Cooling and Accretion of the Lower Oceanic Crust at Fast-Spreading Mid-Ocean Ridges

Dissertation zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften an der Fakultät für Geowissenschaften der Ruhr-Universität Bochum

vorgelegt von Kathrin Faak (Bochum)

Bochum, im Oktober 2012

Gutachter Prof. Dr. Sumit Chakraborty Prof. Dr. Jörg Renner Prof. Dr. Bernd Marschner

Tag der mündlichen Prüfung 20. November 2012

Cooling and Accretion of the Lower Oceanic Crust at Fast-Spreading Mid-Ocean Ridges

Doktoral Thesis by Kathrin Faak

born in Bochum

Faculty of Geosciences Ruhr-Universität Bochum

Bochum, October 2012

Thesis committee Prof. Dr. Sumit Chakraborty Prof. Dr. Jörg Renner Prof. Dr. Bernd Marschner

Defense of doctoral thesis November 20, 2012

Declaration of Authorship

I hereby declare in lieu of an oath that I have written this thesis independently and autonomously using only the sources indicated.

Location, Date Signature Abstract

Magmatism along mid-ocean ridges (MORs) is estimated to account for 75 % of the recent global magmatic budget and involves the emplacement of ~20 km 3 of magma per year. The processes involved in cooling and accretion of this magma to form new oceanic crust are a principal mechanism of heat removal from the Earth’s interior. Circulation of seawater through newly formed crust extracts magmatic heat and produces hydrothermal fluids enriched in base metals and nutrients that form massive sulphide deposits, and feed chemosynthetic ecosystems on the seafloor. Additionally these hydrothermal systems have a profound influence on the composition of the oceans. However, the processes involved in the formation of oceanic crust by cooling and crystallization of the magma, and therefore providing the heat for the hydrothermal circulation, are poorly understood. The existing end-member models of crustal accretion along fast-spreading mid-ocean ridges (the ‘ gabbro glacier ’ and the ‘ sheeted sill ’ model) differ in the proportion of crystallization at different depths within the lower oceanic crust. Therefore, these models predict different thermal evolution, and most significantly, different depths to which hydrothermal fluids circulate in the oceanic crust. As a consequence, this implies different variations of cooling rate as a function of depth. The present study determines cooling rates of natural rock samples of the lower oceanic crust, formed along three different segments of the fast-spreading East Pacific Rise (EPR). Since the individual samples of each location were collected from different depth, the results presented here include information about the variation of cooling rates as a function of depth in the lower oceanic crust. In turn, this allows testing the different models and provides additional constraints for the development of a revised model. To obtain cooling rates from the natural rock samples, a new ‘ Mg-in- plagioclase geospeedometer ’ was developed, which is based on the diffusive exchange of Mg between plagioclase (Pl) and clinopyroxene (Cpx) during cooling. Calibration of this tool required detailed investigation of the diffusion coefficient of

Pl Mg in plagioclase ( DMg ) and the partition coefficient of Mg between plagioclase and

Pl / Cpx clinopyroxene ( K Mg ) in the compositional range of the lower oceanic crust. The

Pl Pl / Cpx diffusion coefficient DMg and the partition coefficient K Mg were determined experimentally as a function of temperature ( T) , anorthite-content in plagioclase

(XAn ) and the silica activity of the system ( a ). SiO 2

Pl Pl / Cpx Reliable results for DMg and K Mg were obtained in a temperature range of

1100 to 1200°C and a compositional range of XAn =0.5 to 0.8. At these conditions,

Pl / Cpx K Mg was found to (i) decrease with decreasing T, (ii) increase with increasing XAn in plagioclase and (iii) increase with increasing a . The diffusion coefficient D Pl SiO 2 Mg was found to (i) decrease with temperature following an Arrhenian relationship and

Pl (ii) to increase with increasing a . No significant dependence of D on XAn in SiO 2 Mg plagioclase was observed. Application of the ‘ Mg-in-plagioclase geospeedometer ’ on the different natural samples suites of the EPR yield cooling rates in the range of 5 °C/year to 0.0001 °C/year, and a general trend of decreasing cooling rate as a function of depth is observed. The observation of fast cooling at the top of the lower oceanic crust and decreasing cooling rates at greater depth is consistent with a ‘ gabbro glacier ’ type model of crustal accretion. The results derived in this study provide a new geothermometer based on Mg exchange between Pl and Cpx with wide application to terrestrial and extraterrestrial rocks containing these two minerals. Furthermore, the developed ‘Mg-in-plagioclase geospeedometer ’ may be applied to these rocks to reconstruct their cooling history. The vertical distribution of cooling rates in the lower oceanic crust obtained in this study provides new information about the thermal structure along fast-spreading MORs, which is an important step in understanding the processes during cooling and accretion of new oceanic crust. Contents

Contents

1. INTRODUCTION 1 1.1 Objectives of this study 1 1.2 Structure of this thesis 3 1.3 The lower oceanic crust at fast-spreading mid-ocean ridges 4 1.4 The existing models for crustal accretion at fast-spreading ridges and their constraints 14 1.4.1 The development of different models 14 1.4.2 Thermal constraints on the models of crustal accretion 18 1.4.3 Summary of the differences of the two end-member models 19 1.5 The approach of this study - Testing models of lower crustal accretion using diffusion calculations and ‘geospeedometry ’ on natural rock samples 21 1.6 The investigated natural sample suites 27 1.6.1 Hess Deep 28 1.6.2 Pito Deep 32 1.6.3 IODP Site 1256 35 1.7 References 37

2. EXPERIMENTAL DETERMINATION OF THE TEMPERATURE DEPENDENCE OF MG EXCHANGE BETWEEN PLAGIOCLASE AND CLINOPYROXENE 49

Abstract 49

i Contents

2.1 Introduction 50 2.2 Theoretical background and previous work on the diffusive exchange of Mg between plagioclase and clinopyroxene 54 2.2.1 Exchange of Mg between plagioclase and clinopyroxene 54 2.2.2 Diffusion of Mg in plagioclase 60 2.3 Experimental setup and run conditions 62 2.3.1 General experimental setup, starting materials and run conditions 62 2.3.2 Special experimental setups 66 2.3.3 Sample preparation after the experiment 67 2.4 Electron microprobe (EMP) analyses 67 2.5 Experimental results and discussion 69 2.5.1 General observations 69

Pl / Cpx Pl 2.5.2 Extracting K Mg and DMg from the experiments 71

Pl / Cpx Pl 2.5.3 Experimental results on K Mg and DMg 73 2.5.4 Uncertainties and error estimation 77

Pl / Cpx 2.5.5 Variation in ln K Mg as a function of

Cpx T, X An , a , and X 82 SiO 2 CaSiO 3

Pl / Cpx 2.5.6 Discussion of the experimental results on K Mg 91 2.5.7. A new thermometer based on the exchange of Mg between plagioclase and clinopyroxene 94

Pl 2.5.8 Variation in D with T, X An and a 95 Mg SiO 2

Pl 2.5.9 Discussion of the experimental results on DMg 98 2.6 Conclusions 105 2.7 References 108

ii Contents

3. COOLING RATES WITH DEPTH IN THE LOWER OCEANIC CRUST DERIVED BY DIFFUSION MODELLING OF MG IN PLAGIOCLASE 113

Abstract 113 3.1 Introduction 114 3.2 Diffusion profiles of Mg in plagioclase and the extraction of cooling rates 118 3.3 The diffusion model 119 3.4 Model parameters and input conditions (for the diffusive exchange of Mg between plagioclase and clinoyproxene and the investigated sample suite) 121 3.4.1 Diffusion coefficient 121

Pl / Cpx 3.4.2 Initial profile determined from K Mg 124

Pl / Cpx 3.4.3 Boundary conditions determined from K Mg 127 3.5 Evolution of concentration profiles of Mg in plagioclase in contact with clinopyroxene during linear cooling 128 3.6 Uncertainties, robustness and sensitivity of the approach 131 3.6.1 A test of robustness and sensitivity of the model 133 3.7 Application to natural sample suites of rocks from different depths within the lower oceanic crust 140 3.7.1 Analytical techniques 141 3.7.2 The sample suites 142 3.8 Results from the Hess Deep (North wall) samples 144 3.8.1 Shapes of Mg-profiles in plagioclase with increasing depth 144 3.8.2 Cooling rates and their vertical distribution 145 3.9 Results from the Pito Deep samples 148 3.9.1 Shapes of Mg-profiles in plagioclase with increasing depth 148 3.9.2 Cooling rates and their vertical distribution 150 3.10 Results from the IODP 312 1256D samples 152

iii Contents

3.11 Discussion 154 3.11.1 Implications for the constraints on the cooling history of each sample 154 3.11.2 Comparison of the different sample suites 158 3.11.3 Comparison of cooling rates obtained from Mg-in-plagioclase and from Ca-in-olivine 161 3.11.4 Interpretation and discussion of the vertical distribution of cooling rates 162 3.11.5 Geological implications 167 3.12 Conclusions 168 3.13 References 169

4. CONCLUSIONS AND FUTURE WORK 175

4.1 Summary of the results from this study 175 4.2 Future work and perspectives 178 4.3 References 184

APPENDIX Appendix I - Table A1: Summary of the petrography Appendix II - Table A2: Summary of the measured profiles Appendix III - Table A3: EMP measurement conditions Appendix IV - Figure A4: Plots of all fitted Mg-concentration profiles Appendix V - Fortran code of the diffusion model Appendix VI -Organization of the Electronic Appendix

ACKNOWLEDGEMENTS

CURRICULUM VITAE

iv 1. Introduction

Chapter 1

1. Introduction

1.1 Objectives of this study

Magmatism along the global mid-ocean ridge (MOR) system is estimated to account for 75 % of the recent global magmatic budget and involves the emplacement of ~20 km 3 of magma per year (e.g. Crisp, 1984). The processes involved in cooling and accretion of this magma to form new oceanic crust are a principal mechanism of heat removal from the Earth’s interior (e.g. Chapman and Pollack, 1975; Davies and Davies, 2010). Plate-spreading at mid-ocean ridges leads to upwelling of the mantle. The rising mantle material undergoes adiabatic decompression, leading to partial melting, as the solidus temperature decreases with decreasing pressure. The basaltic melt generated in the mantle is less viscous and less dense than the surrounding mantle and therefore segregates from the residual mantle and buoyantly rises towards the surface (e.g. McKenzie, 1984 and 1985; Phipps Morgan, 1987; for a review see Turcotte and Phipps Morgan, 1992 and references therein). There, it crystallizes within a thermal boundary layer near the surface and forms new oceanic crust. The rate of magma supply to a mid-ocean ridge depends on the spreading rate, at which the plates diverge from each other (Sinton and Detrick, 1992; Lizarralde et al., 2004). There is a wide range of

1 1. Introduction spreading rates along the global mid-ocean ridge system (e.g. DeMets, 2010). However, for simplicity, they are often divided into end-member fast-and slow- spreading rates (fast-spreading rates being roughly ≥80 mm/year and slow- spreading rates being roughly ≤50 mm/year, following the subdivision by Sinton and Detrick, 1992). The morphology and the seismic structure of mid-ocean ridges are very different along fast- and slow-spreading ridges (e.g. Macdonald, 1998 and references therein; Dunn and Forsyth, 2007), leading to different models to explain the formation of oceanic crust at different spreading rates. This study focuses on the formation of oceanic crust along fast-spreading mid-ocean ridges. Evidence of coarse grained plutonic rocks within the lower oceanic crust formed at modern fast-spreading ridges (e.g. Francheteau et al., 1990; Gillis et al., 1993; Constantin et al., 1996; Hekinian et al., 1996; Wilson et al., 2006), rather evolved composition of mid ocean ridge basalt (MORB) glasses (e.g. Coogan, 2007), and observations based on marine seismic data (e.g. Raitt, 1963; Detrick et al., 1987; Dunn et al., 2000) indicate that the melt does not directly migrate to the surface, where it would be quenched by the seawater to form lavas. Instead, the melt accumulates in one (or multiple) magma chamber(s), where it undergoes slower cooling, differentiation and crystallization, forming the plutonic section of the lower oceanic crust. After variable amounts of differentiation, some portion of the melt rises from the magma chamber(s) to the surface, forming the dikes and lavas of the upper oceanic crust. An intimately linked process to cooling and accretion of the oceanic crust is the circulation of seawater through newly formed crust that extracts magmatic heat (e.g. Baker, 2007) and produces hydrothermal fluids enriched in base metals and nutrients, which form massive sulphide deposits and feed chemosynthetic ecosystems on the seafloor (e.g. Naar et al., 2004; Tivey, 2007). Additionally these hydrothermal systems have a profound influence on the composition of the oceans. However, the processes involved in crystallizing and cooling the magma (and therefore forming the oceanic crust) are poorly understood. Different end-member models for crustal cooling and accretion at fast-spreading mid-ocean ridges predict different thermal histories for the crust, and most significantly, different depths to

2 1. Introduction which hydrothermal fluids circulate in the crust, implying variable relations between cooling rate and depth.

This study aims to determine cooling rates of the lower oceanic crust as a function of depth. This objective requires the calibration of new ‘ geospeedometric ’ tools that are especially suited for this problem. Subsequent application of these tools to natural rocks that are directly sampled from various depths of fast- spreading oceanic crust provides insights in the vertical distribution of cooling rates beneath fast-spreading mid ocean ridges. These results allow testing the existing models. Furthermore, the data may be used as additional constraints for the development of a revised model on crustal cooling and accretion at fast-spreading ridges, aiming to explain all geophysical, petrological and geochemical observations.

1.2 Structure of this thesis

The following introductory sections are arranged as follows: Section 1.3 provides a brief summary of the main characteristic features of the lower oceanic crust, based on geophysical data and observations of ancient and modern oceanic crust. Section 1.4 presents and discusses the different existing models of crustal accretion at fast-spreading ridges that were previously developed to explain these features and constraints. Section 1.5 explains the approach of this study that is to test the different models using a newly calibrated ‘ geospeedometer ’ based on diffusion modelling of Mg in plagioclase to obtain the vertical distribution of cooling rates of the lower oceanic crust. The final part of the introduction, Section 1.6, gives an overview of the natural sample suites investigated in this study. Chapters 2 and 3 are arranged in the format of research papers. These papers necessarily include some information that has been already discussed in the introductory sections. Chapter 2 (i.e. Publication I, in prep.) deals with the experimental calibration of the diffusive exchange of Mg between plagioclase and

3 1. Introduction clinopyroxene that is required for the development of a new ‘ Mg-in-plagioclase geospeedometer’ . Chapter 3 (i.e. Publication II, in prep.) reports the details of the diffusion model of Mg in plagioclase used to obtain cooling rates from natural rock samples. This chapter also reports results of the application of this method on samples from different depths from the lower oceanic crust formed at three different locations from the fast-spreading East Pacific Rise. Finally, Chapter 4 summarizes the results and conclusions of this work and points to new research questions arising from the present study.

1.3 The lower oceanic crust at fast-spreading mid-ocean ridges

Our understanding of the oceanic crust and particularly its plutonic portion is based on observations of ancient oceanic rocks exposed on land (ophiolites) and geophysical data of modern oceanic crust. Additional information arises from the rare possibilities of direct insights into the structure of modern oceanic crust, provided by drill cores and deep sea tectonic exposures. The following section briefly reviews the observed features of the lower oceanic crust, since they will be the features, which any successful model of cooling and accretion of oceanic crust has to explain.

Observations from ophiolites: Investigations in ophiolite complexes (sections of former oceanic crust that have been raised above sea level by tectonic processes) have provided a rich observational database on oceanic gabbroic rocks (e.g. Coleman, 1971; Moores and Vine, 1971; Dewey and Bird, 1971; Coleman, 1977; Nicolas, 1989) and have strongly influenced current models of crustal accretion (e.g. Quick and Denlinger, 1993; Boudier et al., 1996; Kelemen et al, 1997, Boudier and Nicholas, 2011). The current view of the structure of the oceanic crust developed in parallel with studies of ophiolite complexes and seismic data. In the early 1970’s Moores and Vine (1971), Dewey and Bird (1971) and others correlated the layered

4 1. Introduction geologic structure from ophiolites with the seismic layers of the oceanic crust (e.g. see Karson, 1998 for a review). Most ophiolites, however may be atypical of “normal” modern oceanic crust in that they were formed in supra-subduction zone environments and were tectonically emplaced to now be on land (Pearce et al., 1984; Hawkins et al., 1984). Additionally, the exact spreading rate of the ridges at which they formed are unknown and can only be inferred from geological and petrological observations. Nevertheless, since so little is known about the lower oceanic crust, it is necessary to use insights provided by ophiolites, even though these should be critically evaluated. One of the best studied ophiolites is the Oman ophiolite, where the lower oceanic crust is superbly exposed and thus most of the data presented here will refer to this ophiolite. The actual spreading rate is unknown, but the Oman ophiolite is interpreted to have formed along an intermediate- to fast-spreading ridge (Nicholas et al., 2000) and therefore is thought to represent an analogue of modern oceanic crust formed at fast-spreading ridges. The total thickness of gabbroic material in the Oman ophiolite ranges from 1 km to >6 km (Juteau et al., 1988) and this assemblage is bounded by residual upper mantle peridotite (mostly harzburgite) below and sheeted dikes with overlying basaltic lavas above (Coleman and Hopson, 1981). The gabbroic section comprises a thicker (2.5 to 6.6 km) layered and foliated sequence, overlain by a thinner (0.1 to 0.5 km thick), foliated section, in which layering is scarce to absent (e.g. Pallister and Hopson, 1981; Nicolas et al., 1988a and b). Chemically, the lower gabbroic rocks are cumulates, i.e. they are comprised of accumulated crystals that separated from the residual (differentiated) magma (Browning, 1984). Layering in the lower gabbroic section is defined by abrupt to gradual variations in mineralogy and grain size (e.g. Pallister and Hopson, 1981; Boudier et al., 1996). Interlayered gabbroic sills and ultramafic bodies occur close to the inferred mantle-crust transition zone, MTZ (e.g. Juteau et al., 1988; Benn et al., 1988; Nicolas et al., 1988a and b; Boudier et al., 1996; Kelemen at al., 1997; Korenaga and Kelemen, 1997; Fig. 1.3.1). The ultramafics have been interpreted as intrusive wherlite sills (e.g. Juteau et al., 1988; Benn et al., 1988; Nicolas et al., 1988a and b), which are rooted in the MTZ. The foliation in the lower gabbros is sub-

5 1. Introduction parallel to the crust-mantle boundary with a lineation that is sub-parallel to the lineation in the underlying mantle harzburgites (e.g., Nicolas et al., 1988a and b, 2009; Fig. 1.3.1). Towards the top of the lower gabbros, the dip of the foliation steepens, becoming more or less parallel to the overlying sheeted dikes (e.g. Nicolas, 1988a and b; Boudier et al., 1996; Fig. 1.3.1). Outcrop features and microstructures show that the foliation is the result of magmatic deformation, whereas crystal plastic deformation is scarce to absent in the gabbroic rocks from the Oman (e.g. Boudier et al., 1996).

Fig. 1.3.1: Schematic cross section through the oceanic crust exposed in the Oman ophiolite (Nicolas et al., 1988a)

6 1. Introduction

Geophysical data: Early studies of vertical profiles of seismic wave velocities suggested that the structure of the oceanic crust is surprisingly simple and uniform (e.g. Raitt, 1963; Christensen and Salisbury, 1975). Differences in the seismic velocities lead to the subdivision of the oceanic crust into different seismic layers. With improvements in seismic instrumentation, experiment design, and analytical techniques, the early view of the oceanic crust as a small number of homogeneous layers was replaced by structural models involving smooth variations in velocity with depth and sharply depth-dependent vertical gradients in velocity (Spudich and Orcutt 1980). The interpretation of seismic velocities in terms of lithologies has been based on comparison with ophiolite analogues and dredged and drilled rocks from modern oceanic crust (see Solomon and Toomey, 1992 for a review of early work) and led to the inferred ‘layer-cake model’ of the oceanic crust. By analogy with observations made in ophiolites, the upper oceanic crust, or seismic ‘layer 2A’, has been interpreted to be composed of high porosity extrusive basalts, followed by a higher-velocity region (seismic ‘layer 2B’) of sheeted dikes underlain by a yet higher-velocity region of gabbroic rocks (seismic ‘layer 3’).

Fig. 1.3.2: Comparison of the inferred structure of the oceanic crust based on observations in ophiolites to the seismic velocity layers of the oceanic crust (Dilek et al., 1998).

7 1. Introduction

More recent work, however, has modified and disputed this simple ‘layer- cake model’. Investigations of the seismic structure of the oceanic crust in a variety of geological settings around the globe have shown that crustal structure varies with spreading rate, geodynamic setting, and time (e.g. see Dunn and Forsyth, 2007 for a review of more recent work). Our knowledge of the seismic structure of the oceanic crust beneath fast-spreading mid ocean ridges derives mainly from seismic experiments along a section of the northern East Pacific Rise (EPR) between 9° and 13° N and the southern EPR between 12° and 21° S. While the mantle beneath the EPR is characterized by a tens of kilometres wide zone of low seismic velocities (interpreted as the upwelling zone), near the Moho this low-velocity zone narrows abruptly to only 7 to 8 km width in the lower crust (Dunn et al., 2000; Dunn and Forsyth, 2007; Fig. 1.3.3). Tomographic investigations of the structure of the oceanic crust underneath the EPR at 9°30’ N detect a narrow zone (5 km wide at the top and 7 to 8 km wide at the bottom) of low P-wave velocities, referred to as the low velocity zone (LVZ) that extends from ~1.4 km depth below the seafloor down into the mantle (Dunn et al., 2000; Fig. 1.3.3). This LVZ is interpreted to be a partially molten region, containing ≤20 % melt (Dunn et al., 2000). The presence of a lower crustal partial melt zone beneath the EPR at 9°-10°N is also supported by measurements of seafloor deformation under ocean waves (compliance), which reveal a less than 8 km wide zone with less than 18 % melt (Crawford and Webb, 2002). The width of the LVZ is a relative indicator of the efficiency of heat removal from the axial region and the inferred isotherms for this seismic structure do not conform to the predictions of a conductively cooled system (Dunn et al., 2000). Thus, it is interpreted that hydrothermal circulation penetrates deeply off-axis to cool the lower crust, keeping the magmatic system narrow throughout the crust (Dunn et al, 2000; Dunn and Forsyth, 2007). Multichannel seismic reflection imaging along the EPR indicates the presence of a ~1 km wide and ~50 m deep melt lens on top of the LVZ along the base of the sheeted dike complex (~1.5 km deep) that can be continuous along axis for 10’s of km (e.g. Detrick et al., 1987; Kent et al., 1990; Hooft et al., 1997; Singh et al., 1998). This melt lens is commonly referred to as axial magma chamber (AMC) and is

8 1. Introduction thought to form by accumulation of buoyantly rising melt beneath a permeability or viscosity barrier at the top of the magmatic system (e.g. Hooft and Detrick, 1993). The depth of the AMC and the underlying LVZ decreases with increasing spreading- rate (Purdy et al., 1992; Phipps-Morgan and Chen, 1993a), but even for a given spreading-rate there is a variability of the depths of the AMC of about 1500 m. A few seismic studies and compliance data indicate that magma sills accumulate near the crust-mantle transition (e.g. Crawford and Webb, 2002; Nedimovic et al., 2005; Canales et al., 2009). On the basis of ophiolite studies, melt lenses have been predicted to occur in the lower oceanic crust as well (e.g. Reuber 1990; Boudier et al., 1996; Kelemen et al., 1997), but to date no conclusive geophysical evidence has been found in support of this prediction (Dunn and Forsyth, 2007).

Fig. 1.3.3: Three-dimensional perspective of the P-wave velocity structure of the East Pacific Rise at 9°30’ N (relative to a one-dimensional depth-dependent model). The ridge magmatic system is characterized by a narrow low-velocity zone that extends from ~1.4 km depth down into the mantle. Near its top, the low-velocity zone is over 2 kms -1 slower than velocities away from the ridge axis. The axial melt lens reflector, as observed on multichannel seismic reflection imaging data, passes through the low- velocity zone at 1.5 km depth (Dunn and Forsyth, 2007).

9 1. Introduction

Direct observations from modern fast-spreading ocean crust: Direct observations and sampling of the seafloor via submersible, dredging, and drilling show that at fast-spreading ridges the seafloor is composed almost entirely of lavas. Insights into the structure of the lower oceanic crust are provided by drill cores that penetrated down into the lower crust (i.e. International Ocean Drilling Program (IOPD) Hole 1256D; Wilson, 2006; Ocean Drilling Program (ODP) Leg 147 Site 894; Gillis et al., 1993; Fig. 1.3.4) as well as by the rare possibility of natural crustal cross sections along ‘tectonic windows’, where fault zones created major escarpments on the seafloor. Hess Deep and Pito Deep are such tectonic windows into crust formed at the fast-spreading EPR (Fig. 1.3.4 and Fig. 1.3.5), exposing the entire upper oceanic crust (lavas and dikes) and the upper part of the plutonic complex (e.g. Karson et al., 2002; Perk et al., 2007;).

Fig. 1.3.4: Topographic map with locations, which provide insights into the lower crust along the East Pacific Rise (EPR). The locations of Hess Deep and Pito Deep are marked with red lines and the locations of IODP Sites 1256 and 894 are shown as white circles.

10 1. Introduction

(a) (b)

Fig. 1.3.5: 3D-bathymetry of the ocean floor around Hess Deep (a) and Pito Deep (b) to illustrate the concept of ‘tectonic windows’, where natural cross sections through the oceanic crust can be exposed to the seafloor along escarpments of fault zones. The hot colors are shallow seafloor and the cool colors are deep seafloor. The marked zones A and B in (b) represent different studied areas within Pito Deep. Pictures taken from (a) http://www.womenoceanographers.org/emilyklein and (b) unpublished Cruise Report; Expedition RT11-23 of the R/V Atlantis.

At Hess Deep in the equatorial Pacific, ~1 Ma old crust that initially formed at the equatorial EPR (full spreading rate ~135 mm/year) is rifted apart due to the westward propagation of the Cocos-Nazca spreading centre (Lonsdale, 1988; Francheteau et al., 1990). This tectonic window exposes the entire upper crust (lavas and dikes, ~1200 m) as well as the upper part (~1000 m) of the gabbros (Karson et al., 2002). The walls of the rift were investigated and sampled in several dives from two different dive programs (4 dives in the Nautile dive program; Francheteau et al., 1990; and 11 dives in the Alvin dive program; Karson et al., 1992). Additionally, dives surveyed plutonic rocks on a prominent Intra-Rift Ridge at the base of the North wall (Francheteau et al., 1990; Hekinian et al., 1993), which was subsequently drilled by ODP Leg 147 Hole 894G, recovering shallow level gabbros (Gillis et al., 1993). Gabbroic rocks recovered at Hess Deep span a wide range of lithologies and were divided according to grain size, textures and mineral association into olivine gabbro cumulates, gabbronorite cumulates, noncumulate (isotropic) gabbros, and metagabbros (Hekinian et al., 1993). A striking feature of the gabbroic rocks from Hess Deep is the abundance of orthopyroxene (Hekinian et al., 1993; Coogan et al., 2002a). Modal layering, as observed in the ophiolite complexes, is not evident, but the upper gabbros contain many contacts of lithologies with different grain size (Gillis et al., 1993; Coogan et al., 2002a). Whole

11 1. Introduction rock geochemistry from the Hess Deep gabbroic rocks compared to basaltic samples indicate that the gabbros are cumulates that crystallized from evolved melt and were modified by reaction with interstitial melt during solidification (Pedersen et al., 1996; Natland and Dick, 1996; Coogan et al., 2002a). Trace element chemistry indicates a massive enrichment in chlorine in magmatic amphibole in plutonic rocks from the EPR compared to those from the slow-spreading Mid-Atlantic ridge (Gillis et al., 2003). This observation strongly supports the conclusion, drawn from basalt compositions, that chlorine is enriched in MORBs at fast-spreading ridges through assimilation (Michael and Schilling, 1989). Since chlorine enrichment is observed only for fast-spreading ridges it is unlikely to simply result from seawater interaction. Instead, it has been interpreted to indicate assimilation of one or more components that have interacted with hydrothermal fluids (brine, altered roof- and wall-rocks) into magma chambers (Michael and Schilling, 1989; Coogan, 2007). The interpretation that hydrothermally altered material was assimilated into the magma chamber is additionally supported by the observation of hornfelses at the dike/gabbro transition at Hess Deep (Gillis, 2008). Such hornfelses are also documented at the dike/gabbro transition at Pito Deep (Heft et al., 2008; Gillis, 2008), and from IODP Site 1256D (Koepke et al., 2008), as well as in the Oman ophiolite (e.g. Nicolas et al., 2008; France et al., 2009), and the Troodos ophiolite in Cyprus (Gillis and Roberts, 1999; Gillis, 2008), and their occurrence is interpreted to record the vertical migration of the axial magma chamber (Gillis, 2008; Koepke et al., 2008). Gillis (2008) proposed that the hydrated dikes are partially or completely assimilated into the magma chamber by stoping during the upward migration of the AMC into the sheeted dikes, leading to incorporation of exogenic components (e.g. Cl) into the magmatic system. Above the AMC, an impermeable conductive boundary layer (CBL) composed of hornblende and pyroxene hornfels develops as heat transfer drives the recrystallization of hydrothermally altered dikes and the overlying hydrothermal system. Gillis (2008) estimated a minimum duration of thermal overprint of 50 years for samples from Hess Deep. When the AMC subsides, the CBL and hydrothermal system deepens into the upper gabbros. Koepke et al.

12 1. Introduction

(2008) in general support the proposed scenario, but obtain an overprint duration of ~10,000 years for a sample from IODP Hole 1256D. At Pito Deep , located in the southern Pacific, ~3 Ma old crust formed at the EPR (full spreading rate ~140 mm/year) is rifted apart due to a propagating rift tip of the northeastern corner of the Easter Microplate (Francheteau et al., 1988; Hey, 1995), exposing continuous sections of the oceanic crust consisting of basaltic lavas, sheeted dikes and gabbroic rocks (Constantin et al., 1995; Constantin et al., 1996; Hekinian et al., 1996, Perk et al., 2007). Gabbroic rocks from the Pito Deep area were collected during several cruises (the Sonne 65 cruise, Stoffers and Hekinian, 1989; the Pito Nautile cruise, Hekinian et al., 1996; the Jason and Alvin dive programs during cruise AT11-33 of the R/V Atlantis , Perk et al., 2007). The plutonic sample suite from Pito Deep includes mainly gabbros, olivine gabbros and troctolites, which show modal layering (Perk et al., 2007). Bulk-rock geochemistry of these rocks yields compositions that are mainly at the primitive end of the global spectrum of oceanic plutonic rocks (Perk et al., 2007). The difference in the bulk-rock geochemistry of the Hess Deep and Pito Deep gabbros has been interpreted to result from temporal or spatial variations in the mechanism of crustal accretion along the EPR (Perk et al., 2007), which would reflect temporal or spatial variation in the thermal structure of the crust. Gabbros from both Hess Deep and Pito Deep show magmatic fabrics similar to those observed in the Oman ophiolite and the magmatic foliation is largely defined by the alignment of plagioclase laths (Hess Deep: e.g. Gillis et al., 1993; MacLeod et al., 1996; Pito Deep: Perk et al., 2007; Oman: e.g. Boudier et al., 1996). The magnetic fabric of Hess Deep gabbros from ODP Hole 894G is parallel to the plagioclase alignment (Richter et al., 1996), suggesting that magmatic flow within the shallow gabbros beneath the EPR is close to axis-parallel and near-vertical (Coogan et al., 2002a). A ridge parallel, sub-vertical foliation is also reported for the Pito Deep gabbros (Perk et al., 2007). As in the gabbros from the Oman ophiolite, there is little evidence for crystal plastic deformation in gabbroic rocks from Hess Deep (e.g. Coogan et al., 2002a) and crystal plastic deformation in gabbroic rocks from Pito Deep is weak (Perk et al., 2007).

13 1. Introduction

IODP Hole 1256D , located in the eastern Pacific, drilled into ~15 Ma old intact oceanic crust of the Cocos Plate that formed at the superfast spreading EPR (full spreading rate ~220 mm/year). The drill core recovered ~1250 m of oceanic crust, providing a continuous section from extrusive lavas, through sheeted dikes into the top of the plutonic section (Wilson et al., 2006). The penetrated top of the plutonic section consists of two major gabbroic bodies (52 and 24 m thick), separated by a 24 m thick screen of granoblastic dikes (Wilson et al., 2006; Koepke et al., 2008; France et al., 2009; Sano et al., 2011). Both gabbroic bodies mainly consist of isotropic, fine to coarse grained gabbros, including oxide gabbros, gabbronorite, and quartz-rich diorites (Wilson et al., 2006; Sano et al., 2011). The average bulk-rock composition of the gabbroic rocks is less evolved than compositions of lavas and dikes from Hole 1256D, but the gabbros are in general relatively evolved compared to magmas in equilibrium with mantle olivine, which are possible candidates for primary mantle derived magma sources (Wilson et al., 2006; Sano et al., 2011).

More detailed information about the geology and lithology exposed at Hess Deep and Pito Deep as well as drilled in Site 1256D may be found in Section 1.5, where the sample suite investigated for this study is introduced.

1.4 The existing models for crustal accretion at fast-spreading ridges and their constraints

1.4.1 The development of models on crustal accretion A key factor controlling the processes operating in the lower oceanic crust is the rate of magma supply to a mid-ocean ridge, because heat provided from magma injection, together with hydrothermal cooling, mainly determines the thermal structure underneath a mid-ocean ridge. Since the rate of magma supply strongly depends on the spreading-rate (e.g. Sleep, 1975; Sinton and Detrick, 1992; Section

14 1. Introduction

1.1), recent existing models on formation of the oceanic crust are very different for fast- and slow-spreading ridges and this chapter will mainly focus on models for fast-spreading ridges (for more detailed reviews see Karson, 1998 or Coogan, 2007). Early models for the formation of oceanic crust were largely based on the observed layering found in ophiolite complexes and assumed a large (~20 km wide), steady-state, completely molten magma chamber (e.g. Moores and Vine, 1971, Greenbaum, 1972). The ‘ infinite onion ’ model proposed by Cann (1974; Fig. 1.4.1a) assumes that the upper plutonic rocks form by downward freezing from the roof and the lower plutonic rocks form from crystals settling out of the magma. The model by Cann (1974) accounted for compositional zoning of the magma chamber, which then leads to broad-scale compositional layering of the newly formed crust that remained largely horizontal. Pallister and Hopson (1981) proposed a model based on the interpretation that the layered profiles in the Oman ophiolite results from crystallization and deposition on the floor and walls of a 30 km wide and 4.5 km deep axial magma chamber (Fig. 1.4.1b). In their model, material is transported away from the spreading centre without significant deformation and the size of the magma chamber was based on a calculated average layering dip relative to the Moho. The models of Smewing (1981) and Casey and Karson (1981) include essentially a similar size for the magma chamber, but with a different geometry to account for the observed upward steepening of the foliation in ophiolites (Fig. 1.4.1c). However, the documentation of only very small (~1 km wide and ~50 m deep, Section 1.3) magma chambers overlying a crystal-rich mush zone at fast-spreading ridges disproved models with large magma chambers. To explain the formation of a 3 to 5 km thick plutonic section from such a small magma chamber, new models were developed that included substantial vertical mass transport in the mush region. The ‘gabbro glacier’ model (Quick and Denlinger, 1993; Phipps Morgan and Chen, 1993b; Henstock et al., 1993; Fig. 1.4.1.d) builds on the thermal constraints and conceptual model of Sleep (1975; see also section 1.4.1) and assumes most crystallization to occur in a small axial magma chamber (AMC). The latent heat of crystallization is removed from the top of the magma chamber by an overlying

15 1. Introduction hydrothermal system and a crystal mush subsides down- and outwards, producing the layering and foliation orientations observed in ophiolites and tectonic windows. Boudier et al. (1996) proposed a model that builds on the gabbro glacier model, but additionally includes some of the crystallization taking place in situ in deeper sections of the crust after the intrusion of sills. The model of Boudier et al. (1996) is based on the observation of sill-like plutonic bodies at the crust-mantle transition zone (MTZ) in the Oman ophiolite (e.g. Juteau et al., 1988; Benn et al., 1988; see also Section 1.3) and the assumption that the modally graded bedding, defining layering in the lower gabbros, may have similarly originated as sills. The model by Boudier et al. (1996) was extended by Kelemen et al. (1997), who suggest a ‘sheeted sill’ model, in which almost the entire lower oceanic sequence of the Oman ophiolite may have crystallized as a series of sheeted sills (Fig. 1.4.1e). Their conclusions are based on geochemical studies indicating that gabbroic sills in the MTZ in the Oman ophiolite are compositionally similar to the lower, layered gabbros in the Oman ophiolite, but different from the non-layered gabbros near the dike/gabbro transition zone. Thus, Kelemen and co-workers propose that the lower, layered gabbros probably formed from a mantle derived magma that partially (~50 %) crystallized in sills similar to those in the MTZ, while residual liquids rose to form upper gabbros, dikes and lavas. Such ‘ sheeted sill ’ type models were supported by subsequent geochemical and structural studies in the Oman ophiolite (Korenaga and Kelemen, 1997) and other ophiolite complexes (Lissenberg et al., 2004). Korenaga and Kelemen (1997) report that gabbro sills in the MTZ have mm-scale to tens of cm-scale modal layering, which closely resembles layering in lower crustal gabbros of the ophiolite. Additionally, the observed correlations in the mineral chemistry in gabbros sills from the MTZ and in the lower crust led them to conclude that the liquid from which the MTZ gabbros formed was parental to the crustal rocks. Lissenberg et al. (2004) support in situ formation of the lower oceanic crust based on the observation of sill-like gabbroic bodies in the crustal level of the Annieopsquotch ophiolite in Newfoundland, and the calculation of possible parental magmas of these gabbroic bodies, which generally become more evolved upwards. MacLeod and Yaouancq (2000) slightly modified the

16 1. Introduction

‘sheeted sill ’ model and proposed a model in which sills are injected episodically into a largely solid and cooler ‘transition zone’ that lies slightly off-axis. ‘Hybrid’ models such as proposed by Boudier et al. (1996), with some proportion of crystallization happening in the axial magma chamber and some proportion taking place in situ in the lower oceanic crust were supported by petrological and geochemical studies on the lower oceanic crustal rocks from Hess Deep (Coogan et al., 2002a) as well as by thermal modelling with respect to chemical variation in the crust (Maclennan et al., 2004 and 2005; see Section 1.4.1). (a) (b) (c)

0 10 20 0 10 20 km km

0 2 4 km lava sheeted isotropic layered magma crystal solidified ~30MW/km dikes gabbro gabbro mush pluton

melt/mush energylossin hydrothermal 30MW/km transport circulation Megawattsper kmofridgeaxis

~30MW/km ~15MW/km (d) coolingrate (e)

AMC axial magma AMC chamber axial magma

depth chamber

~40 (d) (e) ~55 MW/km MW/km 0 2 4 0 2 4 km km Fig. 1.4.1: Models of formation of the lower oceanic crust. (a) the ‘ infinite onion ’ model (Cann, 1974) in which an ever-present magma chamber generates the lower oceanic crust through crystals plating its margin; (b) a ‘ large magma chamber ’ model (Pallister and Hopson, 1981) based on structural and chemical data from the Oman ophiolite; and (c) another ‘ large magma chamber ’ model with a different geometry (Smewing, 1981) to account for the observed upward steepening of the foliation in ophiolites; (d) a ‘ gabbro glacier ’ model (Sleep, 1975; Quick and Denlinger, 1993; Phipps Morgan and Chen, 1993; Henstock et al., 1993), in which the lower oceanic crust crystallizes in a small sill at the base of the sheeted dike complex from which cumulates subside down to form the lower crust; and (e) a ‘ sheeted sill ’ model (Kelemen et al., 1997; Korenaga and Kelemen, 1997), in which the lower oceanic crust forms through the crystallization of multiple sills. The central panel between (d) and (e) in the lower row illustrates the difference in the predicted cooling rate with depth for both end- member models (green = ‘ gabbro glacier ’ model; purple = ‘sheeted sill ’ model).

17 1. Introduction

1.4.2 Thermal constraints on models of lower crustal accretion The rate of cooling of the plutonic crust (and therefore the mode of accretion) depends on the interplay between the addition of heat by magmatic processes (latent heat and specific heat of crystallization) and the heat loss through conductive and hydrothermal convective transport. Thus, thermal modelling of the heat budget of the plutonic section around the ridge axis provides additional constraints on the models of lower crustal accretion (Sleep, 1975; Morton and Sleep, 1985; Phipps Morgan and Chen, 1993b and 1993b; Chen, 2001; Cherkaoui et al., 2003; Maclennen at al., 2004). Sleep (1975) used thermal constraints to show that processes operating in the lower crust should be sensitive to spreading rate. According to his calculations, permanent magma chambers can not exist at slow-spreading ridges, since the magma body would freeze. In his model for faster spreading ridges, crystals form on the roof of a narrower magma chamber and then settle downwards and out through a wider zone of crystal mush, producing flow lines which are steep near the ridge axis and turn horizontal at depth, compatible with the observed steepening of foliations in the upper gabbros from ophiolite complexes (Section 1.3). Thermal modelling by Phipps Morgan and Chen (1993a and 1993b) showed that a well developed AMC only exists at full spreading-rates >60 mm/year and that the general shallowing of the depth of the AMC with increasing spreading-rate is consistent with thermal control on the average depth of this body. The large variability of the depth of the AMC at a given spreading-rate (~1500 m; Section 1.3) suggests spatial and temporal variability in magma supply and/or hydrothermal cooling leading to variations in the thermal structure of the oceanic crust. Chen (2001) mathematically constrained thermal effects of a second melt lens at the depth of the Moho. His results showed that, if more than 10 % of the lower oceanic crust formed by crystallization in this deeper melt lens, this would require efficient removal of the latent heat of crystallization at depths to prevent a large molten region from forming, which would not have been consistent with seismic observations (e.g. Dunn and Toomey, 1997; Dunn et al., 2000). The thermal model of Maclennan et al. (2004 and 2005) incorporates

18 1. Introduction petrological variation of the oceanic crust and allows for a variable vertical distribution of crystallization. Maclennan and co-workers tested the different proposed models for crustal accretion according to thermal constraints. Both end-member models for crustal accretion, as well as hybrid models, have been shown to be viable based on thermal models (Chen, 2001; Cherkaoui, et al., 2003; Maclennan et al., 2004). However, in situ accretion of the lower oceanic crust is only consistent with thermal models if deep hydrothermal circulation is assumed along the sides of the crystal mush zone (Chen, 2001; Cherkaoui, et al., 2003; Maclennan et al., 2004). Additional thermal constraints are provided by the calculation of cooling rates using ‘ geospeedometers ’ that quantify the diffusive exchange of elements between minerals (e.g. Lasaga, 1983; for a review see Chakraborty, 2008; see also Section 1.5). The ‘ Ca-in-olivine geospeedometer ’ was used to determine cooling rates of plutonic rocks as a function of depth from two different sections of the Oman ophiolite (Coogan et al., 2002b; Coogan et al., 2007; VanTongeren et al., 2008) as well as of plutonic rocks from Hess Deep and Pito Deep (Coogan et al., 2007) with contrasting results. Coogan and co-workers (Coogan et al., 2002b; Coogan et al., 2007) fit complete diffusion profiles and reported a smooth decrease in cooling rate as a function of depth. This observation is consistent with a ‘ gabbro glacier ’ mode of accretion and conductive cooling of the lower oceanic crust. VanTongeren et al. (2007) used only the Ca-content in the cores of the olivine crystals and obtained generally slower cooling rates than Coogan et al. (2002b and 2007). VanTongeren et al. (2007) interpret that no significant change of cooling rate occurred as a function of depth and therefore they favour a ‘ sheeted sill ’ type model.

1.4.3 Summary of the differences of the two end-member models Summarizing, the processes involved in the formation of the lower oceanic crust at fast-spreading mid-ocean ridges remain a topic of debate. Two end-member models on formation of the oceanic crust at fast-spreading mid-ocean ridges mainly differ in the proportion of crystallization which happens in the AMC and in the LVZ.

19 1. Introduction

‘Gabbro glacier’ type models (e.g. Sleep, 1975; Quick and Denlinger, 1993; Phipps Morgan and Chen, 1993b; Henstock et al., 1993; Coogan et al., 2002b; Fig. 1.4.1d) suggest that primitive melt rises from the crust-mantle boundary to the AMC, without significant amounts of crystallization. While some of the melt is fed upward from the AMC to produce dikes and lava, most of it crystallizes in the AMC, from where the crystals subside down- and outwards through a crystal mush zone (the LVZ) and solidify off-axis to form new oceanic crust (Fig. 1.4.1d). Most of the latent heat of crystallization of the plutonic body is removed by hydrothermal circulation from the top of the AMC (Fig. 1.4.1d). This model is consistent with the ridge-parallel, sub-vertical magmatic fabrics and foliations which are observed in gabbroic rocks from Hess Deep and Pito Deep and are interpreted as magmatic flow- lines. Furthermore, ‘ gabbro glacie r’ type models are consistent with the observation of strong crystal alignment from the Oman ophiolite and the general absence of strong crystal plastic deformation in gabbroic rocks from the lower oceanic crust (e.g. Gillis et al., 1993; Perk et al., 2007; Boudier et al., 1996; see also Section 1.3). The other end-member is represented by ‘sheeted sill’ type models (e.g. Kelemen et al., 1997; Korenaga and Kelemen, 1997; MacLeod and Yaouancq, 2000; Garrido et al., 2001; Lissenberg et al., 2004; Fig. 1.4.1e), which suggest that most crystallization happens in situ over the entire depth of the lower oceanic crust in sills and the AMC is simply the uppermost of this series of stacked sills (Fig. 1.4.1e). In this case, deep hydrothermal circulation throughout the lower oceanic crust is required to remove the latent heat of crystallization (e.g. Chen 2001; see Section 1.4.1). This model is consistent with modally graded layering in the lower gabbros in the Oman ophiolite (e.g. Pallister and Hopson, 1981; see also Section 1.3) and a similarity in the composition of these lower layered gabbros and gabbroic sills at the inferred mantle-crust boundary in the Oman ophiolite (Kelemen et al., 1997; Korenaga and Kelemen, 1997). The model is also consistent with geophysical data, indicating a narrow width of the LVZ (Dunn et al., 2000), which requires deep hydrothermal circulation to cool the lower crust and keep the LVZ narrow (Dunn et al., 2000; Dunn and Forsyth, 2007, see also section 1.3).

20 1. Introduction

In fact, both end-member models require some portion of each process. In the ‘ gabbro glacier ’ model, melt in the mush zone lubricates the crystals, allowing them to flow, and crystallizes deeper in the crust. In the ‘ sheeted sill ’ model, more rapid cooling at shallow levels in the crust requires some crystal subsidence to prevent the AMC from solidifying (e.g. Maclennan et al., 2004).

Most important for this study is the fact, that the two different end-member models predict different thermal evolution of the crust, and most significantly, different depths to which hydrothermal fluids circulate in the crust, implying different variation of cooling rate with depth (Fig. 1.4.1d and e). A ‘gabbro glacier’ type model requires most of the latent heat of crystallization to be removed at the top of the AMC, leading to fast cooling rates at in the upper gabbros and a decrease in cooling rate with depth, where cooling would probably largely occur by conduction (Fig. 1.4.1d). In contrast, in a ‘sheeted sill’ type model, the mechanism for heat removal (hydrothermal circulation) is the same over the entire range of the gabbroic crust and therefore, the cooling rate is not expected to change with depth (Fig. 1.4.1e). Consequently, quantification of cooling rates with depth from natural rocks, directly sampled from modern oceanic crust will allow for testing the proposed models.

1.5 The approach of this study - Testing models of lower crustal accretion using diffusion calculations and ‘ geospeedometry ’ on natural rock samples

As outlined in Section 1.4, two end-member models on the formation of the oceanic crust at fast-spreading mid-ocean ridges predict substantial differences in the relation of cooling rates to depth. The following section explains how diffusion modelling (and in particular diffusion modelling of Mg in plagioclase) can be used to determine cooling rates from rock samples. This explanation is necessary to

21 1. Introduction understand the approach of this study, namely testing these models by application of diffusion modelling to natural rock samples of the lower oceanic crust from different depths to determine the vertical distribution of cooling rates.

