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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 km3 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
Mg in plagioclase ( PlMgD ) and the partition coefficient of Mg between plagioclase and
clinopyroxene ( CpxPlMgK / ) in the compositional range of the lower oceanic crust. The
diffusion coefficient PlMgD and the partition coefficient CpxPl
MgK / were determined
experimentally as a function of temperature (T), anorthite-content in plagioclase
(XAn) and the silica activity of the system (2SiOa ).
Reliable results for PlMgD and CpxPl
MgK / 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,
CpxPlMgK / was found to (i) decrease with decreasing T, (ii) increase with increasing XAn
in plagioclase and (iii) increase with increasing 2SiOa . The diffusion coefficient Pl
MgD
was found to (i) decrease with temperature following an Arrhenian relationship and
(ii) to increase with increasing 2SiOa . No significant dependence of Pl
MgD on XAn in
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
i
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
Contents
ii
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
2.5.2 Extracting CpxPlMgK / and Pl
MgD from the
experiments 71
2.5.3 Experimental results on CpxPlMgK / and Pl
MgD 73
2.5.4 Uncertainties and error estimation 77
2.5.5 Variation in ln CpxPlMgK / as a function of
T, XAn, 2SiOa , and Cpx
CaSiOX3
82
2.5.6 Discussion of the experimental results on CpxPlMgK / 91
2.5.7. A new thermometer based on the exchange
of Mg between plagioclase and clinopyroxene 94
2.5.8 Variation in PlMgD with T, XAn and
2SiOa 95
2.5.9 Discussion of the experimental results on PlMgD 98
2.6 Conclusions 105
2.7 References 108
Contents
iii
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
3.4.2 Initial profile determined from CpxPlMgK / 124
3.4.3 Boundary conditions determined from CpxPlMgK / 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
Contents
iv
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
1. Introduction
1
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 km3 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. Introduction
2
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
1. Introduction
3
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
1. Introduction
4
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
1. Introduction
5
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-
1. Introduction
6
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)
1. Introduction
7
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).
1. Introduction
8
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
1. Introduction
9
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).
1. Introduction
10
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.
1. Introduction
11
(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
1. Introduction
12
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.
1. Introduction
13
(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).
1. Introduction
14
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
1. Introduction
15
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
1. Introduction
16
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
1. Introduction
17
‘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).
~30 MW/km
0 2 4
km
0 10 20
km
0 10 20
km
hydrothermalcirculation
crystalmush
melt / mushtransport
30 MW/kmenergy loss inMegawatts perkm of ridge axis
solidifiedpluton
magmasheeteddikes
lava isotropicgabbro
layeredgabbro
(a) (b) (c)
AMCaxial
magmachamber
cooling rate
depth
(d) (e)
~30 MW/km
~40MW/km
0 2 4
km
~15 MW/km
~55MW/km
0 2 4
km
(e)(d)
AMCaxial
magmachamber
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).
1. Introduction
18
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
1. Introduction
19
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.
1. Introduction
20
‘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 glacier’ 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).
1. Introduction
21
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
1. Introduction
22
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
coefficient βα /iK ). At constant pressure, the equilibrium concentration of the same
component i in the same minerals α and β will be different at different temperatures
(i.e. the partition coefficient is a function of temperature ( ) βα /iTK , 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
( ) βα /iTK . 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 Tccore, which depends on the cooling rate and the
diffusion coefficients of the phases, the concentration of the component far from the
1. Introduction
23
interface fails to reach equilibrium (Fig. 1.5.1c and d). At some lower temperature
Tcrim, 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).
1. Introduction
24
tem
pera
ture
T
T1
T2
T3
T4
T5
time t
1/T
T1 T2 T3T4 T5
part
itio
n c
oeffic
ient K
ab/
iconcnetr
ation
ia
time t
T1 T2 T3T4 T5
core
rim
equi
TccoreTcrim
concnetr
ation
ia
distancecorerim rim
(a)
(b)
(c)
(d)
Fig. 1.5.1: Schematic illustration of the evolution of
diffusive concentration profiles during cooling on a
given time(t)-temperature(T)-path. Panel (a) shows a
t-T-plot with an assumed linear decrease of
temperature with time, i.e. a constant cooling rate.
Panel (b) shows a plot of an partition coefficient βα /
iK (ratio of concentration of element i in phases α
and β) against 1/T, showing a decreasing βα /
iK with
decreasing T. Panel (c) shows the evolution of the concentration of element i in mineral α with time and
decreasing temperature on the given t-T-path in (a),
i.e. for a given cooling rate. At temperatures T1 and T2,
an equilibrium distribution of the element i in phase α,
constrained by the partition coefficient βα /
iK at these
temperatures, can be attained over the entire crystal of
mineral α. At temperature Tccore, 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 Tcrim, because the diffusion distance is shorter. Below temperature Tcrim, diffusion
becomes too slow to effectively change the
concentration of i and even the rims cannot attain the
equilibrium concentration (dashed line) anymore. The
whole system is frozen, and the concentration of i at
the rims is lower than in the core. The figure is shown
for a given cooling rate and a given grain size of the
crystal α, but it is noted that Tccore and Tcrim are a
function of cooling rate and grain size and will be
different as these parameters are changed. Panel (d)
shows the successive evolution of concentration profiles of element i in a grain of mineral α during
cooling. At temperature T1 and T2 the entire grain
equilibrates and attains the respective equilibrium
concentrations (red and pink solid lines). The
concentration profile attained at temperature T3
(orange solid line) is slightly bowed, because the core
does not reach the respective equilibrium
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
core was already frozen, but the rims continuously
exchanged up to lower temperatures and
concentrations. The equilibrium concentration at T4
(green dashed line) is however slightly lower than the
developed concentration at the rims at T4, because
Tcrim was reached before T4 (as shown in (c)).
Therefore, the concentration profile attained at T5
(blue solid line) is the same as the concentration
profile attained at T4 (green solid line), because
diffusion effectively does not change the concentration below Tcrim.
1. Introduction
25
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:
( )
−=RT
EDTD exp0 (Eq. 1.5.1)
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):
( ) ( )
−=tRT
EDtD exp0 (Eq. 1.5.2)
The diffusion equation (here for diffusion in 1 dimension)
∂∂
∂∂=
∂∂
x
CD
xt
C (Eq. 1.5.3)
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
( )
∂∂
∂∂=
∂∂
x
CtD
xt
C, (Eq. 1.5.4)
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
1. Introduction
26
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
1. Introduction
27
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
1. Introduction
28
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.
1. Introduction
29
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
1. Introduction
30
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).
1. Introduction
31
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
Sample Depth
below sea level Depth
of d/g boundary Depth
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
1. Introduction
32
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
Sample Depth
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).
1. Introduction
33
(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).
1. Introduction
34
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).
1. Introduction
35
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 below sea level
Depth of d/g boundary
Depth 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).
1. Introduction
36
(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 below sea floor
Depth of d/g boundary
Depth 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
1. Introduction
37
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2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
49
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 (2SiOa ) in the
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.
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
50
The partition coefficient of Mg between plagioclase and clinopyroxene ( CpxPlMgK / ) as
well as the diffusion coefficient of Mg in plagioclase ( PlMgD ) were extracted from non-
linear least square fitting of these profiles. Plots of ln CpxPlMgK / and log Pl
MgD (for
constant XAn=0.6) vs. inverse temperature are linear with a negative slope, and show
a positive correlation with 2SiOa . Isothermal data for different XAn in plagioclase
show a linear increase of ln CpxPlMgK / with increasing XAn, but a strong dependence of
PlMgD on XAn is not observed. Multiple regression of all data allows ln CpxPl
MgK / to be
determined as a function of temperature, XAn and 2SiOa , and application as a
geothermometer reproduces the experimental temperatures within ±20°C:
[ ][ ] [ ]
2ln6.1ln
J/mol16913K9219
K
SiOCpxMg
PlMg
An
aC
C
XRT
−−
+−=
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
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
51
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
( CpxPlMgK / ) 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
CpxPlMgK / according to
CpxMg
PlMgCpxPl
Mg C
CK =/ (Eq. 2.1.1)
where PlMgC is the weight concentration of Mg in plagioclase and Cpx
MgC is the weight
concentration of Mg in clinopyroxene. Figure 2.1.1 shows a plot of ln CpxPlMgK / from
these previous experimental studies versus the reported temperatures. The diagram
clearly shows an overall trend of decreasing CpxPlMgK / with decreasing temperature,
but the large variability in the data allows only poor quantitative constraints.
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
52
Fig. 2.1.1: Calculated values for ln CpxPl
MgK / 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 (2SiOa ). Since the partition coefficient of
Mg between plagioclase and melt ( meltPlMgK / ) is expected to be dependent on XAn in
plagioclase (Blundy and Wood, 1994; Bindeman et al., 1998), CpxPlMgK / is expected to
show a similar dependence on XAn and therefore the effect of temperature on CpxPlMgK /
might not be easily compared for experiments done with different XAn.
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
53
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
the partition coefficient CpxPlMgK / . Thus, diffusion models aiming to describe this
system provide another field of application for more detailed data on the
partitioning between plagioclase and clinopyroxene.
This study aims to quantify CpxPlMgK / 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
Mg in plagioclase ( PlMgD ) to be determined for each experiment.
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
54
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 NaxCa1-xAl2-xSi2+xO8 (e.g. Weill et al., 1970; Drake and
Weill, 1971; Wenk and Wilde, 1973), that could be explained by the additional
components Ca(MgFe2+)Si3O8, (MgFe2+)Al2Si2O8 and [ ]Si4O8 (Longhi et al., 1976; all
Fe is assigned as Fe2+ for simplicity). Theoretically, the following substitutions may
be possible to implement Mg in plagioclase:
(1) Mg2+ + Si4+ = 2 Al3+
(2) Mg2+ = Ca2+
Substitution (1) leads to a CaMgSi3O8-component, where Mg occupies the
tetrahedral site (T-site), and substitution (2) leads to an MgAl2Si2O8-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)Si3O8. Incorporation of Mg into plagioclase as this
component was supported by the study of Sclar et al. (1991, unpublished data), that
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
55
reports the synthesis of metastable feldspar of composition CaMgSi3O8 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
of Mg between plagioclase and melt ( meltPlMgK / ) and the liquid activity product of the
crystallization reaction CaO(liq)+MgO(liq)+3SiO2(liq) = CaMgSi3O8(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
their experimentally determined meltPlMgK / (for: XAn=0.89, P=1 atm, T=1251°C) and a
predicted meltPlMgK / 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: )()( 83262 PlOCaMgSiSiOCpxOCaMgSi =+
(2): Mg on M-site: )()( 8223223 PlOSiMgAlOAlSiOCpxMgSiO =++
However, using CaMgSi2O6 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 CaMgSi2O6-component, as natural
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
56
clinopyroxenes may also consist of other Mg-bearing components (such as
Mg2Si2O6). Alternatively, reaction (1a) can be written as:
(1b): Mg on T-site: )()()( 83233 PlOCaMgSiSiOCpxMgSiOCpxCaSiO =++
For any reaction, in equilibrium we can state:
eqr KRTG ln0 −=∆ , (Eq. 2.2.1.1)
where R is the ideal gas constant (8.314 J/molK), T is temperature in Kelvin, Keq is
the equilibrium constant and 0rG∆ is the change in the standard state Gibbs Free
energy of the reaction. For reaction (1b) 0rG∆ is given by:
)()()()( 20
30
30
8300 SiOGMgSiOGCaSiOGOCaMgSiGGr −−−=∆
(Eq. 2.2.1.2)
where )( 830 OCaMgSiG , )( 3
0 CaSiOG , )( 30 MgSiOG and )( 2
0 SiOG 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:
233 SiOCpxMgSiO
CpxCaSiO
PlCM
eq aaa
aK = , (Eq. 2.2.1.3)
where PlCMa is the activity of the CaMgSi3O8-component in plagioclase, Cpx
CaSiOa3 is the
activity of the (CaSiO3)-component in clinopyroxene, CpxMgSiOa
3 is the activity of the
(MgSiO3)-component in clinopyroxene and 2SiOa is the silica activity of the system.
