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Picro-ilmenites: An experimental study in simple and complexsystems to investigate P-T-fO₂-composition relations at highpressure
Author(s): Semytkivska, Nina
Publication Date: 2010
Permanent Link: https://doi.org/10.3929/ethz-a-006132710
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ETH Library
DISS. ETH NO.18907
Picro-ilmenites: An experimental study in simple and complex systems to investigate P-T- fO2-composition
relations at high pressures
A dissertation submitted to
ETH ZURICH
for the degree of
Doctor of Sciences
presented by
Nina Semytkivska Dipl. Geochemistry, Kiev National Taras Shevchenko University
Born on 3rd August, 1983 Citizen of Ukraine
Accepted on the recommendation of
Prof. Dr. P. Ulmer ETH Zurich examiner Prof. Dr. M. Schmidt ETH Zurich co-examiner Prof. Dr S. Klemme University of Münster co-examiner
2010
ii
iii
Abstract Picro-ilmenites (Mg-rich ilmenites) might be used as sensitive indicators of the physio-chemical
conditions important for understanding the genesis and prospection of potentially diamondiferous
kimberlites and lamproites. However, the role of chromium in the thermodynamic assessment of
equilibria of picro-ilmenites with other oxides and silicates in mantle-like systems was not the main focus
of previous studies, despite the fact that diamondiferous kimberlites are often associated with high Cr,
low Fe3+ ilmenites, which are indicative for high diamond preservation potential.
The experimental study reported here is conducted in peridotite like, Ti-rich systems to specifically
evaluate the behavior of Cr3+ in oxide – silicate mantle-like systems. The prime target is to investigate the
phase relations and composition of coexisting oxide phases, in particular ilmenite, as a function of
pressure, temperature and bulk composition.
Experiments were conducted at high pressures of 25-70 kbar and high temperatures of 1000-1400°C
employing piston cylinder and multi-anvil apparatus. Most of the runs were conducted at relatively
reducing conditions (close to the C-CO-CO2 equilibrium) employing graphite capsules plus a limited
number of additional experiments under more reducing (Mo-MO) and more oxidizing conditions.
The principal coexisting phases found in these experiments are ilmenite, spinel, olivine, orthopyroxene ±
rutile. Ilmenites (and spinel) are characterized by complex, but systematic compositional changes as
functions of bulk composition, temperature and pressure in mantle-like systems when Cr3+ is added as a
component. The stability of ilmenite is linked to XMg of the system and silica-activity. Ilmenite is stable
together with olivine + orthopyroxene (opx) + spinel at bulk XMg of less than 0.8, rutile + olivine + opx +
spinel are coexisting phases at a bulk XMg of 0.85. Compositions with lower SiO2 contents and low XMg
values are characterized by the presence of three coexisting Fe-Ti-oxides: ilmenite + rutile + spinel
coexisting with olivine and opx. Compositions with high XMg (0.85) and lower SiO2 contents result in the
disappearance of opx and rutile; present phases are olivine + spinel + ilmenite. In the iron-free system
(XMg = 1.0), phase parageneses are similar to runs with high Mg# (0.85) and high SiO2 contents: olivine +
opx + spinel + rutile. For composition with lower amount of SiO2, only olivine is present as a silicate
phase and three oxides are observed: spinel + rutile + ilmenite (geikielite).
Ilmenites exhibit Cr contents that increase with increasing temperature and pressure reaching up to 25
wt% Cr2O3 in experiments with XMg=0.73 (Al-free system); such high values are not commonly observed
in natural picro-ilmenite samples from kimberlites and other mantle xenoliths. The incorporation of Cr is
counter balanced by decreasing TiO2 and (Fe,Mg)O contents. In general, increasing temperature leads to
an enrichment of trivalent cations.
The experimental data was subsequently used to derive mixing properties for ilmenite solid solution
incorporating Cr2O3 by evaluating the Fe-Mg and Cr-Ti exchange reactions among the oxide and silicate
phases. Inclusion of Cr was evaluated employing subregular Margules formulations independently for
ilmenite-olivine and spinel-olivine pairs and for the three phase assembly. Mixing parameters were
calculated by least square regression using a regularization procedure (Tikhonov regularization). The
iv
fitted parameters differ significantly for every mineral pair considered due to different exchange
mechanisms. The existence of a miscibility gap for Cr2O3-(Fe,Mg)TiO3 solid solution is predicted for
intermediate composition. The exact position of this immiscibility gap, however, cannot be located
because our model is currently restricted to the ordered R 3 phase and the long range order-disorder
transition is not taken into account. As a consequence of the fitting procedure, the obtained parameters
should strictly be used consistently with the minerals they were derived from as the uncertainties of
individual components are much greater than the differences between them.
