87 Sr/ 86 Sr * , δ 88/86 Sr) of carbonates, hydrothermal solutions and river waters[END_REF][START_REF] Vollstaedt | The Phanerozoic δ 88/86 Sr record of seawater: new constraints on past changes in oceanic carbonate fluxes[END_REF]Pearce et al., 2015a), reducing the offset between the current marine output, defined by Sr precipitated into carbonates, and the inputs (continental and hydrothermal fluxes). While it is unknown whether the stable Sr cycle of the oceans is currently at steady state (and indeed, recent weathering effects indicate that this might not be the case; [START_REF] Vance | Variable Quaternary chemical weathering fluxes and imbalances in marine geochemical budgets[END_REF], the possibility of low-δ 88/86 Sr fluid generation in marine hydrothermal systems highlights the need for further investigation of the variability in marine hydrothermal fluid δ 88/86 Sr to constrain the marine stable Sr cycle.

In the same hydrothermal experiments, the Mg system was dominated by the formation of saponite (trioctahedral smectite), leading to an almost complete removal of Mg from the fluid. The Mg removal was accompanied by isotopic fractionation, and an iterative mass balance model indicates that isotopically heavy Mg was preferentially incorporated into the clays (ε 26/24 Smectite-Liquid ≈ 0.457 ± 0.075 ‰), which is in agreement with previous estimates for similar minerals and environments (Tipper et al., 2006a;[START_REF] Higgins | Constraining magnesium cycling in marine sediments using magnesium isotopes[END_REF][START_REF] Teng | Contrasting lithium and magnesium isotope fractionation during continental weathering[END_REF][START_REF] Wimpenny | Investigating the behaviour of Mg isotopes during the formation of clay minerals[END_REF]. As the magnitude of this isotopic fractionation is small compared to Mg isotopic fractionation during carbonate formation, and due to the almost complete removal of Mg from the fluid in high-temperature marine hydrothermal systems, its influence on the marine Mg cycle is minor, in agreement previous estimates of Pogge von Strandmann et al.

(2014) and [START_REF] Higgins | The Mg isotopic composition of Cenozoic seawater -evidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF]. This confirms that the relatively stable seawater δ 26/24 Mg during Cenozoic rise in seawater Mg/Ca are likely caused by a change in the cycling of Mg-silicates as opposed to changes in the carbonate cycle [START_REF] Higgins | The Mg isotopic composition of Cenozoic seawater -evidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF]. Furthermore, as carbonates preferentially take up isotopically light Mg (e.g., [START_REF] Galy | Mg isotopic composition of carbonate: insight from speleothem formation[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] 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] as opposed to the clay alternation minerals in our experiments, these results highlight the potential of Mg isotopes as tracers of the formation of different types of minerals.

In chapters 4 and 5, the use of the REE concentrations in marine limestone as paleo proxies was evaluated experimentally. In a first step, the solubility of hydroxylbastnasite was determined in dissolution and precipitation experiments at 25 • C. It was found that the solubility of this mineral is lower than that of other known REE carbonates, but other REE phases such as fluorobastnasite and monazite are more stable under typical natural conditions. Yet, the low solubility of hydroxylbastnasite suggests that previous experimental studies of the REE co-precipitation with calcite were potentially affected by the formation of this mineral. To address this issue, a subsequent experimental study of REE/Ca fractionation during the precipitation of calcite from aqueous solutions was performed which confirmed that REEs are preferentially incorporated into calcite. The variation seen in the partition coefficients is consistent with incorporation of REE 3+ into the calcite structure and charge balancing by Na + at the experimental conditions (pH ∼ 6, 0.1 mol/kg NaCl), which is in agreement with independent spectroscopic evidence [START_REF] Fernandes | Site-selective time-resolved laser fluorescence spectroscopy of Eu 3+ in calcite[END_REF][START_REF] Schmidt | Untersuchungen zum Einbaumechanismus von Actiniden und Lanthaniden in Calcium-haltige Sekundärphasen[END_REF]. Under the assumption that this exchange model is valid for seawater, partition coefficients for marine conditions are predicted to vary significantly depending on the fluid composition, but can be estimated based on this exchange model. Therefore, the conditions at the time of formation have to be taken into account when REEs in calcite are used as paleo proxies, and the large variability seen in partition coefficients estimated from previous experimental studies and natural samples is likely a result of this. By further constraining the REE/Ca fractionation during calcite precipitation from aqueous fluids, these experimental results improve the ability of such paleo proxies to trace past weathering cycles and marine redox conditions which imprint their characteristic signature onto marine REE concentrations.

Suggestions for future research

In the context of marine hydrothermal activity, this thesis established the importance of intermediate-temperature reactions to marine chemical budgets. However, it has been previously suggested that low-temperature hydrothermal systems at the ocean floors are a significant factor in marine geochemical cycles as well, affecting the marine radiogenic Sr cycle and the carbon cycle [START_REF] Coogan | Alteration of ocean crust provides a strong temperature dependent feedback on the geological carbon cycle and is a primary driver of the Sr-isotopic composition of seawater[END_REF]. Similarly, potentially stronger Mg isotopic fractionation and less complete Mg removal from the seawater during lower-temperature hydrothermal alterations could significantly impact the marine Mg isotopic budget [START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF][START_REF] Higgins | The Mg isotopic composition of Cenozoic seawater -evidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF]. Although drastically slower reaction kinetics limit the fluid composition change in low-temperature hydrothermal systems, the presumably larger magnitude of isotopic fractionation together with the large water fluxes of these systems, circulating a volume equivalent to that of the entire oceans through them in only 200 000 years [START_REF] Johnson | Fluxes of fluid and heat from the oceanic crustal reservoir[END_REF], highlight the potential of low-temperature alteration on marine geochemical cycles. Yet, there is little experimental knowledge of the isotopic effects of low-temperature fluid-rock interactions in such systems, highlighting the need for the experimental investigation of isotopic fractionation under such conditions. Due to the significantly slower kinetics of the reactions at these temperatures compared to the experiments conducted in this thesis, it is expected that significantly longer durations are necessary to achieve quantifiable isotopic fractionation in this case. A possible solution to this problem is the addition of an isotopic spike to the fluid and/or solid, so that detectable isotopic fractionation is analytically resolvable after reasonable experimental durations.

The behaviour of REEs during the abiogenic precipitation of calcite was experimentally investigated in this thesis. Although it was established that the REE partition coefficients between fluid and calcite are not dependent on the precipitation rate for rates below ∼10 -7.3 mol/m 2 /s, a rate dependence is likely for fast kinetics [START_REF] Yeghicheyan | Etude expérimentale du partage des terres rares entre carbonates de calcium et solutions aqueuses: Influence de la cinétique de cristallisation et de la spéciation des terres rares en solution[END_REF], requiring further investigation of the kinetics of REE partitioning. In addition, although charge balancing of the REE 3+ ion by incorporation of Na + into the calcite structure is likely under our experimental conditions, further testing of this model under marine conditions is necessary in the light of the various exchange reactions that have been found to control Eu partitioning under extreme conditions [START_REF] Curti | Solid solutions of trace Eu(III) in calcite: Thermodynamic evaluation of experimental data over a wide range of pH and pCO 2[END_REF]. Although direct testing of REE/Ca partitioning between modern or past seawater chemistries and calcite is challenging due to the low solubility of hydroxylbastnasite and analytical constraints, testing of the predicted variability of D REE is necessary to confirm the applicability of the model under such conditions. As special attention is paid to the behaviour of Ce in marine environments due to its redox sensitivity, the direct determination of the Ce 4+ partitioning between aqueous fluids and calcite would improve the reliability of REE patterns in calcite. Furthermore, the use of various biogenic carbonates is a promising marine REE paleo proxy as well [START_REF] Webb | Rare earth element geochemistry of scleractinian coral skeleton during meteoric diagenesis: a sequence through neomorphism of aragonite to calcite[END_REF]). Yet, the fractionation of REEs during the formation of these biogenic carbonates has only been inferred from natural samples (e.g., [START_REF] Webb | Rare earth elements in Holocene reefal microbialites: a new shallow seawater proxy[END_REF], which is prone to large uncertainties due to the inherent assumptions. Therefore, the experimental determination of the biological influence on REE partition coefficients between aqueous solutions and calcite are necessary for the reliable interpretation of REE patterns in marine biogenic calcite. manquant dans les budgets maritimes de 87 Sr/ 86 Sr existants (e.g., [START_REF] Davis | Imbalance in the oceanic strontium budget[END_REF], car des températures de fluide plus faibles permettent un flux de fluide hydrothermal plus important dans les contraintes du bilan de la chaleur des dorsales océaniques.

Chapitre 6b

Conclusions générales

Les données expérimentales indiquent également qu'une re-dissolution significative de l'anhydrite peut se produire, en partie grâce à des processus tels que la réduction du liquide causée par la libération de Fe 2+ , mais aussi lors du refroidissement du liquide.

Cela suggère que les abondances d'anhydrite dans les carottes des basaltes océaniques pourraient être affectées par le même processus, cause potentielle de l'écart entre le degré d'altération observé dans les carottes des basaltes océaniques altérées et le bilan radiogénique de Sr des océans (Teagle et al., 1998b). Dans l'ensemble la prise en compte de la composition des fluides hydrothermaux à température intermédiaire pourraient aider à expliquer les déséquilibres dans le bilan radiogénique marin de Sr dans les bilans de chaleur des dorsales océaniques et de l'altération de la croûte océanique (e.g., [START_REF] Davis | Imbalance in the oceanic strontium budget[END_REF], en complément d'autres explications proposées telles que l'érosion des arcs insulaires [START_REF] Allègre | The fundamental role of island arc weathering in the oceanic Sr isotope budget[END_REF], la dissolution des particules riveraines basaltiques (Jones et al., 2012a), et l'altération à basse température entrainant la précipitation de carbonate [START_REF] Coogan | Alteration of ocean crust provides a strong temperature dependent feedback on the geological carbon cycle and is a primary driver of the Sr-isotopic composition of seawater[END_REF]. En outre, la diminution significative de δ 88/86 Sr dans le fluide dans certaines de nos expériences suggère que la signature isotopique de l'activité hydrothermale marine pourrait être inférieure à celle précédemment estimée [START_REF] Krabbenhöft | Constraining the marine strontium budget with natural strontium isotope fractionations ( 87 Sr/ 86 Sr * , δ 88/86 Sr) of carbonates, hydrothermal solutions and river waters[END_REF][START_REF] Vollstaedt | The Phanerozoic δ 88/86 Sr record of seawater: new constraints on past changes in oceanic carbonate fluxes[END_REF]Pearce et al., 2015a) Smectite-Liquid ≈ 0.457 ± 0.075 ‰), en accord avec les estimations précédentes pour des minéraux et environnements similaires (Tipper et al., 2006a ;[START_REF] Higgins | Constraining magnesium cycling in marine sediments using magnesium isotopes[END_REF][START_REF] Teng | Contrasting lithium and magnesium isotope fractionation during continental weathering[END_REF][START_REF] Wimpenny | Investigating the behaviour of Mg isotopes during the formation of clay minerals[END_REF]. Comme l'intensité de ce fractionne-ment isotopique est faible par rapport au fractionnement isotopique du Mg pendant la formation des carbonates, et en raison de la disparition presque complète du Mg du fluide dans les systèmes hydrothermaux marins, son influence sur le cycle marin du Mg est mineure. Cela confirme que le δ 26/24 Mg de l'eau de mer relativement stable lors de l'augmentation du Mg/Ca pendant le Cenozoic est probablement causée par un changement dans le cycle des silicates de Mg par opposition aux changements dans le cycle du carbonate [START_REF] Higgins | The Mg isotopic composition of Cenozoic seawater -evidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF]. En outre, comme les carbonates incorporent préférentiellement le Mg isotopiquement léger (e.g., [START_REF] Galy | Mg isotopic composition of carbonate: insight from speleothem formation[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] 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] par opposition aux argiles dans nos expériences, ces résultats mettent en évidence l'utilité des isotopes de Mg comme traceurs de la formation des différents types de minéraux.

Dans chapitres 4 et 5, l'utilisation des concentrations des terres rares dans les calcaires marins comme « paleo proxies » a été évaluée expérimentalement. Dans une première étape, la solubilité de l'hydroxylbastnasite a été déterminée lors des expériences de dissolution et précipitation à 25 • C. On peut constater que la solubilité de ce minéral est inférieure à celle des autres carbonates des terres rares connus, mais d'autres phases des terres rares telles que le fluorobastnasite et la monazite sont plus stables dans des conditions naturelles typiques. Pourtant, la faible solubilité de l'hydroxylbastnasite suggère que les études expérimentales antérieures de la co-précipitation des terres rares avec la calcite étaient potentiellement affectées par la formation de ce minéral.

Pour résoudre ce problème, une étude expérimentale du fractionnement des terres rares par rapport au Ca pendant la précipitation de la calcite à partir de solutions aqueuses a été effectuée, qui a confirmé que les terres rares sont préférentiellement incorporées dans la calcite. La variation observée dans les coefficients de partage est cohérente avec l'incorporation de REE 3+ dans la structure de la calcite et l'équilibrage des charges par Na + aux conditions expérimentales (pH ∼ 6, 0.1 mol/kg NaCl), qui est en accord avec les études spectroscopiques [START_REF] Fernandes | Site-selective time-resolved laser fluorescence spectroscopy of Eu 3+ in calcite[END_REF][START_REF] Schmidt | Untersuchungen zum Einbaumechanismus von Actiniden und Lanthaniden in Calcium-haltige Sekundärphasen[END_REF]. En supposant que ce modèle d'échange est également valable pour l'eau de mer, les coefficients de partage dans les conditions marines devraient varier considérablement en fonction de la composition des fluides, mais peuvent être estimés avec ce modèle d'échange. Par conséquent, les conditions au moment de la formation doivent être prises en compte lorsque les terres rares dans la calcite sont utilisés comme « paleo proxies », et la grande variabilité observée dans les coefficients de partage estimés par les études expérimentales précédentes et dans les échantillons naturels est probablement le résultat de cela.