Using ji
ji
ji Xa γ= , where j
iX is the equivalent mole fraction of component i in
mineral j and jiγ is the corresponding activity coefficient of component i in mineral
j, we can write:
Keq =γCM
Pl XCMPl
γCaSiO3
Cpx XCaSiO3
Cpx γMgSiO3
Cpx XMgSiO3
Cpx aSiO2
(Eq. 2.2.1.4)
and hence in the equilibrium state we get:
23333
lnln0
SiOCpxMgSiO
CpxMgSiO
CpxCaSiO
CpxCaSiO
PlCM
PlCM
eqraXX
XRTKRTG
γγγ
−=−=∆ (Eq. 2.2.1.5)
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
57
Equation 2.2.1.5 can be rearranged to:
2333
233
3
3
lnlnlnlnln
1lnlnln
00
0
SiOCpxCaSiO
CpxCaSiO
PlCM
CpxMgSiO
rr
SiOCpxCaSiO
CpxCaSiO
PlCM
CpxMgSiOr
CpxMgSiO
PlCM
aXR
S
RT
H
aXRT
G
X
X
+++−+∆
+∆−
=
−+∆−
=
γγγ
γγγ
(Eq. 2.2.1.6)
where 0rH∆ and 0
rS∆ are the standard state enthalpy and standard state entropy of
the reaction, respectively.
To a first approximation the activity coefficients for the (CaSiO3)- and
(MgSiO3)-component in clinopyroxene, CpxCaSiO3
lnγ and CpxMgSiO3
lnγ , are assumed to be
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 CaMgSi3O8-component in
plagioclase (CM) as suggested by Blundy and Wood (1991):
( ) 2ln AnAnAbAnAbCMAnCMAbAnCMAbPlCM XWWWWXWRT −+−−=γ , (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:
RT lnγCMPl = −A − BXAn (Eq. 2.2.1.8)
Application to Eq. 2.2.1.6 yields
2
333
3
ln
lnlnlnln00
SiOAn
CpxCaSiO
CpxCaSiO
CpxMgSiO
rrCpxMgSiO
PlCM
aXRT
B
RT
A
XR
S
RT
H
X
X
+++
+++∆
+∆−
= γγ
(Eq. 2.2.1.9)
which can be rearranged to
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
58
2
333
3
ln
lnlnln1
ln00
SiOAn
CpxCaSiO
CpxCaSiO
CpxMgSiO
rrCpxMgSiO
PlCM
aXRT
B
XR
S
TR
A
R
H
X
X
++
+++∆
+
+
∆−= γγ
(Eq. 2.2.1.10)
Under the assumption made for reaction (1b), that all Mg enters the
plagioclase as a CaMgSi3O8-component, the ratio of the molar fraction of this
component in plagioclase ( XCMPl ) and the molar fraction of the (MgSiO3)-component
in clinopyroxene ( CpxMgSiOX
3) is directly related to the partition coefficient of Mg
between plagioclase and clinopyroxene:
CpxMgSiO
PlCM
CpxMg
PlMgCpxPl
MgX
Xf
C
CK
3
lnlnln / ⋅== ,
where the factor f is the ratio of the normalization factors of wt% MgO into MgX 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:
2333
3
lnlnlnln1
ln
lnlnln
00
/
SiOCpxCaSiOAn
CpxCaSiO
CpxMgSiO
rr
CpxMgSiO
PlCM
CpxMg
PlMgCpxPl
Mg
aXXRT
B
R
S
TR
A
R
Hf
X
Xf
C
CK
+++
++
∆+
+
∆−+=
==
γγ
(Eq. 2.2.1.11)
Thus, CpxPlMgK /ln is expected to show linear dependences on 1/T, XAn, ln
2SiOa and
ln CpxCaSiOX
3.
Eq. 2.2.1.11 may also be written in linear form as:
( ) ( )[ ]23
33
lnln
lnlnlnln 00/
SiOCpxCaSiO
AnCpxCaSiO
CpxMgSiOrr
CpxPlMg
aRTXRT
BXTRSAHfKRT
++
+++∆++∆−+= γγ
(Eq. 2.2.1.12)
and simplified to
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
59
23lnlnln '/
SiOCpxCaSiOAn
CpxPlMg aRTXRTBXCTAKRT ++++= (Eq. 2.2.1.13)
The analysis beginning with Eq. 2.2.1.1 can be used in a similar manner for
reaction (2), where 0rG∆ is given by:
)()()()( 320
20
30
82200 OAlGSiOGMgSiOGOSiMgAlGGr −−−=∆ (Eq. 2.2.1.14)
and the equilibrium constant Keq of reaction (2) can be written as:
322333223 OAlSiOCpxMgSiO
CpxMgSiO
PlMA
PlMA
OAlSiOCpxMgSiO
PlMA
eqaaX
X
aaa
aK
γγ
== (Eq. 2.2.1.15)
with MA denoting the MgAl2Si2O8-component in plagioclase and 32OAla being the
alumina activity of the system.
Following the same approach as outline above, Eq. 2.2.1.6 now has to be
written as:
3223
322
3
3
lnlnlnln
lnlnlnln
00
0
OAlSiOPlMA
CpxMgSiO
rr
OAlSiOPlMA
CpxMgSiO
CpxMgSiO
PlCM
aaR
S
RT
H
aaRT
G
X
X
++−+∆
+∆−
=
+++∆−=
γγ
γγ
(Eq. 2.2.1.16)
Under the assumption underlying reaction (2), that all Mg enters the
plagioclase as a MgAl2Si2O8-component, the ratio of the molar fraction of this
component in plagioclase ( PlMAX ) and the molar fraction of the (MgSiO3)-component
in clinopyroxene ( CpxMgSiOX
3) is again directly related to the partition coefficient of Mg
between plagioclase and clinopyroxene (CpxMg
PlagMgCpxPl
Mg C
CK =/ ) and therefore Eq. 2.2.1.11
now can be written as:
3223
3
lnlnln1
ln
lnlnln
00
/
OAlSiOAnCpxMgSiO
rr
CpxMgSiO
PlCM
CpxMg
PlMgCpxPl
Mg
aaXRT
B
R
S
TR
A
R
Hf
X
Xf
C
CK
+++
+
∆+
+
∆−+=
==
γ
(Eq. 2.2.1.17)
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
60
Hence, if Mg is exchanged between plagioclase and clinopyroxene via reaction (2),
CpxPlMgK /ln is expected to show the same linear dependence on 1/T, XAn, ln
2SiOa as in
the case of reaction (1b). Additionally, for reaction (2) CpxPlMgK /ln is expected to
depend on 32
ln OAla , but should not be a function of ln CpxCaSiOX
3. Eq. 2.2.1.17 can be
written in linear form as:
( ) ( )[ ]3223
lnlnlnln
ln00
/
OAlSiOAnCpxMgSiOrr
CpxPlMg
aRTaRTBXTRSAHf
KRT
++++∆++∆−+
=
γ
(Eq. 2.2.1.18)
and simplified to:
322lnlnln '/
OAlSiOAnCpxPl
Mg aRTaRTBXCTAKRT ++++= (Eq. 2.2.1.19)
Experimental determination of CpxPlMgK / therefore needs to be carried out
under controlled 2SiOa and
32OAla to define all relevant thermodynamic parameters
controlling CpxPlMgK / .
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.
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
61
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 26Mg. 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,
RTEAnMg eDD /
0−= , with D0=7.1±0.1 x 10-8 m2/s and E=254±43 kJ/mol in b-direction,
and D0=1.2±0.1 x 10-6 m2/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:
[ ]/smkJ/mol266
exp1092.2 2)1.31.4(
−⋅= −−
RTD XanPl
Mg .
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
62
Experiments with plagioclase of different anorthite-contents carried out in
this study will determine a possible dependence of PlMgD on XAn and allow for testing
the assumption of Costa et al. (2003) that PlMgD 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
between plagioclase and clinopyroxene ( CpxPlMgK / ) and the diffusion coefficient of Mg
in plagioclase PlMgD as a function of (i) temperature T, (ii) anorthite content in
plagioclase XAn and (iii) silica activity of the system 2SiOa . The effect of
32OAla on
CpxPlMgK / and Pl
MgD was not investigated here, but all experiments were carried out
using Al2O3-crucibles and it will be shown later (section 2.5.3) that this was
sufficient to buffer 32OAla to 1 for all experiments. Plagioclase single crystals with
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 Al2O3-
crucible, such that the matrix powder surrounded the plagioclase cubes from all
sides (Fig. 2.3.1.1).
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
63
Gas mixing funaceO controlled by defined flux of CO and COf 2 2
Al O -
crucible2 3
plagioclasecrystal
justCpx-
powder
Cpx+SiO -
powder2
naturalgabbroic
rockpowder
(a) (b) (c)
B-type thermocouple and ZrO - O -sensor2 2f
Al O -rod2 3
Pt-wire
Fig. 2.3.1.1. Sketch of the experimental setup. In one experimental run, three Al2O3-crucibles are tied
to a Al2O3-rod with Pt-wire and are placed together in the gas mixing furnace. Each Al2O3-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+SiO2, 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 Al2O3-crucible was
pressed by hand on the assemblage of plagioclase cube and matrix powder. In every
experimental run, three filled Al2O3-crucibles were tied to an Al2O3-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 2SiOa , plagioclase cubes cut from the same single
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+SiO2) 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 SiO2-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
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
64
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/CO2-ratio of 83.4/16.6, which corresponds to
fO2=10-11 bars at 1100°C) to induce the breakdown of any hydrous alteration phases
(e.g. amphibole and chlorite).
