Research Collection · 2020. 3. 26. · VI–3. Results 160 VI–3.1. Mo concentrations 160 VI–3.2. Mo isotope data and δ98/95Mo values 160 VI–4. Discussion 166 VI–4.1. Stable

Research Collection

Doctoral Thesis

Stable isotope behaviour during planetary differentiationImplications of mass dependent Fe, Si and Mo isotopefractionation between metal and silicate liquids

Author(s): Hin, Remco Christiaan

Publication Date: 2012

Permanent Link: https://doi.org/10.3929/ethz-a-007621154

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DISS. ETH NO. 20825

STABLE ISOTOPE BEHAVIOUR DURING

PLANETARY DIFFERENTIATION

Implications of mass dependent Fe, Si and Mo isotope fractionation between

metal and silicate liquids

A dissertation submitted to

ETH ZURICH

for the degree of

Doctor of Sciences

presented by

Remco Christiaan Hin

Master of Science in Geosciences of Basins and Lithosphere,

Vrije Universiteit Amsterdam

born on December 1, 1983

citizen of

The Netherlands

accepted on the recommendation of

Prof. Dr. Max W. Schmidt

Prof. Dr. Bernard Bourdon

Prof. Dr. Tim Elliott

2012

(Panta rhei, ouden menei)

“And now that I have unfolded my sail at open sea and go with the wind –

there is nothing in this whole world that remains.

Everything flows, each thing shapes and passes by.

Time too passes by in a continuous motion

like a river that cannot stop its stream just as a running hour cannot stand still;

as water pushes water forward while being pushed forward and pushing forward itself,

as such time runs forward and chases itself and renews itself;

what has been, is now past, and now is, what has not been;

every moment changes.”

Pythagoras explains Herakleitos views, as passed on to us through Ovidius’ Metamorphosae. (Personal translation of the Dutch translation by M. D’Hane-Scheltema.)

Table of Contents

Abstract/Zusammenfassung 3

Chapter I. Introduction 9I–1. Planetary accretion and core formation 10

I–1.1 The formation of the Solar System 10I–1.2. Differentiation of planetary objects 11

I–2. Fractionation of isotopes 15I–2.1 Mass dependent fractionation of stable isotopes 15I–2.2 Theoretical background of stable isotope fractionation 16

I–3. Objectives of this thesis 17

Chapter II. Methodology 19II–1. Experimental 20

II–1.1. Starting mixtures 20II–1.2. Piston cylinder experiments 20

II–2. From a quenched experiment towards chemical dissolution 32II–3. Isotopic analyses 34

II–3.1. Ion exchange chemistry 35II–3.2. MC-ICPMS 37

II–4. Failed Silicon isotope analyses by laser ablation 44

Chapter III. Experimental evidence for the absence of iron isotope fractionation betweenmetal and silicate liquids at 1 GPa and 1250-1300 °C and its cosmochemical consequences 47III–1. Introduction 48III–2. Methods 50

III–2.1. Experimental methods 50III–2.2. Analytical methods 53

III–3. Results 56III–3.1 Textures and elemental compositions of the experimental run products 56III–3.2. Isotopic composition of the experimental liquids 60

III–4. Attainment of equilibrium 62III–5. Discussion 67

III–5.1. Comparison to previous studies 67III–5.2. Implications for Fe isotope variability in natural systems 69

III–6. Conclusions 74III–7. Appendix 75

Chapter IV. Experimental determination of the Si isotope fractionation factor between liquid metal and liquid silicate 89IV–1. Introduction 90IV–2. Methods 92

IV–2.1. Experimental methods 92IV–2.2. Analytical methods 94

IV–3. Results 97IV–3.1 Textures and elemental compositions 97IV–3.2. Isotopic compositions 100

IV–4. Equilibrium isotope fractionation 102IV–5. Discussion 108

IV–5.1. Comparison with previous studies 108IV–5.2. Implications for core formation 110

IV–6. Conclusion 112

Chapter V. Experimental evidence for Mo isotope fractionation between metal and silicate liquids 121V–1. Introduction 122V–2. Methods 124

V–2.1. Experimental methods 124V–2.2. Analytical methods 125

V–3. Results 129V–3.1 Textures and elemental compositions 130V–3.2. Isotopic compositions 134

V–4. Discussion 135V–4.1. Fractionation at 1400 °C 135V–4.1. Fractionation at 1600 °C 142

V–5. Implications for core formation 142V–6. Conclusions 145V–7. Appendix 146

V–7.1. Mo concentration analyses by laser ablation ICPMS 150V–7.1. Double spike calibration 151

Chapter VI. Molybdenum stable isotope composition of meteorites: Constraints on planetary core formation 155VI–1. Introduction 156VI–2. Analytical methods 158

VI–2.1. Sample preparation and Mo separation 158VI–2.2. Mass spectrometry and data reduction 159

VI–3. Results 160VI–3.1. Mo concentrations 160VI–3.2. Mo isotope data and δ98/95Mo values 160

VI–4. Discussion 166VI–4.1. Stable isotope composition of the inner solar system and bulk planetary bodies 166VI–4.2. Comparison of experimental and observed Mo stable isotope fractionation during metal segregation 167

VI–5. Conclusions 172

Chapter VII. Conclusions 173VII–1. Summary of the main conclusions 174VII–2. General conclusions and implications 175

VII–2.1. Stable isotope fractionation 175VII–2.2. Conditions of core formation 177

Bibliography 179

Appendix AI. 190Appendix AII. 194Appendix AIII. 196

Acknowledgements 204

Abstract/Zusammenfassung —

ABSTRACT

Stable isotope fractionation may inform on the conditions and chemical consequences of core-mantle differentiation in planetary objects. Equilibrium fractionation of stable isotopes, however, decreases strongly with increas-ing temperature and at very high temperatures becomes difficult to observe. With the advent of mass spectrometry, though, stable isotope fractionation has in many cases become observable during high temperature processes such as core formation. Nevertheless, the magnitude and direction of equilibrium stable isotope fractionation during such processes still remain largely unknown. In this study, I have experimentally determined the Fe, Si and Mo isotope fractionation factors between liquid metal and liquid silicate. I used these factors to interpret variations in stable isotope compositions in natural rocks and uncover their implications for planetary differentiation processes.

Experiments were performed in a centrifuging piston cylinder in talc/pyrex assemblies at a pressure of 1 GPa. Elemental tin was used to lower the melting temperatures of iron-based alloys to below 1500 °C. Silicate compositions were adapted to reach an appropriate liquidus. The centrifugation segregated the liquid metal and the liquid silicate, enabling analyses of bulk pieces of metal and silicate that were free of cross contamination. The bulk pieces of metal and silicate were cleaned and crushed prior to ion exchange chemistry to separate the element of interest from its matrix. Analyses were then performed on a multi-collector inductively coupled plasma mass spectrometer.

Experiments for Fe isotope fractionation were run at temperatures of 1250-1300 °C. The analyses demonstrate that 8 of the 10 experiments equilibrated in a closed isotopic system. Statistically significant iron isotope fractionation between the quenched metals and silicates was absent in 9 of the 10 experiments and all 10 experiments yield an average fractionation factor of 0.01 ± 0.04‰. The presence or absence of carbon or sulphur did not affect this result. At low pressures, Fe isotopes thus do not fractionate during metal-silicate segregation under magmatic conditions. This implies that the 0.07 ± 0.02‰ heavier composi-± 0.02‰ heavier composi- 0.02‰ heavier composi-tion of bulk magmatic iron meteorites relative to the average of bulk ordinary/carbonaceous chondrites cannot result from equilibrium Fe isotope fractionation during core segregation. The up to 0.5‰ lighter sulphide than metal fraction in iron meteorites and in one ordinary chondrite can only be explained by fractiona-tion during subsolidus processes.

Silicon isotope fractionation between liquid metal and liquid silicate was studied at 1450 °C and 1750 °C. Metal is consistently enriched in light isotopes relative to the silicate, yielding average metal-silicate fractionation factors of -1.48 ± 0.08‰ and -1.11 ± 0.14‰ at 1450 and 1750 °C, respectively. These results are unaffected by the presence or absence of carbon. The temperature

— Abstract/Zusammenfassung

dependence of equilibrium Si isotope fractionation between metal and silicate liquids can therefore be described as Δ30SiMetal-Silicate = -4.47(±0.31)×10

6/T2. Using a bulk silicate Earth δ30Si value of -0.29 ± 0.01‰, this temperature dependence can be used to calculate δ30Si values for Earth’s core. For metal-silicate equili-bration temperatures of 2500-3500 K, the Si isotope composition of Earth’ core is -1.01 ± 0.05‰ to -0.66 ± 0.03‰. Mass balance calculations indicate that for those core compositions, the Bulk Earth has a δ30Si of -0.38 ± 0.02‰ or -0.33 ± 0.01‰, respectively, if Earth’s core is assumed to contain 6 wt% Si, or -0.40 ± 0.02‰ or -0.35 ± 0.02‰, respectively, for 8 wt% Si in the Earth’s core. The reported Si isotope compositions of enstatite chondrites are significantly lighter (-0.62 ± 0.05‰) and they are therefore unlikely to represent the Bulk Earth Si isotope composition. A comparison with the reported Si isotope composition of other chondrites is unfortunately hindered by the dispute about these Si isotope compositions.

Molybdenum isotope compositions in the silicate were 0.193 ± 0.030‰ and 0.120 ± 0.020‰ heavier than in the metal at 1400 and 1600 °C, respectively. This fractionation is independent of the presence or absence of carbon and tin as well as of oxygen fugacity in the range ΔIW-1.79 to ΔIW+0.47. Equilibrium Mo isotope fractionation between liquid metal and liquid silicate can therefore be described as Δ98/95MoMetal-Silicate = -4.80(±0.55)×10

5/T2. The experiments performed at 1600 °C furthermore demonstrate that non-equilibrium isotope fractionation results from highly reactive capsule material. Rapid dissolution of capsule-derived MgO into the silicate melt has led to Δ98/95MoMetal-Silicate of -0.027 ± 0.036‰, clearly resulting from disequilibrium isotope fractionation.