En contraignant le fractionnement terres rares / Ca pendant la précipitation de la calcite à partir des fluides aqueux, ces résultats expérimentaux améliorent l'utilité de ces « paleo proxies » pour la suivi des cycles d'érosion et conditions rédox dans le passé qui impriment leur signature caractéristique dans les concentrations marines des terres rares.

6b.1 Suggestions pour des recherches futures

Dans le contexte de l'activité hydrothermale marine, cette thèse a permis de déterminer l'importance des réactions à température intermédiaire pour les bilans géochimiques marins. Cependant, il a été suggéré précédemment que les systèmes hydrothermaux à basse température au fond des océans sont également un facteur important dans les cycles géochimiques marins, affectant le cycle marin du Sr radiogénique et le cycle du carbone [START_REF] Coogan | Alteration of ocean crust provides a strong temperature dependent feedback on the geological carbon cycle and is a primary driver of the Sr-isotopic composition of seawater[END_REF]. De même, le fractionnement isotopique du Mg potentiellement plus fort et la disparition du Mg de l'eau de mer moins complète lors des altérations hydrothermales à basse température pourraient avoir un impact significatif sur le bilan isotopique marin du Mg [START_REF] Higgins | The Mg isotopic composition of Cenozoic seawater -evidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF]. Bien que la cinétique de ces réactions drastiquement plus lentes limite le changement des compositions fluides dans les systèmes hydrothermaux à basse température, le degré vraisemblablement supérieur du fractionnement isotopique ainsi que les grands fluxes d'eau de ces systèmes, faisant circuler un volume équivalent à celui des océans entiers en seulement 200 000 ans [START_REF] Johnson | Fluxes of fluid and heat from the oceanic crustal reservoir[END_REF], mettent en évidence l'influence potentielle de l'altération à basse température sur les cycles géochimiques marins. Pourtant, il existe peu de données expérimentales sur les effets isotopiques des interactions fluide-roche à basse température dans de tels systèmes, soulignant la nécessité des études expérimentales du fractionnement isotopique dans de telles conditions. En raison de la cinétique nettement plus lente des réactions à ces températures par rapport aux expériences menées dans cette thèse, des durées significativement plus longues sont nécessaires pour atteindre un fractionnement isotopique quantifiable dans ce cas. Une solution possible à ce problème est l'ajout d'un spike isotopique au fluide et/ou au solide, de sorte que le fractionnement isotopique détectable est analytiquement résoluble pour des durées expérimentales raisonnables.

Le comportement des terres rares pendant la précipitation abiogénique de la calcite a été étudié expérimentalement au cours de cette thèse. Bien qu'il ait été établi que les coefficients de partage des terres rares entre le fluide et la calcite ne dépendent pas de la vitesse de précipitation pour les vitesses inférieurs à ∼7.3 mol/m 2 /s, une dépendance à la vitesse est probable pour une cinétique rapide [START_REF] Yeghicheyan | Etude expérimentale du partage des terres rares entre carbonates de calcium et solutions aqueuses: Influence de la cinétique de cristallisation et de la spéciation des terres rares en solution[END_REF], nécessitant une étude plus approfondie de la cinétique du partage des terres rares. En outre, bien que l'équilibrage des charges de l'ion REE 3+ par incorporation de Na + dans la structure de la calcite soit probable dans nos conditions expérimentales, des essais supplémentaires de ce modèle dans des conditions marines sont nécessaires à la lumière des diverses réactions d'échange qui ont été identifiées pour le partage du Eu dans des conditions extrêmes [START_REF] Curti | Solid solutions of trace Eu(III) in calcite: Thermodynamic evaluation of experimental data over a wide range of pH and pCO 2[END_REF]. Bien que l'étude directe du coefficient de partage des terres rares par rapport au Ca entre les compositions récentes ou passées de l'eau de mer et la calcite soit difficile en raison de la faible solubilité de l'hydroxylbastnasite et des contraintes analytiques, il est nécessaire de confirmer la variabilité de D REE pour confirmer l'applicabilité du modèle dans de telles conditions. Etant donné l'intérêt particulier porté au comportement du Ce dans les milieux marins en raison de sa sensibilité rédox, la détermination directe du partage du Ce 4+ entre fluides aqueux et calcite améliorerait la fiabilité des spectres des terres rares dans la calcite. En outre, l'utilisation de divers carbonates biogènes est également un « paleo proxy » prometteur [START_REF] Webb | Rare earth element geochemistry of scleractinian coral skeleton during meteoric diagenesis: a sequence through neomorphism of aragonite to calcite[END_REF]. Pourtant, le fractionnement des terres rares pendant la formation de ces carbonates biogènes n'a été déduit qu'à partir des échantillons naturels (e.g., [START_REF] Webb | Rare earth elements in Holocene reefal microbialites: a new shallow seawater proxy[END_REF], et est sujet à de grandes incertitudes en raison des suppositions associées. Par conséquent, la détermination expérimentale de l'influence biologique sur les coefficients de partage des terres rares entre les solutions aqueuses et la calcite est nécessaire pour l'interprétation fiable des spectres des terres rares dans les calcites biogènes marines.

  : An experimental study of hydroxylbastnasite solubility in aqueous solutions at 25 • C. Chemical Geology 430: 70-77. doi: 10.1016/j.chemgeo.2016.03.012" and reprinted with permission. Copyright 2016 Elsevier. I designed the experiments with input from E. H. Oelkers. J. D. Rodriguez-Blanco, B. Vallina and L. G. Benning provided the synthetic hydroxylbastnasite used as starting material. I carried out the experimental and analytical work as well as the data interpretation, and wrote the manuscript with input from E. H. Oelkers.

2. 1

 1 Experimental parameters of the basalt-seawater experiments. . . . . . . 2.2 Chemical compositions of the basaltic glass and crystalline basalt used as starting materials of basalt-seawater experiments. . . . . . . . . . . . 2.3 Strontium content and isotopic composition of the basalt powders used as reactants in hydrothermal basalt-seawater experiments. . . . . . . . 2.4 Fluid compositions and Sr isotopic data of basalt-seawater experiments. 2.5 XRD analysis data of the solids recovered from the hydrothermal experiments with basalt and seawater. . . . . . . . . . . . . . . . . . . . . . 3.1 Magnesium isotopic data of fluids and the initial basalt from the basaltseawater experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Equilibrium constants used in the calculations of the hydroxylbastnasite solubility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Experimental data of dissolution and precipitation experiments of hydroxylbastnasite and kozoite. . . . . . . . . . . . . . . . . . . . . . . . 5.1 Experimental data of REE co-precipitation with calcite from aqueous solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Partition coefficients and other parameters calculated from REE coprecipitation experiments with calcite. . . . . . . . . . . . . . . . . . . 5.3 Best fit K D and standard errors of model fits of experimental coprecipitation data to different exchange models. . . . . . . . . . . . . . 5.4 Calculated REE/Ca partition coefficients between different marine fluids and calcite as well as coefficients for parameterisations. . . . . . . . . . List of Figures 1.1 Schematic diagram of major processes affecting marine cycles of nonvolatile elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Schematic diagram of a hydrothermal system at the axis of intermediateto fast-spreading mid-ocean ridges. . . . . . . . . . . . . . . . . . . . . 1.3 Rare earth element concentrations patterns of deep seawater and marine hydrothermal fluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Example of the variation of partition coefficients as function of the precipitation rate of minerals as predicted by simple kinetic rate laws. . . . 1.5 Variation between the equilibrium and kinetic mass fractionation laws for the Mg isotopic system. . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Schematic design of the reactors used for hydrothermal experiments with basalt and seawater. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 SEM images of the basalt powders used as reactants in experiments with basalt and seawater, as well as of the solid reaction products. . . . . . . 2.3 Aqueous composition evolution of experiments reacting basalt with seawater at 250 • C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Aqueous composition evolution of experiments reacting basalt with seawater at 290 • C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Strontium concentration, 87 Sr/ 86 Sr and stable δ 88/86 Sr isotope ratios of fluids during seawater-basalt reactions. . . . . . . . . . . . . . . . . . . 2.6 XRD spectra of the basalts used as reactants in comparison to those of the solid alteration products of the hydrothermal experiments with basalt and seawater. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 FTIR spectra of the basalts used as reactants in the experiment in comparison to those of the solid alteration products of the hydrothermal experiments with basalt and seawater. . . . . . . . . . . . . . . . . . . 2.8 Evolution of aqueous compositions during basalt-seawater reactions in comparison with similar experiments of Seyfried and Bischoff (1979) and Seyfried and Bischoff (1981). . . . . . . . . . . . . . . . . . . . . . . . . 2.9 Saturation indices of different minerals, calculated with PHREEQC, during seawater-basalt reactions. . . . . . . . . . . . . . . . . . . . . . 2.10 Comparison of experimental data and model predictions of the Sr isotopic system behaviour during basalt-seawater reactions. . . . . . . . . 2.11 Illustration of the relationship between aqueous Sr concentrations and 87 Sr/ 86 Sr during basalt seawater reactions. . . . . . . . . . . . . . . . . 2.12 Illustration of the best-fit values and uncertainties of the Sr isotopic fractionation factors during basalt-seawater reactions. . . . . . . . . . . 3.1 Plot illustrating the correction of 48 Ca interferences occurring during Mg isotope analysis using MC-ICP-MS. . . . . . . . . . . . . . . . . . . . . 3.2 Chemical composition and δ 26/24 Mg of liquids sampled from basaltseawater experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 SEM images of solids recovered from experiments reacting basalt with seawater at 250 • C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Plots illustrating the modelled evolution of the Mg isotopic system during basalt-seawater reactions at 250 • C. . . . . . . . . . . . . . . . . . .3.5 Plots illustrating the estimated Mg isotope fractionation factors during basalt-seawater reactions at 250 • C. . . . . . . . . . . . . . . . . . . . . 4.1 SEM images of synthesised Nd-hydroxylbastnasite and Nd-kozoite. . . . 4.2 XRD spectra of synthesised Nd-hydroxylbastnasite and Nd-kozoite. . . 4.3 Experimental design used for the determination of hydroxylbastnasite solubility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 pH and Nd evolution during hydroxylbastnasite dissolution experiment CO12A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 pH and Nd evolution during hydroxylbastnasite dissolution experiment CO13B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Comparison of the pH measured during hydroxylbastnasite dissolution experiments with the pH predicted for stoichiometric dissolution. . . . . 4.7 Plot of aqueous REE concentrations vs. pH of hydroxylbastnasite dissolution and precipitation experiments. . . . . . . . . . . . . . . . . . . 4.8 Modelled aqueous F concentrations in equilibrium with hydroxylbastnasite and fluorobastnasite . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9 Modelled aqueous P concentrations in equilibrium with Nd-hydroxylbastnasite and Nd-monazite . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Schematic illustration of the experimental design used for the coprecipitation experiments reported in this study. . . . . . . . . . . . . . 5.2 SEM images of synthetic calcite powder and after before REE coprecipitation experiments. . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 XRD profiles of the solids recovered after REE co-precipitation experiments with calcite. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Evolution of pH, Ca, alkalinity and La fluid concentrations in REE coprecipitation experiment CP15. . . . . . . . . . . . . . . . . . . . . . . 5.5 Diagrams showing experimentally determined REE partition coefficients in relationship to aqueous REE concentrations and the calcite saturation state. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Diagram showing the relationship between determined REE equilibrium constants and ionic size. . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Diagram illustrating experimentally determined REE partition coefficients as function of precipitation rate. . . . . . . . . . . . . . . . . . . 5.8 Plot of calcite precipitation rates from aqueous solutions in the absence of REEs vs. the calcite saturation state. . . . . . . . . . . . . . . . . . 5.9 Plot illustrating the inhibitory effect of aqueous REEs on calcite precipitation rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.10 Comparison of experimentally determined REE partition coefficients during co-precipitation with calcite to other experimental studies and to partition coefficients determined from natural samples. . . . . . . . . 5.11 Predicted REE/Ca partition coefficients between different marine fluid compositions and calcite. . . . . . . . . . . . . . . . . . . . . . . . . . . B.1 Plot of the difference between the isotopic composition of the accumulated product and of the initial reactant versus the fractional yield during irreversible fractionation. . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1 . 1 -

 11 Figure 1.1 -Schematic diagram of major processes affecting marine cycles of nonvolatile elements (see text). The red ellipses and labels designate the settings of the systems relevant to the experimental studies carried out in the context of this thesis.

Figure 1 . 2 -

 12 Figure 1.2 -Schematic diagram of a hydrothermal system at the axis of intermediateto fast-spreading mid-ocean ridges (after Coogan, 2008).

Figure 1 . 3 -

 13 Figure 1.3 -Rare earth element concentrations of deep seawater (Atlantic Ocean, station 161-1, 4033 m, Osborne et al. (2015)) and marine hydrothermal fluids (average from Klinkhammer et al. (1994)), normalised to Post-Archaean Australian Shale (PAAS; McLennan (1989)).

Figure 1 . 4 -

 14 Figure 1.4 -Plot of the partition coefficient as function of R p /R b according to equation (1.12) and arbitrary parameters R b = 1, D eq = 1000 and D f = 50.

  through a series of experiments reacting seawater with basaltic glass and crystalline basalt at temperatures of 250 • C and 290 • C. The interpretation of measured Sr isotopic ratios of the fluid phase during these experiments provides new insight into the behaviour of Sr and its isotopic ratios during seawater-basalt interaction. A discussion of the Mg isotopic fractionation during the 250 • C experiments is provided separately in chapter 3.

  Figure 2.1 -Schematic design of Ti-autoclaves used for the experiments in this study.The autoclaves are rocked so that the solids are well mixed with the seawater, and the cooling apparatus attached to a valve allows fluid samples to be taken during the experimental run.

Figure 2 . 2 -

 22 Figure 2.2 -Scanning electron microscopy images of (a)-(b) the two basalt powders used in the experiment and (c)-(f) solid alteration products recovered from the corresponding experiments at 250 • C.

Figure 2 . 3 -Figure 2 . 4 -Figure 2 . 5 -

 232425 Figure 2.3 -Aqueous concentrations of Ca, Mg, SO 4 2 -, Na, Cl, Fe as well as pH of seawater reacting with basaltic glass (solid lines) and crystalline basalt (dashed lines) at 250 • C. The errors bars show the 95 % confidence intervals (∼ 2 standard errors), which are smaller than the symbol size where no error bars are shown.