The derived thermodynamic data set was, finally, applied to a variety of natural parageneses observed in
kimberlites and associated rocks and compared with the results of existing geothermometers.
Thermometers based on Fe-Mg ilmenite-olivine exchange are not strongly affected by the incorporation
of Cr although the Fe-Mg ilmenite-olivine distribution coefficient exhibits complex dependence on
temperature. The Fe-Mg spinel-ilmenite and three oxide- phase thermometers often results unsatisfactory
results due to uncertainties associated with the estimation of the Fe3+ content of spinels and the absence of
magnetite-rich spinels in the experimental data set. The Cr-Ti ilmenite-spinel thermometer is the most
reliable for the particular set of ilmenites targeted in this study as the Cr2O3 activity is evaluated directly
from the exchange reaction. However, due to the fact that many of the natural spinels coexisting with Cr-
rich ilmenites are actually quite Fe3+-rich, additional calibration for Fe3+-rich compositions (under more
oxidizing conditions) are still required.
The observed experimental oxide parageneses can directly be linked to the formation of ilmenite-spinel
exsolution / intergrowth pairs and are consistent with 2- and 3- phase Fe-Ti oxide minerals stabilities and
compositions delimited as a function of XMg, pressure, temperature and silica activity.
v
Zusammenfassung
Picro-Ilmenite (Mg-reiche Ilmenite) können als sensitive Indikatoren der physikalisch-chemischen
Bedingungen verwendet werden, die grundlegend sind für das Verständnis der Entstehung und für die
Prospektion potentiell Diamant-führender Kimberlite und assoziierter Gesteine. Der Einfluss und die
Rolle von Cr3+ auf die thermodynamischen Grössen, die die Gleichgewichte zwischen Picro-Ilmenit und
den anderen Oxid und Silikatphasen in Mantel-ähnlichen Systemen bestimmen, waren jedoch bis dato
nicht Gegenstand experimenteller Studien. Dies ist umso erstaunlicher, als Diamant-führende Kimberlite
oft mit Cr-reichen, Fe3+-armen Ilmeniten assoziiert sind, die als indikativ für ein hohe Diamant
„Überlebenswahrscheinlichkeit“ betrachtet werden. Die hier vorgestellte experimentelle Studie wurde in
Peridotit-ähnlichen, Ti-reichen System durgeführt um spezifisch das Verhalten von Cr3+ in einem Mantel-
ähnlichen Oxid-Silikat-System zu untersuchen. Das primäre Ziel war die Untersuchung der
Phasenbeziehungen und der Zusammensetzungen koexistierender Oxidphasen, insbesondere Ilmenit, als
Funktion von Druck, Temperatur und Gesamtzusammensetzung.
Die Experimente wurden bei hohen Drücken von 25 - 70 kbar und hohen Temperaturen von 1000 –
1400°C in Stempelzylinder (piston cylinder) und Vielstempel (multi-anvil) Apparaturen durchgeführt.
Die meisten Experimente wurden unter relativ reduzierenden Bedingungen (nahe am C-CO-CO2
Gleichgewicht) in Graphit-Probenkapseln durchgeführt; nur eine kleine Anzahl zusätzlicher Experimente
wurde unter mehr oxidierenden und mehr reduzierenden Bedingungen ausgeführt.