In equilibrium, for a given pressure and temperature in a closed system, the distribution of chemical elements between minerals is defined, i.e. at some sufficiently high temperature, the concentration of a given component i is distributed in equilibrium between two phases α and β (described by a partition

α / β coefficient Ki ). At constant pressure, the equilibrium concentration of the same component i in the same minerals α and β will be different at different temperatures ( )α / β (i.e. the partition coefficient is a function of temperature K T i , Fig. 1.5.1b). During cooling, exchange reactions that depend on temperature, will modify the concentration of i in the two phases at the interface in accordance with the changed ( )α / β K T i . Kinetic processes, such as diffusion of component i to or from the interface, take place, to re-establish an equilibrium distribution under the new conditions in the entire grain of the mineral phases. Since kinetic processes are (by definition) time-dependent, the kinetic (e.g. diffusive) response of minerals trying to re- establish equilibrium can be used to constrain geological timescales (e.g. Lasaga, 1983, for a review see Chakraborty, 2008; Fig.1.5.1). The connection between diffusive processes and timescales has been investigated primarily using analytical solutions to the diffusion equation at different temperatures. This connection allows for determination of the condition, at which chemical diffusion becomes extremely slow and the concentration of chemical elements in crystals undergoing cooling effectively does not change anymore with time (the concept of ‘closure temperature’ ; Dodson, 1973, 1976 and 1986; Fig. 1.5.1). In parallel, Lasaga (1977 and 1983) developed the idea of extracting cooling rates from diffusion processes and introduced the concept of ‘geospeedometry’ .

At some temperature Tc core , which depends on the cooling rate and the diffusion coefficients of the phases, the concentration of the component far from the

22 1. Introduction interface fails to reach equilibrium (Fig. 1.5.1c and d). At some lower temperature

Tc rim , the distribution of the component in the two phases becomes effectively ‘frozen-in’ (Fig. 1.5.1c and d), and it is this distribution between the core and the rim that contains information about the cooling rate (e.g. Onorato et al., 1981; Dodson, 1986, Ganguly and Tirone, 1999).

23 1. Introduction

(a) Fig. 1.5.1: Schematic illustration of the evolution of diffusive concentration profiles during cooling on a T1 given time( t)-temperature( T)-path. Panel (a) shows a

T2 t-T-plot with an assumed linear decrease of temperature with time, i.e. a constant cooling rate. T3 Panel (b) shows a plot of an partition coefficient α β / (ratio of concentration of element i in phases α T4 K i α / β

temperature T and β) against 1/ T, showing a decreasing K with T5 i decreasing T. Panel (c) shows the evolution of the concentration of element i in mineral α with time and timet decreasing temperature on the given t-T-path in (a), i.e. for a given cooling rate. At temperatures T1 and T2,

T1 T2 T3 T4 T5 an equilibrium distribution of the element i in phase α, α β (b) constrained by the partition coefficient K / at these / i

a b i temperatures, can be attained over the entire crystal of mineral α. At temperature Tc core , diffusion has become too slow to remove element i efficiently from the core and the concentration of element i in the core of crystal α can not change significantly anymore by diffusion and is “frozen”. The concentration of i at the rims of crystal α can however still equilibrate down to the lower temperature Tc rim , because the diffusion distance is shorter. Below temperature Tc rim , diffusion partitioncoefficientK becomes too slow to effectively change the 1/T concentration of i and even the rims cannot attain the equilibrium concentration (dashed line) anymore. The

Tccore Tcrim whole system is frozen, and the concentration of i at the rims is lower than in the core. The figure is shown T T T T4 T 1 2 3 5 for a given cooling rate and a given grain size of the (c) crystal α, but it is noted that Tc core and Tc rim are a function of cooling rate and grain size and will be

a

i different as these parameters are changed. Panel (d) shows the successive evolution of concentration core profiles of element i in a grain of mineral α during cooling. At temperature T1 and T2 the entire grain rim equilibrates and attains the respective equilibrium concentrations (red and pink solid lines). The

concnetration concentration profile attained at temperature T3 equi (orange solid line) is slightly bowed, because the core does not reach the respective equilibrium timet concentration (orange dashed line) whereas the rims still attain the equilibrium concentration. This curvature is even stronger for the concentration profile attained at T4 (green solid line), because the (d) core was already frozen, but the rims continuously exchanged up to lower temperatures and

a

i concentrations. The equilibrium concentration at T4 (green dashed line) is however slightly lower than the developed concentration at the rims at T4, because Tc rim was reached before T4 (as shown in (c)). Therefore, the concentration profile attained at T5 (blue solid line) is the same as the concentration

concnetration profile attained at T4 (green solid line), because diffusion effectively does not change the concentration rimcore rim below Tc rim . distance

24 1. Introduction

The extraction of cooling rates from diffusion modelling may be mathematically visualized as follows: Diffusion is a thermally activated process, which becomes significantly slower (i.e. less efficient in changing compositions) with decreasing temperature and can be described by an Arrhenius equation:  − E  D()T = D exp   (Eq. 1.5.1) 0  RT  where D is the diffusion coefficient at absolute temperature T, D0 represents the diffusion coefficient at infinite temperature, E is the energy barrier (activation energy) for the diffusion process and R is the ideal gas constant. Cooling histories and diffusion processes can be related by defining a temperature-time path, T(t) (Fig. 1.5.1a). Consequently, the diffusion coefficient can be defined as function of time along a cooling path (e.g. Chakraborty, 2008):  −  () =  E  D t D0 exp   (Eq. 1.5.2)  RT ()t 

The diffusion equation (here for diffusion in 1 dimension) ∂C ∂  ∂C  =  D  (Eq. 1.5.3) ∂t ∂x  ∂x  describes how a concentration evolves with time and space. Upon insertion of the time-dependent (and for a defined cooling history therefore also temperature- dependent, Fig. 1.5.1a) diffusion coefficient D(t) , in Eq. 1.5.3, the diffusive evolution of a concentration profile along a defined cooling path is described by ∂C ∂  ∂C  =  D()t  , (Eq. 1.5.4) ∂t ∂x  ∂x  as is shown by an exemplary cooling path in Fig. 1.5.1c and d. The resulting diffusive concentration profile, developed along any assumed cooling path, can be simulated by numerical modelling. Given a measured concentration profile, the cooling history responsible for producing this particular concentration profile can be determined by modelling the diffusive evolution of the

25 1. Introduction profile and iteratively changing the assumed cooling path until the best fit between measured and modelled profile is obtained.

A potentially well suited method for determining cooling rates of the lower oceanic crust is the study of the evolution of Mg-concentration profiles in plagioclase crystals surrounded by clinopyroxene in gabbroic rocks. Natural rock samples from the oceanic crust show higher concentrations of MgO in plagioclase phenocrysts in mid ocean ridge basalts (MORBs) than in the cogenetic, but more slowly cooled, gabbroic rocks of the lower oceanic crust (Fig. 10f in Coogan, 2007). The difference in plagioclase Mg-content most likely occurs due to exchange of Mg between these phases during cooling of the gabbroic rocks. If this assumption is correct, it suggests that the partition coefficient of Mg between plagioclase and clinopyroxene (which is the major adjacent phase to the plagioclase in these rocks) decreases with temperature (Fig. 1.5.1b). Therefore, a concentration gradient is developed during cooling and Mg tends to diffuse out of plagioclase and into clinopyroxene. Dependent on the cooling rate of the rock, the evolution of the resulting concentration profile of Mg in plagioclase will be different. For example, for a slow cooling rate, diffusive exchange of Mg between plagioclase and clinopyroxene will be effective enough to change the concentration of Mg in plagioclase down to lower temperatures (i.e. will have a lower ‘closure temperature’ , see also Fig. 1.5.1c and the respective figure caption) than for faster cooling rates (a detailed discussion on the evolution of diffusion profiles for different cooling rates and additional factors influencing the resulting shape of the profile will be given in Section 3.5). Thus, diffusion modelling of Mg-concentration profiles measured in plagioclase from natural rock samples can be used to understand the cooling history of a rock.

Numerous detailed concentration profiles of different elements (among others Mg) in plagioclase from natural rock samples were measured. The samples come from three different locations along the fast-spreading EPR (Hess Deep, Pito Deep and IODP Hole 1256D) and the individual samples of every sample suite were

26 1. Introduction collected from different depths in the lower oceanic crust. A new ‘ geospeedometer ’ based on the diffusive exchange of Mg between plagioclase and clinopyroxene was developed to obtain cooling rates from these samples. Application of this new tool to the natural sample suites allows for obtaining the vertical distribution of cooling rates in the lower oceanic crust. Additionally, a comparison of the results from the different locations provides information about similarities and differences of the thermal structure along axis of the EPR. These results will be used to gain better understanding of the processes during cooling and crustal accretion at fast- spreading mid-ocean ridges.

1.6 The investigated natural sample suites

As described in Section 1.4, a substantial amount of the existing models for lower crustal accretion of fast-spreading oceanic were derived from observations made in ophiolite complexes. Additional constraints come from remote sensing data (see Section 1.3) as well as thermal modelling (see Section 1.4.1). Complementary, this study provides constraints on the thermal history of the lower oceanic crust from natural samples collected from modern oceanic crust. Natural plutonic samples investigated in this study come from three different sections of the lower oceanic crust formed at the fast-spreading East Pacific Rise (EPR): (i) the Hess Deep Rift in the equatorial Pacific, (ii) the Pito Deep in the southern Pacific, and (iii) drill core samples from IODP Hole 1256D located in the eastern Pacific (Fig. 1.3.4). The natural rock samples from these sample suites were chosen according to the following criteria: samples were supposed to (a) represent gabbroic rocks, (b) contain coexisting plagioclase and clinopyroxene, and (c) to show a low level of hydrothermal alteration. Additionally, samples were chosen according to the attempt to investigate samples over the complete depth sequence exposed along each of the three locations (i.e. in general, samples from greater depth appeared less fresh than samples from shallower depth. Still, samples from

27 1. Introduction greater depth were chosen as well, to complete the depth sequence of the sample suite). Thin sections of the chosen samples were studied under a microscope in polarized light to find the most suitable plagioclase crystals for the approach (see Chapter 3 for details). In the course of this study, several robustness criteria were developed for the determination of cooling rates from diffusion modelling of Mg in plagioclase (see Chapter 3 for details) and in the end, only plagioclase crystals fulfilling these criteria were used to obtain cooling rates. Table A2 (Appendix II) summarizes all investigated samples, including information about the number of plagioclase crystals, for which concentration- profiles were measured, and which of the profiles fulfilled the robustness criteria and therefore were used to obtain cooling rates.

1.6.1 Hess Deep The Hess Deep Rift is an about 25 km long and 8 km wide structural depression (Francheteau et al., 1990) in the eastern equatorial Pacific Ocean (~2°15 N and ~101°30 W; Fig. 1.3.4), where crust formed at the East Pacific Rise (EPR) is exposed due to the propagation of the Cocos-Nazca spreading centre westward (Fig. 1.6.1.1). The western end of the Cocos-Nazca spreading centre is propagating into the eastern side of the Galapagos microplate, rifting young (0.5 to 1.2 Ma) oceanic crust (Lonsdale, 1988), formed at the EPR at half spreading rates of about 65 mm/year. Normal faulting associated with lithospheric extension also produced a highstanding, E-W orientated horst (Intra-Rift Ridge; Fig. 1.6.1.1) ~1000 m above the rift floor.

28 1. Introduction

Fig. 1.6.1.1: Location and schematic tectonic map of the Hess Deep Rift (after Lonsdale, 1988). The red box identifies the study area along the northern escarpment, where a well-exposed crustal section of young (~1 Ma) EPR crust has been extensively mapped; the location of ODP Site 894 is shown as a red circle.

This study mainly focuses on submersible collected samples from the North wall of HDR (red box in Fig. 1.6.1.2; Fig. 1.6.1.2a), which slopes gently down to about 3750 and 4400 m. Two US and one French research cruise have sampled this North wall of the HDR in detail, collecting gabbroic samples along several submersible transects (Hékinian et al., 1993; Karson et al., 2002; Fig. 1.6.1.2). The crest of the horst is formed by volcanic rocks, grading down-slope (to the south) into the sheeted dike complex, followed by gabbroic rocks (Fig. 1.6.1.2). The depth of the sheeted dike/gabbro boundary slightly deepens from ~2800 m below sea level (mbsl) in the east to 3000 mbsl about 1 km further in the west (Fig. 1.6.1.2). Since the sheeted dike/gabbro boundary was mapped on four of the dives (Fig. 1.6.1.2), and the depth below sea floor is known for each sample, it is possible to reconstruct the depth below the sheeted dike/gabbro boundary for each sample (Table 1.6.1.1). Additional sampling of gabbroic rocks has been performed by drilling ~10 km to the south during ODP Leg 147 Site 894G (Gillis et al., 1993; red circle in Fig. 1.6.1.1) at the crest of the Intra-Rift Ridge. Since the sheeted dike/gabbro boundary is not exposed here, only the relative depth of the gabbroic samples is

29 1. Introduction known (Table 1.6.1.2), but the absolute depth in the lower crust remains undetermined.

Fig. 1.6.1.2: (a) Simplified geological map of the area around the north wall of Hess Deep showing the seafloor topography and the lithology, mapped along dive tracks. The inferred dike/gabbro boundary is shown as a dashed blue line. (b) shows a blow-up of the area in the yellow box in (a) for better illustration of sample location (yellow stars).

30 1. Introduction

For this study 31 samples from 6 different dives of the Alvin dive programs (1990, 1999) along the North wall of the HDR were investigated (Table 1.6.1.1). Additionally, the Hess Deep sample suite was completed by 15 samples from the ODP Leg 147 Site 894G (Table 1.6.1.2).

Table 1.6.1.1: List of samples from the North wall of the HDR investigated for this study (sorted by depth below dike/gabbro boundary). mbsl = meters below sea level, mbsd = meters below sheeted dike/gabbro boundary

Depth Depth Depth Sample below sea level of d/g boundary below d/g boundary [mbsl] [mbsl] [mbsd] 2212-1358 3000 3000 0 2212-1400 3000 3000 0 2212-1338 3017 3000 17 3369-1418 3000 2950 50 3369-1422 3006 2950 56 3369-1431 3006 2950 56 3369-1355 3032 2950 82 3369-1355b 3032 2950 82 3369-1355c 3032 2950 82 3369-1349 3040 2950 90 3369-1349b 3040 2950 90 3369-1321 3076 2950 126 3374-1031 2997 2870 127 3374-1031b 2997 2870 127 3374-1012 3034 2900 134 3369-1250 3094 2950 144 3369-1250b 3094 2950 144 3369-1329 3100 2950 150 3369-1156 3148 2950 198 3369-1221 3158 2950 208 3369-1221b 3158 2950 208 3369-1110 3161 2950 211 3369-1129 3169 2950 219 3369-1042 3232 2950 282 3369-1050 3232 2950 282 3370-1418 3096 2800 296 3370-1408 3106 2800 306 2213-1110 3250 2870 380 3370-1328 3242 2800 442 2218-1111 3470 3000 470 2218-1132 3520 3000 520

31 1. Introduction

Table 1.6.1.2: List of samples from ODP Leg 147 Site 894G investigated for this study (sorted by depth below sea floor). mbsf = meters below sea floor

Depth Sample below sea floor [mbsf] 02R 02 40-45 29 05R 01 22-27 54 06R 02 56-62 58 07R 01 58-62 66 08R 01 28-32 70 08R 02 105-110 71 09R 04 75-80 78 12R 03 62-67 96 12R 04 40-45 97 12R 05 83-87 99 12R 05 115-120 100 13R 02 90-95 103 17R 02 6-10 127 18R 02 5-10 129 20R 02 35-40 147

1.6.2 Pito Deep At the Pito Deep depression lower crustal rocks are exposed due to a propagating rift tip at the North-eastern end of the Easter Microplate in the SE Pacific (Fig. 1.6.2.1a). The walls of the Pito Deep Rift (Fig. 1.6.2.1b) have >4000 m of relief and expose sections of 3 Ma old crust created at the East Pacific Rise (EPR) at a “superfast” spreading rate of >140 mm/year (e.g. Francheteau et al., 1988). These natural cross sections through the upper half of the oceanic crust expose continuous sequences consisting of basaltic lavas, sheeted dikes, and gabbroic rocks (e.g. Constantin et al., 1995; Constantin et al., 1996; Hekinian et al., 1996; Karson et al., 2005; Perk at al., 2007; Fig. 1.6.2.1c-e). Gabbroic rocks from the Pito Deep area were collected during several cruises along Pito Deep area A and B (the Sonne 65 cruise, Stoffers and Hekinian, 1989; the Pito Nautile cruise, Hekinian et al., 1996; the JasonII and Alvin dive programs during cruise AT11-33 of the R/V Atlantis , Perk et al., 2007; Fig. 1.6.2.1). The sheeted dike/gabbro boundary was mapped on several dives (Fig. 1.6.2.1), which allows to reconstruct the depth below the sheeted dike/gabbro boundary for each sample (Table 1.6.2.1).

32 1. Introduction (a) (b)

(c) (d)

Fig. 1.6.2.1: Geographic location (a), bathymetry (b) and geologic map of Pito Deep areas A (c) and B (d). Alvin dives and Jason tracks from cruise AT11-33 of the R/V Atlantis are highlighted, as well as Nautile dives survey. Geology in between transects is inferred from side-scan sonar images as well as the dive and transects observed geology. Alvin dives labeled with dive number, and Jason transects labeled with T and transect number for each area. Figure (b) is taken from unpublished Cruise Report; Expedition RT11-23 of the R/V Atlantis and Figures (c) and (d) are taken from Chutas, 2007 (M.Sc. thesis).

33 1. Introduction

This study focuses on a sample suite of 23 gabboic rocks, which were collected on Transects T3 and T4 of the JasonII dive programs during cruise AT11- 33 of the R/V Atlantis in 2005 (Fig. 1.6.2.1d; Fig. 1.6.2.2; Table 1.6.2.1).

Fig. 1.6.2.2: (a) Simplified geological map of the Pito Deep Area B showing the seafloor topography and the lithology, mapped along dive tracks of the Alvin dives and Jason tracks from cruise AT11-33 of the R/V Atlantis . Alvin dives labelled with dive number, and Jason transects labelled with T and transect number for each area. The inferred dike/gabbro boundary is shown as a dashed blue line. (b) shows a blow-up of the area in the yellow box in (a) for better illustration of sample location (yellow stars).

34 1. Introduction

Table 1.6.2.1: List of samples from Pito Deep investigated for this study (sorted by depth below dike/gabbro boundary). mbsl = meters below sea level, mbsd = meters below sheeted dike/gabbro boundary

Sample Transect Depth Depth Depth below sea level of d/g boundary below d/g boundary [mbsl] [mbsl] [mbsd] 022205-0259 Jason T4 3938 3897 41 022205-0248 Jason T4 3942 3897 45 022205-0230 Jason T4 3969 3897 72 022005-1522 Jason T3 3468 3291 177 022005-1209 Jason T3 3539 3291 248 022005-1938 Jason T3 3544 3291 253 022005-1052 Jason T3 3626 3291 335 022005-0910 Jason T3 3677 3291 386 022005-0830 Jason T3 3708 3291 417 022005-0800 Jason T3 3759 3291 468 022005-0534 Jason T3 3860 3291 569 022005-0506 Jason T3 3953 3291 662 022005-0454 Jason T3 3958 3291 667 022005-0355 Jason T3 4018 3291 727 022005-0310 Jason T3 4031 3291 740 022005-0245 Jason T3 4050 3291 759 022005-0241 Jason T3 4050 3291 759 022005-0214 Jason T3 4057 3291 766 022005-0155 Jason T3 4071 3291 780 022005-0056 Jason T3 4127 3291 836 022005-0040 Jason T3 4154 3291 863 022005-0024 Jason T3 4162 3291 871 021905-2348 Jason T3 4167 3291 876

1.6.3 IODP Site 1256D IODP Site 1256D is located in the eastern Pacific (Fig. 1.3.4; Fig. 1.6.3.1a), where a bore hole was drilled into ~15 Ma old intact oceanic crust of the Cocos Plate that formed at the superfast spreading EPR (full spreading rate ~220 mm/year). The drilled core recovered ~1250 m of oceanic crust and provides a continuous section from extrusive lavas, through sheeted dikes and into the top of the plutonic section (Wilson, 1996; Wilson et al., 2006; Koepke et al., 2008; France et al., 2009; Sano et al., 2011; Fig. 1.6.3.1b). Gabbroic rocks were recovered from two separated bodies at the top of the plutonic section (52 m and 24 m thick, separated by a 24 m thick screen of granoblastic dikes; Wilson et al., 2006; Fig. 1.6.3.1b). The sheeted dike/gabbro boundary was drilled, and therefore the depth below the sheeted dike complex of the gabbroic samples is known (Table 1.6.3.1).

35 1. Introduction

(a) (b)

Fig. 1.6.3.1: (a) Location of IODP Site 1256D and (b) lithostratigraphic column of the basement drilled to date at Site 1256 showing major lithologies and structural features (after Wilson et al., 2006).

For this study, 7 samples from the upper gabbroic body drilled during Expedition 312 were investigated (Table 1.6.3.1), because these gabbros showed the smallest degree of hydrothermal alteration.

Table 1.6.3.1: List of samples from IODP Site 1256D, Expedition 312, investigated for this study (sorted by depth below dike/gabbro boundary). mbsl = meters below sea level, mbsd = meters below sheeted dike/gabbro boundary

Sample Depth Depth Depth below sea floor of d/g boundary below d/g boundary [mbsf] [mbsf] [mbsd] 216R 01 15-20 1418.1 1406 12.1 216R 01 47-57 1418.4 1406 12.4 216R 01 60-64 1418.5 1406 12.5 216R 01 130-134 1419.2 1406 13.2 218R 01 37-40 1425.7 1406 19.7 218R 01 44-47 1425.8 1406 19.8 219R 01 19-23 1430.2 1406 24.2

36 1. Introduction

1.7 References

Baker, E. T., 2007. Hydrothermal cooling of mid-ocean ridges axes: do measured and modeled heat fluxes agree? Earth and Planetary Science Letters , 263 , 140- 150. Benn, K., Nicolas, A. & Reuber, I., 1988. Mantle-crust transition zone and origin of wehrlitic magmas - evidence from the Oman Ophiolite. Tectonophysics , 151 , 75-85. Boudier, F. & Nicolas, A., 2011. Axial melt lenses at oceanic ridges - A case study in the Oman ophiolite. Earth and Planetary Science Letters , 304 , 313-325. Boudier, F., Nicolas, A. & Ildefonse, B., 1996. Magma chambers in the Oman ophiolite: fed from the top and the bottom. Earth and Planetary Science Letters , 144 , 239-250. Browning, P., 1984. Cryptic variation within the Cumulate Sequence of the Oman ophiolite: magma chamber depth and petrological implications. In: Ophiolites and Oceanic Lithosphere (eds Gass, I. G., Lippard, S. J. & Shelton, A. W.), pp. 71- 82, Special Publication of the Geological Society of London (Blackwell Scientific Publications), Oxford. Canales, J. P., Nedimovic, M. R., Kent, G. M., Carbotte, S. M. & Detrick, R. S., 2009. Seismic reflection images of a near-axis melt sill within the lower crust at the Juan de Fuca ridge. Nature , 460 , 89-93. Cann, J. R., 1974. A model for oceanic crustal structure developed. Geophysical Journal of the Royal Astronomical Society , 39 , 169-187. Casey, J. F. & Karson, J. A., 1981. Magma chamber profiles from the Bay of Islands ophiolite complex. Nature , 292 , 295-301. Chakraborty, S., 2008. Diffusion in solid silicates: A tool to track timescales of processes comes of age. In: Annual Review of Earth and Planetary Sciences , pp. 153-190.

37 1. Introduction

Chapman, D. S. & Pollack, H. N., 1975. Global heat flow - new look. Earth and Planetary Science Letters , 28 , 23-32. Chen, Y. J., 2001. Thermal effects of gabbros accretion from a deeper second melt lens at the fast spreading East Pacific Rise. Journal of Geophysical Research , 106 , 8581-8588. Cherkaoui, A. S. M., Wilcock, W. S. D., Dunn, R. A. & Toomey, D. R., 2003. A numerical model of hydrothermal cooling and crustal accretion at a fast-spreading mid- ocean ridge. Geochemistry Geophysics Geosystems , 4, DOI:10.1029/2001GC000215. Christensen, N. I. & Salisbury, M. H., 1975. Structure and constitution of the lower oceanic crust. Reviews of Geophysics , 13 , 57-86. Chutas, L. A. M., 2007. Structures in upper oceanic crust: Persepectives from Pito Deep and iceland, M.Sc. thesis , Duke University, Durham, N.C. Coleman, R. G., 1971. Plate tectonic emplacement of upper mantle peridotites along continental edges. Journal of Geophysical Research , 76 , 1212-1222. Coleman, R. G., 1977. Ophiolites: Ancient oceanic lithosphere? Springer-Verlag, New York, 229 pp. Coleman, R. G. & Hopson, C. A., 1981. Introduction to the Oman Ophiolite Special Issue. Journal of Geophysical Research , 86 , 2495-2496. Constantin, M., Hekinian, R., Ackermand, D. & Stoffers, P., 1995. Mafic and ultramafic intrusions in upper mantle peridotties from fast spreading centers of the Easter Microplate (South East Pacific). In: Mantle and Lower Crustal Exsposures in Ocean Ridges and in Ophiolites (eds Vissers, R. L. M. & Nicolas, A.), pp. 71-120, Kluwer Academic, Dortrecht. Constantin, M., Hekinian, R., Bideau, D. & Hébert, R., 1996. Construction of the oceanic lithosphere by magmatic intrusions: Petrological evidence from plutonic rocks formed along the fast-spreading East Pacific Rise. Geology , 24 , 731-734. Coogan, L. A., 2007. The lower oceanic crust. In: Treatise on Geochemistry: The Crust (Vol.3) (eds Turekian, K. & Holland, H. D.), pp. 1-45, Elsevier, New York.

38 1. Introduction

Coogan, L. A., Gillis, K. M., MacLeod, C. J., Thompson, G. & Hekinian, R., 2002a. Petrology and geochemistry of the lower ocean crust formed at the East Pacific Rise and exposed at Hess Deep: a synthesis and new results. Geochemistry Geophysics Geosystems, 3, Special issue: The Oman ophiolite and ocean ridge processes, DOI 10.1029/2001GC000230. Coogan, L. A., Jenkin, G. R. T. & Wilson, R. N., 2002b. Constraining the cooling rate of the lower oceanic crust: a new approach applied to the Oman ophiolite. Earth and Planetary Science Letters , 199 , 127-146. Crawford, W. C. & Webb, S. C., 2002. Variations in the distribution of magma in the lower crust and at the Moho beneath the East Pacific Rise at 9 degrees-10 degrees N. Earth and Planetary Science Letters , 203 , 117-130. Crisp, J. A., 1984. Rates of magma emplacement and volcanic output. Journal of Volcanology and Geothermal Research , 20 , 177-211. Davies, J. H. & Davies, D. R., 2010. Earth's surface heat flux. Solid Earth Discussions , 1, 5-45. DeMets, C., Gordon, R. G. & Argus, D. F., 2010. Geologically current plate motions. Geophysical Journal International , 181 , 1-80. Detrick, R. S., Buhl, P., Vera, E., Mutter, J., Orcutt, J., Madsen, J. & Brocher, T., 1987. Multi-channel seismic imaging of a crustal magma chamber along the East Pacific Rise. Nature , 326 , 35-41. Dewey, J. F. & Bird, J. M., 1971. Origin and emplacement of ophiolite suite - Appalachian ophiolites in Newfoundland. Journal of Geophysical Research , 76 , 3179-3206. Dilek, Y., Moores E., M. & Furnes, H., 1998. Structure of modern oceanic crust and ophiolites and implications for faulting and magmatism at oceanic spreading centers. In: Faulting and magmatism at mid-ocean ridges, Geophysical Monographs 106 (eds Buck, R. W., Delaney, P. T., Karson, J. A. & Lagabrielle, Y.), pp. 177-218, American Geophysical Union, Washington. Dodson, M. H., 1973. Closure temperature in cooling geochronological and petrological systems. Contributions to Mineralogy and Petrology , 40 , 259-274.

39 1. Introduction

Dodson, M. H., 1976. Kinetic processes and thermal history of slowly cooled solids. Nature , 259 , 551-553. Dodson, M. H., 1986. Closure profiles in cooling systems. Material Science Forum , 7, 145-154. Dunn, R. A. & Forsyth, D. W., 2007. Crust and Lithospheric Structure – Seismic Structure of Mid-Ocean Ridges. In: Treatise on Geophysics (eds Dziewonski, A. & Romanowicz, B.), pp. 6054, Elsevier Science Ltd. Dunn, R. A. & Toomey, D. R., 1997. Seismological evidence for three-dimensional melt beneath the East Pacific Rise. Nature , 388 , 259-261. Dunn, R. A., Toomey, D. R. & Solomon, S. C., 2000. Three-dimensional seismic structure and physical properites of the crust and shallow mantle beneath the East Pacific Rise at 9°30'N. Journal of Geophysical Research , 105 , 23,537- 23,555. France, L., Ildefonse, B. & Koepke, J., 2009. Interactions between magma and hydrothermal system in Oman ophiolite and in IODP Hole 1256D: Fossilization of a dynamic melt lens at fast spreading ridges. Geochemistry Geophysics Geosystems , 10 , DOI:10.1029/2009GC002652. Francheteau, J., Armijo, R., Cheminee, J. L., Hekinian, R., Lonsdale, P. & Blum, N., 1990. 1 Ma East Pacific Rise oceanic crust and uppermost mantle exposed by rifting in Hess Deep (equatorial Pacific Ocean). Earth and Planetary Science Letters, 101 , 281-295. Francheteau, J., Patriat, P., Segoufin, J., Armijo, R., Doucoure, M., Yelleschaouche, A., Zukin, J., Calmant, S., Naar, D. F. & Searle, R. C., 1988. Pito and Orongo Fracture-Zones - the Northern and Southern Boundaries of the Easter Microplate (Southeast Pacific). Earth and Planetary Science Letters , 89 , 363- 374. Ganguly, J. & Tirone, M., 1999. Diffusion closure temperature and age of a mineral with arbitrary extent of diffusion: theoretical formulation and application. Earth and Planetary Science Letters , 170 , 131-140. Garrido, C. J., Kelemen, P. B. & Hirth, G., 2001. Variation of cooling rate with depth in the lower crust formed at an oceanic spreading ridge: plagioclase crystal size

40 1. Introduction

distributions in gabbros from the Oman ophiolite. Geochemistry Geophysics Geosystems , 2, DOI:10.1029/2000GC000136. Gillis, K. M., 2008. The roof of an axial magma chamber: a hornfelsic heat-exchanger. Geology , 36 , 299-302. Gillis, K. M., Coogan, L. A. & Chaussidon, M., 2003. Volatile behavior in the roof of an axial magma chamber from the East Pacific Rise. Earth and Planetary Science Letters , 213 , 447-462. Gillis, K. M., Mével, C. & Allan, J., 1993. Proceedings of the Ocean Drilling Program, Inititial Reports, 147, pp. 366, Ocean Drilling Program, College Station, Texas. Gillis, K. M. & Roberts, M. D., 1999. Cracking at the magma-hydrothermal transition: evidence from the Troodos ophiolite, Cyprus. Earth and Planetary Science Letters , 169 , 227-244. Greenbaum, D, 1972. Magmatic Processes at ocean ridges - Evidence from Troodos massif, Cyprus. Nature-Physical Science , 238 , 18-21. Hawkins, J. W., Bloomer, S. H., Evans, C. A. & Melchior, J. T., 1984. Evolution of intra- oceanic arc-trench systems. Tectonophysics , 102 , 175-205. Heft, K. L., Gillis, K. M., Pollack, H. N., Karson, J. A. & Klein, E. M., 2008. Role of upwelling hydrothermal fluids in the development of alteration patterns at fast spreading ridges: Evidence from the sheeted dike complex at Pito Deep. Geochemistry Geophysics Geosystems , 9, DOI:10.1029/2007GC001926. Hekinian, R., Bideau, D., Francheteau, J., Cheminee, J. L., Armijo, R., Lonsdale, P. & Blum, N., 1993. Petrology of the East Pacific Rise Crust and Upper Mantle Exposed in Hess Deep (East Equatorial Pacific). Journal of Geophysical Research , 98 , 8069-8094. Hekinian, R., Francheteau, J., Armijo, R., Cogne, J. P., Constantin, M., Girardeau, J., Hey, R., Naar, D. F. & Searle, R., 1996. Petrology of the Easter microplate region in the South Pacific. Journal of Volcanology and Geothermal Research , 72 , 259- 289. Henstock, T. J., Woods, A. W. & White, R. S., 1993. The Accretion of Oceanic Crust by Episodic Sill Intrusion. Journal of Geophysical Research , 98 , 4143-4161.

41 1. Introduction

Hey, R. N., Johnson, P. D., Martinez, F., Korenaga, J., Somers, M. L., Huggett, Q. J., Lebas, T. P., Rusby, R. I. & Naar, D. F., 1995. Plate Boundary Reorganization at a Large-Offset, Rapidly Propagating Rift. Nature , 378 , 167-170. Hooft, E. E. & Detrick, R. S., 1993. The role of density in the accumulation of basaltic melts at mid ocean ridges. Geophysical Research Letters , 20 (6), 423-426. Hooft, E. E. E., Detrick, R. S. & Kent, G. M., 1997. Seismic structure and indicators of magma budget along the Southern east Pacific Rise. Journal of Geophysical Research , 102 , 27,319-37,340. Juteau, T., Beurrier, M., Dahl, R. & Nehlig, P., 1988. Segmentation at a fossil spreading axis - The plutonic sequence of the Wadi Hamymiliyah Area (Haylayn Blocks, Sumail nappe, Oman). Tectonophysics , 151 , 167-197. Karson, J. A., 1998. Internal structure of oceanic lithosphere: A perspective from tectonic windows. In: Faulting and magmatism at mid-ocean ridges , Geophysical Monographs 106 (eds Buck, R. W., Delaney, P. T., Karson, J. A. & Lagabrielle, Y.), pp. 177-218, American Geophysical Union, Washington. Karson, J. A., 2005. Internal Structure of the Upper Oceanic Crust Generated at Fast to Intermediate Rates: The view from tectonic windows in the Pacific. In: EOS Trans AGU 86(52), Fall Meet. Suppl , pp. T23F-03. Karson, J. A., Hurst, S. D. & Lonsdale, P., 1992. Tectonic rotations of dikes in fast- spread oceanic crust exposed near Hess Deep. Geology , 20 , 685-688. Karson, J. A., Klein, E. M., Hurst, S. D., Lee, C., Rivizzigno, P., Curewitz, D., Morris, A. R. & Party, H. D. S., 2002. Structure of uppermost fast-spread oceanic crust exposed at the Hess Deep Rift: Implications for subaxial processes at the East Pacific Rise. Geochemistry Geophysics Geosystems , 3, DOI:10.1029/2001GC000155. Kelemen, P. B., Koga, K. & Shimizu, N., 1997. Geochemistry of gabbro sills in the crust-mantle transition zone of the Oman ophiolite: implications for the origin of the oceanic lower crust. Earth and Planetary Science Letters , 146 , 475-488. Kent, G. M., Harding, A. J. & Orcutt, J. A., 1990. Evidence for a smaller magma chamber beneath the East Pacific Rise at 9°30'N. Nature , 344, 650-653.

42 1. Introduction

Koepke, J., Christie, D. M., Dziony, W., Holtz, F., Lattard, D., Maclennan, J., Park, S., Scheibner, B., Yamasaki, T. & Yamazaki, S., 2008. Petrography of the dike- gabbro transition at IODP Site 1256 (equatorial Pacific): The evolution of the granoblastic dikes. Geochemistry Geophysics Geosystems , 9, DOI:10.1029/2008GC001939. Korenaga, J. & Kelemen, P. B., 1997. Origin of gabbro sills in the Moho transition zone of the Oman ophiolite: Implications for magma transport in the oceanic crust. Journal of Geophysical Research , 102 , 27729-27749. Lasaga, A. C., 1983. Geospeedometry: an extension of geothermometry. In: Kinetics and equilibrium in mineral reactions (ed Saxena, S. K.), pp. 82-114, Springer- Verlag, New York. Lasaga, A. C., Richardson, S. M. & Holland, H. D., 1977. The mathematics of cation diffusion and exchange between silicate materials during retrograde metamorphism. In: Energetics of Geological processes (eds Saxena, S. K. & Bhattacharji, S.), pp. 353-388, Springer-Verlag, New York. Lissenberg, C. J., Bedard, J. H. & van Staal, C. R., 2004. The structure and geochemistry of the gabbro zone of the Annieopsquotch ophiolite, Newfoundland: implications for lower crustal accretion at spreading ridges. Earth and Planetary Science Letters , 229 , 105-123. Lizarralde, D., Gaherty, J. B., Collins, J. A., Hirth, G. & Kim, S. D., 2004. Spreading-rate dependence of melt extraction at mid-ocean ridges from mantle seismic refraction data. Nature , 432 , 744-747. Lonsdale, P., 1988. Structural pattern of the Galapagos microplate and evolution of the Galapagos Triple Junctions. Journal of Geophysical Research , 93 , 13551- 13574. Macdonald, K. C., 1998. Linkages between faulting, volcanism, hydrothermal activity and segmentation on fast spreading centers. In: Faulting and Magmatism at Mid-Ocean Ridges , Geophysical Monographs 106 , (eds Buck, W. R., Delaney, P. T., Karson, J. A. & Lagabrielle, Y.), pp. 27-58, American Geophysical Union, Washington.

43 1. Introduction

Maclennan, J., Hulme, T. & Singh, S. C., 2004. Thermal models of oceanic crustal accretion: linking geophysical, geological and petrological observations. Geochemistry Geophysics Geosystems , 5, DOI:10.1029/2003GC000605. Maclennan, J., Hulme, T. & Singh, S. C., 2005. Cooling of the lower oceanic crust. Geology , 33 , 357-360. MacLeod, C. J., Boudier, F., Yaouancq, G. & Richter, C., 1996. Gabbro Fabrics from Site 894, Hess Deep: Implications for magma Chamber processes at the East Pacific Rise. In: Proceedings of the Ocean Drilling Program, Scientific Results, 147 (eds Mevel, C., Gillis, K. M., Allan, J. F. & Meyer, P. S.), pp. 317-328, Ocean Drilling Program, College station, Texas. MacLeod, C. J. & Yaouancq, G., 2000. A fossil melt lens in the Oman ophiolite: Implications for magma chamber processes at fast spreading ridges. Earth and Planetary Science Letters , 176 , 357-373. McKenzie, D., 1984. The generation and compaction of partially molten rock. Journal of Petrology , 25 , 713-765. McKenzie, D., 1985. The extraction of magma from the crust and mantle. Earth and Planetary Science Letters , 74 , 81-91. Michael, P. J. & Schilling, J.-G., 1989. Chlorine in mid-ocean ridge magmas: Evidence for assimilation of seawater-influenced components. Geochimica et Cosmochimica Acta , 53 , 3131-3143. Moores, E. M. & Vine, F. J., 1971. The Troodos Massif, Cyprus and other ophiolites as oceanic crust: evaluation and implications. Philosophical Transactions of the Royal Society of London, series A , 268 , 443-466. Morton, A. C. & Sleep, N. H., 1985. A mid-ocean ridge Thermal Model: Constraints on the volume of axial hydrothermal heat flux. Journal of Geophysical Research , 90 , 11345-11353. Naar, D. F., Hekinian, R., Segonzac, M., Francheteau, J. & Pito Dive Team, 2004. Vigorous venting and biology at Pito Seamount, easter microplate. In: Mid- Ocean Ridges: Hydrothermal Interactions between the Lithosphere and Oceans (eds German, C. R., Lin, J. & Parson, L. M.) Geophysical Monograph Series , pp. 305-318, American Geophysical Union.

44 1. Introduction

Natland, J. H. & Dick, H. J. B., 1996. Melt migration through high-level gabbroic cumulates of the east pacific rise at the Hess Deep: The origin of magma lenses and the deep crustal structure of fast-spreading ridges. In: Proceedings of the Ocean Drilling Program, Scientific Results, 147 (eds Mevel, C., Gillis, K. M., Allan, J. F. & Meyer, P. S.), pp. 21-58, Ocean Drilling Program, College Station, Texas. Nedimovic, M. R., Carbotte, S. M., Harding, A. J., Detrick, R. S., Canales, J. P., Diebold, J. B., Kent, G. M., Tischer, M. & Babcock, J. M., 2005. Frozen magma lenses below the oceanic crust. Nature , 436 , 1149-1152. Nicolas, A., 1989. Structure of Ophiolites and Dynamics of Oceanic Lithosphere. Kluwer academic publishers , The Netherlands, 367 pp. Nicolas, A., Boudier, E., Ildefonse, B. & Ball, E., 2000. Accretion of Oman and United Arab Emirates ophiolite - Discussion of a new structural map. Marine Geophysical Research , 21 , 147-179. Nicolas, A., Boudier, F. & Ceuleneer, G., 1988a. Mantle flow patterns and magma chambers at ocean ridges - evidence from the Oman ophiolite. Marine Geophysical Researches , 9, 293-310. Nicolas, A., Boudier, F., Koepke, J., France, L., Ildefonse, B. & Mevel, C., 2008. Root zone of the sheeted dike complex in the Oman ophiolite. Geochemistry Geophysics Geosystems , 9, DOI:10.1029/2007GC001918. Nicolas, A., Reuber, I. & Benn, K., 1988b. A new magma chamber model based on structural studies in the Oman Ophiolite. Tectonophysics , 151 , 87-105. Onorato, P. I. K., Hopper, R. W., Yinnon, H., Uhlmann, D. R., Taylor, L. A., Garrison, J. R. & Hunter, R., 1981. Solute partitioning under continuous cooling conditions as a cooling rate indicator. Journal of Geophysical Research , 86 , 9511-9518. Pallister, J. S. & Hopson, C. A., 1981. Samail Ophiolite Plutonic suite - Field relations, phase variation, cryptic variation and layering, and a model of a spreading ridge magma chamber. Journal of Geophysical Research , 86 , 2593-2644. Pearce, J. A., Lippard, S. J. & Roberts, S., 1984. Characteristics and tectonic significance of supra-subduction zone ophiolites. In: Marginal Basin Geology

45 1. Introduction

(eds Kokelaar, P. B & Howells, M. F.) pp. 77-94, Geological Society of London, Special Publications. Pedersen, R. B., Malpas, J. & Falloon, T., 1996. Petrology and geochemistry of gabbroic and related rocks from Site 894, Hess Deep. In: Proceedings of the Ocean Drilling Program, Scientific Results, 147 (eds Mevel, C., Gillis, K. M., Allan, J. F., Meyer, P. S. & al ., e. ), pp. 3-19, College station, Texas. Perk, N., Coogan, L. A., Karson, J. A., Klein, E. M. & Hanna, H., 2007. Primitive cumulates from the upper crust formed at the East Pacific Rise. Contributions to Mineral Petrology , 154 , 575-590. Phipps Morgan, J., 1987. Melt Migration beneath Mid-ocean spreading centers. Geophysical Research Letters , 14 , 1238-1241. Phipps Morgan, J. & Chen, Y. J., 1993a. Dependence of ridge-axis morphology on magma supply and spreading rate. Nature , 364 , 706-708. Phipps Morgan, J. & Chen, Y. J., 1993b. The Genesis of oceanic crust - magma injection, hydrothermal cooling, and crustal flow. Journal of Geophysical Research, 98 , 6283-6297. Purdy, G. M., Kong, L. S. L., Christeson, G. L. & Solomon, S. C., 1992. Relationship between spreading rate and the sesimic structure of mid-ocean ridges. Nature , 355 , 815-817. Quick, J. E. & Denlinger, R. P., 1993. Ductile deformation and the origin of layered gabbro in ophiolites. Journal of Geophysical Research , 98 , 14015-14027. Raitt, R. W., 1963. The crustal rocks. In: The Sea (ed Hill, M. N.), pp. 85-102, Wiley- Interscience, New York. Reuber, I., 1990. Diapiric magam intrusions in the plutonic sequence of the Oman ophiolite traced by the geometry and flow patterns of the cumulates. In: Symposium on Diapirism with special reference to Iran , pp. 315-338, Teheran. Richter, C., Kelso, P. R. & MacLeod, C. J., 1996. Magnetic fabrics and sources of magnetic susceptibility in lower crustal and upper mantle rocks from Hess Deep. In: Proceedings of the Ocean Drilling Program, Scientific Results, 147 (eds Mével, C., Gillis, K. M., Allan, J. & Meyer, P.), pp. 393-404, Ocean Drilling Program, College Station, Texas.

46 1. Introduction

Sano, T., Sakuyama, T., Ingle, S., Rodriguez, S. & Yamasaki, T., 2011. Petrological relationships among lavas, dikes, and gabbros from Integrated Ocean Drilling Program Hole 1256D: Insight into the magma plumbing system beneath the East Pacific Rise. Geochemistry Geophysics Geosystems , 12 , DOI:10.1029/2011GC003548. Singh, S. C., Kent, G. M., Collier, J. S., Harding, A. J. & Orcutt, J. A., 1998. Melt to mush variations in crustal magma chamber properties along the ridge crest at the southern East Pacific Rise. Nature , 394 , 874-878. Sinton, J. M. & Detrick, R. S., 1992. Mid-Ocean Ridge Magma Chambers. Journal of Geophysical Research , 97 , 197-216. Sleep, N. H., 1975. Formation of oceanic crust: some thermal constraints. Journal of Geophysical Research , 80 , 4037-4042. Smewing, J. D., 1981. Mixing characteristics and compositional differences in mantle-derived melts beneath spreading axes: evidence from cyclically layered rocks in the ophiolite of north Oman. Journal of Geophysical Research , 86 , 2645-2659. Solomon, S. C. & Toomey, D. R., 1992. The structure of midocean ridges. Annual Review of Earth and Planetary Sciences , 20 , 329-364. Spudich, P. & Orcutt, J., 1980. A new look at the seismic velocity structure of the oceanic crust. Reviews of Geophysics , 18 , 627-645. Stein, C. A. & Stein, S., 1994. Constraints on hydrothermal heat flux through the oceanic lithosphere from global heat flow. Journal of Geophysical Research , 99 , 3081-3095. Stoffers, P. & Hekinian, R., 1989. Cruise Report SONNE 65 - Midplate II, Hotspot volcanism in the central Southpacific. Berichte - Reports , 40 , 126. Tivey, M. K., 2007. Generation of seafloor hydrothermal vent fluids and associated mineral deposits. Oceanography , 20 , 50-65. Turcotte, D. L. & Phipps Morgan, J., 1992. The physics of magma migration and mantle flow beneath a mid-ocean ridge. In: Mantle Flow and Melt Generation at Mid-Ocean Ridges (eds Phipps Morgan, J., Blackman, D. K. & Sinton, J. M.) Geophysical Monographs , pp. 155-182, American Geophysical Union.

47 1. Introduction

VanTongeren, J. A., Kelemen, P. B. & Hanghoj, K., 2008. Cooling rates in the lower crust of the Oman ophiolite: Ca in olivine, revisited. Earth and Planetary Science Letters , 267 , 69-82. Wilson, D. S., 1996. Fastest known spreading on the Miocene Cocos-Pacific plate boundary. Geophysical Research Letters , 23 , 3003-3006. Wilson, D. S. & others, 2006. Drilling into gabbro in intact ocean crust. Science , 312 , 1016-1020.

48 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Chapter 2

2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Plagioclase and Clinopyroxene

Abstract

The temperature-sensitive exchange of Mg between plagioclase (Pl) and clinopyroxene (Cpx) was experimentally determined, accounting for different anorthite-contents in plagioclase ( XAn ) and various silica activities ( a ) in the SiO 2 system. The experimental data allow a new geothermometer to be calibrated that provides wide application for terrestrial and extraterrestrial rocks with coexisting plagioclase and clinopyroxene. The experiments were carried out in a temperature range of 1100 to 1200°C, using plagioclase single crystals of different composition

(XAn =0.5 to 0.8), surrounded by different Cpx-bearing matrix powders to produce different silica activities between 0.55 and 1.0. The experimental design also allows the determination of the diffusivity of Mg in plagioclase under these conditions. Mg- concentration profiles in plagioclase, resulting from diffusive exchange of Mg with clinopyroxene during the experiment, were analysed using an electron microprobe.