Figure 2 . 6 -

 26 Figure 2.6 -XRD spectra of the basalts used as reactant in the experiment in comparison to those of the solid alteration products of the experiments with (a) basaltic glass and (b) crystalline basalt. Note the presence of amorphous phases in all samples.The hkl-reflections correspond mainly to ferrous saponite. Zincite (20 wt %; grey bars) was used as an internal standard.

Figure 2 . 8 -

 28 Figure 2.8 -Evolution of aqueous (a) Mg and (b) Ca concentrations during the crystalline basalt experiments in comparison with similar experiments of[START_REF] Seyfried | Low temperature basalt alteration by sea water: an experimental study at 70 • C and 150 • C[END_REF] and[START_REF] Seyfried | Experimental seawater-basalt interaction at 300 • C, 500 bars, chemical exchange, secondary mineral formation and implications for the transport of heavy metals[END_REF] conducted at temperatures of 150 • C and 300 • C.

Figure 2 . 9 -

 29 Figure 2.9 -Saturation indices of different minerals in the fluid samples, calculated with PHREEQC and the LLNL database at the experimental temperature and saturated vapour pressure.

  4 2during this period, mass balance constraints allow calculation of the amounts of basalt dissolution and anhydrite precipitation from the composition of the initial seawater and first liquid sample compositions, the liquid mass, and the basalt composition. The results of such calculations suggest that 4.3 ± 0.3 g and 4.7 ± 0.4 g of basalt were dissolved during the basaltic glass experiments at 250 • C and 290 • C, respectively, before the first liquid sample was taken. Consistent with the generally slower chemical exchange, these calculations suggest that 0.62 ± 0.06 g and 1.7 ± 0.2 g of crystalline basalt dissolved prior to the first liquid sample collection at 250 • C and 290 • C. The corresponding masses of anhydrite precipitated during this period are 1.029 ± 0.002 g and 0.85 ± 0.02 g for the basaltic glass experiments at 250 • C and 290 • C, respectively, and 0.513 ± 0.001 g and 0.74 ± 0.02 g for the respective crystalline basalt experiments.

Figure 2 .

 2 Figure 2.11 -Model predictions (dashed curves) of aqueous Sr concentrations and 87 Sr/ 86 Sr until the first sample was taken in the 250 • C and 290 • C experiments. The symbols connected by solid lines show the later evolution of the liquids sampled in the experiments. The grey arrows and labels show the processes leading to the changes in the two parameters during the basalt-fluid reactions. Errors bars and grey areas show the 95 % confidence intervals, which are smaller than the symbol size where no error bars are shown.

  samples in the crystalline basalt experiments (Figure 2.9). Using the mean 87 Sr/ 86 Sr of 0.708938 of the precipitated anhydrite, mass balance calculations suggest that up to 15 % of the anhydrite may have been re-dissolved. Since SO 4 2did not increase significantly as did 87 Sr/ 86 Sr during the later stages of the experiments (Figure 2.3 on page 36), a possible cause for anhydrite re-dissolution is the reduction of aqueous SO 4 2by the oxidation of Fe 2+ released by basalt dissolution, leading to an undersaturation with respect to anhydrite and subsequent re-dissolution. Although the aqueous reduced S concentrations is not available for our experiments (and PHREEQC saturation states are thus calculated assuming that sulfur is present as S 6+ ), calculations by Mottl et al. (1979) under similar conditions suggest that anhydrite became metastable during their experimental runs due to the reducing nature of the final fluids. Liquid δ 88/86 Sr remained relatively constant after the early anhydrite precipita-tion (Figure 2.5 on page 38) with the exception of the crystalline basalt experiment at 290 • C, where the extremely low aqueous δ 88/86 Sr gradually increase towards the basaltic δ 88/86 Sr value due to continued basalt dissolution.

  contribution of these hydrothermal systems to the marine 87 Sr/ 86 Sr budget, assuming the change of 87 Sr/ 86 Sr and Sr concentration in the seawater during hydrothermal alteration is known. Based on such calculations,[START_REF] Davis | Imbalance in the oceanic strontium budget[END_REF] estimated that high-temperature fluids (400 • C), transferring 50 % of the available heat and cooling the lower crust to 860 • C, can only supply 1/6 th of the unradiogenic Sr required to balance the other marine Sr fluxes (mainly the high-87 Sr/ 86 Sr river input). Our experimental results show that fluids with low 87 Sr/ 86 Sr ratios and Sr concentrations comparable to that of seawater can be generated from seawater after reaction with basalt at temperatures of only 250 • C within 2 months, and even faster at 290 • C. This is consistent with the experimental data of[START_REF] James | An experimental study of alteration of oceanic crust and terrigenous sediments at moderate temperatures (51 to 350 • C): insights as to chemical processes in near-shore ridge-flank hydrothermal systems[END_REF], who observed significant Sr exchange with basalt even at 150 • C. The time required for Sr exchange in our experiments are well within the residence times of ≤3 years years estimated for fluids at high-temperature conditions (>200 • C) in the Juan de Fuca Ridge hydrothermal system by[START_REF] Kadko | The relationship of hydrothermal fluid composition and crustal residence time to maturity of vent fields on the Juan de Fuca Ridge[END_REF] using Ra isotopes. It is also within the range of residence times on the order of years estimated independently by[START_REF] Fisher | Geophysical constraints on hydrothermal circulation observations and models[END_REF]. Assuming, as an example and upper limit, that the 50 % of the available heat not re-moved by high-temperature (400 • C) fluids in the[START_REF] Davis | Imbalance in the oceanic strontium budget[END_REF] estimate are lost through intermediate-temperature (250 • C) fluids, the calculated basaltic Sr flux to the oceans increases by a factor of ∼ 3.2x, reducing the missing basaltic Sr flux in the marine 87 Sr/ 86 Sr budget by half. However, there are significant uncertainties in both the amount of heat transferred from the crust to the oceans and the partitioning of hydrothermal fluid temperatures[START_REF] German | Hydrothermal processes[END_REF], limiting a more detailed estimation of the basaltic Sr flux from hydrothermal systems using heat flux estimates.Nevertheless, considering their potential to help reconcile the marine 87 Sr/ 86 Sr budget, intermediate-temperature hydrothermal fluids could play a significant role in the global heat transfer from the crust to the oceans, complementing other proposed unradiogenic 87 Sr/ 86 Sr sources such as island arc weathering[START_REF] Allègre | The fundamental role of island arc weathering in the oceanic Sr isotope budget[END_REF], low-temperature alteration and carbonate precipitation[START_REF] Coogan | Alteration of ocean crust provides a strong temperature dependent feedback on the geological carbon cycle and is a primary driver of the Sr-isotopic composition of seawater[END_REF] and dissolution of river derived basaltic particles(Jones et al., 2012a).Apart from heat flux constraints discussed above,[START_REF] Davis | Imbalance in the oceanic strontium budget[END_REF] noted that the alteration of 87 Sr/ 86 Sr in the ocean crust is inconsistent with the marine Sr budget. This argument is based on the assumption that the alteration occurs by Sr isotopic exchange with the fluids, replacing the low, MORB 87 Sr/ 86 Sr with high, seawater 87 Sr/ 86 Sr while leaving the Sr concentrations unchanged. Our experimental results and Sr isotopic modelling suggest that this isotopic exchange occurs mainly by precipitation of anhydrite during the early stages of the reactions and subsequent release of unradiogenic

  only a few δ 88/86 Sr measurements of hydrothermal fluids are available at present, with Pearce et al. (2015a) deriving a value of δ 88/86 Sr = 0.24 ‰ by extrapolation of eleven hydrothermal fluid measurements to a MORB hydrothermal endmember composition.

  250 • C and 290 • C and at saturated vapour pressure. Chemical exchange was monitored by regular sampling of the liquid phase in the reactor, and the general trends are similar to those suggested by the direct measurement of mid-ocean ridge vent fluid compositions. Minor differences, such as the increase of pH after near complete removal of Mg from the liquid in the experiments, exist, and may be related to the absence of epidote from the alteration mineral assemblage (which is thought to reflect the sluggish kinetics in these experiments). The Sr concentration, radiogenic 87 Sr/ 86 Sr ratio and stable δ 88/86 Sr composition of the fluid phase changed considerably during all the experiments. An initial drop in 87 Sr/ 86 Sr towards basaltic values coupled with a decrease in Sr concentrations can be modelled by assuming Sr removal via anhydrite precipitation, followed by an increased influence of Sr release from basalt dissolution over time as the liquid becomes depleted in SO 4 2 -. The greater decrease of δ 88/86 Sr observed in crystalline basalt experiments during the initial parts of the experiments suggests that isotopically light Sr may be preferentially released during non-stoichiometric crystalline basalt dissolution. In contrast, the observed fractionation pattern suggests that anhydrite shows a slight preference for isotopically heavy Sr with ε 88/86 Anhydrite-liquid = 0.033 ± 0.020 ‰. The later evolution of the Sr isotopic composition of the fluids suggests that up to 15 % of the precipitated anhydrite is re-dissolved at a later stage, potentially resulting from reduction of the liquid due to the release of Fe 2+ from the basalt dissolution.

24

  Mg beam intensities of ∼13.5 V. Mass fractionation occurring during the measurements was corrected using the sample-standard bracketing technique, and values are reported as δ 26/24 Mg ≡ ( 26 Mg/ 24 Mg) Sample ( 26 Mg/ 24 Mg) Standard -1 relative to the DSM3 standard (Galy et al., 2003). Similar to the method outlined by Paton et al. (2010), the drift of standard measurements was modelled using smoothed cubic splines. The degree of smoothing was determined by jack-knife cross-validation, and a term was added to standard and sample variances to account for overdispersion such that the mean squared weighted deviation (MSWD) of the standards from the drift model is equal to 1. Uncertainties in this drift model and overdispersion correction were estimated using Monte Carlo simulations. All samples were run in duplicate, and the weighted mean and propagated uncertainty is given. The long-term 2 standard deviations (SD) in δ 26/24 Mg determinations at the National Oceanography Centre, Southampton are 0.07 ‰, similar to other studies (Pogge von Strandmann et al., 2011; Pearce et al., 2012; Pogge von Strandmann

Figure 3 . 1 -

 31 Figure 3.1 -Plot of δ 26/24 Mg vs. δ 25/24 Mg, showing the theoretical mass dependent fractionation line (blue) and how the two sample compositions affected by 48 Ca interferences during MC-ICP-MS measurements were corrected for these interferences.

Figure 3 . 2 -

 32 Figure 3.2 -Aqueous concentrations of Ca, Mg, SO 4 2as well as δ 26/24 Mg and pH of seawater reacting with basaltic glass and crystalline basalt at 250 • C. The errors bars show the 95 % confidence intervals, which are smaller than the symbol size where no error bars are shown.

Figure 3 . 3 -

 33 Figure 3.3 -Scanning electron microscopy images of the solids recovered from the experiment reaction crystalline basalt with seawater at 250 • C, showing a layer of smectite clay minerals covering the surface of the altered basalt as well as precipitated anhydrite grains.

4 2 -

 2 are only removed from the liquid by precipitation into anhydrite. The latter assumption is likely not entirely satisfied, especially during the later stages of the experiments, when Ca is incorporated into one or more of the other observed alteration phases (saponite and zeolites). Therefore, the calculated amounts of Mg release from basalt dissolution (symbols in Figure 3.4a) and Mg incorporation into smectite (Figure 3.4b) are likely minimum estimates. The evolution of Mg dissolution and precipitation during the experiments (symbols in Figure 3.4a,b)

Figure 3 . 4 -

 34 Figure 3.4 -Estimated mass of Mg (a) released from basalt dissolution and (b) precipitated into alteration minerals, as calculated by mass balance (see text for details), (c) modelled aqueous δ 26/24 Mg during the experiments reacting basalt with seawater (dashed curves), (d) measured Mg concentrations in the liquid and (e) relative abundance (mol%) of the Mg 2+ in the fluid samples as calculated with PHREEQC. The errors bars and shaded areas show the 95 % confidence intervals, which are smaller than the symbol size where no error bars are shown.

  The solid alteration phases recovered after termination of the experiments mainly consisted of ubiquitous saponite (trioctahedral smectite) and anhydrite, and trends in the evolution of the liquid composition were similar to those observed at marine hydrothermal systems. During the experiments, Mg was released into the liquid from basalt dissolution, while the precipitation of alteration minerals such as smectite removed Mg from the liquid, leading to a steady decrease in aqueous Mg concentrations in all experiments. A model of Mg isotopic evolution during the experiments, which assumes constant isotopic fractionation during basalt dissolution (i.e. non-stoichiometric dissolution) and simultaneous irreversible (Rayleigh-type) fractionation during precipitation into smectite, can explain the trends observed in experimentally determined δ 26/24 Mg. The retrieved fractionation factor ε 26/24 Smecite-Liquid = 0.78 +0.50 -0.38 ‰ of the model suggests that heavy Mg is preferentially incorporated into the smectite, explaining the drop in liquid δ 26/24 Mg while aqueous Mg concentrations approach zero. However, the experimental data, together with the model, does not allow a unambiguous identification of the fractionation sense during basalt dissolution: The model prediction of ε 26/24 Basalt-Liquid = -0.57 +0.64 -0.96 ‰ indicates only a slight preference of preferential release of heavy Mg during basalt dissolution, which contrasts the observation of Wimpenny et al. (2010) at lower temperatures. Constraining the model to isotopic fractionation during the formation of smectite (i.e. ε

  pure hexagonal hydroxylbastnasite and orthorhombic kozoite (REE(CO 3 )(OH)) were synthesized at hydrothermal conditions and subsequently used as starting material for aqueous dissolution and precipitation experiments. All closed system experiments were performed in air equilibrated aqueous fluids. Reaction progress was followed by measuring pH and REE concentrations at regular intervals. Experiments at 25 • C in the presence of selected concentrations of HCl and NaOH were run for up to 33 days until steady-state pH and REE concentrations were attained. Results indicate that the solu-bility products (K SP ) of the reaction REE(CO 3 )(OH) --→ ←--REE 3+ + CO 3 2 -+ OH -are log(K SP ) = -23.8 ± 0.1, -24.1 ± 0.3, and -22.3 ± 0.2 for Nd-, La-hydroxylbastnasite, and Nd-kozoite, respectively at 25 • C.