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
65
Table 2.3.1.1: Chemical composition of starting materials. gabbroic rock 022005-1522
Oxide Plag (XAn=0.6)
Plag (XAn=0.12)
Plag (XAn=0.2)
Plag (XAn=0.5)
Plag (XAn=0.7)
Plag (XAn=0.95)
Diopside (Cpx)
Dioside glass
Cpx ~35 vol%
Plag ~50 vol%
Ol** ~5 vol%
Opx ~10 vol%
SiO2 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 K 2O 0.29 0.31 0.95 0.53 0.12 0.01 0.01 0.01 0.02 0.04 0.00 0.01 Na2O 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
*** CpxCaSiOX
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 CpxCaSiOX
3 as explained in Section 2.5.5.
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
66
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 CO2 to control the
oxygen fugacity. The combined flux rates of CO- and CO2 was set to 500 SCCM
(standard cm3 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 ZrO2-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 Al2O3
was added to the matrix powder, in order to test if the Al2O3-crucible is sufficient to
buffer the system for 32OAla . The plagioclase crystal in experimental run KF005 was
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.
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
67
2.3.3 Sample preparation after the experiment
After the experiment, the plagioclase crystal and the surrounding matrix
powder were removed carefully from the Al2O3 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).
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
68
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.
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
69
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
used to determine CpxPlMgK / and Pl
MgD . 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+SiO2, 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 CaAl2Si2O8, NaAlSi3O8, CaMgSi3O8, MgAl2Si2O8 and [ ]Si4O8
(Longhi, 1976), the changes in Na and Ca correlate with an increase in the [ ]Si4O8-
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.
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
70
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+SiO2), (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
( )82283
83,
OSiMgAlOCaMgSi
OCaMgSir MT
Mg += along the profiles yields MT
Mgr , ~1 towards the rims
for the majority of the plagioclase crystals, indicating a preference of Mg for the
tetrahedral site as a CaMgSi3O8-component (Fig.2.5.1.2a and b). Towards the core,
MTMgr , decreases to 0.5 for some plagioclase crystals (e.g. KF026, Fig. 2.5.1.2b).
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
71
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+SiO2) and (b) KF026 (XAn=0.6; T=1200°C; surrounded by just Cpx). Please
note the breakpoint in scaling for the concentrations.
2.5.2 Extracting CpxPlMgK / and Pl
MgD from the experiments
The partition coefficient CpxPlMgK / is extracted from the experiments as the
ratio between PlMgC and Cpx
MgC , at which PlMgC is the concentration of MgO in the
plagioclase at the immediate contact with the clinopyroxene, and CpxMgC 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
CpxPlMgK / . The concentration of Mg in the plagioclase in immediate contact with
clinopyroxene ( PlMgC ) 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
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
72
clusters were plotted versus their distance from the rim of the plagioclase. The data
was fitted using a complementary error function of the form:
tD
xerfcCCC
PlMg
PlMg
20 += (Eq. 2.5.2.1)
where C is the measured concentration of MgO in the plagioclase along the profile,
C0 is the concentration of MgO in the core of the plagioclase crystal, PlMgC is the
concentration of MgO at the contact between the plagioclase and the clinopyroxene,
x is the distance of each analyses from the rim of the plagioclase, PlMgD 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
each profile and t is known. Thus, PlMgC and Pl
MgD are the only fit parameters and are
constrained by minimizing the misfit fitσ (standard deviation) between each
measured concentration and the respective calculated concentration (Fig. 2.5.2.1).
The misfit fitσ is calculated for each profile as
∑ −= 2.)(1 calc
MgmeasuredMgfit CC
Nσ , (Eq. 2.5.2.2)
with N=number of analyses, measuredMgC =measured concentration of MgO and
.calcMgC =calculated concentration of MgO from error-function (Eq. 2.5.2.1) and is given
in Table 2.5.3.1 for each fitted profile used to extract CpxPlMgK / and Pl
MgD .
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
73
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
( CpxMgC ) 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.
2.5.3 Experimental results for CpxPlMgK / and Pl
MgD
Table 2.5.3.1 summarizes the results of the experiments after extraction of
CpxPlMgK / and Pl
MgD as outlined above. Multiple numbers for CpxPlMgK / and Pl
MgD for the
same experiment result from multiple measurements of Mg-concentration profiles
at different positions within one plagioclase crystal. The diffusion coefficient PlMgD
could not be extracted from all measured profiles (e.g. because the profile shape was
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
74
too scattered or disturbed by cracks or inclusions), however, it is still possible to
extract PlMgC to determine CpxPl
MgK / 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+SiO2 and experiments,
where plagioclase was surrounded by Cpx+SiO2+Al2O3, yield similar results for
CpxPlMgK / and Pl
MgD . This observation suggests, that the use of an Al2O3-crucible fixes
32OAla to 1 in all experiments. The assumption of equilibrium between plagioclase
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
the same values of PlMgC within the scatter of the data (e.g. see KF038, KF058 and
KF059, Fig. 2.5.4.1).
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
75
Table 2.5.3.1: Summary of the experimental results after extraction of CpxPl
MgK / and
PlMgD .
Experiment
XAn
Matrix
T
[°C]
log fO2
Run time [[[[d]]]]
CpxMgC
[wt%]
PlMgC
[wt%]
CpxPlMgK /
log
PlMgD
[log (m2/s)]
fitσ
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
KF020 0.6 Cpx 1120 -10 16 16 0.152; 0.155; 0.142;
0.165; 0.150 0.010; 0.010; 0.009;
0.010; 0.009 -16.27; -16.52; -16.70;
-16.82; -16.74 0.012; 0.041; 0.017;
0.027; 0.013 KF021 0.6 Cpx+SiO2 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+SiO2+Al2O3 1120 -10 16 16 0.228; 0.200 0.014; 0.013 -14.89; -15.40 0.045; 0.059
KF023 0.6 Cpx 1180 -9 12 16 0.185; 0.193; 0.208; 0.197; 0.185; 0.203
0.012; 0.012; 0.013; 0.012; 0.012; 0.013
-15.82; -16.15; -16.05; -15.77; -16.19; -16.15
0.017; 0.019; 0.018; 0.012; 0.024; 0.027
KF024 0.6 Cpx+SiO2 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+SiO2+Al2O3 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
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
76
KF027 0.6 Cpx+SiO2 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+SiO2+Al2O3 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
KF038 0.6 gabbro powder 1160 -9 11 15 0.173; 0.163; 0.154; 0.163; 0.155; 0.162;
0.154
0.012; 0.011; 0.010; 0.011; 0.010; 0.011;
0.010
-; -16.20; -; -16.30; -; -16.40;
-16.40
0.023; 0.015; 0.010; 0.038; 0.025; 0.034;
0.013
KF039 0.6 Cpx 1160 -9 11 16 0.185; 0.164; 0.170;
0.160 0.012; 0.010; 0.011;
0.010 -16.10; -16.40; -16.11;
-16.22 0.018; 0.008; 0.017;
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
KF048 0.5 gabbro powder 1150 -10 20 15 0.130; 0.142; 0.132;
0.137 0.009; 0.009; 0.009;
0.009 -16.35; -; -15.82;
-15.70 0.015; -; 0.012;
0.054 KF049 0.8 gabbro powder 1150 -10 20 15 0.200 0.013 - -
KF050 0.5 Cpx 1150 -10 20 16 0.158; 0.163; 0.169;
0.166; 0.161 0.010; 0.010; 0.011;
0.010; 0.010 -16.05; -16.07; -16.10;
-15.98; -16.10 0.017; 0.017; 0.028;
0.019; 0.013
KF051 0.6 Cpx 1150 -10 20 16 0.189; 0.174; 0.171; 0.172; 0.184; 0.173
0.012; 0.011; 0.011; 0.011; 0.012; 0.011
-16.24; -16.15; -15.98; -16.00; -16.12; -16.01
0.015; 0.012; 0.009; 0.013; 0.022; 0.024
KF052 0.7 Cpx 1150 -10 20 16 0.206; 0.187; 0.209; 0.189; 0.194; 0.192
0.013; 0.012; 0.013; 0.012; 0.012; 0.012
-16.40; -16.13; -16.19; -16.09; -16.52; -16.15
0.012; 0.025; 0.014; 0.013; 0.021; 0.015
KF054 0.5 Cpx+SiO2 1150 -10 20 16 0.202 0.013 -15.67 0.016
KF055 0.3 Cpx+SiO2 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+SiO2 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
italics: data results from extracting PlMgC by linear fitting of just the part of the profile, that is closest to the rim (see text for discussion)
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
77
2.5.4 Uncertainties and error estimation
Uncertainties of the absolute values of CpxPlMgK / and Pl
MgD 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
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
78
(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
measured concentrations. For the measurement conditions used, analyticσ 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
of different elements affect each other. The uncertainty of (h) the fit parameters PlMgC
and PlMgD 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
PlMgC , and ~7 % of the average value for Pl
MgD for one set of experimental conditions,
e.g. T=1160°C; XAn=0.6; surrounded by gabbro powder. The individual uncertainty of
the fit parameters and how this can be propagated into ln CpxPlMgK / and log Pl
MgD 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
after the sample preparation and the extracted values for PlMgC and Pl
MgD 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
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
79
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.
Figure 2.4.5.1 shows a plot of the obtained values of ln CpxPlMgK / and log Pl
MgD for the
different profiles measured in experiments KF038, KF058 and KF059 (profiles
number 1, 3, and 5 from KF038 were not used to extract PlMgD ). The 1σ-uncertainties
of the fit parameters PlMgC and Pl
MgD ( PlfitC
σ and fitDσ , respectively) were determined by
non-linear least square fitting of each profile and were propagated into 1σ-
uncertainties in ln CpxPlMgK / and log Pl
MgD using the general relationship to propagate
errors for a function of the type ),( vufx = (e.g. Bevington, 1996):
22
222
uv
vux v
x
u
x
∂∂+
∂∂≅ σσσ . (Eq. 2.5.4.1)
Application of Eq. 2.5.4.1 to CpxMg
PlMgCpxPl
Mg C
CK lnln / = yields:
σln K2 ≅σ
C fitPl
2 1CMg
Pl
2
+σC Cpx2 −1
CMgCpx
2
(Eq. 2.5.4.2)
Assuming that 2CpxC
σ ~0:
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
80
2
22ln,
1
=
PlMg
CKfit CPlfit
σσ . (Eq. 2.5.4.3)
By analogy, application of Eq. 2.5.4.1 to )log(log PlMg
PlMg DD = gives
2
22log, 3023.2
1
≅
PlMg
DDfitDfit
σσ (Eq. 2.5.4.4)
The resulting values for 2ln, Kfitσ and 2
log, Dfitσ are used as error bars for the
determined values for ln CpxPlMgK / and log Pl
MgD 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).
Fig. 2.5.4.1: Obtained values for lnCpxPl
MgK / and log
PlMgD for the multiple profiles measured in
experiments KF038, KF058 and KF059. Error bars are from error propagation of 1σ-uncertainties on
the extracted valued for PlMgC and
PlMgD . 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
the fitting. In order to account for this, the overall uncertainty of the data totalσ is
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
81
calculated from the sum of the variance of the data scatterν and the variance on the
weighted mean µν :
µνννσ +== scattertotaltotal , (Eq. 2.5.4.5)
where
( )( )∑
∑=2
,
2,
/1
/)(
ifit
ifitixmeanweighted
σσ
µ
with xi denoting each individual data point and 2, ifitσ denoting its
individual uncertainty resulting from fitting,
( ) ( )1
var−−
= ∑N
xscatterfromdatatheoniance i
scatter
µν
with N=number of profiles, and
( ) ( )∑=
2,/1
1var
ifit
meanweightedtheonianceσ
ν µ (e.g. Bevington, 1969).