Initial determination of Mo isotope compositions of meteorites as well as ter-restrial and lunar basalts indicates that equilibrium metal-silicate segregation may have occurred at ~1800 °C in the angrite parent body and at ~2100 °C in the Earth-Moon system. These new results suggest that core formation in the Earth did not occur at the base of a deep magma ocean, but rather took place at a shallower depth, either during descent of metal droplets through the magma ocean or by metal-silicate equilibration in Earth’s precursor bodies.

Overall, the findings in this study demonstrate that stable isotope fractiona-tion can occur during metal-silicate differentiation events. It may therefore constitute a tool to further constrain models of core formation. In this respect, Mo isotopes imply that models of high pressure and high temperature equilib-rium core formation at the base of a deep magma ocean may be oversimplified. Finally, it appears that a factor two increase in valence state of an element in the silicate liquid may increase stable isotope fractionation between metal and silicate liquids by an order of magnitude, which appears a stronger effect than that caused by a change from VI-fold to IV-fold coordination state. This further-more emphasises that equilibrium fractionation of stable isotopes is not solely a function of element mass.


ZUSAMMENFASSUNG

Die stabile Isotopenfraktionierung gibt Informationen über die Umstände und chemischen Folgen von Kern-Mantel Differen�ierungspro�essen in pla-schen Folgen von Kern-Mantel Differen�ierungspro�essen in pla-netaren Objekten. Gleichgewichtsfraktionierung stabiler Isotope nimmt mit steigender Temperatur stark ab, bis die Fraktionierung schwer messbar wird. Aufgrund Verbesserungen in der Massenspektrometrie kann heute jedoch die Isotopenfraktionierung in Hoch-Temperatur Pro�essen - wie �um Beispiel der Kernbildung - in vielen Fällen gemessen werden. Trot�dem ist das Ausmass und die Richtung der Gleichgewichtsfraktionierung stabiler Isotope während solcher Pro�esse grösstenteils immer noch unbekannt. In dieser Studie habe ich an Hand von Experimenten die Fe, Si und Mo Isotopenfraktionierungsfaktoren �wischen Metal- und Silikatschmel�en bestimmt. Diese Faktoren habe ich benut�t, um Unterschiede in der stabilen Isotopen�usammenset�ung in Gesteinen �u erklären und ihre Auswirkung auf planetarische Differen�ierung �u ermitteln.

Die Experimente wurden mit Talk/Pyrex Bauteilen in einem �entrifugieren-den Stempel-Zylinder bei einem Druck von etwa 1 GPa ausgeführt. Elementares Zinn wurde benut�t, um den Schmel�punkt von auf Eisen basierten Legierungen bis unter 1500 °C �u senken. Gleich�eitig wurde die Silikat Zusammenset�ung angepasst, um den gewünschten Liquidus �u erreichen. Die Zentrifugierung trennte die Metall- und Silikatschmel�en, wodurch die �wei Phasen ohne Risiko von Kreu�verunreinigungen analysiert werden konnten. Die �wei Phasen wurden gesäubert und pulverisiert bevor das gewünschte Element durch Ionenaustausch-chemie von seiner Matrix getrennt wurde. Die Proben wurden anschliessend auf einem Massenspektrometer gemessen.

Die Experimente für Fe Isotopenfraktionierung wurden bei Temperaturen von 1250 bis 1300 °C ausgeführt. Die Analysen �eigen, dass in 8 von 10 Experi- ausgeführt. Die Analysen �eigen, dass in 8 von 10 Experi-menten das Gleichgewicht in einem isotopisch geschlossenen System erreicht wurde. In 9 von 10 Experimenten gab es keine statistisch bedeutende Fe Iso-topenfraktionierung �wischen den abgeschreckten Metallen und Silikaten. Die 10 Experimente ergaben einen durchschnittlichen Fraktionierungsfaktor von 0.01 ± 0.04‰. Die An- oder Abwesenheit von Kohlenstoff oder Schwefel hatte keinen Effekt auf die Fraktionierung. Folglich findet unter magmatischen Bedingungen und bei tiefen Drücken während der Metall-Silikat Differen�ie-rung keine Fe Isotopenfraktionierung statt. Das bedeutet, dass die 0.07 ± 0.02‰ schwerere Zusammenset�ung magmatischer Eisenmeteorite im Vergleich �u Chondriten nicht durch Gleichgewichtsfraktionierung von Fe Isotopen während der Kernbildung erklärt werden kann. Die bis zu 0.5‰ leichtere sulfidische Zusammenset�ung verglichen mit metallischen Teilen in Eisenmeteoriten und Chondriten können nur durch Fraktionierung während subsolidus Pro�essen erklärt werden.

— Abstract/Zusammenfassung

Die Si Isotopenfraktionierung �wischen Metall- und Silikatschmel�en wurde bei Temperaturen von 1450 und 1750 °C untersucht. Metall war im Vergleich �u Silikat immer mit den leichten Isotopen angereichert und ergab durchschnittliche Fraktionierungsfaktoren von -1.48 ± 0.08‰ und -1.11 ± 0.14‰ für 1450 be�ie-ür 1450 be�ie-r 1450 be�ie-hungsweise 1750 °C. Die An- oder Abwesenheit von Kohlenstoff hatte keinen Einfluss auf die Ergebnisse. Die Temperaturabhängigkeit der Si Isotopenfraktio-nierung �wischen Metall- und Silikatschmel�en kann demnach folgendermassen ausgedrückt werden: Δ30SiMetal-Silicate = -4.47(±0.31)×10

6/T2. Diese Temperaturab-hängigkeit kann da�u verwendet werden, den d30Si Wert des Erdkernes �u berechnen, wenn man einen Wert von -0.29 ± 0.01‰ für die silikatische Erde annimmt. Für Metall-Silikat-Gleichgewichtstemperaturen von 2500-3500 K beträgt die Si Isotopen�usammenset�ung des Erdkernes -1.01 ± 0.05‰ bis -0.66 ± 0.03‰. Massenbilan�berechnungen deuten darauf hin, dass für diese Kern�u-sammensetzung die Gesamterde ein δ30Si von -0.38 ± 0.02‰ oder -0.33 ± 0.01‰ hat, wenn der Erdkern 6 wt% Si enthält, be�iehungsweise -0.40 ± 0.02‰ oder -0.35 ± 0.02‰ wenn der Erdkern 8 wt% Si enthält. Die publi�ierten Si Isotopen-�usammenset�ungen von Enstatit-Chondriten sind wesentlich leichter (-0.62 ± 0.05‰) und repräsentieren daher eher nicht die Si Isotopen�usammenset�ung der Gesamterde. Ein Vergleich �u die publi�ierten Si Isotopen�usammenset�ung von anderen Chondriten ist wegen der Kontroverse um diese Si Isotopen�usam-menset�ungen nicht möglich.

Molybdän Isotopen�usammenset�ungen in Silikaten waren 0.193 ± 0.030‰ und 0.120 ± 0.020‰ schwerer bei 1400 be�iehungsweise 1600 °C als im Metall. Diese Fraktionierung ist unabhängig von der An- oder Abwesenheit von Kohlenstoff und Zinn, sowie von der Sauerstofffugazität zwischen ΔIW-1.79 und ΔIW+0.47. Die Fraktionierung von Mo Isotopen zwischen Metall- und Silikatschmel�en kann wie folgt beschrieben werden: Δ98/95MoMetal-Silicate = -4.80(±0.55)×105/T2. Ferner haben die Experimente bei 1600 °C ge�eigt, dass die Ungleichgewichtsfraktionierung in den jeweiligen Experimenten auf das stark reagierende Kapselmaterial �urück�uführen ist. Sich rasch in Silikatschmel�e auflösendes MgO der Kapsel verursachte Δ98/95MoMetal-Silicate von -0.027 ± 0.036‰, was eindeutig der Ungleichgewichtsfraktionierung �u�uschreiben ist.

Erste Mo Isotopen�usammenset�ungen von Meteoriten sowie terrestrischen und lunaren Basalten deuten darauf hin, dass die Gleichgewichtstrennung �wischen Metall und Silikat in Angrite Mutterplanetoiden bei ~1800 °C und im Erde-Mond System bei ~2100 °C stattfand. Diese neuen Resultate �eigen, dass die Kernbildung nicht am Boden eines tiefe Magmao�eans stattfand sondern in weniger tiefen Bereichen entweder in der Form von Metalltröpfchen, die durch den Magmao�ean wanderten, oder innerhalb von Planetoiden.

Insgesamt �eigt diese Studie, dass die Fraktionierung stabiler Isotope während der Metall-Silikat-Differen�ierung möglich ist. Stablile Isotopenfraktionierung könnte daher bunut�t werden um Modelle des Kernbildungsvorgangs �u verbes-nte daher bunut�t werden um Modelle des Kernbildungsvorgangs �u verbes-


seren. Die Mo Isotope deuten darauf hin, dass solche Modelle unter Annahme von Gleichgewichtsbedingungen bei höheren Temperaturen und Drücken am Boden eines tiefe Magmao�eanes bisher �u stark vereinfacht wurden. Zudem haben die Resultate ge�eigt, dass eine Verdopplung des Oxidierungsgrad eines Elements in der Silikatschmel�e in einer Ver�ehnfachung der Isotopenfraktio-nierung �wischen Metall- und Silikatschmel�e resultiert, was einen grösseren Einfluss als der Koordinierungsgrad scheint zu sein. Dies verdeutlicht letztlich, dass Gleichgewichtsfraktionierung von stabilen Isotopen nicht nur vom Gewicht des Elements abhängt.

INTRODUCTION

CHAPTER I.