Figure 4 . 1 -

 41 Figure 4.1 -SEM images of hydrothermally synthesised (a) Nd-hydroxylbastnasite and (b) Nd-kozoite. The pictures were taken in secondary electron imaging mode.

Figure 4 . 2 -

 42 Figure 4.2 -XRD spectra (relative intensities vs. 2Θ, Co -Kα) of hydrothermally synthesised (a) Nd-hydroxylbastnasite and (b) Nd-kozoite (symbols) compared to synthetic XRD patterns calculated from the structural data of Ni et al. (1993) and Tahara et al. (2007) (blue lines).

Figure 4 . 3 -

 43 Figure 4.3 -Schematic image of the experimental reactor.The mineral was placed in a thermostatically controlled reactor together with the aqueous solution, which was agitated using a suspended stirring bar. Equilibrium with a constant CO 2 partial pressure was achieved by bubbling presaturated air into the reactor with a peristaltic pump. Evaporation was minimised by an air-cooled condenser.

Figure 4 . 4 -

 44 Figure 4.4 -Evolution of pH and aqueous Nd concentrations in dissolution experiment C012A. It can be seen that the dissolution of Nd-hydroxylbastnasite leads to an increase in Nd and pH at the beginning of the experiment, before a steady state is achieved at a later stage. Error bars show one standard deviation of the analytical data.

Figure 4 . 5 -

 45 Figure 4.5 -Evolution of pH and aqueous Nd concentrations in precipitation experiment C013B. Nd-hydroxylbastnasite was added to the reactor in the beginning to achieve a first equilibrium at pH 5.91 ± 0.09. After approximately 13 days (dashed line), a small quantity of NaOH was added to increase the pH and a new steady state was attained, with a lower Nd concentration due to Nd-hydroxylbastnasite precipitation. Where no error bar is visible, analytical uncertainties (one standard deviation) are within the size of the symbols.

Figure 4 . 6 -

 46 Figure 4.6 -Measured pH during the dissolution experiments plotted versus the pH calculated from measured REE concentrations and the initial solution composition and assuming stoichiometric dissolution. Deviations from the 1:1 line suggest an nonstoichiometric release of REE or OH -from the mineral (see text). Error bars show one standard deviation, calculated with a Monte Carlo type method using analytical uncertainties.

Figure 4 .

 4 Figure 4.7 shows modelled Nd concentrations in equilibrium with the Nd endmembers of the two minerals as function of pH, calculated using the solubility products determined in this study and assuming a log(p CO2 ) of -3.30 (as in the experiments).

Figure 4 . 7 -

 47 Figure 4.7 -Plot of aqueous REE concentrations vs. final pH of dissolution and precipitation experiments (symbols) with hydroxylbastnasite and kozoite at 25 • C in equilibrium with log(p CO2 ) = -3.30 ± 0.04. The blue and orange curves show the REE concentrations in equilibrium with Nd-hydroxylbastnasite and Nd-kozoite, respectively, calculated using PHREEQC and the solubility products determined in this study. Where no error bar is visible, analytical uncertainties (one standard deviation) are within the size of the symbols.

Figure 4 . 8 -

 48 Figure 4.8 -Plot of the modelled aqueous F concentration in equilibrium with hydroxylbastnasite and fluorobastnasite (solid line) in aqueous solutions at 25 • C as a function of pH. The exchange reaction whose equilibrium is illustrated by the solid line can be expressed as REEOHCO 3(s) + F ---→ ←--REEFCO 3(s) + OH -. The dashed lines represent the uncertainties (one standard deviation), calculated from the uncertainties in the thermodynamic properties of the minerals. See text for the details of the model calculations.

Figure 5 . 1 -

 51 Figure 5.1 -Schematic illustration of the experimental design used for the coprecipitation experiments reported in this study.

Figure 5 . 2 -

 52 Figure 5.2 -SEM images of the synthetic calcite powder before the experiments (a) and after precipitation experiments CP12 (b), in which no REEs were added, and CP14 (c) where REEs were present in the reactor aqueous solution.

Figure 5 . 3 -

 53 Figure 5.3 -Comparison of the XRD profile of calcite (taken from the RRUFF database, Lafuente et al. (2015)) to that of the solid material recovered after experiment CP13 of the experiments in our study.

Figure 5 . 4 -

 54 Figure 5.4 -Temporal evolution of the pH, aqueous Ca concentration, alkalinity and aqueous La concentration in the reactive fluids the reactor during experiment CP15.

Figure 5 . 5 -

 55 Figure 5.5 -Relationship between the partition coefficient D REE , (a) the steady state aqueous REE concentrations, and (b) the calcite saturation sate Ω in our experiments.The symbols labelled as 'La+Yb' are experiments spiked with both La and Yb, and the REE named in parentheses is the one plotted using the corresponding symbol.

  2.1. While this is only a small conceptual difference, our K D are more closely related to the classic partition coefficients D REE which take into account the aqueous Ca concentrations in addition to the concentrations of REEs in the fluid and solid phases. It should be emphasised, however, that as fluid compositions change other exchange reactions may dominate the incorporation of REEs in calcite (e.g. the incorporation as NaREE(CO 3 ) 2 is not possible in the absence of Na), such that no single exchange model is likely valid at all conditions.

Figure 5 . 6 -

 56 Figure5.6 -Relationship between the effective ionic radii r of the REEs and the equilibrium distribution coefficient of the exchange mechanism involving NaREE(CO 3 ) 2 . The red circles show experimental results from our experiments (La, Yb) and those ofLakshtanov and Stipp (2004) (Eu). The blue curve depicts the best fit to the lattice strain model of[START_REF] Blundy | Prediction of crystal-melt partition coefficients from elastic moduli[END_REF].

Figure 5 . 8 -

 58 Figure5.8 -Plot of the reactive fluid saturation state with respect to calcite, expressed as Ω -1, vs. the calcite growth rate R for REE free experiments (red points). The blue curve shows the best fit to the empirical rate law[START_REF] Morse | Dissolution kinetics of calcium carbonate in sea water; VI, The near-equilibrium dissolution kinetics of calcium carbonate-rich deep sea sediments[END_REF].

Figure 5

 5 Figure 5.10b. Due to the variation of K NaREE(CO3)2 Dwith the identity of the REE in the lattice strain model, a concave REE pattern is predicted for the partition coefficients, regard-

  potential precipitation of REE-carbonate as hydroxylbastnasite in their experiments, as PHREEQC calculations suggest that their final reactive fluids are close to saturation with La-hydroxylbastnasite. Nevertheless, the reason for their relatively high D for the heavy REEs remains unclear. Motivated in part by the application to marine limestone,[START_REF] Zhong | Partitioning of rare earth elements (REEs) between calcite and seawater solutions at 25 • C and 1 atm, and high dissolved REE concentrations[END_REF] performed experiments and modelled REE fractionation into calcite at pH ∼ 8 in seawater. Thermodynamic calculations, however, suggest that their co-precipitation experiments were highly supersaturated with respect to hydroxylbastnasite, so that their partitioning data may be affected by the precipitation of this mineral. As the solubility of hydroxylbastnasite is the lowest for the light REE, their observations of decreasing partition coefficients from light to heavy REEs as well as the correlations between c REE and D REE for the light REEs support this possibility (Figure5.10a). Experimental results of[START_REF] Toyama | Experimental study of rare earth element partitioning between calcite and sodium chloride solution at room temperature and pressure[END_REF] at pH ∼ 8.5 suggest significantly lower partition coefficients, which are likely the result of the high precipitation rates (log(R/(mol/m 2 /s)) ≈ -6.6) considered in their study. Note a negative correlation between precipitation rate and D REE was reported by Yeghicheyan

Figure 5 .

 5 Figure 5.11 -Partition coefficients calculated from experimental K NaREE(CO3)2 D

  de cette thèse était d'étudier expérimentalement le comportement de différents traceurs chimiques pertinents pour les océans et leurs interfaces. Aux chapitres 2 et 3, les signatures isotopiques des réactions hydrothermales du basalte et de l'eau de mer ont été étudiées dans des réacteurs discontinus aux températures de 250 • C et 290 • C. Les données expérimentales montrent que le système Sr a été dominé par la précipitation rapide de l'anhydrite aux premiers phases (< 24 h) des expériences, tandis que la libération de Sr venant de la dissolution du basalte contrôle la systématique du Sr pendant les phases ultérieures. Une légère préférence de l'anhydrite pour le Sr isotopiquement lourd (ε 88/86 Anhydrite-Liquid = 0.033 ± 0.020 ‰) a été mise en évidence en utilisant un modèle de bilan de masse itératif. La dissolution du basalte entraîne l'atteinte rapide des signatures basaltiques de 87 Sr/ 86 Sr dans les fluides, et des changements importants en δ 88/86 Sr dans les expériences avec du basalte cristallin suggèrent que le Sr isotopiquement léger a été libéré de manière préférentielle par dissolution non-stoechiométrique. Les changements isotopiques rapides dans ces expériences suggèrent que les fluides hydrothermaux marins peuvent atteindre des signatures basaltiques 87 Sr/ 86 Sr à des températures allant jusqu'à au moins 250 • C. Par conséquent, ces fluides à température intermédiaire représentent une source potentiellement importante pour le Sr basaltique

  , réduisant le décalage entre le puit marin actuel, défini par le Sr précipité dans les carbonates, et les intrants (flux continentaux et hydrothermaux). Bien que l'on ne sache pas si le cycle du Sr stable des océans est actuellement en état stationnaire (et, en effet, les données d'érosion récente indiquent que ce n'est peut-être pas le cas ; (Vance et al., 2009)) la possibilité de production de fluides à bas δ 88/86 Sr dans les systèmes hydrothermaux marins souligne la nécessité d'une étude plus approfondie de la variabilité en δ 88/86 Sr des fluides hydrothermaux pour contraindre le cycle océanique du Sr stable. Dans les mêmes expériences hydrothermales, le système Mg a été dominé par la formation de la saponite (smectite trioctaédrique), qui a entraîné la disparition presque complète du Mg du fluide. La chute de la concentration en Mg a été accompagnée d'un fractionnement isotopique, et un modèle de bilan de masse itératif indique que le Mg isotopiquement lourd a été préférentiellement incorporé dans les

Chapter 2 Isotopic fractionation during seawater-basalt interaction: Sr

	férents paramètres. Dans le cadre de cette thèse, le comportement de différents traceurs
	élémentaires et isotopiques lors des interactions eau-roche a été étudié expérimentale-
	ment : les chapitres 2 et 3 visent à quantifier les signatures isotopiques de Mg et Sr
	comme traceurs des réactions dans les zones de moyenne à haute température dans les
	systèmes hydrothermaux marins, et les chapitres 4 et 5 caractérisent le comportement
	des terres rares lors des interactions eau-roches en mettant l'accent sur l'application à
	l'utilisation de la précipitation des carbonates dans les milieux marins comme traceur
	des processus marins et d'intrants continentaux vers l'océan (figure 1.1). A version of this chapter will be submitted for publication as "Voigt, M., Pearce, C. R.,
	Baldermann, A., Oelkers, E. H.: Isotopic fractionation during seawater-basalt interaction:
	. Les expériences en labora-
	toire jouent un rôle essentiel dans l'interprétation des signatures de ces traceurs dans
	les échantillons naturels. En simulant expérimentalement un système naturel (ou des
	parties de celui-ci) à petite échelle, il est possible (1) d'identifier les mécanismes, par
	exemple des réactions minéral-fluide, qui se produisent potentiellement dans la nature,
	et (2) de quantifier de manière contrôlée la façon dont les traceurs sont affectés par dif-

Table 2 .1 -Experimental

 2 parameters of the basalt-seawater experiments.

	Experiment T / • C Basalt type	Starting materials / g Duration / days Seawater Basalt
	BSW04	250	Glassy	275.0	27.50	53
	BSW05	250	Crystalline	275.0	27.50	53
	BSW06	290	Glassy	220.0	22.01	92
	BSW07	290	Crystalline	220.0	22.00	93

Table 2 . 2 -

 22 Chemical compositions of the basaltic glass and crystalline basalt used as starting materials of basalt-seawater experiments. Al 2 O 3 Fe 2 O 3 c MgO CaO Na 2 O K 2 O TiO 2 MnO P 2 O 5 Total

	Sample SiO 2 Glass a 48.1	14.6	10.9	9.1	11.8	2.0	0.3	1.6	0.2	0.2	98.8
	Crystalline b 47.9	13.4	12.3	10.0	12.2	1.5	0.3	1.6	0.2	0.2	99.1

a From

[START_REF] Oelkers | The mechanism, rates and consequences of basaltic glass dissolution: I. An experimental study of the dissolution rates of basaltic glass as a function of aqueous Al, Si and oxalic acid concentration at 25 • C and pH= 3 and 11[END_REF]

b From

[START_REF] Gudbrandsson | An experimental study of crystalline basalt dissolution from 2 pH 11 and temperatures from 5 to 75 • C[END_REF]

c Most iron is Fe 2+

Table 2 . 3 -

 23 Strontium content and isotopic composition of the basalt powders used as reactants in the experiments. The uncertainties are the 95 % confidence intervals (∼ 1.96 standard errors).

		Basaltic glass	Crystalline basalt
	Sr / ppm 138	± 20	126	± 20
	87 Sr/ 86 Sr	0.7031929 ± 0.0000028	0.7031887 ± 0.0000026
	δ 88/86 Sr	0.2304	± 0.0075	0.2592	± 0.0075
	HNO

3 to prevent the precipitation of solids and growth of organic material. The pH of the required amount of seawater was re-adjusted to a natural value of ∼ 8.14 by the gradual addition of 25 % ammonia solution (EMD Millipore Suprapur) prior to use in the experiments.

  , attaining values of approximately 42 mmol/kg (the only exception being the experiment with basaltic glass at 290 • C, where 79 mmol/kg Ca was present in the final liquid sample). The greatest increases of Ca coincided with enhanced Mg removal, i.e. an inverse correlation of Ca and Mg trends can be observed. Similarly to Ca, aqueous K concentrations increased during all experiments, reaching values as high as 24 mmol/kg in the 290 • C, basaltic glass experiment and approximately 17 mmol/kg in the other experiments.