Following this approach yields 1σ-uncertainties of totalσ =0.038 for ln CpxPlMgK / and
totalσ =0.109 for log PlMgD .
Generally, totalσ 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.
Thus, totalσ 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,
T=1160°C surrounded by gabbro powder) is used as an estimate for totalσ for the
entire dataset of experiments surrounded by gabbro powder and just Cpx. For the
experimental series, in which plagioclase was surrounded by Cpx+SiO2, an
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
82
additional source of uncertainty arises, resulting from the fact that excess SiO2
seems to increase the number of vacancies in plagioclase (shown by the increase in
the [ ]Si4O8- 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+SiO2 is determined separately,
following the same scheme as outlined for totalσ of the experiments surrounded by
gabbro powder. For the experimental series surrounded by Cpx+SiO2 there are
three sets of experimental conditions with the same, largest number of measured
profiles. Thus totalσ was determined as the average value from the three sets of
experimental conditions, where three profiles each were measured, which yields
totalσ =0.075 for ln CpxPlMgK / and totalσ =0.150 for log Pl
MgD .
2.5.5 Variation of CpxPlMgK / with T, XAn,
2SiOa , and CpxCaSiOX
3
The thermodynamically derived Equation 2.2.1.11 (under the assumption
that Mg only dissolves into plagioclase as a CaMgSi3O8-component) implies that
ln CpxPlMgK / is expected to linearly depend on 1/T, XAn, ln
2SiOa , and ln CpxCaSiOX
3. The same
equation derived assuming that Mg dissolves into plagioclase as a MgAl2Si2O8-
component (Eq. 2.2.1.17) implies the same dependence for ln CpxPlMgK / on 1/T, XAn,
and ln2SiOa , but an additional dependence on ln
32OAla and no dependence on
ln CpxCaSiOX
3. Since
32OAla was kept constant (32OAla =1) for all experimental series, this
study does not allow us to constrain the effect of 32OAla and thus Eqs. 2.2.1.11 and
2.2.1.17 only differ in that Eq. 2.2.1.11 additionally implies a dependence of
ln CpxPlMgK / on Cpx
CaSiOX3
. The thermodynamically expected trends for ln CpxPlMgK / as a
function of T, XAn, and 2SiOa (as implied by both equations) are clearly seen in the
experimental data. Figure 2.5.5.1 shows a linear decrease in ln CpxPlMgK / with
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
83
increasing 1/T (=decreasing temperature) for all three experimental series
(plagioclase surrounded by (a) just Cpx, (b) Cpx+SiO2 and (c) gabbro powder) for
constant XAn=0.6. The plot also shows that the data for ln CpxPlMgK / are systematically
the highest for experiments, in which plagioclase was surrounded by Cpx+SiO2.
Fig. 2.5.5.1: Experimentally determined values for lnCpxPl
MgK / plotted against 1/T for the
experimental series surrounded by just Cpx (green), Cpx+SiO2 (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
of lnCpxPl
MgK / with decreasing temperature and ln
CpxPlMgK /
for the different experimental series
increases with ln2SiOa , i.e. at a constant T, the difference between the experimental series is given by
the difference in ln2SiOa . Y-error bars on the average values are 2σ uncertainties (±0.076 for
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.
The effect of XAn on ln CpxPlMgK / is shown in Fig. 2.5.5.2, where ln CpxPl
MgK / is
plotted as a function of plagioclase compositions for the following data sets: (i)
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
84
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
linear increase in ln CpxPlMgK / with increasing XAn.
Fig. 2.5.5.2: Results for lnCpxPl
MgK / 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+SiO2, because 2SiOa is fixed to 1 due to the presence of excess
SiO2. For experimental runs in which plagioclase was surrounded by gabbro
powder, 2SiOa is buffered by the coexistence of olivine and orthopyroxene in the rock
assemblage by the reaction Mg2SiO4 + SiO2 = 2MgSiO3 (Carmichael, 1970), which
allows 2SiOa to be determined as:
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
85
RT
Ga r
SiO 303.2log
0
2
∆= .
This yields 2SiOa =0.549, 0.552 and 0.553 for the respective experimental
temperatures of 1130°C, 1150°C and 1160°C (at which 0rG∆ was calculated using
the dataset of Ghiorso, 1995). Figure 2.5.5.3 shows a direct comparison of ln CpxPlMgK /
from experiments, in which plagioclase was surrounded by Cpx+SiO2, and
experiments, in which plagioclase was surrounded by gabbro powder at constant
T=1150°C and XAn=0.6. The difference in ln CpxPlMgK / for plagioclase surrounded by
Cpx+SiO2 (average ln CpxPlMgK / =-4.11) and for plagioclase surrounded by gabbro
powder (average ln CpxPlMgK / =-4.59) corresponds reasonably well to the difference in
ln2SiOa of the two experimental series (ln(0.552)=0.6 and ln(1)=0). Figure 2.5.5.3
shows that ln CpxPlMgK / increases with ln 2SiOa 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 CpxPlMgK / on ln
2SiOa .
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
86
Fig. 2.5.5.3: Comparison of lnCpxPl
MgK / from experiments surrounded by gabbro powder (dark
blue; 2SiOa =0.552) and surrounded by Cpx+SiO2 (pink;
2SiOa =1) plotted against their respective
ln2SiOa -values at T=1150°C and XAn=0.6. Open symbols are from individual experiments and
closed symbols show the respective average values. The silica activity for the experimental series
surrounded by Cpx (green) can be determined from the linear relationship between lnCpxPl
MgK /
and ln2SiOa (see upcoming text for explanation). The solid black line shows a linear through the
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+SiO2 (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
described by the thermodynamically derived linear dependence of ln CpxPlMgK / on 1/T,
XAn, and ln2SiOa . For the assumption made for reaction (1b), that all Mg dissolves in
plagioclase as a CaMgSi3O8-component, an additional linear dependence of ln CpxPlMgK /
on ln CpxCaSiOX
3 would be expected (see Eq. 2.2.1.11). The mole fraction of Ca in
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
87
clinopyroxene ( CpxCaSiOX
3) is calculated from the microprobe analysis of the two
different clinopyroxenes used for the different experimental series as follows:
)()()()(
)(
32333
33 OAlXFeSiOXMgSiOXCaSiOX
CaSiOXX Cpx
CaSiO +++= (Eq. 2.5.5.1)
where
X(CaSiO3)=X(Ca)*
X(MgSiO3)=X(Mg)*
X(FeSiO3)=X(Fe2+)*, i.e. all Fe was calculated as Fe2+
X(Al2O3)=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:
CpxCaSiOX
3 (gabbroic Cpx) = 0.430, used for the experimental series in which
plagioclase was surrounded by gabbro powder, and
CpxCaSiOX
3 (diopside) = 0.484, used for the experimental series in which
plagioclase was surrounded by just Cpx and those surrounded by Cpx+SiO2.
Therefore, for a given T and XAn, the theoretical difference in ln CpxPlMgK / due to
different 2SiOa and Cpx
CaSiOX3 between the experimental series surrounded by gabbro
powder and the one surrounded by Cpx+SiO2 can be determined as
( ) ( )CpxCaSiOSiOtheo Xa
32lnln ∆+∆=∆ . At a temperature of 1150°C, this yields
( ) ( ) 71.012.059.0430.0ln()484.0ln(552.0ln()1ln( =+=−+−=∆ theo . Yet, the
experimentally determined difference between the average values of ln CpxPlMgK / 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.
To quantify the effect of T and XAn on ln CpxPlMgK / , 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
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
88
parameters A’, B and C were determined by weighted multiple regression (using
w =1/ 1σtotal( )2 as weighting factors). In a first round, only data from the
experimental series surrounded by Cpx+SiO2 and those surrounded by gabbro
powder were used, where the values for 2SiOa are known. The resulting parameters
(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 CpxCaSiOX
3) were used to quantify ln CpxPl
MgK / as a function of ln2SiOa (for
constant XAn=0.6 and T=1150°C). This gives 02.4ln0.1ln2
/ −⋅= SiOCpxPl
Mg aK , not
accounting for CpxCaSiOX
3 (grey dashed line in Fig. 2.5.5.3) and
93.3ln2.1ln2
/ −⋅= SiOCpxPl
Mg aK , accounting for CpxCaSiOX
3. Now
2SiOa of the experimental
series surrounded by just Cpx can be determined from this linear relationship, using
the average value of the experimentally determined values for ln CpxPlMgK / for
plagioclase surrounded by just Cpx. This yields 2SiOa =0.616 (ln
2SiOa =-0.48; Fig.
2.5.5.3), not accounting for CpxCaSiOX
3 and
2SiOa =0.620, accounting for CpxCaSiOX
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 2SiOa for
experiments surrounded by just Cpx is 0.616 and 0.620, respectively, dependent on
whether CpxCaSiOX
3 is accounted for or not). This yields A’=-76644±6780,
B=16913±1289 and C=13±4, not accounting for CpxCaSiOX
3 and A’=-71014±6780,
B=18514±1289 and C=15±4, accounting for CpxCaSiOX
3.
Summarizing, under the assumption that Mg dissolves into plagioclase as a
MgAl2Si2O8-component, ln CpxPlMgK / can be determined as a function of T, XAn and
2SiOa
(for constant 32OAla =1):
2ln
'ln /
SiOAnCpxPl
Mg aXRT
B
R
C
RT
AK +++= (Eq. 2.5.5.2)
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
89
Under the assumption that Mg dissolves into plagioclase as a CaMgSi3O8-
component, ln CpxPlMgK / is expected to additionally depend on ln Cpx
CaSiOX3:
CpxCaSiOSiOAn
CpxPlMg XaX
RT
B
R
C
RT
AK
32lnln
'ln / ++++= (Eq. 2.5.5.3)
Using the parameters A’, B and C, determined from multiple regression
(separately for Eq. 2.5.5.2 and 2.5.5.3) yields:
[ ] [ ]2
ln J/mol16913
6.11
K-9219ln /SiOAn
CpxPlMg aX
RTTK +++=
(Eq. 2.5.5.4)
and
[ ] [ ] CpxCaSiOSiOAn
CpxPlMg XaX
RTTK
32lnln
J/mol18514 8.1
1K-8542ln / ++++=
(Eq. 2.5.5.5)
Correlation coefficients R2 for the correlation between the experimental data
on ln CpxPlMgK / and the calculated data for ln CpxPl
MgK / 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).
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
90
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 lnCpxPl
MgK / on 1/T for the different experimental series (i.e. different
2SiOa ) at constant
XAn=0.6 and (b) shows the linear dependence of lnCpxPl
MgK / on XAn (for 1150°C and 1130°C).