Die wichtigsten koexistierenden Mineralphasen die in den Experimenten angetroffen wurden, sind
Ilmenit, Spinell, Olivin, Orthopyroxen ± Rutil. Die Ilmenite (und Spinelle) sind durch komplexe, aber
systematische Zusammensetzungsvariationen als Funktion der Gesamtzusammensetzung, der Temperatur
und des Drucks in Mantel-ähnlichen, Cr-führenden Systemen charakterisiert. Die Stabilität von Ilmenit
hängt vom XMg (=molares MgO/(MgO+FeO(tot)) des Gesamtsystems und der Silika-Aktivität ab: Ilmenit
ist zusammen mit Olivine + Orthopyroxen (Opx) + Spinell bei einem XMg < 0.8 stabil, Rutil + Olivin +
Opx + Spinell bilden die stabile Paragenese bei einem höheren XMg (0.85). Zusammensetzungen mit
niedrigerem SiO2 und relativ niedrigem XMg (0.73) sind charakterisiert durch die 3-Oxid-Paragenese
Ilmenite + Spinell + Rutil koexistierend mit Olivin und Opx. Zusammensetzungen mit einem hohen XMg
(0.85) und niedrigem SiO2-Anteil resultieren im Verschwinden von Opx und Rutil, stabile Phasen sind
Olivin + Spinell + Ilmenit. Im Fe-freien System (XMg = 1.0) sind die Phasenbeziehungen vergleichbar mit
hohem XMg und hohem SiO2-Anteil: Olivin + Opx + Spinell + Rutil bilden die stabile Paragenese; bei
niedrigerem SiO2-Anteil ist Olivin die einzige Silikatphase und 3 Oxide, Spinell + Ilmenit (Geikielit) +
Rutil koexistieren.
Ilmenite zeigen steigenden Cr-Gehalt mit steigendem Druck und Temperatur und können bis 25 Gew.%
Cr2O3 in Experimenten mit einem XMg von 0.73 (Al-freie Zusammensetzung) erreichen; so hohe Werte
werden üblicherweise in natürlichen Picro-Ilmenitproben aus Kimberliten und Mantelxenolithen nicht
beobachtet. Der Einbau von Cr wird durch sinkenden Ti- und Fe,Mg-Gehalt ausgeglichen; steigende
Temperatur führt im Allgemeinen zu einer Anreicherung 3-wertiger Kationen in Ilmenit.
vi
Die experimentellen Daten wurden verwendet um die Mischeigenschaften der Ilmenit-
Festkörperlösungen unter Einbezug von Cr3+ zu untersuchen. Dazu wurden die Fe-Mg und Cr-Ti
Austauschgleichgewichte zwischen den Oxid- und/oder Silikatphasen verwendet. Für die
Berücksichtigung von Cr3+ in Ilmenit und Spinell wurde eine sub-reguläre Margulesformulierung
verwendet und zwar unterschiedliche, unabhängige Formulierungen für die Ilmenit-Olivin, Spinell-Olivin
Paare und die 3-Phasen Paragenese. Die Mischparameter wurden durch Minimierung der Fehlerquadrate
(„least square regression“) und einer Regularisationsprozedur („Tikhonov regularization“) berechnet. Die
erhaltenen Parameter unterscheiden sich erheblich für die unterschiedlichen Mineralpaare da
unterschiedliche Austauschgelichgewichte und Mechanismen betrachtet wurden. Die Existenz einer
Mischungslücke in der Cr2O3 – (Mg,Fe)TiO3 Festkörperserie wird für intermediäre Zusammensetzungen
vorhergesagt; die exakte Position der Mischungslücke kann jedoch nicht lokalisiert werden, da unser
Model gegenwärtig nur die geordnete R 3 Phase berücksichtigt und daher die Langdistanz Ordnungs- /
Unordnungsübergänge nicht berücksichtigen kann. Als Konsequenz der spezifischen Fitprozeduren
können die vorgeschlagenen Parameter nur mit und für die Mineralien und Paragenesen verwendet
werden die bei der Berechnung der entsprechenden Datensätze verwendet wurden. Der Grund liegt darin,
dass die berechneten Fehler der einzelnen Parameter sehr viel grösser sind als die Differenzen zwischen
den Parametern.
