Slags plays a significant role at high temperature processes. The estimation of the slag viscosity is vital for the safe run of e.g. entrained flow gasifiers. One opportunity of determination is rotational viscometry. This technique is disadvantageous in view of elevated temperatures, applied materials and the necessary time. Additionally, the viscosity can be predicted by the help of viscosity models, where viscosity is a function of slag composition and temperature. Due to changing slag properties within the technical processes, the calculated viscosities can hugely differ from measured ones. In this work, the viscosities of 42 slags where measured up to 100 Pa s and temperatures up to 1700 °C. Oxidizing and reducing conditions were applied. Additionally, selected slag samples were quenched at defined temperatures to qualitatively and quantitatively determine the formed minerals by X-ray diffraction (XRD). Differential temperature analysis (DTA) was applied to find the onset of crystallization for the complementation of investigations. The Einstein-Roscoe equation was chosen to improve the classic viscosity models. Reducing atmosphere decreased viscosity and the number of formed minerals was increased. Slags show a shear-thinning behavior above ca. 10 vol.-% of solid mineral matter. Also, Newtonian behavior was observed up to 60 vol.-%. To overcome problems with the kinetic cooling behavior of the slags, a viscosity approximation method was applied afterwards. This can result in optimized viscosity predictions when several preconditions are fulfilled.

La Terre contient une quantité significative d’eau et son manteau est très oxydé par rapport aux conditions canoniques de la nébuleuse solaire, ce qui est contradictoire avec l’existence de son noyau métallique et sa position dans le Système solaire. Ceci implique que l’état rédox de la Terre ait augmenté au début de son histoire. Aujourd’hui, de nombreuses études suggèrent que cette évolution se soit faite à travers une accrétion hétérogène. Ainsi les premières briques élémentaires de notre planète seraient constituées de matériel très réduit et une grande partie de la différenciation précoce (extraction du noyau et différenciation silicatée) se seraient donc déroulées en conditions très réductrices (entre IW-5.5 et IW-2). L’objectif de cette thèse est de mesurer l’impact de ces conditions sur le comportement des terres rares (REE) et des éléments fortement chargés (HSFE), et de modéliser leur répartition dans les différents réservoirs lors de la différenciation précoce de la Terre. Nous réalisons une soixantaine d’expériences de fusion – cristallisation à l’équilibre de matériel chondritique à basse (5 GPa) et haute (26 GPa) pression, dans une gamme de conditions rédox allant de IW (tampon fer – wüstite) à IW-8. Afin de caractériser le paramètre fO 2 dans ces conditions extrêmes, nous développons un formalisme thermodynamique adapté, basé sur l’équilibre Si-SiO 2 . En analysant les différentes phases à l’équilibre dans les différents échantillons, nous calculons et établissons la première banque de données de partage cristal (enstatite, bridgmanite = pérovskite silicatée, majorite) – liquide silicaté, métal-silicate et sulfure-silicate pour les HFSE et les REE en conditions très réductrices. Grâce aux données enstatite – liquide nous développons un proxy de la fO 2 , basé sur le rapport D(Cr)/D(V) et grâce auquel nous mesurons la fO 2 de chondres de type I comme étant similaires aux conditions canoniques de la nébuleuse (IW-7). Nos données de partage métal – silicate prouvent que l’extraction du noyau terrestre n’est pas à l’origine d’un fractionnement des terres rares. Au contraire, en mesurant pour la première fois le spectre XANES du Nb 2+ et du Ta 3+ dans des verres silicatés à des teneurs de l’ordre du ppm, nous prouvons que le comportement de Nb et Ta est contrôlé par la fO 2 . En intégrant nos données de partage à un modèle d’accrétion hétérogène nous montrons que la signature sous-chondritique en Nb/Ta de la Terre silicatée peut être le résultat de l’accrétion d’un matériel chondritique évoluant avec le temps combinée à l’extraction du noyau en conditions réductrices, ce qui réfute l’hypothèse d’une Terre se formant à partir d’un matériel oxydé. Nos expériences de haute pression montrent que le partage des REE et des HFSE dans la majorite et la bridgmanite est très sensible à la fO 2. De plus, le processus de dismutation du fer, invoqué pour expliquer l’augmentation de la fO 2 du manteau lors de la cristallisation de l’océan magmatique, ne semble pas être un mécanisme efficace en-dessous de IW. Enfin, nos données montrent que Ti, V, Cr, Mn, Nb et Ta sont chalcophiles en conditions très réductrices. L’extraction précoce d’un liquide sulfuré dans ces conditions a donc pu modifier les rapports élémentaires supposés chondritiques dans la Terre silicatée. L’extraction d’une importante quantité de FeS pourrait aussi être à l’origine d’un découplage Zr/Hf. / The Earth contains significant amounts of water and its mantle is highly oxidized compared to the solar nebula canonical conditions, which is inconsistent with the existence of its metallic core and its location in the Solar System. This implies the redox state of the Earth has increased during its early history as suggested in heterogeneous accretion models. Thus, the first building blocks of our planet would have been made of highly reduced material, and the early Earth’s differentiation (core extraction and silicate differentiation) would have taken place under highly reducing conditions (between IW-5.5 and IW-2). The aim of this thesis is to measure the impact of these conditions on rare earth elements (REE) and high field strength elements (HFSE) behavior, and model their distribution into the main reservoirs formed early in Earth’s history. We run about sixteen melting – crystallization experiments, starting from chondritic material and equilibrating it at low (5 GPa) and high (26 GPa) pressure, spanning a redox range going from IW (iron – wüstite