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
91
2.5.6 Discussion of the experimental results for CpxPlMgK /
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.,
2010). None of these previous studies was designed to determine CpxPlMgK / , 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
above, CpxPlMgK / increases with increasing XAn in the plagioclase. Therefore, for better
comparison, the compositional dependence on CpxPlMgK / determined in this study was
used, to normalize the derived CpxPlMgK / of the previous studies to XAn=0.6. These
normalized results are compared to our data determined for XAn=0.6. In general, all
previous data show a general decrease of CpxPlMgK / with decreasing temperature as
was also observed for CpxPlMgK / determined by this study. The partition coefficient
CpxPlMgK / 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% SiO2 (e.g. Chalot-Prat et al.,
2010), which will lead to increased 2SiOa in these systems and hence (as shown
above) to increased Mg-concentrations in plagioclase. Data from this study from
experiments surrounded by Cpx+SiO2 fall more in a medium range of all data. Since
2SiOa is already 1 for this set of data, no further increase in 2SiOa can be responsible
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
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
92
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.
Fig. 2.5.6.1: Comparison of lnCpxPl
MgK / from previous studies with ln
CpxPlMgK /
determined in this
study, whereas all data is normalized to XAn=0.6 using the compositional dependence of plagioclase
composition on lnCpxPl
MgK / derived in this study. TS=this study
The isothermal data on the XAn-dependence of CpxPlMgK / 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
temperature-dependence of CpxPlMgK / determined in the present study suggests that
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
93
the partition coefficient of Mg between plagioclase and melt meltPlMgK / 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 CaMgSi3O8–component (Eq. 2.2.1.11) or as a
MgAl2Si2O8-component (2.2.1.17). Both equations predict linear dependences of
ln CpxPlMgK / on 1/T, XAn and ln
2SiOa , which is actually found in the experimental data
(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 CpxPlMgK / on ln Cpx
CaSiOX3
. This is not the case for Eq. 2.2.1.17, which
instead predicts linear dependence of ln CpxPlMgK / on ln
32OAla . The experimental setup
of this study does not allow accounting for effect of 32OAla , but it is possible to
account for the effect of different CpxCaSiOX
3. Fitting of the experimental data shows
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 CpxCaSiOX
3 is not accounted for; Fig. 2.5.5.4a
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+SiO2 at T=1150°C and XAn=0.6 (see section 2.5.5.) and may suggest that Mg
dissolves into plagioclase as a MgAl2Si2O8-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 CaMgSi3O8–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
(CaSiO3)- and (MgSiO3)-component in clinopyroxene ( CpxCaSiO3
lnγ and CpxMgSiO3
lnγ ) are
constant. This might not be true and there may be a temperature-dependence of
CpxCaSiO3
lnγ and CpxMgSiO3
lnγ , which compensates the effect of CpxCaSiOX
3. Based on the
experimental results of this study, it is therefore not possible to unambiguously
determine how Mg dissolves into plagioclase. The thermodynamic derivation of the
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
94
Mg-partitioning between plagioclase and clinopyroxene carried out in this study
suggests, however, a different behavior with 32OAla of the two possible sites for Mg in
plagioclase. Thus, investigation of CpxPlMgK / as a function of
32OAla might provide more
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
The experimental results for CpxPlMgK / 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 2SiOa (Eq. 2.5.5.3 and
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 CpxCaSiOX
3, this equation is rearranged to
determine the temperature T as a function of XAn, 2SiOa , Pl
MgC and CpxMgC :
[ ][ ] [ ]
2ln6.1ln
J/mol16913K9219
K
SiOCpxMg
PlMg
An
aC
C
XRT
−−
+−= (Eq. 2.5.7.1)
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 2SiOa =0.549 to 1.
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
95
2.5.8 Variations in PlMgD with T, XAn and
2SiOa
The experimental results on PlMgD are summarized in Table 2.5.3.1. Figure
2.5.8.1 shows that log PlMgD (for constant XAn=0.6) follows Arrhenian behaviour for all
experimental series, and that PlMgD increases for increasing
2SiOa .
Fig. 2.5.8.1: Experimental results on logPlMgD for constant XAn=0.6 plotted against 1/T showing
Arrhenian behaviour for all experimental series, andPlMgD is increased for higher
2SiOa . 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+SiO2).
The effect of plagioclase composition on PlMgD was determined in the same
three experimental series as outlined for the compositional dependence of CpxPlMgK /
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
96
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.
Fig. 2.5.8.2: Experimental results on PlMgD 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 2SiOa on the diffusion coefficient can be incorporated as:
( )m
SiOPlMg a
RT
EDD
2exp0 ⋅
−⋅= , (Eq. 2.5.8.1)
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 2SiOa on the diffusion coefficient, Eq. 2.5.8.1
was rearranged to a linear form:
)log(log2SiO
DD
PlMg am
T
BAD ⋅++= (Eq. 2.5.8.2)
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
97
and AD, BD and m were determined from weighted multiple regression (using
w =1/ 1σtotal( )2 as weighting factors) of all data under the assumption that
2SiOa =0.616 for experiments in which plagioclase was surrounded by just Cpx as
determined from the results on CpxPlMgK / . This yields AD=-2.66±1.59, BD=-18550±2290
and m=2.6±0.3. Therefore, PlMgD as a function of T and
2SiOa can be determined as:
[ ] ( ) [ ] ( ) [ ] ( ) ( )3.06.2232
2
kJ/mol44355exp/sm101.82.2/sm
±− ⋅
±−⋅⋅±= SiOPlMg a
RTD
(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:
[ ] [ ] [ ] ( ) 6.2242
2
kJ/mol321exp/sm1025.1/sm SiO
PlMg a
RTD ⋅
−⋅⋅= −
(Eq. 2.5.8.4)
Figure 2.5.8.3 shows a comparison of the experimentally determined log PlMgD
and the fits using Eq. 2.5.8.3 (fit 1) and Eq. 2.5.8.4 (fit 2).
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
98
Fig. 2.5.8.3: Average values of experimentally determined logPlMgD 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+SiO2).
2.5.9 Discussion of the experimental results for PlMgD
The diffusion coefficient PlMgD 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.
2.5.9.1). A significant dependence of PlMgD 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
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
99
(1998) for a plagioclase composition of XAn=0.95, when extrapolated to the same
temperature (Fig. 2.5.8.2 and 2.5.9.1), supporting the lack of a dependence of PlMgD 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 PlMgD as a function of T and
2SiOa .
The difference between the data of Borinski et al. (in prep.) and the
determined PlMgD of this study may possibly be explained by a difference in
2SiOa .
This study implies a strong dependence of PlMgD on
2SiOa , which was not accounted
for in the study of Borinski et al. (in prep.). However, Eq. 2.5.8.2 can be rearranged
to determine log2SiOa as a function of T and Pl
MgD :
mT
BAD
a
DD
PlMg
SiO
−−=
log)log(
2 (Eq. 2.5.9.1)
Combining Eq. 2.5.9.1 with the determined parameters AD, BD and m, and the
value for PlMgD of Borinski et al. (in prep) for T=1200°C to get an estimate for the
2SiOa -conditions in the experiments of Borkinski et al. (in prep.) yields 2SiOa =0.34.
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 2SiOa .
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
100
Fig. 2.5.9.1: Plot of logPlMgD vs. inverse temperature to compare the results of this study with the
determined PlMgD 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 SiO2. Additionally, plagioclase from these experiments show a distinct
increase of a calculated [ ]Si4O8-endmember towards the rim of the plagioclase.
Therefore, it is concluded, that an increased 2SiOa enhances the formation of a
[ ]Si4O8-type vacancy in plagioclase, which then enhances diffusion.
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
101
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
[ ]Si4O8-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+SiO2. Such a [ ]Si4O8-type
vacancy represents the lack of an atom on the metal site in plagioclase, which is
charge-balanced by the substitution of an additional Si4+-atom for an Al3+-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 [ ]Si4O8-type vacancy), the
diffusion coefficient of element i will be a function of the concentration of that
vacancy, XV, and can be written as:
2lwXfD VVii ⋅⋅⋅= , (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:
∆+∆−=
RT
VPHww mm
VV
000 exp (Eq. 2.5.9.3)
with 0mH∆ and 0
mV∆ 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, a1, a2, …, an-1) (Eq.2.5.9.4)
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
102
The observed dependence of PlMgD on
2SiOa may now be discussed for a
possible formation mechanism of a [ ]Si4O8-type vacancy, using the Kröger-Vink
notation (Kröger & Vink, 1965). In this notation, a [ ]Si4O8-type vacancy has to be
written differently for the albite- and anorthite component in plagioclase:
•+ )('
AlTM SiV in albite and •+ )('' 2 AlTM SiV in anorthite (see legend for explanation of
symbols). Thus, the two different end-members need to be discussed separately:
Ab: •++=++ )('
8324 AlTMxM
xT SiVONaAlSiNaAlSiO (Eq. 2.5.9.5a)
An: •++=++ )(''
8222 224 AlTMxM
xT SiVOSiCaAlCaAlSiO (Eq. 2.5.9.5b)
where
xTAl Al-atom on a tetrahedral site, charge balanced by its surrounding
xMNa Na-atom on a metal site, charged balanced by its surrounding
xMCa Ca-atom on a metal site, charged balanced by its surrounding
'MV vacancy on the metal site in albite (i.e. 1 negative charge)
''MV vacancy on the metal site in anorthite (i.e. 2 negative charges)
•)( AlTSi additional Si4+ on a tetrahedral site, substituting for an Al3+-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:
Ab: ( )
( ) xM
xT
AlTM
xM
xT
AlTM
xM
xT
AlTM
NaAl
PlAbSiV
NaAl
PlAbSiV
SiO
NaAlSiO
PlONaAlSiSiV
eq
XX
XXX
a
aaa
aaa
RT
GK
γγ
γγγ ••
•
⋅⋅=
=
∆−=
)('
)('
2
2
83)('
4
4
0
1
exp
(Eq. 2.5.9.6a)
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
103
An:
( )( ) ( )
( )( )
( )( )
( ) xM
xT
AlTM
xM
xT
AlTM
xM
xT
AlTM
CaAl
PlAnSiV
CaAl
PlAnSiV
SiO
CaAlSiO
PlOSiCaAlSiV
eq
XX
XXX
a
aaa
aaa
RT
GK
γγ
γγγ2
2
2
2
4
24
20
)(''
)(''
2
2
822)(''
1
exp
••
•
⋅⋅=
=
∆−=
(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 γC . Additionally xMNa
X and xMCa
X can be assumed to be 1, in
albite and anorthite respectively, and xTAl
X can be assumed to be ~0.25 in albite and
~0.5 in anorthite. which leads to
Ab: ( ) a
PlAbSiV
SiO
eq CXXX
aRT
GK AlTM
γ25.0
1exp )(
'
2
4
0 •
⋅=
∆−=
(Eq. 2.5.9.7a)
An: ( )( )
( ) b
PlAnSiV
SiO
eq CXXX
aRT
GK AlTM
γ2
2
4
0
5.0
1exp )(
''
2
•
⋅=
∆−= .