— Chapter I

This thesis concerns the experimental investigation of equilibrium, mass dependent fractionation of stable isotopes between liquid metal and liquid silicate. Liquid metal and liquid silicate are thought to be the dominant phases during core-mantle segregation in rocky (terrestrial) planetary bodies. This process leads to the formation of metallic cores and silicate mantles in terres-trial planets and their smaller precursor bodies (planetesimals and planetary embryos). It is the largest chemical and physical event in the history of terrestrial bodies. On Earth, core formation eventually led to a magnetic field that protects us from harmful cosmic radiation. Core formation is also for a large part respon-sible for the rareness of precious metals like gold, because most of the mass of such siderophile elements is hidden from us in Earth’s core.

Differentiation into a metallic core and silicate mantle occurs in the early history of planetary objects, i.e. in roughly the first 100 My after formation of the Solar System 4.567 Ga. This differentiation is normally studied by comparing undifferentiated meteorites (chondrites) to differentiated meteorites or samples from the terrestrial mantle/crust. Such comparisons have evolved from miner-alogical to chemical, the latter focussing on elemental abundances. In the last decade, relative abundances of stable isotopes have emerged as a new tool to investigate core segregation (and many other processes in geosciences). Hitherto, it remains unclear how to link the measured relative abundances of stable isotopes to geological processes, as there is only limited experimental and theo-retical understanding of how stable isotopes behave during geological processes.

Therefore, my study is a further step to better understand the behaviour of stable isotopes during geological processes. Because it is such an important event in the history of various planetary bodies, I have chosen to apply my study to the process that differentiates planetary bodies into a metallic core and silicate mantle. A more personal motivation for that application is that a large scale process that occurred almost 4.5 billion years ago triggers my imagination: I enjoy trying to understand/visualise how that process may have occurred, and I enjoy to search for facts that can serve as the fundament for that understanding and to force my imagination to stick to those facts. I hope that upon reading my work, you will enjoy it as much as I did while performing it, and that you find it brings us a small, but significant step forward in understanding “stable isotope behaviour during planetary differentiation”.

I–1. PLANETARY ACCRETION AND CORE FORMATION

I–1.1. The formation of the Solar SystemThe Solar System formed by collapse of a dense molecular cloud (De Pater

and Lissauer, 2001). Such clouds typically have a few thousand molecules per cm3, have a temperature of 10-30 K, and consist mainly of H2 and He with small amounts of molecules containing H, C, N and O. Usually, such clouds are stable

Chapter I —

in the sense that their kinetic (thermal) energy balances their gravitational energy. When either their cores reach too high densities or, more commonly, a trigger such as (shock) compression occurs, these clouds start to collapse towards the initially densest centre. This process is self-amplifying due to the continuously increasing density and gravitation in the core of the cloud, nearly all mass being attracted into the collapsing core. The Sun contains over 99.8% of the mass of the Solar System. Mainly due to increased pressure and transformation of gravita-tional energy into kinetic (thermal) energy, temperatures inside the growing Sun raised sufficiently high (>107 K) for nuclear reactions.

Over 98% of the angular momentum in the Solar System is in the remaining ≤0.2% of mass. This rotational energy has prevented that mass from accreting into the Sun and formed a flattened (proto-planetary) disk around the equatorial plane of the growing Sun. The heat produced by this flattening and particularly the radiative heat of the Sun is thought to have eventually created temperatures of a few thousand K close to the Sun and ~100 K at 10 AU. This is the main reason that the inner part of the Solar System consists of rocky (‘terrestrial’) planets, while the outer part consists of gas giants.

Upon cooling of the gas in the inner parts of the proto-planetary disk, con-densation temperatures are reached and micrometre particles form. As originally detailed in Grossman (1972), Al2O3 and CaTiO3 are the first condensates. So-called Ca- and Al-rich inclusions (CAI’s) are therefore considered to be the oldest particles in the Solar System, dated to be 4.567 Ga (Amelin et al., 2002). The particles that formed by condensation, together with very few interstel-lar particles (‘pre-solar grains’), rapidly accreted to form ~10 kilometre si�ed bodies. The evolution stage from micrometre particles to 10 km si�ed bodies is poorly understood, but afterwards growth continues by gravitational attraction of surrounding material towards the ≥10 km sized body. Such bodies are thought to still exist in the asteroid belt between Mars and Jupiter, and samples of them occur on Earth as meteorites called chondrites. The final evolution of the Solar System towards its present state encompasses the accretion of the various bodies into the eight planets with their moons, and various asteroids. The formation of the planets involved a stage of run-away growth into planetary embryos (~Mars size) and a final stage with large-scale impacts, such as the Giant Impact that is thought to have formed Earth’s Moon.

I–1.2. Differentiation of planetary objectsOnce bodies reach si�es over 10 km (‘planetesimals’), they may retain suf-

ficient heat to differentiate into a metallic core and silicate mantle due to melting (Hevey and Sanders, 2006). The heat required for this melting can come from conversion of gravitational energy into thermal energy, from impact heating, and from decay of abundant short-lived nuclides early in the Solar System, most notably the decay of 26Al to 26Mg (De Pater and Lissauer, 2001; Ghosh et al.,

— Chapter I

2006). Samples of differentiated bodies occur on Earth in the form of achondritic meteorites originating from the silicate portions of such bodies, and iron meteor-ites originating from their metallic cores.

Numerical modelling and radiogenic age determinations indicate that the above processes from molecular cloud collapse to the growth of the first plane-tesimals lasted about 1 My (De Pater and Lissauer, 2001; Kleine et al., 2009; Krot et al., 2009). Age determinations also indicate that the formation of planetesimals was a somewhat complicated process that continued for at least 4 My (Krot et al., 2009). Due to higher material densities and shorter orbital periods, material close to the Sun accreted faster than material at larger heliocentric distances (Ghosh et al., 2006). As a consequence, there were planetesimals that had accreted when abundant heat was still produced by decay of 26Al. These bodies melted (nearly) completely and had therefore differentiated before the precursor bodies of chon-drites formed (Kleine et al., 2009).

Chondrites, and more specifically the carbonaceous type CI chondrites, are considered to represent the average composition of the Solar System (Zanda, 2004). The CI chondrites have a one-to-one correlation of elemental abundances with the solar photosphere (normalised to 106 Si atoms), except for the volatile noble gases, H, He, C and O. This observation forms the basis of the ‘chondritic model’: the assumption that terrestrial planetary bodies consist of Solar System material with an average bulk composition similar to the Solar System. Excep-tions to this rule are volatile elements that may be lost by volatilisation during planetary accretion and, therefore, do not occur in Solar System abundances.

The chondritic model and the cosmochemical classification of elements form the framework of virtually all studies of core segregation in planetary bodies. The cosmochemical classification (Palme and Jones, 2003) groups elements according to their condensation temperatures as well as according to their pref-erence for metal or silicate phases. Based on these properties, we predict which elements should occur in chondritic relative abundances in a body (i.e. the refrac-tory elements) and which elements would be fractionated between metal cores and various silicate reservoirs (e.g. mantle and crust). Compositions of silicate samples can then be compared to CI chondritic compositions to estimate Bulk Silicate compositions of differentiated planetary objects, i.e. homogenising the various silicate reservoirs. Many such attempts have been made for the Earth (Palme and O’Neill, 2003) and they serve as a basis for estimates of the composi-tion of Earth’s core (McDonough, 2003). This led Ringwood (1959) to propose that Si may be present in the core in wt% levels in addition to a Fe90Ni10 alloy. For bodies such as Mars or the various parent bodies of meteorites, core compo-sition estimates are scarcer because of the limited number of samples relative to the Earth.

Core composition estimates also require more detailed knowledge than cosmo-chemical classification. Experiments determining element distribution between

Chapter I —

metal (liquid) and silicate (liquid) have greatly contributed to our knowledge of core formation (e.g. Wood et al., 2006). The distribution coefficients determined in such studies not only constrain which elements may be extracted from the silicate mantle into the metallic core. They also establish pressure, temperature, composition and oxygen fugacity conditions under which these elements are extracted from the mantle as well as the magnitude of extraction. Element distri-bution coefficients between metal and silicate can therefore be used to constrain hypotheses on the composition of metal cores, but also the conditions of core segregation (Righter and Drake, 1996; Righter, 2003; Wood et al., 2006).

Core segregation in Earth is described with equilibrium and disequilibrium models (Figure I–1). The latter assume that the material that accreted to Earth changed composition in the course of accretion and core formation (Wänke, 1981). Equilibrium models are easier to test against data. Moreover, the recent models explain features of the Bulk Silicate Earth (BSE) that formerly required disequilibrium models, most notably the higher than expected abundances of certain siderophile elements. Employing experimentally determined distribu-tion coefficients, equilibrium models explain present day element abundances by high pressure core segregation in a progressively oxidising Earth (Wade and Wood, 2005).

Completely molten mantle

Molten mantle

Unequilibrated metal blobs

Equilibratedmetal droplets

Metal pond

Metalcore

Solid mantle

Metal diapir

Metalcore

a b

Figure I–1. Sketches that represent two models of core formation. Panel (a) suggests that impacting material emulsifies and that small sinking droplets of metal equilibrate with the molten silicate. At the top of the solid mantle, the metal droplets then pond until sufficient mass allows for large metal diapirs to sink to the core without further equilibration with the surrounding silicate (after Wood et al., 2006.) Panel (b) shows an alternative model in which large impactors melt the entire silicate mantle of the impacted body. The molten metal of the impactor has such high velocities that it does not emulsify, but rapidly merges with the core of the impacted body. In this scenario, no re-equilibration occurs between metal and silicate in the impacted body. Metal-silicate equilibrium conditions are thus inherited from the smaller impactor.