• C. Calcium concentrations, after a period of steady or slightly decreasing values at the beginning of the experiments, increased during the later stages in all experimentspH The ambient temperature pH in the basaltic glass experiment only showed a slight decrease at 250 • C before its steady increase to approximately 9.5 at both temperatures (Figures 2.3 and 2.4, Table 2.4 on page 41). Conversely, the pH attained acidic values of 3.7 and 4.9 during the crystalline basalt experiments at 250 • C and 290 • C, respectively, before it increased to approximately 9.2.

  • C, where similar 87 Sr/ 86 Sr ratios were reached within 4 days. In the corresponding 250 • C experiment the largest decrease in 87 Sr/ 86 Sr occurred between days 7 and 21, but values remained above 0.704210 until the end of the experiment. Here, the drop in 87 Sr/ 86 Sr was preceded by a period of slightly decreasing and then increasing values. During the later stages of all experiments, 87 Sr/ 86 Sr increased slightly and the highest value of 0.705116 was

			1 day 250	°C	1 week	1 month
	Basaltic glass				9
	pH				7	pH
	Crystalline Basalt			3 5
	Ca	Mg	SO 4 2-
	Ca, Mg, SO

attained in the 290 • C crystalline basalt experiment. Stable δ 88/86 Sr values decreased from the initial seawater composition (0.38 ‰)

  Table 2.4 on page 41). However, the magnitude of this change varies among the experiments: In basaltic glass experiments, δ 88/86 Sr values similar to that of the basalt (0.23 ‰) were attained. Conversely, values decreased to levels significantly below that of bulk crystalline basalt (0.26 ‰) in both experiments containing this type of basalt and remained below this basalt value for the remainder of the experiments. In the 250 • C crystalline basalt experiment, a further decrease in δ 88/86 Sr occurred after the first week, similar to that seen for 87 Sr/ 86 Sr in this experiment. The δ 88/86 Sr decrease is most pronounced at 290 • C, where a value of -0.06 ‰ was reached. δ 88/86 Sr increased steadily and significantly towards the

crystalline basaltic signature during the further evolution of this experiment, while only small increases are noticeable in the other experiments.

Table 2

 2 ities in the initial seawater during the first day of the experiments(Figures 2.3 and 2.4,

.4). At 250 • C, silica concentrations reached 14 mmol/kg in the basaltic glass experiment before decreasing slightly and 20 mmol/kg in the reaction with crystalline basalt followed by a slight increase, before stabilising at approximately 10 mmol/kg in both experiments. Similar trends were observed at 290 • C, but higher absolute concentrations (approximately 25 mmol/kg) were attained before a final decrease to 10 mmol/kg and 15 mmol/kg in the basaltic glass and crystalline basalt experiments, respectively.

Table 2 . 4 -

 24 Chemical composition of the seawater used as reactant in the experiment and the liquid samples taken during the experiments. Rows labelled "Quenched" show compositions of the liquid in the reactor after terminating the experiment by quenching. The uncertainties (±) designate the 95 % confidence interval (∼ 2 standard errors), while '< LOD' indicates values that were below the detection limits (listed below the table).

	Exp.	Sample	Duration / days	pH	Fluid mass / g	Na	Mg	Si	K	Concentration / (mmol/kg) Ca Sr Fe	Al	Cl	SO4 2 -	87 Sr/ 86 Sr	δ 88/86 Sr / ‰
		Seawater		8.14		474	55.2	< LOD	11.83	10.32	0.0896	0.0401	0.58	597.42	29.05	0.7091729	0.3724
		±		0.07		13	1.5	< LOD	0.27	0.28	0.0025	0.0069	0.11	0.51	0.024	0.0000028	0.0066
		BSW04-01	1.0	7.71	275.0	489	17.04	14.41	12.93	16.82	0.02097	0.2722	1.82	599.89	0.60394	0.7034758	0.2137
		±		0.07	0.2	8	0.28	0.24	0.30	0.46	0.00065	0.0098	0.14	0.49	0.00049	0.0000027	0.0065
		BSW04-02	3.8	8.72	257.4	491	0.559	13.75	13.55	35.8	0.04346	0.00688	4.12	606.46	0.30533	0.7034811	0.2485
		±		0.07	0.3	11	0.012	0.32	0.28	1.5	0.00067	0.00084	0.35	0.52	0.00026	0.0000025	0.0062
	C -basaltic glass 250 •	BSW04-03 ± BSW04-04 ± BSW04-05 ± BSW04-06 ±	6.8 13.9 21.0 33.9	9.09 0.07 9.48 0.07 9.58 0.07 9.65 0.07	234.9 0.3 211.8 0.4 189.5 0.4 168.8 0.5	493 11 500 9 504 11 575 14	0.1058 0.0064 < LOD < LOD < LOD	13.42 0.21 10.45 0.17 9.84 0.17 9.21 0.17	13.67 0.34 13.81 0.27 13.79 0.39 15.85 0.27	39.7 1.7 43.6 1.7 45.8 1.9 42.8 1.4	0.04968 0.00091 0.0633 0.0012 0.0737 0.0010 0.0566 0.0011	0.00077 0.00044 < LOD < LOD < LOD	9.4 1.0 0.319 0.030 14.2 2.7 10.1 1.2	619.00 0.52 620.40 0.51 624.53 0.53 684.61 0.60	0.28670 0.00024 0.29513 0.00024 0.28931 0.00024 0.34537 0.00029	0.7035802 0.0000026 0.7043252 0.0000028 0.7048168 0.0000028 0.7045957 0.0000027	0.2729 0.0064 0.2805 0.0066 0.3110 0.0068 0.2886 0.0083
		BSW04-07	52.9	9.52	147.9	601	< LOD	10.47	16.87	36.9	0.05934	< LOD	5.32	704.12	0.35008	0.7042755	0.2977
		±		0.07	0.5	12		0.17	0.31	1.6	0.00078		0.37	0.60	0.00029	0.0000026	0.0063
		Quenched				513	< LOD	4.248	9.60	46.9	0.0433	< LOD		621.94	4.0028
		±				12		0.069	0.32	2.0	0.00088			0.52	0.0033
		Detection limits (LOD) in mmol/kg were approximately: Mg: 0.026; Si: 0.018; Fe (BSW04 and BSW05): 0.0001; Fe (BSW06 and BSW07): 0.02

• C reached an Fe concentration of 0.27 mmol/kg after one day before dropping to non-detectable levels, while in the corresponding experiment at 290 • C no Fe was detectable in any samples (Figures 2.3 and 2.4, Table 2.4). Higher Fe concentrations were reached in the experiments with crystalline basalt (2.4 mmol/kg and 4.7 mmol/kg at 250 • C and 290 • C, respectively), and concentrations above 1 mmol/kg were sustained in the lower temperature experiment for two weeks.

Table 2 .4 -continued

 2

	Exp.	Sample	Duration / days	pH	Fluid mass / g	Na	Mg	Si	K	Concentration / (mmol/kg) Ca Sr Fe	Al	Cl	SO4 2 -	87 Sr/ 86 Sr	δ 88/86 Sr / ‰
		BSW05-01	1.0	3.74	275.0	484	46.66	18.18	14.68	1.277	0.00742	1.371	4.11	608.01	14.854	0.7074845	0.1938
		±		0.08	0.2	8	0.84	0.38	0.33	0.028	0.00067	0.067	0.35	0.49	0.012	0.0000027	0.0063
		BSW05-02	3.8	4.01	254.4	479	42.89	20.36	15.22	1.433	0.00661	2.04	2.97	603.75	12.448	0.7075882	0.2248
	crystalline basalt	± BSW05-03 ± BSW05-04 ± BSW05-05	6.8 14.0 21.0	0.08 4.83 0.07 5.89 0.07 9.03	0.3 231.7 0.3 211.5 0.4 192.3	11 490 10 480 11 489	0.67 40.40 0.73 20.86 0.27 0.841	0.34 20.61 0.39 17.10 0.28 5.97	0.68 15.77 0.35 16.12 0.30 16.67	0.022 1.632 0.035 10.27 0.15 35.7	0.00067 0.00977 0.00044 0.01957 0.00043 0.0678	0.12 2.38 0.15 1.430 0.067 0.0138	0.22 2.55 0.39 1.60 0.11 3.80	0.51 610.82 0.51 597.53 0.51 608.29	0.010 10.150 0.008 0.90193 0.00076 0.29065	0.0000030 0.7083240 0.0000026 0.7062790 0.0000027 0.7042098	0.0067 0.2544 0.0063 0.1578 0.0066 0.1677
	C -250 •	± BSW05-06 ±	33.9	0.07 9.01 0.07	0.4 172.4 0.5	12 494 10	0.015 0.311 0.015	0.11 10.36 0.19	0.28 16.72 0.47	1.2 37.7 1.6	0.0012 0.0779 0.0015	0.0016 0.0074 0.0052	0.28 6.71 0.62	0.54 620.11 0.53	0.00025 0.26310 0.00022	0.0000027 0.7044848 0.0000027	0.0067 0.1646 0.0066
		BSW05-07	52.9	9.08	151.2	502	0.1723	9.90	17.08	40.6	0.0926	0.0044	4.58	628.93	0.25440	0.7048623	0.1887
		±		0.07	0.5	11	0.0032	0.18	0.46	1.4	0.0018	0.0028	0.34	0.52	0.00020	0.0000027	0.0066
		Quenched				482	< LOD	3.971	16.11	44.5	0.0982	< LOD		621.96	4.0029
		±				12		0.076	0.53	1.6	0.0020			0.52	0.0038

Detection limits (LOD) in mmol/kg were approximately: Mg: 0.026; Si: 0.018; Fe (BSW04 and BSW05): 0.0001; Fe (BSW06 and BSW07): 0.02

Table 2 .4 -continued

 2

	Exp.	Sample	Duration / days	pH	Fluid mass / g	Na	Mg	Si	K	Concentration / (mmol/kg) Ca Sr Fe	Al	Cl	SO4 2 -	87 Sr/ 86 Sr	δ 88/86 Sr / ‰
		BSW06-01	0.8	8.36	219.6	524	6.94	23.7	11.98	28.6	0.0342	< LOD	10.41		0.1806	0.7034329	0.2344
		±		0.07	0.2	45	0.24	1.3	0.53	1.1	0.0019		0.61		0.0035	0.0000025	0.0062
		BSW06-02	3.0	9.20	200.0	541	0.0784	19.7	12.34	42.4	0.0496	< LOD	16.08		0.1242	0.7034302	0.2609
	C -basaltic glass 290 •	± BSW06-03 ± BSW06-04 ± BSW06-05 ±	7.9 16.0 33.8	0.07 9.40 0.07 9.41 0.07 9.50 0.07	0.3 180.2 0.3 160.4 0.4 141.4 0.4	44 545 41 550 43 561 41	0.0036 0.01537 0.00075 0.00796 0.00036 0.00620 0.00034	1.1 13.55 0.76 15.65 0.85 13.85 0.79	0.54 12.59 0.53 13.51 0.65 14.21 0.67	1.8 45.4 1.9 46.3 1.9 44.9 2.0	0.0019 0.0539 0.0020 0.0611 0.0022 0.0674 0.0024	< LOD < LOD < LOD	0.91 15.08 0.91 18.6 1.1 17.7 1.1		0.0024 0.1199 0.0023 0.1233 0.0024 0.1217 0.0023	0.0000029 0.7035378 0.0000026 0.7036699 0.0000028 0.7038923 0.0000025	0.0111 0.2785 0.0063 0.2730 0.0065 0.2858 0.0063
		BSW06-06	54.9	9.56	122.4	582	0.01051	12.42	18.89	62.4	0.1114	< LOD	7.73		0.1409	0.7038094	0.2756
		±		0.07	0.5	38	0.00048	0.65	0.89	3.0	0.0045		0.76		0.0027	0.0000025	0.0061
		BSW06-07	92.0	9.50	103.6	608	0.01998	10.61	23.94	78.8	0.1706	< LOD	10.64		0.1316	0.7041144	0.2604
		±		0.07	0.5	38	0.00077	0.48	1.16	3.5	0.0083		0.94		0.0025	0.0000026	0.0064

Detection limits (LOD) in mmol/kg were approximately: Mg: 0.026; Si: 0.018; Fe (BSW04 and BSW05): 0.0001; Fe (BSW06 and BSW07): 0.02

Table 2 .4 -continued

 2

	Exp.	Sample	Duration / days	pH	Fluid mass / g	Na	Mg	Si	K	Concentration / (mmol/kg) Ca Sr Fe	Al	Cl	SO4 2 -	87 Sr/ 86 Sr	δ 88/86 Sr / ‰
		BSW07-01	0.9	4.93	219.4	512	30.64	25.8	14.32	2.25	0.00252	4.69	8.90		3.951	0.7040288	-0.0568
		±		0.07	0.2	25	1.4	1.7	0.74	0.12	0.00014	0.41	0.51		0.076	0.0000041	0.0089
	C -crystalline basalt 290 •	BSW07-02 ± BSW07-03 ± BSW07-04 ± BSW07-05 ± BSW07-06	3.8 8.7 16.9 34.6 55.7	8.40 0.07 8.92 0.07 9.01 0.07 9.03 0.07 9.13	200.5 0.3 183.3 0.3 165.4 0.4 147.8 0.4 128.1	516 23 515 19 511 22 528 21 543	5.00 0.23 0.552 0.025 0.408 0.018 0.286 0.011 0.2013	9.81 0.48 14.56 0.83 15.6 1.1 16.62 0.89 16.35	15.47 0.72 15.63 0.74 15.83 0.78 16.38 0.71 16.99	29.9 1.2 38.0 1.6 39.3 1.7 41.7 1.5 43.8	0.0369 0.0019 0.0556 0.0020 0.0619 0.0024 0.0742 0.0026 0.0903	0.503 0.027 0.0442 0.0040 0.0330 0.0038 0.0322 0.0040 < LOD	7.05 0.39 9.72 0.39 7.59 0.34 11.47 0.43 7.74		0.1753 0.0034 0.1317 0.0026 0.1241 0.0024 0.0619 0.0012 0.0575	0.7035317 0.0000029 0.7036126 0.0000027 0.7038432 0.0000029 0.7043048 0.0000026 0.7047286	0.0822 0.0069 0.1246 0.0067 0.1207 0.0071 0.1623 0.0064 0.2021
		±		0.07	0.5	22	0.0081	0.88	0.85	1.5	0.0028		0.31		0.0011	0.0000029	0.0068
		BSW07-07	92.8	9.22	109.9	589	0.1267	14.84	18.37	48.6	0.1124	< LOD	11.32		0.1132	0.7051157	0.1945
		±				24	0.0045	0.79	0.83	1.7	0.0038		0.47		0.0022	0.0000026	0.0064

Detection limits (LOD) in mmol/kg were approximately: Mg: 0.026; Si: 0.018; Fe (BSW04 and BSW05): 0.0001; Fe (BSW06 and BSW07): 0.02

  • C experiments (Figure 2.2 on page 30) show that the initially clean and relatively smooth surfaces of the grains were completely covered by micrometre-scale structures resembling honeycombs typical for smectite clays (e.g., Fiore et al., 2001). While the alteration observed by SEM for the 290 • C experiments is very similar, the textures seem slightly more regular for both crystalline basalt experiments (Figure 2.2c,d). In some cases, a distinct layer covering the underlying grains (Figure 2.2e) was observed. It seems plausible that the separation of the two solids results from quenching and the sample preparation.