(Eq. 2.5.9.7b)
To maintain charge balance and create a neutral []Si4O8-component, the
molar fractions of vacancies on the metal site and on the tetrahedral site have to be
related as follows:
Ab: 'MV
X = •)( AlTSi
X
An: ''MV
X =2 •)( AlTSi
X
which gives:
Ab: ( )
( ) a
SiO
PlAbV
eq Ca
XX
RT
GK M
γ4
20
2
'
25.0exp =
∆−= (Eq. 2.5.9.8a)
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
104
An: ( )
( ) b
SiO
PlAnV
eq Ca
XX
RT
GK M
γ4
30
2
''
25.0
25.0exp =
∆−= (Eq. 2.5.9.8b)
Solving for the concentration of vacancies on the metal site XV yields:
Ab: ( )
( ) ( ) 5.05.0
20 5.0
2exp 2
'
aPlAb
SiO
V CX
a
RT
GX
M
γ
∆−= (Eq. 2.5.9.9a)
An: ( )( ) ( ) 3/13/1
3/40 1
3exp 2
''
bPlAn
SiO
V CX
a
RT
GX
M
γ
∆−= (Eq. 2.5.9.9b)
Using 0000 VPSTHG ∆+∆−∆=∆ and defining the quantities of formation
enthalpy, formation entropy and formation volume as ∆H f = ∆H 0 /n , ∆S f = ∆S0 /n
and ∆V f = ∆V 0 /n , where n=2 for albite and n=3 for anorthite gives:
Ab: ( )
( ) ( ) 5.05.0
25.0
expexp 2'
aPlAb
SiOfff
V CX
a
RT
VPH
R
SX
M
γ
∆+∆−
=
(Eq. 2.5.9.10a)
An: ( )( ) ( ) 3/13/1
3/41
expexp 2''
bPlAn
SiOfff
V CX
a
RT
VPH
R
SX
M
γ
∆+∆
∆=
(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:
Ab: ( ) ( ) ( )
( ) 5.0
2
0
1exp 2
PlAn
SiOmfmfAb
PlMg
X
a
RT
VVPHHDD
−
∆+∆+∆+∆−=
(Eq. 2.5.9.11a)
An: ( ) ( ) ( )
( ) 3/1
3/4
0 2expPlAn
SiOmfmfAn
PlMg
X
a
RT
VVPHHDD
∆+∆+∆+∆−=
(Eq. 2.5.9.11b)
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
105
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:
Ab: ( )
( ) 5.0
2
0
1exp 2
PlAn
SiO
AbPlMg
X
a
RT
EDD
−
−= (Eq. 2.5.9.12a)
An: ( )( ) 3/1
3/4
0 2expPlAn
SiOAn
PlMg
X
a
RT
EDD
−= (Eq. 2.5.9.12a)
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 PlMgD on
2SiOa has to be a positive number between
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 { }•+ )('
AlTM SiV in albite and { }•+ )('' 2 AlTM SiV in anorthite gives a factor of m=4,
indicating that some of the defects may be associated with each other. Additionally,
the derived dependence of PlMgD 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 2SiOa ~0.55 and 1 at
constant 32OAla =1. At temperatures below 1100°C, an exchange of Mg between
plagioclase and different Cpx-bearing matrixes could not be detected. The
calculation of possible Mg-bearing plagioclase end-members for the experimental
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
106
data suggests preferred site occupancy of Mg in the tetrahedral site as a CaMgSi3O8-
component.
The partition coefficient of Mg between plagioclase and clinopyroxene
CpxPlMgK / and the diffusion coefficient of Mg in plagioclase Pl
MgD as a function of T, XAn
and 2SiOa were determined in a temperature range of T=1100 to 1200°C, a
compositional range of XAn=0.5 to 0.8 and at 2SiOa ~0.55 and 1 (at constant
32OAla =1)
with the following results:
(1) CpxPlMgK / is strongly temperature-sensitive and decreases with decreasing
temperature.
(2) CpxPlMgK / increases with increasing XAn in plagioclase.
(3) CpxPlMgK / increases with increasing
2SiOa .
(4) PlMgD 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°.
(5) A significant dependence of PlMgD on XAn in plagioclase is not observed.
(6) PlMgD dependents on
2SiOa and increases by approximately one order of
magnitude from 2SiOa =0.55-1. This observation is consistent with an
observed increase in a [ ]Si4O8-component in plagioclase for increased 2SiOa ,
leading to the conclusion that higher 2SiOa in the systems leads to the
formation of [ ]Si4O8-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
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
107
experimental data also allow for a quantification of the role of plagioclase XAn
content and silica activity in controlling PlMgD .
2. Experimental Determination of the Temperature Dependence of Mg Exchange Between Pl and Cpx
108
2.7 References
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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
113
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
114
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
115
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’
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
116
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).
hydrothermalcirculation
crystalmush
melt / mushtransport
30 MW/km
energy loss in Megawattsper km of ridge axis
solidifiedpluton
magmasheeteddikes
lava
AMCaxial
magmachamber
cooling rate
de
pth
(a) (b)
~30 MW/km
~40MW/km
0 2 4
km
~15 MW/km
~55MW/km
0 2 4
km
(b)(a)
AMCaxial
magmachamber
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
117
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.
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
118
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
119
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
120
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:
∂∂
+∂
∂∂
∂+
∂∂
∂∂
−
∂∂
∂∂
+∂
∂=
∂∂
2
2
2
2
x
XCD
x
X
x
DC
x
X
x
CD
RT
A
x
D
x
C
x
CD
t
CAn
MgMgAnMg
MgAnMg
MgMgMgMg
MgMg
(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).
( ) ( ) ( )( )[ ]
( )( ) ( ) ( ) ( )
( )
+−+
−−+−−
∆∆−
−−++−∆∆+=
−+
−+−+−+−+
−+−+−++
jiAnjiAnjiAnjiji
jiAnjiAnjijijijiAnjiAnjijiji
jijijijijijijijijiji
XXXCD
XXDDCXXCCD
x
t
RT
A
DDCCCCCDx
tCC
,1,,1,,
,1,1,1,1,,1,1,1,1,
2
,1,1,1,1,1,,1,2,1,
24
24
(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.
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
121
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).
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
122
The reported Arrhenian relationship was defined as follows: RTEPlMg eDD /
0−= , with
D0=7.1±0.1 x 10-8 m2/s and E=254±43 kJ/mol in b-direction, and
D0=1.2±0.1 x 10-6 m2/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
from the lower oceanic crust). The diffusion coefficient PlMgD was determined as a
function of temperature, XAn in plagioclase (in the range of XAn=0.5 to 0.67) and silica
activity 2SiOa of the system (in the range of
2SiOa =0.6 to 1). One result of this study
(Chapter 2) was, that no difference in PlMgD was observed along different
orientations within the plagioclase crystal. Furthermore, a significant compositional
dependence of PlMgD on XAn in plagioclase was not found. Instead, it was observed
that PlMgD 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.),
where PlMgD 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)
report no significant dependence of PlMgD on XAn and activation energies of
~336 kJ/mol.
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
123
Since the experimental results of the present study (Chapter 2) show a
dependence of PlMgD on
2SiOa , a diffusion coefficient of the form
DMgPl = D0⋅ exp
−E
RT
⋅ aSiO2( )m
(Eq. 3.4.1.1)
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, 2SiOa is the silica activity of the system and
m is a factor related to the dependence of the diffusion coefficient on 2SiOa (see
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
of Borinski et al. (in prep.). This equation determines PlMgD as a function of T and
2SiOa (for a fixed alumina activity of 32OAla =1):
[ ] [ ] ( ) [ ] ( ) 6.2242
2
kJ/mol35321exp/sm1025.1/sm SiO
PlMg a
RTD ⋅
±−⋅⋅= −
(Eq. 3.4.1.2)
One feature of Eq. 3.4.1.2 is, that PlMgD is independent of XAn, and hence is
constant for all grid points in the model at given time. However, PlMgD 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, 2SiOa in those rocks is
buffered by the reaction Mg2SiO4 + SiO2 = 2MgSiO3 and can be determined according
to the relationship proposed by Carmichael (1970):
RT
Ga r
SiO 303.2log
2
∆= (Eq. 3.4.1.3)
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
124
where rG∆ 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 2SiOa is a function of temperature.
The relationship is not simply described by a linear function with 1/T, because rG∆
itself is a function of temperature. To account for this dependence, 2SiOa was
calculated for different temperatures using the data set of Ghiorso and Sack (1995)
to determine rG∆ . The resulting data are fitted by a 2nd-order polynomial:
0.618707-101.5157010-4.86904 -32-7
2TTaSiO ⋅+⋅= (Eq. 3.4.1.4)
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 2SiOa for
all samples in this study.
3.4.2 Initial profile determined from CpxPlMgK /
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
clinopyroxene ( CpxPlMgK / ). The present study (Chapter 2) investigated the partitioning
of Mg between plagioclase and clinopyroxene in the compositional range of the
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
125
rocks of the lower oceanic crust and determined ln CpxPlMgK / as a function of T, XAn and
2SiOa (see Chapter 2):
[ ] [ ]2
ln J/mol16913
6.11
K-9219ln /SiOAn
CpxPlMg aX
RTTK +++= (Eq. 3.4.2.1)
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
grain size) within a few years (e.g. ~50 to 60 years using PlMgD || b from LaTourette
and Wasserburg, 1998, and PlMgD from Chapter 2 for
2SiOa buffered by Ol+Opx).
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:
[ ] [ ]
+++=2
ln J/mol16913
6.11
K9219-exp SiOAnCpxMg
PlMg aX
RTTCC
(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,
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
126
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.
CpxMgC : 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.
2SiOa : The silica activity is constraint by the coexistence of Ol+Opx for all
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
127
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.
3.4.3 Boundary conditions determined from CpxPlMgK /
During cooling, CpxPlMgK / 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
to CpxPlMgK / . 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
XAn, CpxMgC and
2SiOa as outlined above) is used to calculate the Mg-concentration of
the outermost grid points jiC ,1= and jiC ,100= of the model at any time for the given
temperature.
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
128
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/dt=0.001 °C/year (Fig. 3.5.1b1-b3) and dT/dt=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
Fig. 3.5.2b1). During cooling, CpxPlMgK / 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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
129
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
core than at the rims (green and blue line in Fig. 3.5.1b). Below 800°C, PlMgD 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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
130
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).
rim rimcore
0.7
0.6
0.5
0.4
(a2)
0.20
0.15
0.10
0.05
0.20
0.15
0.10
0.05
(b2)
(c2)
T0 = 1200°Cdiffusion profile “equilibrium” profile
rim rimcore
0.7
0.6
0.5
0.4
XA
n
(a1)
0.20
0.15
0.10
0.05
0.20
0.15
0.10
0.05
MgO
[w
t%] (b1)
(c1)
0.20
0.15
0.10
0.05
0.20
0.15
0.10
0.05
(b3)
(c3)
MgO
[w
t%]
0 500 1000 1500
Distance [µm]
0 500 1000 1500
Distance [µm]
rim rimcore
0.7
0.6
0.5
0.4
(a3)
0 50 100 150
Distance [µm]
T1 = 1100°C T2 = 1000°C T3 = 800°C T4 = 600°C
Plagioclase P1 Plagioclase P2 Plagioclase P3
cooling rate0.001°C/y
cooling rate0.1°C/y
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.