— Chapter I

A recurring issue with equilibrium models, however, is the fact that physical models predict large impactor bodies to merge their core with Earth’s core without re-equilibration. The large impacts in the final stage of accretion of terrestrial planets involves so much energy that the impactor core would not emulsify, a requirement for fast equilibration with the Earth’s molten silicate mantle. In this case, an equilibrium core segregation model would physically not be valid. Rudge et al. (2010), however, showed that elemental abundances of siderophile elements in the BSE can be equally well explained by equilibra-tion of all accreting material as by equilibration of only part (~40%) of it. This implies that conditions of core segregation at lower pressures (and temperatures) in impactors may be inherited in Earth, and, hence, that the high pressures and temperatures (20-60 GPa and ~2500-3000 °C) derived from equilibrium models may not have been a precondition for core segregation on Earth.

Stable isotope fractionation, as opposed to elemental distribution, between metal and silicate (liquids) may provide further insights into core segregation in planetary objects. As detailed in the next section, mass dependent stable isotope fractionation between two phases strongly depends on temperature. Further-more, sudden changes in fractionation may appear due to pressure related phase changes. As such, mass dependent stable isotope fractionation may help dis-criminating between equilibrium and disequilibrium models of core segregation. Williams et al. (2006), for instance, hypothesi�ed that Fe isotopes may imply the presence of the high pressure phase perovskite (>20 GPa) during core seg-regation on Earth. By contrast, Moynier et al. (2011) suggested that Cr isotope compositions imply an inheritance of relatively low temperatures of core segre-gation in smaller impactors.

To fully extract the information stable isotopes may provide, we need to understand their fractionation behaviour. The contrasting hypotheses of Williams et al. (2006) and Moynier et al. (2011) are both based on stable isotope composi-tions of meteorites and terrestrial samples. It requires theoretical understanding of stable isotope fractionation and experimentally determined magnitudes and directions of fractionation (‘fractionation factors’) to interpret those data. While theoretical predictions of fractionation factors can be made, so far they are fairly restricted in number and usually can only be made for solid material (Polyakov et al., 2007). Furthermore, the accuracy of such predictions has rarely been verified by experimental determinations of fractionation factors.

It is therefore the purpose of this thesis to experimentally determine stable isotope fractionation factors between liquid metal and liquid silicate in order to use them for the interpretation of stable isotope compositions of meteorites and terrestrial samples in a framework. By doing so, I aim to shed further light on the process of core segregation.

Chapter I —

I–2. FRACTIONATION OF ISOTOPES

I–2.1. Mass dependent fractionation of stable isotopesIsotopes can be fractionated both independent of and dependent on their

masses. Mass-independent fractionation is well known from radiogenic ingrowth of a single isotope of an element due to decay of another element. There are also other forms of mass-independent fractionation of isotopes, for instance by prefer-ential production of specific isotopes of an element in supernovae or other stellar environments (‘nucleosynthesis’) or by interaction of isotopes with cosmic rays.

These types of isotopic fractionation are not the topic of this thesis, which studies mass dependent fractionation. This type of fractionation is a function only of the masses of the isotopes and involves two sub-types: kinetic and equi-librium fractionation. Kinetic mass dependent fractionation of isotopes can qualitatively be understood to occur because it requires more energy to transport a heavy mass than a light mass. For a given amount of energy, heavy isotopes will thus travel slower than light isotopes, meaning that the residue is relatively enriched in heavy isotopes if a transfer process is interrupted prior to completion.

The specific type of fractionation I have studied is equilibrium mass dependent isotope fractionation (in the remainder I will often refer to this with the slightly simpler term ‘stable isotope fractionation’). This occurs when heavy isotopes relative to light isotopes prefer one phase more than a second phase. Rudge et al. (2009) described the process of mass dependent isotope fractionation mathemati-cally as:

i i

ij j

O j

mX XX X m

α = ⋅

(I.1)

where i and j are the isotopes of element X and m are their isotopic masses. By convention, isotope j in these ratios is usually the heavy isotope. The factor α is the mass fractionation factor. The subscript 0 indicates the initial isotopic ratio prior to fractionation.

Somewhat unfortunate, the symbol α is also used to describe equilibrium mass dependent isotope fractionation between two phases A and B, mathematically defined as:

i

jA

A B i

jB

XX

XX

α −

=

(I.2)

The convention in equation (1.2) is the most commonly used in studies of stable isotope fractionation. This α-notation, though, is mainly used by theoreti-α-notation, though, is mainly used by theoreti--notation, though, is mainly used by theoreti-cians; geochemists mostly use the symbol Δ for the fractionation factor, which is simply the difference between the measured isotopic compositions of the two

— Chapter I

phases A and B (see more about the expressions of isotopic compositions in Chapter X). It is this Δ-notation that I will use throughout this thesis. For geologi-Δ-notation that I will use throughout this thesis. For geologi--notation that I will use throughout this thesis. For geologi-cal purposes, α does generally not deviate from 1.00 by more than 0.01, such that α and Δ can be simply related as:

( ) / / /1000 i j i j i jA B A B A Bln X X Xα d d− −= D = − (I.3)where δi/jX stands for the measured isotopic composition given as the ratio of

isotopes i and j of element X.

I–2.2. Theoretical background of stable isotope fractionationIn principle, stable isotope fractionation can occur between any phases, and

therefore as a consequence of any (geo)chemical process. The preference of heavy isotopes relative to light ones for one phase (A) compared to another (B) arises from differences in the bond stiffness between the two phases A and B. Furthermore, this preference is dependent on the relative masses of isotopes and is proportional to the inverse of the square of temperature, without a first order pressure dependence. Schauble (2007) summarised the general mathematical relationship as:

( ) 2 2A BA BFmln

m Tα −−

DD≈ (I.4)

in which ΔFA-B refers to the difference in force constants (i.e. bond stiffness) between phases A and B. The term Δm refers to the difference in masses of the isotopes. The temperature T is in K.

Equation (1.4) results from simplifications of thermodynamic and quantum mechanical relations used to calculate equilibrium constants for isotope exchange reactions (Bigeleisen and Mayer, 1947). For detailed derivations of those equations and their physicochemical background, I recommend the mainly qualitative descriptions of Bigeleisen (1965) as well as the more quantitative works of Schauble (2004), Urey (1947) and Bigeleisen and Mayer (1947). I have made a summary of the key points in Appendix A1.

It follows from equation (1.4) that stable isotope fractionation may always occur, except when there is no mass difference in the isotopes or when there is no difference in the bond stiffness between the two phases. Smaller differences in isotopic mass or bond stiffness lead to smaller fractionation. In general, heavy isotopes tend to concentrate in the phase with the stiffest bonds. There are some qualitative rules of thumb that are useful for estimating the magnitude of the dif-ference in bond stiffness between two phases of interest (Schauble, 2004). The most important ones for geological materials state that the stiffest bonds tend to occur for i) elements with a high valence state, ii) low coordination numbers, and iii) for transition elements with low-spin electronic configurations. Furthermore, in a general classification of bond types, covalent bonds are stronger than ionic bonds while metallic bonds are weakest. Increases in the element mass and in

Chapter I —

the temperature of fractionation lead to decreases in the fractionation. This is the reason that until the mid-1990’s stable isotope fractionation was almost only detectable in low temperature environments (i.e. below ~200 °C) and for light elements (e.g. H, C, O), which have relatively large differences between their isotopic masses.

With the progress in mass spectrometry, measurement precision has improved to levels at which fractionation at temperatures exceeding 1000°C can be detected for isotope systems of ‘non-traditional’ elements, i.e. elements with masses exceeding those of S. The detectability of stable isotope fractionation enables the use of stable isotope fractionation for (geo)chemical, and thereby geological, processes. This requires full knowledge of the direction and magnitude of stable isotope fractionation that a (geo)chemical process yields.

I–3. OUTLINE OF THIS THESIS

I have chosen to investigate three different isotope systems: Fe, Si and Mo. Isotopic compositions of a variety of meteorites and terrestrial samples were available for Fe and Si, and experimental constraints are necessary to interpret these data (see for instance a discussion about Fe isotopes in EPSL, vol. 256). Molybdenum was chosen as a third element because mass balance calcula-tions, and their inherent uncertainties, are generally not required to interpret Mo isotope compositions of natural silicate samples. In addition, Mo has a high and possibly variable valence state: both Mo4+ and Mo6+ may occur in equilibrium with metal. Finally, these three elements cover a range of atomic masses from 28.0855 atomic mass units (amu) for Si to 95.96 amu for Mo. They also cover a range of valence states in the silicate from 2+ (Fe) to 4+ (Si and Mo) to possibly 6+ (Mo).

The remainder of this thesis thus consists of three main chapters describing, respectively, Fe, Si and Mo isotope fractionation between liquid metal and liquid silicate, and their implications for core segregation in planetary objects. An additional collaborative chapter presents Mo isotope compositions of a variety of meteorites and terrestrial samples. Prior to these chapters, however, I will describe all the methodology involved in this thesis.

METHODOLOGY

CHAPTER II.

— Chapter II

In this work, I have combined methods of experimental petrology and isotope geochemistry. These techniques will be described in the current chapter to provide the details necessary for any future research following up on this work. In addition, this chapter contains information about failed methodologies that may once prove useful. This chapter follows the set-up of my study, starting with the experimental part, followed by elemental analyses and preparation for treatment in a clean chemistry laboratory before I describe the ion exchange chemistry and isotopic analyses in detail. I hope it is educational in the parts where you have no experience.

II–1. EXPERIMENTAL

II–1.1. Starting mixturesAll experiments are based on synthetic powders as starting mixtures. The

silicate components have been prepared from (usually 99.99+%) purified oxide powders, except for the elements Ca, K and Na. These elements are available as carbonates and were first mixed with SiO2 (and Al2O3) powder to create molar ratios of CaO, K2O and Na2O to SiO2 (to Al2O3) equivalent to those of the minerals wollastonite, orthoclase and albite. These powder mixtures were then placed in a furnace at 400 °C and slowly heated to 1500 °C (wollastonite) and ~1100 °C (the two feldspars). The fused material was then crushed and stored for further use in oxide mixtures representing silicate melts, which in my study always (and only) contained additional SiO2, Al2O3, MgO and Fe2O3.