49 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Pl / Cpx The partition coefficient of Mg between plagioclase and clinopyroxene ( K Mg ) as

Pl well as the diffusion coefficient of Mg in plagioclase ( DMg ) were extracted from non-

Pl / Cpx Pl linear least square fitting of these profiles. Plots of ln K Mg and log DMg (for constant XAn =0.6) vs. inverse temperature are linear with a negative slope, and show a positive correlation with a . Isothermal data for different XAn in plagioclase SiO 2

Pl / Cpx show a linear increase of ln K Mg with increasing XAn , but a strong dependence of

Pl Pl / Cpx DMg on XAn is not observed. Multiple regression of all data allows ln K Mg to be determined as a function of temperature, XAn and a , and application as a SiO 2 geothermometer reproduces the experimental temperatures within ±20°C: [ ] − []+ 16913 J/mol 9219 K X An T[]K = R C Pl ln Mg − 6.1 − ln a Cpx SiO 2 CMg

2.1 Introduction

Plagioclase and clinopyroxene coexist in many rocks across a wide range of temperatures and compositions. Therefore, a geothermometer based on a temperature-sensitive exchange reaction between these two minerals will provide a powerful tool of broad application for many terrestrial and extraterrestrial rocks. Yet, up to date, no such plagioclase-clinopyroxene-thermometer has been calibrated. Two empirical observations suggest that Mg exchange between clinopyroxene and plagioclase is temperature-sensitive. Firstly, observations from natural rock samples indicate a strong temperature dependence of the partitioning of Mg between plagioclase and clinopyroxene. Natural rock samples from the oceanic crust show higher concentrations of MgO in plagioclase phenocrysts of mid ocean ridge basalts (MORBs), than found in plagioclase of cogenetic, but more slowly cooled, gabbroic rocks of the lower oceanic crust (Coogan, 2007). The

50 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx difference in plagioclase Mg-content most likely results from the exchange of Mg between these phases during cooling of the gabbroic rocks. If this is correct, it suggests that the partition coefficient of Mg between plagioclase and clinopyroxene

Pl / Cpx ( K Mg ) decreases with temperature, such that on cooling, Mg tends to diffuse out of plagioclase and into clinopyroxene. The second line of empirical evidence suggesting a temperature dependence of the Mg exchange between plagioclase and clinopyroxene comes from experimental studies. Several experimental investigations of the evolution and crystallization of different basaltic melt compositions reported the coeval growth of plagioclase and clinopyroxene from a melt (e.g. Walker et al., 1979; Sack et al., 1987; Tormey et al., 1987; Libourel et al., 1989; Grove and Juster, 1989; Shi and Libourel, 1991; Shi, 1992; Soulard et al., 1992; Yang et al., 1996; Chalot-Prat et al., 2010). Growing together from the same melt, plagioclase and clinopyroxene should be in equilibrium. Hence, the measured MgO- contents in both phases can be used to calculate the partition coefficient

Pl / Cpx K Mg according to

C Pl Pl / Cpx = Mg K Mg Cpx (Eq. 2.1.1) CMg

Pl Cpx where CMg is the weight concentration of Mg in plagioclase and CMg is the weight

Pl / Cpx concentration of Mg in clinopyroxene. Figure 2.1.1 shows a plot of ln K Mg from these previous experimental studies versus the reported temperatures. The diagram

Pl / Cpx clearly shows an overall trend of decreasing K Mg with decreasing temperature, but the large variability in the data allows only poor quantitative constraints.

51 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Pl / Cpx Fig. 2.1.1: Calculated values for ln K Mg from reported Mg-concentration in plagioclase and clinopyroxene of previous studies on basaltic melt compositions varying with inverse temperature.

Previous experimental studies were not designed to determine the partitioning of Mg between plagioclase and clinopyroxene and no special care was taken to precisely measure the low concentrations of MgO in plagioclase (0.08 to 1 wt%), which are at the lower limit of the resolution of an electron microprobe. Additionally, different starting compositions for basaltic melts were chosen for the different experiments, leading to different anorthite-contents ( XAn ) in plagioclase

(XAn =0.18 to 1) and different silica activities ( a ). Since the partition coefficient of SiO 2

Pl / melt Mg between plagioclase and melt ( K Mg ) is expected to be dependent on XAn in

Pl / Cpx plagioclase (Blundy and Wood, 1994; Bindeman et al., 1998), K Mg is expected to

Pl / Cpx show a similar dependence on XAn and therefore the effect of temperature on K Mg might not be easily compared for experiments done with different XAn .

52 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

The temperature-sensitivity of the Mg-exchange between plagioclase and clinopyroxene, as indicated by the above mentioned empirical observations, qualifies this exchange as suitable for the calibration of a geothermometer. Additionally, the fact that Mg is a trace element in plagioclase, but a major component in clinopyroxene, makes this exchange especially suitable for the this purpose, because clinopyroxene can be assumed to act as an infinite reservoir for Mg (see Section 2.2.2 for a discussion). However, application of the Mg-exchange between plagioclase and clinopyroxene for geothermometry requires detailed experiments on the partitioning of Mg between plagioclase and clinopyroxene with respect to XAn in plagioclase aiming for high precision in the measurement of Mg in plagioclase. Methods of ‘ geospeedometry ’, such as diffusion modelling, build on thermometry and are important tools to determine time scales of geologic processes (e.g. Lasaga, 1983). Diffusion modelling of distinct compositional zoning profiles of Mg observed in plagioclase from various geological settings have shown to be a powerful tool for the determination of time scales relevant for processes involving plagioclase bearing rocks (e.g. Costa et al., 2003). However, the modelled results can only be as accurate, as the input parameters, such as the diffusion coefficient and the boundary conditions used for the modelling procedure. The boundary conditions for diffusion modelling of Mg in plagioclase in contact with clinopyroxene are given by

Pl / Cpx the partition coefficient K Mg . Thus, diffusion models aiming to describe this system provide another field of application for more detailed data on the partitioning between plagioclase and clinopyroxene.

Pl / Cpx This study aims to quantify K Mg as a function of temperature and composition in order to calibrate a geothermometer applicable to various compositions of plagioclase in different geochemical settings. The partitioning experiments were designed in a way, which also allows the diffusion coefficient of

Pl Mg in plagioclase ( DMg ) to be determined for each experiment.

53 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

2.2 Theoretical background and previous work on the diffusive exchange of Mg between plagioclase and clinopyroxene

Before quantifying the partitioning of Mg between plagioclase and clinoyproxene, it is necessary to develop a better understanding for the thermodynamics of the diffusive exchange of Mg between these two phases. Therefore, the thermodynamics of the possible exchange reactions of Mg between plagioclase and clinopyroxene are now investigated, based on the different positions where Mg may fit into the plagioclase structure. Subsequently, the knowledge on diffusion of Mg in plagioclase is reviewed from previous experimental studies.

2.2.1 Exchange of Mg between plagioclase and clinopyroxene Possible exchange reactions of Mg between plagioclase and clinopyroxene will depend on the structural site that Mg occupies in plagioclase. However, the position of Mg in the plagioclase structure remains a topic of debate. Investigations of Fe-Mg-rich lunar plagioclase showed significant deviations from the “normal stoichiometric” composition Na xCa 1-xAl 2-xSi 2+x O8 (e.g. Weill et al., 1970; Drake and Weill, 1971; Wenk and Wilde, 1973), that could be explained by the additional components Ca(MgFe 2+ )Si 3O8, (MgFe 2+ )Al 2Si 2O8 and [ ]Si 4O8 (Longhi et al., 1976; all Fe is assigned as Fe 2+ for simplicity). Theoretically, the following substitutions may be possible to implement Mg in plagioclase: (1) Mg 2+ + Si 4+ = 2 Al 3+ (2) Mg 2+ = Ca 2+

Substitution (1) leads to a CaMgSi 3O8-component, where Mg occupies the tetrahedral site (T-site), and substitution (2) leads to an MgAl 2Si 2O8-component with Mg sitting on the M-site. Longhi et al. (1976) examined the substitution of Mg (and Fe) in plagioclase as a function of composition and temperature, recognizing that the dominant component is Ca(MgFe)Si 3O8. Incorporation of Mg into plagioclase as this component was supported by the study of Sclar et al. (1991, unpublished data), that

54 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

reports the synthesis of metastable feldspar of composition CaMgSi 3O8 at 1200°C from high-purity oxide mixtures with a bulk composition corresponding to an equimolar mixture of diopside and silica. Furthermore, Peters et al. (1995) used the positive correlation between their experimentally determined partition coefficient

Pl / melt of Mg between plagioclase and melt ( K Mg ) and the liquid activity product of the crystallization reaction CaO (liq) +MgO (liq) +3SiO 2(liq) = CaMgSi 3O8(Pl) to conclude that Mg is more likely to occupy the tetrahedral site in plagioclase than the M-site. In contrast to this, Blundy & Wood (1994) showed good agreement between

Pl / melt their experimentally determined K Mg (for: XAn =0.89, P=1 atm, T=1251°C) and a

Pl / melt predicted K Mg based on elastic moduli (“lattice strain model”, see also Wood & Blundy, 2001; Blundy &Wood, 2003), for the assumption that Mg occupies the M- site in plagioclase. Building up on this approach, Miller at al. (2006) determined the influence of melt composition on the lattice strain model and derived a thermodynamic model to distinguish between Mg on the M- and on the T-site. Their results indicate Mg to be incorporated in plagioclase on both, the M- and the T-site. Additionally, they report trends in Mg site occupation as a function of composition with Mg increasingly populating the M-site relative to the T-site as the MgO content increases in the system.

For the exchange of Mg between plagioclase and clinopyroxene, different end member exchange reactions for the two different site options for Mg in plagioclase are possible:

+ = (1a): Mg on T-site: CaMgSi 2O6 (Cpx ) SiO 2 CaMgSi 3O8 (Pl ) + + = (2): Mg on M-site: MgSiO 3 (Cpx ) SiO 2 Al 2O3 MgAl 2 Si 2O8 (Pl )

However, using CaMgSi 2O6 as the Mg-bearing component in clinopyroxene for this exchange reaction has some disadvantages. For example, it is not unambiguous to relate the amount of Mg in clinopyroxene to a CaMgSi 2O6-component, as natural

55 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx clinopyroxenes may also consist of other Mg-bearing components (such as

Mg 2Si 2O6). Alternatively, reaction (1a) can be written as: + + = (1b): Mg on T-site: CaSiO 3 (Cpx ) MgSiO 3 (Cpx ) SiO 2 CaMgSi 3O8 (Pl )

For any reaction, in equilibrium we can state: ∆ 0 = − Gr RT ln K eq , (Eq. 2.2.1.1) where R is the ideal gas constant (8.314 J/molK), T is temperature in Kelvin, Keq is ∆ 0 the equilibrium constant and Gr is the change in the standard state Gibbs Free ∆ 0 energy of the reaction. For reaction (1b) Gr is given by: ∆ 0 = 0 − 0 − 0 − 0 Gr G (CaMgSi 3O8 ) G (CaSiO 3 ) G (MgSiO 3 ) G (SiO 2 ) (Eq. 2.2.1.2)

0 0 0 0 where G (CaMgSi 3O8 ), G (CaSiO 3 ), G (MgSiO 3 ) and G (SiO 2 ) are the standard state Gibbs Free energies of the respective components (using the pure components as reference states). The equilibrium constant Keq of reaction (1b) is: a Pl K = CM , (Eq. 2.2.1.3) eq a Cpx a Cpx a CaSiO 3 MgSiO 3 SiO 2

Pl Cpx where a is the activity of the CaMgSi 3O8-component in plagioclase, a is the CM CaSiO 3

Cpx activity of the (CaSiO 3)-component in clinopyroxene, a is the activity of the MgSiO 3

(MgSiO 3)-component in clinopyroxene and aSiO 2 is the silica activity of the system. j = jγ j j Using ai X i i , where X i is the equivalent mole fraction of component i in γ j mineral j and i is the corresponding activity coefficient of component i in mineral j, we can write: γ Pl X Pl K = CM CM (Eq. 2.2.1.4) eq γ Cpx X Cpx γ Cpx X Cpx a CaSiO 3 CaSiO 3 MgSiO 3 MgSiO 3 SiO 2 and hence in the equilibrium state we get: γ Pl X Pl ∆G 0 = −RT ln K = −RT ln CM CM (Eq. 2.2.1.5) r eq γ Cpx X Cpx γ Cpx X Cpx a CaSiO 3 CaSiO 3 MgSiO 3 MgSiO 3 SiO 2

56 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Equation 2.2.1.5 can be rearranged to:

Pl 0 γ Cpx X − ∆G MgSiO 1 ln CM = r + ln 3 − ln X Cpx RT γ Pl X Cpx γ Cpx a MgSiO 3 CM CaSiO 3 CaSiO 3 SiO 2 − ∆H 0 ∆S 0 = r + r + ln γ Cpx − ln γ Pl + ln X Cpx + ln γ Cpx + ln a RT R MgSiO 3 CM CaSiO 3 CaSiO 3 SiO 2 (Eq. 2.2.1.6) ∆ 0 ∆ 0 where H r and S r are the standard state enthalpy and standard state entropy of the reaction, respectively.

To a first approximation the activity coefficients for the (CaSiO 3)- and

Cpx Cpx (MgSiO 3)-component in clinopyroxene, ln γ and ln γ , are assumed to be CaSiO 3 MgSiO 3 constant, since both are major components in clinopyroxene and therefore will not be changed significantly due to Mg-exchange with the plagioclase. Non-ideality in the host plagioclase is accounted for by assuming a ternary mixing between the major components in plagioclase (Ab and An) and the CaMgSi 3O8-component in plagioclase (CM) as suggested by Blundy and Wood (1991): γ Pl = − ( − + )− 2 RT ln CM WCMAb X An WCMAb WCMAn WAnAb WAnAb X An , (Eq. 2.2.1.7) where WCMAb ,WCMAb ,WCMAn ,WAnAb and WAnAb are the interaction parameters between the respective components. Blundy & Wood (1991) showed that the quadratic term in Eq. (2.2.1.7) is not significant for a Sr- and Ba-component in plagioclase. Assuming the same to be true for a Mg-component in plagioclase, Eq. 2.2.1.7 reduces to a linear relation of the form: γ Pl = − − RT ln CM A BX An (Eq. 2.2.1.8) Application to Eq. 2.2.1.6 yields X Pl − ∆H 0 ∆S 0 ln CM = r + r + ln γ Cpx + ln X Cpx + ln γ Cpx X Cpx RT R MgSiO 3 CaSiO 3 CaSiO 3 MgSiO 3 A B + + X + ln a RT RT An SiO 2 (Eq. 2.2.1.9) which can be rearranged to

57 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

X Pl  − ∆H 0 A  1 ∆S 0 ln CM =  r +  + r + ln γ Cpx + ln γ Cpx + ln X Cpx Cpx   MgSiO 3 CaSiO 3 CaSiO 3 X  R R  T R MgSiO 3 B + X + ln a RT An SiO 2 (Eq. 2.2.1.10) Under the assumption made for reaction (1b), that all Mg enters the plagioclase as a CaMgSi 3O8-component, the ratio of the molar fraction of this

Pl component in plagioclase ( XCM ) and the molar fraction of the (MgSiO 3)-component in clinopyroxene ( X Cpx ) is directly related to the partition coefficient of Mg MgSiO 3 between plagioclase and clinopyroxene:

C Pl X Pl ln K Pl / Cpx = ln Mg = ln f ⋅ CM , Mg C Cpx X Cpx Mg MgSiO 3 where the factor f is the ratio of the normalization factors of wt% MgO into X Mg in plagioclase and clinopyroxene. Since these normalization factors depend on the actual composition of plagioclase and clinopyroxene, their ratio is not a fixed number, but depends on the composition of the two phases as well. (For the compositional range of this study f~1.23). Use of the factor f in Eq. 2.2.1.10 leads to:

C Pl X Pl ln K Pl / Cpx = ln Mg = ln f CM Mg C Cpx X Cpx Mg MgSiO 3  − ∆H 0 A  1  ∆S 0  B = ln f +  r +  +  r + ln γ Cpx + ln γ Cpx  + X + ln X Cpx + ln a    MgSiO 3 CaSiO 3  An CaSiO 3 SiO 2  R R  T  R  RT (Eq. 2.2.1.11)

Pl / Cpx Thus, ln K is expected to show linear dependences on 1/ T, XAn , ln a and Mg SiO 2 ln X Cpx . CaSiO 3 Eq. 2.2.1.11 may also be written in linear form as: Pl / Cpx = + (− ∆ 0 + )+ [∆ 0 + ( γ Cpx + γ Cpx )] + RT ln K Mg ln f H r A Sr R ln MgSiO ln CaSiO T BX An 3 3 + RT ln X Cpx + RT ln a CaSiO 3 SiO 2 (Eq. 2.2.1.12) and simplified to

58 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

RT ln K Pl / Cpx = A' + CT + BX + RT ln X Cpx + RT ln a (Eq. 2.2.1.13) Mg An CaSiO 3 SiO 2

The analysis beginning with Eq. 2.2.1.1 can be used in a similar manner for ∆ 0 reaction (2), where Gr is given by: ∆ 0 = 0 − 0 − 0 − 0 Gr G (MgAl 2 Si 2O8 ) G (MgSiO 3 ) G (SiO 2 ) G (Al 2O3 ) (Eq. 2.2.1.14) and the equilibrium constant Keq of reaction (2) can be written as: a Pl γ Pl X Pl K = MA = MA MA (Eq. 2.2.1.15) eq aCpx a a γ Cpx X Cpx a a MgSiO 3 SiO 2 Al 2O3 MgSiO 3 MgSiO 3 SiO 2 Al 2O3 with MA denoting the MgAl 2Si 2O8-component in plagioclase and a being the Al 2O3 alumina activity of the system. Following the same approach as outline above, Eq. 2.2.1.6 now has to be written as:

Pl 0 γ Cpx X − ∆G MgSiO ln CM = + ln 3 + ln a + ln a X Cpx RT γ Pl SiO 2 Al 2O3 MgSiO 3 MA − ∆H 0 ∆S 0 = r + r + ln γ Cpx − ln γ Pl + ln a + ln a RT R MgSiO 3 MA SiO 2 Al 2O3 (Eq. 2.2.1.16) Under the assumption underlying reaction (2), that all Mg enters the plagioclase as a MgAl 2Si 2O8-component, the ratio of the molar fraction of this

Pl component in plagioclase ( X MA ) and the molar fraction of the (MgSiO 3)-component in clinopyroxene ( X Cpx ) is again directly related to the partition coefficient of Mg MgSiO 3

C Plag Pl / Cpx = Mg between plagioclase and clinopyroxene ( K Mg Cpx ) and therefore Eq. 2.2.1.11 CMg now can be written as:

C Pl X Pl ln K Pl / Cpx = ln Mg = ln f CM Mg C Cpx X Cpx Mg MgSiO 3  − ∆H 0 A  1  ∆S 0  B = ln f +  r +  +  r + ln γ Cpx  + X + ln a + ln a    MgSiO 3  An SiO 2 Al 2O3  R R  T  R  RT (Eq. 2.2.1.17)

59 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Hence, if Mg is exchanged between plagioclase and clinopyroxene via reaction (2),

Pl / Cpx ln K is expected to show the same linear dependence on 1/ T, XAn , ln a as in Mg SiO 2

Pl / Cpx the case of reaction (1b). Additionally, for reaction (2) ln K Mg is expected to depend on ln a , but should not be a function of ln X Cpx . Eq. 2.2.1.17 can be Al 2O3 CaSiO 3 written in linear form as: RT ln K Pl / Cpx = Mg ln f + ()− ∆H 0 + A + []∆S 0 + R()ln γ Cpx T + BX + RT ln a + RT ln a r r MgSiO 3 An SiO 2 Al 2O3 (Eq. 2.2.1.18) and simplified to: RT ln K Pl / Cpx = A' + CT + BX + RT ln a + RT ln a (Eq. 2.2.1.19) Mg An SiO 2 Al 2O3

Pl / Cpx Experimental determination of K Mg therefore needs to be carried out under controlled a and a to define all relevant thermodynamic parameters SiO 2 Al 2O3

Pl / Cpx controlling K Mg .

2.2.2 Diffusion of Mg in plagioclase Since Mg is a trace element in plagioclase, but a major element in clinopyroxene, the diffusion exchange rate of Mg between the two minerals is assumed to be kinetically controlled by the diffusion coefficient of Mg in plagioclase, while clinopyroxene can be assumed to act as an infinite reservoir. The concentration of Mg in clinopyroxene is about 2 orders of magnitude higher than the concentration of Mg in plagioclase. Therefore, it is necessary to have only a small flux of Mg to equilibrate plagioclase with clinopyroxene. Although diffusion of Mg in clinoyproxene is slower than in plagioclase (Zhang et al., 2010; Mueller et al., in prep.; LaTourette and Wasserburg, 1998) in the temperature range of interest here, it is not by two orders of magnitude slower, so it is expected, that diffusion in clinopyroxene is sufficiently fast for clinopyroxene to act as an infinite reservoir.

60 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

The self diffusion coefficient of Mg in plagioclase was first investigated by LaTourette and Wasserburg (1998) in an experimental study on natural single crystals of anorthite ( XAn =0.95) at atmospheric pressures from 1200 to 1400°C. Their experimental approach was based on diffusion couples from sections of oriented single crystals from Miyake-jima (Japan) and synthetic glasses having the same composition as the natural crystals, but isotopically enriched in 26 Mg. Isotopic concentration profiles were measured for the crystallographic b- and c-directions and fitted with inverse error functions. La Tourette and Wasserburg (1998) report resulting diffusion coefficients consistent with an Arrhenian relationship,

An = −E / RT -8 2 DMg D0e , with D0=7.1±0.1 x 10 m /s and E=254±43 kJ/mol in b-direction, and D0=1.2±0.1 x 10 -6 m 2/s and E=278±43 kJ/mol in c-direction. They conclude, that Mg self diffusion in anorthite might be slightly anisotropic with diffusion in the c- direction approximately three times faster than in the b-direction (in their experimental temperature range of 1200 to 1400°C). In the same study, they investigated diffusion coefficients of Sr and Ca in plagioclase and observe very little or no preference for crystallographic direction in the Ca data (Sr was too poorly constrained for a distinction to be made). La Tourette and Wasserburg (1998) speculate, that “one reason for this difference might be due to the fact, that Ca and Sr are located in the VI to VIII fold coordinated M site in plagioclase, while the smaller Mg ion most likely substitutes into a tetrahedral site”. They conclude that the difference in coordination environments may result in more possible types of diffusive jumps being available for Mg than for the larger Ca and Sr ions. Costa et al. (2003) derived a diffusion model of Mg in plagioclase, coupled to the anorthite component in plagioclase. They average the D0- and E-values of LaTourette and Wasserburg (1998) data for the b-and c-direction and additionally assumed a dependence of the Mg-diffusion coefficient on XAn , similar to the experimentally derived compositional dependence of Sr-diffusion in plagioclase (Giletti and Casserly, 1994) of the form:

− −  − 266 kJ/mol  D Pl = 92.2 ⋅10 ( 1.4 Xan )1.3 exp  [m 2 /s ]. Mg  RT 

61 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Experiments with plagioclase of different anorthite-contents carried out in

Pl this study will determine a possible dependence of DMg on XAn and allow for testing

Pl the assumption of Costa et al. (2003) that DMg increases with decreasing XAn . The lower temperature range (1100 to 1200°C) of experiments in this study compared to those of LaTourette and Wasserburg (1998) will improve the extrapolation of their high temperature data down to lower temperatures.

2.3 Experimental setup and run conditions

2.3.1 General experimental setup, starting materials and run conditions Experiments were designed to determine the partition coefficient of Mg

Pl / Cpx between plagioclase and clinopyroxene ( K Mg ) and the diffusion coefficient of Mg

Pl in plagioclase DMg as a function of (i) temperature T, (ii) anorthite content in plagioclase XAn and (iii) silica activity of the system a . The effect of a on SiO 2 Al 2O3

Pl / Cpx Pl K Mg and DMg was not investigated here, but all experiments were carried out using Al 2O3-crucibles and it will be shown later (section 2.5.3) that this was sufficient to buffer a to 1 for all experiments. Plagioclase single crystals with Al 2O3 different anorthite contents ( XAn =0.12 to 0.95, Table 2.3.1.1) were cut into cubes of ~2 mm x 2 mm x 2 mm and one side of the cube was polished. The plagioclase cubes were placed together with different sets of Cpx-bearing matrix powder in an Al 2O3- crucible, such that the matrix powder surrounded the plagioclase cubes from all sides (Fig. 2.3.1.1).

62 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Gasmixingfunace f O2 controlledbydefinedfluxofCO2 andCO f B-typethermocoupleandZrO2 -O 2 -sensor

Al2 O 3 -rod Pt-wire (a) (b) (c)

Al2 O 3 - plagioclase crucible crystal natural just gabbroic Cpx+SiO2 - Cpx- powder rock powder powder

Fig. 2.3.1.1. Sketch of the experimental setup. In one experimental run, three Al 2O3-crucibles are tied to a Al 2O3-rod with Pt-wire and are placed together in the gas mixing furnace. Each Al 2O3-crucible is filled with a plagioclase crystal (~2x2x2 mm) which is surrounded by a Cpx-bearing matrix powder ((a) just powdered Cpx, (b) powdered Cpx+SiO 2, and (c) natural gabbroic rock powder with the assemblage Pl-Cpx-Opx-Ol).

To improve the contact between the plagioclase cube and the surrounding matrix powder, a brazen piston of the same diameter as the Al 2O3-crucible was pressed by hand on the assemblage of plagioclase cube and matrix powder. In every experimental run, three filled Al 2O3-crucibles were tied to an Al 2O3-rod with Pt-wire (distance of ~1.5 cm) and were placed into the furnace together (Fig. 2.3.1.1). To determine the effect of a , plagioclase cubes cut from the same single SiO 2 crystal (e.g. XAn =0.6) were put into different matrix powders: (a) just powdered diopside (just Cpx), (b) powdered diopside with excess SiO2 (Cpx+SiO 2) and (c) powder of natural gabbroic rock containing the assemblage Pl-Cpx-Opx-Ol. To produce matrix (a) a diopside single crystal (composition see Table 2.3.1.1) was crushed and ground by hand in an agate mortar until the powder had a grain size of

~50 µm. To produce matrix (b) the powdered diopside was mixed with SiO 2-powder (purity 99.6 %) in a ratio of approximately 1:1 and the mixture was homogenized by grinding in an agate mortar. For matrix (c) a fresh gabbroic rock from the oceanic crust was chosen, that consists mainly of plagioclase ( XAn ~0.6) and clinopyroxene, but also contains orthopyroxene and olivine (sample 022005-1522 from Pito Deep, cruise RT11-33 of the R/V-Atlantis , Karson et al, 2005; Karson, unpublished cruise report, Perk et al., 2007; modal abundance and representative composition of

63 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx minerals given in Table 2.3.1.1). The rock was crushed and ground by hand in an agate mortar to a grain size of ~50 µm. Before using it for the experiments, the gabbroic rock powder was pre-annealed from 600°C-1100°C (with a heating rate of

50 °C/h and constant CO/CO 2-ratio of 83.4/16.6, which corresponds to

-11 fO2=10 bars at 1100°C) to induce the breakdown of any hydrous alteration phases (e.g. amphibole and chlorite).

64 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Table 2.3.1.1: Chemical composition of starting materials.

gabbroic rock 022005-1522 Oxide Plag Plag Plag Plag Plag Plag Diopside Dioside Cpx Plag Ol** Opx (XAn =0.6) (XAn =0.12) (XAn =0.2) (XAn =0.5) (XAn =0.7) (XAn =0.95) (Cpx) glass ~35 vol% ~50 vol% ~5 vol% ~10 vol%

SiO 2 53.03 67.23 66.13 57.61 51.32 44.24 54.83 55.38 51.38 52.37 37.31 53.66 TiO 2 0.06 0.01 0.02 0.06 0.05 0.01 0.06 0.00 0.74 0.06 0.00 0.34 Al 2O3 29.56 21.44 22.22 26.81 30.06 34.93 1.00 0.32 2.07 29.40 0.00 0.89 Cr 2O3 0.01 0.01 0.00 0.02 0.00 0.00 0.12 0.03 0.05 0.02 0.00 0.04 CaO 12.37 2.61 3.61 9.70 13.62 19.48 25.04 25.02 21.67 13.23 0.04 0.86 *FeO 0.39 0.07 0.08 0.38 0.43 0.53 2.90 0.30 8.80 0.64 29.74 20.16 MgO 0.10 0.01 0.01 0.08 0.14 0.08 15.91 18.30 14.90 0.05 33.39 23.78 MnO 0.00 0.00 0.02 0.02 0.01 0.00 0.15 0.02 0.25 0.00 0.45 0.46 K2O 0.29 0.31 0.95 0.53 0.12 0.01 0.01 0.01 0.02 0.04 0.00 0.01 Na 2O 4.41 9.01 8.77 5.80 3.73 0.51 0.47 0.10 0.29 4.09 0.00 0.00 Total 100.23 100.71 101.80 100.99 99.49 99.79 100.50 99.47 100.17 99.87 100.93 100.19 *** X Cpx CaSiO 3 0.484 0.430 * all Fe reported as FeO for all phases ** analysis for Ol in gabbroic rock from Perk et al. (2007) *** calculation of X Cpx as explained in Section 2.5.5. CaSiO 3

65 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

To determine the temperature dependence, the same experimental runs were repeated at different temperatures (from 1050°C to 1200°C) and to determine the compositional dependence of plagioclase, experimental runs were carried out with plagioclase of different XAn at constant temperatures ( XAn =0.5-to 0.8 at 1150°C and XAn =0.2 to 0.65 at 1130°C). Run conditions for individual experiments are summarized in Table 2.5.3.1. All experimental runs (except for KF044) were carried out at 1 atm in a gas-mixing furnace with adjustable flux of CO and CO 2 to control the oxygen fugacity. The combined flux rates of CO- and CO 2 was set to 500 SCCM

(standard cm 3 per minute) and the individual fluxes were adjusted to ensure fO2- conditions between NNO and QFM-buffer for the respective temperatures of the experiment. Temperature and fO2 were monitored in situ using a type B thermocouple and a ZrO 2-fO2-sensor, respectively.

2.3.2 Special experimental setups In some experiments (KF009, KF010, KF012, KF013, KF019), the Cpx- bearing matrix powder was mixed with powdered glass of diopside composition (Table 2.3.1.1) to test if this enhances the contact between the plagioclase and the clinopyroxene. For experimental runs KF025 and KF028, additional excess Al 2O3 was added to the matrix powder, in order to test if the Al 2O3-crucible is sufficient to buffer the system for a . The plagioclase crystal in experimental run KF005 was Al 2O3 not surrounded by any matrix powder, to test if Mg can be lost from the plagioclase due to evaporation (at 1200°C) instead of exchange with the clinopyroxene. For experimental runs KF006, KF007 and KF014 a plagioclase crystal was surrounded by a matrix of powdered plagioclase of a different composition than the plagioclase cube to determine if/how Mg exchanges between plagioclase of different compositions. Experiment KF044 was carried out in a piston cylinder apparatus at 10 kbar at the ambient oxygen fugacity of the pressure cell.

66 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

2.3.3 Sample preparation after the experiment After the experiment, the plagioclase crystal and the surrounding matrix powder were removed carefully from the Al 2O3 crucible. Depending on the temperature of the experiment, the plagioclase composition, and the matrix composition, the plagioclase crystal and the matrix powder were more or less strongly sintered together. Special care was taken to keep the plagioclase crystal and the matrix powder in contact in cases they were not sintered together strongly. The plagioclase and the matrix powder sticking to the crystal were embedded in epoxy together. The whole sample was ground down until the core of the plagioclase cube was at the surface and this surface was polished for microprobe analyses (finishing with 0.25 µm diamond paste).

2.4 Electron microprobe (EMP) analyses

Electron microprobe analyses of Ca, Na, Si, Al, Mg, K, Fe, Ti, Mn and Cr were carried out using a Cameca SX-50 electron microprobe fitted with four wavelength- dispersive spectrometers (WDS) at the Ruhr-University in Bochum. Natural and synthetic mineral standards were used for the analyses (Table A3 in Appendix III). An on-line φ(ρz)/PAP correction procedure was used to correct for absorption, fluorescence and atomic number. The concentration of Mg in plagioclase in the investigated experimental runs is between 0.01 and 0.30 wt% MgO, which is at the lower limit of resolution of an electron microprobe. Therefore, special measurement conditions had to be determined to achieve high accuracy and precision. After multiple tests, the following measurement conditions were found to be ideal for measuring concentration profiles of Mg without the loss of Na from plagioclase: 15 kV and 40 nA, beam defocused to 5 µm, long counting times for Mg (90 sec on peak and 45 sec on each background), and peak and background positions of the spectrometers for Mg that were specially adjusted for Mg in plagioclase (see Table A3 in Appendix III for details of the measurements conditions).

67 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

To prevent loss of Na due to the high beam current, tests were carried out with repeated measurements of the exact same spot with these conditions, but in 60 sec intervals. Results show that the first detectable loss of Na in plagioclase with

XAn =0.6 occurs after 240 sec. Therefore, to be conservative, the above mentioned conditions were used for a maximum of 180 sec. In every plagioclase crystal, 2 perpendicular profiles were measured, each from one rim of the crystal over the core to the opposite rim. The distance between analyzed spots along the profile was 5 µm in approximately the first 150 µm away from each rim and 10 µm between rim areas. Additionally, closely spaced clusters were measured at chosen spots at the rim of the plagioclase (2 µm distance between individual analyses along a profile from the rim of the plagioclase in direction to the core for approximately the first 40 µm, then the distance was increased to 5 µm, see Fig. 2.4.1.1). Since the beam size was defocused to 5 µm, and overlap of analyzed spots should be avoided, the analyses were carried out with a distance of 10 µm perpendicular to the direction of the measured profile (see Fig. 2.4.1.1). The clinopyroxene adjacent to the plagioclase was analyzed as well.

Fig. 2.4.1.1: Schematic sketch to show the arrangement of the two perpendicular profiles measured in each plagioclase crystal, and the closely spaced clusters of analyses at the rim of a plagioclase crystal. (a) Each profiles starts at the rim of the plagioclase crystal and is measured over the core to the opposite rim. The distance between single analyses is 5 µm close to the rim (~first and last 150 µm of the measured profile, more densely spaced dashed lines) and 10 µm for the middle part of the profile (less densely spaced dashed lines). Closely spaced clusters were measured at chosen spots at the contact between the plagioclase crystal and the matrix- clinopyroxene. (b) Blow-up on Cluster 1 to illustrate the representative arrangement of analyses within a cluster. The distance between two measurements in direction of the profile is 2 µm for the first 15 to 20 analyses and 5 µm for the following analyses. The distance between two measurements perpendicular to the profile direction is 10 µm.

68 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

2.5 Experimental results and discussion

2.5.1 General observations For experimental runs at temperatures below 1100°C no exchange between plagioclase and clinopyroxene could be detected. At 1100°C and above, plagioclase exchanged Mg with the matrix powder of pure diopside, but exchange between plagioclase and the matrix of natural rock powder is only observed at temperatures of 1130°C and higher. In the presence of clinopyroxene, plagioclase crystals of oligoclase composition ( XAn =0.12) started melting at temperature above 1130°C, plagioclase with XAn =0.5 started melting above 1150°C, and plagioclase with XAn =0.6 started melting above 1200°C. Experimental runs in which melt occurred, were not

Pl / Cpx Pl used to determine K Mg and DMg . Loss of Mg due to evaporation at temperatures of 1200°C was not observed in experiment KF005.

Observations on plagioclase composition: Plagioclase crystals, which were surrounded by Cpx+SiO 2, show a distinct decrease of Na and increase of Ca towards their rims (Fig. 2.5.1.1a). This change in Na and Ca is not correlated to changes in Al or Si in the plagioclase (Fig. 2.5.1.1b) and diffusion lengths are longer than those of the Mg-profiles. When calculating the measured compositions as theoretical plagioclase components CaAl 2Si 2O8, NaAlSi 3O8, CaMgSi 3O8, MgAl 2Si 2O8 and [ ]Si 4O8

(Longhi, 1976), the changes in Na and Ca correlate with an increase in the [ ]Si 4O8- component. The same tendency for changes in Na and Ca are observed for experiments with plagioclase surrounded by just Cpx-powder and gabbro-powder (Fig. 2.5.1.1c and Fig. 2.5.1.1b), but there the trends are less distinct.

69 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Fig. 2.5.1.1: Chemical distribution profile of (a) Na and Ca per formula unit [p.f.u.] and (b) Al and Si [p.f.u.] in plagioclase from KF027 ( XAn =0.6; T=1200°C; surrounded by Cpx+SiO 2), (c) Na and Ca [p.f.u.] and (d) Al and Si [p.f.u.] in plagioclase from KF026 ( XAn =0.6; T=1200°C; surrounded by just Cpx). Plagioclase from KF027 shows a distinct decrease of Na and increase of Ca towards the rims of the plagioclase crystal (a), but no distinct change for Si and Al (b). Plagioclase from KF026 shows the same general trends for Na and Ca, but they are less prominent.

Calculation of the ratio of the two possible Mg-components CaMgSi O r T ,M = 3 8 along the profiles yields r T ,M ~1 towards the rims Mg ()+ Mg CaMgSi 3O8 MgAl 2 Si 2O8 for the majority of the plagioclase crystals, indicating a preference of Mg for the tetrahedral site as a CaMgSi 3O8-component (Fig.2.5.1.2a and b). Towards the core,

T ,M rMg decreases to 0.5 for some plagioclase crystals (e.g. KF026, Fig. 2.5.1.2b).

70 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Fig. 2.5.1.2: Chemical distribution profiles for calculated plagioclase end-members from (a) KF027 ( XAn =0.6; T=1200°C; surrounded by Cpx+SiO 2) and (b) KF026 ( XAn =0.6; T=1200°C; surrounded by just Cpx). Please note the breakpoint in scaling for the concentrations.

Pl / Cpx Pl 2.5.2 Extracting K Mg and DMg from the experiments

Pl / Cpx The partition coefficient K Mg is extracted from the experiments as the

Pl Cpx Pl ratio between CMg and CMg , at which CMg is the concentration of MgO in the

Cpx plagioclase at the immediate contact with the clinopyroxene, and CMg is the concentration of MgO in the clinopyroxene at the immediate contact with the plagioclase. It will be shown later that plagioclase and clinopyroxene reached equilibrium at the contact between the two phases, as required in the definition of

Pl / Cpx K Mg . The concentration of Mg in the plagioclase in immediate contact with

Pl clinopyroxene ( CMg ) cannot be measured directly, because of two reasons: Firstly, the beam size is defocused to 5 µm, therefore the first analysis will represent an integrated concentration of those 5 µm. Secondly, contamination from hitting the adjacent clinopxroxene has to be avoided, because the clinopyroxene has much higher concentrations of MgO than the plagioclase. Therefore even a little contamination from the clinopyroxene will yield large errors in the analyzed MgO concentration of the plagioclase. Consequently, the analyses closest to the rim were measured at a distance of approximately 2 to 5 µm away from the rim. This was taken into account by extrapolation of the measured profile towards the rim as follows: the MgO contents measured in the plagioclase along the profiles and

71 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx clusters were plotted versus their distance from the rim of the plagioclase. The data was fitted using a complementary error function of the form:

= + Pl x C C0 CMg erfc (Eq. 2.5.2.1) Pl 2 DMg t where C is the measured concentration of MgO in the plagioclase along the profile,

Pl C0 is the concentration of MgO in the core of the plagioclase crystal, CMg is the concentration of MgO at the contact between the plagioclase and the clinopyroxene,

Pl x is the distance of each analyses from the rim of the plagioclase, DMg is the diffusion coefficient of Mg in plagioclase and t is the duration of the experiment.

The variables C and x are measured for each analysis, C0 is measured for

Pl Pl each profile and t is known. Thus, CMg and DMg are the only fit parameters and are σ constrained by minimizing the misfit fit (standard deviation) between each measured concentration and the respective calculated concentration (Fig. 2.5.2.1). σ The misfit fit is calculated for each profile as

σ = 1 measured − calc . 2 fit ∑(CMg CMg ) , (Eq. 2.5.2.2) N

measured with N=number of analyses, CMg =measured concentration of MgO and

calc . CMg =calculated concentration of MgO from error-function (Eq. 2.5.2.1) and is given

Pl / Cpx Pl in Table 2.5.3.1 for each fitted profile used to extract K Mg and DMg .

72 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Fig. 2.5.2.1: A measured chemical distribution profile of MgO in plagioclase (blue dots) and the calculated fit using an inverse error function (Eq. 2.5.2.1, pink line) plotted against distance from the rim of the plagioclase crystal.

The concentration of MgO in clinopyroxene at the contact with plagioclase

Cpx (CMg ) is not expected to be significantly different from the concentration of MgO slightly further away from the contact. The reason for this is that the amount of Mg, which can be exchanged between plagioclase and clinopyroxene, is relatively small compared to the concentration of Mg in clinopyroxene. Therefore, the change of concentration of MgO in the clinopyroxene due to exchange with the plagioclase is not expected to be detected within the analytical uncertainty. This assumption is supported by measurements of MgO in clinopyroxene at different distance away from the contact with the plagioclase single crystal, in which no change in the concentration of MgO was observed.

Pl / Cpx Pl 2.5.3 Experimental results for K Mg and DMg Table 2.5.3.1 summarizes the results of the experiments after extraction of

Pl / Cpx Pl Pl / Cpx Pl K Mg and DMg as outlined above. Multiple numbers for K Mg and DMg for the same experiment result from multiple measurements of Mg-concentration profiles

Pl at different positions within one plagioclase crystal. The diffusion coefficient DMg could not be extracted from all measured profiles (e.g. because the profile shape was

73 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx too scattered or disturbed by cracks or inclusions), however, it is still possible to

Pl Pl / Cpx extract CMg to determine K Mg from the slope of the profile towards the rim of the plagioclase crystal (by linear fitting of just this part of the profile; the resulting data is shown in italics in Table 2.5.3.1). No systematic difference is observed for the measurement of profiles along different orientations within the crystal. Comparison of experiments, in which plagioclase was surrounded by Cpx+SiO 2 and experiments, where plagioclase was surrounded by Cpx+SiO 2+Al 2O3, yield similar results for

Pl / Cpx Pl K Mg and DMg . This observation suggests, that the use of an Al 2O3-crucible fixes a to 1 in all experiments. The assumption of equilibrium between plagioclase Al 2O3 and clinopyroxene at the contact between the two phases is verified by the fact that experimental runs at the same temperature, but with different run durations, yield

Pl the same values of CMg within the scatter of the data (e.g. see KF038, KF058 and KF059, Fig. 2.5.4.1).

74 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Pl / Cpx Pl Table 2.5.3.1: Summary of the experimental results after extraction of K Mg and DMg .

Pl σ Experiment X Matrix T log Run Cpx Pl log D fit An C C Pl / Cpx Mg fO time Mg Mg K 2 Mg [°C] [[[d]]] [wt%] [wt%] 2 [log (m /s)] KF001* 0.6 Cpx 1050 -11 4 16 KF002** 0.6 Cpx 1200 -9 14 16 KF003* 0.6 Cpx 1050 -11 14 16 KF004* 0.12 Cpx 1050 -11 14 16 KF005 0.6 none 1200 -9 4 KF006 0.12 labradorite 1120 -10 10 KF007 0.6 oligoclase 1120 -10 10 KF008** 0.12 Cpx 1190 -9 2 16 KF009** 0.12 Cpx+di gl. 1190 -9 2 16 KF010** 0.12 di gl. 1190 -9 2 KF011** 0.12 Cpx 1170 -9 3 16 KF012** 0.12 Cpx+di gl. 1170 -9 3 16 KF013** 0.12 di gl. 1170 -9 3 KF014* 0.5 labradorite 1150 -10 10 KF015 0.5 Cpx 1150 -10 10 16 0.158 0.010 -16.00 0.041 KF016** 0.12 Cpx 1150 -10 10 16 KF017 0.6 Cpx 1150 -10 17 16 0.189; 0.180; 0.184 0.012; 0.011; 0.012 -16.05; -16.00; -16.05 0.014; 0.016; 0.015 KF018 0.6 Cpx+SiO2 1150 -10 17 16 0.280; 0.241; 0.270 0.018; 0.015; 0.017 -15.45; -15.51; -15.55 0.015; 0.051; 0.026 KF019*** 0.6 Cpx+di gl. 1150 -10 17 16 0.152; 0.155; 0.142; 0.010; 0.010; 0.009; -16.27; -16.52; -16.70; 0.012; 0.041; 0.017; KF020 0.6 Cpx 1120 -10 16 16 0.165; 0.150 0.010; 0.009 -16.82; -16.74 0.027; 0.013

KF021 0.6 Cpx+SiO 2 1120 -10 16 16 0.255; 0.231; 0.251 0.016: 0.014; 0.016 -16.10; -16.26; -16.15 0.010; 0.012; 0.033

KF022 0.6 Cpx+SiO 2+Al 2O3 1120 -10 16 16 0.228; 0.200 0.014; 0.013 -14.89; -15.40 0.045; 0.059 0.185; 0.193; 0.208; 0.012; 0.012; 0.013; -15.82; -16.15; -16.05; 0.017; 0.019; 0.018; KF023 0.6 Cpx 1180 -9 12 16 0.197; 0.185; 0.203 0.012; 0.012; 0.013 -15.77; -16.19; -16.15 0.012; 0.024; 0.027

KF024 0.6 Cpx+SiO 2 1180 -9 12 16 0.278; 0.358; 0.316 0.017; 0.022; 0.020 -15.17; -15.38; -15.51 0.032; 0.020; 0.020

KF025 0.6 Cpx+SiO 2+Al 2O3 1180 -9 12 16 0.358 0.022 -15.03 0.025 KF026 0.6 Cpx 1200 -9 13 16 0.230; 0.208; 0.198 0.014; 0.013; 0.012 -15.74; -15.74; -15.20 0.016; 0.014; 0.020

75 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

KF027 0.6 Cpx+SiO 2 1200 -9 13 16 0.330; 0.344; 0.342 0.021; 0.022; 0.021 -15.10; -15.18; -15.70 0.030; 0.041; 0.044

KF028 0.6 Cpx+SiO 2+Al 2O3 1200 -9 13 16 0.350; 0.398 0.021; 0.025 -14.74; -15.12 0.025; 0.039 KF035* 0.6 gabbro powder 1100 -10 14 15 KF036 0.6 Cpx 1100 -10 14 16 0.142 0.009 -16.66 0.015 KF037* 0.5 gabbro powder 1100 -10 14 15 0.173 ; 0.163; 0.154 ; 0.012 ; 0.011 ; 0.010 ; -; -16.20; -; 0.023; 0.015; 0.010; KF038 0.6 gabbro powder 1160 -9 11 15 0.163; 0.155 ; 0.162; 0.011; 0.010 ; 0.011; -16.30; -; -16.40; 0.038; 0.025; 0.034; 0.154 0.010 -16.40 0.013 0.185; 0.164; 0.170; 0.012; 0.010; 0.011; -16.10; -16.40; -16.11; 0.018; 0.008; 0.017; KF039 0.6 Cpx 1160 -9 11 16 0.160 0.010 -16.22 0.017 KF040** 0.5 gabbro powder 1160 -9 11 15 KF041 0.6 gabbro powder 1130 -10 18 15 0.145; 0.140 ; 0.142 0.010; 0.009 ; 0.009 -16.40; -; -16.60 0.005; -; 0.016 KF042 0.12 Cpx 1130 -10 18 16 0.028; 0.018; 0.048 0.002; 0.001; 0.003 -15.69; -15.06; -15.74 0.011; 0.007; 0.040 KF043 0.5 gabbro powder 1130 -10 18 15 0.110; 0.104; 0.114 0.007; 0.007; 0.008 -16.22; -16.00; -16.77 0.011; 0.011; 0.016 KF044 0.6 gabbro powder 1200 atm 6 15 KF046 0.6 gabbro powder 1150 -10 20 15 0.152; 0.154; 0.153 0.010; 0.010; 0.010 -16.46; -16.48; -16.46 0.013; 0.014; 0.012 KF047 0.7 gabbro powder 1150 -10 20 15 0.166; 0.168 0.011; 0.011 -16.52; -16.40 0.012; 0.020 0.130; 0.142 ; 0.132; 0.009; 0.009 ; 0.009; -16.35; -; -15.82; 0.015; -; 0.012; KF048 0.5 gabbro powder 1150 -10 20 15 0.137 0.009 -15.70 0.054 KF049 0.8 gabbro powder 1150 -10 20 15 0.200 0.013 - - 0.158; 0.163; 0.169; 0.010; 0.010; 0.011; -16.05; -16.07; -16.10; 0.017; 0.017; 0.028; KF050 0.5 Cpx 1150 -10 20 16 0.166; 0.161 0.010; 0.010 -15.98; -16.10 0.019; 0.013 0.189; 0.174; 0.171; 0.012; 0.011; 0.011; -16.24; -16.15; -15.98; 0.015; 0.012; 0.009; KF051 0.6 Cpx 1150 -10 20 16 0.172; 0.184; 0.173 0.011; 0.012; 0.011 -16.00; -16.12; -16.01 0.013; 0.022; 0.024 0.206; 0.187; 0.209; 0.013; 0.012; 0.013; -16.40; -16.13; -16.19; 0.012; 0.025; 0.014; KF052 0.7 Cpx 1150 -10 20 16 0.189; 0.194; 0.192 0.012; 0.012; 0.012 -16.09; -16.52; -16.15 0.013; 0.021; 0.015

KF054 0.5 Cpx+SiO 2 1150 -10 20 16 0.202 0.013 -15.67 0.016

KF055 0.3 Cpx+SiO 2 1150 -10 20 16 0.145; 0.150 0.009; 0.009 -; - 0.09; 0.18 KF058 0.6 gabbro powder 1160 -9 6 15 0.160 0.011 -16.19 0.015 KF059 0.6 gabbro powder 1160 -9 11 15 0.166; 0.156 0.011; 0.011 -16.15; -16.15 0.017; 0.009

KF060 0.6 Cpx+SiO 2 1160 -9 11 16 0.281 0.018 -15.60 0.015 * no contact between plagioclase and matrix ** occurrence of melt *** formation of small, Mg-rich phases in plagioclase Pl italics: data results from extracting CMg by linear fitting of just the part of the profile, that is closest to the rim (see text for discussion)

76 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

2.5.4 Uncertainties and error estimation

Pl / Cpx Pl Uncertainties of the absolute values of K Mg and DMg result from different sources: (i) uncertainties from the experiments itself, (ii) analytical uncertainties associated with the measurement of the concentration profile and (iii) uncertainties from fitting the concentration profile. Uncertainties of the experiment itself include (a) the uncertainty on the temperature,

(b) the uncertainty on fO2, (c) the quality of the contact between plagioclase and clinopyroxene during the experiment, (d) the roughness of the surface of the plagioclase contact and the distribution of defects in the crystal structure, and (e) variations in the composition of the plagioclase crystal.