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
131
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
parameters that enter the calculation (e.g. parameters used to determine PlMgD , and
CpxPlMgK / ), (iii) uncertainties, which result from modelling a one-dimensional
concentration profile, while in fact, diffusion results from fluxes in three dimensions,
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
132
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).
(ii) The diffusion coefficient PlMgD and the partition coefficient CpxPl
MgK / 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
to determine PlMgD and CpxPl
MgK / 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 D0 of the diffusion coefficient) and can not vary independently.
Overall, these uncertainties do not affect relative relations in cooling rate as a
function of depth, because the same parameters for the calculation of PlMgD and
CpxPlMgK / 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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
133
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).
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
134
(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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
135
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
136
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
~ 4101 −⋅ °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
Tstop is related to the partition coefficient CpxPlMgK / 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 2SiOa of the system (Eq. 3.4.2.1).
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.
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
137
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
ation
Mg
O [w
t%]
rim rimcore
P1 Sc1
Xan
0.4
0.5
0.6
0.7
500 1000 1500
dT/dt=3.6 10 °C/year-1
(a) (b)
rim rimcore
Xan
0.4
0.5
0.6
0.7
500 1000 1500
dT/dt=3.6 10 °C/year-1
P1 Sc1
rim rimcore
Xan0.4
0.5
0.6
0.7
200 400 600
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
dT/dt=1.1 10 °C/year-3
(c) (d)P2 Sc1
rim rimcore
Xan0.4
0.5
0.6
0.7
200 400 600
Distance [µm]
dT/dt=1.1 10 °C/year-3
P2 Sc1
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
138
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).
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
139
rim rimcore
Xan
0.4
0.5
0.6
0.7
500 1000 1500
dT/dt=3.7 10 °C/year-1
P1 Sc2
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
(a)
rim rimcore
P1 Sc1
Xan
0.4
0.5
0.6
0.7
500 1000 1500
dT/dt=3.6 10 °C/year-1
rim rimcore
Xan0.4
0.5
0.6
0.7
200 400 600
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
Xan0.4
0.5
0.6
0.7
100 200 300
dT/dt=1.1 10 °C/year-3
dT/dt=1.2 10 °C/year-3
(c) (d)P2 Sc1 P2 Sc2
(b)
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
140
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.
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
Xan
0.4
0.5
0.6
0.7
rim rimcore
Xan
0.4
0.5
0.6
0.7
(b) (c)
500 1000 1500 500 1000 1500
rim rimcore
Xan0.4
0.5
0.6
0.7
200 400 600
dT/dt=5.0 10 °C/year-1
dT/dt=2.0 10 °C/year-1
dT/dt=1.1 10 °C/year-3
rim rimcore
Xan0.4
0.5
0.6
0.7
200 400 600
Distance [µm]
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
Xan0.4
0.5
0.6
0.7
200 400 600
Distance [µm]
dT/dt=4.0 10 °C/year-3
dT/dt=1.0 10 °C/year-4
Distance [µm]
(d) (e) (f)
P1 Sc1 P1 Sc1
P2 Sc1 P2 Sc1 P2 Sc1
rim rimcore
P1 Sc1
Xan
0.4
0.5
0.6
0.7
500 1000 1500
dT/dt=3.6 10 °C/year-1
(a)
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
141
(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.
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
142
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
143
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
144
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.
Location Samples analyzed
Individual plagioclase crystals analyzed
Concentration profiles 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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
145
concentrations of Mg, than longer profiles from the same samples (Fig. A4 in
Appendix IV).
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
2218-1132 C3 Pl3 Sc1
Xan0.4
0.5
0.6
0.7
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
200 400 600
Distance [µm]
rim rimcore
Xan0.4
0.5
0.6
0.73369-1349 C1 Pl1 Sc1
200 400 600
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
2212-1358 C4 Pl4 Sc2
Xan
0.4
0.5
0.6
0.7
200 400 600
0
17
rim rimcore
2212-1338 C3 Pl3 Sc1
Xan
0.4
0.5
0.6
0.7
400 800 1200 1600
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
82
rim rimcore
Xan
0.4
0.5
0.6
0.73369-1355 C1 Pl1 Sc2
200 400 600 800
90
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
Xan
0.4
0.5
0.6
0.73369-1250 C2 Pl2 Sc1
50 100 150
144
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
Xan
0.4
0.5
0.6
0.73369-1221 C1 Pl1 Sc1
50 100 150
208
200
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
211
rim rimcore
3369-1110 C1Pl1 Sc2
Xan0.4
0.5
0.6
0.7
400 800 1200
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
282
rim rimcore
3369-1050 C3Pl3 Sc1
Xan0.4
0.5
0.6
0.7
200 400 600 800
282
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
Xan0.4
0.5
0.6
0.73369-1042 C1Pl1 Sc2
400 800 1200 1600
380
rim rimcore
2213-1110 C3 Pl3 Sc1
Xan0.4
0.5
0.6
0.7
100 200 400300
470
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
2218-1111 C2 Pl2 Sc2
Xan0.4
0.5
0.6
0.7
100 200 400300 500
520
0.02
0.04
0.06
0.08
0.10
0.12
0.14C
on
ce
ntr
atio
n M
gO
[w
t%]
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
Distance [µm] Distance [µm]
Depth
[m
bsd]
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
146
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).
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
147
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
148
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
149
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.
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
150
0.02
0.04
0.06
0.08
0.10
0.12
0.14C
on
ce
ntr
atio
n M
gO
[w
t%]
rim rimcore
022205-0248 C2Pl2 Sc2
Xan
0.6
0.8
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
022005-0230 C1 Pl1 Sc1
Xan
0.6
0.8
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
022005-0506 C2Pl2 Sc1
Xan
0.6
0.8
200 400 600 800
200 400 600
41
rim rimcore
022205-0259 C2 Pl2 Sc2
Xan
0.6
0.8
200 400 600
0.02
0.04
0.06
0.08
0.10
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0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
45
72
0.02
0.04
0.06
0.08
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Co
nce
ntr
atio
n M
gO
[w
t%]
355
rim rimcore
022005-1052 C3 Pl3 Sc2
Xan
0.6
0.8
250 500125 375
386
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
022005-0910 C2 Pl2 Sc1
Xan
0.6
0.8
250 500125 375
569
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
022005-0534 C2 Pl2 Sc2
Xan
0.6
0.8
400 800200 600
662
780
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
022005-0155 C2 Pl2 Sc1
Xan
0.6
0.8
200 400 600 800
836
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
022005-0056 C3 Pl3 Sc1
Xan
0.6
0.8
Distance [µm]
100 200 300 400
Distance [µm]Distance [µm]
100 200 300
De
pth
[m
bsd
]
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
151
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
152
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
153
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).
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim
rim
core
216 R0115-20 C3 Pl3 Sc1
Xan
0.4
0.5
0.6
0.7
12.1
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
Distance [µm]
12.4
100 200 300 400
rim
rim
core
216 R0149-57 C1 Pl1 Sc1
Xan
0.4
0.5
0.6
0.7
200 400 600
(a) (b)
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
154
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
155
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.
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
156
(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.
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
157
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.
Co
olin
g r
ate
[°C
/ye
ar]
Temperature [°C]
TstopTstart
0.5
1200 80090010001100
Tc
700 600
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.
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
158
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).
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
159
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
160
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.
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
161
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.
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
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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.
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
163
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 Mg-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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
164
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
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
165
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).
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
166
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.
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
167
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.
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
168
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.
3. Cooling Rates with Depth in the Lower Oceanic Crust Derived by Diffusion Modelling of Mg in Pl
169
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4. Conclusions and Future Work
175
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.
4. Conclusions and Future Work
176
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
plagioclase ( PlMgD ) and the partition coefficient of Mg between plagioclase and
clinopyroxene ( CpxPlMgK / ) in the compositional range of the lower oceanic crust. The
diffusion coefficient PlMgD and the partition coefficient CpxPl
MgK / were determined as a
function of temperature (T), anorthite-content in plagioclase (XAn) and the silica
activity of the system (2SiOa ). This was accomplished in a set of experiments at
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 (2SiOa ~0.55 to 1, the exact values depend on the given
temperature of an experiment). All experiments were carried out at a constant
alumina activity (32OAla ) of 1. Reliable results for Pl
MgD and CpxPlMgK / 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, CpxPlMgK / was found to (i) decrease during cooling, (ii) increase with
increasing XAn in plagioclase and (iii) increase with increasing 2SiOa . This is
quantified in Eq. 2.5.5.4 of Chapter 2:
[ ] [ ]2
ln J/mol16913
6.11
K-9219ln /SiOAn
CpxPlMg aX
RTTK +++=
(Eq. 2.5.5.4)
The diffusion coefficient PlMgD was found to (i) decrease with temperature in
an Arrhenian relationship and (ii) to increase with increasing 2SiOa . No significant
dependence of PlMgD on XAn in plagioclase was observed. The experimental data
obtained from this study are in good agreement with the data from the study of
4. Conclusions and Future Work
177
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 2SiOa . Therefore, to quantify Pl
MgD as a function of T and 2SiOa , the
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:
[ ] [ ] [ ] ( ) 6.2242
2
/320924exp/1025.1/ SiO
PlMg a
RT
molJsmsmD ⋅
−⋅⋅= −
(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
Chapter 3), but uses the newly calibrated data for PlMgD (Eq. 2.5.8.4). The initial and
boundary conditions of the new model are calculated from the partition coefficient
CpxPlMgK / (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.
4. Conclusions and Future Work
178
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 32OAla , whereas the second one (reaction 2 in Chapter 2) will
be dependent on 32OAla . Additional experiments to investigate the exchange of Mg
between plagioclase and clinopyroxene as a function of 32OAla may help to
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
4. Conclusions and Future Work
179
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
(except KF044), therefore, the effect of pressure on CpxPlMgK / and Pl
MgD 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. In 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.
4. Conclusions and Future Work
180
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
4. Conclusions and Future Work
181
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.
4. Conclusions and Future Work
182
T1 T2 T3 T4
“fast”diffusingelement
“slower”diffusingelement
“very slow”diffusingelement
T1 T2 T3 T4
T1 T2 T3 T4
cooling
(a)
(b)
(c)
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
4. Conclusions and Future Work
183
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.
4. Conclusions and Future Work
184
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.