Metal components are all available as element powders so that they can simply be weighed in the desired proportions prior to homogenisation. Such homogeni-sation is generally done with a pestle and mortar. Because metals can be very soft and easily smear out under the pestle, I always first mixed the harder oxides before adding the softer metals. After gentle and patient stirring under acetone or ethanol, a fine and homogeneous powder forms, although the homogeneity decreases by density separation during evaporation of the excess acetone or ethanol. The resulting heterogeneity is, however, easily homogenised again with a short step of dry stirring. Most of the various starting mixtures are presented in the relevant chapters and in Appendix AII.

II–1.2. Piston cylinder experimentsII–1.2.1. General

The technique to generate high pressures and temperatures to simulate condi-tions below the Earth’s surface is straightforward. Temperatures of up to 2500 °C are generated by running an electric current of up to ~400 A through a graphite cylinder (‘furnace’) inside which the sample powder is positioned inside a container (‘capsule’). The resistance of the graphite furnace then produces the heat, a process no different than the process that produces heat in a standard light

Chapter II —

bulb. Quenching is done by cutting power. Pressures ≥ 0.5 GPa are produced by pumping oil into a hydraulic cylinder reservoir with a large surface which in turn pressuri�es a small surface (or volume), the latter con-taining the sample capsule. Pressure transfer onto the sample capsule inside the furnace takes place through material that becomes very soft at the temperatures and pressures of interest, yielding approximately hydrostatic pressures. In my study, these materials were always talc and pyrex/silica glass (see Figure II–1 for a sketch of an assembly).

A piston cylinder generates pressures of 0.5-4 GPa and allows for relatively large capsules. The pressure transfer in this apparatus takes place through a conically shaped ‘bridge’ and a tungsten-carbide (WC) piston that is in contact with the furnace and other assembly materials surrounding the capsule. A sketch of a Boyd and England type (Boyd and England, 1960) end-loaded piston cylinder is shown in Figure II–2. The term end-loaded refers to an additional axial pressure that is exerted on the WC core material column, but that is not transferred onto the sample itself. This ‘end-load’ serves to compress the WC also axially, lateral support being provided by the pressure vessel, thus counteracting the pressure exerted onto the sample. Non-end-loaded piston cylinders are consequently used until lower pressures (< 2 GPa).

A special type of piston cylinder at ETH Zurich is the centrifuging piston cylinder, details of which can be found in Schmidt et al. (2006). It is a min-iaturised version of a non-end-loaded piston cylinder that is mounted into a rotating table (Figure II–3). Its usage is a little more elaborate than that of a standard version, because oil cannot be pumped in during centrifugation to adjust

Pyrex

Pyrex

MgO

MgO

Talc

Cement

Corundum

Metaljacket

~10.53.7

thermocouple wire in Al2O3 or Mullite sleeve graphite furnace

Capsule

Sample

14 mm

36.0

6 mm

Figure II–1. Design of assembly. Dimensions are in millimetre.

— Chapter II

pressures. In contrast, it is advisable to heat only during centrifugation, such that high currents are only pulsed through the slip rings when rotating. As the material compacts due to the exerted pressure, particularly after the talc and pyrex/silica glass soften, pressure is lost during heating. A multi-step oil pumping/heating procedure is thus required for experiments in the centrifuging piston cylinder.

All the experiments I analysed for their isotopic compositions have been run in this centrifuging piston cylinder, because the analyses require metal and silicate powders that are free of cross contamination. As the experi-ments were designed to contain liquid metal and liquid silicate, which have densities of ~7500 and ~3000 kg m-3, respectively, near-perfect separation can be achieved during the experi-ment by centrifugation (Figure II–4a). Cross contamination, if any, only consists of tiny

Figure II–3. Picture of the centrifuging piston cylinder at ETH Zurich. Highlighted are the min-iaturised non-end-loaded piston cylinder (similar to the design in Figure 2, but without the end-load ram) and the counter-mass. Both are mounted on the rotating table.

metal frame

bomb withWC corepiston (WC)bridgeram with WC-pushing pieceend-load ram

20 cm100

hy

drau

lic o

il(e

nd-lo

ad)

cool

ing

wat

erhy

drau

lic o

il(p

isto

n)

cooling water plate

Figure II–2. Design of a Boyd and England-type piston cylinder. Inside the metal frame, the parts with solid, dark grey fill are made of tungsten-car-bide. The bomb has a white to dark grey gradient fill. Parts with a sand pattern fill are non-moveable. Moveable parts are moved up by pumping hydraulic oil in the reservoir underneath them, while they are moved downwards by pumping oil in the reservoir along their sides. Pressure is calculated with a conversion factor between the ram and the piston (surface of ram divided by surface of piston) with a correction for friction determined from pressure calibration. (Courtesy of Peter Ulmer.)

Chapter II —

droplets of the contaminating phase (< 2 μm in diameter) remaining in the main pool of one of the phases, such that the analysed silicate and metal phases are >99.9% pure. This contrasts with a conventional static experiment that can lead to phase separation as poor as in Figure II–4b. Such experiments would require careful hand picking to separate the metal and silicate phases, an approach unlikely to lead to purities as high as by centrifugation.

Richter et al. (2008) have found that temperature gradients can lead to similar isotopic fractionation in a single phase as investigated here between two phases. Temperatures in a cylindrical graphite furnace vary between the cold ends in contact with metal from the stack and a hotspot region near the centre. Because temperature gradients are smallest in the hotspot, I have carefully investigated where exactly in the furnace the hotspot was located, so as to place my samples there. In order to determine the location of the hotspot, I have calibrated the temperature along the long axis of the graphite furnace following the technique described in Watson et al. (2002). They found that when MgO and Al2O3 are in direct contact, spinel will grow according to the reaction:

2 3 2 4 MgO Al O MgAl O+ (II.1)This growth is diffusion limited and therefore strongly dependent on tempera-

ture, a relation that Watson et al. (2002) empirically determined to be:

11 488658.58 10 2.08X exp P tT

D = × ⋅ − − ⋅ ⋅

(II.2)

in which DX is the thickness of the spinel growth layer in μm, T the tempera-ture in Kelvin, P the pressure in GPa and t the time in seconds. The design of the assembly for this temperature calibration and its results are presented in Figure II–5. From the regression equation, it appears that for the length of capsules used in my study, the maximum temperature difference is 9 °C between the hotpot and the coldest end of the capsule.

Figure II–4. Back-scatter electron image of a centrifuged experiment (a) compared to a static experiment (b) under identical conditions. White reflections are metal, grey are silicate and black are graphite or laromin epoxy.

— Chapter II

II–1.2.2. Strategy for experiments involving metal and silicate liquids and isotope fractionation

A number of specific details concerning the design of the assemblies had to be investigated. These mainly concern sample interactions with the capsule material and compositions of the starting mixtures. With respect to the former, the presence of both liquid metal and liquid silicate limits suitable materials for capsules. Any metal capsule will chemically interact with the liquid metal, while generally oxides or silicates will interact with the silicate liquid. It was further-more important to avoid contamination of the sample with the element of interest from the capsule; e.g. with an SiO2 capsule for Si isotopes.

As presented in Appendix AIII, I have tried a number of different capsule materials. Among these were crushable ZrO2 (two types with porosities of ~30% and ~10%), Al2O3 (porosity

Chapter II —

this can be avoided with shorter run durations. Tests with simple plugs as bottom and top sealings resulted in too much leaking along the contact between plugs and tube, indicating that more complex sealing is necessary (RH29 and RH34 in Appendix AIII).

My final choices fell on graphite and, depending on the isotopic system under consideration, SiO2 glass and single crystal MgO. Although the pores of graphite capsules seem to close well under 1 GPa pressure, particularly the low viscosity metal liquids were still able to permeate into the graphite capsule along grain boundaries. This, in fact, initially led to severe problems with capsule collapses (Figure II–7a-c), and I experimented with various sources of graphite (Appendix AIII). Although I have not made it my scientific purpose to identify the exact reason for this problem, it seems related to the permeability of the graphite. As a rule of thumb, the various tests I performed imply that the permeability increases with decreasing grain si�e, although there was at least one exception to this pattern among my tests. A piece of graphite with measured low gas permeability (kindly donated by Colin Maden) yielded satisfactory results. Professor Bernard J. Wood (University of Oxford), however, brought my attention to the graphite produced by Morgan Industrial Carbon, which provided the best results (Figure II–7d) and has been the material of choice for all later experiments in graphite capsules (Appendix AIII).

All three capsule materials mentioned above, however, react with the metal liquid (graphite) or silicate liquid (SiO2 and MgO). Graphite dissolves in the metal, but its solubility is limited to about 5 wt% depending on pressure (P), tem-perature (T), composition (X), and oxygen fugacity (fO2) conditions (Bouchard and Bale, 1995). Because the presence of carbon in a metal is considered to affect elemental partitioning (Jana and Walker, 1997), I have chosen to also perform experiments in SiO2 glass and single crystal MgO capsules in addition to those

Figure II–6. Back-scatter electron image of a failed experiment in a ZrO2 capsule. Due to the high porosity of the capsule, the liquid sample permeated into the capsule that then collapsed towards the central part. All metal in the sample has disappeared because it alloyed with the metal jacket, which forms an infinite reservoir compared to the volume of the sample. The zone between the sample and the former capsule-sam-ple contact is a mixture between ZrO2 grains from the capsule and silicate glass from the sample.

— Chapter II

in graphite capsules. The reactivity of SiO2 glass capsules is relatively limited compared to MgO, SiO2 contents increasing from 50 wt% in the starting mixture to 60 wt% in the run product. Reaction progress can furthermore be kept minimal when run durations are kept to a minimum.