Die berechneten thermodynamischen Daten wurden schliesslich dazu verwendet
Gleichgewichtstemperaturen für eine Anzahl natürlicher Paragenesen und Zusammensetzungen aus
Kimberliten und assoziierten Gesteinen zu berechnen und mit existierenden Geothermometern zu
vergleichen. Thermometer die auf dem Fe-Mg Austausch zwischen Ilmenit und Olivin basieren werden
durch den Einbau von Cr nicht sehr stark beeinflusst, obwohl die Fe-Mg Verteilung zwischen Olivin und
Ilmenit eine recht komplexe Temperaturabhängigkeit zeigt. Die Fe-Mg Spinell-Ilmenit und die 3-Phasen
Thermometer ergeben häufig unbefriedigende Resultate bedingt durch die grosse Ungenauigkeit die mit
der Abschätzung des Fe3+ Gehaltes der Spinelle und der Abwesenheit Magnetit-reicher Spinelle im
experimentellen Datensatz zusammenhängen dürfte. Der Cr-Ti Ilmenit-Spinell Thermometer ist der
zuverlässigste Indikator für die Bildungsbedingungen der Ilmenite die spezifisch in dieser Studie
untersucht werden sollten, da die Cr2O3 Aktivität direkt via das Cr-Austauschgleichgewicht evaluiert
wurde. Da jedoch viele natürliche Spinelle, die mit Cr-reichen Ilmeniten koexistieren, relativ Fe3+-reich
sind, werden zusätzliche Kalibrationsexperimente für Fe3+-reiche Zusammensetzungen (stärker
oxidierende Bedingungen) benötigt.
Die experimentell beobachteten Oxidparagenesen können direkt mit der Bildung von Ilmenit-Spinell
Entmischungs- / Verwachsungspaaren wir sie in Kimberliten beobachtet werden, verwendet werden: Die
Entstehung dieser speziellen Strukturen ist konsistent mit den 2- und 3-Phasen Fe-Ti-Oxid
Stabilitätsfeldern und Zusammensetzungen als Funktion von Gesamtsystems XMg, Druck, Temperatur und
Silika-Aktivität.
vii
Table of contents
Abstract iii
Zusammenfassung v
1. Introduction 1
1.1 Occurrence and composition of picro-ilmenites 1
1.2 Experimental studies on ilmenite-bearing assemblages 6
1.3 Aims of this study 12
1.4 Organization of the thesis 12
1.5 Reference 13
2. Experimental and analytical methods 18
2.1 Experimental apparatus 18
2.1.1 Boyd and England type endloaded piston cylinder 18
2.1.2 Walker-type multi-anvil apparatus 19
2.1.3 Pressure calibration of the multi-anvil apparatus 20
2.2 Capsule design 21
2.3 Starting material 22
2.4 Factors controlling oxygen fugacity 24
2.5 Analytical Techniques 25
2.5.1 Electron microprobe 25
2.5.2 Powder X-ray diffraction (XRD) 26
2.5.3 Micro-Raman spectroscopy 26
2.6 Reference 27
3. An experimental study of picro-ilmenites in the system
TiO2-Cr2O3-FeO-Fe2O3-MgO-SiO2±Al2O3 at 2.5-7.0 GPa and 1000-1400°C 29
3.1 Introduction 29
3.2 Experimental setup 30
3.2.1 Experimental apparatus 30
3.2.2. Analytical Techniques 31
3.2.3 Starting material and capsule design 31
3.3 Results 32
3.3.1 Attainment of equilibrium 32
3.3.2 Bulk composition and phase relations 33
3.3.3 Effect of different oxidizing condition 43
3.3.4 Phase compositions 45
3.3.4.1 Ilmenite. 45
viii
3.3.4.2 Spinel 49
3.3.4.3. Rutile 51
3.3.4.4 Olivine 52
3.3.4.5 Orthopyroxene 53
3.3.4.6 Garnet 54
3.3.5 Partitioning of Iron and Magnesium. 54
3.3.5.1 Ilmenite-Silicates 54
3.3.5.2 Spinel-Silicates 56
3.3.5.3 Ilmenite-Spinel 57
3.4 Discussion 58
3.5 Conclusions 61
3.6 Reference 62
4. Thermodynamic modeling of Fe2+-Ti-Cr-Fe3+-Mg±Al ilmenite solid
solution as a function of pressure and temperature 66
4.1 Introduction 66
4.2 Gibbs free energy of solid solution 67
4.3 Structures and thermodynamic formulation of minerals 69
4.3.1 Ilmenite 69
4.3.2 Olivine 73
4.3.3 Spinel 75
4.3 Ilmenite-olivine exchange 78
4.4 Ilmenite - spinel exchange 85
4.4.1 Fe-Mg exchange spinel ilmenite 86
4.4.2 Cr-Ti exchange spinel ilmenite 91
4.5 Internally consistent solution 94
4.6 Calibration for pressure 96
4.7 Discussion 97
4.8 Conclusion 102
4.9 Reference 103
5 Application of ilmenite-oxide-silicate exchange equilibria to the genesis of
picroilmenite bearing assemblages 109
5.1 Introduction 109