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
Sample Depth Pl crystal Profile 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
Sample Depth Pl crystal Profile 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 Pl crystal Profile
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 Depth Pl crystal Profile
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 TiO2 40nA, 15kV PET 20/20/0 Mn spessartine 40nA, 15kV LIF 20/20/0 Cr Cr2O3 40nA, 15kV LIF 20/20/0
Counting times given as peak/background/background
Appendix IV
Appendix IV – Plots of all fitted profiles 14
rim rimcore
Xan
0.4
0.5
0.6
0.73369-1355 C1 Pl1 Sc1
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
600 1200 1800 2400
rim rimcore
Xan0.4
0.5
0.6
0.73369-1349 C1 Pl1 Sc1
200 400 600
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
2212-1358 C4 Pl4 Sc2
Xan
0.4
0.5
0.6
0.7
200 400 600
rim rimcore
2212-1338 C1 Pl1 Sc1
Xan
0.4
0.5
0.6
0.7
100 200 300 400
0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
17
rim rimcore
2212-1338 C3 Pl3 Sc1
Xan
0.4
0.5
0.6
0.7
400 800 1200 1600
rim rimcore
2212-1338 C3 Pl3 Sc2
Xan
0.4
0.5
0.6
0.7
400 800 1200
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
82
rim rimcore
Xan
0.4
0.5
0.6
0.73369-1355 C1 Pl1 Sc2
200 400 600 800
rim rimcore
Xan
0.4
0.5
0.6
0.73369-1355 C3 Pl3 Sc1
100 200 300 400 500
rim rimcore
Xan
0.4
0.5
0.6
0.73369-1355 C3 Pl3 Sc2
100 200 300
90
rim rimcore
Xan0.4
0.5
0.6
0.73369-1349 C2 Pl3 Sc1
200 400 600 800
rim rimcore
Xan0.4
0.5
0.6
0.73369-1349 C2 Pl3 Sc2
100 200 300
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
Xan0.4
0.5
0.6
0.73374-1031 C1 Pl1 Sc1
200 400 600
127
rim rimcore
Xan0.4
0.5
0.6
0.73374-1031 C1 Pl1 Sc2
50 100 150 200 250
rim rimcore
Xan0.4
0.5
0.6
0.73374-1031 C1 Pl1 Sc2
200 400 600 800
rim rimcore
Xan0.4
0.5
0.6
0.73369-1349 C3 Pl4 Sc1
400 800 1200 1600
rim rimcore
Xan0.4
0.5
0.6
0.73369-1349 C3 Pl4 Sc2
400 800 1200 1600
Depth
[m
bsd]
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
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Concentr
ation M
gO
[w
t%]
rim rimcore
Xan
0.4
0.5
0.6
0.73369-1250 C2 Pl2 Sc1
144
rim rimcore
Xan
0.4
0.5
0.6
0.73369-1250 C2 Pl2 Sc2
50 100 150 50 100 150 200 250
0.14 0.73369-1221 C1 Pl1 Sc1
Concentr
ation M
gO
[w
t%]
0.60.12 Xan
0.5208 0.10 0.4
0.08
0.06
0.04
0.02
rim rimcore
50 100 150 200
3369-1110 C1Pl1 Sc1 0.70.14 3369-1110 C1Pl1 Sc2 0.7
0.6
Concentr
ation M
gO
[w
t%]
0.6
Xan0.50.12
211Xan0.5
0.40.10 0.4
0.08
0.06
0.04
0.02
rim rimcore rim rimcore
100 200 300 400 800 1200400
3369-1050 C2Pl2 Sc2 0.70.14
Concentr
ation M
gO
[w
t%] 3369-1050 C3Pl3 Sc1 0.7 3369-1050 C3Pl3 Sc2 0.73369-1050 C1Pl1 Sc1 0.7 3369-1050 C2Pl2 Sc1 0.7
0.60.12
0.6 0.60.6 0.6
Xan0.5
282Xan0.5 Xan0.5Xan0.5 Xan0.5
0.40.10 0.4 0.40.4 0.4
0.08
0.06
0.04
0.02
rim rimcore rim rimcore rim rimcorerim rimcore rim rimcore
200 400 600 200 400 600 800 100 200 300 400500 1000 1500400 800 1200
0.73369-1042 C1Pl1 Sc10.14
Concentr
ation M
gO
[w
t%] 0.73369-1042 C1Pl1 Sc2
0.60.12
0.6
Xan0.5 0.5
0.4
282 0.10Xan0.4
0.08
0.06
0.04
0.02
rim rim rim rimcore core
400 800 1200 400 800 1200 1600
Depth
[m
bsd]
Distance [µm] Distance [µm] Fig. A4.1 continued.
Appendix IV – Plots of all fitted profiles 16
0.14 2213-1110 C2 Pl2 Sc2 0.7 2213-1110 C3 Pl3 Sc1 0.7 2213-1110 C4 Pl4 Sc2 0.7 2213-1110 C5 Pl6 Sc1 0.7 2213-1110 C5 Pl6 Sc2 0.7
Concentr
ation M
gO
[w
t%]
0.6 0.6 0.6 0.6 0.60.12
Xan0.5 Xan0.5 Xan0.5 Xan0.5 Xan0.5
0.10 0.4 0.4 0.4 0.4 0.4
380 0.08
0.06
0.04
0.02
rim rimcore rim rimcore rim rimcore rim rimcore rim rimcore
200 400 600 100 200 400300 100 200 400300 500 200 400 600 100 200 400300 500
2218-1111 C1 Pl1 Sc10.14 2218-1111 C1 Pl1 Sc2 2218-1111 C2 Pl2 Sc20.7
Concentr
ation M
gO
[w
t%] 0.7 0.7
Xan
0.60.12
Xan
0.6
Xan
0.6
0.4
0.5
470 0.4
0.5
0.4
0.5
0.10
0.08
0.06
0.04
0.02
rim rimcore rim rimcore rim rimcore
100 200 300 200 400 600 100 200 400300 500
2218-1132 C3 Pl3 Sc1 0.70.14
Concentr
ation M
gO
[w
t%] 2218-1132 C3 Pl3 Sc2 0.7 2218-1132 C4 Pl5 Sc2 0.7
0.60.12
0.6 0.6
Xan0.5 Xan0.5 Xan0.5
0.40.10 0.4 0.4
520 0.08
0.06
0.04
0.02
rim rimcore rim rimcore rim rimcore
200 400 600 100 200 300 200 400 600
Distance [µm] Distance [µm] Distance [µm]
Depth
[m
bsd]
Fig. A4.1 continued.
Appendix IV – Plots of all fitted profiles 17
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Concentr
ation M
gO
[w
t%]
rim rimcore
022205-0259 C1 Pl1 Sc1
rim rimcore
022205-0248 C2Pl2 Sc2
Xan
Xan
0.6
0.8
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Concentr
ation M
gO
[w
t%]
rim rimcore
022005-1052 C2 Pl2 Sc1
Xan
0.6
0.8
rim rimcore
022005-0910 C1 Pl1 Sc2
Xan
0.6
0.8
rim rimcore
022005-0230 C1 Pl1 Sc1
Xan
0.6
0.8
100 200 300
200 400 600 800
100 200 300
250 500 750
50 100 150 200
Distance [µm]
41
0.6
0.8
rim rimcore
022205-0259 C1 Pl1 Sc2
Xan
100 200 300
0.6
0.8
400
rim rimcore
022205-0259 C2 Pl2 Sc1
Xan
100 200 300
0.6
0.8
400
rim rimcore
022205-0259 C2 Pl2 Sc2
Xan
0.6
0.8
200 400 600
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Concentr
ation M
gO
[w
t%]
45
rim rimcore
022205-0248 C4Pl4 Sc1
Xan
0.6
0.8
50 100 150 200
72
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Concentr
ation M
gO
[w
t%]
355
rim rimcore
022005-1052 C2 Pl2 Sc2
Xan
0.6
0.8
100 200 300 400
rim rimcore
022005-1052 C3 Pl3 Sc1
Xan
0.6
0.8
250 500 750
rim rimcore
022005-1052 C3 Pl3 Sc2
Xan
0.6
0.8
250 500125 375
386
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Concentr
ation M
gO
[w
t%]
rim rimcore
022005-0910 C2 Pl2 Sc1
Xan
0.6
0.8
250 500125 375
rim rimcore
022005-0910 C4 Pl4 Sc2
Xan
0.6
0.8
200 400100 300
Distance [µm] Distance [µm]
Depth
[m
bsd]
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
rim rimcore
022005-0534 C2 Pl2 Sc1
Xan
0.6
0.8
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
022005-0506 C2Pl2 Sc1
Xan
0.6
0.8
rim rimcore
022005-0155 C1 Pl1 Sc1
Xan
0.6
0.8
rim rimcore
022005-0056 C2 Pl2 Sc1
Xan
0.6
0.8
200 400 600
100 200 300
500 1000 1500
Distance [µm]
569
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
250 500125 375
rim rimcore
022005-0534 C2 Pl2 Sc2
Xan
0.6
0.8
400 800200 600
662
rim rimcore
022005-0506 C2Pl2 Sc2
Xan
0.6
0.8
250 500 750 1000
780
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
022005-0155 C1 Pl1 Sc2
Xan
0.6
0.8
200 400 600 800
rim rimcore
022005-0155 C2 Pl2 Sc1
Xan
0.6
0.8
200 400 600 800
836
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Co
nce
ntr
atio
n M
gO
[w
t%]
rim rimcore
022005-0056 C2 Pl2 Sc2
Xan
0.6
0.8
Distance [µm]
200 400 600 800
rim rimcore
022005-0056 C3 Pl3 Sc1
Xan
0.6
0.8
Distance [µm]
100 200 300 400
rim rimcore
022005-0056 C3 Pl3 Sc2
Xan
0.6
0.8
Distance [µm]
200 400 600 800
rim rimcore
022005-0056 C5 Pl5 Sc1
Xan
0.6
0.8
Distance [µm]
200 400 600 800
De
pth
[m
bsd
]
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
Electronic Appendix
Natural Sample SuitesExperiments Modelling
KF0XX
Hess
Deep
Pito
Deep312
1256D
147
894G
Hess
Deep
Pito
Deep312
1256D
Sample X Sample X
BSE
Maps*
Microprobe Data
Mineral Calculation
Photos
TEM*
BSE
Maps*
Microprobe Data
Mineral Calculation
Photos
REM*
CX PlX ScX
assa_forward assa_inverse
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, 10th, 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
![Mechanisms of normal fault development at mid-ocean ridges › science › GG › people › jlin › papers › ... · 1. Introduction [2] The structure of oceanic crust formed at](https://img.pdfslide.us/doc/110x75/5f11c2173f046871bf168083/mechanisms-of-normal-fault-development-at-mid-ocean-ridges-a-science-a-gg-a.jpg)
![Mechanisms of normal fault development at mid-ocean ridges · 1. Introduction [2] The structure of oceanic crust formed at a ridge axis is controlled by the interplay between magmatic](https://img.pdfslide.us/doc/110x75/5ee15985ad6a402d666c43a6/mechanisms-of-normal-fault-development-at-mid-ocean-ridges-1-introduction-2-the.jpg)