Analytical uncertainties on the measurement of the concentration profile include (f) the analytical uncertainty on the measurement of concentration of elements from the electron microprobe, i.e. the uncertainty in each element and how it affects other elements (e.g. uncertainty of measuring Si affects Mg concentration and hence the concentration profile of Mg), and (g) the uncertainty in the measurement of the location of each analysis.

Uncertainties from fitting the concentration profiles include (h) the misfit between the measured and the fitted profile, (i) the appropriateness of the model used itself (e.g. how good is an error function solution Eq. 2.5.2.1 and the assumption of clinopyroxene acting as an infinite reservoir, and

77 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

(j) the uncertainty of the distance between the first measured analysis and the actual rim of the plagioclase (which is a combination of (g) and the uncertainty in the measurement of this distance itself).

Some of these uncertainties can be reasonably quantified, e.g. the uncertainty of (a) temperature is small (approximately ±2°C), the uncertainty of (b) the fO2 is also small (approximately 0.5 log units). The analytical uncertainty (f) in the EMP measurements of the Mg-concentration in plagioclase depends on the count statistics on the sample and on the standard, and it is linearly correlated to the σ measured concentrations. For the measurement conditions used, analytic of the measurement of MgO in plagioclase is in the order of 0.5 % of the measured concentration. Yet, it is hard to quantify how the uncertainties of the measurement

Pl of different elements affect each other. The uncertainty of (h) the fit parameters CMg

Pl and DMg can be constrained from non-linear least square fitting of the individual profiles. This yields uncertainties in the order of ~1.5 % of the average value for

Pl Pl CMg , and ~7 % of the average value for DMg for one set of experimental conditions, e.g. T=1160°C; XAn =0.6; surrounded by gabbro powder. The individual uncertainty of

Pl / Cpx Pl the fit parameters and how this can be propagated into ln K Mg and log DMg will be discussed in more detail later. However, some of the above mentioned sources of uncertainty are hard to quantify individually, e.g. (d) the roughness of the plagioclase surface or (c) the quality of the contact between plagioclase and clinoyproxene during the experiment. No systematic relationship between the studied quality of this contact

Pl Pl after the sample preparation and the extracted values for CMg and DMg can be observed. Yet, the quality of the contact, present during the experiment itself, could have been modified after the experiment in two ways: (1) The thermal expansion coefficients of plagioclase and clinopyroxene are different. Therefore, the contact might be modified, when the assemblage is removed from the furnace and cooled rapidly. (2) The assemblage of plagioclase crystal and matrix powder was removed

78 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx from the crucible to be embedded in epoxy, which is not always possible without changing the contact between the two phases.

Even though it is not possible to quantify the effect of each source of uncertainty individually, the total effect of the uncertainties on the data can be constrained from multiple measurements of concentration profiles within one sample, and the repetition of experiments under the same conditions. Seven profiles were measured in the same plagioclase crystal from experiments KF038 ( T=1160°C;

XAn =0.6; surrounded by gabbro powder) and the experimental conditions were repeated in experiment KF058 (1 profile measured) and KF059 (2 profiles measured). Overall, these ten profiles represent the largest number of measured profiles from one set of nominally identical experimental conditions within this study and are therefore used to constrain the uncertainty in the extracted data.

Pl / Cpx Pl Figure 2.4.5.1 shows a plot of the obtained values of ln K Mg and log DMg for the different profiles measured in experiments KF038, KF058 and KF059 (profiles

Pl number 1, 3, and 5 from KF038 were not used to extract DMg ). The 1σ-uncertainties

Pl Pl σ σ of the fit parameters CMg and DMg ( Pl and D , respectively) were determined by C fit fit non-linear least square fitting of each profile and were propagated into 1σ-

Pl / Cpx Pl uncertainties in ln K Mg and log DMg using the general relationship to propagate errors for a function of the type x = f (u,v) (e.g. Bevington, 1996):

 ∂x  2  ∂x  2 σ 2 ≅ σ 2   + σ 2   . (Eq. 2.5.4.1) x u ∂ v ∂  u v  v u C Pl Pl / Cpx = Mg Application of Eq. 2.5.4.1 to ln K Mg ln Cpx yields: CMg

2 2  1   −1  σ2 ≅σ2   +σ2   ln K Pl  Pl  Cpx  Cpx  (Eq. 2.5.4.2) C fit C  CMg   CMg 

Assuming that σ 2 ~0: C Cpx

79 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

  2 σ 2 = σ 2  1  fit ln, K Pl . (Eq. 2.5.4.3) C fit  Pl   CMg 

Pl = Pl By analogy, application of Eq. 2.5.4.1 to log DMg log( DMg ) gives

2  1  σ 2 ≅ σ 2   (Eq. 2.5.4.4) fit , log D D fit  Pl   .2 3023 DMg 

σ 2 σ 2 The resulting values for fit ln, K and fit , log D are used as error bars for the

Pl / Cpx Pl determined values for ln K Mg and log DMg for each profile (Fig. 2.5.4.1). It can be seen from Fig. 2.5.4.1 that the overall scatter of the data, resulting from the different sources of uncertainty outlined above, is significantly larger than the uncertainty resulting from fitting the data (i.e. the width between the dashed lines in Fig. 2.5.4.1 is larger than the individual error bars of each data point).

Pl / Cpx Pl Fig. 2.5.4.1: Obtained values for ln K Mg and log DMg for the multiple profiles measured in experiments KF038, KF058 and KF059. Error bars are from error propagation of 1σ-uncertainties on Pl Pl the extracted valued for CMg and DMg . Dashed lines illustrate the range of scatter from all individual data points.

Calculation of the standard deviation of the data points would not account for the fact, that there is an additional uncertainty of each data point, that results from σ the fitting. In order to account for this, the overall uncertainty of the data total is

80 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

ν calculated from the sum of the variance of the data scatter and the variance on the weighted mean ν µ :

σ = ν = ν +ν total total scatter µ , (Eq. 2.5.4.5) where ( σ 2 ) ∑ xi / fit , i µ (weighted mean ) = ()σ 2 ∑ /1 fit , i

σ 2 with xi denoting each individual data point and fit , i denoting its individual uncertainty resulting from fitting, ( − µ) ∑ xi ν ()var iance on the data from scatter = scatter N −1 with N=number of profiles, and 1 ν ()var iance on the weighted mean = (e.g. Bevington, 1969). µ ()σ 2 ∑ /1 fit , i

σ Pl / Cpx Following this approach yields 1σ-uncertainties of total =0.038 for ln K Mg and

σ Pl total =0.109 for log DMg .

σ Generally, total could be determined as outlined above for each set of experimental conditions. However, since only one profile was measured for some sets of experimental conditions (e.g. XAn =0.6, T=1100°C, surrounded by just Cpx or

XAn =0.8, T=1150°C, surrounded by gabbro powder), this would result in unreasonably low uncertainties for experimental series with only few data points. σ Thus, total determined for the set of experimental conditions from the largest number of measured profiles (KF038, KF058 and KF059 all carried out at XAn =0.6, σ T=1160°C surrounded by gabbro powder) is used as an estimate for total for the entire dataset of experiments surrounded by gabbro powder and just Cpx. For the experimental series, in which plagioclase was surrounded by Cpx+SiO 2, an

81 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

additional source of uncertainty arises, resulting from the fact that excess SiO 2 seems to increase the number of vacancies in plagioclase (shown by the increase in the [ ]Si 4O8- component; Fig. 2.5.1.2a) and stoichiometry in the plagioclase is no longer maintained (profiles in Ca and Na, but not in Al and Si; Fig. 2.5.1.1a and b). Therefore, a higher uncertainty of the measurement of the concentration of Mg in these plagioclase crystals is expected, which is also seen in the data. Thus, the uncertainty for experiments surrounded by Cpx+SiO 2 is determined separately, σ following the same scheme as outlined for total of the experiments surrounded by gabbro powder. For the experimental series surrounded by Cpx+SiO 2 there are three sets of experimental conditions with the same, largest number of measured σ profiles. Thus total was determined as the average value from the three sets of experimental conditions, where three profiles each were measured, which yields σ Pl / Cpx σ Pl total =0.075 for ln K Mg and total =0.150 for log DMg .

Pl / Cpx Cpx 2.5.5 Variation of K with T, X An , a , and X Mg SiO 2 CaSiO 3 The thermodynamically derived Equation 2.2.1.11 (under the assumption that Mg only dissolves into plagioclase as a CaMgSi3O8-component) implies that

Pl / Cpx Cpx ln K is expected to linearly depend on 1/ T, XAn , ln a , and ln X . The same Mg SiO 2 CaSiO 3 equation derived assuming that Mg dissolves into plagioclase as a MgAl 2Si 2O8-

Pl / Cpx component (Eq. 2.2.1.17) implies the same dependence for ln K Mg on 1/ T, XAn , and ln a , but an additional dependence on ln a and no dependence on SiO 2 Al 2O3 ln X Cpx . Since a was kept constant ( a =1) for all experimental series, this CaSiO 3 Al 2O3 Al 2O3 study does not allow us to constrain the effect of a and thus Eqs. 2.2.1.11 and Al 2O3 2.2.1.17 only differ in that Eq. 2.2.1.11 additionally implies a dependence of ln K Pl / Cpx on X Cpx . The thermodynamically expected trends for ln K Pl / Cpx as a Mg CaSiO 3 Mg function of T, XAn , and a (as implied by both equations) are clearly seen in the SiO 2

Pl / Cpx experimental data. Figure 2.5.5.1 shows a linear decrease in ln K Mg with

82 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx increasing 1/ T (=decreasing temperature) for all three experimental series

(plagioclase surrounded by (a) just Cpx, (b) Cpx+SiO 2 and (c) gabbro powder) for

Pl / Cpx constant XAn =0.6. The plot also shows that the data for ln K Mg are systematically the highest for experiments, in which plagioclase was surrounded by Cpx+SiO 2.

Pl / Cpx Fig. 2.5.5.1: Experimentally determined values for ln K Mg plotted against 1/T for the experimental series surrounded by just Cpx (green), Cpx+SiO 2 (pink) and gabbro powder (blue) for constant XAn =0.6. Open symbols represent individual measured profiles and closed symbols are average values for one set of experimental conditions. All experimental series show a linear decrease Pl / Cpx Pl / Cpx of ln K Mg with decreasing temperature and ln K Mg for the different experimental series increases with ln a , i.e. at a constant T, the difference between the experimental series is given by SiO 2 the difference in ln a . Y-error bars on the average values are 2σ uncertainties (±0.076 for SiO 2 experiments surrounded by gabbro powder and experiments surrounded by just Cpx and ±0.15 for experiments surrounded by Cpx+SiO2, respectively) determined as outlined in section 2.5.4.

Pl / Cpx Pl / Cpx The effect of XAn on ln K Mg is shown in Fig. 2.5.5.2, where ln K Mg is plotted as a function of plagioclase compositions for the following data sets: (i)

83 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

surrounded by gabbro powder at 1150°C (for XAn ~0.5 to 0.8), (ii) surrounded by diopside powder at 1150°C (for XAn ~0.5 to 0.68) and (iii) surrounded by gabbro powder at 1130°C (for XAn ~0.5 to 0.65). In general, all three data sets show a similar

Pl / Cpx linear increase in ln K Mg with increasing XAn .

Pl / Cpx Fig. 2.5.5.2: Results for ln K Mg for experimental runs with different plagioclase composition at 1150°C and 1130°C. Y-error bars on the average values are 2σ uncertainties (±0.076) determined as outlined in section 2.5.4.

The silica activity is known for the experimental series in which plagioclase is surrounded by Cpx+SiO 2, because a is fixed to 1 due to the presence of excess SiO 2

SiO 2. For experimental runs in which plagioclase was surrounded by gabbro powder, a is buffered by the coexistence of olivine and orthopyroxene in the rock SiO 2 assemblage by the reaction Mg 2SiO 4 + SiO 2 = 2MgSiO 3 (Carmichael, 1970), which allows a to be determined as: SiO 2

84 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

∆G 0 log a = r . SiO 2 2.303 RT This yields a =0.549, 0.552 and 0.553 for the respective experimental SiO 2 ∆ 0 temperatures of 1130°C, 1150°C and 1160°C (at which Gr was calculated using

Pl / Cpx the dataset of Ghiorso, 1995). Figure 2.5.5.3 shows a direct comparison of ln K Mg from experiments, in which plagioclase was surrounded by Cpx+SiO 2, and experiments, in which plagioclase was surrounded by gabbro powder at constant

Pl / Cpx T= 1150°C and XAn =0.6. The difference in ln K Mg for plagioclase surrounded by

Pl / Cpx Cpx+SiO 2 (average ln K Mg =-4.11) and for plagioclase surrounded by gabbro

Pl / Cpx powder (average ln K Mg =-4.59) corresponds reasonably well to the difference in ln a of the two experimental series (ln(0.552)=0.6 and ln(1)=0). Figure 2.5.5.3 SiO 2

Pl / Cpx shows that ln K Mg increases with ln aSiO 2 with a factor of 0.8 (solid black line in Fig. 2.5.5.3). However, since a slope of 1 (grey dashed line in Fig. 2.5.5.3) would be within the scatter of the data, the experimental data is in good agreement with the thermodynamically derived dependence of ln K Pl / Cpx on ln a . Mg SiO 2

85 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Pl / Cpx Fig. 2.5.5.3: Comparison of ln K Mg from experiments surrounded by gabbro powder (dark blue; a =0.552) and surrounded by Cpx+SiO 2 (pink; a =1) plotted against their respective SiO 2 SiO 2 ln a -values at T=1150°C and XAn =0.6. Open symbols are from individual experiments and SiO 2 closed symbols show the respective average values. The silica activity for the experimental series Pl / Cpx surrounded by Cpx (green) can be determined from the linear relationship between ln K Mg and ln a (see upcoming text for explanation). The solid black line shows a linear through the SiO 2 individual experiments surrounded by gabbro powder and those surrounded by Cpx+SiO2. The grey dashed line shows a linear with a slope of 1, determined using the results of multiple regression (using Eq. 2.2.1.19) through all data from the experimental series surrounded by gabbro powder and those surrounded by Cpx+SiO 2 (see text for further explanation). Y-error bars are 2σ uncertainties, determined as outlined in section 2.5.4.

As shown in Fig. 2.5.5.1, 2.5.5.2 and 2.5.5.3, the data is qualitatively well

Pl / Cpx described by the thermodynamically derived linear dependence of ln K Mg on 1/ T,

XAn , and ln a . For the assumption made for reaction (1b), that all Mg dissolves in SiO 2

Pl / Cpx plagioclase as a CaMgSi 3O8-component, an additional linear dependence of ln K Mg on ln X Cpx would be expected (see Eq. 2.2.1.11). The mole fraction of Ca in CaSiO 3

86 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx clinopyroxene ( X Cpx ) is calculated from the microprobe analysis of the two CaSiO 3 different clinopyroxenes used for the different experimental series as follows: X (CaSiO ) X Cpx = 3 (Eq. 2.5.5.1) CaSiO 3 + + + X (CaSiO 3 ) X (MgSiO 3 ) X (FeSiO 3 ) X (Al 2O3 ) where

X(CaSiO 3)=X(Ca)*

X(MgSiO 3)=X(Mg)*

X(FeSiO 3)=X(Fe 2+ )* , i.e. all Fe was calculated as Fe 2+

X(Al 2O3)=0.5 X(Al)* (*all calculated as cation per formula unit, based on 6 oxygens)

Application of Eq. 2.5.5.1 to the respective clinopyroxene compositions gives: X Cpx (gabbroic Cpx) = 0.430, used for the experimental series in which CaSiO 3 plagioclase was surrounded by gabbro powder, and X Cpx (diopside) = 0.484, used for the experimental series in which CaSiO 3

plagioclase was surrounded by just Cpx and those surrounded by Cpx+SiO 2.

Pl / Cpx Therefore, for a given T and XAn , the theoretical difference in ln K Mg due to different a and X Cpx between the experimental series surrounded by gabbro SiO 2 CaSiO 3 powder and the one surrounded by Cpx+SiO 2 can be determined as ∆ = ∆(ln a )+ ∆(ln X Cpx ). At a temperature of 1150°C, this yields theo SiO 2 CaSiO 3 ∆ = ( − )+ ( − ) = + = theo ln( )1 ln( .0 552 ln( .0 484 ) ln( .0 430 59.0 12.0 71.0 . Yet, the

Pl / Cpx experimentally determined difference between the average values of ln K Mg of ∆ these two experimental series for T=1150°C and XAn =0.6 is exp =0.48 (Fig. 2.5.5.3). Possible reasons for this discrepancy will be discussed in Section 2.5.6.

Pl / Cpx To quantify the effect of T and XAn on ln K Mg , Eq. 2.2.1.11 and 2.2.1.17 were rearranged to a linear form (Eq. 2.2.1.13 and 2.2.1.19) and the independent

87 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx parameters A’, B and C were determined by weighted multiple regression (using = σ 2 w 1/( 1 total ) as weighting factors). In a first round, only data from the experimental series surrounded by Cpx+SiO 2 and those surrounded by gabbro powder were used, where the values for a are known. The resulting parameters SiO 2 (A’ =-76837±14475, B=18647±1487 and C=12±10 using Eq. 2.2.1.17 and A’ =- 57017±14475, B=20301±1487 and C=5±10 using Eq. 2.2.1.11, i.e. accounting for the difference in X Cpx ) were used to quantify ln K Pl / Cpx as a function of ln a (for CaSiO 3 Mg SiO 2

Pl / Cpx constant XAn =0.6 and T=1150°C). This gives ln K = 0.1 ⋅ ln a − 02.4 , not Mg SiO 2 accounting for X Cpx (grey dashed line in Fig. 2.5.5.3) and CaSiO 3 ln K Pl / Cpx = 2.1 ⋅ ln a − 93.3 , accounting for X Cpx . Now a of the experimental Mg SiO 2 CaSiO 3 SiO 2 series surrounded by just Cpx can be determined from this linear relationship, using

Pl / Cpx the average value of the experimentally determined values for ln K Mg for plagioclase surrounded by just Cpx. This yields a =0.616 (ln a =-0.48; Fig. SiO 2 SiO 2 2.5.5.3), not accounting for X Cpx and a =0.620, accounting for X Cpx . CaSiO 3 SiO 2 CaSiO 3

After this, the parameters A’ , B and C were then re-determined, this time using the data from all experimental series (under the assumption that a for SiO 2 experiments surrounded by just Cpx is 0.616 and 0.620, respectively, dependent on whether X Cpx is accounted for or not). This yields A’ =-76644±6780, CaSiO 3 B=16913±1289 and C=13±4, not accounting for X Cpx and A’ =-71014±6780, CaSiO 3 B=18514±1289 and C=15±4, accounting for X Cpx . CaSiO 3

Summarizing, under the assumption that Mg dissolves into plagioclase as a

Pl / Cpx MgAl 2Si 2O8-component, ln K can be determined as a function of T, XAn and a Mg SiO 2 (for constant a =1): Al 2O3 A' C B ln K Pl / Cpx = + + X + ln a (Eq. 2.5.5.2) Mg RT R RT An SiO 2

88 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Under the assumption that Mg dissolves into plagioclase as a CaMgSi 3O8- component, ln K Pl / Cpx is expected to additionally depend on ln X Cpx : Mg CaSiO 3 A' C B ln K Pl / Cpx = + + X + ln a + ln X Cpx (Eq. 2.5.5.3) Mg RT R RT An SiO 2 CaSiO 3

Using the parameters A’ , B and C, determined from multiple regression (separately for Eq. 2.5.5.2 and 2.5.5.3) yields: 1 16913 [J/mol ] ln K Pl / Cpx = -9219 []K + 6.1 + X + ln a Mg T RT An SiO 2 (Eq. 2.5.5.4) and 1 18514 [J/mol ] ln K Pl / Cpx = -8542 []K + 8.1 + X + ln a + ln X Cpx Mg T RT An SiO 2 CaSiO 3 (Eq. 2.5.5.5)

Correlation coefficients R2 for the correlation between the experimental data

Pl / Cpx Pl / Cpx on ln K Mg and the calculated data for ln K Mg using Eq. 2.5.5.4 and Eq.2.5.5.5 are R2=0.94 and R2=0.90, respectively. Figures 2.5.5.4a and b show a comparison between the averages of the experimentally determined values and the calculated values using Eq. 2.5.5.4 (solid lines) and Eq. 2.5.5.5 (dashed lines).

89 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Fig. 2.5.5.4: Comparison between the averages of the experimentally determined values and the calculated values using Eq. 2.5.5.4 (solid lines) and Eq. 2.5.5.5. (dashed lines). (a) shows the linear dependence of ln K Pl / Cpx on 1/ T for the different experimental series (i.e. different a ) at constant Mg SiO 2 Pl / Cpx XAn =0.6 and (b) shows the linear dependence of ln K Mg on XAn (for 1150°C and 1130°C).

90 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Pl / Cpx 2.5.6 Discussion of the experimental results for K Mg Figure 2.5.6.1 shows how the data of this study relate to previously determined data for the partitioning of Mg between plagioclase clinopyroxene grown from a basaltic melt for different temperatures (Walker et al., 1979; Sack et al., 1987; Tormey et al., 1987; Libourel et al., 1989; Grove & Juster, 1989; Shi & Libourel, 1991; Shi, 1992; Soulard et al., 1992; Yang et al., 1996; Chalot-Prat et al.,

Pl / Cpx 2010). None of these previous studies was designed to determine K Mg , so no special care was taken regarding the measurement of Mg-concentrations in plagioclase. Additionally, various starting compositions were used, leading to very different XAn -contents in the plagioclase crystals grown from the melt. As shown

Pl / Cpx above, K Mg increases with increasing XAn in the plagioclase. Therefore, for better

Pl / Cpx comparison, the compositional dependence on K Mg determined in this study was

Pl / Cpx used, to normalize the derived K Mg of the previous studies to XAn =0.6. These normalized results are compared to our data determined for XAn =0.6. In general, all

Pl / Cpx previous data show a general decrease of K Mg with decreasing temperature as

Pl / Cpx was also observed for K Mg determined by this study. The partition coefficient

Pl / Cpx K Mg for experiments surrounded by gabbro powder and experiments surrounded by just Cpx powder from this study show rather lower Mg- concentrations in plagioclase than from previous studies. In the latter, plagioclase was surrounded by a melt phase with up to 60 wt% SiO 2 (e.g. Chalot-Prat et al., 2010), which will lead to increased a in these systems and hence (as shown SiO 2 above) to increased Mg-concentrations in plagioclase. Data from this study from experiments surrounded by Cpx+SiO 2 fall more in a medium range of all data. Since a is already 1 for this set of data, no further increase in a can be responsible SiO 2 SiO 2 for some of the data points from previous studies showing even higher values. However, those previous studies were not designed to precisely measure Mg in plagioclase. Additionally, the melt surrounding plagioclase in these studies has MgO- contents up to 13.5 wt% (e.g. Chalot-Prat et al., 2010) and an average value of

91 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

5.7 wt% MgO, hence only small contaminations by the melt during measurement of the plagioclase could lead to significantly increased Mg-contents in plagioclase.

Pl / Cpx Pl / Cpx Fig. 2.5.6.1: Comparison of ln K Mg from previous studies with ln K Mg determined in this study, whereas all data is normalized to XAn =0.6 using the compositional dependence of plagioclase Pl / Cpx composition on ln K Mg derived in this study. TS=this study

Pl / Cpx The isothermal data on the XAn -dependence of K Mg of this study show a positive linear relation for all experimental series (Fig. 2.5.5.2 and 2.5.5.4b). This trend is opposite to the reported trend of Bindeman et al. (1998) for the XAn - dependence of the Mg-partitioning between plagioclase and melt. However, the experiments used by Bindeman et al. (1998) were not carried out under isothermal conditions, but XAn in plagioclase is a function of temperature. Since the

Pl / Cpx temperature-dependence of K Mg determined in the present study suggests that

92 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Pl / melt the partition coefficient of Mg between plagioclase and melt K Mg may also depend on temperature, it is crucial to determine the XAn -dependence isothermally.

Different equations for the behavior of Mg partitioning between plagioclase and clinopyroxene were derived thermodynamically under the assumption that Mg either dissolves into plagioclase as a CaMgSi 3O8–component (Eq. 2.2.1.11) or as a

MgAl 2Si 2O8-component (2.2.1.17). Both equations predict linear dependences of

Pl / Cpx ln K on 1/ T, XAn and ln a , which is actually found in the experimental data Mg SiO 2 (Fig. 2.5.5.1, 2.5.5.2, and 2.5.5.3). Additionally, Eq. 2.2.1.11 predicts a linear dependence of ln K Pl / Cpx on ln X Cpx . This is not the case for Eq. 2.2.1.17, which Mg CaSiO 3 instead predicts linear dependence of ln K Pl / Cpx on ln a . The experimental setup Mg Al 2O3 of this study does not allow accounting for effect of a , but it is possible to Al 2O3 account for the effect of different X Cpx . Fitting of the experimental data shows CaSiO 3 good agreement in both cases (based on Eq. 2.2.1.11 as well as on Eq. 2.2.1.17), but fits are better based on Eq. 2.2.1.17 (where X Cpx is not accounted for; Fig. 2.5.5.4a CaSiO 3 ∆ ∆ and b). This was already indicated by comparison of theo and exp of the experimental series surrounded by gabbro powder and the one surrounded by

Cpx+SiO 2 at T=1150°C and XAn =0.6 (see section 2.5.5.) and may suggest that Mg dissolves into plagioclase as a MgAl 2Si 2O8-component. On the other hand, calculation of plagioclase end-members based on the microprobe analysis of the measured concentration profiles in plagioclase after the experiments shows a larger abundance of a CaMgSi 3O8–component (Fig. 2.5.1.2a and b). However, Eq. 2.2.1.11 was derived under certain assumptions, e.g. that the activity coefficients for the

Cpx Cpx (CaSiO 3)- and (MgSiO 3)-component in clinopyroxene ( ln γ and ln γ ) are CaSiO 3 MgSiO 3 constant. This might not be true and there may be a temperature-dependence of ln γ Cpx and ln γ Cpx , which compensates the effect of X Cpx . Based on the CaSiO 3 MgSiO 3 CaSiO 3 experimental results of this study, it is therefore not possible to unambiguously determine how Mg dissolves into plagioclase. The thermodynamic derivation of the

93 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Mg-partitioning between plagioclase and clinopyroxene carried out in this study suggests, however, a different behavior with a of the two possible sites for Mg in Al 2O3 plagioclase. Thus, investigation of K Pl / Cpx as a function of a might provide more Mg Al 2O3 insights towards the issue of site-occupancy of Mg in plagioclase (see also Chapter 4).

2.5.7 A new thermometer based on the exchange of Mg between plagioclase and clinopyroxene

Pl / Cpx The experimental results for K Mg show, that the exchange of Mg between plagioclase and clinopyroxene is very sensitive to changes in temperature. Therefore, measured concentrations of Mg in plagioclase and clinopyroxene in equilibrium with each other can be used to determine their equilibrium temperature. The results of this study also constrained, how the partitioning of Mg between plagioclase and clinopyroxene depends on XAn and a (Eq. 2.5.5.3 and SiO 2 2.5.5.4), and therefore these parameters should be accounted for when calculating the equilibrium-temperature. Since the experimental data is better fitted based on Eq. 2.5.5.4, which does not account for X Cpx , this equation is rearranged to CaSiO 3

Pl Cpx determine the temperature T as a function of X An , a , C and C : SiO 2 Mg Mg [ ] − []+ 16913 J/mol 9219 K X An T[]K = R (Eq. 2.5.7.1) C Pl ln Mg − 6.1 − ln a Cpx SiO 2 CMg

Using this equation, the experimental temperatures can be reproduced within ±20°C. The calibration of the thermometer is based on a temperature range of T=1100 to 1200°C, XAn =0.5 to 0.8 and a =0.549 to 1. SiO 2

94 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Pl 2.5.8 Variations in D with T, X An and a Mg SiO 2

Pl The experimental results on DMg are summarized in Table 2.5.3.1. Figure

Pl 2.5.8.1 shows that log DMg (for constant XAn =0.6) follows Arrhenian behaviour for all experimental series, and that D Pl increases for increasing a . Mg SiO 2

Pl Fig. 2.5.8.1: Experimental results on log DMg for constant XAn =0.6 plotted against 1/ T showing Arrhenian behaviour for all experimental series, and D Pl is increased for higher a . Y-error bars Mg SiO 2 2σ-uncertainties as determined in section 2.5.4 (± 0.2 for experiments surrounded by just Cpx and experiments surrounded by gabbro powder and ± 0.3 for experiments surrounded by Cpx+SiO 2).

Pl The effect of plagioclase composition on DMg was determined in the same

Pl / Cpx three experimental series as outlined for the compositional dependence of K Mg

95 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx and is shown for constant T=1150°C in Fig. 2.5.8.2. A strong compositional dependence is not observed for any of the three experimental series.

Pl Fig. 2.5.8.2: Experimental results on DMg for plagioclase compositions XAn=0.5-0.67 at a constant temperature of 1150°C in comparison to calculated values for 1150°C using the data from LaTourette and Wasserburg (1998) and Costa et al. (2003).

The effect of a on the diffusion coefficient can be incorporated as: SiO 2

 − E  m D Pl = D ⋅ exp   ⋅ ()a , (Eq. 2.5.8.1) Mg 0  RT  SiO 2 where m is related to the point defect chemistry within the solid (for details see section 2.5.9 as well as Dohmen and Chakraborty, 2007 and Costa et al., 2008).

To quantify the effect of T and a on the diffusion coefficient, Eq. 2.5.8.1 SiO 2 was rearranged to a linear form: B log D Pl = A + D + m ⋅ log( a ) (Eq. 2.5.8.2) Mg D T SiO 2

96 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

and AD, BD and m were determined from weighted multiple regression (using = σ 2 w 1/( 1 total ) as weighting factors) of all data under the assumption that a =0.616 for experiments in which plagioclase was surrounded by just Cpx as SiO 2

Pl / Cpx determined from the results on K Mg . This yields AD=-2.66±1.59, BD=-18550±2290 and m=2.6±0.3. Therefore, D Pl as a function of T and a can be determined as: Mg SiO 2

−  − 355 (± 44 ) [kJ/mol ] 6.2 ()± 3.0 D Pl [m 2 /s ]= 2.2 ()± 1.8 ⋅10 3 [m 2 /s ]⋅ exp   ⋅ ()a Mg  RT  SiO 2 (Eq. 2.5.8.3)

Borinski et al. (in prep.) determined the self diffusion coefficient of Mg in plagioclase over a large temperature range of 750 to 1285°C and obtained an activation energy E=321 kJ/mol. The experimental data obtained in the present study was fitted using the activation energy E of Borinski et al (in prep.), giving AD=-

3.91, BD=-16764 (taken from Borinski et al., in prep.) and m=2.6, (since E was assumed to be an exact value in this case, it is not reasonable to give uncertainties on the other parameters here). Using these parameters yields:

−  − 321 [kJ/mol ] 6.2 D Pl [m 2 /s ]= 25.1 ⋅10 4 [m 2 /s ]⋅ exp   ⋅ ()a Mg  RT  SiO 2 (Eq. 2.5.8.4)

Pl Figure 2.5.8.3 shows a comparison of the experimentally determined log DMg and the fits using Eq. 2.5.8.3 (fit 1) and Eq. 2.5.8.4 (fit 2).

97 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Pl Fig. 2.5.8.3: Average values of experimentally determined log DMg vs. 1/ T in comparison with the calculated values using Eq. 2.5.8.3 (solid lines) and Eq. 2.5.8.4 (dotted lines), which result from fitting the experimental data. Y-error bars 2σ-uncertainties as determined in section 2.5.4 (± 0.2 for experiments surrounded by just Cpx and experiments surrounded by gabbro powder and ± 0.3 for experiments surrounded by Cpx+SiO 2).

Pl 2.5.9 Discussion of the experimental results for DMg

Pl The diffusion coefficient DMg determined from experiments in which plagioclase was surrounded by just Cpx, and experiments in which plagioclase was surrounded by gabbro powder for XAn =0.6 and T=1100 to 1200°C match very well with an extrapolation of the data derived by LaTourette and Wasserburg (1998) for

XAn =0.95 and T=1200 to 1400°C down to the temperature range of this study (Fig.

Pl 2.5.9.1). A significant dependence of DMg on XAn is not observed in this study (Fig.

2.5.8.2), covering a range of XAn =0.5 to 0.65. The isothermal data (for T=1150°C) presented here match very well with the data from LaTourette and Wasserburg

98 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

(1998) for a plagioclase composition of XAn =0.95, when extrapolated to the same

Pl temperature (Fig. 2.5.8.2 and 2.5.9.1), supporting the lack of a dependence of DMg on

XAn for a broader range of plagioclase compositions. Borinski et al. (in prep.) investigated the self diffusion coefficient of Mg in plagioclase over a broad range of plagioclase compositions ( XAn =0.12 to 0.95) and temperatures (750 to 1285°C), and they also observe no compositional dependence. Since their data rely on a much broader temperature range, they are able to put very good constraints on the activation energy E. Thus, Eq. 2.5.8.4, based on fitting the experimental data of the present study using the activation energy E of Borinski et al. (in prep.), is recommended to determine D Pl as a function of T and a . Mg SiO 2

The difference between the data of Borinski et al. (in prep.) and the determined D Pl of this study may possibly be explained by a difference in a . Mg SiO 2 This study implies a strong dependence of D Pl on a , which was not accounted Mg SiO 2 for in the study of Borinski et al. (in prep.). However, Eq. 2.5.8.2 can be rearranged to determine log a as a function of T and D Pl : SiO 2 Mg B Pl − − D log DMg AD log( a ) = T (Eq. 2.5.9.1) SiO 2 m

Combining Eq. 2.5.9.1 with the determined parameters AD, BD and m, and the

Pl value for DMg of Borinski et al. (in prep) for T=1200°C to get an estimate for the a -conditions in the experiments of Borkinski et al. (in prep.) yields a =0.34. SiO 2 SiO 2 This value is between an Ol+Opx-buffer and an Ab+Ne-buffer and thus within the stability field of feldspar (e.g. Carmichael, 1970). Therefore, the difference between the data of this study and the data of Borinski et al. (in prep.) may be due to a difference in a . SiO 2

99 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Pl Fig. 2.5.9.1: Plot of log DMg vs. inverse temperature to compare the results of this study with the Pl determined DMg of other studies. The symbols indicate the averages of individual experiments with their respective error bars of this study (coloured symbols), the study of Borinski et al. (in prep, black circles) and the study of La Tourette and Wasserburg (1998, grey stars). Coloured solid lines are calculated based on Eq. 2.5.8.3, coloured dashed lines are calculated based on Eq. 2.5.8.4. B = Borinski et al. (in prep); LTW (1998) b = La Tourette and Wasserburg (1998), ║b; LTW (1998) c = La Tourette and Wasserburg (1998), ║c.

Diffusion of Mg in plagioclase is significantly faster for experiments with excess SiO 2. Additionally, plagioclase from these experiments show a distinct increase of a calculated [ ]Si 4O8-endmember towards the rim of the plagioclase. Therefore, it is concluded, that an increased a enhances the formation of a SiO 2

[ ]Si 4O8-type vacancy in plagioclase, which then enhances diffusion.

100 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Relationship between diffusion of Mg in plagioclase and point defects: For diffusion to occur within a solid it is necessary to have point defects (e.g., see Flynn, 1972 for a discussion or Costa et al., 2008 for a more recent review), such as vacancies (e.g., an atom missing in a crystallographic site). The formation of an

[ ]Si 4O8-type vacancy is suggested based on the calculation of possible plagioclase end-members from the microprobe analysis of the plagioclase crystals after the experiments in which plagioclase was surrounded by Cpx+SiO 2. Such a [ ]Si 4O8-type vacancy represents the lack of an atom on the metal site in plagioclase, which is charge-balanced by the substitution of an additional Si 4+ -atom for an Al 3+ -atom in an tetrahedral-site. Point defects (like vacancies) can be treated as quasi-chemical species having a chemical potential like any other solid solution component. Hence, concentrations of the individual point defects depend, in addition to P and T, on the activities of the thermodynamic components (e.g. Kröger and Vink, 1965). If diffusion of an element i occurs by a vacancy mechanism (as suggested here for the diffusion of Mg occurring along the presence of a [ ]Si 4O8-type vacancy), the diffusion coefficient of element i will be a function of the concentration of that vacancy, XV, and can be written as: = ⋅ ⋅ ⋅ 2 Di fi X V wV l , (Eq. 2.5.9.2) where fi is the correlation factor of the diffusion of element i, wV is the jump frequency of the vacancy and l is the jump distance (e.g. Costa et al., 2008). While fi and l can be treated as constants for a given diffusion mechanism, wV is a function of P and T:  − ∆H 0 + P∆V 0  = 0  m m  wV wV exp   (Eq. 2.5.9.3)  RT 

∆ 0 ∆ 0 with H m and Vm denoting the migration enthalpy and migration volume of the standard state, respectively.

The molar fraction of the vacancy XV itself is a function of P and T, but also the activities of the different components of the system. So, if n is the number of thermodynamic components of a crystal, then:

XV=f(P, T, a 1, a 2, …, a n-1) (Eq.2.5.9.4)

101 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

The observed dependence of D Pl on a may now be discussed for a Mg SiO 2 possible formation mechanism of a [ ]Si 4O8-type vacancy, using the Kröger-Vink notation (Kröger & Vink, 1965). In this notation, a [ ]Si 4O8-type vacancy has to be written differently for the albite- and anorthite component in plagioclase: ' + • '' + • VM Si T ( Al ) in albite and VM 2Si T ( Al ) in anorthite (see legend for explanation of symbols). Thus, the two different end-members need to be discussed separately: + x + x = + ' + • Ab: 4SiO 2 Al T Na M NaAlSi 3O8 VM Si T ( Al ) (Eq. 2.5.9.5a)

+ x + x = + '' + • An: 4SiO 2 2Al T Ca M CaAl 2 Si 2O8 VM 2Si T ( Al ) (Eq. 2.5.9.5b) where

x Al T Al-atom on a tetrahedral site, charge balanced by its surrounding

x Na M Na-atom on a metal site, charged balanced by its surrounding

x Ca M Ca-atom on a metal site, charged balanced by its surrounding

' VM vacancy on the metal site in albite (i.e. 1 negative charge)

'' VM vacancy on the metal site in anorthite (i.e. 2 negative charges)

• 4+ 3+ Si T ( Al ) additional Si on a tetrahedral site, substituting for an Al -atom (i.e. 1 positive charge)

In a real experiment, equilibration of reaction 2.5.9.5a and b requires that Al, Na and Ca have to be supplied from the surface of the plagioclase crystal itself, but still are assumed to be charge balanced by their crystallographic surrounding.

In equilibrium and at constant P and T, an equilibrium constant Keq can be formulated, by analogy to any other chemical reaction, as:

Pl 0 − ∆ a ' a • aNaAlSi O  G  VM Si T ( Al ) 3 8 K = exp   = eq   ()4  RT  aSiO a x a x Ab: 2 Al T Na M Pl γ γ γ Pl X ' X • X Ab ' • Ab = 1 ⋅ VM Si T ( Al ) ⋅ VM Si T ( Al ) 4 γ γ ()a X x X x x x SiO 2 Al T Na M Al T Na M (Eq. 2.5.9.6a)

102 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

( )2 Pl 0 a '' a • a  − ∆G  V Si CaAl 2Si 2O8 K = exp   = M T ( Al ) eq   ()4 ()2  RT  a a x a x SiO 2 Al Ca An: T M ( )2 Pl γ (γ )2 γ Pl X '' X • X '' • 1 V Si An V Si An = ⋅ M T ( Al ) ⋅ M T ( Al ) ()4 ()2 ()γ 2 γ aSiO X x X x x x 2 Al T Ca M Al T Ca M (Eq. 2.5.9.6b)

Because the point defects are highly diluted, at constant P and T and for a given XAn , the activity coefficients can be assumed to be constant (Henry’s law) and

are combined to a factor Cγ . Additionally X x and X x can be assumed to be 1, in Na M Ca M

albite and anorthite respectively, and X x can be assumed to be ~0.25 in albite and Al T ~0.5 in anorthite. which leads to

Pl 0 − ∆ X ' X • X Ab  G  1 VM Si T ( Al ) Ab: =   = ⋅ K eq exp   4 Cγa  RT  ()a 25.0 SiO 2 (Eq. 2.5.9.7a) ( )2 Pl 0 X '' X • X  − ∆G  1 V Si An =   = ⋅ M T ( Al ) An: K eq exp   4 2 Cγb .  RT  ()a ()5.0 SiO 2 (Eq. 2.5.9.7b)

To maintain charge balance and create a neutral []Si 4O8-component, the molar fractions of vacancies on the metal site and on the tetrahedral site have to be related as follows:

Ab: X ' = X • VM Si T ( Al )

An: X '' =2 X • VM Si T ( Al ) which gives:

2 Pl 0 (X ) X  − ∆G  V ' Ab =   = M Ab: K eq exp   4 Cγa (Eq. 2.5.9.8a)  RT  25.0 ()a SiO 2

103 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

3 Pl 0 ( ) 25.0 X '' X  − ∆G  V An =   = M An: K eq exp   4 Cγb (Eq. 2.5.9.8b)  RT  25.0 ()a SiO 2

Solving for the concentration of vacancies on the metal site XV yields:

0 ( )2  − ∆G  aSiO 5.0 =   2 Ab: X ' exp   5.0 5.0 (Eq. 2.5.9.9a) VM 2RT ()Pl ()   X Ab Cγa

0 ( ) 3/4  − ∆G  aSiO 1 =   2 An: X '' exp   3/1 3/1 (Eq. 2.5.9.9b) VM 3RT ()Pl ()   X An Cγb

Using ∆G 0 = ∆H 0 − T∆S 0 + P∆V 0 and defining the quantities of formation ∆ = ∆ 0 ∆ = ∆ 0 enthalpy , formation entropy and formation volume as H f H /n, S f S /n ∆ = ∆ 0 and V f V /n, where n=2 for albite and n=3 for anorthite gives:    ∆ + ∆  ( )2 S H P V aSiO 5.0 =  f  − f f  2 Ab: X ' exp exp 5.0 5.0 VM  R   RT  ()Pl ()     X Ab Cγa (Eq. 2.5.9.10a) ∆ ∆ + ∆ ( ) 3/4  S   H P V  aSiO 1 = f f f 2 X '' exp   exp   An: V     3/1 3/1 M R RT ()Pl ()     X An Cγb (Eq. 2.5.9.10b)

Combining Eq. 2.5.9.10a and b with Eq. 2.5.9.2 and 2.5.9.3 allows obtaining final equations for the diffusion coefficient of Mg in plagioclase as a function of P, T and XAn :

 (∆H + ∆H )+ P(∆V + ∆V ) (a )2 Pl = 0 − f m f m  SiO 2 Ab: DMg DAb exp  RT  ()− Pl 5.0   1 X An (Eq. 2.5.9.11a)

 (∆H + ∆H )+ P(∆V + ∆V ) (a ) 3/4 Pl = 0 − f m f m  SiO 2 An: DMg DAn exp  RT  ()Pl 3/1   X An (Eq. 2.5.9.11b)

104 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Since macroscopic diffusion coefficient measurements as a function of temperature yield combined values of energies and volumes of migration and formation these can be combined to give: ( )2  E  aSiO Pl = 0 − 2 Ab: DMg DAb exp   (Eq. 2.5.9.12a)  RT  ()− Pl 5.0 1 X An ( ) 3/4  E  aSiO Pl = 0 − 2 An: DMg DAn exp   (Eq. 2.5.9.12a)  RT  ()Pl 3/1 X An

The plagioclase composition in the experiments was a solid solution of the two end-members, therefore it is only possible to conclude here, that the factor m, that describes the dependence of D Pl on a has to be a positive number between Mg SiO 2 4/3 and 2. The experimentally determined value of m, however, is 2.6. Repeating the calculations done in Eq. 2.5.9.6 to Eq. 2.5.9.12 under the assumption that the vacancy on the metal site and the additional Si in a tetrahedral Al-site are associated { ' + • } { '' + • } as VM Si T ( Al ) in albite and VM 2Si T ( Al ) in anorthite gives a factor of m=4, indicating that some of the defects may be associated with each other. Additionally,

Pl the derived dependence of DMg on XAn is small (power of 1/3), which is also obtained from the experiments (see Fig. 2.5.8.2).

2.6 Conclusions

The exchange of Mg between plagioclase and clinopyroxene was investigated in an experimental study in the temperature range T=1050 to 1200°C, for a compositional range of XAn =0.12 to 0.95 and at silica activities of a ~0.55 and 1 at SiO 2 constant a =1. At temperatures below 1100°C, an exchange of Mg between Al 2O3 plagioclase and different Cpx-bearing matrixes could not be detected. The calculation of possible Mg-bearing plagioclase end-members for the experimental

105 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

data suggests preferred site occupancy of Mg in the tetrahedral site as a CaMgSi 3O8- component. The partition coefficient of Mg between plagioclase and clinopyroxene

Pl / Cpx Pl K Mg and the diffusion coefficient of Mg in plagioclase DMg as a function of T, XAn and a were determined in a temperature range of T=1100 to 1200°C, a SiO 2 compositional range of XAn =0.5 to 0.8 and at a ~0.55 and 1 (at constant a =1) SiO 2 Al 2O3 with the following results:

Pl / Cpx (1) K Mg is strongly temperature-sensitive and decreases with decreasing temperature.

Pl / Cpx (2) K Mg increases with increasing XAn in plagioclase.

(3) K Pl / Cpx increases with increasing a . Mg SiO 2

Pl (4) DMg for T=1100 to 1200°C and XAn =0.6 from this study matches very well with an extrapolation of the data of LaTourette and Wasserburg (1998) for

T=1200 to 1400°C and XAn =0.95 and is consistent with the data of Borinski et

al. (in prep.) for XAn =0.12 to 0.95 and T=750 to 1285°.

Pl (5) A significant dependence of DMg on XAn in plagioclase is not observed.

(6) D Pl dependents on a and increases by approximately one order of Mg SiO 2 magnitude from a =0.55-1. This observation is consistent with an SiO 2

observed increase in a [ ]Si 4O8-component in plagioclase for increased a , SiO 2 leading to the conclusion that higher a in the systems leads to the SiO 2

formation of [ ]Si 4O8-type vacancies in plagioclase, which enhance diffusion of Mg in plagioclase.

The new experimental data allow a new geothermometer to be calibrated for the exchange of Mg between plagioclase and clinopyroxene, which accounts for differences in plagioclase composition and in the silica activity of the system and may be applied to a wide range of plagioclase and clinopyroxene bearing rocks. The

106 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

experimental data also allow for a quantification of the role of plagioclase XAn

Pl content and silica activity in controlling DMg .