In order to use relatively low temperatures (~1300-1400 °C) to maximise isotopic fractionation required modifications to the compositions of starting mixtures compared to a binary Fe-Ni alloy and peridotite in metal-silicate equi-libration experiments. Lowering the liquidus of the silicate can be achieved by increasing the silica and alkali contents in the starting mixture. For the Fe-metal, there are few elements that lower the melting point, alloy with iron in liquid form and allow for the desired range of oxygen fugacity, i.e. close to the iron-wüstite (IW) buffer. An attempt with Zn (melting temperature of 420 °C at 1 bar) failed, because too much Zn oxidised, which led to the formation of Zn-rich

Figure II–7. Back-scatter electron images of experiments with various types of graphite. Brightest reflections are metal, darkest reflections are graphite or epoxy. Experiments presented in panels (a) and (b) were performed in the same type of graphite. Its per-meability was so high that particularly in panel (b) the original sample area is barely distinguishable from the capsule. The graphite used in the experiment presented in panel (c) is a large improvement, but the best results occurred from runs in the graphite used in the experiment presented in panel (d), in which the black reflections inside the grey silicate glass are epoxy, not graphite.

Chapter II —

spinel crystals. Tin (melting temperature of 232 °C) remained as best choice, and all experiments below the melting temperature of pure Fe (1540 °C) have been performed including Sn.

II–1.2.3. Fe isotope specific settingsFor the study of Fe isotope fractionation, experiments were performed at

1250-1300 °C in graphite and SiO2 glass capsules. The use of MgO capsules was avoided, because these would lead to FeO-MgO exchange rendering an uncontrollable, open system with respect to Fe (isotopes). Starting mixtures with approximately 50 wt% metal were prepared including and excluding S, as well as with and without an isotope tracer. Sulphur-bearing compositions were run in graphite capsules, because of liquid immiscibility in the ternary Fe-C-S system (Corgne et al., 2008). Further details are provided in chapter III.

II–1.2.4. Si isotope specific settingsFor experiments performed to study Si isotope fractionation, the main purpose

was to find a composition that would render sufficient metallic Si for analyses. The relative amount of metal was therefore larger with ~75 wt% than in experi-ments performed for Fe isotope fractionation. Additionally, the experiments had to be more reducing and starting mixtures were therefore based on the starting and equilibrated compositions of mixture/experiment MK15 and MKX presented in Table 1 and 3 in Kilburn and Wood (1997). Two starting mixtures were prepared, because the relatively large isotopic fractionation of Si enabled run temperatures (1750 °C) above the liquidus of pure Fe (see chapter IV for more details).

The ability to perform experi-ments at 1750 °C presented a problem, though. Pyrex becomes too weak and too reactive as an assembly part at such high tem-peratures, and therefore it is recommended to use silica glass instead. This material, however, has a much higher softening tem-perature of ~1500 °C compared to ~800 °C for pyrex. I experi-mentally found that softening

Figure II–8. Back-scatter electron image of an experiment that was run at 1750 °C with a talc/silica glass assembly in the centrifug-ing piston cylinder following the multi-step heating and re-pumping procedure. A crack as it occurred in 75% of the 1750 °C experi-ments that followed that procedure is visible in the upper left corner of the image. The con-sequence of the crack is a pathway for liquid sample to reach the Pt jacket. Due to the high temperature, this leads to Pt entering the sample as can be seen from the (Pt-bearing) metal dispersed in the silicate glass.

— Chapter II

starts around 1200 °C. In centrifuge experiments therefore, I initially pumped to about 0.4 GPa, heated to 1200 °C to soften the silicate glass, quenched and then re-pumped to ~1.2 GPa prior to heating to the desired run temperature. Either the higher temperature or the properties of silica glass, however, led to a 75% failure rate due to cracking of the inner capsule perpendicular to its long axis (Figure II–8). The cracking occurred with both graphite and MgO capsules, but was never observed when using pyrex instead of silica glass sleeves. Neither slow cooling instead of quenching after softening, nor pressurising to 0.25 instead of 0.4 GPa led to successful experiments. Only pumping directly to ~1 GPa and omitting the softening step has led to an acceptable failure rate of about 20%, albeit with consequently lower and less predictable final run pressures.

Finally, the use of stepped furnaces (necessary for temperatures >1600 °C in the centrifuge) often leads to shearing where the step in wall thickness occurs. This can lead to temperature instabilities, and stepped furnaces are therefore also to be avoided when possible.

II–1.2.5. Mo isotope specific settingsThe main issue with experiments performed to investigate Mo isotope frac-

tionation was the content of Mo in the silicate phase. Because Mo is siderophile, the vast majority (> 99%) of all bulk Mo resides in the metal phase. Silicate phases only contain traces (ppm level) of Mo, as found by analysis of several experiments with laser ablation ICP-MS following standard protocols. Because at least 60 ng Mo is required for a single isotopic analysis (see section II–3.2. below for more details), 10 mg of silicate powder must be recovered for a silicate with 6 ppm Mo. Recovering more than 10 mg, however, is difficult from a typical experiment. In addition, 60 ng is a minimum, because for statistical reasons > 3 analyses of one sample are preferable. To reach relatively high contents of Mo in the silicate, I have therefore used about 10 wt% Mo in the metal phase. In addition, I used single crystal MgO capsules instead of SiO2 glass capsules, as the solubility of elements with valence states ≥ 3+, such as Mo, increases with depolymerisation in the silicate liquid (Ellison and Hess, 1986; Walter and Thibault, 1995; Hillgren et al., 1996). Finally, the oxygen fugacity of the experi-ments was kept higher than 2 log units below the iron-wüstite buffer (ΔIW-2). This was done because at more reducing conditions, Mo becomes too siderophile and even with 10 wt% Mo in the metal, Mo contents of the silicate would not reach 5 ppm. Experiments between ΔIW-1 and ΔIW-2 have been performed in capsules with an inner and outer diameter of 2.8 mm and 4.5 mm, respectively, compared to the standard si�es presented in Figure II–1. The experiments were performed at 1400 °C and 1600 °C and various starting mixtures were prepared to vary oxygen fugacity (by varying Fe2O3 contents) and compositional param-eters (Sn). Further details about published experiments are provided in chapter V.

Chapter II —

Fe

Mo

S

Fe

1150°C1540°C

Mo (at.%)

1020

30 MoS2

L

γ-Fe

δ-Fe

α-Fe + MoS2

δ-Fe + L

1020

3040

5060

7080

90S

(at.%

)M

oS

L

L +

S 2 (g

)

Mo

Mo 2

S 3MoS

2

665°

C

1550

°C

2620

°C

1750

°C

MoS

2 +

S (g)

MoS

2 +

S (l)

MoS

2 +

S (s)

Mo +

L

Mo +

Mo 2

S 3

Mo +

MoS

2

L +

MoS

2

L +

Mo 2

S 3M

o 2S 3

+ M

oS2

1020

3040

5060

7080

90

S (at.%

)

Fe

S

L 1 + L 2

Fe + L

L

γ-FeS

990°C

1080°C

1540°C

FeS 2 + S (

s)

α-Fe +

α-FeS

γ-Fe

δ-Fe

α-Fe +

β-FeSα

-Fe + γ

-FeS

α

β

FeS 2 + S (

l)FeS 2

+ S (g)

γ-FeS+FeS 2

β-FeS+FeS 2

α-FeS+FeS 2

γ-FeS

+ L 2γ-F

eS+

L

Fe (at.

%)

Fe

Mo

L

1450°C

1540°C

2620°C

α-Fe

Mo

1020

3040

5060

7080

90160

0°C

γ-Fe

Mo + L

µ

λ + α−

Fe

σ

δ-Fe

RΜο

+ µ

λ+µ

µ + α−

Fe

R + α−

Fe

σ + R

Μο + σ

σ + µ

σ + L

µ + R

R + L

1150

°C(e

utec

tic?)

Expe

rimen

t at 1

600°

C, 1

GPa

Lite

ratu

re d

ata

for 1

atm

.

L

Figure II–9. Phase relations in the ternary system Fe-Mo-S. Only the three binaries and one thermal section through the ternary are known. Data inside the ternary are from an experiment I performed at 1600 °C. Tie lines connect the phases I observed in the experiment, the open star represents the bulk composition. Binaries are from the Landolt-Börnstein database, the ternary section from Villars et al. (1995).

— Chapter II

In addition to the experiments presented in chapter V, I performed a number of experiments with an S-bearing metal to investigate the influence of S on Mo isotope fractionation. For the metal component, I used a ternary Fe-S-Mo system. Consequently, the experiments were performed in MgO instead of graphite capsules. These experiments are presented here, because none of them were sufficiently successful to be included in chapter V. The reason for the low success rate is the lack of information for the Fe-S-Mo system: only the three binary phase diagrams and one ternary section exist (Figure II–9). I performed several experiments at 1400 °C and 1600 °C with various compositions aimed to be near the binary Fe-S eutectic. However, metal crystals were stable at 1400 °C as well as 1600 °C in experiments with a metal starting composition by weight of ~Fe67S26Mo7 (Figure II–10a). Adjusting the metal starting composition to the S-rich metal liquid in these experiments subsequently resulted in two immisci-ble metal/sulphide liquids at 1400 °C (Figure II–10b). Another attempt to reach a single metal liquid by adjusting the metal component of the starting mixture to one of the two immiscible liquids again resulted in two immiscible metal liquids, albeit with different compositions (Figure II–10c). It seems therefore that the ternary Fe-S-Mo system is a complex system whose eutectics/peritectics

Figure II–10. Back-scatter electron images of experiments with metal liquids in the Fe-Mo-S compositional system. Panel (a) shows the four phases that occurred in an experiment at 1600 °C with their approximate compositions by mass. Panel (b) shows a centrifuged experiment performed at 1400 °C with a Mo-poorer starting composition. This produced two immiscible liquids. Possibly due to the presence of small amounts of Pt, the experiment shown in panel (c) has also produced two liquids, one of which is richer in Mo and poorer in S than the Mo-rich phase shown in panel (b).