Apart from the ubiquitous clay minerals, SEM images together with EDS scans reveal that abundant anhydrite formed during all experiments (Figure

2

.2f). Precipitated anhydrite formed crystals ranging from approximately 1 µm to over 200 µm in diameter.

Table 2

 2

	reflection in the XRD spectra (Baldermann et al., 2014), the ferrous saponite contains
	approximately 0.5 to 0.7 atoms per formula unit (a.p.f.u.) octahedral Fe in the exper-
	iment with crystalline basalt, and from 0.8 to almost 1 a.p.f.u. octahedral Fe in the
	basaltic glass experiment (Table 2.5).

.5, Figure 2.6). Furthermore, XRD spectra suggest that an analcime/heulandite type zeolite formed during the two basaltic glass experiments. At 290 • C, plagioclase (close to albitic composition) and chlorite-smectite minerals were formed in the basaltic experiments according to the XRD analyses. FTIR analyses allow the more specific identification of the clays as trioctahedral saponite (Figure 2.7). Based on the position of the d 060

Table 2 . 5 -

 25 Proportions (wt.%) of phases identified by quantitative XRD measurements in the basaltic glass and crystalline basalt used as reactants in the experiments, as well as in the solids recovered from the reactors after the experiments were terminated. The last row shows the total octahedral Fe contents of the smectite, estimated using the position of the d 060 reflection and the relationship found by[START_REF] Baldermann | The Fe-Mg-saponite solid solution series a hydrothermal synthesis study[END_REF].

		Basaltic glass	BSW04 BSW06	Crystalline basalt	BSW05 BSW07
	Amorphous	95	24	15	-	-	-
	Quartz	2	<1	<1	<1	<1	<1
	Olivine	3	<1	2	9	<1	<1
	Anhydrite	-	<1	1	-	4	2
	Zeolite	-	8	5	-	-	-
	Plagioclase	-	-	13	43	53	42
	Pyroxene	-	-	-	47	25	23
	Fe-rich saponite	-	66	55	-	18	33
	VI Fe tot / a.p.f.u.		0.816	0.968		0.488	0.687

  , Mg was transferred from seawater to the saponite and smectite-chlorite clays that formed rapidly during the experiments, leading to the almost complete removal of Mg from the liquid (Figures 2.3 and 2.4). Furthermore, the kinetics of Mg removal and the Ca trends at 250 • C fit are consistent with experiments at 150 and 300 • C reported by

		1 day	1 week 1 month
	/ mmol/kg
	Mg
	(a)
	150 °C, S&B (1979) 300 °C, S&B (1981) 250 °C, this study 290 °C, this study
	/ mmol/kg
	Ca
	(b)
	Initial	10 1	10 2	10 3	10 4
	Seawater	Duration / h
	Seyfried and Bischoff (1979) and Seyfried and Bischoff (1981), as illustrated for the
	crystalline basalt experiments in Figure 2.8. The formation of saponite is consistent
	with the saturation indices for Mg-saponite calculated with PHREEQC, which indic-

ate that the liquid is extremely oversaturated with respect to this phase at all times (Figure

2

.9). The formation of anhydrite removed seawater SO 4 2and Ca, including

  Basalt ) using a set of equations defined by the constraints explained below and in appendix §A.1.The rate of anhydrite precipitation (relative to basalt dissolution) was assumed to be proportional to (Ω Anhydrite -1), where Ω Anhydrite stands for the saturation state of the liquid with respect to anhydrite, which is calculated by PHREEQC at each

	model step (cf. appendix §A.1). The amount of Sr incorporated into anhydrite is
	calculated assuming a constant partitioning coefficient between Sr in anhydrite and
	liquid D Sr ≡ dm Sr Anhydrite / dm Ca Anhydrite / m Sr Liquid /m Ca Liquid for each experiment, where
	m i p denotes the mass of element i in phase p. The Sr isotopic evolution is constrained
	by two fractionation factors defined as
	α	88/86 Anhydrite-Liquid ≡	d 88 Sr Anhydrite / d 86 Sr Anhydrite 88 Sr Liquid / 86 Sr Liquid	(2.1)
	and
	α CrystBasalt-Liquid ≡ 88/86

In this model, the mass of precipitated anhydrite (m Anhydrite ), Sr concentration, 87 Sr/ 86 Sr and δ 88/86 Sr are predicted as functions of the mass of dissolved basalt (m 88 Sr CrystBasalt / 86 Sr CrystBasalt d 88 Sr Liquid / d 86 Sr Liquid (2.2) where A Sr p stands for the amount of the Sr isotope with mass number A in phase p. The use of the differentials (d) signifies that isotopic fractionation is assumed to be irreversible. The latter factor, describing fractionation between Sr released from the dissolving crystalline basalt ('dSr Liquid ') and the isotopic composition of the bulk crystalline basalt ('Sr CrystBasalt '), was introduced because the experimental data show systematically larger δ 88/86 Sr changes in the experiments with crystalline basalt (Figure 2.5

  Model predictions (dashed curves) of anhydrite precipitation as well as aqueous Sr concentrations, 87 Sr/ 86 Sr ratios and stable δ 88/86 Sr values until the first sample was taken (∼24 h) in the experiments conducted in this study. The symbols show the initial seawater and first sample compositions, and the errors bars and grey areas show the 95 % confidence intervals, which are smaller than the symbol size where no error bars are shown. For the crystalline experiment at 250 • C, the δ 88/86 Sr model evolution between 7 and 14 days is shown as well.

	88/86 Anhydrite-liquid = α Anhydrite-Liquid -1 = 0.033 ± 0.020 ‰. This value is 88/86 slightly positive suggesting that anhydrite preferentially incorporates heavier Sr iso-topes. Values determined for the apparent Sr fractionation factors released during crystalline basalt dissolution, ε 88/86 CrystBasalt-Liquid , are 0.21 ± 0.20 ‰ and 0.33 ± 0.03 ‰ at 250 • C and 290 • C, respectively (Figure 2.12). This suggests that lighter Sr isotopes are preferentially released during crystalline basalt dissolution. It seems likely that this is caused by the preferential dissolution of minerals with Sr isotopic compositions lighter Glass Crystalline Seawater 0.0 0.2 0.4 0.6 0.8 1.0 Precipitated anhydrite / g 250 °C 2 4 6 Sr / ppm 0.704 0.705 0.706 0.707 0.708 0.709 87 Sr/ 86 Sr 0.0 0.1 0.2 0.3 δ 8886 Sr / ‰ 0 1 2 3 4 Dissolved basalt / g 0.0 0.2 0.4 0.6 0.8 1.0 Precipitated anhydrite / g 290 °C 2 4 6 Sr / ppm 0.704 0.705 0.706 0.707 0.708 0.709 87 Sr/ 86 Sr 0.0 0.1 0.2 0.3 δ 8886 Sr / ‰ 0 1 2 3 4 Dissolved basalt / g 0.703 0.704 0 2 4 6 8 Sr / ppm 0.703 0.704 0.0 2.5 5.0 7.5 10.0 12.5 Sr / ppm Figure 2.10 -Glass Crystalline Seawater 0.705 0.706 0.707 0.708 0.709 87 Sr/ 86 Sr 250 °C 0.705 0.706 0.707 0.708 0.709 diss. 87 Sr/ 86 Sr 290 Anhydrite precipitation °C Basalt diss. + Basalt Re-dissolution anhydrite precip. of anhydrite?
	than that of the bulk basalt. Figure 2.12 shows that the uncertainties of modelled
	ε	88/86 Anhydrite-liquid and ε	88/86 CrystBasalt-Liquid are inversely correlated, so that if a lower degree of
	apparent fractionation during non-stoichiometric crystalline basalt dissolution in our
	experiments could be inferred from independent constraints, the best fit ε	88/86 Anhydrite-liquid

The best-fit anhydrite-liquid fractionation factor is ε would increase. In addition to the model of the first 24 h, Figure

2

.10 shows that the

Table 3 . 1 -

 31 Magnesium isotopic composition of the seawater and basalt used as reactants in the experiment and of the liquid samples taken during the experiments. Uncertainties (±) designate the 95 % confidence interval (∼ 2 standard errors). See Table2.4 for the complete chemical composition.

	Experiment	Sample	Duration / days	δ 25/24 Mg / ‰ δ 26/24 Mg / ‰ Value ± Value ±
		Basaltic glass		-0.15	0.10 -0.28	0.18
		Crystalline basalt		-0.20	0.10 -0.38	0.18
		Seawater		-0.37	0.10 -0.68	0.18
	250 • C basaltic glass	BSW04-01 BSW04-02 BSW04-03	1.0 3.8 6.8	-0.54 -0.53 -1.67	0.10 -1.02 0.12 -1.02 0.44 a -3.27	0.19 0.22 0.87 a
		BSW05-01	1.0	-0.42	0.06 -0.80	0.12
		BSW05-02	3.8	-0.44	0.06 -0.85	0.13
	250 • C crystalline basalt	BSW05-03 BSW05-04 BSW05-05	6.8 14.0 21.0	-0.48 -0.58 -0.41	0.06 -0.92 0.06 -1.11 0.07 -0.79	0.13 0.13 0.14
		BSW05-06	33.9	-0.47	0.07 -0.89	0.14
		BSW05-07	52.9	-0.64	0.21 a -1.26	0.41 a

a These uncertainties include the extrapolation of 48 Ca interference effects of alteration minerals with honeycomb-like structures typical for smectite clays (e.g.,

  24 Mg Basalt d 26 Mg Liquid / d 24 Mg Liquid

	26/24 Smectite-Liquid ≡	d 26 Mg Smectite / d 24 Mg Smectite 26 Mg Liquid / 24 Mg Liquid	(3.1)
	is assumed in this model. Furthermore, a constant fractionation factor
	α	26/24 Basalt-Liquid ≡

26

Mg Basalt /

  A version of this chapter is published as "Voigt, M., Rodriguez-Blanco, J. D.,[START_REF] Voigt | An experimental study of hydroxylbastnasite solubility in aqueous solutions at 25 •[END_REF]: An experimental study of hydroxylbastnasite solubility in aqueous solutions at 25 • C. Chemical Geology 430: 70-77. doi: 10.1016/j. chemgeo.2016.03.012" and reprinted with permission. Copyright 2016 Elsevier.

• C

Table 4

 4

.2. During the dissolution experiments, stable pH and aqueous

Table 4 . 1 -

 41 Values of equilibrium constants of reactions used in the thermodynamic calculations, as well as the solubility products obtained in this study (cf. section §4.3.3).

	HB: Hydroxylbastnasite
	Reaction	log K	Source
	La 3+ + CO 3 La 3+ + 2 CO 3 Nd 3+ + CO 3 Nd 3+ + 2 CO 3 CO 2(g) + H 2 O --→ ←--H + + HCO 3 + 2 ---→ ←--LaCO 3 -2 ---→ ←--La(CO 3 ) 2 + 2 ---→ ←--NdCO 3 -2 ---→ ←--Nd(CO 3 ) 2 HCO 3 -+ H + --→ ←--CO 2(aq) + H 2 O -HCO 3 2 ----→ ←--H + + CO 3 H 2 O --→ ←--H + + OH -	12.52 8.33 13.59 8.75 -7.8136 -6.3447 -10.3288 -13.9951	Ohta and Kawabe (2000) Ohta and Kawabe (2000) Ohta and Kawabe (2000) Ohta and Kawabe (2000) Johnson et al. (2000) Johnson et al. (2000) Johnson et al. (2000) Johnson et al. (2000)

Table 4 . 2 -

 42 Characteristics of dissolution and precipitation experiments performed in aqueous solutions at 25 • C and in equilibrium with atmospheric CO 2 log(p CO2 ) = -3.30 ± 0.04. pH and REE concentrations are the final values measured after attainment of steady state, and log(K SP ) values were calculated using the procedure explained in the text. Reported uncertainties are one standard deviation, which were calculated from uncertainties in measured parameters using a Monte Carlo method in the case of log(K SP ). The term Nd/La-HB refers to Nd/La-Hydroxylbastnasite. Experiments that begin with the same prefix (e.g. C013B-05 and C013B-19) represent individual samples collected from the same reactor, for which a new equilibrium was established by addition of small amounts of HCl or NaOH and subsequent dissolution or precipitation of the mineral of interest (see section §4.2.4).

	Exp. Number Mineral	pH (final)	REE / (mol/kg)	NaCl / (mol/kg)	HCl / (mol/kg) a	NaOH / (mol/kg) a	I / (mol/L)	log(K SP )
					Dissolution experiments
	C012A	Nd-HB	5.07 ± 0.04 3

  tested several solid solution endmembers for Eu incorporation into calcite, including Eu 2 (CO 3 ) 3 , EuOH(CO 3 ), EuNa(CO 3 ) 2 , EuO x/2 (OH) 3 -x , EuH(CO 3 ) 2 and EuO(CO 3 ) 0.5 , by applying thermodynamic relationships to experimental data obtained at various conditions. Based on this analysis they concluded that the EuH(CO 3 ) 2 endmember is the predominant mode of Eu incorporation at low pH, while the EuO x/2 (OH) 3 -x dominates Eu incorporation at high pH. These various models are tested against the results of new REE co-precipitation experiments in the presence of NaCl bearing aqueous solutions as described below.