107 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

2.7 References

Bevington, P., R., 1969. Data reduction and error analysis for the physical sciences. McGraw-Hill, 336 pp. Bindeman, I. N., Davies, A. M. & Drake, M. J., 1998. Ion microprobe study of plagioclase-basalt partition experiments at natural concentration levels of trace elements. Geochimica et Cosmochimica Acta , 62 , 1175-1193. Blundy, J. D. & Wood, B. J., 1991. Crystal chemical controls on partitioning of Sr and Ba between plagioclase feldspar, silicate melts, and hydrothermal solutions. Geochimica et Cosmochimica Acta , 55 , 193-209. Blundy, J. D. & Wood, B. J., 1994. Prediction of crystal-melt partition coefficients from elastic moduli. Nature , 372 , 452-454. Blundy, J. D. & Wood, B. J., 2003. Partitioning of trace elements between crystals and melts. Earth and Planetary Science Letters , 210 , 383-397. Carmichael, I. S. E., Nicholls, J. & Smith, A. L., 1970. Silica activity in igneous rocks. American Mineralogist , 55 , 246-263. Chalot-Prat, F., Falloon, T. J., Green, D. H. & Hibberson, W. O., 2010. An experimental study of liquid compositions in equilibrium with plagioclase plus spinel lherzolite at low pressures (0.75 GPa). Journal of Petrology , 51 , 2349-2376. Coogan, L. A., 2007. The lower oceanic crust. In: Treatise on Geochemistry: The Crust (Vol.3) (eds Turekian, K. & Holland, H. D.), pp. 1-45, Elsevier, New York. Costa, F., Chakraborty, S. & Dohmen, R., 2003. Diffusion coupling between major and trace elements and a model for the calculation of magma chamber residence times using plagioclase. Geochimica et Cosmochimica Acta , 67 , 2189-2200. Costa, F., Dohmen, R. & Chakraborty, S., 2008. Time Scales of Magmatic Processes from Modeling the Zoning Patterns of Crystals. In: Minerals, Inclusions and Volcanic Processes, Reviews in Mineralogy & Geochemistry 69 (ed Putirka, K. D.& Tepley, F. J.), pp. 545-594, Mineralogical Society of America, Virginia.

108 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Dohmen, R. & Chakraborty, S., 2007. Fe-Mg diffusion in olivine II: Point defect chemistry, change of diffusion mechanisms and a model for calculation of diffusion coefficients in natural olivine. Physics and Chemistry of Minerals , 34 , 409-430. Drake, M. J. & Weill, D. F., 1971. Petrology of Apollo-11 sample-10071 - Differentiated mini-igneous complex. Earth and Planetary Science Letters , 13 , 61-70. Flynn, C. P., 1972. Point defects and diffusion. Clarendon Press, Oxford. Ghiorso, M. S. & Sack, R. O., 1995. Chemical mass transfer in magmatic processes IV. A revised and internally consistent thermodynamic model for the interpolations of liquid-solid equilibria in magmatic systems at elevated temperatures and pressures. Contributions to Mineralogy and Petrology , 119 , 197-212. Giletti, B. J. & Casserly, J. E. D., 1994. Strontium diffusion kinetics in plagioclase feldspars. Geochimica et Cosmochimica Acta , 58 , 3785-3793. Grove, T. L. & Juster, T. C., 1989. Experimental investigations of low-Ca-pyroxene stability and olivine pyroxene liquid equilibria at 1 atm in natural basaltic and andesitic liquids. Contributions to Mineralogy and Petrology , 103 , 287- 305. Karson, J. A., 2005. Internal structure of the upper oceanic crust generated at fast to intermediate rates: The view from tectonic windows in the Pacific. In: EOS Trans AGU 86(52), Fall Meet. Suppl , pp. T23F-03. Kröger, F. A. & Vink, H. J., 1965. Relation between the concentrations of imperfections in crystalline solids. Solid State Physics , 3, 307-435. Lasaga, A. C., 1983. Geospeedometry: an extension of geothermometry. In: Kinetics and equilibrium in mineral reactions (ed Saxena, S. K.), pp. 82-114, Springer- Verlag, New York. LaTourrette, T. & Wasserburg, G. J., 1998. Mg diffusion in anorthite: implications for the formation of early solar system planetesimals. Earth and Planetary Science Letters , 158 , 91-108.

109 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Libourel, G., Boivin, P. & Biggar, G. M., 1989. The univariant curve liquid=forsterite+anorthite+diopside in the system CMAS at 1 bar - solid- solutions and melt structure. Contributions to Mineralogy and Petrology , 102 , 406-421. Longhi, J., Walker, D. & Hays, F., 1976. Fe and Mg in plagioclase. Proceedings in Lunar Science Conference , 7, 1281-1300. Miller, S. A., Asimow, P. D. & Burnett, D. S., 2006. Determination of melt influence on divalent element partitioning between anorthite and CMAS melts. Geochimica et Cosmochimica Acta , 70 , 4258-4274. Perk, N., Coogan, L. A., Karson, J. A., Klein, E. M. & Hanna, H., 2007. Primitive cumulates from the upper crust formed at the East Pacific Rise. Contributions to Mineral Petrology , 154 , 575-590. Peters, M. T., Shaffer, E. E., Burnett, D. S. & Kim, S. S., 1995. Magnesium and titanium partitioning between anorthite and type-B CAI liquid - dependence on oxygen fugacity and liquid composition. Geochimica et Cosmochimica Acta , 59 , 2785-2796. Sack, R. O., Walker, D. & Carmichael, I. S. E., 1987. Experimental petrology of alcalic lavas - Constraints on cotectics of multiple saturation in natural basic liquids. Contributions to Mineralogy and Petrology , 96 , 1-23. Shi, P., 1992. Basalt evolution at low pressure: implications from an experimental study in the system CaO-FeO-MgO-Al2O3-SiO2. Contributions to Mineralogy and Petrology , 110 , 139-153. Shi, P. & Libourel, G., 1991. The effects of FeO on the system CMAS at low-pressure and implications fro basalt crytsallisation. Contributions to Mineralogy and Petrology , 108 , 129-145.

Soulard, H., Provost, A. & Boivin, P., 1992. CaO-MgO-Al 2O3-SiO2-Na 2O (CMASN) at 1 bar from low to high Na2O contents - topology of an analog for alkaline basic rocks. Chemical Geology , 96 , 459-477. Tormey, D. R., Grove, T. L. & Bryan, W. B., 1987. Experimental petrology of N-MORB near the Kane Fracture Zone: 22-25°N, mid-Atlantic ridge. Contributions to Mineralogy and Petrology , 96 , 121-139.

110 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

Walker, D., Shibata, T. & DeLong, S. E., 1979. Abyssal tholeiites from the Oceanographer Fracture Zone. Contributions to Mineralogy and Petrology , 70 , 111-125. Weill, D. F., McCallum, I. S., Bottinga, Y., Drake, M. J. & McKay, G. A., 1970. Mineralogy and petrology of some Apollo 11 igneous rocks. Proceedings of the Apollo 11 Lunar Science Conference , 973-956. Wenk, H. R. & Wilde, W. R., 1973. Chemical anomalies of lunar plagioclase, described by substitution vectors and their relation to optical and structural properties. Contributions to Mineralogy and Petrology , 41 , 89-104. Wood, B. J. & Blundy, J. D., 2001. The effect of cation charge on crystal-melt partitioning of trace elements. Earth and Planetary Science Letters , 188 , 59- 71. Yang, H.-J., Kinzler, R. J. & Grove, T. L., 1996. Experiments and models of anhydrous, basaltic olivine-plagioclase-augite saturated melts from 0.001 to 10 kbar. Contributions to Mineralogy and Petrology , 124 , 1-18. Zhang, X., Ganguly, J. & Ito, M., 2010. Ca-Mg diffusion in diopside: tracer and chemical inter-diffusion coefficients. Contributions to Mineralogy and Petrology , 159 , 175-186.

111 2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx

112 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

Chapter 3

3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Plagioclase

Abstract

Models of crustal accretion along fast-spreading mid-ocean ridges differ in the proportion of crystallization at different depths within the lower oceanic crust. Therefore, these models predict different thermal evolution, and most significantly, different depths to which hydrothermal fluids circulate must in the oceanic crust. As a consequence, this implies different variations of cooling rate as a function of depth. Here, a new ‘ Mg-in-plagioclase geospeedometer ’ is presented, that is based on the diffusive exchange of Mg between plagioclase (Pl) and clinopyroxene (Cpx) during cooling and allows for determination of cooling rates from Pl and Cpx bearing rocks. A revised diffusion model for Mg in plagioclase was applied, based on newly calibrated data for the diffusion coefficient of Mg in plagioclase. The initial and boundary conditions of the new model are built on the partition coefficient of Mg between Pl and Cpx, which was experimentally determined in the compositional range of the lower oceanic crust. The approach was tested and applied to three

113 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl different samples suites of lower oceanic crust, formed along different segments of the fast-spreading East Pacific Rise (EPR). Since the individual samples of each location were collected from different depths, the results presented here include information about the variation of cooling rates as a function of depth in the lower oceanic crust. The obtained cooling rates range from 5 °C/year to 0.0001 °C/year, and show a general trend of decreasing cooling rates with depth. Therefore, the data of this study supports models of crustal accretion, which are consistent with faster cooling at the top of the lower oceanic crust and slower cooling at deeper levels (e.g. ‘gabbro glacier ’ type models). Models, predicting no significant changes of the cooling rate as a function of depth (e.g. ‘ sheeted sill ’ type models) are inconsistent with the data obtained here.

3.1 Introduction

The formation and cooling of new oceanic lithosphere along the global mid- ocean ridge (MOR) system is one of the principal mechanisms of cooling of the Earth's interior (e.g. Chapman and Pollack, 1975; Davies and Davies, 2010). The cooling rate of the plutonic crust, and therefore the mode of accretion, depends on the balance between the addition of heat by magmatic processes (latent heat and specific heat of crystallization) and the heat loss through conductive and hydrothermal convective transport. However, the details of this oceanic crustal accretion process are not well understood. The existing end-member models of crustal accretion at fast-spreading mid-ocean ridges mainly differ in the proportion of crystallization at different depths within the lower oceanic crust. The ‘gabbro glacier’ type model (e.g. Sleep, 1975; Quick and Denlinger, 1993; Phipps Morgan and Chen, 1993; Henstock et al., 1993; Fig. 3.1.1a) suggests that primitive melt rises from the crust-mantle boundary to an axial magma chamber (AMC) without significant amounts of crystallization at lower levels in the oceanic crust. While some of the melt moves upward from the AMC to produce dikes

114 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl and lava, most of it crystallizes in the AMC. From there, the crystals subside down and outwards through a crystal mush zone, characterized by low seismic velocities (the LVZ), and the melt solidifies off-axis to form new oceanic crust (Fig. 3.1.1a). Most of the latent heat of crystallization of the plutonic body is removed by hydrothermal circulation at the top of the AMC (Fig. 3.1.1a). The other end-member is represented by the ‘sheeted sill’ type model (e.g. Kelemen et al., 1997; Korenaga and Kelemen, 1997; MacLeod and Yaouancq, 2000; Garrido et al., 2001; Lissenberg et al., 2004; Fig. 3.1.1b), in which new crust is formed in situ , by crystallization of the magma in sills over the entire depth of the lower oceanic crust. The AMC, in this model, is simply the uppermost of a series of stacked sills (Fig. 3.1.1b). In this case, deep hydrothermal circulation is required throughout the lower oceanic crust to remove the latent heat of crystallization (e.g. Chen 2001). In fact, both end-member models require some portion of each process. In the ‘ gabbro glacier ’ model, melt in the mush zone lubricates the crystals, allowing them to flow, and this melt crystallizes deeper in the crust. In the ‘ sheeted sill ’ model, more rapid cooling at shallow levels in the crust requires some crystal subsidence to prevent the AMC to solidify (e.g. Maclennan et al., 2004). Therefore, ‘hybrid’ models (e.g. Boudier et al., 1996; Coogan et al., 2002a; Maclennan et al., 2004 and 2005) suggest some proportion of crystallization taking place in the AMC and some proportion taking place at deeper levels in the lower oceanic crust. In summary, these two end-member models predict different thermal evolution of the crust, and most significantly, different depths to which hydrothermal fluids circulate, implying different relations between cooling rate and depth (central panel in Fig. 3.1.1). A ‘gabbro glacier’ type model requires most of the latent heat of crystallization to be removed by hydrothermal circulation at the top of the AMC, leading to fast cooling rates in the upper gabbros. With increasing depth, heat conduction probably becomes the dominant process of heat removal. Since heat conduction is a less efficient mechanism of heat removal than hydrothermal circulation, it is however expected that the cooling rate will decrease with increasing depth (central panel in Fig.3.1.1, green line). In contrast, in a ‘sheeted sill’

115 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl type model, the mechanism for heat removal is the same over the entire depth of the gabbroic crust (hydrothermal circulation) and therefore, the cooling rate is not expected to change as a function of depth (central panel in Fig.3.1.1, purple line).

~30MW/km ~15MW/km (a) coolingrate (b)

AMC axial magma AMC chamber axial magma

depth chamber

~40 (a) (b) ~55 MW/km MW/km 0 2 4 0 2 4 km km

30MW/km lava sheeted magma crystal solidified melt/mush hydrothermal energylossinMegawatts dikes mush pluton transport circulation perkmofridgeaxis

Fig. 3.1.1: Schematic diagrams of two existing end-member models on cooling and accretion of the lower oceanic crust at fast-spreading mid-ocean ridges; (a) the ‘ gabbro glacier ’ type model (e.g. Sleep, 1975; Quick and Denlinger, 1993; Phipps Morgan and Chen, 1993b; Henstock et al., 1993), in which the lower oceanic crust crystallizes in a axial magma chamber (AMC) at the base of the sheeted dike complex from which cumulates subside down to form the lower crust and (b) the ‘sheeted sill’ model (e.g. Kelemen et al., 1997; Korenaga and Kelemen, 1997), in which the lower oceanic crust forms through the crystallization of multiple sills, with the AMC simply being the uppermost of a series of stacked sills. The central panel between (a) and (b) illustrates the difference in the predicted cooling rate with depth for both end-member models (green= ’gabbro glacier ’ model; purple= ’sheeted sill ’ model), showing an inferred decrease in cooling rate as a function of depth for model (a), whereas no significant changes in cooling rate are expected for model (b) (see text for further explanation).

One approach of testing these models and improving the understanding of the cooling of the oceanic lithosphere is to use ‘ geospeedometric ’ tools to quantify cooling rates of samples from the lower oceanic crust formed at fast-spreading ridges as a function of depth (e.g. Ozawa, 1984; Coogan et al., 2002b; Coogan et al., 2007; VanTongeren et al., 2008). ‘ Geospeedometers ’ make use of the fact that the diffusive exchange of elements between minerals is a thermally activated process. The connection between diffusive processes and timescales has been investigated primarily using analytical solutions of the diffusion equation at different temperatures. This allows to determine the condition, at which chemical diffusion becomes extremely slow and the concentration of chemical elements in crystals

116 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl undergoing cooling effectively does not change anymore with time (the concept of ‘closure temperature’ Tc ; Dodson, 1973, 1976 and 1986; see also Section 3.2 and Chapter 1 Section 1.5). In parallel, Lasaga (1977 and 1983) developed the idea of extracting cooling rates from diffusion processes and introduced the concept of ‘geospeedometry’ . In equilibrium, for a given pressure and temperature in a closed system, the distribution of chemical elements between minerals is defined. At constant pressure, the equilibrium concentration of a particular species in a particular mineral will be different at different temperatures. During cooling, exchange reactions, which depend on temperature, will modify the chemical distribution among minerals to re-establish equilibrium under the new conditions, at which the timescale of the chemical equilibration is controlled by kinetic processes, such as diffusion. A potentially well suited method to determine cooling rates of the lower oceanic crust is the study of the evolution of Mg-concentration profiles in plagioclase crystals surrounded by clinopyroxene in gabbroic rocks. Natural rock samples from the oceanic crust show higher concentrations of MgO in plagioclase phenocrysts in mid ocean ridge basalts (MORBs) than in the cogenetic, but more slowly cooled, gabbroic rocks of the lower oceanic crust (Fig. 10f in Coogan, 2007). The difference in plagioclase Mg-content most likely occurs due to exchange of Mg between these phases during cooling of the gabbroic rocks. The partition coefficient of Mg between plagioclase and clinopyroxene (which is the major adjacent phase to the plagioclase in these rocks) decreases with temperature (see Chapter 2). Therefore, a concentration gradient is developed during cooling and Mg tends to diffuse out of plagioclase and into clinopyroxene. Depending on the cooling rate of the rock, the evolution of the resulting concentration profile of Mg in plagioclase will be different (a detailed discussion on the evolution of diffusion profiles for different cooling rates and additional factors influencing the resulting shape of the profile is given in section 3.5). Therefore, diffusion modelling of Mg-profiles measured in plagioclase from natural rock samples can be used to understand the cooling history of a rock.

117 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

Here, a new ‘ Mg-in-plagioclase geospeedometer ’ is presented, based on the diffusive exchange of Mg between plagioclase and clinopyroxene during cooling. A revised diffusion model for Mg in plagioclase is applied, built on the model of Costa et al. (2003), but based on newly calibrated data for the diffusion coefficient of Mg in plagioclase (see Chapter 2). The experimentally determined, temperature- dependent partition coefficient of Mg between plagioclase and clinopyroxene (see Chapter 2) is used to determine initial and boundary conditions of the new model. This new ‘ Mg-in plagioclase geospeedometer ’ is applied to obtain cooling rates from natural sample suites of the lower oceanic crust, formed at the fast-spreading East Pacific Rise (EPR). The natural rocks were sampled from different locations and different depths within the lower oceanic crust. Therefore, application of the new ‘geospeedometer’ to this samples allows the determination of the vertical distribution of cooling rates within a single lithospheric section, as well as determination of the distribution of cooling rates between different segments within the same mid-ocean ridge. Furthermore, this data provides additional constraints on magmatic, tectonic and hydrothermal processes during lower crustal accretion at fast-spreading ridges.

3.2 Diffusion profiles of Mg in plagioclase and the extraction of cooling rates

A compositional zoning profile of Mg in plagioclase is developed during crystallization from a melt. The chemical variation of Mg in plagioclase depends on intensive thermodynamic variables, such as temperature, melt composition from which the crystal is growing, and additionally the anorthite content XAn in the growing plagioclase (e.g. Blundy and Wood, 1994; Bindeman et al., 1998). After crystallization however, the developed Mg-profile is not “frozen”, but can be modified due to changes in temperature, which affect the composition at the interface between plagioclase and its adjacent phase. The variation of the

118 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl concentration of Mg at the interface is one of the driving forces for diffusion of Mg in plagioclase. How, and to what extent, an existing Mg-profile may be altered by diffusion during continuous cooling after crystallization is controlled by: (a) the chemical driving force, (b) the boundary conditions, (c) the diffusion coefficient of Mg in plagioclase, and (d) the cooling rate, under which the systems continues to cool after crystallization.

However, since diffusion is a temperature controlled process, at a sufficiently low temperature Tc , the exchange of Mg-atoms between plagioclase and their surroundings will become very slow. Beyond Tc , a developed concentration profile of Mg in plagioclase is not significantly changed anymore by diffusion and therefore, this concentration profile in the crystal now is considered to be “frozen” (Dodson, 1973, 1976 and 1986; see also Chapter 1, Section 1.5). This “frozen” Mg- concentration profile can be measured by electron microprobe analysis. As shown in detail in Section 3.5, the evolution and resulting shape of such a Mg-concentration profile in plagioclase depends on the cooling rate (see also Chapter 1, Section 1.5). Hence, cooling rates can be extracted from iterative diffusion modelling of Mg in plagioclase, in which the modelled concentration profile is fitted to a measured concentration profile in a plagioclase crystal from a natural rock.

3.3 The diffusion model

Costa et al. (2003) proposed that the diffusion of trace elements in plagioclase is coupled with the anorthite-content (XAn ) in plagioclase. In their diffusion model for Mg in plagioclase the Mg flux depends on two components: (1) a direct contribution due to a Mg concentration gradient, and (2) a contribution related to a gradient in the XAn -content in plagioclase. The dependence of the flux on

119 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl the second component is the result of the fact, that the activity or chemical potential of Mg in plagioclase depends strongly on XAn . The differential equation for the diffusion equation of the model of Costa et al., (2003) is given by their Eq. 7:

∂C  ∂ 2C ∂C ∂D  A  ∂C ∂X ∂D ∂X ∂ 2 X  Mg =  D Mg + Mg Mg  −  D Mg An + C Mg An + D C An   Mg 2   Mg Mg Mg Mg 2  ∂t  ∂x ∂x ∂x  RT  ∂x ∂x ∂x ∂x ∂x  (Eq. 3.3.1)

where CMg = concentration of Mg in plagioclase, t = time, DMg = diffusion coefficient of Mg in plagioclase, x = distance, and A = factor to describe the partitioning of Mg in dependence of XAn . This differential expression for the diffusion equation was solved numerically by applying the method of central finite differences (Crank, 1975, Costa et al., 2008).

∆t C + = C + [D (C + − 2C + C − )+ (C + − C − )(D + − D − )] i, j 1 i, j ()4∆x 2 i, j i ,1 j i, j i ,1 j i ,1 j i ,1 j i ,1 j i ,1 j ()− ()− + ()− ()− ∆ Di, j Ci+ ,1 j Ci− ,1 j X An X An Ci, j Di+ ,1 j Di− ,1 j X An X An  − A t  i+ ,1 j i− ,1 j i+ ,1 j i− ,1 j  RT ()4∆x 2 + D C ()X − 2X + X   i, j i, j An i+ ,1 j An i, j An i− ,1 j  (Eq. 3.3.2)

where i = step in distance and j = step in time. Ci,j and Di,j are the concentration of Mg in plagioclase and the diffusion coefficient of Mg in plagioclase at given i and j, respectively. The above Equation 3.3.2 describes how the concentration of Mg at point i is changed from time j to time j+1 . Assuming a small time step ∆t (i.e. the difference between time j and j+1 is small), the change in temperature ∆T is small and the diffusion within a time step ∆t is assumed to proceed at constant temperature T. At each point i in space, the new concentration of Mg at the next time step is calculated based on a gradient in the Mg-concentration and on a gradient in the XAn content of its neighbouring grid points i-1 and i+1 , and based on the diffusion coefficient Di,j .

120 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

This process is repeated over time. To simulate a cooling path, the temperature T decreases as a function of time t, according to a cooling function (which is a variable input of the model). For reasons of stability during the calculation, a parameter defined as r = D∆t /∆x 2 has to be <0.5 at any space grid point and over time (e.g. see Crank, 1975). The space grid in the simulation consists 100 points ( i = 1-100) at equal internal spacing ∆x. The size of ∆x is given by l/100, where l is the length of the crystal. The time step ∆t is not kept constant during the modelling procedure, but is calculated according to a more restrictive criteria than the stability condition defined by r: ∆t = 0.45 (∆x 2 /D) at each iteration j.

In order to calculate the concentration at any grid point i at a time j>0 ( Ci,j+ 1) the following information is needed:

(a) the diffusion coefficient Di,j at any grid point i and any time step j, (b) the initial concentration of Mg at any grid point i at the initial time

(Ci=1-100,j=0 ),

(c) the concentration of the outermost grid points defined as C1 and

Cgrid=100 , since they can not be calculated as Ci-1 and Ci+1 . Therefore, the

model runs from grid point 2 to 99, and C1 and Cgrid=100 have to be determined by boundary conditions for every time step.

(d) the concentration of XAn i,j at any grid point i and any time step j.

3.4 Model parameters and input conditions (for the diffusive exchange of Mg between plagioclase and clinoyproxene and the investigated sample suite)

3.4.1 Diffusion coefficient The diffusion coefficient is a crucial parameter in the determination of cooling rates using the approach of this study. LaTourette and Wasserburg (1998) experimentally determined the diffusion coefficient of Mg in anorthite ( XAn =0.95).

121 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

Pl = −E / RT The reported Arrhenian relationship was defined as follows: DMg D0e , with

D0=7.1±0.1 x 10 -8 m 2/s and E=254±43 kJ/mol in b-direction, and

-6 2 D0=1.2±0.1 x 10 m /s and E=278±43 kJ/mol in c-direction. Costa et al. (2003) used the average of the D0- and E-values of LaTourette and Wasserburg’s data for the b- and c-direction in their diffusion model of Mg in plagioclase. Additionally, they assumed a compositional dependence of the Mg-diffusion coefficient on XAn , similar to the compositional dependence of Sr-diffusion in plagioclase, which was determined experimentally (Giletti and Casserly, 1994). The present work includes an experimental study to investigate the diffusive exchange of Mg between plagioclase and clinopyroxene (Chapter 2), which was particularly designed to be applied to the sample suites investigated here. In a series of experiments at different temperatures, plagioclase crystals were surrounded by different Cpx-bearing matrix powders (including also powdered gabbroic rocks

Pl from the lower oceanic crust). The diffusion coefficient DMg was determined as a function of temperature, XAn in plagioclase (in the range of XAn =0.5 to 0.67) and silica activity a of the system (in the range of a =0.6 to 1). One result of this study SiO 2 SiO 2

Pl (Chapter 2) was, that no difference in DMg was observed along different orientations within the plagioclase crystal. Furthermore, a significant compositional

Pl dependence of DMg on XAn in plagioclase was not found. Instead, it was observed

Pl that DMg increases with increasing silica activity. The fit of the experimental data yields activation energies, which are about a factor of ~1.5 higher than the ones determined by LaTourette and Wasserburg (1998). The results of the present study (Chapter 2) are consistent with the experimental study of Borinski et al. (in prep.),

Pl where DMg was investigated over a wider temperature range (700 to 1285°C) and a wider range of plagioclase compositions ( XAn =0.1 to 0.95). Borinski et al. (in prep)

Pl report no significant dependence of DMg on XAn and activation energies of ~336 kJ/mol.

122 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

Since the experimental results of the present study (Chapter 2) show a dependence of D Pl on a , a diffusion coefficient of the form Mg SiO 2

 −E  m DPl = D ⋅ exp  ⋅ (a ) (Eq. 3.4.1.1) Mg 0  RT  SiO 2

will be used here, where D0 is a pre-exponential factor, E is the activation energy, R is the gas constant, T is the temperature, a is the silica activity of the system and SiO 2 m is a factor related to the dependence of the diffusion coefficient on a (see SiO 2 Chapter 2 for details). The parameters of equation Eq. 2.5.8.4 suggested in Chapter 2 are applied. These parameters result from fitting experimental data, using the activation energy

Pl of Borinski et al. (in prep.). This equation determines DMg as a function of T and a (for a fixed alumina activity of a =1): SiO 2 Al 2O3

−  − 321 (± 35 ) [kJ/mol ] 6.2 DPl [m2/s ] = 25.1 ⋅10 4 [m2/s ]⋅ exp   ⋅ ()a Mg  RT  SiO 2 (Eq. 3.4.1.2)

Pl One feature of Eq. 3.4.1.2 is, that DMg is independent of XAn , and hence is

Pl constant for all grid points in the model at given time. However, DMg is a function of T, therefore it is modified at each time step. Additionally, Eq. 3.4.1.2 requires the input of the silica activity of the system. Several of the natural rocks to be modelled here contain coexisting olivine and orthopyroxene. Therefore, a in those rocks is SiO 2 buffered by the reaction Mg 2SiO 4 + SiO 2 = 2MgSiO 3 and can be determined according to the relationship proposed by Carmichael (1970): ∆G log a = r (Eq. 3.4.1.3) SiO 2 2.303 RT

123 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

∆ where Gr is the Gibbs Free energy of the reaction, R is the gas constant and T is the temperature in K. Equation 3.4.1.3 shows that a is a function of temperature. SiO 2 ∆ The relationship is not simply described by a linear function with 1/ T, because Gr itself is a function of temperature. To account for this dependence, a was SiO 2 calculated for different temperatures using the data set of Ghiorso and Sack (1995)

∆ nd to determine Gr . The resulting data are fitted by a 2 -order polynomial: a = -4.86904 ⋅10 -7 T 2 +1.51570 ⋅10 -3 T - 0.618707 (Eq. 3.4.1.4) SiO 2

The silica activity of samples without coexisting olivine and orthopyroxene is not known; nevertheless, it is assumed to be not very different from silica activity of the Ol+Opx-bearing samples. Therefore, Eq. 3.4.1.4 is applied to constrain a for SiO 2 all samples in this study.

Pl / Cpx 3.4.2 Initial profile determined from K Mg To model the modification of a compositional zoning profile due to diffusion, an initial profile is needed. After crystallization, a given plagioclase crystal most likely will be zoned in Mg. However, the exact shape of such a crystallization profile of Mg in plagioclase depends on many variables (such as the melt composition and evolution during crystallization of the rock), which may be difficult to determine from the mineral composition in the host rock. After crystallization however, the plagioclase crystal will still try to maintain equilibrium with its surrounding solid phases. In the investigated natural rocks from the oceanic crust, plagioclase mainly occurs in contact with clinopyroxene. Hence, after crystallization, the distribution of Mg in plagioclase in equilibrium with the adjacent clinopyroxene at a given temperature depends on the partition coefficient of Mg between plagioclase and

Pl / Cpx clinopyroxene ( K Mg ). The present study (Chapter 2) investigated the partitioning of Mg between plagioclase and clinopyroxene in the compositional range of the

124 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

Pl / Cpx rocks of the lower oceanic crust and determined ln K Mg as a function of T, XAn and a (see Chapter 2): SiO 2 1 16913 [J/mol ] ln K Pl / Cpx = -9219 []K + 6.1 + X + ln a (Eq. 3.4.2.1) Mg T RT An SiO 2

Starting the diffusion model from an equilibrium distribution of Mg between plagioclase and clinopyroxene is plausible for the following reasons: The anorthite-content in plagioclase from the sample suite investigated here is mainly between XAn =0.6 and 0.8. At temperatures around 1200°C, which is below the solidus of the eutectic system Di-An-Ab for the studies samples, diffusion of Mg in plagioclase is fast enough to attain equilibrium in a mm-large crystal (i.e. gabbroic Pl || grain size) within a few years (e.g. ~50 to 60 years using DMg b from LaTourette and Wasserburg, 1998, and D Pl from Chapter 2 for a buffered by Ol+Opx). Mg SiO 2 Published cooling rates of the lower oceanic crust derived from different methods vary from 10 -2 to 10 -5 °C/year (e.g. Coogan et al., 2002a; Maclennan et al., 2004; Maclennan et al, 2005; Coogan et al., 2007; VanTongeren et al., 2008; Schmitt et al., 2011). Hence, even for the fastest published cooling rates, a decrease in temperature of 10°C takes about 1000 years. Around 1200°C, diffusion of Mg in plagioclase is fast enough that chemical zoning would not be observed within this cooling interval. Therefore, in the given geological framework, it seems justified to start the Mg- diffusion model at temperatures around 1200°C from an initial profile, which is calculated after rearranging Eq.3.4.2.1 to:  [ ]  Pl = Cpx [] 1 + + 16913 J/mol + CMg CMg exp - 9219 K 6.1 X An ln aSiO   T RT 2  (Eq. 3.4.2.2) Thereby, the following input is used: T: The starting temperature was chosen around 1200°C (to speed up the calculations, the exact starting temperature was calculated as a function of the actual grain size of the profile to be modelled, i.e. smaller crystals had lower starting temperatures than larger ones,

125 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

because they still can maintain equilibrium over the entire crystal down to lower temperatures. For the exact calculations of starting temperatures and more detailed explanations please see Appendix V).

XAn : The equilibrium distribution of Mg in plagioclase depends on XAn (e.g. Blundy and Wood, 1994; Bindeman et al., 1998; Chapter 2). However, the inter-diffusion of NaSi-CaAl in plagioclase is very sluggish (Grove

et al., 1984; Liu and Yund, 1992), such that the XAn -profile, once formed, remains essentially unmodified by subsequent diffusion

under most geological circumstances. Therefore, the XAn -profile is considered to be constant over time. The compositional zoning profile

of XAn for each natural plagioclase modelled in this study was measured along the same traverse as the Mg-profile.

Cpx CMg : The Mg-content in clinopyroxene was generally measured adjacent to each profile (where applicable, i.e. where clinopyroxene occurs adjacent to plagioclase) or in a clinopyroxene in close proximity to the modelled plagioclase crystal. Mg is a major component in clinopyroxene, but a minor component in plagioclase (~12 to 20 wt% MgO in clinopyroxene compared to typically ~0.1 to 0.3 wt% MgO in plagioclase crystals for rocks from the lower oceanic crust). Thus, the change of Mg-content in clinopyroxene due to diffusion from the plagioclase is relatively small, so that the Mg-content in clinopyroxene is assumed to be constant after crystallization. a : The silica activity is constraint by the coexistence of Ol+Opx for all SiO 2 samples as argued for the diffusion coefficient and was calculated for the respective temperature using Eq. 3.4.1.4.

The application of Eq. 3.4.2.2 to determine the equilibrium distribution of Mg in a plagioclase crystal, which may be zoned in XAn , is not entirely straightforward. If the plagioclase is not homogeneous in its XAn -content, by definition it is not in thermodynamic equilibrium. However, since the inter-diffusion of NaSi-CaAl in

126 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl plagioclase is exceedingly slow compared to the diffusion of Mg in plagioclase, it has been proposed that Mg would strive to come to equilibrium with the XAn -content in each zone, which remains unmodified (Zellmer et al., 1999; Costa et al., 2003). Thus, there will be a metastable compositional zoning of Mg in plagioclase, which is related to the zoning in XAn . This metastable Mg-distribution can be calculated according to Eq. 3.4.2.2 and will be referred to as “equilibrium” in the following sections.

Pl / Cpx 3.4.3 Boundary conditions determined from K Mg

Pl / Cpx During cooling, K Mg decreases (see Chapter 2) and consequently, the equilibrium concentration of Mg decreases at the interface of a plagioclase crystal in contact with clinopyroxene. This drop of Mg creates a concentration gradient at the rim of the plagioclase and a driving force for Mg to diffuse out of the plagioclase during cooling. Hence, a variable edge composition (VEC) model must be applied (e.g. Chakraborty and Ganguly, 1991), which implies that the boundary concentration of Mg in plagioclase changes over time (i.e. during cooling) according

Pl / Cpx to K Mg . Under the assumptions, that (i) the interfaces between the plagioclase and the clinopyroxene (i.e. the outermost grid points in the model) maintain equilibrium at any temperature , and that (ii) this equilibrium concentration is attained instantaneously, the above equation Eq. 3.4.2.2 (with the same parameters

Cpx XAn , C and a as outlined above) is used to calculate the Mg-concentration of Mg SiO 2 the outermost grid points Ci= ,1 j and Ci=100 , j of the model at any time for the given temperature.

127 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

3.5 Evolution of concentration profiles of Mg in plagioclase in contact with clinopyroxene during linear cooling

The following section aims to provide some illustrative examples of the evolution of Mg-diffusion profiles in plagioclase in contact with clinopyroxene during cooling for (i) different cooling rates, (ii) different shapes of XAn -profiles in the plagioclase and (iii) different grain sizes of the plagioclase crystal on three theoretical examples (Fig. 3.5.1). The model described above was applied to three different theoretical plagioclase crystals (P1: XAn =0.4, length=1500 µm; P2:

XAn =step-profile with 0.4 at the rims and 0.6 in the core, length=1500 µm; P3:

XAn =step-profile with 0.4 at the rims and 0.6 in the core, length=150 µm). The modelling procedure was started at 1200°C for two different linear cooling rates of dT/d t=0.001 °C/year (Fig. 3.5.1b1-b3) and d T/d t=0.1 °C/year (Fig. 3.5.1c1-c3) The temperature interval is 600°C. As described in Section 3.4.2, an initial profile is determined from Eq. 3.4.2.2. According to this equation, this initial profile depends on temperature, the Mg-content in the adjacent Cpx (here 14 wt% MgO for all three examples), and the XAn -profile in the plagioclase. An “equilibrium” profile for Mg in plagioclase P1 at any temperature is always homogeneous, because the XAn -content is homogeneous (dashed lines in Fig. 3.5.1b1 and c1). According to Eq. 3.4.2.2, the concentration of Mg in this plagioclase P1 in contact with the theoretical Cpx yields 0.129 wt% MgO at 1200°C (red line in

Pl / Cpx Fig. 3.5.2b1). During cooling, K Mg decreases (see Chapter 2), i.e. the “equilibrium” concentration of Mg in the plagioclase in contact with Cpx decreases. The plagioclase crystal tries to re-attain “equilibrium” with the adjacent Cpx by diffusion of Mg out of the plagioclase into the clinopyroxene. For cooling from 1200°C to 1100°C with a cooling rate of 0.001 °C/year, diffusion of Mg in plagioclase is fast enough, such that the whole plagioclase crystal always maintains “equilibrium” and the modelled diffusion profile is the “equilibrium” profile at 1100°C (orange line in Fig. 3.5.1b1). Diffusion is still efficient enough at 1000°C to almost maintain “equilibrium” with the adjacent Cpx at the outer portion of the plagioclase, but it is

128 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl not fast enough, to transport all Mg out of the core of the plagioclase. Thus, the modelled diffusion profile at 1000°C shows slightly higher concentrations of Mg near the core (purple line in Fig. 3.5.1b1). This effect is even stronger for the modelled diffusion profiles at 800°C and 600°C. The rims of the plagioclase are assumed to be in “equilibrium” with the Cpx at the respective temperatures instantaneously, but diffusive transport of Mg at these temperatures is too slow to let the core of the plagioclase be in “equilibrium”. Therefore, the shapes of the modelled diffusion profiles are bowed and have higher concentrations of Mg in the

Pl core than at the rims (green and blue line in Fig. 3.5.1b). Below 800°C, DMg is so slow, that the shape of the diffusion profile effectively does not change anymore and the diffusion profile “freezes”. Thus, the modelled diffusion profiles for 800°C and 600°C are identical, except for the outermost rim of the plagioclase. In example c1 in Fig. 3.5.1 the same plagioclase crystal P1 is cooled over the same temperature intervals, but with a faster cooling rate of 0.1 °C/year. At these conditions, diffusion is not efficient enough to maintain the “equilibrium” concentration away from the rims around 1100°C. The modelled diffusion profiles at 1100°C, 1000°C, 800°C and 600°C all have stronger bowed profile shapes with higher Mg-concentration in the core, when compared to with the profiles computed using the slower cooling rate. The diffusion profile already “freezes” around 1000°C and the profile shape does not change significantly below this temperature (except for the rim of the plagioclase). “Equilibrium” profiles of Mg in plagioclase P2 and P3 in contact with Cpx are zoned (dashed lines in Fig. 3.5.1b2, c2, b3, and c3) because the XAn -profiles of plagioclase P2 and P3 are not homogeneous. The absolute difference in concentration between the rim and the core becomes smaller for lower temperatures. As shown in detail for plagioclase P1, the cooling rate controls the temperature, at which diffusion ceases to maintain the equilibrium distribution of Mg over the whole crystal during cooling. However, the cooling rate is not the only controlling factor. A comparison of plagioclase P2 and plagioclase P3 (which have the same XAn -profile) shows the effect of the crystal size on the shape of the diffusion

129 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl profile. For the same cooling rate of 0.001 °C/year, the larger plagioclase P2 is not in “equilibrium” at 1000°C, whereas for the smaller plagioclase P3, the distribution of Mg is at “equilibrium” (purple lines in Fig. 3.5.1b2 and b3). Additionally, the comparison of the “frozen” diffusion profiles at 600°C shows higher concentrations of Mg in the core of the larger plagioclase P2 than in the smaller plagioclase P3 for both cooling rates (blue lines in Fig. 3.5.1b2 and b3 as well as c2 and c3).

PlagioclaseP1 PlagioclaseP2 PlagioclaseP3 0.7 (a1) 0.7 (a2) 0.7 (a3) 0.6 0.6 0.6

An

X 0.5 0.5 0.5

0.4 0.4 0.4

rimcore rim rimcore rim rimcore rim

0.20 0.20 0.20 (b1) (b2) (b3) 0.15 0.15 0.15 coolingrate 0.001°C/y 0.10 0.10 0.10

MgO[wt%] 0.05 0.05 0.05

0.20 0.20 0.20 (c1) (c2) (c3) 0.15 0.15 0.15 coolingrate 0.1°C/y 0.10 0.10 0.10

MgO[wt%] 0.05 0.05 0.05

0 500 1000 1500 0 500 1000 1500 0 50 100 150 Distance[µm] Distance[µm] Distance[µm]

T0=1200°C T1=1100°C T2=1000°C T3=800°C T4=600°C diffusionprofile “equilibrium” profile Fig. 3.5.1: Schematic evolution of Mg-profiles in plagioclase during cooling in contact with clinopyroxene (MgO=14 wt%) for three different assumed plagioclase crystals. Plagioclase P1 has a flat XAn -profile and a profile length of 1500 µm, plagioclase P2 has a zoned XAn -profile and the same profile length as plagioclase P1 (=1500 µm), and plagioclase P3 has the same XAn -zoning-pattern as plagioclase P2, but the profile length is only 150 µm. Panels a1-a3 show the different assumed zoning profiles for XAn in plagioclase. Panels b1-b3 show the calculated Mg-profiles at different temperatures (red = T0 = 1200°C, orange = T1 = 1100°C, purple = T2 = 1000°C, green = T3 = 800°C and blue = T4 = 600°) for a linear cooling rate of 0.001 °C/year. Panels c1-c3 shows the calculated Mg-profiles for the same temperatures as panels b1-b3, but for faster linear cooling of 0.1 °C/year. Dashed lines show the calculated “equilibrium” profiles, using Eq. 3.4.2.2 for the respective temperatures. Some solid lines are bigger only for visibility reasons of overlapping lines.

130 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

In summary: (i) “Equilibrium” profiles for the Mg-concentration in plagioclase as defined

in Section 3.4.2 (Eq. 3.4.2.2) are strictly correlated to the variation of XAn in the plagioclase. (ii) For slower cooling rates, “equilibrium” profiles for Mg in plagioclase can be maintained up to lower temperatures (e.g. up to approximately 1000°C for a cooling rate of 0.001 °C/year in a 1500 µm long profile). (iii) For any linear cooling model, there is a temperature, at which the diffusion profile “freezes” and effectively does not change its shape anymore. (iv) According to a linear cooling model, the composition at the rim is continuously modified up to lower temperatures than for the inner part of the crystal. Consequently, the “frozen” profile is always bowed with higher concentration of Mg in the core than at the rims. (v) The temperature, at which a diffusion profile “freezes” is higher for faster cooling rates. (vi) The “frozen” Mg-concentration in the core is higher for faster cooling rates. (vii) The “frozen” Mg-concentration in the core is higher for a larger grain size.

3.6 Uncertainties, robustness and sensitivity of the approach

Uncertainties in cooling rates obtained from the diffusion model described above mainly result from four different sources: (i) uncertainties related to the inferred conditions or model, at which diffusion is assumed to take place (e.g. initial and boundary conditions, and cooling history), (ii) uncertainties linked to the

Pl parameters that enter the calculation (e.g. parameters used to determine DMg , and

Pl / Cpx K Mg ), (iii) uncertainties, which result from modelling a one-dimensional concentration profile, while in fact, diffusion results from fluxes in three dimensions,

131 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl and (iv) uncertainties related to whether diffusive exchange with clinopyroxene is the only process controlling the concentration of Mg in plagioclase. These uncertainties are addressed as follows: (i) The initial and boundary conditions applied here were chosen to suite the inferred geological situation of the lower oceanic crust (i.e. solidification of a basaltic melt around 1200°C, which produces plagioclase and clinopyroxene in contact with each other, that can exchange Mg via diffusion during continuous cooling; see Sections 3.4.2 and 3.4.3 for details). As a first approximation, a linear cooling history is assumed. The cooling history can be modified to more complex functions, if this is necessary to fit the measured Mg-profile shapes in the natural plagioclase crystals (it will be shown later, that this is the case here).

Pl Pl / Cpx (ii) The diffusion coefficient DMg and the partition coefficient K Mg used for the calculation were specifically determined for the diffusive exchange of Mg between plagioclase and clinopyroxene in the compositional range of the lower oceanic crust (see Chapter 2). The effect of the uncertainty on the parameters used

Pl Pl / Cpx to determine DMg and K Mg on the obtained cooling rates was determined as follows: the parameters were varied individually one at a time in the maximum range of their uncertainties (for details on the uncertainties of the single parameters see Chapter 2), while the other parameters were kept constant. This yields uncertainties of one order of magnitude in the absolute value for the cooling rate obtained from a given Mg-profile in plagioclase. However, this reflects a maximum uncertainty in the cooling rate, because in fact, some of the individual parameters are highly correlated to each other (e.g. the activation energy E and the pre- exponential factor D 0 of the diffusion coefficient) and can not vary independently. Overall, these uncertainties do not affect relative relations in cooling rate as a

Pl function of depth, because the same parameters for the calculation of DMg and

Pl / Cpx K Mg were used for all samples. (iii) Extracting time scales from one-dimensional (or two-dimensional) models of a process that occurred in 3-D can introduce errors, because the diffusive

132 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl fluxes from dimensions, that are not being modelled, are neglected (e.g. Costa et al., 2003; Costa and Chakraborty, 2004; Costa et al., 2008). This leads to an overestimate of the time required to obtain a given extent of diffusive modification of a concentration distribution. It is difficult to generalize this effect, because it depends on the shape and size of the crystal, on the diffusion coefficient, and on the duration of the diffusion process. Costa et al. (2003) investigated the effect of multidimensional diffusion of Mg in plagioclase, when a finite difference adaptation of Eq. 3.3.1 for two dimensions is used, instead of modelling diffusion only in one dimension. They showed that the effects of two-dimensional diffusion become significant for relatively small and prismatic crystals. If this is ignored, in spite of good fits to profile shapes, one would retrieve incorrect cooling rates, which underestimate the effective cooling rate. (iv) If diffusive exchange of Mg between plagioclase and clinopyroxene is not the mechanism producing the observed Mg-profile shapes in plagioclase, it is unlikely, to fit multiple diverse profile shapes with diffusion modelling. Therefore, if the observed profiles can be reproduced reasonably well with the diffusion model, it is concluded, that diffusion is the main process controlling the distribution of Mg in these observed profiles.

3.6.1 A test of robustness and sensitivity of the model Reliable cooling rates can only be extracted from diffusion modelling, if certain conditions are satisfied for the measured data, and certain robustness criteria are applied to the interpreted concentration profiles of Mg in plagioclase.

(1) Traverse profiles from the rim to the opposite rim of a plagioclase crystal were measured and fitted. Analyzing the full profile is necessary to account for variations in the detailed shape of the profiles, which is the result of

coupling the diffusion of Mg to the XAn -content in the plagioclase crystal (see

Eq. 3.3.1), as well as coupling of the boundary conditions to the XAn -content at the rims of the plagioclase crystal (see Eq. 3.4.2.1).

133 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

(2) In general, two perpendicular concentration profiles were measured in a single plagioclase crystal and the resulting cooling rates from fitting these concentration profiles were checked for internal consistency. If the results from the two profiles from the same crystal were inconsistent (i.e. differ by more than one order of magnitude), the concentration profiles would have been considered to be affected by other processes than diffusion and would have been rejected (this was never necessary in this study). (3) For plagioclase crystals with an observed aspect ratio greater than 1:3, only the shorter profile was used to obtain a cooling rate. This procedure was adopted in order to obtain the most reliable effective cooling rate without considering a full 3-D diffusion model. (4) Results of multiple crystals, that shared the same evolutionary history, should be consistent with each other. Therefore, whenever possible, multiple plagioclase crystals from one sample were fitted and checked for internal consistency. This could not be applied to every sample, because among some of the investigated samples, only one crystal was found, to satisfy criteria 1- 3). (5) When the cooling rate obtained from large plagioclase crystals in both dimensions was significantly slower than the cooling rate obtained from smaller plagioclase crystals in the same sample then the cooling rate retrieved from the larger crystal was rejected. Given the preferred tabular shape of plagioclase crystals, one dimension is expected to be much shorter than the other two. Therefore, for crystals for which both dimension on the plane of the thin section are large, diffusion is likely to have been most effective along the missing, shorter third dimension. However, for full disclosure, the cooling rates from these crystals are included in the data tables, but will not be used for geological implications (this applies to 4 measured profiles, see Table 3.8.2.1 and Table 3.9.2.1).

