Major element diffusion in garnet and the exsolution of majoritic garnet from aluminous enstatite in Earth's Upper Mantle

Major element diffusion in garnet and the exsolution of majoritic garnet from aluminous enstatite in Earth's Upper Mantle Dissertation Von der Fakultät für Biologie, Chemie und Geowissenschaften der Universität Bayreuth zur Erlangung der Würde eines Doktors der Naturwissenschaften - Dr. rer. nat. - vorgelegt von Willem Louis van Mierlo Geboren in Leidschendam / die Niederlande Bayreuth, 2011 Diese Dissertation wurde am Bayerischen Geoinstitut, Universität Bayreuth im Zeitraum von Januar 2008 bis Mai 2011 unter der Betreuung von Prof. Dr. Falko Langenhorst angefertigt. Vollständiger Abdruck der von der Fakultät für Chemie, Biologie und Geowissenschaften der Universität Bayreuth genehmigten Dissertation zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.). Dissertation eingereicht am: 25.05.2011 Zulassung durch die Prüfungskommission: 11.07.2011 Wissenschaftliches Kolloquiem: 26.07.2011 Prüfungsausschuss: Prof. Dr. Falko Langenhorst (Erstgutachter) Prof. Dr. David Rubie (Zweitgutachter) Prof. Dr. Jörgen Senker (Vorsitz) Prof. Dr. Tomoo Katsura Prof. Dr. Klaus Bitzer Acknowledgements I would like to thank the European Commission for providing the funding of the presented PhD project under the Marie Curie Research Training Network 'Crust to Core– the fate of subducted material' (MRTN-CT-2006035957). I would like to thank my supervisor during for my PhD, Falko Langenhorst, for his patience and help in teaching me, the many fruitful discussions and the invaluable feedback he gave me, which significantly improved the quality of the dissertation. Dan Frost, David Rubie, Nobuyoshi Miyajima, Florian Heidelbach, Hans Keppler, Catherin McCammon, Guðmundur Guðfinnson and Detlef Krauße I would like to thank for their advise and instructions on using the different kinds of equipment that was used to produce results presented in this dissertation. My scientific productivity was greatly increased by the meticulous preparation work done by Uwe Dittmann, Hubert Schulze, Stefan Übelhack and Heinz Fischer in the workshops. Their work is greatly appreciated! Lydia Kison-Herzing, Petra Buchert, and Stefan Keyssner I thank for their help in solving administrative and other problems not directly related to my scientific work. I would like to thank all my colleagues and friends at the Bayerisches Geoinstitut for creating a great environment to work in and the nice social life outside BGI. I also want to thank my friends in Holland, that they are there for me and it is always nice to see them again! To conclude I would like to thank my family for all the help and support they provided through all of my life, without them I would not be where I would be now. Table of contents 1 Introduction 1.1 Phase relations in the Earth's Transition Zone 1.2 Diffusion kinetics of the major elements in Earth's mantle 1.2.1 Olivine 1.2.2 High pressure polymorphs of olivine 1.2.3 Perovskite (MgSiO3) 1.2.4 Magnesiowüstite 1.2.5 Garnets 1.2.6 Pyroxenes 1.3 Reaction kinetics in Earth’s mantle 1.4 Goals of this PhD study 1.5 References 2 Garnets and diffusion kinetics 2.1 Garnets and majorite, a high pressure polymorph of enstatite 2.1.1 Garnet 2.1.2 Majorite 2.1.3 Majoritic garnet and UHP rocks 2.2 Diffusion in minerals 2.2.1 The different diffusion coefficients 2.2.2 Fick's laws 2.2.3 Pressure and temperature dependence 2.2.4 Vacancies and oxygen fugacity 2.2.5 Multi-component models 2.3 References 3 Experimental and analytical techniques 3.1 High pressure – high temperature experiments 3.1.1 The Multi-anvil apparatus 3.2 Transmission electron microscopy 3.2.1 Sample preparation 3.2.2 Basic principles of the TEM 3.2.3 Elastic scattering within the specimen 3.2.4 Inelastic scattering – Energy dispersive spectroscopy 3.2.5 Electron energy loss spectroscopy 3.3 The electron microprobe 3.4 References 1 1 5 5 7 8 10 11 14 15 18 19 28 28 28 29 30 32 32 33 33 34 35 37 41 41 42 47 47 50 51 54 58 60 63 4 Numerical modeling of diffusion phenomena 4.1 Planar 1-D multi-component diffusion 4.2 Diffusion in a spherical or cylindrical geometry 4.3 References 5 Diffusion of the majorite component in garnet 5.1 Introduction 5.1.1 Diffusion in minerals 5.2 Experimental methods 5.2.1 Starting materials 5.2.2 Apparatus and pressure cell 5.3 Analytical methods 5.4 Results 5.4.1 Characterization of the samples after the experiments 5.4.2 Temperature dependence 5.4.3 Pressure dependence 5.4.4 Magnesium – iron interdiffusion 5.4.5 Almandine – (Mg) majorite diffusion 5.5 Discussion 5.5.1 Homogenization of the upper mantle 5.5.2 Rheology of garnet in the transition zone 5.5.3 Comparison with previous experimental data 5.5.4 Effect of majorite content on diffusivity of the elements 5.6 Conclusions 5.7 References Appendix 5.1: Radiation damage correction Appendix 5.2: Quantification of the EDS analyses Appendix 5.3:Precision of TEM EDS measurements Appendix 5.4: Majoritic garnet – Dora Maira pyrope diffusion couple profiles 6 Exsolution of garnet from orthopyroxene 6.1 Introduction 6.2 Experimental setup 6.3 Analytical setup 6.4 Results 6.4.1 Determination of the enstatite polymorph 6.4.2 Microstructure 6.4.3 Majoritic garnet precipitates 6.4.4 Diffusion of Al in high clinoenstatite 6.5 Discussion 66 66 69 71 72 72 72 74 74 76 76 78 78 82 83 84 85 88 89 89 92 92 94 95 98 100 100 102 104 104 105 106 107 107 107 109 111 112 6.5.1 Pyroxene microstructure 6.5.2 Garnet precipitates 6.5.3 Aluminium diffusivity in clinoenstatite 6.6 Conclusions 6.7 References 112 114 115 116 118 Summary Majorite is a high pressure polymorph of enstatite with the garnet structure. The amount of enstatite that can be dissolved in garnet as a majorite component increases significantly with pressure, and therefore, majoritic garnet is thought to be a major constituent of the Earth's transition zone. The transport properties of majoritic garnet are, however, not well constrained at the moment. The magnitude of the diffusivity of the majorite component in garnet influences our understanding of the homogenization time scale of Earth's mantle. This is important in subduction zone settings, where the subducting oceanic crust will form a majorite inhomogeneity in the transition zone because of its higher aluminium content. Reaction kinetics in the dry transition zone are diffusion controlled and therefore an improved dataset on the diffusivity of the majorite component in garnet will enable us to better understand the of role of disequilibrium in subduction zones. This dissertation therefore reports the results of diffusion experiments on garnet. Slow diffusion kinetics of the majorite component in garnet will also will hamper the dissolution of pyroxene in garnet and pyroxene will therefore be metastably preserved during subduction. Natural pyroxenes always contain aluminium, which is expected to cause exsolution of a garnet phase during subduction. Therefore, high pressure and temperature experiments have been conducted on aluminous enstatite, to simulate this process, of which the results are also presented in this dissertation. Diffusion experiments have been conducted with diffusion couples of majoritic garnet – Dora Maira pyrope, Dora Maira pyrope and Ötztal almandine and Ötztal almandine and majoritic garnet in a multi-anvil press between 1400 – 1900 °C and 12 – 20 GPa. The diffusion experiments with the majoritic garnet – Dora Maira pyrope garnet couples show that the diffusion of the majorite component in garnet is very slow, comparable to the diffusivity of silicon in wadsleyite and ringwoodite. The activation energy, activation volume and the preexponential for diffusion of the majorite component in garnet were determined to be 241 ± 54 kJ mol-1, 3.3 ± 0.1 cm3 mol-1 and 2.3 x 10-7 cm2 s-1, respectively. The diffusivity of the majorite component in garnet was determined to be 2-3 orders of magnitude slower than the self-diffusivity of Mg, Fe and Ca in garnet at the same conditions. Comparison with diffusion data on wadsleyite and ringwoodite shows that the diffusivity of the majorite component in garnet is very similar to that of the silicon self-diffusivity in the high-pressure polymorphs of olivine. Another set of diffusion experiments was conducted with Ötztal almandine – majoritic garnet diffusion couples. The diffusion profiles obtained from these experiments are strongly asymmetric, and indicate that there is an increased tracer-diffusivity of Mg and Fe by one order of magnitude in majoritic garnet part of the diffusion couple. The increased diffusivity of Mg and Fe in majoritic garnet appears to be an intrinsic property of majoritic garnet, which can be explained by the fact that the octahedral sites short cut the diffusion path through the garnet structure. In almandine the octahedral sites are all occupied by aluminium, whereas in the majoritic garnet a proportion of the octahedral sites are also occupied by Mg and Fe. To determine whether solid state diffusion can homogenize the mantle the diffusion distance of the majorite component in garnet, assuming grain boundary diffusion is the dominant diffusion mechanism, has been calculated. The results show that within the range of temperatures prevailing in the transition zone, majorite is able to diffuse 5 – 15 m on the time scale of the age of the Earth. Solid state diffusion is thus not able to homogenize the mantle. Another important question is whether or not diffusion of the majorite component in garnet is fast enough to enable pyroxene to dissolve in garnet, thus forming majoritic garnet in the subducting oceanic slab. A finite difference code has been developed to assess this question that models diffusion in a spherical grain and diffusion controlled growth of a spherical grain. The results show that during the subduction process all pyroxene can be dissolved in garnet in the case of the lithospheric mantle part of the slab. The oceanic crust shows however a different result, due to its lower temperature, and only a small amount of pyroxene can be dissolved into garnet. Metastable phases will thus be preserved in the subducting oceanic crust during the subduction process. Natural pyroxenes contain small amounts of aluminium. During subduction pyroxene is thought to dissolve into garnet. However, as the diffusion experiments reported in this thesis show, there is a significant delay in the dissolution of pyroxene in garnet as result of the limited diffusivity of the majorite component in garnet. Therefore, garnet will exsolve from pyroxene before pyroxene is dissolved into garnet, because the aluminium solubility in pyroxene decreases with increasing pressure. Experiments with Dora Maira pyrope – Tanzania enstatite couples have been conducted at 1700 °C and 15 GPa to simulate the process of subduction into the transition zone. The recovered samples reveal in low clinoenstatite extensive twinning on (100) and a high density of stacking faults on (100) with displacement vector R = [½ ½ w]. From crystal structure considerations one finds that w is most likely ½. The stacking fault plane in combination with the displacement vector can be explained by the phase transformation of HP high clinoenstatite to low clinoenstatite. The topotactic relationship between the majoritic garnet precipitates and the low clinoenstatite host was also determined. Though there is not a unique topotactic relationship, most of the garnet precipitates have their <111> direction parallel to the [001] direction in low clinoenstatite. The lack of a unique topotactic relation is probably due to a lack of an oxygen close packing direction in garnet. The observed dominant topotactic relationship is therefore interpreted as the result of the low diffusivity of silicon and is thus a topotactic relation controlled by kinetics. From the aluminium diffusion profiles measured in low clinoenstatite, the diffusivity of Al in high clinoenstatite was determined to be at least 6 x 10-11 cm2 s-1 at 1700 °C and 15 GPa. Comparison with data in diopside shows there is a discrepancy between diffusion data at high pressure and at low pressure, which might indicate a strong dependence of Al diffusivity in clinopyroxene on Ca contents or a change in diffusion mechanism. The results of the experiments conducted in this PhD study show that the low diffusivity of components in the Earth may severely hamper reaction kinetics in the Earth in the case where mass transport is required. To better understand dynamics of the Earth it would therefore be useful study the role of diffusion in other phase transitions in the Earth where mass transport is required. Zusammenfassung Majorit ist eine Hochdruck-Modifikation von Enstatit mit Granatstruktur. Mit steigendem Druck nimmt der Enstatit-Gehalt, der als Majorit-Komponente in Granat gelöst sein kann, deutlich zu, weswegen vermutet wird, dass majoritischer Granat eine Hauptkomponente in der Übergangszone der Erde ist. Dennoch sind die Transporteigenschaften von majoritischem Granat noch nicht genau bekannt. Vom Ausmaß des Diffusionsvermögens des majoritischen Anteils in Granat hängt unser Verständnis vom zeitlichen Ablauf der Homogenisation des Erdmantels ab. Dieses spielt in Subduktionszonen eine wichtige Rolle, wo die subduzierte ozeanische Kruste aufgrund ihres höheren Aluminium-Gehalts eine Majorit-Inhomogenität in der Übergangszone bildet. Da Reaktionsabläufe in einer trockenen Übergangszone diffusionskontrolliert sind, werden verbesserte Daten über das Diffusionsverhalten der majoritischen Komponente in Granat dazu beitragen, Ungleichgewichte in Subduktionszonen besser zu verstehen. Die Ergebnisse solcher DiffusionsExperimente werden in dieser Dissertation vorgestellt. Eine langsame Diffusion der Majorit-Komponente in Granat behindert die Auflösung von Pyroxen in Granat, wodurch Pyroxen während des Subduktionsprozesses metastabil erhalten bleibt. Natürlicher Pyroxen enthält immer Aluminium, das sich während der Subduktion als Granat-Phase entmischt. Um diesen Prozess zu simulieren, wurden Hochdruckund Hochtemperatur-Experimente an Aluminium-reichem Enstatit durchgeführt. Die Ergebnisse werden ebenfalls in dieser Dissertation präsentiert. Diffusionsexperimente wurden an den folgenden Diffusions-Paaren durchgeführt: (1) majoritischer Granat – Dora Maira-Pyrop, (2) Dora Maira-Pyrop und Ötztal-Almandin und (3) Ötztal-Almandin und majoritischer Granat in einer Multi-Anvil-Presse bei Temperaturen von 1400 – 1900 °C und Drücken von 12 – 20 GPa durchgeführt. Jene Experimente mit Paaren von majoritischem Granat – Dora Maira-Pyrop zeigen, dass die Diffusion der majoritischen Komponente in Granat sehr langsam vonstatten geht, vergleichbar mit dem Diffusionsvermögen von Silizium in Wadsleyit und Ringwoodit. Die Aktivitätsenergie, das Aktivitätsvolumen und der präexponentielle Faktor der Diffusion der majoritischen Komponente in Granat betragen 241 ± 54 kJ mol-1, beziehungsweise 3.3 ± 0.1 cm3 mol-1 und 2.3 x 10-7 cm2 s-1. Das Diffusionsvermögen der majoritischen Komponente in Granat ist 2 bis 3 Größenordnungen langsamer als die Selbstdiffusion von Mg, Fe und Ca in Granat unter denselben Bedingungen. Vergleiche mit den Diffusionsdaten von Wadsleyit und Ringwoodit zeigen, dass das Diffusionsvermögen der Majorit-Komponente in Granat der Selbstdiffusion von Silizium in den Hochdruck-Polymorphen von Olivin sehr ähnlich ist. Eine weitere Reihe von Diffusionsexperimenten wurde an Diffusionspaaren von Ötztal-Almandin und majoritischem Granat durchgeführt. Die aus diesen Experimenten hervorgegangenen Diffusionsprofile sind stark asymmetrisch und belegen ein um eine Größenordnung erhöhtes Diffusionsvermögen von Spuren von Mg Frost 2008), making majoritic garnet the second most abundant phase in the transition zone after the high pressure polymorphs of olivine, wadsleyite and ringwoodite (figure 1.2). The mineralogy of the bulk part of Earth’s mantle can be described by the system CaO – MgO – Al2O3 – SiO2 (CMAS-system). Iron mainly exchanges with magnesium and therefore affects the size of the stability fields of the phases involved and the depth range over which phase transition occurs (Akaogi et al. 1989, Katsura and Ito 1989, Frost 2003). The presence of iron generally does not lead to the appearance of new phases. The addition of CaO and Al2O3 to the system leads to the stability of clinopyroxene and garnet at lower pressures. High pressure experiments in the CMS-system have shown that the HP high-clinoenstatite phase mentioned above, however, does not form a solid-solution with the diopside (CaMgSi2O6) rich clinopyroxenes stable at lower pressure and are thus two distinct phases (Gasparik 1990). The mutual solubility of HP-clinoenstatite and the clinopyroxene jadeite (NaAlSi2O6) is significantly higher, however in the transition zone the solubility of jadeite in HP-clinoenstatite is also reduced to virtually zero (Gasparik 1989, 1990). The breakdown of diopsidic clinopyroxene above 17 – 18 GPa (figure 1.3) results in the formation of a majorite rich garnet (En80Di20 when the composition is expressed as pyroxene end-members) in equilibrium with calcium perovskite at temperatures above 1400 °C, and the formation of a calcium perovskite + stishovite + wadsleyite / ringwoodite below 1400 °C. The calcium content of the garnet phase is however strongly dependent on temperature and pressure and increases with increasing temperature and decreasing pressure (Canil 1994, Oguri et al. 1997). Gasparik (1989, 1990) observed the formation of a new non-quenchable phase as breakdown product of diopside with a close to diopside stoichiometry at pressures above 14 GPa, which is however not confirmed by other studies and no crystal structure determination of this new phase was attempted by the 3 Figure 1.1: Phase diagram of the Mg2Si2O4 – Fe2SiO4 join at 1600 °C. Modified after Katsura and Ito (1989). authors. Similar breakdown to garnet at high temperatures and pressures is observed for sodium bearing pyroxenes. On the jadeite – enstatite joint at 1650 °C, pure jadeite transforms to a garnet structure above 21 GPa (Gasparik 1990).The sodium atom is incorporated in a dodecahedral site and the additional silicon atom is incorporated in an octahedral site (Ringwood and Major 1971). Liu (1978) however, showed that at lower temperatures (1000 °C) jadeite disproportionates to stishovite + calcium-ferrite structured NaAlSiO4 above 24 GPa. The stability of garnets with a calcic and sodic clinopyroxene stoichiometry at high pressure and temperature indicates that, like enstatite, the major rock-forming clinopyroxene end-members diopside and jadeite can be dissolved into garnet in the transition zone, also bearing in mind that calcium can be incorporated in garnet as a grossular component. Since MORBs have a relative high aluminium, calcium and sodium content, this has important consequences for the subducted oceanic crust in the transition zone. Irifune and Ringwood (1986) and Irifune et al. (1993) performed high-pressure experiments in a multi-anvil press on materials with a MORB composition, of which the oceanic crust is made. These experiments showed that virtually all pyroxene will be dissolved into garnet in the transition zone, forming a garnetite assemblage consisting of ~ 90 vol. % of garnet between 15 GPa and 20 GPa (figure 1.2). Garnet at these conditions have a strong majorite component (up to ~ 40%). At pressures above 21 GPa (at 1200 °C) majoritic garnet starts to exsolve its Ca4Si4O12 component as calcium perovskite. At pressures above ~25 GPa an Al-rich phase with a calcium-ferrite structure starts to exsolve from garnet (Irifune and Ringwood 1993, Hirose et al. 1999). At ~ 27 GPa the remaining majoritic garnet transforms to Mg-perovskite (Hirose et al. 1999, Ono et al. 2001). In the subducted oceanic crust, majoritic garnet is thus a dominant phase between 15 GPa and 27 GPa. 4 Figure 1.2: a) Mineralogy of the mantle assuming a pyrolite composition (Frost 2008) and b) a MORB composition, the subducted oceanic crust (Irifune & Ringwood 1993), as function of pressure. ab 1.2 Diffusion kinetics of the major elements in Earth's mantle The diffusion of atoms in minerals control a number processes in the Earth's interior and properties of the Earth in which geologists are interested in. Among these are the reaction kinetics during phase transformations, especially when they require long-range transport of the components (Putnis 1992), order – disorder phase transitions (Sipling and Yund 1973, Carpenter 1982), re-equilibration of metamorphic assemblages and its geothermo-barometric applications (Lasaga 1983, Lasaga and Jiang 1995), geochronology (Dodson 1973) and rheology of phases in the Earth's interior (Weertman et al. 1978, Poirier 1985). This section will give a short review of diffusion data on minerals relevant to the Earth's mantle. 