5.2 Formulation of ilmenite – oxide and ilmenite – silicate geothermometers 110
5.3 Application to natural assemblage 111
5.4 Comparison with ilmenite – spinel intergrowths 118
5.5 Crystallization of ilmenite 121
5.6 Conclusion 122
5.7 References 123
ix
6. Summary and outlook 128
6.1 Outlook 129
Appendix I Gexch equations 131
Appendix II Regularization tools 136
Acknowledgements 147
Curriculum Vitae 149
x
-1.Introduction-
1
1. Introduction
1.1 Occurrence and composition of picro-ilmenites
Mg-rich, Cr-bearing ilmenites, often called picro-ilmenites, occur nearly exclusively in ultramafic
kimberlites, lamproites (Mitchell, 1973, 1986; Haggerty, 1975, 1991; Gagarin et al., 1980; Moore, 1987)
and associated alkaline ultramafic rocks such as MARID-type (mica-amphibole-rutile-ilmenite-diopside
suite, Dawson and Smith, 1977; Jones et al., 1982; Waters, 1987) and IRPS (ilmenite-rutile-phlogopite-
sulfide, Harte, 1987) xenoliths in kimberlites. Their occurrence is thought to be related either to
crystallization of ultramafic, alkaline liquids such as kimberlites or lamproites (Moore,1987; Griffin et al.
1997) or produced through reaction of a Ti-Fe-rich alkaline ultramafic liquid/fluid with common
lherzolite /harzburgite mantle rocks (Eggler et al., 1979; Zhang et al, 2001). Kimberlitic ilmenites are
essentially members of solid solutions between ilmenite (FeTiO3), geikilite (MgTiO3) and hematite
(Fe2O3). Significant amount of Cr2O3 are commonly present, typically they contain minor amount of
Al2O3 (<1%), SiO2 (<0.5%) and MnO (<1%).
Several different paragenetic types of ilmenites in kimberlites can be distinguished (e.g. Mitchell, 1986):
(1) Large rounded single crystals or polycrystalline aggregates and macrocrysts with sizes up to 15
cm (sometimes referred to as xenocrystic/macrocrystic ilmenites)
(2) Lamellar intergrowth of ilmenite with clinopyroxene and more rarely with enstatite ('graphic'
intergrowths)
(3) Euhedral to anhedral primary groundmass or matrix ilmenite
(4) Rounded to subhedral inclusions in olivine and/or phlogopite macrocrysts
(5) Subsolidus oxidation ilmenites in spinel (exsolution lamellae)
(6) llmenite-spinel-perovskite overgrowth rims on megacrystic ilmenites
(7) Intergrowth with rutile and ilmenite-rutile-armalcolite intergrowth
Megacrystic/macrocrystic ilmenites from kimberlites, (1) and (2) from the list above, are the primary
target of this study. Compositionally, the megacryst suite is divided into high and low Cr varieties, with
the high Cr group also being high in Mg and low in Fe (Haggerty et al., 1979). Within a given province
each kimberlite contains a characteristic suite of ilmenite as defined by its major element compositional
range and average value. Ilmenites can be used to ‘fingerprint’ individual kimberlites.
Picro-ilmenites occurrences and diagnostic chemistries are an important tool in prospecting of potentially
diamondiferous kimberlite and lamproite pipes and dikes. They are, however, not thought to be related to
the source of (most) diamonds. Picro-ilmenites are typically used to trace kimberlites and/or lamproites
that are essential for the transport of diamonds to the surface. They commonly provide a guide to the
presence of kimberlite in drainage or loan samples. Some authors clearly link them to the megacryst suite
consisting of relatively Fe-Ti-rich garnet, pyroxenes and olivines. Their genesis is not clear yet, but a
-1.Introduction-
2
close genetic link to 'proto-kimberlite' crystallization at depths (4-7 GPa) and/or to mantle metasomatism
produced by interaction of kimberlitic liquids with sub-lithospheric mantle has been inferred. High-Cr
picro-ilmenites have very rarely been observed as inclusions in atypical diamonds, e.g. in Yakutia
(Sobolev et al., 1997) and South Africa (Viljoen et al., 1999) coexisting with olivine; a (mantle)
metasomatic origin is usually interred for these ilmenites.