Chapter II —

are deeply entrenched in the liquidus surface. Compositional changes during an experimental run due to redox reactions can shift the bulk metal system into another stability field. I have summarised the results of the 1400 °C experiments in a provisional ternary diagram (Figure II–11).

1020

3040

5060

7080

90S

(at.%

)M

oS

L

L +

S 2 (g

)

Mo

Mo 2

S 3MoS

2

665°

C

1550

°C

2620

°C

1750

°C

MoS

2 +

S (g)

MoS

2 +

S (l)

MoS

2 +

S (s)

Mo +

L

Mo +

Mo 2

S 3

Mo +

MoS

2

L +

MoS

2

L +

Mo 2

S 3M

o 2S 3

+ M

oS2

Fe (at.

%)

Fe

Mo

L

1450°C

1540°C

2620°C

α-Fe

Mo

1020

3040

5060

7080

90160

0°C

γ-Fe

Mo + L

µ

λ + α−

Fe

σ

δ-Fe

RΜο

+ µ

λ+µ

µ + α−

Fe

R + α−

Fe

σ + R

Μο + σ

σ + µ

σ + L

µ + R

R + L

1020

3040

5060

7080

90

S (at.%

)

Fe

S

L 1 + L 2

Fe + L

L

γ-FeS

990°C

1080°C

1540°C

FeS 2 + S (

s)

α-Fe +

α-FeS

γ-Fe

δ-Fe

α-Fe +

β-FeSα

-Fe + γ

-FeS

α

β

FeS 2 + S (

l)FeS 2

+ S (g)

γ-FeS+FeS 2

β-FeS+FeS 2

α-FeS+FeS 2

γ-FeS

+ L 2γ-F

eS+

L

1150

°C(e

utec

tic?)

Fe

Mo

S

Expe

rimen

ts a

t 140

0°C

, 1 G

PaSi

mpl

ified

bin

arie

s for

1 a

tm.

L

L

Figure II–11. Phase relations in the ternary system Fe-Mo-S with updated information at 1400 °C. Open stars indicate bulk compositions, tie lines connect the stable phases. Apparently there is only a narrow field close to the Fe-S binary that results in a completely molten system at 1400 °C.

— Chapter II

II–2. FROM A QUENCHED EXPERIMENT TOWARDS CHEMICAL DISSOLUTION

After quenching of an experiment, preparatory procedures are carried out. Most important among these are electron imaging and microprobe analyses that serve both as a quality check of the experiments (e.g. no cracks in the capsule) and as a basis for mass balance calculations after isotopic analyses. Prior to microprobe analyses, however, the capsule is removed from the assembly and embedded in epoxy. This is then ground on SiC grinding paper until the sample material is exposed. Because the silicate glass is brittle and mostly cracked, I always impregnated the sample with the low viscosity epoxy Laromin prior to final grinding to remove approximately a third of the capsule radius. The exposed material is subsequently polished with 3 or 1 μm diamond paste and coated with carbon.

Coated samples were analysed with an electron microprobe to examine textures and determine elemental compositions. For details of this technique, see Reed (1993). If experiments were performed as tests, I analysed them semi-quantitatively by EDS with a scanning electron microprobe (SEM). For good signal intensities, the rule of thumb is that the acceleration voltage of the incident electron beam should be twice that of the excitation potential of the electrons that produce the X-rays that are analysed. For my samples, the K-shell of Fe had the highest excitation potential of about 7.1 keV and I therefore always used an acceleration voltage of 15 keV. To avoid diffusion of elements in the glasses due to the intensity of the incident electron beam, silicate glasses were analysed with a beam current of 6-7 nA. Metals, on the other hand, were analysed with a current of 20 nA. Beam diameters were 1-10 μm for silicates and 10 μm for metals and between 7 and 16 spots were analysed on each phase. For each session, pure metal standards were analysed, relative to which the metal samples were analysed. The more common silicate and oxide standards used for silicate analyses were only standardised when necessary, i.e. when their compositions were found to deviate by more than one per cent from the previous standard analysis.

After microprobe analyses, samples were prepared for dissolution. First, I removed excessive epoxy with a diamond saw. Subsequently, I used a diamond wire saw with a diameter of 220 or 300 μm to cut the samples at the contact between metal and silicate, and at the sample-capsule contacts at the top and bottom as well as the sides of the capsule (Figure II–12). Capsule material thus remained on one side of the sample, and this I removed by grinding on ~30 μm SiC (for Fe isotopes) or 30 μm Al2O3 grinding paper (Si and Mo isotopes). The same type of grinding paper was also used to clean each side that was cut with the diamond wire saw to remove any contamination by the sawing procedure. I used Al2O3 instead of SiC grinding paper for Si as well as Mo because Mo readily forms carbides and might therefore be present as contaminant in the SiC paper.

Chapter II —

This method results in one clean piece of metal and one clean piece of silicate, each compris-ing a volume of approximately 1-2 mm3.

The final preparatory step I performed consisted of crushing the metal and silicate pieces with a pestle and mortar. For samples in preparation for Fe isotope analyses, I used the agate pestle and mortar for common use in the laboratory. For Si isotopes, I purchased two alumina sets to prevent cross contamina-tion: one for the low Si content (~5 wt%) metallic samples and a separate one for the high Si content (~25 wt%) silicate samples. I expected the concentrations of Mo in the silicates for Mo isotope analyses to be below 100 ppm. Therefore, I crushed these samples in the alumina pestle and mortar that had previously only been used for the silicate glasses of which I analysed their Si isotope composition, which contained < 100 ppb Mo. All crushed material was transferred from the mortar into a glass or polypropyl-ene vial for transfer into a clean chemistry laboratory.

Type Beakers14 M HNO3 x

H2OMQ rinse x

Table II–1. Material cleaning for Fe chemistry. Beakers were cleaned by filling them with acid, closing them and putting them on hotplates at 130°C.

Purpose Acid type Volume (ml)Pre-clean ~2.8 M HNO3 2x2

Equilibration 6 M HCl 2x0.5

Load 6 M HCl ~0.5

Rinse 6 M HCl 6x0.5

Collect 1 M HCl 7x0.5Clean prior to storage in 0.05M HCl

~2.8 M HNO3 2x1.5

0.05 M HCl 0.5

Table II–2. Anion exchange protocol for Fe. 1 ml AG1-X4, 200-400 mesh.

Figure II–12. Representation of the removal of the sample from the capsule. Areas where the sample/capsule is cut with the diamond wire saw are indicated. The remaining pieces of metal and silicate are then further cleaned with abrasive paper and crushed prior to dissolution in a clean chemistry laboratory.

— Chapter II

II–3. ISOTOPIC ANALYSES

Isotopic analyses consist of two proce-dures: ion exchange chemistry to separate the element of interest from all other elements present, and actual analysis in a multi-collector mass spectrometer. The ion exchange proce-dures are different for every element, but the actual analyses of the elements in my study all took place on a multi-collector inductively coupled plasma mass spec-trometer (MC-ICPMS). More specifically, the MC-ICPMS was a large geometry type Nu1700 at ETH Zurich. Part of the Mo isotope analyses, though, were performed on a Neptune Plus at the University of Münster, produced by Thermo Fisher Scientific.

Both ion exchange and MC-ICPMS analyses are performed in liquid state and all samples therefore have to be dissolved. The crushed samples are weighed in PFA beakers, which are highly resistant to acids, and then dissolved with acids. For metals, usually 12 M HCl with a bit of 14 M HNO3 are sufficient for dis-solution. Silicates, on the other hand, have such strong bonds that they require a more aggressive combination of 24 M HF and 14 M HNO3. After dissolution, the samples are dried and treated further with acids depending on the requirement of the specific ion exchange procedures.

Type Beakers Columns

at ~24°C in PP-beakers

6 M HCl x

H2OMQel x

at ~80°C in glass beakers; all chemicals

p.a. grade

H2OMQ x

7 M HNO3 x

H2OMQ rinse x

H2OMQ x

at ~130°C in teflon beakers; all chemicals

p.a. grade

6 M HCl-1 M HF (48 h) x

H2OMQ rinse x

H2OMQel (24 h) x

H2OMQ rinse x

H2OMQel (24 h) x

Table II–3. Material cleaning for Si chemistry.

Purpose Acid type Volume (ml)

Pre-clean

H2O ~1.5

3 M HCl ~1.5

6 M HCl ~1.5

14 M HNO3 ~1.5

6 M HCl ~1.5

3 M HCl ~1.5

6 M HCl ~1.5

3 M HCl ~1.5

Equilibration H2O 4x~1.5Load+collect1 ~0.01 M HCl ~0.5

Collect2 H2O 2x1

1 The exact acid molarity and volume in this step are sample dependent.2 The indicated 2x1 ml is used for silicates; for metals this step consitst of 4x1 ml.

Table II–4. Cation exchange protocol for Si. 1 ml AG50W-X8, 200-400 mesh.

Chapter II —

However, the dissolution procedure depends on the element of interest: the above details are valid for most elements analysed by MC-ICPMS, but they are different for Si isotopes, because Si becomes volatile below a critical Si/HF ratio. Samples for Si isotopes were therefore treated differently, as described in chapter IV.