1.2.1 Olivine As already pointed out above, olivine is the most abundant phase in Earth's upper mantle. It has therefore been the focus of a great number of studies. Buening and Buseck (1973) and Misener (1974) performed pioneering work on the interdiffusion of magnesium and iron in olivine. They showed that diffusion in this system is highly asymmetric and diffusion down the c-axis in olivine is up to one order of magnitude faster than down the aor b-axis. The highly asymmetric profiles indicated that the iron content is of great influence on the Mg-Fe interdiffusivity in olivine. Buening and Buseck (1973) argued therefore, that the increased interdiffusivity can be attributed to a vacancy process where the oxidation of iron in the olivine structure introduces extrinsic vacancies and thereby increases the Mg-Fe interdiffusivity in olivine. This was also later confirmed by other studies, where vacancy concentrations in olivine as function of oxygen fugacity were determined (Nakamura and Schmalzried 1983, Tsai and Dieckmann 2002) and where the Fe-Mg interdiffusivity as function of oxygen fugacity was observed to increase in a similar way as the vacancy concentrations (Chakraborty 1997, Dohmen et al. 2007). 5 Figure 1.3: Phase diagram of diopside showing the breakdown above ~ 18 GPa. After Oguri et al. (1997). Buening and Buseck (1973) also found a change in slope in the log10 DFe-Mg vs. reciprocal temperature plot around 1125 °C and mentioned that a change in Fe-Mg interdiffusion mechanism in olivine, from an extrinsic mechanism at low temperatures to an intrinsic mechanism at high temperatures, might cause such a kink. A (tentatively interpreted) similar intrinsic – extrinsic transition has been observed for Co – Mg interdiffusion in olivine at 1300 °C by Morioka (1980). The interpretation as intrinsic – extrinsic diffusion regime transition of the observed kink transition has been contested by Chakraborty (1997), who claimed that the kink observed by Buening and Buseck (1973) was probably due to the setup of their experiments. A more recent study, where the oxygen was more carefully controlled, showed that a transition from one extrinsic to a different extrinsic mechanism was present at an oxygen fugacity of 10-10 Pa and 900 °C. At lower oxygen fugacities Fe-Mg interdiffusion is independent of the oxygen fugacity, whereas at high oxygen fugacities Fe-Mg interdiffusion becomes dependent on oxygen fugacity. There is also a slight increase in the activation energy for Fe-Mg interdiffusion from ~201 kJ mol-1 in the fO2 dependent regime to ~ 220 kJ mol-1 in the fO2 independent regime (Dohmen and Chakraborty 2007, Dohmen et al. 2007). Diffusion studies have also been of interest because they shed more light upon the rheological properties of the materials of Earth's mantle. The two deformation mechanism that are deemed to be the most important in the Earth's mantle, i.e. dislocation creep and diffusion creep, are both controlled by the diffusivity of the mineral constituents (Ranalli and Fischer 1984, Ranalli 2001). The slowest diffusing species, usually oxygen or silicon in silicates, will then control the rheological properties. Therefore, a number of experiments have been performed in the past on the oxygen and silicon diffusivity in olivine. Jaoul et al. (1980) performed diffusion experiments determining the oxygen self diffusivity in forsterite. They determined the oxygen self-diffusivity to be 5 order of magnitude slower than that of Mg-Fe interdiffusion at the 1500 K and room pressure. They also showed, that for iron-free forsterite, the oxygen self-diffusivity is independent of the oxygen fugacity. Houlier et al. (1988) performed silicon and oxygen tracer-diffusion experiments at 1300 °C at a pO2 ranging from 10-4 Pa to 10 Pa in a natural San Carlos olivine crystal. Although they were not able to determine whether there was a dependence of silicon and oxygen tracer-diffusivity on the oxygen fugacity or not, they showed that silicon is the slowest diffusing cation in natural olivine, about 1 – 2 orders of magnitude slower than oxygen. A comparison of the different studies that have been performed on natural olivines, shows that the activation energy for diffusion of oxygen in olivine, ~300 – 320 kJ mol-1 (Jaoul et al. 1980, 1983, Gérard and Jaoul 1989), only Ryerson et al. (1989) produced at lower activation energy of 266 kJ mol-1, is higher than that of Fe-Mg interdiffusion which is ~200 – 220 kJ mol-1 (Misener 1974, Chakraborty 1997, Dohmen et al. 2007). Houlier et al. (1990) measured an activation energy for silicon self-diffusion of 291 kJ mol-1, whereas Dohmen et al. (2002b) determined the activation energy for silicon self-diffusion to be 531 kJ mol-1. The latter ascribes the relative low activation energy of Houlier et al. (1990) to the fact that diffusion profiles for silicon diffusion in olivine are very short and close to the limits of instrumental precision and analyses, which causes an apparent broadening of the diffusion profiles. Dohmen et al. (2002) took this into account in their study, which would give a similar activation energy otherwise. The results from Dohmen et al. (2002) 6 correspond better to experimental deformation data on olivine (Mei and Kohlstedt 2000, Karato and Jung 2003). Except for Misener (1974), the previously mentioned experiments were all conducted at room pressures. Clearly, since diffusivity is generally pressure-dependent, it can not be simply assumed that these diffusion coefficients are representative for the Earth's interior, where pressure are in the GPa range. The activation volume for Fe-Mg interdiffusion in olivine was determined by several authors to be ~5.0 – 5.5 cm3 mol-1 (Misener 1974, Farber et al. 2000, Holzapfel et al. 2007). This value corresponds well to the value for Mg tracer diffusion in olivine (~ 5 cm3 mol-1) calculated using atomistic modeling by Béjina et al (2009). The group around Jaoul (Bertran-Alvarez et al. 1992, Jaoul et al. 1995) and Chakraborty et al. (1999) determined lower activation volumes for Fe-Mg interdifusion, however the interdiffusion data by the Jaoul group is anomalously high (Dohmen et al. 2007) and the data by Chakraborty et al (1999) was obtained using misaligned crystals in the diffusion couples, which gave an apparent reduction in the Fe-Mg interdiffusivity at high pressures (Holzapfel et al. 2007). In contrast to Fe-Mg interdiffusion in olivine at high pressure, high pressure data on silicon is rather scarce and on oxygen is absent. The effect of pressure on the tracer diffusivity of silicon in olivine was studied by Béjina et al (1997, 1999). Their results indicated that the activation volume for silicon tracer-diffusion in olivine is negligible. Figure 1.4 displays the magnitude of the different ionic diffusivities in olivine. 1.2.2 High pressure polymorphs of olivine Because wadsleyite and ringwoodite compose ~60 vol. % of the Earth's transition zone, they have been the focus of several studies. Chakraborty et al (1999) conducted Fe-Mg interdiffusion experiments on diffusion couples consisting of olivine couples and wadsleyite couples. Their results indicated that Fe-Mg interdiffusion in wadsleyite is roughly 2 orders of magnitude faster than in olivine. This observation was confirmed by Farber et al (2000) in their experiments, who already observed a similar phenomenon on the Mg2SiO4 – Ni2SiO4 joint earlier, where Mg-Ni interdiffusion in the high pressure phases where observed to be three orders of magnitude faster than in the olivine phase (Farber et al. 1994). Kubo et al. (2004), however, expressed concerns about the effect of water in wadsleyite, since it greatly enhances the Fe-Mg interdiffusivity and wadsleyite is known to have a high water solubility (Inoue et al. 1995, Kohlstedt et al. 1996). Holzapfel et al. (2009) performed more diffusion experiment on nominally dry wadsleyite and showed that when one takes into account the effect of fO2, fH2O and iron contents of olivine and wadsleyite in the two phase region in the transition zone,the Fe-Mg interdiffusivity is expected to be 7 orders of magnitude faster in wadsleyite than in olivine. In the same study they also combined all data published on Fe-Mg interdiffusion in wadsleyite to calculate an activation 229 kJ mol-1, which is similar to that for olivine, and an activation volume of 13.9 kJ mol-1, significantly greater than that for olivine. In their diffusion experiments Farber et al. (2000) simultaneously determined the Fe-Mg interdiffusivity of olivine, wadsleyite and ringwoodite. They showed that the Fe-Mg interdiffusivity is very similar in wadsleyite and ringwoodite. Because of the great similarity between both structures, this is in line with expectations. 7 The silicon and oxygen self-diffusivity in wadsleyite have been determined by Simojuku et al. (2004, 2009). Comparison with Fe-Mg interdiffusion in wadsleyite data (Holzapfel et al. 2009) shows that like in olivine, diffusion of silicon and oxygen in the high pressure polymorphs of olivine is 5 – 6 orders of magnitude slower than Fe-Mg interdiffusion (figure 1.4). They determined an activation enthalpy for diffusion in olivine of 291 kJ mol-1 and 409 kJ mol-1 for oxygen and silicon, respectively. This difference in activation enthalpy for diffusion between oxygen and silicon leads to a change of silicon being the slowest diffusing species below 1800 °C to oxygen being the slowest diffusing species above 1800 °C at 16 GPa. In their experiments they were also able to determine the grain boundary diffusivity of silicon and wadsleyite. Their results show that grain boundary is 4 – 5 orders of magnitude faster than volume diffusion at the experimental conditions. The activation energies for grain boundary diffusion they determined to be for silicon ~ 80 kJ mol-1 lower than that for volume diffusion in both wadsleyite and ringwoodite and for oxygen to be 50 kJ mol-1 smaller in wadsleyite and 120 kJ mol-1 smaller in ringwoodite than for volume diffusion. 1.2.3 Perovskite (MgSiO3) Magnesium-silicate perovskite (hereafter perovskite) is the dominant phase in the lower mantle, where it constitute ~ 80 % of the total volume(Fiquet 2001). Therefore it will control to a large extent the rheological 8 Figure 1.4 : a) Iron – magnesium interdiffusivity in wadsleyite and olivine. (1) wadsleyite 13 GPa (Holzapfel et al. 2009) (2) wadsleyite15 GPa (Holzapfel et al. 2009) (3) wadsleyite 16 GPa (Holzapfel et al. 2009) (4) wadsleyite 17 GPa (Holzapfel et al. 2009) (5) olivine 1 atm (Dohmen et al. 2007) (6) olivine 15 GPa (Holzapfel et al. 2009; Dohmen et al. 2007), open circle: Kubo et al. (2004), solid circle:Chakraborty et al. (1999), open square: Farber et al. (2000), solid square: Holzapfel et al. (2009) b) Oxygen and silicon diffusion in olivine and its high pressure polymorphs. (1) Si, olivine 1 atm (Dohmen, Chakraborty, et al. 2002) (2) Si, ringwoodite 22 GPa (Shimojuku et al. 2009) (3) Si, wadsleyite 16 GPa (Shimojuku et al. 2009) (4) O, ringwoodite 22 GPa (Shimojuku et al. 2009) (5) O, wadsleyite 16 GPa (Shimojuku et al. 2009) (6) O, olivine 1 atm (Dohmen, Chakraborty, et al. 2002). After Chakraborty (2010). a b properties of the lower mantle. Since perovskite is only stable at high pressures (above ~ 22 GPa), conducting diffusion experiments on perovskite is challenging and experimentally reported diffusion coefficients are scarce. Yamazaki et al. (2000) were the first to report on silicon self-diffusion in perovskite. They determined that the activation enthalpy for silicon self-diffusion in perovskite is ~ 336 kJ mol-1, which for silicon is a rather low value considering that the experiments were conducted at 25 GPa. The nature of their experiments also made it possible to determine the grain boundary diffusivity of silicon, showing that it was ~4 order of magnitude faster than volume diffusion. The activation enthalpy for grain boundary diffusion was determined to be very similar to the activation enthalpy for volume diffusion, implying that grain boundary diffusion may play an important role independent of temperature. Holzapfel et al. (2005) measured the Fe-Mg interdiffusivity in perovskite between 22 GPa and 26 GPa between 1700 °C and 2000 °C. They determined that the Fe-Mg interdiffusion coefficient is three orders of magnitude slower than in olivine at 12 GPa and is of the same order magnitude as that of silicon self-diffusion reported by Yamazaki et al. (2000). This is a rather surprising result, since in the other dominant phases present in the Earth's interior, Fe-Mg interdifussion is several orders of magnitude faster than silicon self-diffusion. In the same study they also determined the activation enthalpy for Fe-Mg interdiffusion in perovskite to be ~414 kJ mol-1, which is slightly greater beyond experimental error than that for silicon self-diffusion. Dobson et al. (2008) performed silicon and oxygen tracer-diffusion experiments similar to the experiments from Yamazaki et al. (2000). For silicon, they basically confirmed the tracer-diffusivities measured by Yamazaki et al. (2000). The oxygen diffusivity was determined to be about two orders of magnitude faster than silicon diffusion, although it has a rather larger activation enthalpy for oxygen diffusion of ~500 kJ mol-1, which is significantly greater than the activation enthalpy for Si determined by Yamazaki et al (2000). Due to the relative large errors on the diffusion coefficients for both Fe-Mg interdiffusion (Holzapfel et al. 2005) and oxygen diffusion (Dobson et al. 2008) it is not possible to determine whether the activation enthalpy of one is greater than the other. Due to the difficulties in conducting experiments at high pressures it is generally very difficult to measure accurate activation volumes for diffusion in perovskite. People have therefore resorted to atomistic methods the determine the diffusivity of the major elements in perovskite. Earlier atomistic studies were able to calculate migration enthalpies of magnesium and oxygen reasonably well, when diffusion in the extrinsic regime was assumed for magnesium diffusion and either the intrinsic and extrinsic regime for oxygen diffusion (Wright and Price 1993, Dobson 2003, Karki and Khanduja 2007, Dobson et al. 2008). They failed however in reproducing the migration enthalpy for silicon diffusion. Ammann et al. (2009) performed a more thorough search for the silicon saddle point, which defines the activation energy for diffusion. They found a more reasonable value for the activation enthalpy for silicon diffusion of about 453 kJ mol-1, at 26.2 GPa. Ito and Torumi (2010) took a different approach using molecular dynamics simulation that does not make any assumptions about the location of the saddle point and obtained an activation enthalpy at 25 GPa for silicon diffusion in perovskite of ~ 332 kJ mol-1, though their simulation were performed at temperatures (~ 3900 °C – 9 5600 °C) well above the Earth's geotherm. The activation volumes for silicon diffusion in perovskite determined by the above mentioned atomistic studies are usually below 3.5 cm3 mol-1 at lower mantle conditions and decreases with increasing pressure. Activation volumes for magnesium diffusion are slightly higher than those for silicon diffusion. It can thus be concluded that Fe-Mg interdiffusion is anomalously sluggish in perovskite, and it might be the rate limiting process in deformation during diffusion creep or dislocation creep. In this case there might be a strong dependence of the rheological properties of the lower mantle on the oxygen fugacity, since the number of iron and magnesium vacancies is usually dependent on the oxidation state of the mantle. 1.2.4 Magnesiowüstite Magnesiowüstite or ferropericlase (Mg,Fe1-x)O is the second most abundant phase in Earth's lower mantle, constituting about 20 vol.% of the lower mantle. Though not the most abundant phase in the lower mantle, as a weak phase it may still play a significant role in determining the rheological behaviour of the lower mantle (Stretton et al. 2001, Heidelbach et al. 2003). Again the mobility and thus diffusivity of iron, magnesium and oxygen in magnesiowüstite will play an important role in determining the rheological properties of this mineral. As with the other previously mentioned minerals Mg-Fe interdiffusion profiles in magnesiowüstite are usually highly asymmetric (Rigby and Cutler 1965, Blank and Pask 1969, Mackwell et al. 2005). This is no surprise, as wüstite is one of the classical examples exhibiting non-stoichiometry due to oxidation of divalent iron. Though the earlier study by Rigby and Cutler (1965) showed no dependence of the activation energy for Fe-Mg interdiffusion in magnesiowüstite on iron content, Blank and Pask (1969) showed there was a positive exponential dependence of the activation enthalpy on the iron concentration in magnesiowüstite. This was subsequently also confirmed by other studies, where the effect roughly amounts to a decrease of the activation enthalpy of 1.0 – 1.3 kJ mol-1 per molar percent of FeO. (Chen and Peterson 1980, Sata and Goto 1982, Holzapfel et al. 2003, Yamazaki and Irifune 2003, Mackwell et al. 2005). The activation energy for Fe-Mg interdiffusion in these studies was determined to be ~210 kJ mol-1. Different studies have also shown there is a D = D' fO21/n dependence of the Fe-Mg interdiffusivity on the oxygen fugacity, for which n is in the range of 5 -6 for geological relevant compositions (Chen and Peterson 1980, Sata and Goto 1982, Mackwell et al. 2005). This indicates that oxidation of ferrous iron in magnesiowüstite is balanced by the formation of vacancies on the metal sites (see also chapter 2). Not many diffusion experiments have been conducted at pressures relevant to the Earth's lower mantle. Holzapfel et al. (2003) and Yamazaki and Irifune (2003) performed Fe-Mg interdiffusion experiments at conditions relevant to the upper part of the lower mantle. Both studies reported different activation volumes for Fe-Mg interdiffusion, 3.3 cm3 mol-1 was reported in the former and 1.8 cm3 mol-1 in the latter study. Mackwell et al. (2005) showed that both studies could be reconciled with each other, if the oxygen dependence of Fe-Mg interdiffusion was taken into account, since both studies were conducted using a different oxygen buffer. Both studies however also reported a different activation energy for diffusion, which would mean that 10 the activation energy for Fe-Mg interdiffusion is also dependent on the oxygen fugacity. Hints to this were given by Sata and Goto (1982), who found that the decrease of apparent activation energy for Fe-Mg interdiffusion as function of iron content is dependent on the oxygen fugacity. Oishi et al. (1983) determined the oxygen self-diffusivity in pure end-member MgO. Their results showed that there was a change in activation energy around 1500 °C. The activation energy in the high temperature regime appeared to be independent of the impurity concentration. This break has therefore been interpreted as being a transition from an extrinsic regime below 1500 °C, characterized by an activation energy of ~ 213 kJ mol-1, to an intrinsic regime, characterized by an activation energy of ~ 536 kJ mol-1. Ando et al. (1983) showed that in contrast to Fe-Mg interdiffusion, the oxygen diffusivity is independent on the iron concentration. Van Orman et al. (2003) confirmed that the oxygen diffusivity in MgO is also independent on trivalent impurity content at high pressures. As their study was a tracer diffusion study, they were able to determine the activation volume for magnesium tracer diffusion in MgO, and determined it to be ~ 3.0 cm3 mol-1., which is in good agreement with the magnesium self-diffusion coefficients obtained from atomistic simulations (Ita and Cohen 1997). The latter predict also a decreasing activation volume for magnesium self-diffusion with increasing pressure. 1.2.5 Garnets Though garnets constitute an important part of Earth's upper mantle and transition zone, in the latter they constitute up to ~40 vol.%, only a few experiments have been conducted at conditions prevalent in the transition zone. Most of the diffusion studies were conducted at pressure below 4 GPa. Though diffusion models in garnet based on zoning in natural garnets have been formulated earlier (Anderson and Buckley 1973, Loomis 1978), the first report from diffusion experiments on garnet is by Freer (1979). In this study Fe-Mn interdiffusion was observed in almandine garnet – sintered spessartine garnet diffusion couples at 1 bar and between 822 °C and 1200 °C. A concentration dependent manganese diffusivity was observed, which was fitted against an exponential function, similar to as what has been done in the case for magnesiowüstite and olivine. The manganese diffusivity increases about half an order of magnitude from a garnet containing 5 wt.% of Mn to a garnet containing 20 wt.