buffer) to IW-8. In order to characterize the fO 2 parameter in these extreme conditions, we develop an adapted thermodynamic formalism, based on Si-SiO 2 equilibrium. Analyzing the various equilibrated phases within our experimental samples, we calculate and propose the first crystal (enstatite, bridgmanite = Mg-perovskite, majorite) – silicate liquid, metal – silicate, sulfide – silicate partition coefficients database for HFSE and REE under highly reducing conditions. Using our enstatite-liquid data we develop a fO 2 proxy based on D(Cr)/D(V) ratio and we measure type I chondrule fO 2 as being similar to canonical nebular conditions (IW-7). Our metal-silicate partitioning data prove that Earth core extraction is not responsible for REE fractionation. On the contrary, recording for the first time Nb 2+ and Ta 3+ XANES spectra in silicate glasses and at ppm level concentrations, we prove that Nb and Ta behavior is mainly controlled by fO 2 . Using our partitioning data in a heterogeneous accretion model, we show that sub-chondritic Nb/Ta signature of the silicate Earth (14 ± 0.3) can be the result of the accretion of chondritic material changing with time, combined with the progressive extraction of the core in reducing conditions. This refutes the hypothesis of an oxidized material building the Earth. Our high-pressure experiments show that REE and HFSE partitioning in majorite and bridgmanite is very sensitive to fO 2 . Moreover, iron dismutation process, invoked to explain mantle fO 2 increase during magma ocean crystallization, does not seem to be an efficient mechanism below IW. Finally, our data show that Ti, V, Cr, Mn, Nb and Ta are chalcophiles under highly reducing conditions. Consequently, early extraction of a sulfide melt at an early and reduced stage could have modified chondritic elementary ratios in the silicate Earth. Extraction of a substantial amount of FeS may also cause a Zr/Hf decoupling.

Slags plays a significant role at high temperature processes. The estimation of the slag viscosity is vital for the safe run of e.g. entrained flow gasifiers. One opportunity of determination is rotational viscometry. This technique is disadvantageous in view of elevated temperatures, applied materials and the necessary time. Additionally, the viscosity can be predicted by the help of viscosity models, where viscosity is a function of slag composition and temperature. Due to changing slag properties within the technical processes, the calculated viscosities can hugely differ from measured ones. In this work, the viscosities of 42 slags where measured up to 100 Pa s and temperatures up to 1700 °C. Oxidizing and reducing conditions were applied. Additionally, selected slag samples were quenched at defined temperatures to qualitatively and quantitatively determine the formed minerals by X-ray diffraction (XRD). Differential temperature analysis (DTA) was applied to find the onset of crystallization for the complementation of investigations. The Einstein-Roscoe equation was chosen to improve the classic viscosity models. Reducing atmosphere decreased viscosity and the number of formed minerals was increased. Slags show a shear-thinning behavior above ca. 10 vol.-% of solid mineral matter. Also, Newtonian behavior was observed up to 60 vol.-%. To overcome problems with the kinetic cooling behavior of the slags, a viscosity approximation method was applied afterwards. This can result in optimized viscosity predictions when several preconditions are fulfilled.:List of Tables ............................................................................................................ vi List of Figures ........................................................................................................ viii Symbols and Abbreviations .................................................................................. xviii 1. Introduction and Aim ....................................................................................... 1 2. General Overview of Slag ............................................................................... 2 2.1 Viscosity ...................................................................................................... 2 2.1.1 Viscosity Introduction ........................................................................... 2 2.1.2 Flow behavior of fluids ......................................................................... 3 2.2 Slag Definition and Phase Diagrams ........................................................... 4 2.3 Solid Slag Structure .................................................................................... 5 2.4 Liquid Slag Structure ................................................................................. 10 2.5 Basicity and B/A-ratio ................................................................................ 11 2.6 Slag Components...................................................................................... 13 2.6.1 Silicon dioxide .................................................................................... 13 2.6.2 Aluminum oxide ................................................................................. 13 2.6.3 Calcium oxide .................................................................................... 15 2.6.4 Iron oxide ........................................................................................... 16 2.6.5 Magnesium Oxide .............................................................................. 18 2.6.6 Potassium Oxide ................................................................................ 19 2.6.7 Sodium Oxide .................................................................................... 20 2.6.8 Titanium Oxide ................................................................................... 21 2.6.9 Phosphorous ...................................................................................... 22 2.6.10 Sulfur .............................................................................................. 