  • C. The CO 2 was first bubbled into an Erlenmeyer flask filled with ultrapure water to saturate the gas with water, and then into the reactor fluid, thus limiting fluid evaporation in the reactor. The saturation state of the resulting reactor fluid was confirmed by pH measurements indicating that steady state pH was attained. Moreover, the measured pH values were consistent with PHREEQC predictions of the fluid composition in equilibrium with calcite at the experimental conditions. This solution was filtered through a 0.22 µm polyethersulfone (PES) membrane prior to its use in the experiments.All experiments were run in equilibrium with a CO 2 partial pressure (p CO2 ) of

	Gas outlet
	Condenser (air cooled)	Plug for sampling	and pH electrode		Peristaltic pump
	To
	thermostat	Reactor	From thermostat	CO 2 cylinder
					CaCl 2
					+	Na 2 CO 3
					REEs
		Orbital shaker

  Table5.2), which shows slightly higher La concentrations at steady state, further suggesting that no pure REE carbonate phases precipitated during the experiments. The calculated values of X La and X Yb , the cation molar fractions of La and Yb in the precipitated calcite, for our experiments are listed in Table5.2 and range from approximately 4 × 10 -5 to 1.4 × 10 -4 , indicating that that less than one REE 3+

Table 5 . 1 -

 51 Summary of experimental conditions, measured composition of the inlet fluids and average composition of the reactor fluid after attainment of steady state (SS) in all experiments. Calculated parameters of all experiments during steady state. Ω La-HB designates the La-hydroxylbastnasite saturation state.

	Exp.	pH	c Inlet Ca	/	c SS Ca /	c Inlet Alk /	c SS Alk /	c Inlet La	/	c SS La /	c Inlet Yb /		c SS Yb /	I /	m Seeds	m Precip	Duration	S End /
	ID		(mmol/kg)	(mmol/kg)	(meq/kg)	(meq/kg)	(µmol/kg)	(nmol/kg)	(µmol/kg)	(nmol/kg)	(g/day)	/ g	/ g	/ days	(m 2 /g)
	CP12 6.02 110.3 ± 1.1	13.70 ± 0.85	99.1 ± 1.5 12.24 ± 0.35	-		-	-		-	19.76 ± 0.07	0.994	0.39	3	0.348
	CP13 6.03 109.4 ± 1.4	16.0 ± 1.1	98.6 ± 1.8 12.37 ± 0.30 4.774 ± 0.044 1.48 ± 0.25	-		-	20.03 ± 0.20	1.027	0.35	3	0.356
	CP14 6.03 111.5 ± 1.3	16.3 ± 1.9	99.0 ± 1.5 12.72 ± 0.30	-		-	4.725 ± 0.057	1.98 ± 0.21 20.24 ± 0.08	1.000	0.34	3	0.526
	CP15 6.06	87.10 ± 0.67 15.0 ± 1.0	78.9 ± 1.4 13.26 ± 0.33 4.749 ± 0.043 2.39 ± 0.43	-		-	19.62 ± 0.32	1.000	0.20	3	0.554
	CP16 6.43	92.75 ± 0.72 28.2 ± 5.2	98.6 ± 1.8 31.25 ± 0.59 4.702 ± 0.075 39.6 ± 3.1	3.776 ± 0.053 104	± 15	17.29 ± 0.30	1.038	0.20	7	0.459
	CP19 6.18 139.4 ± 1.4	14.88 ± 0.95 147.2 ± 2.4 17.40 ± 0.33 4.673 ± 0.088 6.3 ± 1.0	-		-	19.05 ± 0.38	0.753	1.29	7	0.626
	CP21 6.32	92.9 ± 1.1	19.0 ± 1.3	99.2 ± 2.0 23.17 ± 0.36 2.396 ± 0.029 7.9 ± 1.3	2.291 ± 0.024 24.0 ± 3.8	8.46 ± 0.57	0.749	0.46	13	0.437
	CP22 6.15	66.8 ± 1.2	13.85 ± 0.81	68.9 ± 1.4 15.23 ± 0.32 4.467 ± 0.070 3.45 ± 0.29	-		-	9.14 ± 0.61	2.012	0.33	13	0.455
	CP23 6.13	65.1 ± 1.3	13.44 ± 0.75	69.3 ± 1.3 14.29 ± 0.32 2.380 ± 0.033 2.04 ± 0.83 2.274 ± 0.028	2.21 ± 0.37	9.24 ± 0.62	1.996	0.38	13	0.477
	CP24 6.16	94.1 ± 1.6	12.15 ± 0.73	99.8 ± 1.9 15.22 ± 0.83 4.698 ± 0.084 4.6 ± 1.5	-		-	16.99 ± 0.82	0.997	0.73	7	0.454
	CP25 6.19	95.1 ± 1.9	11.82 ± 0.76	98.8 ± 2.0 15.9 ± 1.1	4.676 ± 0.077 4.72 ± 0.38	-		-	17.2 ± 1.1	0.998	0.74	7	0.404
	CP26 6.11	86.9 ± 1.7	15.3 ± 1.1	98.5 ± 1.5 13.66 ± 0.94 3.228 ± 0.051 3.26 ± 0.61 2.440 ± 0.029	3.34 ± 0.69 17.10 ± 0.83	1.006	0.82	7	0.539
	CP27 6.22	64.9 ± 1.4	17.6 ± 1.4	69.0 ± 1.5 17.2 ± 1.1	4.535 ± 0.074 17.2 ± 1.3	-		-	17.34 ± 0.70	2.000	0.23	7	0.417
	CP28 6.17	91.94 ± 0.83 13.43 ± 0.17	89.7 ± 1.9 15.27 ± 0.30 5.042 ± 0.099 8.0 ± 3.5	-		-	9.08 ± 0.04	0.997	0.11	11	0.422
	CP31 6.18	67.35 ± 0.45 15.81 ± 0.51	69.8 ± 1.4 16.14 ± 0.39 4.993 ± 0.096 9.5 ± 2.1	-		-	8.51 ± 0.03	1.996	0.06	11	0.449
	CP32 6.07	95.11 ± 0.72 11.63 ± 0.18	96.9 ± 1.5 11.72 ± 0.47	-		-	-		-	13.32 ± 0.23	1.987	0.32	4	0.391
	CP34 6.09	95.11 ± 0.72 13.39 ± 0.18	96.9 ± 1.5 11.96 ± 0.87	-		-	-		-	44.6 ± 1.0	1.005	0.80	4	0.563

  Table 5.1. It should be noted that deviations from steady-state occur due to the slow increase of the surface area, A, of the solids present during each experiment; this variation in surface area is accounted for in the calculation of the calcite precipitation rates R through equations (C.7) and (C.8) in appendix §C.1.

	Comparison of the calcite precipitation rates calculated using either aqueous cal-
	cium concentrations R Ca t or alkalinity measurements R Alk t

  isms (see section §5.2.1). Statistical criteria can then be used to infer the model most consistent with the observations. Resulting values for the exchange reactions involving the NaREE(CO 3 ) 2 , REE 2 X(CO 3 ) 3 and H(REE)(CO 3 ) 2 solid endmembers are shown in Table5.3. It can be seen that the standard deviations for K

	REE2X(CO3)3 D	are signific-
	antly higher than that of the other two exchange models, indicating a worse fit of this
	exchange model to the experimental observations. The K D of the other two examined
	exchange reactions have similar standard errors, but based on spectroscopic evidence
	(Marques Fernandes et al., 2008; Schmidt, 2009) and previous REE co-precipitation ex-
	periments showing a correlation between D Na and aqueous REE concentrations (Zhong

Table 5 . 3 -

 53 Best model fit estimates and standard errors (SE) for equilibrium constants K D for different exchange reactions of REEs between an aqueous solution and calcite calculated for our experimental data. The experimental data of[START_REF] Lakshtanov | Experimental study of europium (III) coprecipitation with calcite[END_REF] was used to calculate the values for NaEu(CO 3 ) 2 and HEu(CO 3 ) 2 .

	Solid REE endmember	K D	SE
	NaLa(CO 3 ) 2	2.399 0.046
	NaYb(CO 3 ) 2	3.266 0.049
	La 2 X(CO 3 ) 3	8.613 0.067
	Yb 2 X(CO 3 ) 3 10.494 0.082
	HLa(CO 3 ) 2	7.443 0.042
	HYb(CO 3 ) 2	8.249 0.050
	NaEu(CO 3 ) 2	3.821 0.041
	HEu(CO 3 ) 2	8.534 0.039
	Due to REE inhibition of calcite growth rates, our datasets exhibit a high degree
	of covariation between aqueous REE concentrations and fluid supersaturation state

with respect to calcite. As aqueous REE strongly inhibit calcite growth rates, it is not possible to distinguish how partition coefficients depend on one or the other without knowledge of the exchange reaction. In principle, experiments at high Ω but low c REE could resolve such ambiguities, however, the difficulty of achieving sufficiently

  .4) with thermodynamic activityconcentrations relationships (cf. appendix §C.3). The form of equation (5.7) suggests that D REE is close to independent of the REE content of the aqueous solution (assuming only trace quantities are present), if all other compositional parameters remain constant. This implies that the other compositional parameters in the equation, namely the aqueous calcium, CO 3 2 -, H + and Na + concentrations, have a major influence on D REE . Due to analytical restrictions and to keep the ionic strength relatively constant, experiments at significantly higher aqueous Na + concentrations were not possible performed in this study, and increasing fluid Ca 2+ without changing c REE will influence D REE through precipitation kinetic effects as described above. Since aqueous sodium concentrations and pH are relatively constant in our experiments, the aqueous calcium and CO 3 2concentrations, and therefore Ω, are likely the primary causes of the variability in the partition coefficient D REE observed in our experiments.

Table 5 . 4 -

 54 Partition coefficients of REE between calcite and different aqueous solutions, calculated assuming incorporation of REEs into the solid as NaREE(CO 3 ) 2 using experimentally determined K

	NaREE(CO3)2
	D

  , and Mg, Ca and SO 4 for Cretaceous seawater are estimated from[START_REF] Horita | Chemical evolution of seawater during the Phanerozoic: Implications from the record of marine evaporites[END_REF].Columns x i show coefficients for the equation D REE = (x 1 c Na ) / c Ca 0.45 + 10 5 x 2 a CO3 2-+ 10 10 x 3 a CO3 2-

	less of the aqueous REE complex used in the modelled exchange reaction. This find-
	ing is consistent with partition coefficients estimated by
					2	which allows the calcula-
	tion of partition coefficients for seawater-like fluids based on an approximation of
	the model developed in this study.
			log D REE		Coefficients for parameterisation
		Present-day seawater	Pore Water	Cretaceous seawater	x 1		x 2	x 3
	La	2.8 ± 0.1	2.4 ± 0.1	2.7 ± 0.1	64 ± 12	3.08	1.15
	Ce	2.99 ± 0.08	2.43 ± 0.08 2.96 ± 0.08	175 ± 25	6.59	3.30
	Pr	3.17 ± 0.06	2.53 ± 0.06 3.18 ± 0.06	395 ± 45	9.75	6.90
	Nd	3.38 ± 0.05	2.73 ± 0.05 3.41 ± 0.05	745 ± 68	10.94	8.49
	Sm	3.44 ± 0.04	2.71 ± 0.04 3.51 ± 0.04 1480 ± 107 16.56	19.45
	Eu	3.43 ± 0.04	2.69 ± 0.04 3.49 ± 0.04	537 ± 37	5.51	7.78
	Gd	3.55 ± 0.04	2.84 ± 0.04 3.59 ± 0.04	556 ± 38	4.48	5.51
	Tb	3.35 ± 0.04	2.55 ± 0.04 3.45 ± 0.04	523 ± 37	5.27	11.00
	Dy	3.17 ± 0.04	2.36 ± 0.04 3.29 ± 0.04	449 ± 33	6.63	14.84
	Ho	3.02 ± 0.05	2.19 ± 0.05 3.16 ± 0.05	360 ± 29	6.48	18.26
	Er	2.81 ± 0.05	1.96 ± 0.05 2.97 ± 0.05	275 ± 24	7.44	24.07
	Tm	2.56 ± 0.06	1.69 ± 0.06 2.74 ± 0.06	204 ± 20	8.74	33.99
	Yb	2.37 ± 0.06	1.51 ± 0.06 2.53 ± 0.06	150 ± 16	11.79	36.42
	Lu	2.20 ± 0.07	1.32 ± 0.07 2.39 ± 0.07	110 ± 13	10.27	42.80

Table 5

 5 Na + /c N a and a Ca 2+ /c Ca are constant and ignoring REE complexes, which are present only in minor amounts in seawater (REECl + , REESO 4

	.4). Combining equation (5.7) with equa-

+ , REEOH 2+ , REEHCO 3 2+ , cf. Schijf et al. (2015)), a simplified equation for the calculation of D REE in seawater-like aqueous solutions is obtained:

Table 5

 5 For the case of an aqueous solution in equilibrium with a gas having a CO 2 partial pressure, p CO2 , a CO3 2-in equation (5.11) can be calculated based on thermodynamic constraints using a CO3 2-= 7.1 × 10 -1910 2pH p CO2 .

			.4 for the individual REEs, which are based the values
	of K	NaREE(CO3)2 D	estimated from our experimental results and their fit to the crystal
	lattice-strain model.

Mg,

Mg) for the range of fractionation found in nature is shown in Figure1.5. The precision necessary to distinguish between both laws is achievable under optimised analytical conditions today[START_REF] Young | The isotope geochemistry and cosmochemistry of magnesium[END_REF], but δ values associated with uncertainties of ∼ 0.1 ‰ are not sufficient to discriminate between them, and for small degrees of fractionation increasingly high precision is required. This thesis will use the above relationships to describe elemental and isotopic fractionation in natural systems of relevance to geochemical cycles (cf. section §1.1).Chapters 2 and 3 describe the results of experiments elucidating the fractionation of stable Sr and Mg isotopes between seawater and alteration minerals under hydrothermal conditions to infer the processes controlling these tracers in marine hydro-

Acknowledgements

I would like to take this opportunity to acknowledge the help of all people who provided their support during the development of this thesis.