% Mn at a temperature of 1002 °C. From the constant pressure experiments also an activation energy for Fe – Mn/Mg interdiffusion of 132 ± 45 kJ mol-1, which as will be discussed later, is significantly lower than the other studies on Fe-Mg interdiffusion in garnet. The early theoretical models (Anderson and Buckley 1973, Loomis 1978, Lasaga 1979) for interdiffusion in garnet note that during diffusion the fluxes of cations cannot be considered to be independent, but are correlated by cross terms in the matrix of diffusion coefficients. This thus introduces a compositional dependence in the diffusivity of the component. This occurs, however, through a different mechanism as Fe-Mg interdiffusion mentioned in the above minerals, where the iron concentration modifies the both vacancy concentration and the activation enthalphy for diffusion and thereby makes Fe-Mg interdiffusion concentration dependent. In the experiments conducted on Fe-Mg-Mn interdiffusion on spessartine – almandine couples by Elphick et al. 11 (1985) it was noted that their diffusion profiles could not be fitted by a single composition independent diffusion coefficient. Subsequently they fitted their profiles by two diffusion coefficients, one for both ends of the diffusion couple. Loomis et al. (1985) re-analysed the data of Elphick et al. (1985) and fitted the diffusion models of Lasaga (1979) and Manning (1968) to the data. Doing so, he determined that the tracer diffusivity of manganese is roughly 3 – 5 times larger than the tracer diffusivity of iron and magnesium. The tracer diffusivity of the latter two was determined to be very similar in magnitude in the almandine – spessartine diffusion couples. Using their method, Elphick et al. (1985) determined a difference up to a factor two in interdiffusivities between both sides. Loomis et al. (1985) also determined that the activation enthalpy for (tracer) diffusion at 40 kbar of magnesium is (251 ± 33 kJ mol-1) and iron (257 ± 36 kJ mol-1) is significantly greater than that of manganese (202 ± 33 kJ mol-1). The activation volume for tracer diffusion in garnet they determined to be ~4.7 cm3 mol-1 in the two studies. The dataset of Loomis et al. (1985) has been extended by Chakraborty and Ganguly (1992) to cover a greater pressure and temperature range. The determined activation energies for tracer diffusion were slightly higher ( Fe: 276 ± 36 kJ mol-1, Mg: 285 ± 38 kJ mol-1, Mn: 254 ± 37 kJ mol-1). The activation volumes for diffusion was also a bit higher than in the study by Loomis et al. (1985), but within experimental error of the latter (5 – 6 cm3 mol-1 with a ~ 3 cm3 mol-1 error). Ganguly et al. (1998) extended the dataset further with data from interdiffusion experiments conducted at the almandine – pyrope joint and also include calcium and manganese diffusion data. These diffusion experiments showed a strong contrast in relative diffusivities of magnesium, iron and manganese in almandine – pyrope couples as compared to almandine – spessartine couples by Loomis (1985). The relative tracer diffusivities in the Ganguly et al. (1998) study are approximately DMg = 10 DFe = 3 DCa and manganese tracer diffusivity is similar to that of iron, whereas at the almandine – spessartine join iron selfdiffusion is similar to magnesium tracer diffusion. The activation energies and volume for diffusion along the CO buffer in the spessartine – almandine couples and almandine – pyrope couples are equal within each others errors, indicating that the change in relative diffusivities in not very likely caused by a change in diffusion mechanism. Ganguly et al. (1998) also showed that the oxygen fugacity has a profound effect on the determined apparent activation volume for diffusion. Schwandt et al. (1996) performed calcium tracer diffusion experiments on garnet between 800 – 1000 °C and at 1 bar. They obtained extremely short diffusion profiles (~ 20 nm) which indicated that calcium self-diffusion is at least one order of magnitude slower than magnesium self-diffusion at the same conditions in their earlier experiments (Schwandt et al. 1995). Their activation energy for self-diffusion is significantly lower than that determined in other studies (Freer and Edwards 1999, Perchuk et al. 2008), which might be a result of the extremely short profiles. The Ca self-diffusion coefficients from Freer and Edwards (1999) are however 3 – 4 orders of magnitude faster than obtained by other workers (Schwandt et al. 1996, Ganguly et al. 1998, Vielzeuf et al. 2007, Perchuk et al. 2008). Although there is some discrepancy in calcium diffusion data from the above mentioned workers, they generally agree that calcium is the slowest diffusing divalent cation in garnet. 12 it may be expected that the dissolution of pyroxene is hindered and thus pyroxene may be present to depths greater than expected for an equilibrium assemblage. As there is a significant density contrast between garnet and pyroxenes, this may have important implications for the dynamics of subduction zones. The results of Sharp and Rubie (1995) have shown that HP high clinoenstatite catalyses the nucleation of ringwoodite during the transformation of olivine to wadsleyite and/or ringwoodite. Though reaction kinetics of the olivine to wadsleyite and ringwoodite transformation are controlled by the growth kinetics, and therefore the metastable preservation of HP clinoenstatite is unlikely to influence the transformation kinetics, it may result in a reduced grain size of wadsleyite and ringwoodite after transformation. This in turn may enhance superplasticity, which is thought to cause deep-focus earthquakes in subduction zones, as explained. Furthermore, pyroxene exsolution needles have been found in several UHP provinces (Song et al. 2004, van Roermund 2009, Pandey et al. 2010). The rate of dissolution of pyroxene into garnet and the rate exsolution of pyroxene from garnet in these cases will also be controlled by the diffusivity of the majorite component. The lack of exsolution needles in pre-Scandian garnets from Norway in combination with diffusion data on the majorite component in garnet may be used to constrain the duration of UHP metamorphism in these provinces. It is thus clear our understanding of important geological process occurring in the interior of the Earth will benefit from constraints on the major element diffusivity in garnet at depth. At present unfortunately, there is neither data on major element diffusion in garnet available at the conditions prevalent in the Earth's transition zone, nor data on the majorite diffusivity in garnet. During this PhD experiments it has been attempted to, at least partially, fill this gap in garnet diffusion data. Additionally, there is no data available on the aluminium diffusivity in HP high clinoenstatite. As reviewed in the reaction kinetics chapter the microstructure of phases in the transition zone controls among others the strength of the subducting slab. It is expected that the aluminium component will be exsolved as majoritic garnet. This requires long-range transport of aluminium in enstatite and the exsolution of garnet from HP high clinoenstatite will therefore be controlled by the aluminium diffusivity in HP high clinoenstatite. In this PhD study it has been attempted to study the microstructure of the majoritic garnet exsolution products from high clinoenstatite and to determine the diffusivity of aluminium in HP high clinoenstatite to gain a better understanding of the properties of metastable HP high clinoenstatite at transition zone conditions. This dissertation therefore reports on two different studies perfomed during this PhD. The first part reports (chapter 5) on the results of an experimental study on the major element diffusivity in garnet at transition zone conditions. 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Natural garnets are often described in terms of end-member components, which are listed in table 2.1 . The space group of natural garnet is Ia3d, which is one of the cubic Bravais lattices, and the unit cell contains 8 formula units (160 atoms). Its lattice parameters depend on composition (and physical conditions), but range at ambient conditions between a = 11.4 Å for pyrope to a = 12.7 Å for the (hypothetical) end-member hydrogrossular. The 96 oxygen atoms in garnet occupy the h-position in this unit cell, and the metal cations either occupy the 16 apositions (octahedral sites), 24 c-positions (dodecahedral sites) or 24 d-positions (tetrahedral sites). Though natural garnets have 96 oxygen atoms and 64 metal cations in its unit cell, it can conveniently be described by the general chemical formula X3Y2Z3O12. The X metal cations (Mg, Fe2+, Ca and Mn) occupy the distorted cubic c sites of garnets, the Y metallic cations (Al3+, Fe3+, Cr3+) occupy the octahedral sites, and the Z metallic cations (mostly Si4+) occupy the tetrahedral sites. The tetrahedra share two edges with the neighbouring dodecahedra, the octahedra share six edges with neighbouring dodecahedra and the dodecahedra share two edges with neighbouring tetrahedra, four with neighbouring and four with other neighbouring dodecahedra (figure 2.1). Since garnet is a common mineral in high pressure metamorphic terranes and its end-members form a complete solid-solution with each other, they are often used when in equilibrium with other phases as geothermometers. O'Neill and Wood (1979) calibrated a thermometer for the Mg-Fe exchange between garnet and olivine, and geothermometer were developed for Fe-Mg exchange between garnet and biotite (Holdaway 2000), between clinopyroxene and garnet (Ellis and Green 1979, Powell 1985)., and between orthopyroxene and garnet (Harley 1984). Next to its use as a geothermometer, garnet is also often used as a geochronometer dating metamorphic event, using the Lu-Hf, Sm-Nd and U-Pb systems. Therefore, garnet constitute an 28 Table 2.1: Chemical composition of the most important garnet end-members. End-member name Chemical formula Pyrope Mg3Al2Si3O12 Almandine Fe2+3Al2Si3O12 Grossular Ca3Al2Si3O12 Spessartine Mn3Al2Si3O12 Andradite Ca3Fe3+2Si3O12 Uvarovite Ca3Cr2Si3O12 Skiagite Fe2+3Fe3+2Si3O12 Hydrogrossular Ca3Al2H12O12 Hydroandradite Ca3Fe3+2H12O12 3FeFe+½O2(gas)⇋2FeFe +VFe '' +FeO (2.8) for which the equilibrium constant can be written as: K=[FeFe ]2[VFe ' ' ]aFeO fO2 ½ (2.9) Where [ ] denotes the concentrations of the reactants. Subscripts in the two above equations denote the site that is occupied by the ion (V for vacancy) and the superscript denotes the electrical charge of the site. A solid circle denotes that the site is positively charged (every solid circle corresponds to an electron hole), a prime denotes a negatively charged site (every prime corresponds to a surplus electron). From equation 2.8 it can be seen that [Fe•Fe] = 2 [V''Fe] and assuming that activity of FeO does not change significantly with oxygen fugacity fO2 they write the concentration of iron or metal vacancies as function of oxygen fugacity as: [VFe ' ' ]∝fO2 1/6 (2.10) This mechanism requires that Fe3+ can be accommodated on an Fe2+ site, which might be questionable for normal garnets, since as of yet, there is no convincing evidence that Fe3+ can occupy the dodecahedral site in garnet (C. McCammon, pers. comm.). However, for majoritic garnet it has been found that there is charge transfer between adjacent docecahedrally coordinated Fe2+ and octahedral coordinated Fe3+ (Keppler and McCammon 1996), so the dodecahedrally coordinated Fe3+ ion (directly after oxidation) might receive an electron from its neighbouring octahedrally coordinated Fe2+ ion, effectively exchanging its 3+ charge with the 2+ charge of its octahedral neighbour. However the strong partitioning between Mg and Fe on the octahedral site in majorite, with Mg preferentially on the octahedral site (O’Neill et al. 1993), might inhibit this mechanism. Also the presence of octahedrally coordinated ferrous iron in majorite might enable the above mentioned mechanism at higher pressure. Mackwell et al. (2005) developed the following general expression based upon point defect chemistry:  D=DV 0e−Qm/RT  k1 0k2 0fO2 mxpe−Qf x/ RT  (2.11) where k01 and k02 are equilibrium constants for the intrinsic and extrinsic vacancy mechanisms respectively, m and p are constants depending on the vacancy mechanism (1/6 for equation 2.8), Qm is the migration enthalpy for a metal vacancy, Qf the formation enthalpy for metal vacancies at low iron concentrations, x is the iron concentration and the term -α·x in the exponential corrects for change in formation enthalpy at higher iron and vacancy levels. 2.2.5 Multi-component models When more than one component or element is diffusing at the same time, as a result of mass conservation and from the Gibbs-Duhem equation, their fluxes have to be coupled. Irreversible thermodynamics shows that fluxes can often be linearly related to their driving forces (Groot and Mazur 1984). In the absence of temperature gradients and external forces the driving force for diffusion in an n-component system becomes 35 the gradient in chemical potential μi of the components (Groot and Mazur 1984, Ganguly 2002): Ji=−∑ k n−1 Lik  ∇k−n T  (2.12) Where L is a matrix of phenomenological coefficients. The last flux is calculated considering conservation of mass. In the case that the off diagonal elements in L can be neglected the equation leads to the following expression for the diffusion coefficient Di: Di=Di +  1∂ln i ∂ln Ci  (2.13a) where γi is the activity coefficient and Di +=RLi Ci (2.13b) where R is the gas constant. Equation (2.13a) splits the chemical diffusion coefficient in two parts, an ideal part and a thermodynamic part, the part within brackets is usually referred to the thermodynamic factor. Note that although off diagonal terms in L are negligible, the diffusion coefficients and fluxes still coupled through the activity coefficients. In the case that the off diagonal terms in L are not negligible one needs to rewrite (2.1) as: Ji=−∑ j Dij ∇Cj (2.14) Loomis (1978) derived an expression for the diffusion coefficient matrix D from irreversible thermodynamics: Dij=ij Di 0Di 0Xi [ ∂ln i ∂Xj −∂ln i ∂Xn ] −Xi∑ k=1 n−1 XkDk 0−Dn 0 [ jk Xk ∂ln k ∂Xj −∂ln k ∂Xn ] (2.15a) δij is kronecker's delta (δij = 0 for i ≠ j, δij = 1 for i = j) and Di0 denotes the tracer diffusion coefficient for component i. In the case of ideal solutions this reduces to: Dij=ij Di 0XiDn 0−Dj 0 (2.15b) Lasaga (1979) derived, also from irreversible thermodynamics, a different expression for the D matrix in the case of ionic diffusion, which is more appropriate to minerals: Dij=Di 0ijDi 0ci [ ∂ln i ∂cj −∂ln i ∂cn ⋅zj zn ] −  Di 0zici ∑ k=1 n zk 2ckDk 0  × { zjDj 0−Dn 0∑ k=1 n zkckDk 0 [ ∂ln k ∂cj −∂ln k ∂cn ⋅zi zn ] } (2.16a) which reduces for (near) ideal solutions or negligible activity coefficient gradients to a more comprehensible form: 36 Dij=Di 0ij−Di 0zizj ∑ k=1 n zk 2ckDk 0 ⋅ Dj 0−Dn 0 (2.16b) In the equations zi is the charge of ion i and the size of the diffusion matrix D is (n – 1)x(n – 1), the last profile is calculated by charge balance. In the case that there are only two ions diffusing, both with an equal charge, equation 2.10b becomes the well known expression for binary interdiffusion of charged species (Manning 1968): D11=Dbinary ionic =D1 0D2 0 X1D1 0X2D2 0 (2.17) where Xi is the cation mole fraction of cation i, i.e. X1 = c1 / (c1 + c2). Chakraborty and Ganguly (1992) used the ideal Lasaga model successfully to model Fe – Mg – Mn diffusion profiles in garnet and to obtain tracer diffusion coefficients for Fe, Mg and Mn. The validity of the model for garnets was confirmed by a Mg tracer diffusion study on garnet by Chakraborty and Rubie (1996). 2.3 References Akaogi, M., Akimoto, S. (1977), Pyroxene-garnet solid-solution equilibria in the systems Mg4Si4O12 – Mg3Al2Si3O12 and Fe4Si4O12 – Fe3Al2Si3O12 at high pressures and temperatures. Phys Earth Planet Inter 15:90106. doi: 10.1016/0031-9201(77)90013-9 Andersen, T.B. (2010), Excursion Guide, Western Norway 3-4 June 2010. 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Nature 407:734-736. doi: 10.1038/35037566 40 Chapter 3: Experimental and analytical techniques 3.1 High pressure – high temperature experiments To simulate actual geological processes that are occurring in the Earth's upper mantle and transition zone one needs to reproduce the conditions prevalent there. It is usually assumed that heat transport due to thermal conduction is negligible in the Earth's mantle (Fowler 2005). The temperature profile in the mantle can thus be well approximated by an adiabatic temperature profile for which the temperature gradient as a function of depth r is given by (Fowler 2005):  ∂T ∂r  S =−Tg Cp (3.1) where T is temperature, α is the coefficient of thermal expansion for the bulk mantle, g acceleration due to gravity and Cp the heat capacity at constant pressure. The figure below shows three different mantle adiabats for different potential temperatures, i.e. the temperature of the adiabat extrapolated to the surface, thought to be representative for the Earth's present mantle (McKenzie and Bickle 1988, Anderson 2000, Fowler 2005, Katsura et al. 2010). To simulate the conditions prevalent in the mantle transition zone one thus needs a device to generate pressures in the range of 15 – 24 GPa (ca. 410 – 670 km) and temperatures in the range of 1450 – 1800 °C. Two different devices are generally used to reach these conditions, i.e. the diamond anvil cell and the multi-anvil apparatus. The last device has been used for this dissertation and is therefore explained in more detail below. 41 Figure 3.1:The mantle adiabat calculated for three different potential temperatures (temperatures extrapolated to the Earth's surface). The thermal expansion coefficient is taken from Katsura et al. (2010) and approximated by an exponentially decaying function as function of depth. 3.1.1 The Multi-anvil apparatus High pressure devices can generate high pressures following two different approaches which can be understood from the general equation for pressure: p=F A (3.2) where p is pressure, F is force and A is the surface area over which the force is applied. The first approach would be to apply a reasonable force over a very small surface area, an example of such a device is the diamond anvil cell (DAC). The down side of this type of devices is that the sample volume is also very small, which might pose a problem with analytical techniques, and large pressure and temperature gradients exist in a DAC. The second approach is to generate a large force and apply this on a (reasonable) small surface area. Such a device is the multi – anvil press, which was used in this diffusion study. The sample volume that can be used in the multi-anvil apparatus is considerably larger than that of the DAC, and in addition it generates more hydrostatic conditions and temperature gradients within the assembly are smaller (Ito 2007).The down side of the multi-anvil apparatus is that in-situ measurements are more complicated than in the DAC, and generally require a high brilliance x-ray source like a synchrotron in the case of a study requiring x-rays (Keppler and Frost 2005). The first modern multi-anvil device used in most laboratories now, was designed by Kawai and Endo (1970). It consisted of a 6 / 8 type split-sphere multi-anvil device. This means that a set of six hardened steel outer anvils that form a sphere when assembled were used as first stage anvils. The six outer anvils are truncated in such a way, that in the centre of the sphere they create a cubic cavity. In this cubic cavity a set of eight second stage tungsten carbide anvils are put. Each of the eight WC cubes has (at least) one of its corners truncated. Assembled, these WC cubes form an octahedral cavity in its centre in which the pressure medium with the 42 Figure 3.2: sketch of the 6 / 8 split-sphere design incorporated in a metal guide block. The top and lower part of the first stage anvils are truncated to inhibit rotation of the anvils. The MgO pressure cell has been put in the centre of the 8 WC cube second stage anvils, with truncated corners. experimental load is placed. In the original design of Kawai and Endo the spherical assembly was contained in a rubber shell and then submerged in an oil reservoir. This oil reservoir was pressurized and the pressure exerted by the oil reservoir is then transmitted and concentrated by the anvils on the octahedral pressure medium contained within the octahedral cavity created by the WC anvils. In later designs the oil reservoir was replaced by guide blocks in which the lower and upper half of the spherical anvil assembly was placed, greatly reducing the cumbersome preparation of the experiments (Kawai et al. 1973). The upper and lower guide blocks are driven together by a uni-axial hydraulic press. The hydrostatic conditions in this case must be provided by using appropriate pressure media. In later designs the top and lower parts of the first stage anvils were truncated in order to inhibit the rotation of the anvils (Keppler and Frost 2005). Using traditional WC anvils the maximum attainable pressures are around 28 – 30 GPa, which is sufficient for the upper mantle, transition zone and top part of the lower mantle. Higher pressures however, can be obtained by using sintered diamond anvils, which are also more costly. Recently, pressures up to 90 GPa have been reached using a multi-anvil apparatus equipped with sintered diamond second stage anvils (Ito et al. 2010). The cavity in the second stage anvils is filled with a (usually) MgO pressure cell, which needs to be longer than the truncation lengths of the WC anvils to generate the high pressure conditions. The maximum attainable pressure is dependent on the ratio of octahedral edge length to truncation edge length and their absolute sizes, the compressibility of the pressure medium, the resistance to plastic deformation of the anvils, the sealing action of the gasket material, and the maximum load of the press. As the pressure medium will get compressed during loading, the pressure medium will be extruded out of the octahedral cavity, forming a gasket. Usually an additional set of pyrophyllite gasket strips are placed around the octahedral cavity, to give better lateral support to the second stage anvil assembly and to prevent blow-outs (Ito 2007). At high loads most of the applied force by the press will be put in extruding the gasket material, and thus reducing the pressure generating efficiency of the press and the deformation properties of the gasket is thus an important factor in determining the maximum attainable pressure (Ito 2007). In the early designs of Kawai and Endo (1970) and Kawai et al.