22 2.7 Summary of Last Chapters ........................................................................ 23 3. Slag Viscosity Toolbox .................................................................................. 25 3.1 Slag Viscosity Predictor............................................................................. 25 3.2 Slag Viscosity Database............................................................................ 26 3.3 Prediction Quality of Viscosity Models ....................................................... 27 4. Classic Slag Viscosity Modelling ................................................................... 30 4.1 Selected Classic Viscosity Models ............................................................ 31 4.1.1 S2 ....................................................................................................... 32 4.1.2 Watt-Fereday ..................................................................................... 32 4.1.3 Bomkamp ........................................................................................... 32 4.1.4 Shaw .................................................................................................. 32 4.1.5 Lakatos .............................................................................................. 33 4.1.6 Urbain ................................................................................................ 33 4.1.7 Riboud ............................................................................................... 33 4.1.8 Streeter .............................................................................................. 34 4.1.9 Kalmanovitch-Frank ........................................................................... 34 4.1.10 BBHLW .......................................................................................... 34 4.1.11 Duchesne ....................................................................................... 34 4.1.12 ANNliq ............................................................................................ 35 4.2 Need of Improvement in Viscosity Literature ............................................. 35 4.3 Summary of Last Chapters ........................................................................ 36 5. Advanced Slag Viscosity Modelling .............................................................. 37 5.1 Crystallization ............................................................................................ 37 5.1.1 Nucleation .......................................................................................... 38 5.1.2 Crystallization Rate ............................................................................ 39 5.1.3 Crystallization Measurement Methods ............................................... 39 5.2 Slag Properties Changes During Crystallization ........................................ 40 5.2.1 Slag Density ....................................................................................... 40 5.2.2 Solid Volume Fraction ........................................................................ 46 5.2.3 Estimation of Slag Composition During Cooling ................................. 46 5.3 Viscosity Depending on Particles and Shear Rate..................................... 47 5.3.1 Einstein-Roscoe Equation .................................................................. 48 5.3.2 Improved Modelling Approach by Modified Einstein-Roscoe .............. 49 5.4 Summary of Last Chapters ........................................................................ 50 6. Experimental Procedures ............................................................................. 52 6.1 Viscosity Measurements ........................................................................... 52 6.1.1 Estimating Parameter Ranges of Viscosity Measurements ................ 53 6.1.2 Viscosity Measurement Procedure ..................................................... 54 6.2 Thermal Analysis of Slags ......................................................................... 55 6.2.1 Experimental Conditions of DTA ........................................................ 55 6.3 Phase Determination ................................................................................. 55 6.3.1 Quench Experiment Processing ......................................................... 56 6.3.2 Phase Determination on XRD Results ............................................... 56 6.4 Summary of Last Chapters ........................................................................ 57 7. Results and Discussion ................................................................................ 58 7.1 Selected Slag Samples ............................................................................. 58 7.1.1 Slag Sample Composition Before Viscosity Measurements ............... 58 7.1.2 Slag Sample Composition After Viscosity Measurements .................. 59 7.2 General Results of Viscosity Measurements ............................................. 60 7.2.1 Viscosity under Air Atmosphere ......................................................... 63 7.2.2 Viscosity under Reducing Atmospheres ............................................. 65 7.2.3 Viscosity under Constant Partial Oxygen Pressure ............................ 66 7.2.4 Summary of Last Chapter .................................................................. 68 7.3 Mineral Formation ..................................................................................... 69 7.3.1 General Results on Primarily Mineral Formation ................................ 69 7.3.2 Influences on Primarily Mineral Formation ......................................... 70 7.3.3 Mineral Formation over Wide Temperature Ranges ........................... 71 7.3.4 Summary of Last Chapter .................................................................. 77 7.4 Results Obtained by DTA .......................................................................... 78 7.4.1 Comparing Results obtained by DTA and Quenching ........................ 