The uncertainty of the modelling procedure after application of the above criteria, and the sensitivity of the quality of the fit of the profile shape as a function

134 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl of the cooling model were tested on two different plagioclase crystals. The two chosen plagioclase crystals represent end-member Mg-profile shapes of the investigated sample suite. Plagioclase P1 has high concentration of Mg in the core (0.13 wt%MgO) and lower concentrations of Mg at the rims (0.04 wt% MgO) (e.g.

Fig. 3.6.1.2a and b). The XAn -profile is also bowed, with higher XAn at the core than at the rims (e.g. Fig. 3.6.1.2a and b). Plagioclase P2 has an almost homogeneous XAn - content and a flat Mg-profile of around 0.04 wt% MgO (e.g. Fig. 3.6.1.2c and d).

(i) The effect of the starting temperature on the final profile shape

The effect of changing the starting temperature Tstart on the final shape of the Mg-profile after the modelling is discussed in this section. The starting temperature

Tstart , which in general is around 1200°C, was first set to higher temperatures (1250°C, 1300°C and 1400°C). No changes in the resulting final Mg-profile shapes, compared to the profiles obtained from starting the model around 1200°C, were observed for the two plagioclase crystals P1 and P2. In a second set of runs, Tstart was set to progressively lower temperatures, until a change in the final profile shape in comparison to the profile obtained from starting around 1200°C was observed.

For P1, Tstart could be lowered by 40°C without any changes in the resulting final profile shape. When Tstart was lowered by 50°C, the initial concentration at the core of the plagioclase crystal matched the measured concentration of Mg at the core and the final profile shape was slightly different to the profile shape obtained from starting around 1200°C. For P2, Tstart could be lowered by 200°C without any changes in the final profile shape.

Therefore, Tstart around 1200°C is considered to be sufficiently high, so that Mg-diffusion in plagioclase is fast enough to attain initial Mg-distributions as calculated by Eq. 3.4.2.2 for the given end-member Mg-profile shapes investigated in this study.

(ii) The effect of the final temperature on the profile shape The closure temperature Tc , at which diffusion of Mg in plagioclase becomes so slow, that a given concentration is effectively not changed anymore over

135 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl geological time scales, depends among other factors on the cooling rate and the position within the crystal (i.e. Tc is higher at the core than at the rims, see Section 1.5 in Chapter 1). A posteriori, the slowest cooling rates determined in this study are ~1⋅10 −4 °C/year. For this cooling rate, 2 µm away from the rim of the plagioclase the composition does not change significantly (less than 0.001 wt% MgO) during continuous cooling below 600°C. However, the concentration at the rim is forced to change continuously according to the boundary conditions described by Eq. 3.4.2.2. To fit the core concentrations at the rims of the plagioclase crystal, the modelling procedure was stopped at a certain temperature Tstop . This temperature

Pl / Cpx Tstop is related to the partition coefficient K Mg and thus depends on the concentration of Mg at the rim of the plagioclase, the concentration of Mg in the adjacent Cpx, and the silica activity a of the system (Eq. 3.4.2.1). SiO 2 The strongly bowed Mg-profiles measured in P1 require fast cooling rates (~0.36 °C/year) to obtain good fits (Fig. 3.6.1.1a and b). For such fast cooling rates, the overall shape of the modelled profile is not changed significantly, if modelling is continued up to lower temperatures (Fig. 3.6.1.1a and b). To obtain the fit shown in

Fig. 3.6.1.1a, the model was stopped at Tstop =960°C to match the rim concentration of this plagioclase. Fig. 3.6.1.1b shows the fit, which is obtained, if the same cooling rate (0.36 °C/year) is applied, but the model is continued down to lower temperatures (600°C). In this case, the modelled rim concentration is lower, because the boundary conditions are such, that the outermost grid point always maintains “equilibrium” with the Cpx instantaneously. However, the general shape of the profile away from the rim is the same as in Fig. 3.6.1.1a. The concentration of Mg at the interface between the plagioclase and the Cpx can not be determined easily and in fact, measured profiles always start ~2 to 5 µm inside the plagioclase crystal (for a discussion see Chapter 2). Therefore, in the case of strongly bowed Mg- profiles, which require fast cooling rates, it seems justified to continue modelling down to lower temperatures.

136 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

(a) (b) 0.14 P1Sc1 P1Sc1 0.12

0.10 0.08 dT/dt=3.610-1 °C/year dT/dt=3.610-1 °C/year 0.06 0.7 Xan 0.7 Xan 0.04 0.6 0.6 0.5 0.5 0.02 ConcentrationMgO[wt%] 0.4 0.4 rim core rim rim core rim 500 1000 1500 500 1000 1500 (c) (d)

0.14 P2Sc1 0.7 P2Sc1 0.7 0.6 0.6 0.12 0.5 Xan 0.5 Xan 0.10 0.4 0.4

0.08 -3 -3 0.06 dT/dt=1.110 °C/year dT/dt=1.110 °C/year

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim 200 400 600 200 400 600 Distance[µm] Distance[µm] Fig. 3.6.1.1: Measured (blue circles) and fitted (pink line) Mg-concentration profiles in two different plagioclase crystals P1 and P2. The insets in all panels show the respective XAn -profiles, which were measured along the same traverse as the Mg-profiles. Panels (a) and (b) show the same profile Sc1 in P1. The fit shown in (a) results from stopping the model at Tstop =960°C, to obtain the best fit for the concentration of Mg at the rim. The cooling rate obtained from this fit is 0.36 °C/year. The fit shown in (b) results, if the same cooling rate (0.36 °C/year) is applied, but the model was continued up to lower temperatures (527°C, see text for discussion). Panels (c) and (d) show the same profile Sc1 in P2. The fit shown in (c) results from stopping the model at Tstop =860°C, to obtain the best fit for the concentration of Mg at the rim. The cooling rate obtained from this fit is 0.0011 °C/year. The fit shown in (d) results, if the same cooling rate (0.0011 °C/year) is applied, but the model was continued up to lower temperatures (600°C).

Flat profiles with low Mg-concentrations (e.g. Fig. 3.6.1.1f-h) require slower cooling rates to obtain good fits. In fact, homogeneous profiles at low concentrations indicate long tempering around lower temperatures (i.e. slow cooling rates around these temperatures). However, to “freeze” these homogeneous profiles, a non-linear cooling history is required (see also Section 3.5 and Section 3.11.1). If linear cooling at these slow cooling rates is extended below Tstop , the whole profile shape is continuously modified by diffusion and the flat shape cannot be fitted anymore. This

137 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl is illustrated by comparison of Fig. 3.6.1.1c and d. The two figures show the same measured profile (Sc1 in P2), but the fitted profile in Fig. 3.6.1.1c was modelled down to Tstop =860°C to fit the rim, and the fitted profile in Fig. 3.6.1.1d was modelled down to 600°C. It can be seen, that the flat profile shape cannot be fitted under the latter conditions (Fig. 3.6.1.1d). Slightly faster cooling rates improve the fit of the concentration at the core, but the overall shape is even more strongly bowed in this case.

(iii) Robustness of the obtained cooling rate tested on two profiles within the same plagioclase crystal The robustness of the obtained cooling rates was tested on two perpendicular profiles, which were measured within the same plagioclase crystals. Ideally, they should yield the same cooling rate. Figures 3.6.1.2a and b show two perpendicular Mg-profiles (Sc1 and Sc2) within plagioclase crystal P1, which have approximately the same length (Sc1=1590 µm, Sc2=1550 µm). The resulting cooling rates for the best fits are in excellent agreement ( dT/dt =0.36 °C/year and 0.37 °C/year, respectively, Fig. 3.6.1.2a and b). Cooling rates determined by fitting the two perpendicular profiles in the second plagioclase P2, are also very similar (dT/dt =0.0011 °C/year and 0.0012 °C/year, respectively, Fig. 3.6.1.2c and d), even though the two profiles have significantly different lengths (Sc1=600 µm and Sc2=300 µm).

138 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

(a) (b) 0.14 P1Sc1 P1Sc2 0.12

0.10 0.08 dT/dt=3.610-1 °C/year dT/dt=3.710-1 °C/year 0.06 0.7 Xan 0.7 Xan 0.04 0.6 0.6 0.5 0.5 0.02 ConcentrationMgO[wt%] 0.4 0.4 rim core rim rim core rim 500 1000 1500 500 1000 1500 (c) (d)

0.14 P2Sc1 0.7 P2Sc2 0.7 0.6 0.6 0.12 0.5 Xan 0.5 Xan 0.10 0.4 0.4

0.08 -3 -3 0.06 dT/dt=1.110 °C/year dT/dt=1.210 °C/year

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim 200 400 600 100 200 300 Distance[µm] Distance[µm] Fig. 3.6.1.2: Two perpendicular Mg-profiles (Sc1 and Sc2) measured in the two different plagioclase crystals P1 and P2. Blue circles represent measured Mg-concentrations and the fitted profiles are shown as a pink line. The insets in all panels show the respective XAn -profiles, which were measured along the same traverse as the Mg-profiles. Panels (a) and (b) show two perpendicular profiles Sc1 and Sc2 within crystal P1. The cooling rates, which give the best fit, are dT/dt =0.36 °C/year (a) and 0.37 °C/year (b). Panels (c) and (d) show two perpendicular profiles Sc1 and Sc2 within crystal P2. The cooling rates, which give the best fit, are dT/dt =0.0011 °C/year (c) and 0.0012 °C/year (d).

(iv) Sensitivity of the obtained profile shape to the applied cooling rate The sensitivity of the modelled profile shape to changes in the cooling rate is illustrated in Fig. 3.6.1.3a-c for plagioclase P1 and Fig. 3.6.1.3d-f for plagioclase P2. For the strongly bowed Mg-profiles of plagioclase P1, changing the cooling rate from 0.36 °C/year, which gives the best fit (Fig. 3.6.1.3a), to 0.5 °C/year (Fig. 3.6.1.3b) and 0.2 °C/year (Fig. 3.6.1.3.c) leads to significant misfits of the profile. Fitting of the flat Mg-profiles of plagioclase P2 is less sensitive to changes in the cooling rate (Fig. 3.6.1.3d-f). If the cooling rate is changed from 0.0011 °C/year (which gives the best

139 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl fit; Fig. 3.6.1.3d) to 0.004 °C/year (Fig. 3.6.1.3e) or 0.0001 °C/year (Fig.3.6.1.3f), the calculated and measured profiles are not in good agreement.

(a) (b) (c) 0.14 P1Sc1 P1Sc1 P1Sc1 0.12

0.10 0.08 dT/dt=3.610-1 °C/year dT/dt=5.010-1 °C/year dT/dt=2.010-1 °C/year 0.06 0.7 Xan 0.7 Xan 0.7 Xan 0.04 0.6 0.6 0.6 0.5 0.5 0.5 0.02 ConcentrationMgO[wt%] 0.4 0.4 0.4 rim core rim rim core rim rim core rim 500 1000 1500 500 1000 1500 500 1000 1500 (d) (e) (f) 0.14 P2Sc1 0.7 P2Sc1 0.7 P2Sc1 0.7 0.6 0.6 0.6 0.12 0.5 Xan 0.5 Xan 0.5 Xan 0.10 0.4 0.4 0.4

0.08 -3 -3 -4 0.06 dT/dt=1.110 °C/year dT/dt=4.010 °C/year dT/dt=1.010 °C/year

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim rim core rim 200 400 600 200 400 600 200 400 600 Distance[µm] Distance[µm] Distance[µm]

Fig. 3.6.1.3: Measured (blue circles) Mg-concentration profiles in two different plagioclase crystals compared to modelled profiles (pink line), which were calculated at different cooling rates. The insets in all panels show the respective XAn -profiles, which were measured along the same traverse as the Mg- profiles. Panels (a)-(c) show the same profile Sc1 in plagioclase P1, which was fitted with different cooling rates. The best fit is obtained for a cooling rate of dT/dt =0.36 °C/year (a). If the cooling rate is increased to 0.5 °C/year (b) or decreased to 0.2 °C/year (c), the quality of the fit is visually worse. Panels (d)-(f) show a comparison of fits at different cooling rates for profile Sc1 in plagioclase P2. The best fit is obtained for a cooling rate of dT/dt =0.0011 °C/year (d). Visual misfits are observed, if the cooling rate is changed to 0.004 °C/year (e) and 0.0001 °C/year (f).

3.7 Application to natural sample suites of rocks from different depths within the lower oceanic crust

The ‘ Mg-in-plagioclase geospeedometer ’ described earlier was applied to three different sample suites of plutonic rocks formed at the fast-spreading East Pacific Rise (EPR). The individual samples of every sample suite originate from different depths within the lower oceanic crust. The following criteria were applied to choose the most suitable rock samples for this study: samples were supposed to

140 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

(a) represent gabbroic rocks, (b) contain coexisting plagioclase and clinopyroxene, and (c) to appear fresh (i.e. nearly unaltered by hydrothermal processes). In addition the robustness criteria outlined in Section 3.6.1 were applied, and plagioclase crystals with nearly idiomorphic grain shapes were preferentially selected (whenever this was possible).

3.7.1 Analytical techniques Electron microprobe (EMP) analyses of Ca, Na, Si, Al, Mg, K, Fe, Ti, Mn and Cr in plagioclase and the surrounding clinopyroxene were carried out using a Cameca SX-50 electron microprobe fitted with four wavelength-dispersive spectrometers (WDS) at the Ruhr-University in Bochum. Natural and synthetic mineral standards were used for calibration and an on-line φ(ρz)/PAP correction procedure was used to correct for absorption, fluorescence and atomic number. The concentration of Mg in plagioclase in the investigated samples is between 0.005 and 0.13 wt% MgO, which is at the lower limit of the resolution of an electron microprobe. Therefore, a special measurement procedure had to be applied to achieve high accuracy and precision. The analytical technique applied for the natural samples in this study follows the one outlined in Chapter 2, used for plagioclase crystals of approximately the same composition ( XAn ~0.6). Operating power was 15 kV and 40 nA, beam size was defocused to 5 µm, peak and background positions of the spectrometer for Mg was specifically adjusted for the measurement of Mg in plagioclase (see Chapter 2 and Table A3 in Appendix III for details). Counting time for Mg was 90 sec on the peak and 45 sec on each background. With these measurement conditions it was possible to determine compositional zoning profiles of high accuracy even for low Mg-concentrations in plagioclase (e.g. Fig. 3.8.1.1l or 3.9.1.1d). The distance between analyzed spots along the profile was 5 µm for shorter profiles and 10 µm for longer profiles. The first and last measurements at the rims of the plagioclase were approximately 2 to 5 µm away from the interface, to avoid contamination of Mg from the adjacent clinopyroxene.

141 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

3.7.2 The sample suites We investigated and fitted concentration profiles of Mg in plagioclase in natural rocks, which were formed along the EPR in the following three different areas:

1) Hess Deep (equatorial Pacific), where ~1 Ma old crust initially formed at the equatorial EPR (full spreading rate ~135 mm/year), is rifted apart due to the westward propagation of the Cocos-Nazca spreading centre (Lonsdale, 1988; Francheteau et al., 1990). This tectonic window exposes the entire upper crust (lavas and dikes, ~1200 m) as well as the upper part (~1000 m) of the gabbros (Karson et al., 2002). Therefore, the depth below the sheeted dike complex of each gabbroic rock sample can be determined. Additionally, Ocean Drilling Program (ODP) Hole 894G drilled into a rift horst at Hess Deep, recovering shallow level gabbros (Gillis et al., 1993). Since the sheeted dike/gabbro boundary is not exposed here, only the relative depth of the gabbroic samples is known, but the absolute depth in the lower crust remains undetermined.

2) Pito Deep (southern Pacific), where ~3 Ma old crust formed at the EPR (full spreading rate ~140 mm/year) is rifted apart due to a propagating rift tip of the northeaster corner of the Easter Microplate (Francheteau et al., 1988; Hey, 1995), exposing continuous sections of the oceanic crust formed by lavas, sheeted dikes and gabbroic rocks (Constantin et al., 1995; Hekinian et al., 1996, Constantin et al., 1996; Perk et al., 2007).

3) ODP Hole 1256D (eastern Pacific) drilled into ~15 Ma old intact oceanic crust of the Cocos Plate that formed at the superfast spreading EPR (full spreading rate ~220 mm/year). In this drilling project ~1250 m of oceanic crust were sampled, providing a continuous section from extrusive lavas, through sheeted dikes and into the top of the plutonic section (Wilson, 1996; Wilson et al., 2006). The penetrated top of the plutonic section consists of two major bodies of gabbro (52 m and 24 m

142 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl thick, separated by a 24 m thick screen of granoblastic dikes; Wilson et al., 2006; Koepke et al., 2008; France et al., 2009; Sano et al., 2011).

Fig. 3.7.2.1: Topographic map with locations of the investigated sample suites: Hess Deep (North Wall and ODP Site 894), Pito Deep and IODP Site 1256. The locations of Hess Deep and Pito Deep are marked with red lines and the locations of IODP/ODP Sites 1256 and 894 are shown as white circles.

In total 181 profiles were measured in 111 plagioclase crystals from 33 different samples from the 3 localities (Tab. 3.7.2.1). However, some of the measured Mg-profiles showed scattered Mg-concentration. Others had Mg- concentrations below the detection limit of the EMP analysis. In both cases, the profiles could not be used to determine cooling rates. Table 3.7.2.1 summarizes the number of profiles in different plagioclase crystals and different samples from the three sample suites. Details about all measured profiles in the different plagioclase crystals of each sample are given in Table A2 in Appendix II, including information, about the profiles, that were excluded from the process of retrieving cooling rates. Additionally, the composition of the pyroxene adjacent to each profile was measured when possible. If no pyroxene was directly adjacent to a profile, then a

143 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl pyroxene in close proximity to the respective plagioclase was measured. To have a better understanding of the 2-dimensional distribution of Mg in plagioclase, element maps were measured for selected plagioclase crystals.

Table 3.7.2.1: Number of analyzed samples, individual plagioclase crystals therein, and the number of measured concentration profiles in each crystal for the three different sample suites from Hess Deep (North wall and ODP Site 894), Pito Deep and ODP Site 1256D.

Samples Individual plagioclase Concentration profiles Location analyzed crystals analyzed measured

Hess Deep, North wall 14 44 77 Hess Deep, ODP 147 894G 3 6 11 Pito Deep 12 45 63 ODP 312 1256D 4 16 30

3.8 Results from the Hess Deep (North wall) samples

3.8.1 Shapes of Mg-profiles in plagioclase with increasing depth In general the investigated plagioclase crystals from the ODP Hole 894G show flat profiles with concentrations around 0.05 wt% MgO. However, the measured profiles show a high degree of scatter in the MgO-concentration (with up to 1 wt% MgO) and therefore were not used to determine cooling rates. The measured concentrations of MgO in plagioclase from the North wall of the Hess Deep sample suite vary between 0.01 wt% (at some of the rims) and 0.13 wt% (at the cores of the shallowest samples). The samples show a systematic decrease of MgO at the cores with increasing sample depth (Fig. 3.8.1.1); ranging from 0.13 wt% in sample 2212-1338 (17 mbsd; Fig. 3.8.1.1b) down to 0.035 wt% in sample 2218-1132 (520 mbsd; Fig 3.8.1.1l). The rims of all plagioclase crystals show MgO-concentrations between 0.01 to 0.05 wt%, with no systematic variation with the sampling depth. Mg-profiles from shallower samples show more variation between core and rim (e.g. Fig. 3.8.1.1a-d), at which the cores have higher concentrations of Mg than the rim. Plagioclase crystals in samples from greater depth show rather homogeneous Mg-profiles at lower concentrations (e.g. Fig. 3.8.1.1j-l). In general profiles from smaller plagioclase crystals show lower

144 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl concentrations of Mg, than longer profiles from the same samples (Fig. A4 in Appendix IV).

(a) (e) (i) 0.14 2212-1358C4Pl4Sc2 0.14 3369-1250C2Pl2Sc1 0.7 0.14 3369-1042C1Pl1Sc2 0.7 0.6 0.6 0.12 0.12 Xan 0.12 0.5 0.5 Xan 0.10 0.10 0.4 0.10 0.4

0.08 0.08 0.08

0 0.06 144 0.06 282 0.06 0.7 Xan 0.04 0.6 0.04 0.04 0.5 0.02 0.02 0.02

ConcentrationMgO[wt%]

ConcentrationMgO[wt%] ConcentrationMgO[wt%] 0.4 rim core rim rim core rim rim core rim 200 400 600 50 100 150 400 800 1200 1600 (b) (f) (j)

0.14 2212-1338C3Pl3Sc1 0.14 3369-1221C1Pl1Sc1 0.7 0.14 2213-1110C3Pl3Sc1 0.7 0.6 0.6 0.12 0.12 Xan 0.12 0.5 0.5 Xan 0.10 0.10 0.4 0.10 0.4

0.08 0.08 0.08

17 0.06 208 0.06 380 0.06 0.7 Xan 0.04 0.6 0.04 0.04 0.5 0.02 0.02 0.02

ConcentrationMgO[wt%]

ConcentrationMgO[wt%] 0.4 ConcentrationMgO[wt%] rim core rim rim core rim rim core rim 400 800 1200 1600 50 100 150 200 100 200 300 400 (c) (g) (k)

0.14 3369-1355C1Pl1Sc2 0.7 0.14 3369-1110C1Pl1Sc2 0.7 0.14 2218-1111C2Pl2Sc2 0.7 0.6 0.6 0.6 0.12 0.12 0.12 0.5 Xan 0.5 0.5

Depth[mbsd] Xan Xan 0.10 0.4 0.10 0.4 0.10 0.4

0.08 0.08 0.08

82 0.06 211 0.06 470 0.06

0.04 0.04 0.04

0.02 0.02 0.02

ConcentrationMgO[wt%]

ConcentrationMgO[wt%]

ConcentrationMgO[wt%] rim core rim rim core rim rim core rim 200 400 600 800 400 800 1200 100 200 300 400 500 (d) (h) (l) 0.14 3369-1349C1Pl1Sc1 0.7 0.14 3369-1050C3Pl3Sc1 0.7 0.14 2218-1132C3Pl3Sc1 0.7 0.6 0.6 0.6 0.12 0.12 0.12 0.5 Xan 0.5 Xan 0.5 Xan 0.10 0.4 0.10 0.4 0.10 0.4

0.08 0.08 0.08

90 0.06 282 0.06 520 0.06

0.04 0.04 0.04

0.02 0.02 0.02

ConcentrationMgO[wt%]

ConcentrationMgO[wt%] ConcentrationMgO[wt%] rim core rim rim core rim rim core rim 200 400 600 200 400 600 800 200 400 600 Distance[µm] Distance[µm] Distance[µm] Fig. 3.8.1.1: Representative measured concentration profiles of Mg in plagioclase (blue circles) and the respective fitted profiles (pink line) for samples from the Hess Deep sample suite. The depth below sheeted dike complex of each sample is given on the left hand side of each panel. The depth increases from (a) to (l). The inset in each panel shows the respective XAn -content, which was measured along the same traverse as the Mg-profile.

3.8.2 Cooling rates and their vertical distribution Cooling rates determined from fitting the measured Mg-profiles in plagioclase crystals from the Hess Deep sample suite are summarized in Table 3.8.2.1, and range from ~0.5 °C/year (sample 2212-1358; Table 3.8.2.1) to 0.00066 °C/year (sample 2218-1132; Table 3.8.2.1). Figure 3.8.2.1 shows the obtained cooling rate as a function of sample depth below the sheeted dike complex. A general trend of decreasing cooling rate with increasing depth of the sample is observed (Table 3.8.2.1; Fig. 3.2.8.1). The variation in cooling rate determined for

145 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl different profiles from the same sample is generally within 0.5 log units. However, for three samples (3369-1355, 3369-1349, and 3369-1050) the variation is approximately one log unit, even though all used profiles fulfil the robustness criteria discussed in Section 3.6.1. Since the generally observed decrease in cooling rate as a function of depth spans 3 log units (Table 3.8.2.1; Fig. 3.8.2.1), the systematic variation among the whole sample suite is larger, than the scatter of the obtained cooling rate from one single sample. Cooling rates obtained from different samples, which originate from approximately the same depth, overlap with each other (e.g. samples 3369-1050 and 3369-1042 both come from 282 m below the sheeted dike/gabbro boundary and the obtained cooling rates are 0.045 to 0.009 °C/year and 0.012 to 0.01 °C/year, respectively).

146 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

Table 3.8.2.1: Summary of the fitted Mg-profiles in plagioclase from the Hess Deep sample suite and the obtained cooling rates. The sample depth is given in meters below sheeted dike/gabbro boundary [mbsd]. The last column reports the temperature range, over which each profile was modelled. The starting temperature depends on the crystal size (see Section 3.4.2 and Appendix V for details), the temperature, where the model was stopped, in general was chosen to fit the rim concentration of the measured profile (see Section 3.6.1). * indicates that the profile was modelled down to lower Tstop without significant changes in the overall profile shape and modelled was stopped automatically before going below 0°C (see Section 3.6.1). italics = crystal did not fulfil robustness criteria no.5

Sample Depth Pl-crystal Profile Length dT/dt log dT/dt T range [mbsd] [µm] [°C/y] [°C]

2212-1358 0 C4Pl4 2 610 4.96E-01 -0.304 1155-750*

2212-1338 17 C1Pl1 1 500 4.83E-01 -0.316 1141-735* 2212-1338 17 C3Pl3 1 1590 3.60E-01 -0.444 1223-527* 2212-1338 17 C3Pl3 2 1550 3.71E-01 -0.431 1221-624*

3369-1355 82 C1Pl1 1 2400 8.04E-03 -2.095 1252-970 3369-1355 82 C1Pl1 2 860 6.92E-02 -1.160 1179-980 3369-1355 82 C3Pl3 1 530 3.95E-02 -1.403 1145-850 3369-1355 82 C3Pl3 2 380 4.72E-02 -1.326 1121-880

3369-1349 90 C1Pl1 1 590 2.86E-02 -1.544 1152-900 3369-1349 90 C2Pl3 1 860 8.58E-03 -2.067 1179-830 3369-1349 90 C2Pl3 2 350 4.83E-02 -1.316 1115-880 3369-1349 90 C3Pl4 1 1490 4.48E-03 -2.349 1218-880 3369-1349 90 C3Pl4 2 1360 4.72E-03 -2.326 1112-880

3374-1031 127 C1Pl1 1 590 3.40E-02 -1.468 1152-900 3374-1031 127 C1Pl1 2 260 5.99E-02 -1.222 1094-900 3374-1031 127 C2Pl2 1 910 1.42E-02 -1.848 1183-900

3369-1250 144 C2Pl2 1 190 2.11E-02 -1.675 1072-820 3369-1250 144 C2Pl2 2 275 1.69E-02 -1.772 1098-820

3369-1221 208 C1Pl1 1 207 2.27E-02 -1.643 1078-800

3369-1110 211 C1Pl1 1 460 1.13E-02 -1.948 1135-930 3369-1110 211 C1Pl1 2 1410 1.65E-02 -1.783 1214-900

3369-1050 282 C1Pl1 1 1470 2.59E-03 -2.586 1217-950 3369-1050 282 C2Pl2 1 1900 1.73E-03 -2.762 1236-950 3369-1050 282 C2Pl2 2 660 2.74E-02 -1.562 1060-900 3369-1050 282 C3Pl3 1 960 9.61E-03 -2.017 1187-960 3369-1050 282 C3Pl3 2 450 4.55E-02 -1.342 1133-960

3369-1042 282 C1Pl1 1 1410 1.24E-02 -1.907 1214-800 3369-1042 282 C1Pl1 2 1590 1.04E-02 -1.985 1223-850

2213-1110 380 C2Pl2 1 640 4.94E-03 -2.306 1158-950 2213-1110 380 C3Pl3 1 470 5.80E-03 -2.236 1136-930 2213-1110 380 C4Pl4 2 510 7.22E-03 -2.142 1142-930 2213-1110 380 C5Pl6 1 610 4.78E-03 -2.321 1155-930 2213-1110 380 C5Pl6 2 560 4.33E-03 -2.364 1149-930

2218-1111 470 C1Pl1 1 350 1.06E-02 -1.976 1115-910 2218-1111 470 C1Pl1 2 690 4.37E-03 -2.359 1164-910 2218-1111 470 C2Pl2 2 510 3.37E-03 -2.472 1142-910

2218-1132 520 C3Pl3 1 600 1.06E-03 -2.976 1154-860 2218-1132 520 C3Pl3 2 300 1.22E-03 -2.915 1104-870 2218-1132 520 C4Pl5 2 670 6.60E-04 -3.180 1162-850

147 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

Fig. 3.8.2.1: Plot of cooling rate vs. depth in m below sheeted dike/gabbro transition [mbsd] for the fitted Mg-profiles, which were measured in plagioclase of samples from the Hess Deep sample suite to illustrate the vertical variation of cooling rates. Derived cooling rates generally decrease with sample depth.

3.9 Results from the Pito Deep samples

3.9.1 Shapes of Mg-profiles in plagioclase with increasing depth The MgO-concentrations measured in plagioclase from the Pito Deep sample suite vary between ~0 wt% at the rims of some plagioclase crystals (e.g. sample 022205-0248, 45 mbsd; Table 3.9.2.1 and Fig. 3.9.2.1b) and 0.13 wt% at the cores of the shallowest sample (sample 022205-0259, 41 mbsd; Table 3.9.2.1 and Fig. 3.9.2.1a). Some of the investigated samples show great scattering of the measured Mg-concentration and therefore were not used to determine cooling rates (for

148 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl details see Table A2 in Appendix II). Mg-concentrations analysed in plagioclase crystals from the deepest samples of the studied sample suite (sample 022005- 0024; 871 mbsd) were 0 wt% MgO over the entire crystals and are interpreted to be below detection limit of the EMP analysis (see Table A2 in Appendix II). In general, plagioclases from the Pito Deep sample suite show a trend of decreasing Mg-concentration at the core with increasing sample depth, similar to plagioclases from Hess Deep (see Fig. 3.9.1.1a-i; e.g. core concentrations of 0.13 wt% MgO in the shallowest sample 022205-0259, 41 mbsd, Fig. 3.9.1.1a, compared to 0.05 wt% MgO in sample 022005-0056, 836 mbsd, Fig. 3.9.1.1i). However, the observed trend is less systematic for the Pito Deep samples, than for the Hess Deep samples. For example, the Mg-concentration in the Pito Deep sample 022005-1052 (355 mbsd; Fig. 3.9.1.1d) is anomalously low, compared to samples deeper within the sequence. This sample is different from all other samples used to obtain cooling rates though, in that it consists of almost only plagioclase and only very little clinopyroxene (Table A1 in Appendix I, see 3.11.2 for discussion of possible interpretations for the low Mg-concentrations in this sample). The shapes of the Mg-profiles from shallower samples are bowed, with higher Mg-concentrations at the core than at the rims, and tend to become more homogeneous with increasing sample depth (Fig. 3.9.1.1). Again, this trend is not as systematic as in the Hess Deep samples. The two shallowest Pito Deep samples investigated here (samples 022205-0259, 41 mbsd and 022205-0248, 45 mbsd; Fig. 3.9.1.1a and b) show strongly bowed Mg-profiles, but even though both samples were collected from almost the same depth, sample 022205-0259 shows core concentrations of 0.13 wt% MgO, whereas sample 022205-0248 has concentrations of only 0.08 wt% MgO in the core (at approximately the same length and XAn , Fig. 3.9.1.1a and b). Plagioclase crystals from samples deeper than 45 m below the sheeted dike/gabbro boundary generally show flatter profiles with less difference between Mg-concentrations at the core and at the rims.

149 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

(a) (d) (g) 0.14 022205-0259C2Pl2Sc2 0.14 022005-1052C3Pl3Sc2 0.14 022005-0506C2Pl2Sc1 0.8 0.8 0.12 0.12 0.12 0.6 0.6 0.10 0.10 Xan 0.10 Xan 0.08 0.08 0.08

41 0.06 355 0.06 662 0.06

0.04 0.8 0.04 0.04

0.02 0.6 0.02 0.02

ConcentrationMgO[wt%] ConcentrationMgO[wt%] ConcentrationMgO[wt%] rim core Xan rim rim core rim rim core rim 200 400 600 125 250375 500 200 400 600

(b) (e) (h) 0.14 022205-0248C2Pl2Sc2 0.14 022005-0910C2Pl2Sc1 0.14 022005-0155C2Pl2Sc1 0.8 0.8 0.8 0.12 0.12 0.12 0.6 0.6 0.6 0.10 Xan 0.10 Xan 0.10 Xan 0.08 0.08 0.08

45 0.06 386 0.06 780 0.06

0.04 0.04 0.04

0.02 0.02 0.02

ConcentrationMgO[wt%] ConcentrationMgO[wt%] ConcentrationMgO[wt%] rim core rim rim core rim rim core rim

Depth[mbsd] 200 400 600 800 125 250375 500 200 400 600 800

(c) (f) (i) 0.14 022005-0230C1Pl1Sc1 0.14 022005-0534C2Pl2Sc2 0.14 022005-0056C3Pl3Sc1 0.8 0.8 0.8 0.12 0.12 0.12 0.6 0.6 0.6 0.10 Xan 0.10 Xan 0.10 Xan 0.08 0.08 0.08

72 0.06 569 0.06 836 0.06

0.04 0.04 0.04

0.02 0.02 0.02

ConcentrationMgO[wt%] ConcentrationMgO[wt%] ConcentrationMgO[wt%] rim core rim rim core rim rim core rim 100 200 300 200 400 600 800 100 200 300 400 Distance[µm] Distance[µm] Distance[µm] Fig. 3.9.1.1: Representative measured concentration profiles of Mg in plagioclase (blue circles) and the respective fitted profiles (pink line) for the Pito Deep sample suite. The depth below sheeted dike complex of each sample is given on the left hand side of each panel and the depth increases from (a) to (i). The inset in each panel shows the respective XAn -content, which was measured along the same traverse as the Mg-profile.

3.9.2 Cooling rates and their vertical distribution Cooling rates obtained from fitting the measured Mg-profiles in plagioclase crystals from the Pito Deep sample suite range from ~5 °C/year (sample 022205- 0259; Table 3.9.2.1) down to 0.00001 °C/year (sample 022005-1052; Table 3.9.2.1). Figure 3.9.2.1 shows the obtained cooling rate as a function of sample depth below the sheeted dike complex. A strong decrease in cooling rate from 5 °C/year to 0.005 °C/year is observed within the three shallowest samples (022205-0259, 41 mbsd; 022205-0248, 45 mbsd and 022205-0230, 72 mbsd), at which cooling rates determined from different profiles within the same sample are very robust for these three samples (Table 3.9.2.1). Cooling rates obtained from sample 022005- 1052 (355 mbsd), which has relatively low Mg-concentrations (see Section 3.9.1), are relatively slow (0.00002 °C/year) compared to all other cooling rates determined in this study (see also Section 3.11.12). The next deepest sample for

150 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl which cooling rates were determined, was located 386 m below the sheeted dikes (sample 022005-0910) and the determined cooling rates from the different profiles of this sample indicate faster cooling (between 0.01 and 0.002 °C/year, Table 3.9.2.1) than cooling rates obtained from the shallower sample 022005-1052 (355 mbsd). For samples below 385 mbsd, the obtained cooling rates generally decrease with increasing depth (Fig. 3.9.2.1).

Table 3.9.2.1: Summary of the modelled profiles in the Pito Deep sample suite and the obtained cooling rates. The sample depth is given in meters below sheeted dike/gabbro boundary [mbsd]. The last column indicates the temperature range, over which each profile was modelled. The starting temperature depends on the crystal size (see Section 3.4.2 and Appendix V for details), the temperature, where the model was stopped, was chosen to fit the rim concentration of the measured profile (see Section 3.6.1).

Sample Depth Pl-crystal Profile Length dT/dt log dT/dt T range [mbsd] [µm] [°C/y] [°C]

022205-0259 41 C1Pl1 1 323 4.98E+00 0.697 1160-1010 022205-0259 41 C1Pl1 2 415 4.84E+00 0.685 1178-1000 022205-0259 41 C2Pl2 1 480 4.98E+00 0.698 1188-791 022205-0259 41 C2Pl2 2 702 2.33E+00 0.367 1215-920

022205-0248 45 C2Pl2 2 888 1.26E-01 -0.899 1182-700 022205-0248 45 C4Pl4 1 200 1.61E-01 -0.792 1076-700

022205-0230 72 C1Pl1 1 370 5.19E-03 -2.285 1119-700

022005-1052 355 C2Pl2 1 900 1.00E-05 -4.999 1182-740 022005-1052 355 C2Pl2 2 420 2.00E-05 -4.699 1128-730 022005-1052 355 C3Pl3 1 970 1.20E-05 -4.920 1188-680 022005-1052 355 C3Pl3 2 500 2.30E-05 -4.638 1141-730

022005-0910 386 C1Pl1 1 490 5.24E-03 -2.281 1139-800 022005-0910 386 C1Pl1 2 240 1.06E-02 -1.975 1089-830 022005-0910 386 C2Pl2 1 530 1.97E-03 -2.705 1145-700 022005-0910 386 C4Pl4 2 460 5.46E-03 -2.263 1135-800

022005-0534 569 C2Pl2 1 560 1.55E-03 -2.809 1149-750 022005-0534 569 C2Pl2 2 850 4.90E-04 -3.309 1178-780

022005-0506 662 C2Pl2 1 730 1.01E-04 -3.998 1168-600 022005-0506 662 C2Pl2 2 1050 1.77E-04 -3.752 1193-600

022005-0155 780 C1Pl1 1 350 4.96E-03 -2.304 1115-700 022005-0155 780 C1Pl1 2 830 8.63E-04 -3.064 1177-700 022005-0155 780 C2Pl2 1 850 4.75E-04 -3.323 1178-700

022005-0056 836 C2Pl2 1 1510 1.00E-04 -4.000 1219-600 022005-0056 836 C2Pl2 2 830 2.81E-04 -3.551 1177-600 022005-0056 836 C3Pl3 1 470 3.81E-04 -3.485 1136-600 022005-0056 836 C3Pl3 2 800 2.61E-04 -3.825 1174-600 022005-0056 836 C5Pl5 1 840 2.31E-04 -3.357 1178-600

151 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

Fig. 3.9.2.1: Plot of cooling rate vs. depth of the modelled samples of the Pito Deep sample suite.

3.10 Results from the IODP 312 1256D samples

Most of the measured Mg-profiles of the IODP Site 1256D sample suite investigated here either show larger scattering of the Mg-concentration or have Mg- concentrations below the detection limit of the EMP measurement (see Table A2 in Appendix II for details). Therefore, only two out of 30 measured profiles were suited for the determination of cooling rates (Fig. 3.10.1 and Table 3.10.1). These two profiles were measured within the two shallowest samples of the investigated sample suite (12.1 mbsd and 12.4 mbsd). However, one of these profiles shows a decrease of Mg-concentration towards the core of the crystal, that is associated with a crack, which is likely to have altered the original profile. Since it is not clear, if a

152 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl fluid circulating through this crack was in equilibrium with the surrounding clinopyroxene, the partition coefficient is ambiguous and the boundary conditions of the model described above may not be applicable. This profile may be modelled using boundary conditions that account for the effect of a fluid (as outlined by Dohmen et al., 2003 and Dohmen and Chakraborty, 2003), which was not done in the scope of this study. However, under the assumption, that the fluid was in equilibrium with the surrounding clinopyroxene, the measured profile can be modelled as two separate crystals using the above described boundary conditions. The cooling rate obtained from sample 216 R01 15-20 is 0.16 °C/year, and the cooling rate determined from modelling the profile in sample 216 R01 49-57 as two separate parts is 0.31 °C/year for each part of the profile (Table 3.10.1). (a) (b)

0.14 216R01 0.7 Xan 216R01 0.7 Xan 0.14 0.6 0.6 0.12 15-20C3Pl3Sc1 49-57C1Pl1Sc1 0.5 0.12 0.5 0.10 0.4 0.4 rim 0.10 rim 0.08 0.08 12.1 0.06 12.4 0.06 0.04 0.04 0.02 ConcentrationMgO[wt%] 0.02 rim core ConcentrationMgO[wt%] rim core 100 200 300 400 200 400 600 Distance[µm] Distance[µm] Fig. 3.10.1: Measured concentration profiles of Mg in plagioclase (blue circles) and the respective fitted profiles (pink line) for the two modelled samples from the IODP Site 1256D sample suite. The depth below sheeted dike complex of each sample is given on the left hand side of each panel. The inset in each panel shows the respective XAn -content, which was measured along the same traverse. The decrease in the MgO-concentration towards the core of profile in (b) is associated with a crack in the plagioclase crystal, which may have altered the original profile, therefore, the profile was modelled as two separate profiles, assuming the same boundary conditions at the interface with the crack (see text for discussion)

Table 3.10.1: Summary of the fitted profiles in the IODP Site 1256D sample suite and the obtained cooling rates. The sample depth is given in meters below sheeted dike/gabbro boundary [mbsd]. The last column indicates the temperature range, over which each profile was modelled. The starting temperature depends on the crystal size (see Section 3.4.2 and Appendix V for details), the temperature, where the model was stopped, was chosen to fit the rim concentration of the measured profile (see Section 3.6.1).

Sample Depth Pl-crystal Profile Length dT/dt log dT/dt T range [mbsd] [µm] [°C/y] [°C]

216 R01 15-20 12.1 C3Pl3 1 460 1.60E-01 -0.796 1135-800

216 R01 49-57 12.4 C1Pl1 a 1 318 3.13E-01 -0.504 1107-750

216 R01 49-57 12.4 C1Pl1 b 1 385 3.05E-01 -0.516 1122-750

153 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

3.11 Discussion

3.11.1 Implications for the constraints on the cooling history of each sample The cooling rates reported here are based on the assumption of a linear cooling history within a given temperature interval (Table 3.8.2.1, Table 3.9.2.1 and

Table 3.10.1). The starting temperature Tstart was chosen around 1200°C, where the initial Mg-concentration was calculated according to Eq. 3.4.2.2. However, homogeneous profiles at low Mg-concentrations require slow cooling rates to fit the final profile near the temperature at which the profile is “frozen”. For these profiles, the cooling rate at higher temperatures (around Tstart ) is not well constrained and could have been faster than the one given in Table 3.8.2.1, Table 3.9.2.1 and Table 3.10.1. The reason for this ambiguity is that for sufficiently slow cooling rates at high temperatures, Mg-diffusion is fast enough to maintain “equilibrium” over the entire plagioclase crystal. In this case, the information is lost how this Mg-distribution at high temperatures was achieved, and the final Mg-profile contains no direct information about the cooling history at higher temperatures. Therefore, the cooling rates obtained from homogeneous Mg-profiles at low concentrations are more reliable for a temperature interval of approximately 100°C above the temperature

Tstop , at which the modelling procedure was stopped to fit the Mg-concentration at the rims (solid blue line in Fig. 3.11.1.1). This temperature interval is larger for the bowed Mg-profiles with higher concentrations at the core, because higher concentrations at the core put a tighter constraint on the cooling rates at higher temperatures (solid orange line in Fig. 3.11.1.1). For example, for the Mg-profiles with up to 0.13 wt% MgO at the cores, the temperature interval, in which the obtained cooling rates can be considered reliable, starts around 1150°C. Additionally, the cooling rates determined from Mg-profiles with high core concentrations (e.g. ~0.5 °C/year from sample 2212-1338) provide maximum cooling rates for the high temperature cooling history of the plagioclase crystals with homogeneous Mg-profiles at lower concentrations (Fig. 3.11.1.1). Cooling around 1150°C can not have been faster than this, because otherwise diffusion

154 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl would not have been efficient enough to remove Mg from the cores of the crystals with the homogeneous, low Mg-concentrations.

The fact, that the model is stopped at Tstop to fit the overall profile shape and the concentrations at the rims may be explained by several hypotheses, which will be evaluated below: (i) a change in the kinetics of partitioning of Mg between plagioclase and clinopyroxene during cooling (in analogy to fluid-mediated exchange reactions as investigated by Dohmen and Chakraborty, 2003; Dohmen et al., 2003). The model applied here is based on the assumption, that the rims of the plagioclase crystals always attain “equilibrium” with the clinopyroxene instantaneously. If the kinetics of Mg partitioning between the two minerals becomes very slow below a certain temperature (e.g. Tstop ), the rims of the plagioclase would effectively “freeze” before the actual closure temperature Tc of diffusion. (ii) the diffusion rate of Mg in clinopyroxene drops below a critical value, such that even trace element exchange of Mg with the plagioclase is not possible. The diffusion-model applied here assumes, that the diffusive exchange of Mg between plagioclase and clinopyroxene is controlled by the diffusion of Mg in plagioclase. Although diffusion of Mg in clinopyroxene is slower than in plagioclase (Zhang et al., 2010), Mg is a major element in clinopyroxene and therefore it is necessary to have transport of only a few atoms to equilibrate a plagioclase with clinopyroxene. If diffusion rates in clinopyroxene drop below a critical value at a certain temperature (e.g. Tstop ), such that even this small flux is not possible, then Mg contents in plagioclase would “freeze” before the actual closure temperature Tc of diffusion of Mg in plagioclase. (iii) a change in the diffusion mechanism during cooling, such that diffusion rates at lower temperatures are slower than that expected from an Arrhenian extrapolation. A more effective diffusion mechanism at higher temperatures than at lower temperatures would imply an abrupt decrease in diffusivity below a certain temperature (e.g. Tstop ) and therefore less efficient removal of Mg out of the plagioclase during continuous cooling. Thus the rim concentration would effectively “freeze” at higher temperatures.

155 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

(iv) a change in cooling rate during cooling. If the cooling rate becomes fast below a certain temperature (e.g. Tstop ), diffusion effectively may be too slow to continuously change the shape of the developed profile significantly and the profile “freezes” around this temperature.

If (i) and/or (ii) apply, the assumption of equilibrium at the interface between plagioclase and clinopyroxene would not be justified anymore and the approach taken here would not be valid. However, in the case of general disequilibrium between the two phases, the obtained cooling rates from the approach taken here would not be expected to be as systematic as they are.

Furthermore, in the case of (ii) and (iii), Tstop is expected to depend only on the cooling rate. Therefore, for a given cooling rate, Tstop should be the same for the Hess and Pito Deep sample suite, which is not the case (Table 3.8.2.1 and Table

3.9.2.1; Fig. 3.11.2.2). Similar Tstop values for the different sample suites at a given cooling rate are also expected, if (i) applies, unless, the partitioning is for example fluid assisted and the availability of fluid on the interfaces of the plagioclase crystals is different for Hess and Pito Deep. Yet, no observation was found to support this hypothesis. The observed Mg-profile shapes can be explained by a change in cooling rate as suggested in (iv), if a cooling rate of ~0.5 °C/year (or higher) for continuous cooling below Tstop is assumed. This was tested for several Mg-profiles in plagioclase from different samples and a significant change in the profile shapes away from the rim was not observed. Furthermore, a change in cooling rate is also supported by the fact, that homogeneous Mg-concentration profiles are observed. As shown and discussed in Section 3.5, a linear cooling history always produces bowed concentration profiles. This is also true for the more general case of any cooling path with a monotonously decreasing cooling rate. Therefore, the observation of homogeneous concentration profiles itself already indicates a non-linear (or in general non-monotonous) cooling history.

156 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

In summary, the obtained linear cooling rates are considered to be reliable for a temperature interval of about 100°C above Tstop for homogeneous profiles at low Mg-concentrations. For Mg-profiles with higher concentrations at the core, the temperature interval above Tstop , for which the linear cooling rates are reliable, is larger (Fig. 3.11.1.1). Cooling rates obtained from the Mg-profiles with the highest core concentrations provide a maximum estimate for cooling rates at higher temperatures (~0.5 °C/year) for all other profiles with lower Mg-concentrations at the core. The shapes of the observed Mg-profiles can be explained, if a cooling rate of ~0.5 °C/year (or higher) is assumed for continuous cooling from Tstop down to 600°C. Below 600°C, diffusion of Mg in plagioclase is so slow, that no more significant changes in the Mg-profiles can be observed at the given conditions.

0.5

Coolingrate[°C/year] Tstart Tstop Tc 1200 1100 1000 900 800 700 600

Temperature[°C] Fig. 3.11.1.1: Schematic diagram to illustrate the constraints on the cooling history of the two different plagioclase crystals. Blue lines are related to plagioclase with homogeneous Mg-profiles at low concentrations and orange lines are related to plagioclase with Mg-profiles showing higher Mg- concentrations at the core. Solid bold lines show the temperature interval, over which the determined linear cooling rates are regarded to be reliable. Tstop is assumed to be 800°C for both examples, i.e. the concentration of Mg at the rims is assumed to be the same. Around Tstart , the cooling rates can not be determined exactly with the approach take here (indicated by dashed lines), but the maximum cooling rates at high temperatures are around 0.5°C (see text for discussion). The observed shapes of the Mg-profiles can be explained, if a cooling rate of ~0.5 °C/year is assumed below Tstop .