(1973) the used pressure medium was pyrophyllite (Al2Si4O10(OH)2), which is a phyllosilicate mineral. However, pyrophyllite breaks down above 600 °C and 10 GPa successively into stishovite + an unknown hydrous aluminosilicate and stishovite + Al5Si5O17(OH) and above 20 GPa into stishovite + corundum, which resulted in a reduction of pressure during high pressure runs (Ito 2007). Nowadays, semi-sintered MgO (with a porosity of ~ 35%) is being used as pressure media. Under high temperatures MgO has a very low shear strength and thus generates a good hydrostatic pressure regime (Keppler and Frost 2005). Through the centre of one of the faces of the octahedron a cylindrical hole is drilled in which a hollow cylinder of ZrO2 is put surrounding the heater. The role of the ZrO2 cylinder is to thermally isolate the resistance heater, since the thermal conductivity of MgO is high, making it very difficult to heat the experiment above 1000 °C without the thermal insulator. Different materials can function as heater, the most common being a metal foil (e.g. platinum or rhenium), LaCrO3, TiC3 / diamond mixture or graphite heater. At the Bayerisches Geoinstitut usually LaCrO3 heaters were used. LaCrO3 also reduces temperature gradients within 43 the furnace because of its negative resistance dependence on temperature, especially for smaller pressure cells (Kawashima and Yagi 1988). Further reduction of temperature gradients inside the furnace can be achieved by using a stepped heater, where the heater consists of three cylinders of which the thickness of the wall of the middle one is greater than the outer ones (Kawashima et al. 1990). The temperature is measured by thermocouples in the multi-anvil apparatus. Thermocouples work because thermal gradients in (semi-)conductors induce an electrostatic potential difference between the hot and cold end, also known as the Seebeck effect. If two conductors (or metal) with different Seebeck coefficients are used to create a circuit, an electrical current will start to flow, of which the magnitude is dependent on the actual temperature gradient along the thermocouple wire. Thermocouples used in the multi-anvil usually consist of W3%Re – W25%Re thermocouple wires or W5%Re – W26%Re thermocouple wires because of their high melting points and the small pressure effect of thermocouple voltage on pressure, which is unknown quantitatively (Keppler and Frost 2005). The thermocouple can be incorporated in two ways in the octahedral pressure cell. The first way, and as used in the diffusion study in this dissertation, the thermocouple is put close to the capsule 44 Figure 3.3: Two sketches of the MgO pressure cell used in the multi-anvil apparatus. a) Pressure cell with where the thermocouple is brought in radially. b) Pressure cell where the thermocouple is brought in axially. The former one is used at the Bayerisches Geoinstitut for smaller assemblies. a b 200 kV (though high voltage TEMs go up to 3 MeV), which would thus correspond to a wavelength of 4.2 pm and 2.5 pm respectively. To compare, the radius of a silicon atom is 111 pm (1.1 Å). Since high energy electrons cannot be focused by glass lenses (they would be absorbed and backscattered like in the case of bulk samples), magnetic lenses are used in a TEM. Those lenses consist of a hollow cylindrically symmetric soft magnetic core, i.e. the core is easily magnetized and demagnetized, surrounded by a copper coil which generates a radially symmetric magnetic field when a current flows through it. The objective lens is the most important and complicated lens in the TEM since it produces the image and diffraction pattern, which the other image forming lenses merely magnify (Williams and Carter 2009). 3.2.3 Elastic scattering within the specimen As the electrons enter the specimen they will interact with the electrostatic potential of the specimen lattice, resulting in elastic scattering of the incident electrons. This kind of scattering is associated with only a negligible loss of energy of the incident electron beam. The other kind of scattering, inelastic scattering, where there is a significant transfer of energy between the involved particles is giving another kind of information, and is treated later. The TEM has four different modes of imaging: •Diffraction mode •Amplitude contrast imaging (BD/DF mode) •High resolution mode (HRTEM) •STEM mode In diffraction mode an image of the back-focal plane of the objective lens is produced on the imaging plane. In the case that the incident electron beam is illuminating the specimen parallel, the image produced will consist of a pattern of spots. Each such a spot corresponds to a beam that is refracted from a plane that (nearly) satisfies the Bragg condition: n=2dsinB (3.5) where n is an integer, d is the spacing of the refracting lattice planes and θB is the refraction angle (know as Bragg's angle). The diffraction pattern is defined by the intersection of the reciprocal lattice and the Ewald sphere, which can be shown to be a geometrical reconstruction of the Bragg conditions. Amplitude contrast imaging can be done by either selecting the direct beam or one of the diffracted beams by the use of an objective aperture. In the former case it is called bright field (BF) imaging, in the latter case dark field (DF) imaging. The names originate from the fact that in DF imaging, holes in the foil appear black and the picture is generally darker than for BF imaging. These two imaging techniques can be used to image strain fields within crystals. Strain is defined by the displacement of an atom from its position that would be expected from the ordinary periodicity of the crystal. Causes of such a strain field can be dislocations, planar defects or other imperfections in the crystal lattice. 51 The distortion of the lattice around a dislocation core may alter the lattice in such a way that diffracted beams that are in the undistorted lattice not excited, become exited in the distorted lattice. The displacement field around a dislocation core for an isotropic solid is given by (Williams and Carter 2009): R=1 2  b 1 41− {beb×u21−2ln rcos2}  (3.6) where be is the edge component of the burgers vector, ν Poisson's ratio and r and φ are the spherical coordinates along the dislocation line. The Howie-Whelan (HW) equations, the equations that describe the intensity of the direct and diffracted beam and thus the contrast in amplitude contrast images, can be modified to include a lattice distortion (Williams and Carter 2009): dg dz =i 0 gi g exp [ −2iszg⋅R ] (3.7) where g is the diffracted beam used to image. The only difference to the HW-equations for an undistorted lattice is the additional g∙R term, and thus only a change in contrast will be observed when the scalar product of the diffraction vector and displacement field will be non-zero. If the displacement field is the one corresponding to a pure screw dislocation R reduces to R = bφ / 2π. The dislocation for a screw dislocation will thus not be visible is the Burgers vector is perpendicular to the diffracted beam. In the case of a pure edge dislocation we need the complete form of 3.6, so the invisibility criteria become g∙b = 0 and g∙(b x u) = 0. The last term can be ascribed to the buckling of lattice planes perpendicular to both the Burgers vector and dislocation line (Williams and Carter 2009). Using dark field imaging, one can thus determine the Burgers vector and slip system of the studied phase. Another type of defects are planar defects. Examples are stacking faults, anti-phase domain boundaries and grain boundaries. Again one can use a displacement vector R to describe the translation of the lattice over the planar defect, a point rn corresponds on the other side of the planar fault to the point rn' = rn + R. Since R on either side of the planar defect is independent of z, equation 3.7 comes down to adding a phase term to HowieWhelan equations for the diffracted beam, which can be written as eiα; where α = 2πg∙R. Again, no change will be visible when α = 0. When α ≠ 0, there will be a change in contrast depending on the depth of the planar defect. In the case of an inclined planar defect, light and dark fringes will be visible, since one needs to integrate 3.7 over the amount of foil under the planar defect. Similarly to dislocations, one can determine the displacement vector by a more detailed investigation of the fringes with different g∙R conditions. Bright field, dark field and weak beam dark field imaging are all amplitude contrast imaging techniques, which is one of the two main imaging modes of the TEM, as already explained. The other imaging mode is phase contrast imaging, where the contrast in the image is caused by interference of multiple beams. To do so, one uses an aperture if the back focal plane of the objective lens to let some of the diffracted beams pass through and block the others. When one selects a 2D array of diffracted beams in the objective aperture, a phase contrast image will be formed with a two dimensional structure. The image formed in HRTEM images can be 52 expressed as the product of several contributions. The first one being the specimen function describing how the specimen interacts with the incident electron beam and what wave function of the electron beam is after they emerge from the specimen. The other contributions arise because of the electron optical system and its main components are those from the apertures, attenuation of the wave in the lens and aberration of the lens from a perfect lens (Williams and Carter 2009). The image one observes in the end can be written as a convolution of these contributions: gr=∫fr'hr−r'dr'=fr∗hr (3.8) where f is the specimen function and h is the function describing the electron optical system, the * denotes the convolution f with h. The convolution can be written as the product of the Fourier transform of the functions that are convolved together. If we break down h into the contributions mentioned above one can write: Gu= AuEuBuFu (3.9) where A is the Fourier transform of the aperture function, E the Fourier transform of the envelope (attenuation) function, B the fourier transform of the aberration function, F the Fourier transform of the specimen function an u a reciprocal lattice vector. Equation 3.9 decribes how the detail on a certain scale (u) is affected by the electron optical system. The specimen function can be written in the phase object approximation (POA), which holds for thin specimens and when absorption can be neglected (Spence 2009, Williams and Carter 2009): fr=exp  −iVpr  (3.10) where Vp is the projected electrostatic potential of the lattice parallel to the x-y plane (perpendicular to the incident electron beam) and σ = π/λE the interaction constant. The specimen function is thus directly related to the (projected) electrostatic potential inside the specimen itself. 53 Figure 3.7 :Lattice fringes in enstatite. The dominant structure visible are lattice fringes related to the 18.2 Å lattice repeat ((1 0 0) plane spacings). Stacking faults run from the top left to the bottom right. The final mode is the scanning transmission electron microscope (STEM) mode. In this mode the electron optical system creates a condensed probe which scans the specimen, similar to in an SEM. For every pixel the intensity of either the direct beam (bright field STEM) or diffracted beams (dark field STEM) are measured using an angular detector. In this way the image is build by scanning over the specimen with the condensed beam. This mode has been used to measure the diffusion profiles presented in chapter 4. 3.2.4 Inelastic scattering – Energy dispersive spectroscopy Al already stated, the other type of interaction between high energy incident electrons and the atoms of the specimen is inelastic scattering. The main difference between elastic scattering and inelastic scattering is that the latter one involves a significant amount of energy transfer from the incident electron to the particle with which it interacts. To get an impression of the importance of the different types of scattering, one can have a look at the probability that a particular process will occur and scatters an incident high energy electron, which is given by the scattering cross section. An overview of the importance of the different scattering processes is given in figure 3.8. Inelastic scattering can occur due to energy transfer during electron – atom interactions, electron – electron interactions, and interactions with multiple atoms or electrons simultaneously. The first kind of interaction is also the cause for elastic scattering, and in a crystal lattice it will result in a sharply peaked distribution of scattering directions, called diffraction as described in the previous section. During high angle scattering, enough energy can be transferred to the atoms such that the atom is knocked out of its position in the specimen lattice, resulting in knock-on or displacement damage within the specimen. (Egerton 1996), a process that can lead to complications during the chemical analyses of specimens. In appendix 5.1 a method is described to correct for this kind and other kinds of radiation damage. The second kind of interactions, electron – electron interactions, results in the transfer of energy from the incident electron to electrons of the scattering atom in 54 Figure 3.8: Scattering cross sections in Al in the case of forward scattering (θ = 0°) for different types of electron - specimen interactions. P = plasmon scattering, E = elastic scattering, K and L are K and L shell ionization and SE is secondary electron generation. Plasmon generation and elastic scattering are the dominant scattering processes in the TEM. Reproduced from Williams and Carter (2009). the specimen. The energy transferred in this process can be the result of two kinds of interactions with the electrons of an atom: •If the energy transfer is small, it can be used for intraand interband electronic transitions in the atom being excited, or in the ejection of an outer (valance) electron from the atom (secondary electron). It can also lead to the collective oscillation of outer shell electrons of many atoms, a process which is called plasmon resonance. •At higher amounts of transferred energies, i.e. few hundred eV to tens of kEv, inner shell electrons (K, L or M) can be excited to a higher unoccupied bound state or to the continuum level, the latter one resulting in ionization of the atom. The last type of interaction form the basis of two widely used spectroscopic techniques in the TEM, i.e. Electron Energy Loss Spectroscopy (EELS) and Energy Dispersive Spectroscopy (EDS), whereby the name of the latter refers to the device used to measure the spectra and will be handled in more detail in this section. Figure 3.9 shows the physical process which forms the basis for EDS. A high energy electron in the incident electron beam passes through the electron cloud of an atom. Due to Coulombic interaction with other electrons in the electron cloud, the incident electron gets deflected and transfers a part of its energy to an electron in the electron cloud. The latter electron then can get ejected from the atom if the transferred energy is greater than the ionization energy of the particular shell. The creation of a hole in the shell represents an excited state of an atom, i.e. it is in an energy state higher than its ground state. The atom can get back to its ground state by 55 Figure 3.9: Generation of x-rays by inner shell ionization of a specimen atom. a) A high energy incident electron penetrates the electron clouds and passes close to the inner shell electron. b) Coulombic interaction with inner shell electrons causes a change of incident electron direction and transfer of energy from the incident electron to the inner shell electron, ejecting the latter one from the specimen. c) An electron from a higher shell falls back to fill the electron hole in the inner shell and thereby releasing the potential energy as an x-ray. ac b moving an electron from one of its higher shells to fill the electron hole, which was created by the interaction with the incident high energy electron. Moving an electron from a higher shell to a lower shell results in the lowering of the potential energy of the atom. This energy can be released from the atom by either the emission of a photon of a characteristic energy or another electron from a higher shell, the released electron is called an Auger electron and the transition is called a non-radiative transition. The probability of a radiative (one during which a photon is emitted) vs. non-radiative transition is given by the fluorescence yield ω, and for the following approximation can be used (Williams and Carter 2009): = Z4 aZ4 (3.11) where a is a constant dependent on the shell and Z is the atomic number. The fluorescence yield is thus a strong function of atomic number and the intensity of the CKα line is therefore much less intense than that of the FeKα. The low probability of a radiative transition for light elements in combination with strong absorption in the specimen and detector window of x-rays with low energies makes EDS not the ideal technique to measure light elements. In such case, the complimentary technique to analyse light elements is EELS. Next to characteristic x-ray lines through which elements in the specimen can be uniquely determined, another kind of radiation is emitted by the incident high energy electron when it interacts with the specimen, called Bremsstrahlung (German for breaking-radiation). Interaction of the incident electron with the electric field of the nucleus results in a change of propagation direction of the incident electron. The centripetal acceleration that is associated with this change in direction or momentum results in the loss of energy of the incident electron, which is emitted as electromagnetic radiation (Egerton 1996). The generated intensity I as function of photon energy is given by Kramers (Williams and Carter 2009): 56 Figure 3.10: Top-hat filter applied to a measured EDS spectrum of almandine, applying the top-hat filter removes the background but changes the shape of the x-ray peaks. Quantification of the x-ray peak intensity is then done by comparing the filtered spectrum to other filtered (elemental) reference spectra. IE= KZ E0−E E (3.12) where E0 is the energy of the incident electron, E the energy of the emitted Bremsstrahlung, Z the average atomic number and K is Kramers' constant, which may itself also be a function of the average atomic number (Small et al. 1987). The total spectrum is a sum of the characteristic x-ray lines and the Bremsstrahlung or background radiation. The bremsstrahlung can be removed from the spectrum by either fitting an equation related to 3.12 or to remove the background from the spectrum by a digital filter method. The latter one uses a top-hat filter which removes any linear component from the spectrum including the Bremsstrahlung component since the latter one is nearly a linear function of energy with minor deviations only at low energies (Reed 1993). If the Bremssstrahlung background was stripped using a modified form of 3.12, Gaussian peaks are fitted to the characteristic x-ray lines and the area under the peaks gives the intensity of each line. If the filter-fit method is used, top-hat filtered reference spectra are used to fit the filtered measured spectra and from this the intensity of each characteristic x-ray is determined. For the results presented in this dissertation the background modelling in combination with fitting of Gaussian peaks have been used, since the filter-fit methods requires good elemental reference spectra that were not available. Unless the specimen is very thin, absorption of x-rays in the specimen must be considered, which can be expressed by following the equation: I=I0 Acosec  [ 1−e− At cosec  ] (3.13) where I0 is the generated x-ray intensity, μA the mass absorption coefficient for element A in the specimen, ρ the mass density, t the thickness of the thin foil and α the take-off angle of the x-rays from the foil to the x-ray detector (see figure 3.11). Since foils in the TEM are generally thin and therefore energy loss of the electron beam within the foil can be neglected one can write for the concentration of an element: CA CR =kAR ⋅fAR ⋅IA IR with (3.14) 57 Figure 3.11: Sketch of the sample – detector geometry during an EDS measurements. The incident electron beam ionizes and excites a volume in the TEM foil (dark gray area), which emits x-rays when atoms again return to their lowest energy state. The angle between the xrays reaching the detector and the sample surface is called the take-off angle (TOA). Note that ion-milled foils don´t have parallel surface but are wedge shaped. fAR=A spec R spec [ 1−exp R spec t cosec 1−exp A spec t cosec ] kAR is the Cliff-Lorimer factor for element A using R as ratio element, fAR represents an absorption correction factor, IA and IR are the net counts of element A and element R and μspeci is the mass absorption coefficient for element i in the specimen, which can be calculated from the mass absorption coefficients in a pure standard j (μij): i spec=∑ j Cji j (3.15) Using as additional constraint that the total concentration should add up to 100%, one can calculate the composition for an unknown specimen, if the thickness is known. Though it is possible to determine the thickness by EELS, thickness fringes or convergent beam electron diffraction (Williams and Carter 2009), these methods are often cumbersome and impractical when it comes down to measuring many points. Van Cappellen and Doukhan (1994) proposed to use the net charge of all elements as an alternative constraint to determine the thickness of the specimen, or x-ray absorption thickness of the specimen. Using an approximation to 3.14 they expressed the total charge as function of specimen thickness as a second order polynomial and from this they determined the thickness and composition of the specimen at the place of analyses. A program was developed during the work on the diffusion study that employs a modified version of their method (see appendix 5.2) A major issue with high pressure phases is their instability under the intense electron beam, which can lead to preferential loss of some elements. In this dissertation a method is developed to correct for a change in composition due to radiation damage during EDS analyses, and which is described in more detail in appendix 5.1. 