Fig 1.1 Hypothetical cross section of an Archean craton with an extinct ancient mobile belt (once associated with subduction?) and a young rift. The low cratonic geotherm causes the graphite-diamond transition to rise in the central portion. Lithospheric diamonds, therefore, occur only in the peridotites and eclogites of the deep cratonic root, where they are potentially incorporated into rising magmas (mostly kimberlitic- “K”). Lithospheric orangeites (“O”) and some lamproites (“L”) may also scavenge diamonds. Melilitites (“M”) are generated by more extensive partial melting of the asthenosphere. Depending on the depth of segregation they may contain diamonds. Nephelinites (“N”) and associated carbonatites develop from extensive partial melting at shallow depths in rift areas. After Mitchell (1995).
Discrete ilmenite megacrysts in kimberlites and lamproites display unique features not observed in any
other terrestrial ilmenites (but partly in common with some ilmenites occurring in lunar rocks in particular
in the anorthosites and the KREEP basalts, e.g. Powell and Weiblen, (1972). They are MgO-rich (XMg
varies between 0.2 - 0.6) and variably Cr- and Nb-rich (e.g. Moore et al., 1992; Griffin et al., 1997;
Griffin and Ryan. 1995). Haggerty (1975) observed a 'peculiar' parabolic (more rarely hyperbolic) trend
of megacrystic ilmenites in a Cr2O3 versus MgO diagram (e.g. Fig. 1.2). Such relationships have been
observed for many megacryst suites worldwide (e.g. Eggler et al., 1979; Moore, 1987; Schulze et al),
1995). The empirical rule is that ilmenites on the right hand branch of the parabola are indicative of
kimberlites with higher diamond contents than those on the left. The relationship of ilmenite to diamond
is indirect because, as pointed out earlier, inclusions of ilmenite in diamond are extremely rare. High Mg
and Cr and low Fe3+ contents of ilmenites are possibly more indicative for diamond survival potential
than diamond genesis potentially linking high Mg-Cr ilmenite chemistry to lower oxygen fugacity (fO2)
permitting prolonged diamond survival in a hot kimberlitic transport medium.
-1.Introduction-
3
0 2 4 6 8 10 12 14 16 18 200
1
2
3
4
5Cr
2O3 w
t. %
MgO wt.%0 2 4 6 8 10 12 14 16 18 20
0
1
2
3
4
5
MgO wt.%
Haggerty1975 Wesselton
Liqhobong
Orapa
LakeEllen
Sloan-Nix-Ferris
IronMountain
Figure 1.2 Cr2O3 versus MgO diagram of megacrystal ilmenites. Each limb of the parabola is defined by ilmenites from a particular group of kimberlites but the overall parabolic relationship cannot be defined by ilmenites from a single intrusion (Mitchell, 1986). The causes of these parabolic trends are not yet clear. Several different mechanisms have been proposed
for the generation of megacrystic ilmenites and the 'peculiar' geochemical trends, among them:
(1) A solvus relationship (Haggerty and Tomkins, 1983) in the Cr-Fe-Mg-Ti-O system between
Fe2O3-rich rhombic oxides and (Mg,Fe)TiO3-rich rhombic oxides that closes with increasing
FeTiO3 and/or Cr2O3 component.
(2) Igneous crystallization of rhombic oxide coexisting with different silicate assemblages, e.g.
garnet-bearing at high pressures that depletes Cr and Mg and garnet/pyroxene free (olivine -
carbonate) that is responsible for the high Mg- high Cr limb of the parabola (at lower pressures)
(e.g. Boyd and Dawson, 1970; Boyd and Nixon, 1975; Haggerty et al., 1979; Hearn, 1994; Moore
and Lock, 2001). Some aspects of the proposed 'igneous' crystallization trends could be
reconciled with the aid of trace element contents of ilmenite megacrysts in particular Nb - Zr
relationships (Griffin & Ryan, 1995; Griffin et al., 1997) and with isotopic evidence indicating
identical isotopic signatures for megacrystic ilmenites and their host group I kimberlites (Nowell
et al., 1999) or so called archetypical kimberlites (basaltic kimberlites) as opposed to K-
rich micaceous kimberlites denoted „orangeites“ by Mitchell (1995).