157 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

3.11.2 Comparison of the different sample suites A comparison of the obtained vertical distribution of cooling rates for the three sample suites from different locations within the EPR is shown in Fig. 3.11.2.1. All three data sets show a trend of decreasing cooling rates with increasing sample depth below their respective sheeted dike complexes. Furthermore, the three data sets appear to be consistent with each other (e.g. Hess Deep sample 2213-1110 from 380 mbsd and Pito Deep sample 022005-0910 from 386 mbsd yield cooling rates of 0.0043 to 0.0072 °C/year and 0.002 to 0.019 °C/year, respectively; Table 3.8.2.1, Table 3.9.2.1 and Fig. 3.11.2.1). However, two samples from the Pito Deep sample suite fall outside the general trend: (i) Cooling rates determined from sample 022005-1052 (355 mbsd) are slower than the cooling rates indicated by the general trend at the given depth. The relatively slow cooling rates result from the relatively low concentration of Mg in plagioclase from this sample (Fig. 3.9.1.1d). The sample differs from all others samples used to obtain cooling rates, because it consists of almost only plagioclase and only very little clinopyroxene (Table A1 in Appendix I), suggesting that most plagioclase crystals in this sample were at no time in equilibrium with clinopyroxene. Therefore, this sample is not suited for the approach taken here and will not be used for interpretation of the vertical distribution of cooling rates. (ii) Cooling rates determined from the shallowest sample of the Pito Deep sample suite (022205-0259, 41 mbsd) are faster than indicated by the general trend in cooling rates at the given depth (Fig. 3.11.2.1). The very fast cooling rates obtained from this sample may be explained by formation of these rocks from the intrusion and subsequent cooling and crystallization of magma into a particularly cold region of the crust. However, this should be considered a preliminary interpretation, since sample 022205-0248 was collected in very close proximity (45 mbsd) and the obtained cooling rates are about one order of magnitude slower (Table 3.9.2.1, Fig. 3.9.2.1 and Fig. 3.11.2.1).

158 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

Fig. 3.11.2.1: Comparison of the vertical distribution of cooling rates from the three sample suites from different locations along the EPR (Hess Deep: black crosses; Pito Deep: red squares; IODP Site 1256D: blue triangles). The cooling rates obtained from the different localities match extremely well. They define a trend of decreasing cooling rates with increasing sample depth below their respective sheeted dike complexes (except for two samples from the Pito Deep samples suite; see text for further explanation).

Special care needs to be taken when comparing the obtained cooling rates with each other, since they are based on the assumption of linear cooling in different temperature intervals. This is illustrated in Fig. 3.11.2.2, where the average temperature Tstop , at which modelling was stopped for each sample, is plotted in addition to the vertical distribution of the obtained cooling rates. In general, fitting the Mg-profiles in plagioclase from the Hess Deep sample suite requires higher temperatures Tstop , than the Mg-profiles in plagioclase from the Pito Deep sample suite. Furthermore, profiles measured in samples from greater depth can be modelled down to lower temperatures Tstop . This causes some bias when cooling

159 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl rates from the different samples suites are compared as a function of depth, because cooling rates may simply become slower with decreasing temperature. However, samples from the same depth of the different sample suites give the same cooling rate, even though they were modelled up to different temperatures Tstop . For example, modelling of Hess Deep sample 2213-1110 from 380 mbsd was stopped at 930°C and that of Pito Deep sample 022005-0910 from 386 mbsd was stopped at an average temperature of 780°C, but the obtained cooling rates are in good agreement (Table 3.8.2.1, Table 3.9.2.1 and Fig. 3.11.2.1). Thus, the effect induced by comparing cooling rates, which are obtained for slightly different cooling intervals, is considered to be negligible in the range of cooling intervals of this study.

Fig. 3.11.2.2: Same plot as in Fig. 3.11.2.1, but in addition, the average temperature Tstop , at which modelling was stopped to fit the rim concentrations, it shown for each sample.

160 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

3.11.3 Comparison of cooling rates obtained from Mg-in-plagioclase and from Ca-in-olivine The ‘ Ca-in-olivine geospeedometer ’ was used previously to determine the vertical distribution of cooling rates in the lower oceanic crust from two different sections of the the Oman ophiolite (Coogan et al., 2002b; Coogan et al., 2007; VanTongeren et al., 2008) as well as of plutonic rocks from Hess Deep and Pito Deep (Coogan et al., 2007). However, cooling rates from these studies were not always in agreement. Coogan and co-workers (Coogan et al., 2002b; Coogan et al., 2007) fitted complete diffusion profiles and report a smooth decrease in cooling rate as a function of depth (with cooling rates between ~0.1 °C/year up to ~0.00003 °C/year for their deepest samples around 3600 mbsd; Coogan et al., 2007). VanTongeren et al. (2007) used only the Ca-content in the cores of the olivine crystals and obtained in general slower cooling rates than Coogan et al. (2002b and 2007). VanTongeren et al. (2007) interpret their data to show no significant change in cooling rate as a function of depth. However, since the data set of Coogan et al. (2007) includes cooling rates determined for samples from Hess and Pito Deep, their results provide a more direct comparison to the cooling rates determined for the sample suite here. Figure 3.11.3.1 shows a comparison of the vertical distribution of cooling rates determined from the ‘ Mg-in-plagiolcase geospeedometer ’ from this study with the results of Coogan et al. (2007) for the ‘ Ca-in-olivine geospeedometer ’. The two data sets match extremely well (Fig. 3.11.3.1). Cooling rates from the two approaches can be compared directly for one sample from Pito Deep (022205-0230) and one sample from Hess Deep (3369-1355), where data is available for exactly the same sample. The cooling rate for the Pito Deep sample 022205-0230 obtained from Mg-in- plagioclase is 0.0052 °C/year (Table 3.9.2.1) and 0.0012 °C/year obtained from Ca- in-olivine (Coogan et al., 2007). The Hess Deep sample 3369-1355 yields a range of cooling rates of 0.008 to 0.069 °C/year from Mg-in-plagioclase (Table 3.9.1.1) and 0.045 to 0.058 °C/year from Ca-in-olivine (Coogan et al., 2007). Therefore, cooling rates obtained from two completely different approaches are in excellent agreement, suggesting that the obtained cooling rates are robust.

161 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

Fig. 3.11.3.1: Comparison of the vertical distribution of cooling rates determined from ‘ Mg-in- plagioclase geospeedometry ’ from this study (red symbols) with the results from Coogan et al. (2007) obtained from ‘ Ca-in-olivine geospeedometry ’ (black symbols) for the same depth range.

3.11.4 Interpretation and discussion of the vertical distribution of cooling rates The prominent decrease of cooling rate with increasing depth in the lower oceanic crust implies, that the mechanism of heat removal is not the same over the investigated depth sequence (0 to 900 mbsd). Instead, heat removal is more efficient close to the gabbro/dike boundary (i.e. the inferred location of the AMC) and becomes less efficient with increasing depth. The simplest model to potentially explain a smooth decrease in the cooling rate with depth in the lower oceanic crust might be a half-space model in which the heat is assumed to be vertically conducted from the crust to the surface (Fig.

162 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

3.11.4.1). The upper crust is assumed to be cooled by hydrothermal circulation, which keeps the temperature at the dike/gabbro transition constant. The lower crust is cooled conductively as it moves off-axis. In the reference frame of a single column of crust, this can be modelled as one-dimensional vertical conductive cooling of a semi-infinite body with a fixed surface temperature and an initial constant temperature. Here, the top of the lower crust is held constant at 400°C and the initial temperature of the entire crust and upper mantle is assumed to be 1300°C. The cooling of this half-space is modelled using Equation 4.124 of Turcotte and Schubert (2002) with a thermal diffusivity of 1 x 10 -6m2/s. Conductive cooling in this half-space model is not linear, so it is crucial, over which temperature interval the cooling rates are compared. Here, cooling rates for a purely conductive cooling model were calculated in a temperature interval of 700 to 600°C and 900 to 600°C (grey and black solid lines in Fig. 3.11.4.1). These temperature intervals are around Tstop for most of the samples investigated here. The conductive cooling model suggests nearly linear cooling for the temperature interval from 700-600°C. For the temperature interval from 900 to 600°C, cooling is nearly linear below a depth of 500 mbsd. Conductive cooling rates in these two temperature intervals approximately match the variations of cooling rate with depth obtained from diffusion modelling of Mg in plagioclase, but in general are slightly offset to faster cooling rates (Fig. 3.11.4.1). Especially above 200 mbsd, the cooling rates from the conductive model are faster than the ones obtained from Mg-in-plagioclase. One possible explanation for this discrepancy is that this very simple conductive half-space model does not account for horizontal heat transport from a melt lens. At low depth around 0- 200 mbsd, the half-space model yields timescales of 20 to 8000 years to attain temperatures around 600°C. At a given full spreading rate of 135 to 140 mm/year (see Section 3.7.2), these timescales imply a distance of less than 1 km off-axis. Therefore, the slower cooling rates at shallower depths obtained from M g-in- plagioclase may be explained by additional horizontal heat transport from the melt lens, which would affect cooling in a distance of 1 km and slow it down. At greater depth, the conductive half-space model requires more time to attain temperatures

163 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl around 600°C (e.g. 128 000 years at 800 mbsd). At the same spreading rate, this implies greater distance off-axis (8.9 km after 128 000 years). Therefore, cooling rates around 600°C are not expected to be affected significantly by horizontal heat transport from a melt lens at the ridge axis. Maclennan et al. (2005) calculated more detailed thermal models, with various amounts of hydrothermal circulation in the lower oceanic crust (dashed and dotted lines in Fig. 3.11.4.1). The model geometry is split in two regions: an axial region, where the thermal structure is modelled only in vertical dimension, and an off-axis region, where horizontal advection at the half spreading rate of the ridge is included, and therefore the thermal structure is modelled in two dimensions. They use a thermal diffusivity oft 8 x 10 -7m2/s. Their Model 1 is a ‘ gabbro glacier ’ type model, which assumes intensive hydrothermal circulation above a shallow melt lens, but also allows for some hydrothermal circulation in the lower crust (which is not necessary for a ‘ gabbro glacier ’ model, but also not excluded). Different ‘hybrid models ’ (Model 2 and 3) assume less hydrothermal circulation at the top and allow different amounts of hydrothermal circulation in the lower crust. Model 4 is another ‘gabbro glacier ’ type model, which again includes intensive hydrothermal cooling at the top, and assumes purely conductive cooling at lower levels. The results of Maclennan et al. (2005) for the ‘ hybrid models ’ (Model 2 and 3) show no significant variation of cooling rates with depth in the range of the lower crust investigated here and are offset to faster cooling rates when compared to the results from Mg-in- plagioclase (Fig. 3.11.4.1). Their prediction of variation of cooling rate with depth of their Model 1 in general is very similar to the cooling rates of the ‘ hybrid models ’, except for the uppermost level of the lower oceanic crust, where heat is removed more efficiently due to the assumption of intensive hydrothermal cooling in this region. The Model 4 of Maclennan et al (2005) matches the cooling rates determined from Mg-in-plagioclase for the lower crust below 500 mbsd and above 100 mbsd. In between, cooling rates from this Model 4 are offset to slower cooling rates when compared to the results presented here. The major difference between Model 4 of Maclennan et al. (2005) and the conductive half-space model described above, is the fact, that the Model 4

164 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl additionally accounts for advective heat transport from the side in their off-axis region, which starts after 1 km away from the axis to match geophysical observations. Therefore, the cooling rates obtained in their Model 4 are slower, than the ones obtained from the purely one dimensional conductive half-space model described above. The data obtained from Mg-in-plagioclase generally falls between the predictions from these two models, implying that there is some additional horizontal heat supply from the region of the ridge axis.

Fig. 3.11.4.1: Comparison of the vertical distribution of cooling obtained from Mg-in-plagioclase from this study with different thermal models: (i) a simple half-space model, in which heat is assumed to conduct vertically out of the crust using a thermal diffusivity of 1 x 10 -6m2/s. The initial temperature through the crust and mantle is assumed to be 1300°C and the temperature at the dike/gabbro boundary is held constant at 400°C. The cooling rate was calculated for a temperature interval of 700 to 600°C (solid grey line) and for 900 to 600°C (solid black line). (ii) four thermal models from Maclennan et al. (2005). Three (Model 1-3) include hydrothermal circulation in the lower oceanic crust (dashed black line, dashed grey line, and dotted grey line). The other model (Model 4) does not include hydrothermal circulation in the lower oceanic crust (dotted black line).

165 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

In summary, the results on the vertical distribution of cooling rates obtained from Mg-in-plagioclase are inconsistent with the predictions of thermal models that allow for hydrothermal circulation at greater depth of the lower oceanic crust (Model 1-3 from Maclenan et al., 2005; Fig. 3.11.4.1). However, the data obtained from this study generally fall between the vertical distributions of cooling rates, predicted from thermal models, in which hydrothermal circulation removes heat from the top of a shallow magma chamber and the crust at deeper levels is cooled conductively (simple conductive half-space models and Model 4 of Maclennan et al., 2005; Fig. 3.11.4.1). As discussed in Section 3.6, a 1-D diffusion model neglects diffusive fluxes from dimensions, that are not being modelled, which leads to an overestimation of the time required to obtain a given Mg-concentration profile. In other words, the use of a 1-D diffusion model might underestimate the cooling rate obtained from a given Mg-profile. Modelling the measured profiles with a 2-D diffusion model might help to resolve this issue (see also Chapter 4). The absolute cooling rates obtained from a 2-D model are expected to be slightly faster, compared to those of a 1-D model. However, this might influence the absolute values, but the observed relative trend of decreasing cooling rate as a function of depth is not expected to be changed. Furthermore, the observed trend of decreasing cooling rate as a function of depth is very systematic for the different sample suites (Fig. 3.8.2.1 and 3.9.2.1) as well as for the comparison among the sample suites (Fig. 3.11.2.1) and a comparison with data obtained from Ca-in-olivine (Fig. 3.11.3.1). No systematic difference is observed for cooling rates obtained from plagioclase crystals with different grain size. If the results obtained from 1-D modelling are expected to yield very different cooling rates compared to results obtained from a 2-D (or 3-D) model, this should be indicated by greater scatter in the data, and the overall results are not expected to be very systematic (e.g. Costa and Chakraborty, 2004). Therefore, the simplification of using a 1-D diffusion model compared to a 2-D diffusion model is considered to be tolerable here.

166 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

3.11.5 Geological implications The cooling rates between different segments of the EPR are very similar for a given depth below the respective sheeted dike complex (Fig. 3.11.2.1). This close similarity of cooling rates as a function of depth in the lower crust implies a very comparable thermal structure in the off-axis region along the EPR. The general observation of decreasing cooling rates as a function of depth in the lower oceanic crust is consistent with a ‘ gabbro glacier ’ type model of crustal accretion. This model suggests most of the heat to be removed by hydrothermal circulation at the top of the AMC, leading to fast cooling rates in the upper gabbros (central panel in Fig. 3.1.1, green line). With increasing depth, heat conduction becomes the dominant process of heat transfer. Since heat conduction is a less efficient mechanism of heat removal than hydrothermal circulation, the cooling rates are expected to decrease with increasing depth, which is consistent with the data presented here. The data obtained in this study are inconsistent with hydrothermal circulation being a major mechanism of heat removal at deeper levels of the lower oceanic crust. This is a major constraint for the existence of extensive in situ crystallization in multiple sills at various depths (e.g. Chen, 2001; Maclennan et al., 2004 and 2005), as suggested by a ‘ sheeted sill ’ type model. Therefore, this type of model is not supported by the data acquired in this study.

The temperature Tstop , at which modelling had to be stopped to fit the profile shape and the concentration at the rim, is between 980 and 800°C for the Hess Deep sample suite and ranges from 830 to 600°C for the Pito Deep sample suite (excluding the samples which fall outside the general trend). The shape of all profiles can be fitted reasonably well, if modelling below Tstop is continued with a cooling rate of 0.5 °C/year. This cooling rate is similar to the cooling rates obtained from the shallower samples, which are interpreted to be associated with heat removal by hydrothermal circulation. Therefore, one way to explain the studied Mg- profile shapes is an increase of hydrothermal activity in the lower oceanic crust below a certain temperature. While the rocks cool and move away from the ridge axis, they might become more brittle, which could allow the formation of pathways for hydrothermal fluids and hence, increased hydrothermal cooling of the rocks.

167 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

3.12 Conclusions

A new ‘ Mg-in-plagioclase geospeedometer ’ was developed, based on the diffusive exchange of Mg between plagioclase and clinopyroxene during cooling. This new ‘ geospeedometer ’ was tested with regard to the robustness of the obtained cooling rates and the sensitivity of the developed Mg-profile shape in plagioclase on the cooling history. It has been shown, that the method is very reliable, if certain conditions are satisfied for the measured data, and certain robustness criteria are applied to the interpreted concentration profiles of Mg in plagioclase. Therefore, the presented ‘ Mg-in-plagioclase geospeedometer ’ is considered to provide a powerful tool for the determination of cooling rates in rocks, containing coexisting plagioclase and clinopyroxene. The approach was applied to three different sample suites of the lower oceanic crust formed at the fast-spreading EPR. The individual samples from every sample suite were collected from different depth, which allowed determination of the vertical distribution of cooling rates in the lower oceanic crust. The obtained cooling rates range from 5 to 0.0001 °C/year, and a general decrease of cooling rate as a function of depth is observed. The vertical distribution of cooling rates is very similar for the different investigated segments of the EPR. The observation of fast cooling at the top of the lower oceanic crust and decreasing cooling rates at greater depth is consistent with a ‘ gabbro glacier ’ model of crustal accretion, in which most of the heat is predicted to be removed by hydrothermal circulation at the top of the AMC. The data presented here are inconsistent with a ‘ sheeted sill ’ model of crustal accretion. Deep hydrothermal circulation is required, if extensive in situ crystallization occurs in multiple sills at various depths (e.g. Chen, 2001; Maclennan et al., 2004 and 2005; see Chapter 3), as suggested by a ‘ sheeted sill ’ type model. The slow cooling rates obtained from samples formed at greater depths are not consistent with extensive hydrothermal circulation at these depths.

168 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

3.13 References

Bindeman, I. N., Davies, A. M. & Drake, M. J., 1998. Ion microprobe study of plagioclase-basalt partition experiments at natural concentration levels of trace elements. Geochimica et Cosmochimica Acta , 62 , 1175-1193. Blundy, J. D. & Wood, B. J., 1991. Crystal chemical controls on partitioning of Sr and Ba between plagioclase feldspar, silicate melts, and hydrothermal solutions. Geochimica et Cosmochimica Acta , 55 , 193-209. Boudier, F., Nicolas, A. & Ildefonse, B., 1996. Magma chambers in the Oman ophiolite: fed from the top and the bottom. Earth and Planetary Science Letters , 144 , 239-250. Carmichael, I. S. E., Nicholls, J. & Smith, A. L., 1970. Silica activity in igneous rocks. American Mineralogist , 55 , 246-263. Chakraborty, S. & Ganguly, J., 1991. Compositional zoning and cation diffusion in aluminosilicate garnets. In: Diffision, atomic ordering and mass transport; Advances in physical geochemistry, 8, (ed Ganguly, J.), pp 120-175, Springer, Berlin. Chapman, D. S. & Pollack, H. N., 1975. Global heat flow - new look. Earth and Planetary Science Letters , 28 , 23-32. Chen, Y. J., 2001. Thermal effects of gabbros accretion from a deeper second melt lens at the fast spreading East Pacific Rise. Journal of Geophysical Research , 106 , 8581-8588. Coogan, L. A., 2007. The lower oceanic crust. In: Treatise on Geochemistry: The Crust (Vol.3) (eds Turekian, K. & Holland, H. D.), pp. 1-45, Elsevier, New York. Coogan, L. A., Gillis, K. M., MacLeod, C. J., Thompson, G. & Hekinian, R., 2002a. Petrology and geochemistry of the lower ocean crust formed at the East Pacific Rise and exposed at Hess Deep: a synthesis and new results. Geochemistry Geophysics Geosystems , 3, Special issue: The Oman ophiolite and ocean ridge processes, DOI 10.1029/2001GC000230.

169 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

Coogan, L. A., Jenkin, G. R. T. & Wilson, R. N., 2002b. Constraining the cooling rate of the lower oceanic crust: a new approach applied to the Oman ophiolite. Earth and Planetary Science Letters , 199 , 127-146. Coogan, L. A., Jenkin, G. R. T. & Wilson, R. N., 2007. Contrasting cooling rates in the oceanic lithosphere at fast- and slow-spreading mid-ocean ridges derived from geospeedometry. Journal of Petrology , 48 , 2211-2231. Costa, F. & Chakraborty, S., 2004. Decadal time gaps between mafic intrusion and silicic eruption obtained from chemical zoning patterns in olivine. Earth and Planetary Science Letters , 227 , 517-530. Costa, F., Chakraborty, S. & Dohmen, R., 2003. Diffusion coupling between major and trace elements and a model for the calculation of magma chamber residence times using plagioclase. Geochimica et Cosmochimica Acta , 67 , 2189-2200. Costa, F., Dohmen, R. & Chakraborty, S., 2008. Time Scales of Magmatic Processes from Modeling the Zoning Patterns of Crystals. In: Minerals, Inclusions and Volcanic Processe; Reviews in Mineralogy & Geochemistry, 69, (ed Putirka, K. D.& Tepley, F. J.), pp. 545-594, Mineralogical Society of America, Virginia. Crank, J., 1975. The mathematics of diffusion. Oxford Scientific Publications, Oxford. Davies, J. H. & Davies, D. R., 2010. Earth's surface heat flux. Solid Earth Discussions , 1, 5-45. Dodson, M. H., 1973. Closure temperature in cooling geochronological and petrological systems. Contributions to Mineral Petrology , 40 , 259-274. Dodson, M. H., 1976. Kinetic processes and thermal history of slowly cooled solids. Nature , 259 , 551-553. Dodson, M. H., 1986. Closure profiles in cooling systems. Material Science Forum , 7, 145-154. Dohmen, R. & Chakraborty, S., 2003. Mechanism and kinetics of element and isotopic exchange mediated by a fluid phase. American Mineralogist , 88 , 1251-1270. Dohmen, R., Chakraborty, S., Palme, H. & Rammensee, W., 2003. Role of element solubility on the kinetics of element partitioning: in situ observations and themodynamic kinetic model. Journal of Geophysical Research , 108 , 1251- 1270.

170 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

Francheteau, J., Armijo, R., Cheminee, J. L., Hekinian, R., Lonsdale, P. & Blum, N., 1990. 1 Ma East Pacific Rise oceanic crust and uppermost mantle exposed by rifting in Hess Deep (equatorial Pacific Ocean). Earth and Planetary Science Letters , 101 , 281-295. Francheteau, J., Patriat, P., Segoufin, J., Armijo, R., Doucoure, M., Yelleschaouche, A., Zukin, J., Calmant, S., Naar, D. F. & Searle, R. C., 1988. Pito and Orongo Fracture-Zones - the Northern and Southern Boundaries of the Easter Microplate (Southeast Pacific). Earth and Planetary Science Letters , 89 , 363- 374. Garrido, C. J., Kelemen, P. B. & Hirth, G., 2001. Variation of cooling rate with depth in the lower crust formed at an oceanic spreading ridge: plagioclase crystal size distributions in gabbros from the Oman ophiolite. Geochemistry Geophysics Geosystems , 2, DOI 10.1029/2000GC000136. Ghiorso, M. S. & Sack, R. O., 1995. Chemical mass transfer in magmatic processes IV. A revised and internally consistent thermodynamic model for the interpolations of liquid-solid equilibria in magmatic systems at elevated temperatures and pressures. Contributions to Mineral Petrology , 119 , 197- 212. Giletti, B. J. & Casserly, J. E. D., 1994. Strontium diffusion kinetics in plagioclase feldspars. Geochimica et Cosmochimica Acta , 58 , 3785-3793. Gillis, K. M., Mével, C. & Allan, J., 1993. Proceedings of the Ocean Drilling Project, Inititial Reports, 147 , pp. 366, Ocean Drilling Program, College Station, Texas. Grove, T. L., Baker, M. B. & Kinzler, R. J., 1984. Coupled CaAl-NaSi diffusion in plagioclase feldspar: Experiments and applications to cooling rate speedometry. Geochimica et Cosmochimica Acta , 48 , 2113-2121. Hekinian, R., Francheteau, J., Armijo, R., Cogne, J. P., Constantin, M., Girardeau, J., Hey, R., Naar, D. F. & Searle, R., 1996. Petrology of the Easter microplate region in the South Pacific. Journal of Volcanology and Geothermal Research , 72 , 259- 289. Henstock, T. J., Woods, A. W. & White, R. S., 1993. The accretion of oceanic crust by episodic sill intrusion. Journal of Geophysical Research , 98 , 4143-4161.

171 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

Hey, R. N., Johnson, P. D., Martinez, F., Korenaga, J., Somers, M. L., Huggett, Q. J., Lebas, T. P., Rusby, R. I. & Naar, D. F., 1995. Plate boundary reorganization at a large-offset, rapidly propagating rift. Nature , 378 , 167-170. Karson, J. A., Klein, E. M., Hurst, S. D., Lee, C., Rivizzigno, P., Curewitz, D., Morris, A. R. & Party, H. D. S., 2002. Structure of uppermost fast-spread oceanic crust exposed at the Hess Deep Rift: Implications for subaxial processes at the East Pacific Rise. Geochemistry Geophysics Geosystems , 3, DOI:10.1029/2001GC000155. Kelemen, P. B., Koga, K. & Shimizu, N., 1997. Geochemistry of gabbro sills in the crust-mantle transition zone of the Oman ophiolite: implications for the origin of the oceanic lower crust. Earth and Planetary Science Letters , 146 , 475-488. Korenaga, J. & Kelemen, P. B., 1997. Origin of gabbro sills in the Moho transition zone of the Oman ophiolite: Implications for magma transport in the oceanic crust. Journal of Geophysical Research, 102 , 27,729-27,749. Lasaga, A. C., 1983. Geospeedometry: an extension of geothermometry. In: Kinetics and equilibrium in mineral reactions (ed Saxena, S. K.), pp. 82-114, Springer- Verlag, New York. Lasaga, A. C., Richardson, S. M. & Holland, H. D., 1977. The mathematics of cation diffusion and exchange between silicate materials during retrograde metamorphism. In: Energetics of Geological processes (eds Saxena, S. K. & Bhattacharji, S.), pp. 353-388, Springer-Verlag, New York. LaTourrette, T. & Wasserburg, G. J., 1998. Mg diffusion in anorthite: implications for the formation of early solar system planetesimals. Earth and Planetary Science Letters , 158 , 91-108. Lissenberg, C. J., Bedard, J. H. & van Staal, C. R., 2004. The structure and geochemistry of the gabbro zone of the Annieopsquotch ophiolite, Newfoundland: implications for lower crustal accretion at spreading ridges. Earth and Planetary Science Letters , 229 , 105-123. Liu, M. & Yund, R. A., 1992. NaSi-CaAl Interdiffusion in plagioclase. American Mineralogist , 77 , 275-283.

172 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

Lonsdale, P., 1988. Structural pattern of the Galapagos microplate and evolution of the Galapagos Triple Junctions. Journal of Geophysical Research , 93 , 13551- 13574. Maclennan, J., Hulme, T. & Singh, S. C., 2004. Thermal models of oceanic crustal accretion: linking geophysical, geological and petrological observations. Geochemistry Geophysics Geosystems , 5, DOI:10.1029/2003GC000605. Maclennan, J., Hulme, T. & Singh, S. C., 2005. Cooling of the lower oceanic crust. Geology , 33 , 357-360. MacLeod, C. J. & Yaouancq, G., 2000. A fossil melt lens in the Oman ophiolite: Implications for magma chamber processes at fast spreading ridges. Earth and Planetary Science Letters , 176 , 357-373. Perk, N., Coogan, L. A., Karson, J. A., Klein, E. M. & Hanna, H., 2007. Primitive cumulates from the upper crust formed at the East Pacific Rise. Contributions to Mineral Petrology , 154 , 575-590. Phipps Morgan, J. & Chen, Y. J., 1993. The Genesis of oceanic crust - magma injection, hydrothermal cooling, and crustal flow. Journal of Geophysical Research , 98 , 6283-6297. Quick, J. E. & Denlinger, R. P., 1993. Ductile deformation and the origin of layered gabbro in ophiolites. Journal of Geophysical Research , 98 , 14015-14027. Schmitt, A. K., Perfit, M. R., Rubin, K. H., Stockli, D. F., Smith, M. C., Cotsonika, L. A., Zellmer, G. F., Ridley, W. I. & Lovera, O. M., 2011. Rapid cooling rates at an active mid-ocean ridge from zircon thermochronology. Earth and Planetary Science Letters , 302 , 349-358. Sleep, N. H., 1975. Formation of oceanic crust: some thermal constraints. Journal of Geophysical Research, 80 , 4037-4042. VanTongeren, J. A., Kelemen, P. B. & Hanghoj, K., 2008. Cooling rates in the lower crust of the Oman ophiolite: Ca in olivine, revisited. Earth and Planetary Science Letters , 267 , 69-82. Wilson, D. S., 1996. Fastest known spreading on the Miocene Cocos-Pacific plate boundary. Geophysical Research Letters , 23 , 3003-3006.

173 3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl

Wilson, D. S. et al., 2006. Drilling into gabbro in intact ocean crust. Science , 312 , 1016-1020. Zhang, X., Ganguly, J. & Ito, M., 2010. Ca-Mg diffusion in diopside: tracer and chemical inter-diffusion coefficients. Contributions to Mineralogy and Petrology , 159 , 175-186.

174 4. Conclusions and Future Work

Chapter 4

4. Conclusions and Future Work

4.1 Summary of the results from this study

The present study allows testing different models of cooling and accretion of the lower oceanic crust, using diffusion calculations and ‘ geospeedometry ’ on natural rock samples. The existing end-member models (the ‘gabbro glacier ’ model and the ‘sheeted sill ’ model) predict different thermal evolution, and most significantly, different depths to which hydrothermal fluids circulate in the oceanic crust. As a consequence, this implies different variations of cooling rate as a function of depth. Here, cooling rates were determined for natural rocks from three different sample suites of the lower oceanic crust that formed along different segments of the fast-spreading East Pacific Rise (EPR). Since the individual samples of each location were collected from different depths, the results presented here provide information about the variation of cooling rates as a function of depth in the lower oceanic crust. Additionally, the comparison of the vertical distribution of cooling rates from the three different locations provides information about variations of the thermal structure along-axis of the EPR.

175 4. Conclusions and Future Work

To obtain cooling rates from natural samples of the lower oceanic crust, a new ‘ Mg-in-plagioclase geospeedometer ’ was developed, which is based on the diffusive exchange of Mg between plagioclase and clinopyroxene during cooling. This required experimental determination of the diffusion coefficient of Mg in

Pl plagioclase ( DMg ) and the partition coefficient of Mg between plagioclase and

Pl / Cpx clinopyroxene ( K Mg ) in the compositional range of the lower oceanic crust. The

Pl Pl / Cpx diffusion coefficient DMg and the partition coefficient K Mg were determined as a function of temperature ( T) , anorthite-content in plagioclase ( XAn ) and the silica activity of the system ( a ). This was accomplished in a set of experiments at SiO 2 different temperatures ( T=1050 to 1200°C), in which plagioclase single crystals with different anorthite-content (XAn =0.12 to 0.95) were surrounded by different Cpx-bearing matrix powders. The use of different matrix powders buffered the silica activity at different values ( a ~0.55 to 1, the exact values depend on the given SiO 2 temperature of an experiment). All experiments were carried out at a constant alumina activity ( a ) of 1. Reliable results for D Pl and K Pl / Cpx were obtained in a Al 2O3 Mg Mg temperature range of 1100 to 1200°C and a compositional range of XAn =0.5 to 0.8. At

Pl / Cpx these conditions, K Mg was found to (i) decrease during cooling, (ii) increase with increasing XAn in plagioclase and (iii) increase with increasing a . This is SiO 2 quantified in Eq. 2.5.5.4 of Chapter 2:

1 16913 [J/mol ] ln K Pl / Cpx = -9219 []K + 6.1 + X + ln a Mg T RT An SiO 2 (Eq. 2.5.5.4)

Pl The diffusion coefficient DMg was found to (i) decrease with temperature in an Arrhenian relationship and (ii) to increase with increasing a . No significant SiO 2

Pl dependence of DMg on XAn in plagioclase was observed. The experimental data obtained from this study are in good agreement with the data from the study of

176 4. Conclusions and Future Work

Borinski et al. (in prep.), that investigated the diffusion of Mg in plagioclase over a wider range of temperature and XAn in plagioclase. However, their study did not account for a . Therefore, to quantify D Pl as a function of T and a , the SiO 2 Mg SiO 2 experimental data obtained from the present study were fitted using the activation energy E from Borinski et al. (in prep.), which led to Eq. 2.5.8.4 in Chapter 2:

−  − 320924 [J / mol ] 6.2 D Pl [m 2 / s]= 25.1 ⋅10 4 [m 2 / s]⋅ exp   ⋅ ()a Mg  RT  SiO 2 (Eq. 2.5.8.4)

The new ‘ Mg-in-plagioclase geospeedometer ’ is based on a revised model of Mg diffusion in plagioclase, that builds on the model of Costa et al. (2003, see

Pl Chapter 3), but uses the newly calibrated data for DMg (Eq. 2.5.8.4). The initial and boundary conditions of the new model are calculated from the partition coefficient

Pl / Cpx K Mg (Eq. 2.5.5.4). The approach was tested with regard to the robustness of the obtained cooling rates and the sensitivity of the developed Mg-profile shape in plagioclase on the cooling history. It has been shown, that the method is very reliable, if certain conditions are satisfied for the measured data, and certain robustness criteria are applied to the interpreted concentration profiles of Mg in plagioclase. Therefore, the presented ‘ Mg-in-plagioclase geospeedometer ’ is considered to provide a powerful tool for the determination of cooling rates in terrestrial and extraterrestrial rocks with coexisting plagioclase and clinopyroxene.

Application of the ‘ Mg-in-plagioclase geospeedometer ’ to the different natural sample suites of the EPR yield cooling rates in the range of 5 °C/year to 0.0001 °C/year, and a general trend of decreasing cooling rate as a function of depth is observed. The vertical distribution of cooling rates is very similar for the different investigated segments of the EPR, which implies a comparable thermal structure along the EPR.

177 4. Conclusions and Future Work

The observation of fast cooling at the top of the lower oceanic crust and decreasing cooling rates at greater depth is consistent with a ‘ gabbro glacier ’ type model of crustal accretion. This model suggests that most of the heat is removed by hydrothermal circulation at the top of the axial magma chamber (AMC). With increasing depth, heat conduction becomes the dominant process to remove the heat. Since heat conduction is a less efficient mechanism of heat removal than hydrothermal circulation, the cooling rates are expected to decrease with increasing depth, which is supported by the data presented here. The data obtained here are inconsistent with hydrothermal circulation as a mechanism of heat removal at deeper levels of the lower oceanic crust. Deep hydrothermal circulation is required, if extensive in situ crystallization occurs in multiple sills at various depths (e.g. Chen, 2001; Maclennan et al., 2004 and 2005; see Chapter 3), as suggested by a ‘ sheeted sill ’ type model. Therefore, this type of model is not supported by the data acquired in this study.

4.2 Future work and perspectives

(i) In the course of the experimental investigation on the Mg exchange between plagioclase and clinopyroxene, two possible exchange reactions were discussed, which imply different site occupancy of Mg in the plagioclase structure. It was shown thermodynamically that one reaction (reaction 1b in Chapter 2) is not expected to depend on a , whereas the second one (reaction 2 in Chapter 2) will Al 2O3 be dependent on a . Additional experiments to investigate the exchange of Mg Al 2O3 between plagioclase and clinopyroxene as a function of a may help to Al 2O3 distinguish between the two possibilities, and hence provide additional information about the preferred site occupancy of Mg in plagioclase. No exchange of Mg between plagioclase and clinopyroxene could be observed for experiments below 1100°C, but Mg-concentrations in plagioclase from the investigated natural rock samples indicate the continuous exchange of Mg at

178 4. Conclusions and Future Work lower temperatures. One possible reason for this might be imperfect contact between the plagioclase single crystal and the surrounding Cpx-bearing matrix powder in the experiments at temperatures below 1100°C. A different experimental setup with the use of clinopyroxene single crystals in good contact with plagioclase single crystals may improve on this situation. The experiments reported here were carried out at atmospheric pressure

Pl / Cpx Pl (except KF044), therefore, the effect of pressure on K Mg and DMg remains undetermined and might be investigated in further studies.

(ii) A one-dimensional diffusion model was applied to obtain cooling rates from fitting Mg-profiles, which were measured in natural plagioclase crystals. However, as discussed briefly in Section 3.6, in fact, diffusion results from fluxes in three dimensions. The use of a one-dimensional model neglects fluxes from other dimensions and leads to an overestimate of the time required to obtain a given extent of diffusive modification of a concentration distribution. I n order to obtain the most reliable effective cooling rate without considering a full 3-D diffusion model, certain robustness criteria were established in this study. For example, for plagioclase crystals with an observed aspect ratio greater than 1:3, only the shorter profile was used to obtain a cooling rate. However, the effect of fluxes from diffusion in multiple dimensions could be accounted for in a 2-D (or 3-D) diffusion model. For most investigated plagioclase crystals of this study, two perpendicular Mg- concentration profiles were measured, which allows a 2-D diffusion model to be applied without additional measurements. As a first approach, it may not be necessary to model the Mg-concentration in every plagioclase crystal again using a 2-D diffusion model. A comparison of cooling rates obtained from the 1-D model with those obtained from a 2-D model for some of the plagioclase crystals already will provide a better understanding, to what extent the use of a 1-D model overestimates the time required to obtain a given Mg- concentration profile.

179 4. Conclusions and Future Work

However, the general trend of decreasing cooling rate with depth observed in this study is not likely to be changed, and based on the very systematic trends observed in this study, the effect of using a 1-D model compared to a 2-D model is not expected to significantly change the conclusions drawn here.

(iii) In the course of this study, Mg-diffusion profiles were fitted under the assumption of linear cooling in a certain temperature interval. For temperature above this temperature interval, a maximum cooling rate could be inferred (see Section 3.11.1 of Chapter 3). However, the diffusion model applied here could be modified, to put tighter constraints on the high temperature cooling history, as follows: At the present stage of the model, the cooling history at high temperatures remains undetermined for Mg-profiles with low concentrations at the core. The reason for this is that, if diffusion at a given temperature and cooling rate is fast enough to attain an “equilibrium” profile as described by Eq. 3.4.2.2, the profile provides no information, how this “equilibrium” profiles was attained. However, a single maximum cooling rate at high temperatures was inferred from profiles with the highest Mg-concentration at the core. In fact, the maximum cooling history at high temperatures could be constrained in more detail: It is possible to calculate the time that Mg-diffusion requires to attain “equilibrium” for any temperature step ∆T during cooling along the high temperature cooling history. These calculations may be done for the entire cooling path above the temperature interval, in which reliable cooling rates can be determined from the Mg-profile shape. Therefore, instead of only one single maximum cooling rate at high temperature, it is possible to obtain a maximum cooling path for temperatures above the reliable temperature interval.

(iv) The temperature interval, over which reliable cooling rates can be determined from diffusion modelling, is restricted by the diffusivity of the element that is being modelled (Fig. 4.2.1). For example, the distribution of elements with fast diffusivities can be changed continuously to lower temperatures, than the distribution of elements with slow diffusivities. Therefore, fast-diffusing elements

180 4. Conclusions and Future Work provide information about the cooling history at lower temperatures, than slow- diffusing elements. In turn, fast diffusing elements attain “equilibrium” at higher temperatures and sufficiently slow cooling rates and therefore, they may not provide information about the cooling history at high temperatures. In this case, elements with slower diffusivities, which did not attain “equilibrium”, but still diffused significantly enough to have changed their initial distribution, provide information about the cooling history at higher temperatures. Additionally, as discussed in Section 3.11.1 of Chapter 3, the temperature interval, over which reliable cooling rates can be extracted from diffusion modelling of a given element, depends on the cooling rate itself. For faster cooling rates, the reliable temperature interval is around higher temperatures, than for slower cooling rates.

181 4. Conclusions and Future Work

cooling

T1 T2 T3 T4 (a) “fast” diffusing element

T1 T2 T3 T4 (b) “slower” diffusing element

T1 T2 T3 T4 (c)

“veryslow” diffusing element

Fig. 4.2.1: Scheme to illustrate the effect of the diffusivity of different elements in plagioclase on the temperature interval, over which they can provide information about the cooling history. This temperature interval is marked by a pink box. For simplicity, a homogenous anorthite-profile in plagioclase is assumed, which means that “equilibrium” distributions of the different elements are also homogeneous. Furthermore, for comparison, the partition coefficients of all elements are assumed to be such, that the element diffuses out of plagioclase during cooling. Panel (a) illustrates the evolution of a diffusion profile of an element with a relatively fast diffusivity. At temperatures T1 and T2 , the distribution of this element is in “equilibrium” with its surrounding. Since T2 is lower than T1 , according to the partition coefficient, the concentration of this element at T2 is lower than at T1 . At T3 , diffusion was not fast enough to remove the element from the core, leading to a bowed concentration profile. Diffusion continuously changed the rim concentration up to T4 . Panel (b) show the evolution of a diffusion profile of an element with slower diffusivity than the one in (a) over the same temperature intervals. In this case, a bowed profile shape is attained already at T2 and the profile is not changed significantly by diffusion below T3 . Panel (c) shows the evolution of a diffusion profile of an element with very slow diffusivity compared to the elements in (a) and (b). The profile at T1 is not necessarily an equilibrium profile, but could be a crystallization profile. At T2 , this profile is only changed at the rims of the crystal. Below T2 , the profile shape is not changed anymore by diffusion.

In this study, reliable cooling rates have been obtained from diffusion modelling of Mg in plagioclase in a temperature range of 1150°C to 600°C. However, the individual reliable temperature intervals of each sample depend on the cooling

182 4. Conclusions and Future Work rate. In addition to the Mg-concentration profiles, concentration profiles of different elements were measured along the same traverses in the plagioclase crystals (see Electronic Appendix). These elements include K, which diffuses faster than Mg in plagioclase (Giletti and Shanahan, 1997), and Sr, Ba, and some REE, which have slower diffusivities than Mg in plagioclase (Giletti and Casserly, 1994; Cherniak and Watson, 1994; Cherniak, 2002; Cherniak, 2003). Diffusion modelling of the measured concentrations profiles of these elements potentially provides information about the cooling history at lower temperatures (K) and higher temperatures (Sr, Ba and REE) compared to Mg. This would complement the information about the cooling history obtained in this study.

(v) The sample suite investigated in this study covers approximately the first 900 m of the plutonic portion of modern oceanic crust. This depth sequence was mainly limited by the general lack of natural rock samples of modern, fast-spreading oceanic crust collected from greater depth. However, the upcoming IODP Expedition 345 aims to drill plutonic rocks from Hess Deep. Application of the ‘ Mg-in- plagioclase geospeedometer ’ to this potentially deeper sample suite would provide additional information about the distribution of cooling rates at greater depth. The combination with cooling rates determined from the ‘ Ca-in-olivine geospeedometer ’ on the same samples could provide complementary information to enhance our understanding of the thermal structure of the lower oceanic crust. The detailed vertical distribution of cooling rates in the lower oceanic crust from a combination of these two approaches may be used as additional constraints for thermal models and a revised model of cooling and accretion of the lower oceanic crust.

183 4. Conclusions and Future Work

4.3 References

Chen, Y. J., 2001. Thermal effects of gabbros accretion from a deeper second melt lens at the fast spreading East Pacific Rise. Journal of Geophyical Research. , 106 , 8581-8588. Cherniak, D. J., 2002. Ba diffusion in clinopyroxene. Geochimica et Cosmochimica Acta , 66 , 1641-1650. Cherniak, D. J., 2003. REE diffusion in feldspar. Chemical Geology , 193 , 25-41. Cherniak, D. J. & Watson, E. B., 1994. A study of strontium diffusion in plagioclase using Rutherford backscattering spectroscopy. Geochimica et Cosmochimica Acta , 58 , 5179-5190. Costa, F., Chakraborty, S. & Dohmen, R., 2003. Diffusion coupling between major and trace elements and a model for the calculation of magma chamber residence times using plagioclase. Geochimica et Cosmochimica Acta , 67 , 2189-2200. Giletti, B. J. & Casserly, J. E. D., 1994. Strontium diffusion kinetics in plagioclase feldspars. Geochimica et Cosmochimica Acta , 58 , 3785-3793. Giletti, B. J. & Shanahan, T. M., 1997. Alkali diffusion in plagioclase feldspar. Chemical Geology , 139 , 3-20. Maclennan, J., Hulme, T. & Singh, S. C., 2004. Thermal models of oceanic crustal accretion: linking geophysical, geological and petrological observations. Geochemistry Geophysics Geosystems , 5, DOI:10.1029/2003GC000605. Maclennan, J., Hulme, T. & Singh, S. C., 2005. Cooling of the lower oceanic crust. Geology , 33 , 357-360.

184

Appendix I

Appendix I – Table A1: Petrography 1

Table A1.1: Summary of the petrography of the studied rock samples of the North Wall of the Hess Deep sample suite. Sample depth is given in meters below sheeted dike complex. For plagioclase (Pl), clinopyroxene (Cpx), orthopyroxene (Opx) and olivine (Ol), the modal abundance and the average grain size are given in Vol% (estimated from the thin section) and mm respectively. Additional phases are: chlorite (Chl), amphibole (Amph), Quartz (Qtz), Serpentinite (Serp), and opaque phases (opq).

Sample Depth Pl Cpx Opx Ol Ad. Phases Alteration [mbsd] [Vol%]/[mm] [Vol%]/[mm] [Vol%]/[mm] [Vol%]/[mm]

2212-1358 0 40/0.5 30/0.5 - - Chl, opq Cpx altered to Chl, Pl moderately fresh 2212-1400 0 40/0.5 30/0.5 - - Chl, opq Cpx altered to Chl, Pl moderately fresh 2212-1338 17 3369-1418 50 50/1 30/0.7 10/0.5 - Chl, opq Cpx partially altered, partially very fresh, Pl strongly fractured 3369-1422 56 50/1 30/0.7 10/0.5 - Chl, opq Cpx partially altered, partially very fresh, Pl strongly fractured 3369-1431 56 40/0.7 50/0.7 10/0.5 - Chl, opq Cpx partially altered, partially very fresh, Pl strongly fractured 3369-1355 82 20/0.5 20/2 30/3 10/2 Chl Cpx and Opx moderately altered, Pl very fresh, Ol slightly serp. 3369-1349 90 20/3 30/4 40/5 - Chl Cpx and Opx moderately altered, Pl very fresh 3369-1321 126 40/1 20/0.5 30/1 - Chl Cpx and Opx moderately altered and fractured, Pl fairly fresh 3374-1031 127 50/2 40/2 - - Chl Cpx altered to Chl, Pl fresh, but sometimes fractured, Chl veins 3374-1012 134 40/0.5 30/0.5 20/0.5 - Chl Cpx and Opx strongly altered, Pl moderately altered 3369-1250 144 30/2 40/1 - - Chl, opq Cpx strongly altered, Pl very fresh 3369-1329 150 20/0.5 Qtz, Ep myrmekites 3369-1156 198 50/2 30/1 10/0.5 - Chl Cpx and Opx fresh, Pl fresh 3369-1221 208 50/0.1 20/0.1 30/1 - Chl moderately altered 3369-1110 211 3369-1129 219 40/4 20/2 30/3 - Chl very fresh 3369-1042 282 50/5 20/1 20/1 - Chl Cpx and Opx moderately altered, Pl highly fractured 3369-1050 282 50/2 20/1 20/1 5/1 Chl Cpx and Opx moderately altered, Pl fresh 3370-1418 296 40/1 40/0.1 - - Chl, opq highly altered 3370-1408 306 20/0.5 - - - Qtz, Ep myrmekites 2213-1110 380 40/1 30/1 10/1 - Chl very fresh 3370-1328 442 contact between gabbro and X? 2218-1111 470 50/1 40/1 5/1 - Chl, opq fresh 2218-1132 520 40/0.5 50/0.5 - - ?, opq moderately altered Appendix I – Table A1: Petrography 2

Table A1.2: Summary of the petrography of the studied rock samples from OPD Expedition 147 Site 894G of the Hess Deep sample suite. Sample depth is given in meters below sea floor. For plagioclase (Pl), clinopyroxene (Cpx), orthopyroxene (Opx) and olivine (Ol), the modal abundance and the average grain size are given in Vol% (estimated from the thin section) and mm respectively. Additional phases are: chlorite (Chl), amphibole (Amph), Quartz (Qtz), Serpentinite (Serp), and opaque phases (opq).