3.2.5 Electron energy loss spectroscopy A complementary analytical technique to EDS is EELS, where not the produced x-ray intensity is measured, but the energy loss of the transmitted electrons. The physical process underlying EELS is the same as the one underlying EDS, i.e. inelastic scattering of the incident beam. Since EELS is independent of the fluorescence yield of a certain electronic transition, EELS can also be used for light elements, which have a low fluorescence yield and where absorption by the specimen and the window in front of the EDS detector may cause problems. The fact that low energy losses of the high energy incident beam are more likely than high energy losses, also makes EELS a favourable method to determine the concentration of light elements. The EELS spectrum is usually divided in two parts, a low loss part below ± 50 eV and a core loss spectrum, the measured energy loss region above ± 50 eV. The low loss spectrum contains the zero-loss peak, which represent the transmitted electrons that did not loose any energy, and is by far the most intense peak in the spectrum. The width of the ZLP gives the ultimate resolution of the analyses. The peak after the ZLP and usually located somewhere between 5 and 35 eV energy loss is the plasmon peak. High energy electrons penetrating the 58 specimen induce collective oscillations of the outer shell electrons of the specimen, so called plasmons, which give rise to the plasmon peak. The shape of the plasmon peak is controlled among others by the type of bonding and can be used for phase identification (Egerton 2009, Williams and Carter 2009). Figure 3.12 shows the features of a typical core-loss spectrum. The shape of an edge when without any contributions of bonding, unfilled higher states and background of previous edges would look like (A), a sharp increase at the ionization edge energy followed by a long tail which can be approximated by a power-law decay in intensity after the ionization edge. In (B) the background is added to this ionization edge, which is the sum of the tails of previous edges and the plasmon peak, and can thus also be approximated by a power-law function (Egerton 1996). If the core-level electron is ejected from its shell, but did not gain enough energy to get into the vacuum level, it will end up in some unfilled state above the Fermi level, but still bound to the nucleus by Coulomb forces. The probability that an electron will go to a certain state within an associated energy range is dependent on the number of states in this energy range, and is thus given by the Density Of States (DOS) of the system. This will give rise to additional spectral structure upon the background and ionization edge (C), the Energy-Loss Near-Edge Structure (ELNES) up to 30-50 eV after the onset of the ionization edge and Extended Energy-Loss Fine structure (EXELFS) beyond there (D). In the case that these empty states are well defined empty states (in the sense of their energy), they will give rise to peaks, or white lines, on top of the ionization 59 Figure 3.12:The structure of core loss spectra. a) The shape of hydrogenetic absorption edge. b) The hydrogenetic is superimposed on the tail of other absorption edges and the plasmon peak, due to plural-scattering. c) When electrons can be exited to bound unoccupied states, this leads to the superposition of white lines on top of the absorption edge, the ELNES structure. d) Beyond the ELNES structure is the EXELFS structure. Modified after Williams and Carter (2009). d b a c edge, which can give valuable information on for example the bond type or oxidation state (Egerton 1996, Williams and Carter 2009). In this dissertation EELS has been used to determine the oxidation state of iron in garnet. Van Aken et al. (1998) and Van Aken and Liebscher (2002) used the shape of the FeL2,3 edge to determine the ferric / ferrous in different minerals of known ferric/ferrous iron ratio, and produced a universal curve to determine the ferric/ferrous iron ratio in unknown minerals. The FeL3 edge at 707.8 eV consists of several white lines, of which the most prominent are one at 707.8 eV and one at 709.5 eV. The latter one becomes more intense with increasing Fe3+ content. A similar behaviour is seen for the FeL2 edge, which also consist of multiple peaks, of which the ones at 720 eV and 721.5 eV react most strongly to the Fe3+ content, the latter one becoming more intense with increasing Fe3+ content. Van Aken et al. (1998) used the integrated intensity ratio in two energy windows at 708.5 – 710.5 eV and 719.7 – 721.7 eV to produce a universal curve from which one can determine the Fe3+ / Fe2+ ratio using the same method. To correct for transitions to the continuum state, they fit a double arctan function to the regions outside of the edge after the power-law background has been removed: f E= h1 ⋅ [ arctan   w1  E−E1   2 ] h2 ⋅ [ arctan   w2  E−E2   2 ] (3.16) where h1 and h2 are the heights of the peaks, w1 and w2 the widths of the continuum transition, ΔE the energy lost and E1 = 708.65 eV and E2 = 721.65 eV the positions of the continuum transitions. In specimens that are not very thin, multiple scattering plays an important role, and therefore the measured core-loss spectra are a convolution of the single scattering core-loss spectra, i.e. the detected electron only lost energy by a single inner shell scattering event, and the low-loss spectra since the low energy loss scattering events are most likely to occur. For good quantification of the Fe3+/Fe2+ ratio in the specimen the multiple scattering effect needs to be removed, or deconvolved. This can be achieved by using the Fourier-ratio technique (Egerton 1996): k1=I0jk / jl  (3.17) where k1(ν) is the Fourier transform of the single-scattering core-loss spectrum, I0 the intensity of the zero-loss peak, jk(ν) the Fourier transform of the measured core-loss spectrum and jl(ν) the Fourier transform of the lowloss spectrum. Doing this, however, is not straight forward and requires additional treatment of the spectra which is beyond the scope of this dissertation but can be found in more detail in Egerton (1996). 3.3 The electron microprobe Chemical characterization on the sample scale of the recovered samples was done by electron microprobe analysis (EMPA) using wavelength dispersive spectroscopy (WDS). The electron microprobe is an electron microscope like the TEM. The main differences are that it works on bulk samples, i.e. the sample is not transparent to electrons, and the electron optical system therefore consists only of a set of condenser and objective lenses that focus the electron beam on the sample. The operating voltage of an electron microprobe is 60 The numerical scheme has been tested against an analytical solution for a semi-infinite half space problem with a constant boundary concentration C0 and an initial concentration profile of C(t=0) = 0 (Crank 1980): C=C0erfc  x 2  Dt  (4.4) where x is the spatial coordinate, D is the diffusion coefficient, t time and erfc is the complementary error function erfc x = 1 – erf x. As figure 4.1 shows, the error is smaller than 0.0015 on a total range of 1.0, which corresponds to an error of less than 0.15%. The error can be further reduced by taking a finer grid or take smaller time steps. The program allows for different diffusion models to be used, by calculating the matrix of diffusion coefficients using the relations corresponding to each diffusion model. Currently four models are supported:(1) the most simple diffusion model with constant diffusion coefficients independent of composition and all off-diagonal elements of D equal to zero, (2) the diffusion model of Lasaga (1979) for ideal solutions, (3) the diffusion model of Lasaga (1979) using a symmetric non-ideal solution described by Margules parameters and (4) the diffusion model by Loomis (1978) for an ideal solution. The program also has options to modify the tracer diffusion coefficients used in the different diffusion models to model the diffusivity dependence of elements on other elements that can have multiple valence states, for example iron. Following Mackwell et al. (2005) the following equation is used to model this:  Di 0=Di 0k1Cmv k2e−k3Cmv (4.5) where k1, k2 and k3 are adjustable parameters for the model and Cmv is the concentration of the multi-valent ion. Next to this a different kind of compositional dependence can also be modelled, according to the following equation: 67 Figure 4.1: The results of the numerical vs. analytical solution for the multicomponent diffusion program mcdiff. The analytical solution is not visible since it overlaps with the numerical solution at the scale of the figure. The difference between the two is plotted on the right y-axis. The difference between the analytical and numerical solution is less than 0.15%. Simulation conditions: grid spacing dx = 0.005, time step 0.01, time interval 0 – 1, diffusion coefficient 0.01.  Di 0=Di 0  1∑ j=1 n kijCj  (4.6) where kij are adjustable parameters. A second program (mcfitter) was developed to fit the measured diffusion profiles to calculated profiles. The program uses the routines in the mcdiff program to calculate a profile and then to fit this profile to measured profiles. It allows for fitting the tracer diffusivities used in the diffusion models, initial compositions and the adjustable parameters in equation 4.5. A gap in the diffusion profile can also be fitted, as well as a shift in the profile to fit the initial interface. The profiles are simultaneously fitted by minimizing the χ2 value defined by: 2=∑ i=1 k∑ i=1 l  Oij−Mij  eij  2 (4.7) where k is the number of components, l the number of measurements, Oij is the measured concentration of component i in measurement j, Mij is the modelled concentration of component i in measurement j and eij is the error in the measurement of component i in measurement j. The minimization is done using the Levenberg – Marquardt method contained in the MINPACK fortran software routine package1. The errors on the fitted parameters are calculated using the bootstrap method (Efron and Tibshirani 1994) which is a resampling method to calculate errors on fitted parameters. After the profiles have been fitted, the residuals are calculated and scaled to their measurement error. New 'pseudo-profiles' are then calculated using the fitted profile and the residuals by random sampling the scaled residuals and adding this to fitted values of the measured profiles. The 'pseudo-profiles' are then again fitted to obtain the 'pseudo-parameters'. This was repeated for 5000 'pseudo-profiles' and the errors in the fitted parameters are then determined by finding the symmetric interval around the originally fitted parameters that encompasses 90% (for the 90% confidence interval) of the fitted 'pseudo-parameters'. 1 http://www.netlib.org/minpack/ 68 Figure 4.2: The results of the numerical vs. analytical solution for the 3D spherical radially symmetric diffusion program raddiff. The analytical solution is not visible since it overlaps with the numerical solution at the scale of the figure. The difference between the two is plotted on the right y-axis. The absolute error (difference between numerical and analytical solution) is less than 0.0002% for the steady state solution. Simulation conditions: grid spacing dr = 0.005, time step 0.01, time interval 0 – 100, diffusion coefficient 0.01. 4.2 Diffusion in a spherical or cylindrical geometry To model diffusion in a grain and diffusion controlled growth of a grain or needle a finite difference model was used. The basic equation that governs diffusion in a spherical and cylindrical geometry assuming a constant diffusion coefficient D is given by (Crank 1980): ∂C ∂t=D  n r ∂C ∂r∂2C ∂r2  (4.8) where C is the concentration, r the radius from the centre, t time, D the diffusion coefficient, and n = 1 for a cylindrical geometry and n = 2 for a spherical geometry. Equation 4.8 has been discretized using a fully implicit scheme: Ci k=−  1 rn 2ri  Ci1 k1  1−2 r  Ci k1−  1 r−n 2ri  Ci−1 k1 With = Dt r (4.9) where k is the time index, i the spatial index, Δr the distance between two nodes, and Δt the time step for temporal discretization. Equation 4.9 describes a tridiagonal linear system and can be solved using standard methods included in the LAPACK software library for example. The code has been tested against a steady state analytical solution for a hollow sphere and hollow cylinder, which are respectively given by (Crank 1980): C=aC1b−rbC2r−a rb−a (4.10) and C=C1lnb/rC2lnr/a lnb/a (4.11) where r is the radial distance from the centre of the sphere/cylinder, C1 is the concentration on the inside surface, C2 the concentration on the outside surface, a the radial distance from the centre of the sphere or cylinder to the inside surface and b the radial distance from the centre of the sphere/cylinder to the outer surface. Figure 4.2 shows the result for the spherical geometry, the error is less than 0.0002% for the steady state solution. For the cylindrical solution the error is less than 0.002% in the case of the steady state solution (see figure 4.3). Grain growth (or shrinkage) was modelled by dividing the domain into three parts; the internal part, the boundary and the external part (figure 4.4). The internal part corresponds to the grain and for this part equation 4.9 is solved for every time step. The boundary has a constant concentration, corresponding to the composition of the internal phase when in equilibrium with the external phase, and its position determines the size of the external and internal parts. The external part corresponds to the external phase and also has a constant concentration, not necessarily equal to the boundary concentration. Since the boundary concentration is 69 different from the concentration of the internal part, material will flow in or out of the grain. The total flux of material that has flown in/out off the grain is determined after every time step by integration of the concentration profile over the complete grain, taking into account the proper geometry. The boundary position is then updated for the next time step based on the total flux of material that has flown in/out of the grain (Mint) and the concentration or density of material in the external part (ρext): Vgrain=Mint−M0 ext (4.12) M0 is the starting concentration of material in the grain. In the case of grain growth, the composition of the new nodal points in the internal part is set to the boundary composition. The growth of the grain can be stopped after a certain amount of material has flown into the grain. The boundary position is kept constant after this point has reached. To stop material from flowing in or out of the 70 Figure 4.3 : The results of the numerical vs. analytical solution for the 3D cylindirical radially symmetric diffusion program raddiff. The analytical solution is not visible since it overlaps with the numerical solution at the scale of the figure. The difference between the two is plotted on the right y-axis. The absolute error is less than 0.002% for the steady state solution. Simulation conditions: grid spacing dr = 0.005, time step 0.01, time interval 0 – 100, diffusion coefficient 0.01. Figure 4.4 : Sketch of the setup of the domain. Solid black circles denote nodal points at which the solution is calculated. In the internal part the relevant descretized differential equation is solved, whereas the external part functions as a kind of reservoir to accommodate grain growth or shrinkage. The position of the boundary is calculated by determining the amount of material at flowed into the internal part. grain, the boundary flux is forced to be zero using a Neumann boundary condition: Cb k1−Cb−1 k1=0 (4.13) where b is the boundary node. In the case that the internal part contains the first node, also a Neumann type boundary condition was used for the first node. 4.3 References Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Croz, J. Du, Greenbaum, A., Hammarling, S., McKenney, A., Sorensen, D. (1999), LAPACK Users’ Guide. Society for Industrial and Applied Mathematics, Philadelphia, PA Crank, J. (1980), The Mathematics of Diffusion. Oxford University Press, USA Efron, B., Tibshirani, R.J. (1994), An Introduction to the Bootstrap. Chapman and Hall/CRC, London Lasaga, A.C. (1979), Multicomponent exchange and diffusion in silicates. Geochem Cosmochem Acta 43:455469. doi: 10.1016/0016-7037(79)90158-3 Loomis, T.P. (1978), Multicomponent diffusion in garnet; I, Formulation of isothermal models. Am J Sci 278:1099-1118 Mackwell, S., Bystricky, M., Sproni, C. (2005), Fe–Mg Interdiffusion in (Mg,Fe)O. Phys Chem Miner 32:418-425. doi: 10.1007/s00269-005-0013-6 71 Chapter 5: Diffusion of the majorite component in garnet 5.1 Introduction Majorite is a high pressure polymorph of enstatite (Mg2Si2O6) and forms a solid solution with the other garnets in Earth's mantle. Garnet with a large majorite component, so called majoritic garnet, is thought to constitute up to 40 - 60 volume % of the Earth's transition zone (Bass and Parise 2008, Frost 2008), whereas subducted oceanic crust might contain up to 80 volume % majoritic garnet in the transition zone (Irifune and Ringwood 1993). Also, the recognition of pyroxene lamellae and needles within garnet with a clear topotaxial relationship as being the products of exsolution from majoritic garnets (Song et al. 2004, Scambelluri et al. 2008, van Roermund 2009), refocused the interest of the scientific community to the solubility of the majorite component in garnet. Different studies have shown that the solubility of the majorite component in garnet increases with increasing pressure (Akaogi and Akimoto 1977, Gasparik 2003), which is the reason why majoritic garnet is an important phase in Earth's transition zone. A subducting (oceanic) slab should thus dissolve its (clino)pyroxene into garnet, by a mechanism which under dry conditions is probably diffusion controlled. The preservation of exsolved pyroxene lamellae from earlier events as well as lack of new precipitates after a UHP metamorphic event, as in the case of the Western Gneiss Region (Scambelluri et al. 2008, van Roermund 2009), might thus give important information on the duration of this UHP metamorphic event, provided that the diffusivity and solubility of the majorite component in garnet at the relevant conditions is known. As the subducting slab descends deeper into the mantle, diffusion of the majorite component into garnet will also be an important factor in the thermodynamic equilibration of the slab. However, the mass transport properties of majoritic garnet and especially diffusion properties of the majorite component in garnet at high pressure are not well constrained. Therefore diffusion experiments have been conducted at transition zone conditions to determine the diffusivity of the majorite component in garnet as function of temperature, pressure and also composition. 