Acknowledgements vi

about factors in the marine 87 Sr/ 86 Sr fluxes.

In contrast to 87 Sr/ 86 Sr, stable Sr isotope ratios (δ 88/86 Sr) are affected by both the mixing of sources with different δ 88/86 Sr and isotopic fractionation during precipitation. At steady state, the δ 88/86 Sr composition of the marine Sr input and output fluxes should be equal. However, it has been demonstrated that the δ 88/86 Sr of marine carbonates (the dominant Sr sink in the oceans) is significantly lower than the flux--24-Chapter 2. Basalt-seawater interaction: Sr isotopes Auteur : Martin Voigt Titre : Nouveaux traceurs chimiques pour quantifier les interactions eau-roche dans les systèmes marins Directeur de thèse : Eric H. Oelkers Lieu et date de soutenance : Toulouse, le 27 septembre 2017

Les interactions fluide-roche intervenant dans les systèmes hydrothermaux océaniques ont été étudiées expérimentalement en surveillant les isotopes du Mg et Sr. Les résultats suggèrent que les réactions rapides à températures moyennes pourraient expliquer en partie les divergences identifiées précédemment dans le bilan marin du Sr. De plus, la ré-dissolution de l'anhydrite dans les stades avancés peut expliquer les faibles quantités d'anhydrite trouvée dans les échantillons de basalte océanique altérés. L'évolution du δ 26/24 Mg dans les fluides indique que le Mg isotopiquement lourd a été incorporé préférentiellement dans les minéraux des argiles.

Le fractionnement entre les terres rares et le Ca pendant la précipitation de calcite a été étudié expérimentalement. Ces données suggèrent que l'incorporation du REE 3+ dans la structure de la calcite est probablement équilibrée par l'incorporation de Na + et que les coefficients de partage déduits pour les conditions marines peuvent varier considérablement selon la composition du fluide. Enfin, l'étude de la solubilité de l'hydroxylbastnasite (REE(CO 3 )(OH)), conduite au cours de ce travail, indique que cette phase est moins soluble que les autres carbonates des terres rares connus.

This work was funded by the European Union through the Marie Curie Initial Training

Network CO 2 -REACT. I am very grateful for the opportunity to work as an early career scientist in this network, which gave me the chance to connect with many other scientists and initiate new collaborations. This is especially true for the other fellows in

Abstract

To better quantify the behaviour of rare earth elements (REE) in low temperature natural systems, calcite was precipitated from NaCl-bearing aqueous solutions in the presence of La and Yb using a constant addition technique at pH ∼ 6 and 25

Analytical methods

All pH measurements were performed in situ during the experiments, because of the high p CO2 in the reactor, using an Orion 8103NUWP ROSS Ultra pH electrode. This electrode was rinsed with dilute HCl and ultrapure water before and after each use.

The reactor was shaken at ∼50 rpm until a stable potential was attained, after which mixing was stopped (to avoid the build-up of stirring potentials) and the potential was recorded while CO 2 was continuously bubbled through the reactor solution. The pH electrode was calibrated using Fluka 4.0, 6.9 and 9.2 NIST traceable pH buffer solutions before each use at 25 • C. The precision of these measurements is estimated to be ±0.03 pH units based on replicate analyses of buffers and samples. Alkalinity of inlet and sampled fluids was determined by titration using a Schott Titroline alpha plus titrator, usually within 24 h after sampling to avoid calcite precipitation in the sample vial. Atomic absorption spectrometry (AAS) was used to determine the calcium concentrations in all aqueous solutions. Prior to AAS analysis on the Perkin Elmer AAnalyst 400, the samples were diluted using 0.01 mol/kg HNO 3 and a small amount of lanthanum was added to avoid matrix effects. The detection limit of this method is approximately 2 × 10 -7 mol/kg and their reproducibility was approximately 1 % as indicated by replicate measurements. The standards, ranging from 10 -5 to 10 -4 mol/kg Ca, were prepared from an aqueous 1000 mg/L Merck Certipur Ca solution. The REE contents of inlet and sampled fluids were measured by inductively coupled plasma mass spectrometry (ICP-MS) using a Thermo Fisher Element XR spectrometer. The samples were diluted by a factor of 60 with bi-distilled 0.37 mol/kg HNO 3 prior to analysis to reduce matrix effects, resulting in a total solute concentration of approximately 100 ppm. Quantification limits, determined by analysis of blanks that were subjected to the same experimental and analytical procedures as actual samples, are Eu [START_REF] Yeghicheyan | Etude expérimentale du partage des terres rares entre carbonates de calcium et solutions aqueuses: Influence de la cinétique de cristallisation et de la spéciation des terres rares en solution[END_REF] Figure 5.7 -Relationship between the logarithm of the partition coefficient D REE and the logarithmic calcite precipitation rate. The symbols represent our experimental data (see Figure 5.5 for a legend). The dark and light grey areas show the range of values obtained by [START_REF] Zhong | Partitioning of rare earth elements (REEs) between calcite and seawater solutions at 25 • C and 1 atm, and high dissolved REE concentrations[END_REF] for a mix of REEs and [START_REF] Lakshtanov | Experimental study of europium (III) coprecipitation with calcite[END_REF] for Eu, respectively, while the orange line shows a best fit equation determined by [START_REF] Yeghicheyan | Etude expérimentale du partage des terres rares entre carbonates de calcium et solutions aqueuses: Influence de la cinétique de cristallisation et de la spéciation des terres rares en solution[END_REF] for the correlation they observed using Eu.

processes such as growth entrapment do not occur [START_REF] Watson | A conceptual model for near-surface kinetic controls on the traceelement and stable isotope composition of abiogenic calcite crystals[END_REF][START_REF] Depaolo | Surface kinetic model for isotopic and trace element fractionation during precipitation of calcite from aqueous solutions[END_REF][START_REF] Thien | A unified approach to model uptake kinetics of trace elements in complex aqueous-solid solution systems[END_REF]. However, correlations between precipitation rates and cation partitioning is observable for rates as low as ∼10 -8 mol/m 2 /s for Mg and Ni [START_REF] Lakshtanov | Experimental study of nickel (II) interaction with calcite: Adsorption and coprecipitation[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF], indicating that this observation is not generally valid for trace cation incorporation into calcite.

Inhibition of calcite growth by aqueous REE

To quantify the effect of aqueous REE concentration on calcite growth, we adopt the empirical rate law [START_REF] Morse | Dissolution kinetics of calcium carbonate in sea water; VI, The near-equilibrium dissolution kinetics of calcium carbonate-rich deep sea sediments[END_REF])

Chapter 6

General conclusions

The goal of this thesis was to experimentally investigate the behaviour of different chemical tracers relevant to the oceans and their interfaces. In chapters 2 and 3, the , but also during quenching of the liquid. This suggests that anhydrite abundances in MORB drill cores might be affected the same process, a potential cause for the discrepancy between degree of alteration observed in altered MORB drill cores and the radiogenic Sr budget of the oceans (Teagle et al., 1998b). Taken together, intermediate temperature hydrothermal fluids could help to explain the imbalances in Appendix A

Appendix to Chapter 2 A.1 Model details

The rate of anhydrite precipitation is constrained in the model using the relationship

where Ω Anhydrite stands for the saturation state of the liquid with respect to anhydrite, and k is a model parameter. This corresponds to a simple form of the empirical rate law [START_REF] Morse | Dissolution kinetics of calcium carbonate in sea water; VI, The near-equilibrium dissolution kinetics of calcium carbonate-rich deep sea sediments[END_REF] under the approximations that dm Basalt / dt does not vary significantly with liquid composition and that basalt dissolution and anhydrite precipitation have the same relative dependency on temperature during the short initial heating period.

The anhydrite saturation state is calculated from the aqueous solution composition using PHREEQC and the LLNL database at the experimental temperature at each calculation step in the model (cf. section §2.2.4). For this PHREEQC calculation, the aqueous solution composition, other than Ca, Sr, and SO Basalt-Liquid (expressed here as ε 26/24 = α 26/24 -1) are calculated based on the minimum inverse variance weighted squared errors using the Nelder-Mead method [START_REF] Nelder | A simplex method for function minimization[END_REF]. As mass balance constraints require inclusion of 25 Mg into the equations, α 25/24 are calculated internally based on α 26/24 and the kinetic mass-dependent fractionation law [START_REF] Young | Kinetic and equilibrium massdependent isotope fractionation laws in nature and their geochemical and cosmochemical significance[END_REF], which was used as opposed to the equilibrium mass fractionation law due to the relatively fast kinetics of the involved processes.

However, due to the small difference between the two fractionation laws, the choice does not significantly affect the model results. The mean covariance between measured δ 25/24 Mg and δ 26/24 Mg, 0.81, was included in the uncertainty propagation calculations.

B.2 Irreversible isotopic fractionation in a closed system

Isotopic fractionation occurring during a reaction where the product is immediately isolated from the reactant can be described by

where R R and R P,i designate the isotopic ratios of the reactant and of an increment of the product during the reaction, respectively. The reaction progress is commonly Appendix B. Appendix to Chapter 3 expressed as fractional yield, defined as f ≡ m P /m R,0 , where m P and m R,0 are the masses of the product and of the reactant before the reaction, respectively. Bothner-By and [START_REF] Bothner-By | Fractionation of the carbon isotopes in decarboxylation reactions. III. The relative rates of decomposition of carboxyl-C 12 and -C 13 mesitoic acids[END_REF] showed that the isotopic composition of the total accumulated product follows the relationship

where R P, Total and R 0 R designate the isotopic ratios of the accumulated product. Substituting R X = (δX + 1)R Standard and solving for δ P,Total gives

3)

The difference δ P,Total -δ R,0 is given by

Appendix C

Appendix to Chapter 5

C.1 Calculation of partition coefficients and precipitation rates

The relative REE contents of the precipitated calcite are calculated in this study from the composition of the sampled reactive aqueous fluids and mass balance constraints.

Assuming steady-state conditions, the molar ratio of the molar of REEs and Ca in the precipitated calcite can be calculated from

where c stands for the aqueous concentration of the subscripted element in the inlet fluid ('Inlet') or at steady state ('SS') in the reactive fluid, I refers to the injection rate of the inlet fluids, and the factor of two is introduced because two separate aqueous inlet fluids were injected into the reactor at equal pump rates. Using this expression together with equation (5.1), the Henderson-Kracek partition coefficient (D REE ) for the REEs can be calculated from

and a corresponding equation can be used to calculate D ω .

Since the REEs are only incorporated into the precipitating calcite in trace amounts, the surface area normalised molar calcite precipitation rate (or growth rate), R, at time t can be calculated from the aqueous solution Ca concentrations once steady-state is assuming constant c SS Ca . Because the calcite precipitation rate at time t is defined as

where m Calcite t designates the mass of calcite in the reactor at time t, and S t refers to the specific surface of the calcite at time t. As the rate at which m Calcite t changes over time can be approximated as

where M Calcite refers to the molar mass of calcite, the amount of calcite precipitated from a time t until the end of the experiment t End is given by

Assuming that the specific surface area changes from the initial value S 0 to the final value S End proportionally with the increase in calcite mass, it can be approximated as

where m Seeds is the initial mass of calcite seeds present in the reactor, which allows the calculation of R Ca t . Furthermore, the rates can be calculated independently using the equivalent equations and alkalinity measurements according to

C.2 Theoretical demonstration of attainment of steady state

As described in section §5.3.1, the reactors in our study contained an initial mass of calcite-saturated solution, but this mass gradually increased as fluid is injected into the reactor and calcite precipitated. This experimental method has the advantage of being able to start the experiment with a small volume of aqueous solution in the reactor, leading to a rapid attainment of steady-state. Taking account of the reactor design, the rate of calcite growth can be computed using

where A refers to the calcite surface area, t signifies the time, and n Inlet Ca , n t Ca and n 0 Ca are the total molar amounts of calcium in the inlet reservoir fluid, in the reactor fluid at time t and at the beginning of the experiment, respectively. For a constant pump injection rate, I, the total mass of injected fluid equals It, and it follows that

where c Ca stands for the concentration of calcium in the corresponding aqueous fluid and m 0 Fluid is the initial fluid mass in the reactor. The factor of two is introduced because two separate aqueous fluids were pumped into the reactor at equal pump rates, such that the volume in the reactor increases at twice the pump rate. It can be seen that for t → ∞ (after the initial phase of the experiment), the second term on the right hand side of this equation becomes negligible and the equation becomes identical to equation (2) in [START_REF] Zhong | Calcite precipitation in seawater using a constant addition technique: A new overall reaction kinetic expression[END_REF] so that their theoretical argumentation for the attainment of steady-state can also be applied to our experimental design.

C.3 Relationship between D REE and K D

The relationship between the partition coefficient D REE , which is defined by equation (5.1), and the equilibrium constant K

, defined by equation (5.4), can be derived by combining the relationships The fluid-rock interactions occurring in hydrothermal systems at or near mid-oceanic ridges (MOR) were studied experimentally while monitoring the Mg and Sr isotopic evolution. The results suggest that fast intermediate-temperature reactions could partly explain previously identified discrepancies in the marine 87 Sr/ 86 Sr budget. Furthermore, late-stage anhydrite re-dissolution caused by fluid reduction and temperature decreases in our experiments represent a potential explanation for the low amounts of anhydrite found in altered oceanic basalt samples. The fluid δ 26/24 Mg indicate that isotopically heavy Mg was preferentially incorporated into the clays.

Towards the interpretation of rare earth element (REE) patterns in marine calcite, the fractionation between the REEs and Ca during the precipitation of calcite was studied experimentally. These data suggest that the incorporation of REE 3+ ions into the calcite structure was likely charge balanced by incorporation of Na + , and that inferred partition coefficients for marine conditions can vary substantially depending on the fluid composition. Furthermore, the solubility of hydroxylbastnasite (REE(CO 3 )(OH)) was determined, indicating that this phase is less soluble than other known REE carbonates.