Sample Depth Pl Cpx Opx Ol Ad. Phases Alteration [mbsf] [Vol%]/[mm] [Vol%]/[mm] [Vol%]/[mm] [Vol%]/[mm]

02R 02 40-45 29 50/0.1 40/0.1 - 5/0.5 Chl, opq moderately altered 05R 01 22-27 54 40/1 50/1 - - Amph Cpx partially altered, partially very fresh, Pl fresh, 06R 02 56-62 58 40/0.5 40/0.5 - 10/0.5 Chl Cpx partially altered, partially very fresh, Pl fresh, Ol altered 07R 01 58-62 66 30/0.5 50/2 - 10/0.5 Chl, opq moderately altered 08R 01 28-32 70 40/4 50/4 5/1 - Chl Cpx partially altered to Chl, Pl fresh 08R 02 105-110 71 50/1 40/1 - - Chl Cpx moderately altered, Pl fairly fresh 09R 04 75-80 78 40/0.5- 40/0.5 - 10/0.5 Chl, opq moderately altered 12R 03 62-67 96 40/0.2 40/0.2 10/0.5 - Chl, opq moderately altered 12R 04 40-45 97 40/0.2 40/0.2 10/0.5 - Chl, opq moderately altered 12R 05 83-87 99 40/0.5 40/1 10/1 - Chl, opq highly altered 12R 05 115-120 100 50/1 40/1 - - Chl, opq Cpx altered, Pl moderately altered 13R 02 90-95 103 50/0.5 40/0.5 - - Chl, opq Cpx altered, Pl moderately altered 17R 02 6-10 127 50/0.5 40/0.5 - - Chl, opq moderately altered 18R 02 5-10 129 40/0.5 40/0.5 - 10/0.5 Chl, opq altered 20R 02 35-40 147 40/0.5 30/0.5 20/1 - Chl, opq moderately altered

Appendix I – Table A1: Petrography 3

Table A1.3: Summary of the petrography of the studied rock samples of the Pito Deep sample suite. Sample depth is given in meters below sheeted dike complex. For plagioclase (Pl), clinopyroxene (Cpx), orthopyroxene (Opx) and olivine (Ol), the modal abundance and the average grain size are given in Vol% (estimated from the thin section) and mm respectively. Additional phases are: chlorite (Chl), amphibole (Amph), Quartz (Qtz), Serpentinite (Serp), and opaque phases (opq).

Sample Depth Pl Cpx Opx Ol Ad. Phases Alteration [mbsd] [Vol%]/[mm] [Vol%]/[mm] [Vol%]/[mm] [Vol%]/[mm]

022205-0259 41 40/0.2 40/0.2 - - Chl, Amph, opq Cpx highly altered, Pl fairly fresh 022205-0248 45 50/0.5 40/0.5 - - Chl, Amph Cpx moderately altered, Pl fairly fresh 022205-0230 72 50/1 40/1 - 5/0.1 Chl, Amph, opq Cpx moderately altered, Pl fresh 022005-1522 177 40/0.7 40/0.5 10/0.5 5/0.2 Chl, opq Cpx moderately altered, Pl fresh 022005-1209 248 40/2 10/1 - 40/1 highly altered and fractured 022005-1938 253 50/3 10/1 - - Amph, Chl highly altered 022005-1052 335 80/1 10/0.1 - 5/1 opq Ol slightly altered, Pl fresh 022005-0910 386 70/1 20/2 - 10/1 very fresh 022005-0830 417 80/0.5 5/0.5 - - ? highly altered 022005-0800 468 30/1 30/1 - 30/0.5 Serp highly altered and fractured 022005-0534 569 70/2 10/1 - 20/1 Serp moderately altered, Pl fresh 022005-0506 662 90/2 - - 5/05 Serp, ? moderately altered 022005-0454 667 80/2 5/0.2 - 10/0.5 Serp moderately altered 022005-0355 727 60/3 10/0.5 - 20/0.5 Serp, ? moderately altered 022005-0310 740 30/1 10/5 - 40/2 Serp moderately altered 022005-0245 759 70/1 - - 20/0.5 Serp, ? moderately altered 022005-0241 759 60/1 20/0.5 - 10/0.5 Serp, ? moderately altered 022005-0214 766 70/1 5/0.6 - 20/0.5 Serp, ? moderately altered 022005-0155 780 50/1 30/2 - 10/0.5 Serp moderately altered 022005-0056 836 50/1 30/0.5 - 10/0.5 Serp moderately altered 022005-0040 863 40/1 10/0.3 40/2 Serp moderately altered and fractured 022005-0024 871 40/1 - 10/0.5 40/2 Serp moderately altered and fractured 021905-2348 876 50/1 - - 40/1 Serp highly altered and fractured

Appendix I – Table A1: Petrography 4

Table A1.4: Summary of the petrography of the studied rock samples of IODP Expedition 312 Site 1256D sample suite. Sample depth is given in meters below sheeted dike complex. For plagioclase (Pl), clinopyroxene (Cpx), orthopyroxene (Opx) and olivine (Ol), the modal abundance and the average grain size are given in Vol% (estimated from the thin section) and mm respectively. Additional phases are: chlorite (Chl), amphibole (Amph), Quartz (Qtz), Serpentinite (Serp), and opaque phases (opq).

Sample Depth Pl Cpx Opx Ol Ad. Phases Alteration [mbsd] [Vol%]/[mm] [Vol%]/[mm] [Vol%]/[mm] [Vol%]/[mm]

216R 01 15-20 12.1 40/0.5 40/1 5/0.5 - Chl, Amph highly altered 216R 01 47-57 12.4 50/0.5 30/0.5 - - Chl, Amph, opq moderately altered 216R 01 60-64 12.5 50/0.5 30/0.5 - - Chl, Amph, opq moderately altered 216R 01 130-134 13.2 50/0.2 30/0.5 - - Chl, Amph, opq highly altered 218R 01 37-40 19.7 50/0.2 30/0.5 - 5/0.2 Chl, Amph, opq highly altered 218R 01 44-47 19.8 40/0.2 40/1 - - Chl, Amph, opq moderately altered 219R 01 19-23 24.2 40/0.2 40/1 - - Chl, Amph, opq highly altered

Appendix II

Appendix II – Table A2 5

Table A2.1: Summary of the studied rock samples of the North Wall of the Hess Deep sample suite. Sample depth is given in meters below sheeted dike complex. bold = samples were used to determine cooling rates; r.c. = robustness criteria; EMP = electron microprobe; d.l. = detection limit

Profile Sample Depth Pl crystal Profile length Comment [mbsd] [µm]

2212-1358 0 C1 Pl1 1 320 2212-1358 0 C1 Pl1 2 310 2212-1358 0 C2 Pl2 1 440 2212-1358 0 C2 Pl2 2 250 2212-1358 0 C3 Pl3 1 440 2212-1358 0 C3 Pl3 2 320 2212-1358 0 C4 Pl4 1 440 2212-1358 0 C4 Pl4 2 610 bowed, asymmetrical 2212-1358 0 C5 Pl5 1 360 2212-1358 0 C6 Pl6 1 360 2212-1358 0 C6 Pl6 2 120

2212-1400 0 C1 Pl1 1 163 scattered 2212-1400 0 C2 Pl2 1 56 scattered 2212-1400 0 C3 Pl3 1 130 scattered 2212-1400 0 C3 Pl3 2 166 scattered

2212-1338 17 C1 Pl1 1 1270 problem with EMP 2212-1338 17 C1 Pl1 2 500 strongly bowed, asymmetrical 2212-1338 17 C2 Pl2 1 1280 scattered 2212-1338 17 C2 Pl2 2 640 scattered 2212-1338 17 C3 Pl3 1 1590 bowed 2212-1338 17 C3 Pl3 2 1550 strongly bowed, asymmetrical

3369-1418 50 -

3369-1422 56 -

3369-1431 56 -

3369-1355 82 C1 Pl1 1 2400 slightly bowed 3369-1355 82 C1 Pl1 2 860 slightly bowed 3369-1355 82 C2 Pl2 1 700 failed r.c. 3369-1355 82 C2 Pl2 2 170 failed r.c. 3369-1355 82 C3 Pl3 1 530 slightly bowed 3369-1355 82 C3 Pl3 2 380 slightly bowed 3369-1355b 82 - 3369-1355c 82 -

3369-1349 90 C1 Pl1 1 590 slightly bowed 3369-1349 90 C1 Pl2 1 150 failed r.c. 3369-1349 90 C1 Pl2 2 1120 failed r.c. 3369-1349 90 C2 Pl3 1 860 slightly bowed, asymmetrical 3369-1349 90 C2 Pl3 2 350 slightly bowed 3369-1349 90 C3 Pl4 1 1490 failed r.c. 3369-1349 90 C3 Pl4 2 1360 failed r.c. 3369-1349b 90 -

Appendix II – Table A2 6

3369-1321 126 -

3374-1031 127 C1 Pl1 1 590 3374-1031 127 C1 Pl1 2 260 3374-1031 127 C2 Pl2 1 900 3374-1031b 127 -

3374-1012 134 -

3369-1250 144 C1 Pl1 1 260 3369-1250 144 C2 Pl2 1 190 slightly bowed, almost flat 3369-1250 144 C2 Pl2 2 275 slightly bowed, almost flat 3369-1250b 144 -

3369-1329 150 -

3369-1156 198 -

3369-1221 208 C1 Pl1 1 207 slightly bowed, very low MgO 3369-1221 208 C2 Pl2 1 2340 failed r.c. 3369-1221b 208 -

3369-1110 211 C1 Pl1 1 460 3369-1110 211 C1 Pl1 2 1400 3369-1110 211 C2 Pl2 1 520 problem with EMP 3369-1110 211 C2 Pl2 2 630 problem with EMP

3369-1129 219 -

3369-1042 282 C1 Pl1 1 1665 slightly bowed 3369-1042 282 C1 Pl1 2 1590 slightly bowed 3369-1042 282 C2 Pl2 1 790 scattered 3369-1042 282 C2 Pl2 2 710 scattered

3369-1050 282 C1 Pl1 1 1470 failed r.c. 3369-1050 282 C1 Pl1 2 590 scattered 3369-1050 282 C2 Pl2 1 2000 failed r.c. 3369-1050 282 C2 Pl2 2 660 flat, only changes at rim 3369-1050 282 C3 Pl3 1 960 slightly bowed 3369-1050 282 C3 Pl3 2 450 slightly bowed

3370-1418 296 -

3370-1408 306 -

2213-1110 380 C1 Pl1 1 510 scattered 2213-1110 380 C1 Pl1 2 190 scattered 2213-1110 380 C2 Pl2 1 640 flat 2213-1110 380 C2 Pl2 2 250 surrounded by Opx 2213-1110 380 C3 Pl3 1 470 flat 2213-1110 380 C3 Pl3 2 310 scattered 2213-1110 380 C4 Pl4 1 170 scattered 2213-1110 380 C4 Pl4 2 510 flat 2213-1110 380 C4 Pl5 1 265 failed r.c. 2213-1110 380 C4 Pl5 2 1850 failed r.c. 2213-1110 380 C5 Pl6 1 600 flat Appendix II – Table A2 7

2213-1110 380 C5 Pl6 2 560 flat

3370-1328 442 -

2218-1111 470 C1 Pl1 1 350 slightly bowed 2218-1111 470 C1 Pl1 2 690 slightly bowed 2218-1111 470 C2 Pl2 1 80 failed r.c. 2218-1111 470 C2 Pl2 2 510 failed r.c.

2218-1132 520 C2 Pl2 1 700 failed r.c. 2218-1132 520 C2 Pl2 2 150 failed r.c. 2218-1132 520 C3 Pl3 1 600 flat 2218-1132 520 C3 Pl3 2 300 flat 2218-1132 520 C4 Pl5 2 670 flat

Appendix II – Table A2 8

Table A2.2: Summary of the studied rock samples from OPD Expedition 147 Site 894G of the Hess Deep sample suite. Sample depth is given in meters below sea floor. bold = samples were used to determine cooling rates; r.c. = robustness criteria; EMP = electron microprobe; d.l. = detection limit

Profile Sample Depth Pl crystal Profile length Comment [mbsf] [µm]

02R 02 40-45 29 C1 Pl1 1 2080 scattered 02R 02 40-45 29 C1 Pl1 2 1060 scattered 02R 02 40-45 29 C2 Pl2 1 447 scattered 02R 02 40-45 29 C2 Pl2 2 634 scattered

05R 01 22-27 54 -

06R 02 56-62 58 -

07R 01 58-62 66 C1 Pl1 1 411 scattered 07R 01 58-62 66 C2 Pl2 1 343 scattered 07R 01 58-62 66 C2 Pl2 2 410 scattered

08R 01 28-32 70 C1 Pl1 1 1100 scattered 08R 01 28-32 70 C1 Pl1 2 1490 scattered 08R 01 28-32 70 C2 Pl2 1 950 scattered 08R 01 28-32 70 C2 Pl2 2 840 scattered

08R 02 105-110 71 -

09R 04 75-80 78 -

12R 03 62-67 96 -

12R 04 40-45 97 -

12R 05 83-87 99 -

12R 05 115-120 100 -

13R 02 90-95 103 -

17R 02 6-10 127 -

18R 02 5-10 129 -

20R 02 35-40 147 -

Appendix II – Table A2 9

Table A2.3: Summary of the studied rock samples of the Pito Deep sample suite. Sample depth is given in meters below sheeted dike complex. bold = samples were used to determine cooling rates; r.c. = robustness criteria; EMP = electron microprobe; d.l. = detection limit

Sample Depth Profile Pl crystal Profile length Comment [mbsd] [µm]

022205-0259 41 C1 Pl1 1 440 strongly bowed 022205-0259 41 C1 Pl1 2 415 strongly bowed 022205-0259 41 C2 Pl2 1 480 strongly bowed 022205-0259 41 C2 Pl2 2 777 strongly bowed

022205-0248 45 C2 Pl2 1 490 strange shape 022205-0248 45 C2 Pl2 2 1008 very low MgO at rim, in contact with Qtz 022205-0248 45 C4 Pl4 1 200 bowed, but much lower MgO than 0259

022205-0230 72 C1 Pl1 1 470 almost flat, pretty low MgO 022205-0230 72 C1 Pl1 2 580 scattered 022205-0230 72 C2 Pl2 1 1220 failed r.c. 022205-0230 72 C2 Pl2 2 1340 failed r.c. 022205-0230 72 C3 Pl3 1 1160 failed r.c. 022205-0230 72 C3 Pl3 2 2700 failed r.c.

022005-1522 177 C1 Pl1 1 700 scattered 022005-1522 177 C1 Pl1 2 1050 scattered 022005-1522 177 C2 Pl2 1 360 scattered 022005-1522 177 C2 Pl2 2 610 scattered 022005-1522 177 C3 Pl3 1 210 scattered 022005-1522 177 C3 Pl3 2 355 scattered

022005-1209 248 -

022005-1938 253 -

022005-1052 335 C1 Pl1 1 760 strange shape 022005-1052 335 C1 Pl1 2 1110 strange shape 022005-1052 335 C2 Pl2 1 940 flat, CMgO~0.025 022005-1052 335 C2 Pl2 2 450 flat, CMgO~0.025 022005-1052 335 C3 Pl3 1 1030 flat, CMgO~0.025 (even lower at the rims) 022005-1052 335 C3 Pl3 2 570 flat, CMgO~0.025 (even lower at the rims) 022005-1052 335 C4 Pl4 1 1230 scattered 022005-1052 335 C4 Pl4 2 850 scattered

022005-0910 386 C1 Pl1 1 660 slightly bowed 022005-0910 386 C1 Pl1 2 310 slightly bowed 022005-0910 386 C2 Pl2 1 530 failed r.c. 022005-0910 386 C2 Pl2 2 180 slightly bowed 022005-0910 386 C3 Pl3 1 405 scattered 022005-0910 386 C3 Pl3 2 590 scattered 022005-0910 386 C4 Pl4 1 470 strange shape 022005-0910 386 C4 Pl4 2 590 slightly bowed

022005-0830 417 -

022005-0800 468 - Appendix II – Table A2 10

022005-0534 569 C1 Pl1 1 720 not ideal transverse 022005-0534 569 C1 Pl1 2 930 not ideal transverse 022005-0534 569 C2 Pl2 1 550 slightly bowed 022005-0534 569 C2 Pl2 2 1080 slightly bowed 022005-0534 569 C3 Pl3 1 970 strange shape 022005-0534 569 C3 Pl3 2 1160 strange shape

022005-0506 662 C1 Pl1 1 940 scattered 022005-0506 662 C1 Pl1 2 490 scattered 022005-0506 662 C2 Pl2 1 990 slightly bowed 022005-0506 662 C2 Pl2 2 1150 slightly bowed 022005-0506 662 C3 Pl3 1 285 surrounded by Ol 022005-0506 662 C3 Pl3 2 140 surrounded by Ol

022005-0454 667 -

022005-0355 727 C1 Pl1 1 400 scattered 022005-0355 727 C1 Pl1 2 1130 scattered 022005-0355 727 C2 Pl2 1 1200 scattered 022005-0355 727 C2 Pl2 2 710 scattered

022005-0310 740 -

022005-0245 759 -

022005-0241 759 -

022005-0214 766 -

022005-0155 780 C1 Pl1 1 350 slightly bowed 022005-0155 780 C1 Pl1 2 830 slightly bowed 022005-0155 780 C2 Pl2 1 870 slightly bowed 022005-0155 780 C2 Pl2 2 910 scattered

022005-0056 836 C1 Pl1 1 330 022005-0056 836 C1 Pl1 2 260 022005-0056 836 C2 Pl2 1 1890 slightly bowed 022005-0056 836 C2 Pl2 2 820 slightly bowed 022005-0056 836 C3 Pl3 1 520 slightly bowed 022005-0056 836 C3 Pl3 2 800 slightly bowed 022005-0056 836 C4 Pl4 1 2200 022005-0056 836 C4 Pl4 2 1300 022005-0056 836 C5 Pl5 1 840 slightly bowed

022005-0040 863 -

022005-0024 871 C1 Pl1 1 649 MgO below d.l. 022005-0024 871 C1 Pl1 2 169 MgO below d.l. 022005-0024 871 C2 Pl2 1 231 MgO below d.l. 022005-0024 871 C2 Pl2 2 97 MgO below d.l. 022005-0024 871 C3 Pl3 1 603 MgO below d.l. 022005-0024 871 C3 Pl3 2 362 MgO below d.l. 022005-0024 871 C4 Pl4 1 226 MgO below d.l. 022005-0024 871 C4 Pl4 2 910 MgO below d.l. 022005-0024 871 C5 Pl5 1 181 MgO below d.l. Appendix II – Table A2 11

022005-0024 871 C5 Pl5 2 660 MgO below d.l.

021905-2348 876 -

Appendix II – Table A2 12

Table A2.4: Summary of the studied rock samples of IODP Expedition 312 Site 1256D sample suite. Sample depth is given in meters below sheeted dike complex. bold = samples were used to determine cooling rates; r.c. = robustness criteria; EMP = electron microprobe; d.l. = detection limit

Sample Profile Depth Pl crystal Profile length Comment [mbsd] [µm]

216R 01 15-20 12.1 C1 Pl1 1 355 strange shape 216R 01 15-20 12.1 C1 Pl1 2 544 scattered 216R 01 15-20 12.1 C2 Pl2 1 328 MgO below d.l. 216R 01 15-20 12.1 C2 Pl2 2 159 MgO below d.l. 216R 01 15-20 12.1 C3 Pl3 1 461 strongly bowed 216R 01 15-20 12.1 C3 Pl3 2 549 strange shape

216R 01 47-57 12.4 C1 Pl1 1 719 strongly bowed 216R 01 47-57 12.4 C1 Pl1 2 1134 hydroth. altered 216R 01 47-57 12.4 C2 Pl2 1 456 hydroth. altered 216R 01 47-57 12.4 C2 Pl2 2 552 hydroth. altered 216R 01 47-57 12.4 C3 Pl3 1 269 hydroth. altered 216R 01 47-57 12.4 C3 Pl3 2 546 hydroth. altered

216R 01 60-64 12.5 -

216R 01 130-134 13.2 -

218R 01 37-40 19.7 -

218R 01 44-47 19.8 C1 Pl1 1 455 scattered 218R 01 44-47 19.8 C1 Pl1 2 595 scattered 218R 01 44-47 19.8 C2 Pl2 1 285 MgO below d.l. 218R 01 44-47 19.8 C3 Pl3 1 222 MgO below d.l. 218R 01 44-47 19.8 C3 Pl3 2 578 scattered 218R 01 44-47 19.8 C4 Pl4 1 551 scattered 218R 01 44-47 19.8 C4 Pl4 2 337 scattered

219R 01 19-23 24.2 C1 Pl1 1 473 scattered 219R 01 19-23 24.2 C1 Pl1 2 553 scattered 219R 01 19-23 24.2 C1 Pl2 1 473 scattered 219R 01 19-23 24.2 C1 Pl2 2 541 scattered 219R 01 19-23 24.2 C2 Pl3 1 188 scattered 219R 01 19-23 24.2 C2 Pl3 2 507 scattered 219R 01 19-23 24.2 C2 Pl4 1 417 scattered 219R 01 19-23 24.2 C2 Pl4 2 139 scattered 219R 01 19-23 24.2 C3 Pl5 1 524 scattered 219R 01 19-23 24.2 C4 Pl6 1 893 scattered 219R 01 19-23 24.2 C4 Pl6 2 245 scattered

Appendix III

Appendix III – Table A3 13

Table A3: Analytical run conditions for the EMP analyses of plagioclase and clinopyroxene.

Element Standard material Conditions Spectrometer Counting times [s] Si andradite 40nA, 15kV TAP 20/20/0 Al spessartine 40nA, 15kV TAP 20/20/0 Ca andradite 40nA, 15kV PET 20/20/0 Na jadeite 40nA, 15kV TAP 20/20/0 Mg pyrope 40nA, 15kV TAP 90/45/45 K K-glas 40nA, 15kV PET 50/50/0 Fe andradite 40nA, 15kV LIF 50/50/0 Ti TiO 2 40nA, 15kV PET 20/20/0 Mn spessartine 40nA, 15kV LIF 20/20/0 Cr Cr 2O3 40nA, 15kV LIF 20/20/0 Counting times given as peak/background/background

Appendix IV

Appendix IV – Plots of all fitted profiles 14

0.14 2212-1358C4Pl4Sc2

0.12

0 0.10

0.08

0.06 0.7 Xan 0.04 0.6 0.5 0.02 ConcentrationMgO[wt%] 0.4 rim core rim 200 400 600

0.14 2212-1338C1Pl1Sc1 2212-1338C3Pl3Sc1 2212-1338C3Pl3Sc2 0.12 17 0.10 0.08

0.06 0.7 Xan 0.7 Xan 0.7 Xan 0.04 0.6 0.6 0.6 0.5 0.5 0.5 0.02 ConcentrationMgO[wt%] 0.4 0.4 0.4 rim core rim rim core rim rim core rim 100 200 300 400 400 800 1200 1600 400 800 1200

0.14 3369-1355C1Pl1Sc1 0.7 3369-1355C1Pl1Sc2 0.7 3369-1355C3Pl3Sc1 0.7 3369-1355C3Pl3Sc2 0.7 0.6 0.6 0.6 0.6 0.12 Xan Xan 0.5 Xan 0.5 Xan 0.5 0.5 82 0.10 0.4 0.4 0.4 0.4 0.08

0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim rim core rim rim core rim 600 1200 1800 2400 200 400 600 800 100 200 300 400 500 100 200 300

Depth[mbsd]

0.14 3369-1349C1Pl1Sc1 0.7 3369-1349C2Pl3Sc1 0.7 3369-1349C2Pl3Sc2 0.7 3369-1349C3Pl4Sc1 0.7 3369-1349C3Pl4Sc2 0.7 0.6 0.6 0.6 0.6 0.6 0.12 0.5 Xan 0.5 Xan 0.5 Xan 0.5 Xan 0.5 Xan 0.10 0.4 0.4 0.4 0.4 0.4 90 0.08 0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim rim core rim rim core rim rim core rim 200 400 600 200 400 600 800 100 200 300 400 800 1200 1600 400 800 1200 1600

0.14 3374-1031C1Pl1Sc1 0.7 3374-1031C1Pl1Sc2 0.7 3374-1031C1Pl1Sc2 0.7 0.6 0.6 0.6 0.12 0.5 Xan 0.5 Xan 0.5 Xan 0.10 0.4 0.4 0.4 127 0.08 0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim rim core rim 200 400 600 50 100 150 200 250 200 400 600 800 Distance[µm] Distance[µm] Distance[µm] Fig. A4.1: Measured concentration profiles of Mg in plagioclase (blue circles) and the respective fitted profiles (pink line) for samples from the Hess Deep sample suite. The depth below sheeted dike complex of each sample is given on the left hand side of each panel. The depth increases from top to bottom. The inset in each panel shows the respective XAn -content, which was measured along the same traverse as the Mg-profile.

Appendix IV – Plots of all fitted profiles 15

0.14 3369-1250C2Pl2Sc1 0.7 3369-1250C2Pl2Sc2 0.7 0.6 0.6 0.12 Xan Xan 0.5 0.5 144 0.10 0.4 0.4 0.08

0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim 50 100 150 50 100 150 200 250

0.14 3369-1221C1Pl1Sc1 0.7 0.6 0.12 Xan 0.5 208 0.10 0.4 0.08

0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim 50 100 150 200

0.14 3369-1110C1Pl1Sc1 0.7 3369-1110C1Pl1Sc2 0.7 0.6 0.6 0.12 0.5 Xan 0.5 Xan 211 0.10 0.4 0.4 0.08

0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim

Depth[mbsd] 100 200 300400 400 800 1200

0.14 3369-1050C1Pl1Sc1 0.7 3369-1050C2Pl2Sc1 0.7 3369-1050C2Pl2Sc2 0.7 3369-1050C3Pl3Sc1 0.7 3369-1050C3Pl3Sc2 0.7 0.6 0.6 0.6 0.6 0.6 0.12 0.5 Xan 0.5 Xan 0.5 Xan 0.5 Xan 0.5 Xan 282 0.10 0.4 0.4 0.4 0.4 0.4 0.08

0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim rim core rim rim core rim rim core rim 400 800 1200 500 1000 1500 200 400 600 200 400 600 800 100 200 300 400

0.14 3369-1042C1Pl1Sc1 0.7 3369-1042C1Pl1Sc2 0.7 0.6 0.6 0.12 0.5 Xan 0.5 0.10 0.4 0.4 Xan

282 0.08

0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim 400 800 1200 400 800 1200 1600 Distance[µm] Distance[µm] Fig. A4.1 continued.

Appendix IV – Plots of all fitted profiles 16

0.14 2213-1110C2Pl2Sc2 0.7 2213-1110C3Pl3Sc1 0.7 2213-1110C4Pl4Sc2 0.7 2213-1110C5Pl6Sc1 0.7 2213-1110C5Pl6Sc2 0.7 0.6 0.6 0.6 0.6 0.6 0.12 0.5 Xan 0.5 Xan 0.5 Xan 0.5 Xan 0.5 Xan 0.10 0.4 0.4 0.4 0.4 0.4 380 0.08 0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim rim core rim rim core rim rim core rim 200 400 600 100 200 300400 100 200 300 400 500 200 400 600 100 200 300 400 500

0.14 2218-1111C1Pl1Sc1 0.7 2218-1111C1Pl1Sc2 0.7 2218-1111C2Pl2Sc2 0.7 0.6 0.6 0.6 0.12 0.5 Xan 0.5 Xan 0.5 Xan 470 0.10 0.4 0.4 0.4 0.08

0.06

0.04

Depth[mbsd] 0.02

ConcentrationMgO[wt%] rim core rim rim core rim rim core rim 100 200 300 200 400 600 100 200 300 400 500

0.14 2218-1132C3Pl3Sc1 0.7 2218-1132C3Pl3Sc2 0.7 2218-1132C4Pl5Sc2 0.7 0.6 0.6 0.6 0.12 0.5 Xan 0.5 Xan 0.5 Xan 0.10 0.4 0.4 0.4

0.08

520 0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim rim core rim 200 400 600 100 200 300 200 400 600 Distance[µm] Distance[µm] Distance[µm]

Fig. A4.1 continued.

Appendix IV – Plots of all fitted profiles 17

0.14 022205-0259C1Pl1Sc1 022205-0259C1Pl1Sc2 022205-0259C2Pl2Sc1 022205-0259C2Pl2Sc2

0.12

0.10 41 0.08 0.06

0.04 0.8 0.8 0.8 0.8

0.02 0.6 0.6 0.6 0.6

ConcentrationMgO[wt%] rim core Xan rim rim core Xan rim rim core Xan rim rim core Xan rim 100 200 300 100 200 300 400 100 200 300 400 200 400 600

0.14 022205-0248C2Pl2Sc2 022205-0248C4Pl4Sc1 0.8 0.8 0.12 0.6 0.6 0.10 Xan Xan 45 0.08 0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim 200 400 600 800 50 100 150 200

0.14 022005-0230C1Pl1Sc1 0.8 0.12 0.6 0.10 Xan 0.08

72 0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim 100 200 300

Depth[mbsd]

0.14 022005-1052C2Pl2Sc1 022005-1052C2Pl2Sc2 022005-1052C3Pl3Sc1 022005-1052C3Pl3Sc2 0.8 0.8 0.8 0.8 0.12 0.6 0.6 0.6 0.6 0.10 Xan Xan Xan Xan 355 0.08 0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim rim core rim rim core rim 250 500 750 100 200 300 400 250 500 750 125 250375 500

0.14 022005-0910C1Pl1Sc2 022005-0910C2Pl2Sc1 022005-0910C4Pl4Sc2 0.8 0.8 0.8 0.12 0.6 0.6 0.6 0.10 Xan Xan Xan 386 0.08 0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim rim core rim 50 100 150 200 125 250375 500 100 200300 400

Distance[µm] Distance[µm] Distance[µm]

Fig. A4.2: Measured concentration profiles of Mg in plagioclase (blue circles) and the respective fitted profiles (pink line) for samples from the Pito Deep sample suite. The depth below sheeted dike complex of each sample is given on the left hand side of each panel. The depth increases from top to bottom. The inset in each panel shows the respective XAn -content, which was measured along the same traverse as the Mg-profile.

Appendix IV – Plots of all fitted profiles 18

0.14 022005-0534C2Pl2Sc1 022005-0534C2Pl2Sc2 0.8 0.8 0.12 0.6 0.6 0.10 Xan Xan 0.08

569 0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim 125 250375 500 200 400 600 800

0.14 022005-0506C2Pl2Sc1 022005-0506C2Pl2Sc2 0.8 0.8 0.12 0.6 0.6 0.10 Xan Xan 0.08

662 0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim 200 400 600 250 500 750 1000

0.14 022005-0155C1Pl1Sc1 022005-0155C1Pl1Sc2 022005-0155C2Pl2Sc1 0.8 0.8 0.8 0.12

Depth[mbsd] 0.6 0.6 0.6 0.10 Xan Xan Xan 0.08

780 0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim rim core rim 100 200 300 200 400 600 800 200 400 600 800

0.14 022005-0056C2Pl2Sc1 022005-0056C2Pl2Sc2 022005-0056C3Pl3Sc1 022005-0056C3Pl3Sc2 022005-0056C5Pl5Sc1 0.8 0.8 0.8 0.8 0.8 0.12 0.6 0.6 0.6 0.6 0.6 0.10 Xan Xan Xan Xan Xan 0.08

836 0.06

0.04

0.02

ConcentrationMgO[wt%] rim core rim rim core rim rim core rim rim core rim rim core rim 500 1000 1500 200 400 600 800 100 200 300 400 200 400 600 800 200 400 600 800 Distance[µm] Distance[µm] Distance[µm] Distance[µm] Distance[µm]

Fig. A4.2 continued.

Appendix V

Appendix V – Fortran code for the diffusion model of Mg in plagioclase 19 c======

PROGRAM DIFF MG PLAG c======

implicit none c------c Define variables c------

real, dimension(:), allocatable :: c,cini,dobs real, dimension(:), allocatable :: xan,xanall real, dimension(:), allocatable :: b,ffact real*8, dimension(:), allocatable :: DIF real A,coolrate,Tend,misfit real DC1,DC2,DD,f,EE,MgCpx,MgMelt real Tstart,length,dx,T0,duration

integer i,igrid,ipoints,help,j integer n

real AT,Tfactor,aSiO2,m real xanmax,xanmin real expD,ffactm,dxsq real Tabs,T,Tstop real*8 expE,dtnew,runtime c------c Define I/O c------

open(UNIT=8,FILE='xan_500.txt',STATUS='old') open(UNIT=11,FILE='datain.txt',STATUS='old') open(UNIT=9,FILE='cout.txt',STATUS='unknown') open(UNIT=10,FILE='mgini.txt',STATUS='unknown') open(UNIT=12,FILE='xangrid.txt',STATUS='unknown') open(UNIT=13,FILE='mg_100.txt',STATUS='old') c------c Set problem parameters c------

read(11,*) ipoints write(6,*) ipoints read(11,*) MgCpx write(6,*) MgCpx read(11,*) length Appendix V – Fortran code for the diffusion model of Mg in plagioclase 20

write(6,*) length

read(11,*)igrid read(11,*)A read(11,*)DC1 read(11,*)DC2 read(11,*)DD read(11,*)f read(11,*)EE read(11,*)m read(11,*)coolrate read(11,*)Tend c------c Allocate memory c------

allocate(c(igrid),cini(igrid)) allocate(dobs(igrid)) allocate(xan(igrid),xanall(ipoints)) allocate(DIF(igrid),b(igrid),ffact(igrid))

dx = length/igrid ! defines dx c------c Compute T0 for each crystal c------

T0 = 71.*alog(length)+700. ! T0 dependent on grain size ! function determined from ! Dodson closureT as a function ! of grain size ! and shifted by 700°C write(6,*)T0 c------c Read xan c------

help = ipoints/igrid

READ(8,*)(xanall(i),i=1,ipoints)

DO i=1,igrid xan(i) = xanall(help*i-(help-1)) xan(igrid) = xanall(ipoints) WRITE(12,*) i,xan(i) ENDDO

Appendix V – Fortran code for the diffusion model of Mg in plagioclase 21 c------c Read observed data c------

do i=1,igrid read(13,*) dobs(i) enddo c------c Start loop over crystals c------

n = igrid misfit = 0. c------c Pre-compute constant factors for efficiency c------

ffact = 10.**(f*xan(:))

if (f .gt. 0.) then xanmax = maxval(xan(:)) ffactm = 10.**(f*xanmax) else

xanmin = minval(xan(:)) ffactm = 10.**(f*xanmin) endif

dxsq = dx*dx c------c Initialize parameters c------

runtime = 0.d0 T = T0 c(:) = cini(:) aSiO2 = -0.0000004869039*(T0+273.)*(T0+273.) & +0.0015156955277*(T0+273.)-0.6187067267845

c------c Initialize Mg profile c------

cini(:) = MgCpx*exp(((DC1/(T0+273.))+DC2)+(A/((T0+273.) & *8.314))*xan(:)+log(aSiO2))

Appendix V – Fortran code for the diffusion model of Mg in plagioclase 22

WRITE (6,*)"cini",cini(:) WRITE (10,*)cini(:)

c(:) = cini(:) c------c Run diffusion loop c------

T = T0 do while (T .gt. Tend)

Tabs = T+273.15 Tfactor = 8.314*Tabs AT = A/Tfactor expE = dble(EE/Tfactor+alog(1.e12)) ! Log of expE expD = exp((DC1/Tabs)+DC2) aSiO2 = -0.0000004869039*(Tabs)*(Tabs) & +0.0015156955277*(Tabs)-0.6187067267845

dtnew = alog(0.4)+alog(dxsq)-alog(DD)-alog(ffactm)-expE & -m*alog(aSiO2) dtnew = exp(dtnew)

duration=runtime/3.15576e7 runtime = runtime+dtnew

b = c(:)

c(1) = MgCpx*exp(((DC1/Tabs)+DC2)+(AT*xan(1))+log(aSiO2)) c(n) = MgCpx*exp(((DC1/Tabs)+DC2)+(AT*xan(n))+log(aSiO2))

DIF = alog(DD)+alog(ffact)+expE+m*alog(aSiO2) ! Log of D DIF = exp(DIF)

c(2:n-1) = b(2:n-1)+dtnew/dxsq*( & DIF(2:n-1)*(b(3:n)-2.*b(2:n-1)+b(1:n-2))+ ! Term 1 & (DIF(3:n)-DIF(1:n-2))*(b(3:n)-b(1:n-2))/4.- ! Term 2 & AT*DIF(2:n-1)*(b(3:n)-b(1:n-2))* & (xan(3:n)-xan(1:n-2))/4.- ! Term 3 & AT*b(2:n-1)*(DIF(3:n)-DIF(1:n-2))* & (xan(3:n)-xan(1:n-2))/4.- ! Term 4 & AT*DIF(2:n-1)*b(2:n-1)*(xan(3:n)-2* & xan(2:n-1)+xan(1:n-2))) ! Term 5

Tstop=T T = T0-coolrate*runtime/3.15576e7 enddo

Appendix V – Fortran code for the diffusion model of Mg in plagioclase 23 c------c Calculate misfit c------

misfit = misfit+alog(sum( (c(2:n-1)-dobs(2:n-1))**2) ) & *float(igrid)/2. c------c Write data c------

WRITE(9,*)c(:) WRITE(9,*)'T0',T0 WRITE(9,*)'Tstop',Tstop WRITE(9,*)'duration',duration WRITE(6,*)'c',c(:) WRITE(6,*)T WRITE(6,*)Tstop WRITE(6,*)duration WRITE(6,*)misfit WRITE(9,*)'misfit',misfit

end program

Appendix VI

Appendix VI – Organization of the Electronic Appendix 24

Organization of the Electronic Appendix

The Electronic Appendix contains supplementary material of this work and is organized as follows (see also Fig. A6):

The three main folders are: 1) Experiments 2) Natural Sample Suites 3) Modelling

1) The folder Experiments contains 61 subfolders, one for each experiment, named KF001 - KF060 and one additional folder named X-ray diffraction , which contains data about the x-ray diffraction patters of the gabbroic rock powder before and after the pre-experimental tempering procedure.

KF0XX: Each of the subfolders for the individual experiments KF001 - KF060 in general contains the following subfolders: (i) BSE – containing the BSE-pictures taken for documentation during the EMP measurements. (ii) Maps* - containing element distribution maps of some selected spots (iii) Microprobe Data – containing the raw data of the EMP measurements as .dos-and .mcc-files, the measurement conditions as .txt-files, and .mct-files with the processed data, sorted by minerals (the .mct-files may be opened with Excel). (iv) Mineral Calculation – containing the end-member calculation of the different minerals. Each mineral has a separate .xcl spreadsheet and every measured profile or cluster has a separate page in the spreadsheet, which includes the measurement data, plots of different elements and oxides vs. distance, and the respective BSE pictures of the areas of interest. Appendix VI – Organization of the Electronic Appendix 25

(v) Photos – containing photos of the plagioclase crystals before the experiments and photos of the polished samples after the experiments, where the analyzed spots are documented. (vi) TEM * - containing data from TEM analysis.

*These subfolders are optional and only available for some samples, where this data was measured.

The .xcl-spreadsheet for plagioclase in every subfolder Mineral Calculations contains all documentation of the measured profiles in plagioclase: the first page in each spreadsheet is just the last raw data, that was processed; the second page contains the documentation of the experiment itself, including photographs of the samples, information about the run conditions, etc…; the third page was used to calculate the distance of each analysis, projected on a profile line between the first and last analysis of each profile; the following pages contain information about the individual profiles and cluster, including plots of different components vs. distance, and photographs and BSE-pictures for documentation of the areas of interest.

2) The folder Natural Sample Suites contains 4 subfolders, one for each sample suite, named Hess Deep, Pito Deep, 312_1256D and one additional folder for the drill core samples from Hess Deep, named 147_894G . (Additionally, the folder Natural Sample Suites contains a .doc file with the analytical conditions for the Laser ICP-MS measurements)

Each of these subfolders contains multiple subfolders, one for every analyzed sample from the respective sample suites. Each of these folders for the individual samples is organized very similar to the folders for the individual experiments, and in general contains the following subfolders and files: (i) BSE – containing the BSE-pictures taken for documentation during the EMP measurements. (ii) Maps* - containing element distribution maps of some selected spots. Appendix VI – Organization of the Electronic Appendix 26

(iii) Microprobe Data – containing the raw data of the EMP measurements as .dos-and .mcc-files, the measurement conditions as .txt-files, and .mct-files with the processed data, sorted by minerals (the .mct-files may be opened with Excel). (iv) Mineral Calculation – containing the end-member calculation of the different minerals. Each mineral has a separate .xcl spreadsheet and every measured profile has a separate page in the spreadsheet, which includes the measurement data, plots of different elements and oxides vs. distance, and the respective BSE pictures of the areas of interest. (v) Photos – containing thin section photos of the samples, including photos of each measured plagioclase crystal. (vi) REM * - containing data from REM analysis. (vii) SampleX-Dataplots – is an .xcl-spreadsheet, that summarizes the documentation and measured data of the individual plagioclase crystals in separate pages of the spreadsheet.

*These subfolders are optional and only available for some samples, where this data was measured.

The .xcl-spreadsheet for plagioclase in every subfolder Mineral Calculations contains all documentation of the measured profiles in plagioclase: the first page in each spreadsheet is just the last raw data, that was processed; the second page was used to calculate the distance of each analysis, projected on a profile line between the first and last analysis of each profile; the following pages contain information about the individual profiles, including plots of different components vs. distance, and photographs and BSE-pictures for documentation of the areas of interest.

3) The folder Modelling contains 3 subfolders, one for each modelled sample suite, named Hess Deep, Pito Deep, 312_1256D .

Each of these subfolders contains multiple subfolders, one for every modelled sample from the respective sample suites. Appendix VI – Organization of the Electronic Appendix 27

Each of these folders for the individual samples contains again multiple subfolders, one for every modelled profile from the respective sample, named CX PlX ScX , and an .xcl-spreadsheet, in which the measured data for the individual concentration profiles was processed to serve as input for the modelling. Each of the CX PlX ScX -folders contains two more subfolders, named assa_forward and assa_inv , which contain the input data, the Fortran code, and the output data of the forward modelling procedure and the inverse modelling procedure, respectively.

Appendix VI – Organization of the Electronic Appendix 28

ElectronicAppendix

Experiments NaturalSampleSuites Modelling

Hess Pito 312 147 Hess Pito 312 Deep Deep 1256D 894G Deep Deep 1256D

KF0XX SampleX SampleX

CXPlXScX

BSE BSE assa_forward assa_inverse Maps* Maps* MicroprobeData MicroprobeData MineralCalculation MineralCalculation Photos Photos TEM* REM*

Fig. A6: Scheme to illustrate the organization of the Electronic Appendix. Appendix VI – Organization of the Electronic Appendix 29

Acknowledgements

This thesis would not have been possible unless for my supervisors Prof. Sumit Chakraborty (Ruhr-Universität Bochum) and Prof. Laurence Coogan (University of Victoria) , who set up this fascinating project. I am grateful for their valuable ideas, discussion, guidance, and support.

It is a pleasure to thank our team of research scientists and technicians in Bochum and Victoria for their support: Dr. Ralf Dohmen (Ruhr-Universität Bochum) for discussion about element partitioning and diffusion in plagioclase, patient help with the experiments, and sharing his office with me for a while; Prof. Thomas Müller (Ruhr-Universität Bochum) , for numerous fruitful discussions, help and advice with the experiments, great company during lunch time, and cheering me up whenever needed; Dr. Max Tirone (Ruhr-Universität Bochum) for constructive and patient discussions about cooling histories and closure temperature, allowing me to use his computers for modelling, and letting me borrow his books all the time; Prof. Stan Dosso (University of Victoria) for his help with speeding up the Fortran code, and implementation of the diffusion program into an inversion procedure; Dr. Heinz-Jürgen Bernhardt (Ruhr-Universität Bochum) for introduction to the EMP and numerous, endless EMP sessions; Jodi Spence (University of Victoria) for great help with the Laser-ICP MS facilities in Victoria; Dr. Jan Meijer and the team of the RUBION in Bochum for so much fun at the DTL during PIXE-measurements; and our great team of thin section preparators in Bochum Ellen Kessler, Sabine Schremmer, and ‘Herr Dettmar’ for the best technical support concerning sample preparation. I would like to thank Björn, Sara, Mandy, Julia, and Ferdi for having a great time at the institute in Bochum, and for all our adventures. My sincere thank is dedicated to Matěj for his encouragement, support and patience.

Financial support from the German Research Foundation (DFG) within the scope of this research project is gratefully acknowledged. I am also very grateful for the financial support of the Willhelm und Günther Esser Stiftung during the last stage of this thesis. Curriculum Vitae

Personal Information

Surname Faak ADDRESS First name Kathrin Schaffnerweg 29 Date of birth May, 10 th , 1983 44795 Bochum Citizenship German Germany

Education

2009-2012 PhD studies at the Ruhr-Universität Bochum, Germany funded by the DFG (Deutsche Forschungsgesellschaft - German Science Foundation)

PhD Thesis Cooling and Accretion of the Lower Oceanic Crust at Fast- Spreading Mid-Ocean Ridges.

Supervision Sumit Chakraborty , Ruhr-Universität Bochum, Germany Laurence Coogan , School of Earth and Ocean Science, University of Victoria, Canada

2006-2007 M.Sc. studies in geoscience (focus on petrology) at the Ruhr-Universität Bochum, Germany

M.Sc. Thesis Petrological Analysis of Mafic Lenses of the Lesser Himalaya, Sikkim. (Petrologische Untersuchungen an mafischen Linsen des Lesser Himalaya, Sikkim.)

2002-2006 B.Sc. studies in geoscience at the Ruhr-Universität Bochum, Germany

B.Sc. Thesis Sedimentpetrographical Analysis of Waterworks-Pellets. (Sedimentpetrographische Untersuchungen an Wasserwerks- Pellets.)

1993-2002 Goethe-Gymnasium in Bochum, Germany graduation with Abitur

Publications and Abstracts

Faak, K., Chakraborty, S. & Dasgupta, S., 2012 Petrology and tectonic significance of metabasite slivers in the Lesser and Higher Himalayan domains of Sikkim, India. Journal of Metamorphic Geology , doi:10.1111/j.1525-1314.2012.00987.x

Faak, K., Chakraborty, S. & Coogan, L.A., 2011, Evaluation of the variation in cooling rate with depth in the lower oceanic crust at fast-spreading ridges using a newly developed Mg in plagioclase geospeedometer. Eos Trans AGU , Fall Meet. Suppl., Abstract V13F-04.

Faak, K., Chakraborty, S. & Dasgupta, S., 2008, Petrological analysis of mafic lenses in the Lesser and Higher Himalaya, Sikkim. Eos Trans. AGU , 89, Fall Meet. Suppl., Abstract V41A-2065.

Invited Talks

07.02.2012 Mineralogisches Seminar, Leibnitz Universiät Hannover Kinetic Modelling to Determine the Cooling History of the Lower Oceanic Crust

Short Courses Attended

2008 MSA Short Course on Minerals, Inclusions and Volcanic Processes, San Francisco, U.S.A 2009 ECORD Summer School on Geodynamics of Mid-ocean Ridges , Bremen, Germany 2010 Marie Curie EURISPET Seminar on Experimental Petrology and Rock Deformation , Zürich, Switzerland

Work Experience

2009-2012 Research Assistant at the Ruhr-Universität Bochum, Germany Institute for Geology, Mineralogy and Geophysics Working group: Petrology

2008-2009 Research Assistant at the Ruhr-Universität Bochum, Germany RUBION, Central Unit for Ionbeams and Radionuclides

2006-2008 Student Assistant at the Ruhr-Universität Bochum, Germany Institute for Geology, Mineralogy and Geophysics Working Group: Petrology

2004-2006 Student Assistant at the Ruhr-Universität Bochum, Germany Institute of Geology, Mineralogy and Geophysics Working Group: Crystallography

2003-2004 Student Assistant at the Ruhr-Universität Bochum, Germany Institute of Geology, Mineralogy and Geophysics Working Group: Sedimentology