5.1.1 Diffusion in minerals In the absence of a fluid phase, volume diffusion is the main mechanism to reduce concentration gradients and to equilibrate mineral assemblages in the solid earth. The diffusivity of components in minerals is thus an important factor controlling the rate at which mineral assemblages equilibrate and diffusion profiles have therefore been used to place constraints on the rate at which geological processes occur in the Earth (Lasaga and Jiang 1995, Chakraborty 2008). Garnets, as one of the important minerals found on the surface of the Earth, has been in the focus of several diffusion studies (Elphick et al. 1985, Loomis et al. 1985, Chakraborty and Ganguly 1992, Chakraborty and Rubie 1996). However, the application of these data was directed towards the interpretation of diffusion profiles that developed in garnet during a metamorphic event, and therefore the pressure range at which these studies were done was limited to below 4 GPa, with one point at 8.5 GPa by Chakraborty and Rubie (1996). For the same reason, the above mentioned studies only focused on the diffusivity of divalent cations, that occupy the dodecahedral site in garnet. The study presented here 72 investigates the diffusion at higher pressure conditions, as well as the diffusivity of the majorite component, which involves diffusion of divalent, trivalent and tetravalent ions occupying both the dodecahedral and octahedral sites. Since the experiments presented here involve diffusion of more than one component, the profiles are treated as multi-component diffusion profiles. The general one dimensional form for a n-component system is: ∂Ci ∂t=∑ i n−1∂ ∂x  Dij ∂Cj ∂x  (5.1) where Ci is the concentration of component i, t time, x the spatial coordinate and D is a (n – 1) x (n – 1) matrix of diffusion coefficients, which makes it a system of coupled partial differential equations. The off-diagonal elements in D represent the influence of one diffusing component on the other. The last component (Cn) is calculated from charge balance. The matrix D is calculated using either the ideal multi-component model of Lasaga (1979) or, if from visual inspection there was no reason to think that there is a compositional dependence of the diffusion coefficient, constant diffusion coefficients were used, where the off-diagonal elements of D were set to zero, effectively reducing 5.1 to: ∂Ci ∂t=∂ ∂x  Di ∂Ci ∂x  (5.2) In the case that the diffusion model with constant parameters did not give a satisfactory fit, the model of Lasaga (1979) for ideal ionic (solid) solutions was used: Dij=Di 0ij−Di 0zizj ∑ k=1 n zk 2ckDk 0 ⋅ Dj 0−Dn 0 (5.3) where D0i is the tracer diffusivity of component i, i.e. when component i would diffuse independently from all other components, δij is Kronecker's delta ( δij = 1 if i = j, otherwise zero) and zi the charge of component i. In the case of a binary system, equation 5.1 reduces to 5.2 with D1 given by: D1=D0 0D1 0 X0D0 0X1D1 0 (5.4) where X0 and X1 are the cationic mole fractions (X0 = C0 / (C0 + C1)). This model was already successfully used by Chakraborty and Ganguly (1992) to model multi-component diffusion profiles in garnets. The modelling and fitting of the diffusion profiles was done by two programs that were developed, mcdiff and mcfitter, that solve equation 4.1 and allows for different models for the calculations of the D matrix. A more detailed explanation of the programs was given in chapter 4. One of the objectives of this study is, next to determining the actual diffusion coefficients themselves, to determine the activation enthalpy of diffusion ΔH, which is a measure of the temperature dependence of the diffusivity of the components. The temperature dependence can be expressed by an Arrhenius style relation: 73 ln Di 0T=ln D 'i 0−H RT (5.5) The activation enthalpy for diffusion is determined from the slope in a log D – 1/T plot, which gives a straight line. The pressure dependence, expressed through the activation volume ΔV, can be obtained through the standard relation of thermodynamic potentials and leads to: ln Di 0=ln D 'i 0−ΔE+(P−1)ΔV RT (5.6) where ΔE is the activation energy and P pressure in bars, and which also defines a straight line in a log D – (P - 1) plot at constant temperature. 5.2 Experimental methods 5.2.1 Starting materials Three different sets of experiments were conducted with various starting materials, all experiments were conducted using the diffusion couple method, i.e. two cylinders of garnet were placed together with their polished faces facing each other in a capsule and then annealed at transition zone conditions. The first set of experiments was conducted with polished cylinders of synthetic majoritic garnet (composition Py55Mj45) and natural pyrope garnet (Py93Alm5Gr2) from the Dora Maira Massif in Italy (Schertl et al. 1991) to determine the pyrope – majorite interdiffusivity. Natural almandine garnet (Alm70Py15Gr15) from the Ötztal in Austria together with the same majoritic garnet were used in the second set of experiments to determine almandine – majorite interdiffusivity. The last set of experiments was a single experiment to determine the pyrope – majorite interdiffusivity, the starting materials for this experiment were Dora Maira pyrope garnet and Ötztal almandine garnet also used in the other sets of experiments. The cylinders were mirror-polished on the sides where they contact each other. Before the experiment the ferric iron contents have been determined by Mössbauer spectroscopy. The Dora Maira garnet contains no detectable 74 Table 5.1: Composition determined by electron microprobe of the starting materials used in the diffusion experiments Element Dora Maira garnet Ötztal almandine Majoritic garnet Wt. % per 12 O Wt. % per 12 O Wt. % per 12 O MgO 27.88 2.83 3.32 0.39 35.43 3.52 FeO 1.93 0.11 43.37 2.14 0.01 0.00 CaO 0.62 0.05 5.20 0.44 0.00 0.00 MnO 0.04 0.00 0.21 0.01 0.00 0.00 Al2O3 25.04 2.01 21.56 2.01 12.61 0.99 TiO2 0.02 0.00 0.08 0.00 0.04 0.00 SiO2 44.05 3.00 37.83 2.99 52.54 3.50 Total 99.58 8.00 100.57 8.00 100.63 8.01 amount of ferric iron (detection limit 0.5 %) whereas the almandine garnet from Ötztal contains 2 ± 1 % of ferric iron. The water contents of Dora Maira pyrope was determined by Lu & Keppler (1997) to be 58 ppm, which corresponds to a protonation of 0.02% of the tetrahedral sites assuming that the hydrogarnet substitution is the dominant substitution mechanism. Since majoritic garnet is not commonly found in nature, it was necessary to synthesize it using the multi-anvil apparatus. First reagent grade MgO, Al2O3 and SiO2 oxide powders were mixed in a mortar together with ethanol to create a suspension. Subsequently the ethanol was evaporated using an infra-red lamp and after this the mixed powders were fused in a furnace at 1650 °C. The glass obtained was then crushed and grounded to a fine powder under ethanol, after which the ethanol was again evaporated. The powder was then again fused in a 1650°C furnace, after which it was crushed again and ground to a fine powder. This powder was then loaded into a Pt capsule (inner diameter 0.8 mm, outer diameter 1.2 mm, length 2.2 mm) for synthesizing majoritic garnet. Just before the synthesis experiments, the tube with powder was put for 5 minutes in a 1000 °C furnace to dry the powder, afterwards it was sealed by putting the Pt tube in a capsule die and pressing it in a bench vice. Majoritic garnet was then synthesized in a multi-anvil apparatus using a 10/5 assembly (numbers denote octahedron edge length and WC cube truncation edge length, respectively) at 1800 °C and 16 GPa for 8 hours. After recovery of the platinum capsule, it was cut into discs of 0.5 mm thickness and a single side was polished. The grain size of the synthetic majoritic garnet was 5 – 10 μm and the grains were, as far as could be determined by TEM, randomly orientated. The cylinders of natural garnet were single crystal, though some of the crystals were cracked. The crystal size of the natural garnets was generally bigger than 200 μm. The Dora Maira pyrope garnet contained a minor amount of hydrous minerals, which were destroyed before the experiments by 75 Table 5.2: Run conditions of the diffusion experiments. 1Type of diffusion couple: Py – Mj = Dora Maira pyrope – majoritic garnet diffusion couple, Py – Alm = Dora Maira pyrope – Ötztal almandine diffusion couple, Alm – Mj = Ötztal almandine – majoritic garnet diffusion couple. 2Octahedron edge size / inner anvil truncation size notation Run number Diffusion couple1 Pressure cell2Pressure Temperature Run duration H2986 Py - Mj 14/8 15 GPa 1600 °C 4 h H3050 Py - Mj 14/8 15 GPa 1800 °C 2 h H3076 Py - Mj 14/8 15 GPa 1500 °C 24 h H3084 Py - Mj 10/5 20 GPa 1800 °C 20 h H3086 Py – Alm 14/8 15 GPa 1500 °C 12 h H3088 Alm - Mj 14/8 15 GPa 1600 °C 7 h H3106 Py – Mj 14/8 15 GPa 1900 °C 2 h H3119 Alm - Mj 14/8 15 GPa 1600 °C 4 h H3201 Py - Mj 14/8 12 GPa 1800 °C 4 h H3244 Alm - Mj 10/5 15 GPa 1400 °C 24 h H3257 Py - Mj 10/5 15 GPa 1400 °C 24 h putting the cylinders in a furnace at 1000 °C for 5 minutes. After this treatment no peaks of hydrous minerals could be found by x-ray diffraction and also inspection by SEM could not identify any hydrous minerals. 5.2.2 Apparatus and pressure cell The diffusion experiments were carried out in a 1000 ton multi-anvil apparatus at the Bayerisches Geoinstitut in Bayreuth. The multi-anvil apparatus used was of the 6/8 split-sphere type (Kawai et al. 1973, Keppler and Frost 2005), referring to the number of outer and inner anvils and guidie block geometry. The inner anvils consisted of 8 tungsten carbide cubes with their corners truncated, to form an octahedral shaped pressure chamber in which the pressure cell resided. The length of the thermocouple was increased such that the thermocouple junction was inside the central heater, the capsule was therefore made smaller than in the standard assembly. The diffusion couple was contained within a platinum capsule in the case of the pyrope – majoritic garnet diffusion couples and within an iron capsule in case of the almandine – majoritic garnet diffusion couples, the length of the capsules was 1.7 mm, the diameter 1.6 mm, and the wall thickness was 0.2 mm. The iron capsule in the experiments with almandine should have buffered the oxygen fugacity near the iron-wüstite (IW) buffer. A tungsten 3% rhenium - tungsten 25% rhenium thermocouple was used to measure the temperature, the pressure effect on the EMF is unknown and has therefore not been corrected for. To prevent the platinum capsule from entering into the thermocouple tube or from reacting with the iron capsule the thermocouple has been separated from the capsule with a 25 μm thick rhenium disc in the former case and a 200 μm thick densified Al2O3 disc in the latter case. Before the experiments, the samples were dried in a vacuum oven at 175 °C for 24 hours, after which the capsules were pressure sealed as fast as possible in a bench vice. Since the iron capsules oxidized even in a vacuum oven, they were not dried but stored in a desiccator with silica gel. After the pressure cell was loaded in the multi-anvil apparatus and was pressurized to the desired pressure, increasing the temperature was done at a rate of 100 °C / minute, with the last 200 °C in one minute. Quenching was done by cutting of the power, the sample was quenched in this way to ~ 100 °C in roughly 10 seconds. Temperature was controlled automatically with a Eurotherm controller. For a more detailed account of the calibration of the multi-anvil apparatus the reader is referred to chapter 3 or Keppler & Frost (2005). 5.3 Analytical methods After recovery of the sample the capsule was cut perpendicular to the contact interface between the two halves of the diffusion couple (hereafter referred to as the diffusion interface) and prepared as a 30 µm thick thin section. These thin sections were subsequently analysed by a JEOL JXA-8200 electron microprobe to gain insight into the length of the diffusion profiles. Since in all cases the diffusion profiles were too short to be measured by electron microprobe, the samples were further prepared for TEM. Molybdenum meshes with a mesh size of 135 µm were glued with epoxy glue on the thin section after which the sample with mesh was separated from the slide by dissolving the crystalbond glue in acetone. The sample was then further milled down in an Ar ion-miller at 4.5 keV and 1.0 mA to electron transparency. From experiments H3201 about 25076 The results for the other pyrope – majoritic garnet experiments at 15 GPa are given in table 5.3. As expected, there is clearly a temperature dependence of the diffusion coefficient for both majorite and pyrope in garnet. The activation enthalpy obtained by fitting the measured 'binary' diffusion coefficient to equation (4.5) was 291± 51 kJ mol-1 with the pre-expontial being 2.3 x 10-7 cm2 s-1 when using the diffusion coefficients for the majorite component. For the pyrope component the values are 302 ± 61 kJ mol-1 for the activation enthalpy and 4.3 x 10-7 cm2 s-1 for the pre-exponential. 5.4.3 Pressure dependence In order to determine the effect of pressure on the diffusivity of the majorite and pyrope components diffusion experiments were conducted at 12 and 20 GPa, both at 1800 °C using the same pyrope – majoritic garnet diffusion couples as in the experiments described above. The measured profiles for experiment H3201 are shown in figure 5.7, run at 12 GPa and 1800 °C for 4 hours, and can be compared to the profile shown in figure 5.5 for run H3050, which was an experiment at 15 GPa and 1800 °C for 2 hours. The diffusion profiles for experiment H3050, run at 15 GPa, are about half the length of the diffusion profiles obtained from experiment 83 Figure 5.7: Diffusion profiles for run H3201, ran at 12 GPa and 1800 °C. a) Shows the measured diffusion profile expressed as garnet end-member fraction. b) The location (black line) of the measured diffusion profile. The white spots are contamination marks of other analyses. b a Pyrope Majorite H3201, which was run at 12 GPa. Since the diffusion distance is proportional to √(Dt), where D is the diffusion coefficient and t the run length of the experiment, one can estimate that a 3 GPa increase in pressure leads to a factor ~1.4 decrease in diffusivity. Figure 5.8 shows the fitted diffusion coefficients for the majorite component in garnet in a Log10 D – P plot for the experiments conducted at 1800 °C between 12 – 20 GPa. From this plot, using equation 5.6, the activation volume for diffusion of the majorite component in garnet was determined to be 3.3 (1) cm3 mol-1. Combining this with the already previously determined activation enthalpy at 15 GPa, one can deduce an activation energy for diffusion of the majorite component in garnet of 241 ± 54 kJ mol-1 and a pre-exponential factor of 1.4 x 10-7 cm2 s-1. 5.4.4 Magnesium – iron interdiffusion To determine the magnitude of the diffusivity of the majorite component relative to that of magnesium – iron interdiffusion in garnet, an experiment (H3086) on a pyrope – almandine diffusion couple was conducted at 15 GPa and 1500 °C. Since the diffusion profiles obtained from the recovered sample of this experiment were much longer than those obtained from the Dora Maira pyrope – majoritic garnet runs, it was possible to measure profiles with a larger scanning pattern and radiation damage correction was not necessary. Since both halves of the diffusion couple separated during decompression there was a gap in the diffusion profile of unknown width. The position of the gap is denoted in figure 5.9 by the dashed vertical line. The mcfitter program was modified for this, to fit the width of the gap along with the other variables. For this sample the ideal model of Lasaga (1979) was used, since it gave a significantly better result than the simple constant diffusion coefficient model (a decrease of 49% in the χ2 value). The tracer diffusion coefficient obtained by fitting the profiles are DMg = 2.1 x 10-13 cm2 s-1, DFe = 4.8 x 10-13 cm2 s-1 and DCa = 3.6 x 10-14 cm2 s-1, i.e. the diffusivity of dodecahedrally coordinated Mg and Fe in garnet is 2 – 3 orders of magnitude faster than the diffusivity of the majorite component at the same conditions (run H3076) and the diffusivity of Ca is 1 – 2 orders of magnitude faster than that of the majorite component. 84 Figure 5.8: Pressure dependence of the diffusivity of the majorite component in garnet. The obtained activation volume for diffusion is 3.3(1) cm2 mol-1. 5.4.5 Almandine – (Mg) majorite diffusion Experiments H3088 (15 GPa, 1600 °C), H3119 (15 GPa, 1600 °C) and H3244 (15 GPa, 1400 °C) were conducted with almandine – majorite diffusion couples, to investigate the effect of iron on diffusion. The diffusion profile for experiment H3244 is shown in figure 5.10, and is distinctly different from the diffusion profiles with the pyrope – majorite couples and the almandine – pyrope couples. The asymmetry in the profiles is clear, with the gradients in Fe and Mg (and to al lesser extent Ca too) extending much farther into the majoritic garnet half than into the almandine part. Due to the complexity of the diffusion profile the fitting was adjusted manually done, since the mcfitter program did not produce realistic fits near the diffusion interface and on the almandine side of the diffusion couple. The values for the diffusion coefficients for Mg, Fe and Ca were chosen by keeping in mind the relative magnitudes of the diffusion coefficients of Mg, Fe and Ca obtained from the pyrope – almandine diffusion experiment (H3086). The asymmetry of the diffusion profile could only be modelled when a strong dependence of the diffusion coefficient of the divalent cations on majorite composition was assumed. The concentration dependence of the diffusion coefficient was expressed in the following form: D=D0  1∑ i=1 N iCi  (5.9) where N is the number of components in the system, αi is a coefficient determined by fitting and Ci is the concentration of component i. Though the fit is not perfect, the main characteristics are well reproduced and it is still possible to make some qualitative inferences. The fitted tracer diffusivities for Mg, Fe and Ca are 3.5 x 1014 cm2 s-1, 9.3 x10 -14 cm2 s-1 and 9.3 x 10-15 cm2 s-1 respectively. For Al and Si these are 2.3 x 10-15 cm2 s-1 and 4.6 x 10 -15 cm2 s-1, respectively. The absolute magnitude of the diffusion coefficients may however not be 85 Figure 5.9 : a) the measured diffusion profiles of the divalent cations in experiment H3086 at 15 GPa and 1500 °C. The cation fractions are calculated as XMg = XMg / (XMg + XFe + XCa). The fitted tracer diffusion coefficients are DMg = 2.1 x 10-13 cm2 s-1, DFe = 4.8 x 10-13 cm2 s-1 and DCa = 3.6 x 10-14 cm2 s-1. The vertical dashed line indicates the position of the gap in the profile. b) A darkfield STEM image of the location of the diffusion profile (black line) in experiment H3086. The horizontal lines are due to the picture being a mosaic of several pictures. b aPyrope Almandine representative of the bulk diffusion coefficient, since both sides contain a relatively high density of dislocations. The ' shoulder' in Fe and Mg extending into the majoritic garnet side could only be modelled if the diffusivity in majoritic garnet for Mg was at least a factor 15 faster than in the almandine side (αMg = 30 -50) and the diffusivity for Fe a factor 5 higher. (αFe = 10-15). The compositions were also expressed in terms of pyrope, almandine, grossular and Mg-majorite components (fugure 5.11). The addition of an andradite component did not change the profiles (the andradite component was nearly equal to zero), which is also supported by the EELS measurements in the other almandine – pyrope and almandine – majoritic garnet diffusion couples that were run in Fe capsules which showed a Fe3+ / (Fe2+ + Fe3+) ratio of nearly zero. The addition of an Fe-majorite component produced a large negative Mg-majorite component at the almandine side of the diffusion profile, and was thus considered unrealistic. Expressing the 86 Figure 5.10:The measured diffusion profile (a) and location (black line) (b) for experiment H3244, run at 1400 °C and 15 GPa for 24 hours. Note the shoulder of Fe in the diffusion profile extending into the majoritic garnet part of the diffusion couple. b a Almandine Mj garnet Majorite Almandine composition in terms of garnet components resulted in a pyrope peak near the point where the Mg-majorite component drops to zero. In principle this could be the result of presence of a miscibility gap between almandine rich garnet and Mg-majorite rich garnet. However, there is no evidence for a miscibility gap between majorite rich garnet and almandine rich garnet, Ringwood and Major (1971) synthesized majoritic garnets near the almandine – majorite join at 1000 °C. Because miscibility gaps tend to close at higher temperatures it is thus unlikely that one exists at the conditions of the diffusion anneals. Moreover, the existence of a miscibility gap would also require next to the precipitation of a pyrope rich phase, the precipitation of a Fe-majorite rich phase which is not observed and is not very likely considering that end-member Fe-majorite is not stable (Ohtani et al. 1991). Diffusion in the almandine – majoritic garnet experiments has therefore not been interpreted in terms of diffusion of garnet components, as in the experiments described above, but in terms of the diffusion of cations. The fitting has been done without regard to end-member components, i.e. magnesium in the Mg-majorite and pyrope component has been treated as a single diffusing component. Experiment H3119 (see figure 5.12) shows a similarly shaped profile, with again a shoulder for Mg, Fe and Ca 87 Figure 5.12: Diffusion profile obtained from experiment H3119, ran at 1600 °C and 15 GPa for 4 hours. The shape of the diffusion profiles show great similarity with those from experiment H3244. Again, the diffusion profiles could only be modelled by assuming a strong dependency of the diffusivity of Mg, Fe and Ca on the majorite content. Figure 5.11: Profile H3244 expressed in terms of pyrope, almandine, grossular and Mg-majorite components. Note the spike in the pyrope component at the location where the Mgmajorite component decreases to zero. Majorite Almandine penetrating deeper into the majoritic garnet side than into the almandine side. The diffusion profile has again been fitted by hand using the above mentioned method. The obtained tracer diffusion coefficients are for Mg, Fe and Ca 2.1 x 10-13 cm2 s-1, 5.6 x 10-13 cm2 s-1 and 3.1 x 10-14 cm2 s-1, respectively. For Al and Si 2.8 x 10-14 cm2 s-1 and 2.4 x 10-14 cm2 s-1, respectively. The values for Mg, Fe and Ca are very similar to those obtained in the almandine – pyrope diffusion experiment, however this run was performed at a temperature 100 °C higher. However it must again be stressed that the fit of the model to the measured diffusion profiles for this run is not optimal which might be caused by the used minimization routine or negligence of the effect of iron on the diffusivity of the elements. The other almandine – majoritic garnet run shows a similar diffusion profile. 