80 7.4.2 Summary of Last Chapter .................................................................. 82 7.5 Shear Rate Influence on Slag Viscosity ..................................................... 82 7.5.1 Shear Rate Influence under Oxidizing Atmospheres .......................... 83 7.5.2 Shear Rate Influence under Reducing Atmospheres .......................... 87 7.5.3 Shear Rate Influence under Constant Atmospheres .......................... 91 7.5.4 Summary of chapter ........................................................................... 92 7.6 Atmospheric Influence on Viscosity ........................................................... 93 7.6.1 Summary of Last Chapter .................................................................. 95 7.7 Cooling Rate Influence on Slag Viscosity .................................................. 95 7.7.1 Summary of Last Chapter .................................................................. 97 8. Advanced Viscosity Modelling Approach ...................................................... 99 8.1 Prediction Quality of Classical Viscosity Models ........................................ 99 8.1.1 Selecting the Best Viscosity Model for Newtonian Flow ..................... 99 8.1.2 Summary of Last Chapter ................................................................ 103 8.2 Predicting Liquidus Temperature ............................................................. 103 8.2.1 Comparing Liquidus Calculations and Quenching Experiments ....... 103 8.2.2 Comparing DTA Results and Liquidus Calculations ......................... 105 8.2.3 Summary of Last Chapter ................................................................ 107 8.3 Predicting Liquid Slag Composition ......................................................... 108 8.3.1 Results of Slag Composition Calculations at Oxidizing Conditions ... 108 8.3.2 Results of Slag Composition Calculations at Reducing Conditions ... 110 8.3.3 Summary of Last Chapter ................................................................ 111 8.4 Modelling Approach ................................................................................ 112 8.4.1 Development of Datasets for Advanced Viscosity Modeling ............. 113 8.4.2 Summary of Last Chapter ................................................................ 116 8.5 Results of Advanced Slag Viscosity Modelling Approach ........................ 116 8.5.1 Summary of Last Chapter ................................................................ 121 9. Summary .................................................................................................... 123 10. Appendix: Information on Classic Viscosity Modelling ................................. 126 10.1 Backgrounds of Applied Viscosity Models............................................ 126 10.2 Viscosity Model of the BCURA (S2) ..................................................... 129 10.3 Watt-Fereday ....................................................................................... 130 10.4 Bomkamp ............................................................................................ 130 10.5 Shaw ................................................................................................... 131 10.6 Lakatos Model ..................................................................................... 132 10.7 Urbain Model ....................................................................................... 133 10.8 Riboud Model ...................................................................................... 134 10.9 Streeter Model ..................................................................................... 136 10.10 Kalmanovitch-Frank Model .................................................................. 137 10.11 BBHLW Model ..................................................................................... 137 10.12 Duchesne Model .................................................................................. 139 10.13 ANNliq Model ...................................................................................... 141 11. Appendix: Settings of Equilibrium Calculations ........................................... 143 12. Appendix: Parameters of Einstein-Roscoe Equation ................................... 153 13. Appendix: Ash and Slag Sample Preparation ............................................. 155 14. Appendix: Experimental Procedures: Viscometer ....................................... 159 14.1 General Viscometer Description .......................................................... 159 14.2 Temperature Calibration ...................................................................... 160 14.3 Viscometer Calibration ......................................................................... 160 14.4 Accuracy and Reproducibility of HT-Viscosity Measurements .............. 161 14.5 Influence of Inductive Heating .............................................................. 163 14.6 Influence of Measurement System Materials ....................................... 164 15. Appendix: Experimental Procedures: Quenching Furnace .......................... 167 16. Appendix: Slag Sample Parameters and Composition ................................ 168 17. Appendix: Slag Viscosity Measurements Results ....................................... 175 18. Appendix: Viscosities at Different Cooling Rates ........................................ 182 19. Appendix: Slag Viscosity Modelling: AALE Calculations ............................. 187 20. Appendix: Advanced Viscosity Modelling: a-factors .................................... 193 21. Appendix: Slag Mineral Phase Investigations and Modelling ...................... 197 22. Appendix: Results of DTA Measurements on Slags .................................... 207 23. Appendix: Advanced Slag Viscosity Modelling Approach ............................ 211 References ........................................................................................................... 228