II–3.1. Ion exchange chemistryThe separation of elements occurs through ion exchange, which relies on the

variable distribution coefficients (or adsorption coefficients) between an acid and grains of a solid substance. The solid substance is usually an organic polymer (‘resin’) that has either cations (e.g. H+) or anions (e.g. Cl-) on exchangeable sites in its structure. If the distribution coefficient (KD) of an element or molecule (e.g. FeCl2

-) is larger than 1, it will replace the cation or anion on its site and stick to the resin. The resin is therefore placed in a column, such that the acid can be washed through to separate elements with KD’s >> 1 from those with KD’s

— Chapter II

cleaning procedures for Fe, Si and Mo are provided in Table II–1 to II–6 and in chapters III to V.

a. Cation exchange; 3 ml AG50W-X8 200-400 mesh


Pre-clean

6 M HCl ~8

1 M HF ~8

6 M HCl ~8

1 M HF ~8

6 M HCl ~8

1 M HF ~8

Equilibration 1 M HCl-0.1 M HF 2x3

Load+collect 1 M HCl-0.1 M HF 1

Collect 1 M HCl-0.1 M HF 4

Clean prior to storage in mM

6 M HCl ~8

1 M HF ~8

mM ~8

b. Anion exchange; 2 ml AG1-X8 200-400 mesh


Pre-clean

6 M HCl-1 M HF ~9

H2O ~9

3 M HNO3 (2x) ~9

H2O ~9

1 M HCl ~9

0.1 M HCl ~9

Equilibration 1 M HCl 2x4

Load 1 M HCl 1

Collect 1 M HCl 1

Collect 1 M HCl 2x6


3 M HNO3 (2x) ~9

mM ~9

c. Anion exchange; 2 ml AG1-X8 200-400 mesh


Pre-clean

6 M HCl-1 M HF ~9

mM 2x2

6 M HCl-1 M HF ~9

mM 2x2

6 M HNO3-0.2 M HF ~9

3 M HNO3 (2x) ~9

Equilibration 1 M HF 2x3

Load 1 M HF 6

Rinse 1 M HF 2x6Rinse Ti/Zr/

Hf/W6 M HCl-1 M HF 2x8

Rinse H2O 2

Collect 3 M HNO3 6.5


6 M HCl-1 M HF ~9

mM ~9

d. Cation exchange; 1 ml TRU-Spec


Pre-clean1

H2O ~7

1 M HNO3 ~7

0.1 M HNO3 ~7

H2O ~7

1 M HCl ~7

0.1 M HCl ~7

Equilibration 1 M HCl 2x1.5

Load 1 M HCl 1

Rinse 1 M HCl 6

Collect 0.1 M HCl 6.51 This procedure is repeated twice.

Table II–6. Ion exchange protocol for Mo. mM = 0.5 mM HCl-0.5 mM HF.

Chapter II —

II–3.2. MC-ICPMSPrecise analysis of isotopic ratios relies mainly on two basic principles: ionisa-

tion of the element to be analysed and separation of its isotopes by travel through a magnetic field (Figure II–13). Once the samples have been cleared of all elements except the element of interest, the weakly acidic measurement solution is aspirated from a vial. The weak acid is then normally evaporated in a desolvat-ing unit (DSN-100) and separated from the precipitated element aerosols by a membrane. The aerosols are then transferred with a noble gas flow (usually Ar) to a plasma. That plasma is created by collisions of Ar with free electrons in an electromagnetic field generated by a high-frequency alternating electric current. Temperatures in such plasma reach up to 10000 K, under which the aerosols of sample material disintegrate into single atoms that are then ionised, i.e. they lose an electron. Aided by the directed Ar flow and the lower (vacuum) air pressure behind the plasma, the ions then travel through cones with narrow holes to let a narrow beam of ions enter an electric field with various high voltages. The ions convert that potential energy into kinetic energy and are directed into a narrow beam of ions travelling at the same velocities before they enter a magnetic field (Figure II–13). In the magnetic field, ion travel paths are deflected as a function of their mass-to-charge ratio, which is effectively a function of mass because the vast majority of atoms will have lost only one electron. The separated isotope trajectories are finally directed into collector cups where the charge built up by the entered ions is converted into an electric current that is measured as output simultaneously on all cups.

Specific settings for MC-ICPMS apply to each element of interest, e.g. the strength of the magnetic field

Cup L7 L6 L5 L4 L3 L2 L1 Ax- - 52Cr - - - 54Fe -

Cup H1 H2 H3 H4 H5 H6 H7 H8- - - - 56Fe 57Fe - -

Table II–7. Cup configuration Fe isotope analyses.

Cup L7 L6 L5 L4 L3 L2 L1 Ax- - - 28Si - - 29Si -

Cup H1 H2 H3 H4 H5 H6 H7 H8- - - - - 30Si - -

Table II–8. Cup configuration Si isotope analyses.

Cup L7 L6 L5 L4 L3 L2 L1 AxNu1700 - 90Zr 92Mo - 94Mo 95Mo - 96MoNeptune Plus - 91Zr 92Mo 94Mo 95Mo 96Mo

Cup H1 H2 H3 H4 H5 H6 H7 H8Nu1700 - 97Mo - 98Mo 99Ru 100Mo - -Neptune Plus 97Mo 98Mo 99Ru 100Mo -

Table II–9. Cup configuration Mo isotope analyses.

— Chapter II

102 Pa 10-2 Pa 10-6 Pa 10-7 PaElectroStatic

Analyser plates

Magnet

Monitorplate

Quadrupolefocussing

lenses

Lensstack 1(HV)

Lensstack 2(HV)

Rotarypump

Turbo pumps

Collectors

Resistors(typically 1011 Ω)

Desolvator

Samplesolution

Focussinglenses 3

Cone

Heavy isotope enrichedto collectors

Light isotopeenriched

Light isotopeenriched

Figure II–13. Schematic representation of isotopic analyses by multi-collector induc-tively coupled plasma mass spectrometry (MC-IPCMS). The dissolved sample is aspirated from a beaker and sprayed into a desolvator with a nebuliser. The dry aerosols are then transported into the plasma, where they disintegrate and ionise. Out of the cloud of ions, heavy isotopes pass preferentially through the series of cones compared to light isotopes, causing an instrumental mass bias (see inset). After acceleration and focussing of the ion beam, the mass separation of the isotopes occurs in the magnetic field. The various beams are finally focussed into the collector cups, in which the positively charged ions build up an electric potential and generate an electric current that is measured as output value. The ratio of two simultaneously measured electric currents from two different cups then forms the (raw) isotopic ratio. (Figure modified after Nu Instruments Ltd.)

Chapter II —

has to be changed for each element depending on the masses of its isotopes. Cup configurations of the MC-ICPMS are presented for each element in Table II–7, 8 and 9. Further details are provided in chapters III to V. For each element, I used an ASX-100 (Cetac) auto-sampler and a PFA nebuliser (~140 μl min-1 uptake rate) to aspirate the samples and transfer them into a DSN-100 desolvator attached to the Nu1700. In all cases, each analysis consisted of 36 cycles of 5 s integration each.

Some of the Mo analyses were performed on a Neptune Plus at the University of Münster. This MC-ICPMS had a sensitivity that was about 3 times higher than that of Nu1700 at ETH Zurich, meaning that 4 times less sample material was consumed for a single analysis (see chapter V for more details). This was required for the small amounts of Mo (

— Chapter II

spike to the measurement solution. This is possible only when the element of interest has a minimum of four isotopes, because three isotope ratios are required to unravel the instrumental fractionation from the ‘natural’ fractionation, i.e. the sample composition relative to a standard. The procedure relies on the known composition of both a double spike and a standard, the latter having a natural (i.e. unspiked) isotopic composition. With mass dependent fractionation laws that describe natural and instrumental fractionation, and with mass balance equations, it is then possible to solve iteratively for the natural mass dependent fractionation factor (α; Figure II–14). The isotopic composition of the sample in δ units is then related to α and the isotopic masses (m):

/ 1000 ln( )i j ij

mXm

d α= − ⋅ (4)

The mathematical background for this double spike deconvolution is given in Rudge et al. (2009). It should be noted however, that this procedure can only be used for analysis of mass dependent fractionation, because of the intrinsic assumption that the natural fractionation is mass dependent. Without this assumption, the double spike deconvolution consists of a task that is not analyti-cally solvable (see Appendix A in Rudge et al., 2009), unless another law can be written to estimate the three sample ratios (see Figure II–15 for a graphical representation).

In the study I have performed, I used the double spike procedure for Mo isotope analyses, because it has additional advantages compared to standard-sample bracketing. First, for a trace element like Mo impurities of other elements that occurred in tens of weight per cent in the sample can always remain after ion

Figure II–14. Schematic representation of double spike analyses (after Rudge et al., 2009). Squares indicate that compositions are known, stars represent unknowns. Two single spikes of known composition (S1 and S2) are mixed to form a double spike (D.S.). The D.S. is then mixed in unknown molar proportion p with a sample (Sa) of unknown composition to form an unknown mixture (M). That mixture (M) is analysed, but the output of the analysis (m) is fractionated relative to the true composition M by an instru-mental mass bias that can be described with a mass dependent fractionation law with instru-mental fractionation factor β. Furthermore, the sample composition can be calculated with the assumption that it is fractionated with the same mass dependent fractionation law (now with natural fractionation factor α) relative to a standard (Std) of known composition.

β

α

p

1-p

D.S.

StdSa

S1 S2

M m

Chapter II —

exchange chemistry. Such impurities, however, would make the measurement solution slightly different from the standard solution, thereby causing different instrumental fractionation for the two solutions; an effect referred to as ‘matrix effect’. Furthermore, by adding the double spike to the sample prior to dissolu-tion, any mass dependent fractionation during ion exchange chemistry as a result of yields that are

— Chapter II

The compositions and calibration scheme for the Mo double spike and standard NIST SRM3134 are given in Table II–10. The double spike was mixed after dissolution of a 97Mo and 100Mo metal powder purchased from the Oak Ridge National Laboratory (ONRL). These two isotopes were chosen because (i) they have relatively low isotopic abundances (~9.6% each), (ii) there is only isobaric interference from 100Ru (isotopic abundance of 12.6%), (iii) it results in small intrinsic errors on the quoted δ98/95Mo (Rudge et al., 2009), and (iv) several other studies h

Research Collection · 2020. 3. 26. · VI–3. Results 160 VI–3.1. Mo concentrations 160 VI–3.2. Mo isotope data and δ98/95Mo values 160 VI–4. Discussion 166 VI–4.1. Stable

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