5.5 Discussion Although the diffusion experiments were conducted at relatively high temperatures, the diffusion profiles were still too short to be measured by electron microprobe, indicating that diffusion of the majorite component is much slower than the interdiffusion of the divalent cations in garnet (Mg, Ca, Fe and Mn, which diffuse fast enough such that they can be measured after experiments on a microprobe at these conditions). This is also confirmed by the pyrope – almandine diffusion couple (H3086), which produced profiles that are considerably longer and of which the fitted diffusion coefficients for the dodecahedrally coordinated cations are 2 – 3 orders of magnitude faster for Mg and Fe, and 1 – 2 orders of magnitude faster for Ca, as compared to the diffusivity of the majorite component in garnet. The actual values at 1600 °C and 15 GPa, DMj = 1.4 x 10-15 cm2 s-1, are 88 Figure 5.13: The diffusion distance of the majorite component as function temperature and time. The numbers on the lines are in meters. See text for more explanation. comparable to the (tracer) diffusivity of Si in wadsleyite at 1600 °C and 16 GPa, which was also determined to be 1.4 x 10-15 cm2 s-1 (Shimojuku et al. 2009). This again stresses that diffusion of the majorite component in garnet is slow. 5.5.1 Homogenization of the upper mantle Because of its higher alumina content, the oceanic crust will consist of 80 – 90 vol. % garnet in the transition zone (Irifune et al. 1986). Therefore, when the oceanic crust is subducted, it will form a majorite inhomogeneity in the Earth's mantle. For the understanding of the differentiation of the mantle, it is important to know whether the oceanic crust will persist as an inhomogeneity in the mantle or not over geological time scales. The diffusion distance of the majorite component has been calculated as function of temperature and time at 18 GPa using the diffusion data presented in this chapter. When diffusion occurs over a length scale that is significantly longer then the grain size, grain boundary diffusion is the dominant diffusion mechanism at conditions where grain boundary diffusion is significantly faster (Harrison 1961). The grain boundary coefficient has been taken as 104 x the bulk diffusion coefficient, based on grain boundary diffusion experiments on YAGgarnet crystals at 1500 °C (Marquardt (née Hartmann) et al. 2011). The diffusion distance was calculated as: x=  Dgbt (5.10) where Dgb is the grain boundary coefficient and t diffusion time. The results are plotted in figure 5.13. Estimates for the temperature on the mantle adiabat at 18 GPa range from 1500 °C to 1800 °C (chapter 3). The figure shows that at these conditions, the majorite component will only be able to diffuse over a distance of 5 – 15 meters on the time scale of the age of the Earth. It is clearly not possible to homogenize the mantle by solid state diffusion and the oceanic crust will persist as a majorite homogeneity in the Earth's mantle. 5.5.2 Rheology of garnet in the transition zone In deformation processes controlled by dislocation creep (through dislocation climb) and diffusion creep mechanisms, the volume diffusivity of the slowest diffusing ion is an important rate controlling factor (Weertman 1957, Poirier 1985). As will be explained below, there are arguments to assume that octahedral and tetrahedral Si do not diffuse as independent components, but diffuse as one component, which might be even faster than the diffusion of Al in garnet. It can thus be assumed that the diffusivity of the majorite component is representative of the diffusivity of the slowest component. The creep rates for dislocation creep (by the Weertman model) and diffusion creep are given by respectively: ˙=disl Dsd b3.5 M0.5     4.5  kT and ˙=diff Dsd   d2k T (5.11) where α is a geometric factor, Dsd the self-diffusivity of the rate controlling ion, b the burgers vector of the dislocation, M the density of dislocation sources, σ the applied stress, μ the shear modulus, k Boltzmann's 89 constant, T temperature, d grain size, Ω volume of the vacancy. Using a shear modulus at 16 GPa and 1600 °C of 85 GPa for majoritic garnet and 104 GPa for wadsleyite (Nishihara et al. 2008, Hunt et al. 2010), and the <1 1 1> or <1 0 0> Burgers vectors for the activated slip systems in (majoritic) garnet (Cordier et al. 1996) and <1 1 1> or [1 0 0] for wadsleyite (Demouchy et al. no date), and assuming similar dislocation source densities, grain size and volume of vacancies for garnet and wadsleyite one finds that if the diffusivity of tetrahedrally coordinated Si in garnet is less than in wadsleyite, majoritic garnet will be more resistant to flow than wadsleyite (i.e. 'stronger'). The relative deformation rates are then given by the following equation: ˙ ϵgt ˙ ϵwads ≈0.2 Dsd gt Dsd wads (5.12) 90 Figure 5.14: Composition of a growing garnet grain as function of the radial distance and for several times. a) Graphical representation of the model. The spherical garnet grain (light red) is surrounded by pyroxene (green). Dissolution of pyroxene into garnet (heavy arrows) leads to the growth of the garnet grain (dark red circle and light arrows). The graph in the right side of the grain shows how to interpret the concentration profiles in b) and c). b) A 1 cm grain representative for the lower part of the subducting lithospheric mantle, conditions are 18 GPa and 1400 °C, and c) is representative for the subducted oceanic crust, conditions are 18 GPa and 1000 °C. Grain growth is stopped after an amount of majorite component corresponding to a homegonous composition of Py60Mj40 has fluxed into the grain. After this the grain is let to homogenize. The grain size can be determined by finding the position where the profiles cut the upper 70% majorite line (b) or the 55% majorite (c) line. b c a for dislocation creep, and ˙ ϵgt ˙ ϵwads ≈Dsd gt Dsd wads for diffusion creep. If the diffusivity of the majorite component in garnet is of the same order as that of the diffusivity of Si in wadsleyite, there will be no great contrast between majoritic garnet and wadsleyite. However, if due to the low diffusivity of the majorite component the garnet phase did not equilibrate, one might expect a lower diffusivity for Si, since it will be confined to the tetrahedral site. The strength of garnet in subduction zones, the location where most likely there will be lack of equilibration due to lower temperatures and its dynamic character, in this case will be controlled by the degree of equilibration and thus the diffusivity and grain size of garnet. To model this, a program has been developed that simultaneously models diffusion in a (spherical) grain, and diffusion controlled growth of the same grain. A more detailed explanation of the code is given in chapter 4.2. Figure 5.14 shows how long it will take for enstatite to dissolve into a garnet grain and then homogenize the grain for two different scenarios. Scenario A (figure 5.14b) correspond to a grain in the middle to lower part of the subducting lithospheric mantle. Conditions here are assumed to be 1400 °C and 18 GPa, which correspond to conditions on an average subduction geotherm (Emmerson and McKenzie 2007). The composition of the newly grown majoritic garnet (Py30Mj70) was inferred from phase diagrams by Gasparik (2003) and Akaogi and Akimoto (1977). The maximum influx of majorite component was chosen such that the final composition after homogenization was Py60Mj40, corresponding to high-pressure experiments on pyrolitic compositions (Irifune 1987). The initial grain size is 1 cm. The results of the modelling show that it takes about 4 Myr for the grain to grow to its final size. However, after this it still has a large core of almost pure pyrope composition. It takes about 20 Myr before the grain is homogenized. Assuming an average rate of burial due to subduction of 20 mm y-1, it would take 12.5 Myr to pass the transition zone. For the subducted lithospheric mantle homogenization is thus roughly at the same timescale as the subduction process. Things, however, are different for the subducted oceanic crust (scenario B, figure 5.14c ). Conditions in this case are 1000 °C and 18 GPa, again from the computed subduction geotherm of Emmerson and McKenzie (2007). The composition of the newly grown majoritic garnet was Py45Mj55, from Akaogi and Akimoto (1977) and the maximum influx was again chosen such that the final composition would be Py60Mj40, corresponding to experiments conducted on refractory MORB material after partial melting and transformation to an eclogite assemblage, representative of the subducted oceanic crust (Irifune et al. 1986). The initial grain size was taken as 1 mm, which is also a typical grain size for eclogites. The plot in figure 5.14b shows that it takes over 300 Myrs for complete equilibration. After 12.5 Myr only about 38% of the pyroxene would have dissolved into garnet. It might thus be more likely that the basaltic crust will preserve a metastable assemblage of garnet + clinopyroxene + orthopyroxene during its subduction instead of the garnetite assemblage or, since enstatite breaks down to stishovite + wadsleyite or ringwoodite above 17 GPa at these conditions (Akaogi and Akimoto 1977), garnet + clinopyroxene + wadsleyite/ringwoodite + stishovite. The sluggish reaction kinetics of enstatite 91 breakdown may then also result in the formation akimotoite at greater depths (Hogrefe et al. 1994). The middle to lower part of the subducting slab is thus expected to be able to dissolve all its enstatite into garnet during the time that, though with a significant delay. This would mean that there would be no significant contrast in strength between garnet and wadsleyite in the transition zone, except perhaps for the upper ~80 km of the transition zone. Diffusion of the majorite component in garnet is too slow to dissolve al the pyroxene into garnet in the oceanic crust during subduction. It might therefore be expected that a significant amount of pyroxene we be preserved as metastable phase. This would make garnet relatively strong, however since pyroxenes are relatively weak (Ohuchi et al. 2010), the preservation of pyroxene may make the oceanic crust weaker than expected in the transition zone. Extrapolation of the diffusion data in this study to the higher pressures prevailing in the ringwoodite stability field shows that the diffusivity of the majorite component at these conditions is again similar to the diffusivity of silicon self-diffusion in ringwoodite, i.e. 3.5 x 10-17 cm2 s-1 for majoritic garnet vs. 8.5 x 10-17 cm2 s-1 at 22 GPa and 1500 °C (Shimojuku et al. 2009). The conclusions in the previous paragraph thus also hold for ringwoodite stability field. 5.5.3 Comparison with previous experimental data Chakraborty and Ganguly (1992) determined the value of the activation volume for diffusion of Mg in garnet to be 5.3 ± 3.0 cm3 mol-1. Chakraborty and Rubie (1996) extended their data with their own to include Mg tracer diffusivity data done over a broader range of pressures to reduce the error in activation volume determined by Chakraborty and Ganguly (1992). They determined from the combined data set an activation volume for Mg tracer diffusion in garnet of 8 ± 1 cm3 mol-1. The pressure dependence of the majorite component, 3.3 ± 0.1 cm3 mol-1, determined in this study is thus significantly lower. Chakraborty and Ganguly (1992) also determined the activation enthalpy of Mg diffusion in garnet to be 285 ± 38 kJ mol-1 from a multi-component diffusion study, Chakraborty and Rubie (1996), in their tracer diffusion study, determined a lower value of the activation enthalpy for Mg diffusion of 226 ± 21 kJ mol-1. Comparing these to the values determined in this study show that they are very similar, i.e. 241 ± 54 kJ mol for the diffusion of the majorite component in garnet. The fact that diffusion of the majorite component involves diffusion of both dodecahedrally and octahedrally coordinated cations does not seem to influence the activation energy profoundly. The difference in activation volumes between diffusion of the majorite component and diffusion of the eight-fold coordinated Mg, as determined by Chakraborty and Rubie (1996), suggest a different diffusion mechanism involving a less compressible site. Hazen and Finger (1978) indeed report that the octahedral site of garnet is less compressible than the dodecahedral site, which might explain the difference in activation volumes. 5.5.4 Effect of majorite content on diffusivity of the elements Though the diffusion profiles obtained from the almandine – majoritic garnet diffusion couples were too complex to model well enough to determine absolute diffusion coefficients from, it is still possible to reach some qualitative conclusions. One of the prominent features of all diffusion profiles in the almandine – majoritic 92 by: Icor =IsI0 u (5.18) Fitting of 5.17 to the data has been done by minimizing the χ2 – value, which is defined as: 2=∑ i nOi−Ei2 Oi (5.19) Where Oi is the observed intensity of the characteristic x-ray line and Ei is the expected or fitted intensity of the characteristic x-ray line. The minimization is done by using the non-linear Levenberg – Marquandt minimization algorithm available in the Matlab software package. There are now two scenarios. In the first scenario, the standard case, beam damage is not significant and we can use the standard method, i.e. using the simple arithmetic mean of all measurement, to calculate the intensity of the measured x-ray peak. In the second one, where radiation damage is significant, equation 5.17 should be used to determine the radiation corrected intensity for the measured x-ray peak. To do this, we can use the ratio of the χ2 – value for both models corrected for the degrees of freedom in both models in an F-test with the following F statistic: F=n 2 c 2⋅n−3 n−1 (5.20) Where χn2 is the χ2 value for the normal case and χc2 is the χ2 value for the radiation damage corrected case. The expected value for F when using 8 measurements per spot is 1 2/3 when there is no difference between the 99 Figure 5.15 :The intensity of the MgKα peak in majoritic garnet as function of the time elapsed since the start of the measurement. Solid dots correspond to the actual measurements, each dot correspond to the cumulative counts over a 15 second interval. The solid line is the fitted intensity using the model proposed here. models. The radiation damage corrected model is used when the F value exceeds a certain minimum value, which can be obtained from standard tables for the F-distribution (in this thesis 4.88, which corresponds to a 95% confidence level when using 8 measurements per spot). Appendix 5.2: Quantification of the EDS analyses The actual elemental concentration can be calculated from the intensities of the characteristic x-ray peaks using Cliff-Lorimer k-factors when absorption can be neglected: CA CR =kAR IA IR (5.21) where A and R denotes element A and the ratio-element R respectively, C are the concentrations, I the characteristic x-ray intensities and kAR is the Cliff-Lorimer k-factor for element A using R as ratio-element. The Cliff-Lorimer k-factors are determined by measuring specimens with a known composition. As additional constraint to calculate the actual concentrations can be used that the concentrations of all elements should add up to 100%. Usually absorption can not be completely neglected and one should correct the k-factors for absorption: kAR *=kAR A spec R spec 1−exp −R spec tcosec  1−exp −A spec tcosec  (5.22) where k*AR is the corrected k-factor, μspeci is the mass absorption coefficient (MAC) for characteristic line i in the specimen, ρt the mass thickness of the foil and α the take-off angle of the x-rays that hit the detector. The MAC is calculated as follows: i spec=∑ j Cji j (5.23) where Cj is the concentration of element j and μij is the MAC for the characteristic line of element I by pure element j. As can be seen in these equations, one needs to know the thickness of the specimen. Because measuring the exact thickness of the foil is often difficult, Van Cappellen and Doukhan (1994) used net neutral charge as an additional criterion to determine the thickness. For easier calculation, they approximated equation 5.22 with a first order Taylor expansion, which makes the net charge as function of thickness quadratic in nature and easily solvable. In this thesis the Brent root finding algorithm (Press et al. 1992) in combination with the full expression of 5.22 is used to quantify the elemental concentrations. The source code of the program (TemQuant) is available upon request. Appendix 5.3:Precision of TEM EDS measurements The diffusion profiles for the majoritic garnet – pyrope diffusion experiments were modelled with a constant composition independent diffusion coefficient. Though binary diffusion profiles can be modelled by a single diffusion coefficient, it should still be composition dependent through equation 5.0, unless the diffusion 100 coefficients for the majorite component and pyrope component are equal. Chakraborty and Ganguly (1992), for example, modelled their diffusion profiles for diffusion in the almandine – spessartine diffusion couples with two different diffusion coefficient for each side of the couple, pointing out the compositional dependence of the diffusion coefficients. However, the precision of the analyses on the TEM may let it appear as if the binary diffusion coefficient is composition independent, since only slightly asymmetric profiles are not distinguishable from perfectly symmetric profiles. To determine what the sensitivity is of the profiles measured by the TEM to the composition dependence of the binary diffusion coefficient, several profiles have been modelled with a different composition dependence with the use of the Lasaga model. From the calculated profile a set of 25 points has been taken as 'measurement data' and this data has been fitted by the composition independent diffusion model. The fit or misfit is plotted in figure 5.16. The gray area line gives the typical error for the analytical TEM using EDS, which is 1.5 % under optimal conditions. The best element to check for this would be Al, since for every 1 % of majorite component incorporated, the Al fraction will be reduced by 0.02 per formula unit. Figure 5.16 shows that the ratio r of DPy to DMj should be below 10, otherwise asymmetry of the diffusion profiles would be too strong to remain undetected by the TEM. However the error in the determined diffusion coefficient would be smaller, as is pointed out in table 4.4, since the determined diffusion coefficient using the composition independent diffusion 101 Figure 5.16: A plot of the misfit by fitting a composition independent diffusion model to data generated from a composition dependent model. The r value is the ratio of DPy to DMj and the gray area denotes the precision of the TEM for Al in majoritic garnet. Table 5.4 : The obtained values when using the constant diffusion coefficient model when fitting data to the Lasaga multi-component model. On the left side the DMj – DPy ratio used to model the 'measured' data with the use of the ideal multi-component model by Lasaga, on the right side the diffusion coefficient obtained by fitting the measured data to a constant composition independent diffusion coefficient relative to the DPy value used as input for the Lasaga model. DMj – DPy ratio Fitted coefficient 0.01 0.013 0.1 0.13 0.5 0.56 1 1.0 2 1.63 5 2.67 10 3.32 coefficient model would lie between the actual values of DPy and Dmj. Appendix 5.4: Majoritic garnet – Dora Maira pyrope diffusion couple profiles H2986 P = 15 GPa T = 1600 °C t = 4h DPy = 1.4(2) x 10-15 cm2 s-1 DMj = 1.4(2) x 10-15 cm2 s-1 H3076 P = 15 GPa T = 1500 °C t = 24 h DPy = 4(2) x 10-16 cm2 s-1 DMj = 3(1) x 10-16 cm2 s-1 H3106 P = 15 GPa T = 1900 °C t = 2h DPy = 3.7(7) x 10-14 cm2 s-1 DMj = 4(1) x 10-14 cm2 s-1 102 H3257 P = 15 GPa T = 1400 °C t = 24 h DPy = 2.5(8) x 10-16 cm2 s-1 DMj = 3.4(8) x 10-16 cm2 s-1 H3084 P = 20 GPa T = 1800 °C t = 20 h DPy = 2.2(7) x 10-15 cm2 s-1 DMj = 2(1) x 10-15 cm2 s-1 103 Chapter 6: Exsolution of garnet from orthopyroxene 6.1 Introduction Orthopyroxene, with spacegroup Pbca and composition ranging from end-members enstatite Mg2Si2O6 to ferrosilite Fe2Si2O6 can incorporate aluminium by two different substitution mechanisms. The first mechanism is the calcium or magnesium Tschermak substitution mechanism (end-members CaAl2SiO6 and MgAl2SiO6). Both Ca/Mg and Si atoms are substituted for two Al atoms in the pyroxene structure. The Al incorporated in the tetrahedral chains strongly prefers the Si(B) site, in accordance with the Al-avoidance principle (Okamura et al. 1974). The aluminium in the octahedral layers has a preference for the M1 site, however the M2 sites accommodate Al too (Okamura et al. 1974, Ganguly and Ghose 1979). In the presence of excess silica, aluminium can also be incorporated (by the second mechanism) by a calcium Eskola component (Ca0.5AlSi2O6), where discrepancy in charge on the M sites between Al3+ and Ca2+ is balanced by a vacancy on the M2 site (Gasparik and Lindsley 1980). The enstatite end-member of the pyroxene series has different polymorphs depending on the pressure and temperature conditions. Figure 6.1 shows the phase diagram of MgSiO3 at upper-mantle pressure. Up to ± 15 GPa the different pyroxene polymorphs are stable, after which it breaks down to either majorite or wadsleyite/ringwoodite + stishovite. The different polymorphs that are stable are orthoenstatite (space group Pbca), protoenstatite (space group Pbcn), low clinoenstatite (space group P21/c), high temperature high clinoenstatite (space group C2/c) and high pressure high clinoenstatite (space group C2/c). Though the last two polymorphs have the same space group, their oxygen packing sequence is different, i.e. the high pressure polymorph has a cubic close packing sequence and the high temperature form has a hexagonal close packing sequence (Thompson and Downs 2003). Though the pure end-member HT clinoenstatite MgSiO3 has only a 104 Figure 6.1: The phase diagram of MgSiO3 at the condition of Earth's upper mantle showing the stability of the different enstatite polymorphs, after Gasparik 2003. very limited stability field, the substitution of Mg by Fe expands the stability field of HT high clinoenstatite significantly (Arlt et al. 1998). Previous studies have shown that both high clinoenstatite polymorphs are not quenchable and transform back to the P21/c low enstatite polymorph upon return to room conditions (Kanzaki 1991, Arlt et al. 1998). For the sake of simplicity in the rest of this chapter, when high clinoenstatite is mentioned, the high pressure form of high clinoenstatite is meant. As argued in chapter 5, slow diffusion kinetics of the majorite component in garnet hampers the dissolution of pyroxene in garnet in the cold subducted slab. Therefore the pyroxene component in the subducted slab can be viewed as a (semi-)isolated system. Experimental studies (Irifune et al. 1986; Irifune 1987) have shown that the amount of aluminium that can be dissolved in pyroxene decreases with increasing pressure. As a result of this, garnet will be exsolved from pyroxene while the slab is subducted into the mantle. The rate at which this will occur in pyroxene will be controlled by the diffusivity of aluminium in high clinoenstatite at enhanced pressures, for which there are currently no data available. For pyroxene exsolutions in garnet it has been shown that there is a topotactic relationship between the garnet host and the pyroxene exsolutions (Spengler 2006). However, the topotactic relation between pyroxene and exsolved garnet at high pressure, i.e. in the Earth's transition zone, where pyroxene has a monoclinic structure (high clinoenstatite C2/c) is unknown at present. Therefore, experiments on natural aluminous enstatite have been conducted to investigate what happens to orthopyroxene that is present in the subducted slab when it is transported into the mantle. Experiments were conducted in the presence of garnet, to closer simulate what occurs in the Earth during subduction. 6.2 Experimental setup Experiments have been conducted in a 1000-ton multi-anvil device at the Bayerisches Geoinstitut, using a 14 / 8 pressure cell, indicating the octahedron edge length and the truncation edge length of the tungsten-carbide anvils in millimetres, respectively. The pressure cells were MgO octahedra with a central hole into which sample and a LaCrO3 stepped furnace was placed, for a more detailed description see chapter 3 on experimental methods. The length of the platinum capsules was 2.4 mm, the diameter 1.6 mm and the wall thickness 0.2 mm. Temperature was measured by W3%Re – W25%Re thermocouples with a junction just on top of the capsule. The thermocouple wires were isolated from the capsules by a 25 μm rhenium disc to prevent platinum from intruding into the thermocouple tubes. The starting materials were couples of single crystal mirror polished Dora Maira pyrope and Tanzania enstatite cylinders. The Dora Maira pyrope crystals were the same as used in the diffusion experiments described in chapter 5. The chemical composition (see table 6.1) of the Tanzania enstatite crystals were determined by electron microprobe and correspond to those determined by 105 Table 6.1 : Chemical composition of the Tanzania enstatite, after Rauch (2000) Oxide Wt. % SiO258.10 FeO 2.00 MgO 38.50 Al2O31.50 MnO 0.10 CaO 0.15 Na2O 0.01 Total 100.35 Fe3+/Fetot 23% Rauch (2000). The experiments were conducted at 1700 °C and 15 GPa, with run durations between 1 hour and 19 hours, the conditions are listed in table 6.2. After the end of the run the sample was quenched by cutting of the power, resulting in a temperature drop in 10 seconds to roughly 100 °C. 6.3 Analytical setup After recovery of the samples the capsule were cut by a diamond wire saw along the length of the capsule and mounted in an epoxy block, polished and further prepared for analyses by electron microprobe and SEM. The chemical compositions of the samples were measured by means of an electron microprobe, using 20 s counting time for the peak position and 10 s counting time for the background position, 15 kV acceleration voltage and 15 nA beam current. The standards and characteristic x-ray peaks used to determine the chemical composition are listed in table 6.3. Two experiments, H2975 and S4378, were also prepared for further examination by TEM. The TEM samples were first polished down to a thickness of 30 μm, after which a molybdenum mesh with a square size of 135 μm was glued upon them using Araldite epoxy glue. The crystalbond glue between the sample and the glass slide which was used for polishing down the sample to 30 μm was then dissolved by acetone. The sample was then Ar-ion milled to electron transparency in a Gatan Duomill 600, under an angle of 14 ° at 4.5 kV and 1.0 A. Microstructural characterization and determination of topotactic relations between the (clino-)enstatite host and the garnet exsolutions were performed using a Philips CM20 FEG TEM operating at an acceleration voltage of 200 kV. 106 Table 6.2: Run conditions of the experiments Run number Pressure Temperature Duration H2975 15 GPa 1700 °C 19 h S4378 15 GPa 1700 °C 19 h S4391 15 GPa 1700 °C 1h Table 6.3 : Electron microprobe standards & peaks Element Standard Characteristic peak Mg Forsterite MgKα Fe Metallic iron FeKα Ca Diopside CaKα Al Pyrope AlKα Mn MnTiO3 MnKα Si Forsterite SiKα Ti Rutile TiKα 6.4 Results 6.4.1 Determination of the enstatite polymorph As explained, enstatite has several polymorphs and therefore is important to determine for which polymorph the topotactic relationship between the enstatite host and majoritic garnet was determined. The polymorphs that were considered are orthoenstatite (Pbca), protoenstatite (Pbcn), low clinoenstatite (P21/c), and high clinoenstatite (C2/c). The systematic presence (fig. 6.2a) of 100 reflections in the [001] zone axis pattern indicate that it cannot be either the protoenstatite or high clinoenstatite polymorph. From the geometry of the zone axis pattern it can also be excluded that the h00 reflections are caused by double diffraction. Figure 6.2b shows the diffraction pattern taken down the <013> zone axis. The spacing of the h31 reflections indicates that the dspacing of the 100 planes is ± 9.2 Å. This d-spacing excludes the possibility that the investigated enstatite crystal is the orthoenstatite polymorph (where the d-spacing is 18.2 Å) and thus needs to be the low clinoenstatite polymorph. 6.4.2 Microstructure Figure 6.3 shows a backscattered electron (BSE) image of the enstatite part of the sample of experiment H2975. The enstatite part contains a high density of garnet precipates with a The exsolved grains of majoritic garnet show a clear arrangement relative to the host pyroxene, the long axis of the precipitates are parallel to the (100) planes of the pyroxene host. The left side of the picture shows recrystallized grains of clinoenstatite that 107 Figure 6.2: Diffraction patterns of the recovered low clinoenstatite sample that show it is the low clinoenstatite polymorph (see text). a) Diffraction pattern down the [001] direction in low clinoenstatite and b) down the <013> direction. a b Figure 6.3: BSE image of the low clinoenstatite part of experiment H2975. The shape preferred orientation of the garnet precipitates in the undeformed single crystal part (center) is clearly visible. On the left the deformed part is visible. The middle gray phase is low clinoenstatite, the light gray phase majoritic garnet and the dark gray phase is stishovite. probably formed due to the indentation of the thermocouple. The composition of the majoritic garnet precipitates are listed in table 6.4. The component fractions are calculated using the method explained in chapter 5. The precipitates have a high majorite component (± 61 %), which is slightly higher than the equilibrium composition in the Mg3Al2Si3O12 – Mg4Si4O12 system at the experimental conditions (chapter 2), based on data from Gasparik (2003). The thickness of the majoritic garnet layer that formed at the garnet – enstatite interface was generally thin (< 3 µm for the 19 hour experiments and absent within the resolution of the microprobe for the 1 hour experiment). This agrees well with the low majorite diffusivity in garnet that was determined from majoritic garnet – pyrope diffusion couples and of which the results are presented in chapter 5. The recovered sample of run H2975 has been investigated in detail by TEM. Figure 6.4 shows a dark field (DF) image obtained using g = 6 13 as diffraction vector. Twinning on the (100) mirror planes is pervasive in the sample, and is indicated by the short white arrows. Next to twinning, one can also observe stacking faults parallel to the twin plane throughout the sample (figure 6.4 and 6.5). Figure 6.5a shows a DF image using g = 021 as diffraction vector, demonstrating again the pervasive nature of the stacking faults in this sample. The corresponding HRTEM image in an a*-b projection (* denoting the reciprocal direction) of clinoenstatite shows a single stacking fault (fig. 6.5b). From this HRTEM image one can deduce that the displacement vector across the stacking fault is R = <½ ½ w>, the exact components can be 108 Figure 6.4: DF TEM image of twins (and stacking faults) parallel to (100) in clinoenstatite in experiment H2975. Two twin planes are indicated by the white arrows. The diffraction vector (g = 6 1 3) is indicated by the light gray arrow. The garnet precipitates are indicated by Gt. As can be seen, the large precipitate on the right has its long axis (semi-)parallel to the twin planes and stacking faults in low clinoenstatite. Table 6.4:Composition of the exsolved majoritic garnet precipitates. Oxide Wt% MgO 34.80 CaO 0.24 FeO 1.65 Al2O39.83 SiO253.66 Total 100.18 Component Fraction Majorite 0.610 Pyrope 0.352 Almandine 0.032 Grossular 0.007 complete crystal is parallel to {211} since every tubular column is shifted relative to a neighbouring tubular column by 1/3 of the tetrahedra plus octahedra layer thickness. In the view down the <111> direction the space between the tubular columns forms channels parallel to {110}. Though the structures of pyroxene and garnet are vastly different, silica tetrahedra also form a linear structure in garnet structure down the <111> direction. For the transformation from pyroxene to garnet, the chains of silica tetrahedra down the c-axis in pyroxene need to be broken into isolated silica tetrahedra. The distance over which the silica tetrahedra need to be diffused (or translated and rotated) may thus be minimal when the new garnet crystal forms with its <111> direction down the original c-axis of high clinoenstatite. The topotactic relationship would in this case thus not be controlled by minimization of the strain energy on the interface between both phases, but by the diffusion kinetics of silicon, because silicon is usually the slowest diffusing species. 6.5.3 Aluminium diffusivity in clinoenstatite The diffusion in high clinoenstatite down the [101]*direction was determined to be 6 x 10-11 cm2 s-1 at 15 GPa and 1700 °C, which is 3 – 4 orders of magnitude faster than the diffusion of the majorite component in garnet. The reported diffusivity is a lower limit, since the exact time required before a majoritic nucleus formed is unknown. However, the measured profile used in the fit model was the longest that was found in the sample and thus probably also corresponds to one of the nucleus that formed first during the experiment. The region around the measured precipitate is relatively devoid of other precipitates, which also indicates that the precipitate from which the profile was measured nucleated during an early stage of the experiment. Experiment S4391 (figure 6.6) was run at the same conditions, but only for 1 hour. The presence of garnet precipitates in this experiment indicate the first precipitates nucleate within the first hour. Since the run duration of experiment S4378 was 19 hours, it is thought that the error due to the uncertainty about the exact time of nucleation of the precipitates is not significant. To project the diffusion coefficients to subduction zone conditions one needs the activation energy for diffusion of aluminium in pyroxene (or ideally high clinoenstatite). There is, however, a general lack of diffusion data on aluminium in minerals in the literature, the only data on aluminium diffusion in diopside is by Sautter et al. (1988) and Jaoul et al. (1991) over a limited temperature range between 1000 – 1180 °C at 1 bar. They obtain an activation energy of 273 kJ mol-1. The activation enthalpy, describing the temperature dependence, for diffusion of aluminium in high clinoenstatite will probably be higher, since the experiments in this study were conducted at a pressure of 15 GPa. Therefore a typical range of activation enthalpies have been assumed, i.e. between 275 kJ mol-1 and 350 kJ mol-1, corresponding to an activation volume for the diffusion of aluminium in clinoenstatite between 0 – 5 cm3 mol-1. For the upper part of the subducting slab at a temperature of 1000 °C (Emmerson and McKenzie 2007), corresponding to the subducted oceanic crust, it gives an aluminium diffusion coefficient in the range of 5 x 10-16 cm2 s-1 to 6 x 10-15 cm2 s-1. For the middle to lower part of the subducting slab at 1400 °C (Emmerson and McKenzie 2007), corresponding to the subducted mantle lithosphere, the range is smaller due to a smaller temperature difference between the extrapolated temperature and the experimental condition, and is in the range between 3 x 10-12 cm2 s-1 and 4 x 10-12 cm2 s-1. Again this shows that diffusion of aluminium in 115 high clinoenstatite (in the [101]* direction) is significantly faster than the diffusion of the majorite component in garnet, i.e. 3 – 4 orders of magnitude slower. Since the distance over which a component can diffuse can be approximated by x = √(Dt), with t the time for which the component is allowed to diffuse, one can calculate the distance over which aluminium can diffuse in pyroxene. At 1000 °C and 10 Myr, which is a typical time scale for subduction (see chapter 5), this is between 0.5 – 1.5 cm and at 1400 °C between 20 – 30 cm. If grain boundary diffusion plays a significant role, the values will be a factor 100 larger, i.e. at the meter scale at 1000 °C and at the decameter scale at 1400 °C. Comparing the absolute values of the diffusion study by Jaoul et al. (1991) to the data presented in this study shows that our data is significantly faster, Jaoul et al. obtained a diffusivity of 3.7 x 10-17 cm2 s-1 at 1180 °C at 1 bar and our study 6 x 10-11 cm2 s-1 at 1700 °C. This would correspond to an activation energy for diffusion of aluminium in clinopyroxene of 655 kJ mol-1 (when the effect of pressure is neglected), which is anomalously high, or when using their activation energy for Al diffusion this corresponds to an activation volume for diffusion of aluminium in clinopyroxene of -25 cm3 mol-1, which would mean that with increasing pressure diffusion would become faster. From this it can be concluded that there is a large difference in diffusivity between that of aluminium in HP clinoenstatite at high pressure and that of aluminium diffusion in diopside at low pressure, which possibly can be attributed to different diffusion mechanism in both clinopyroxene phases at the different conditions or a strong dependence of the diffusivity of aluminium in clinopyroxene on the calcium content. 6.6 Conclusions •Twins and stacking faults on (100) are pervasive throughout the enstatite sample after quenching and decompression from 15 GPa and 1700 °C. The displacement vector across the stacking fault boundary was determined to be <½ ½ w>, most likely being ½ <111>. This displacement vector can be explained be the transformation of high clinoenstatite to low clinoenstatite. •The twin boundaries and stacking faults that formed in high clinoenstatite parallel to the (100) planes during the transition from Pbca orthorombic to the C2/c high pressure phase seem to have acted as nucleation sites for majoritic garnet precipitates. •In the case that there was a well defined long axis of the garnet precipitate in the observed TEM section, this long axis was predominantly oriented parallel to (100) and the twin planes / stacking faults in low clinoenstatite. •There is no unique topotactic relationship between the low clinoenstatite host and the majoritic garnet precipitates. However, a dominant linear relationship was found with the <111> direction in garnet being parallel to the [001] direction in low clinoenstatite. This direction is probably controlled by the diffusivity of silicon in pyroxene and not by minimization of strain energy at the interface between the clinoenstatite host and majoritic garnet precipitates. The latter is probably due to the absence of a well defined oxygen close packing direction in garnet. 116 •The diffusivity of aluminium in C2/c HP-clinoenstatite in the [101]* direction at 15 GPa and 1700 °C was determined to be at least 6 x 10-11 cm2 s-1, which is 3 – 4 orders of magnitude faster than the diffusivity of the majorite component in garnet at the same conditions. •There is a large difference in the diffusivity of aluminium in clinopyroxene at high pressure and the diffusivity of aluminium in clinopyroxene at room pressure, which eventually indicates a change in diffusion mechanism with pressure or a strong dependence of the diffusivity of aluminium on calcium content in clinopyroxene. 117 6.7 References Angel, R.J., Chopelas, A., Ross, N.L. 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Am Mineral 88:653-666 119 Ich erkläre hiermit, dass ich die vorliegende Arbeit ohne unzulässige Hilfe Dritter und ohne Benutzung anderer als der angegebenen Hilfmittel angefertigt habe. Die aus fremden Quellen direkt oder indirekt übernommenen Gedanken sind als solch kenntlich gemacht. Die Arbeit wurde bisher weder im Inland noch im Ausland in gleicher oder ähnlicher Form als Dissertation eingereicht und ist als Ganzes auch noch nicht veröffentlicht. Ferner erkläre ich hiermit, dass ich nicht bereits anderweitig mit oder ohne Erfolg versucht habe, eine Dissertation einzureichen oder mich der Doktorprüfung zu unterziehen. Ulm, 29. März 2012 Willem Louis van Mierlo