Another unique feature of ilmenite bearing megacryst suites is the occurrence of graphic intergrowth of
high-Mg ilmenites with cpx or opx (rare). This intergrowth described from many different kimberlite
localities has been attributed to
(1) igneous co-precipitation (e.g. Boyd and Dawson, 1970; Boyd and Nixon, 1975; Rawlinson and
Dawson, 1979; Schulze, 1983),
(2) reaction of 'proto-kimberlite' with peridotitic mantle (Eggler et al., 1979)
(3) exsolution from a precursor phase (e.g. Dawson and Reid, 1 970; Ringwood and Lovering, 1970)
such as ilmenite-structured enstatitic pyroxene (akimotite) or majoritic garnet, both stable in the
Earth's transition zone.
-1.Introduction-
4
Figure 1.3 Photomicrograph in reflected light of clinopyroxene-ilmenite intergrowths. Left: run carried out at 38 kb, cooled from 1570°C and quenched at 1200°C, right: run carried out at 38 kbar, cooled from 1570 and quenched on the solidus (1404°C) (Wyatt, 1977). Limited experimental studies (e.g. Wyatt, 1977) show that an igneous co-precipitation of ilmenite and
pyroxene could be a possible mechanism as they reproduced lamellar or graphic intergrowths of ilmenite
and pyroxenes under high-pressure, high-temperature conditions (2-7 GPa, 1000-1600°C) (Fig.1.3). A
rare xenolith from Weltevreden Floors (RSA; Meyer et 1979) contains not only an enstatite megacryst,
but a 'full assemblage' consisting of garnet, cpx, opx, olivine and ilmenite that displays local pyroxene-
ilmenite intergrowth overgrowing a garnet ‘xenocryst’. Compositions of the minerals are unlike common
lherzolite/harzburgite mantle rocks contained as 'normal’ xenoliths in the kimberlite, but are consistent
with the macrocryst/megacryst suite described above (Fe, Ti-rich). Rare intergrowth of ilmenite and rutile
has been described by Haggerty (1983) from the Jagersfontein kimberlite that has been attributed to
breakdown of a precursor titanite phase, either α-PbO structured TiO2 or perovskite structured
(Fe,Mg)TiO3).
Ilmenite megacrysts have been successfully used to constrain the oxygen fugacity through their relatively
evaluated hematite component (0.05-0.40 mole fractions, c.f. Haggerty. 1991). Haggerty & Tomkins
1993) and Arculus et al. (1994) have used ilmenites to determine the oxygen fugacity of the assemblage
that crystallized the ilmenite megacrysts. Both studies, based on two different techniques (thermodynamic
phase equilibrium and intrinsic oxygen fugacity measurements using electrolyte cells respectively),
resulted in rather oxidizing conditions around the reference equilibria Ni-NiO (NNO) and fayalite-
magnetite-quartz (FMQ). Such fO2 conditions are above the (calculated) stability limit of
graphite/diamond under upper mantle conditions (3-6 GPa, 900-1200°C) that is delimited for peridotitic
rocks by the oxygen fugacity of the reaction enstatite + magnesite = olivine + diamond/graphite + O2
(EMOD/G, Eggler and Baker 1982). These results have considerable consequences for the role of
megacrystic ilmenites in kimberlites and diamond grade evaluation: It has been suggested that the
presence of 'oxidized' ilmenites in the megacryst suite (e.g. Gurney & Zweistra, 1995) or in MARlDs (e.g.
Zhao et al., 1999) is indicative for a rather oxidizing environment during transport or during a
-1.Introduction-
5
metasomatic event in the cratonic root that is thought to be the major source area of diamonds (shown
schematically in Fig. 1.4.
0 2 4 6 8 10 12 14 16 180
1
2
3
4
5
6
Cr2O
3 wt.
%
MgO wt.%
Metasomatic
Transitional
Megacrysts
LOW-Cr MEGACRYSTS
CRUSTAL ILMENITES (magnetic+ LOW Mg & Cr)
High diamond preservation potential(decrease in oxidising condions)
Low diamond preservation potential (oxidising conditions)
LOW INTEREST
POSSIBLE HIGH INTEREST
Figure 1.4 Schematic correlation between oxidation state and Cr content of ilmenites and the diamond grade (De Beers unpublished data). Therefore, it is proposed that ilmenite megacrysts with high hematite components could be indicative for
a reduced 'survival potential' of diamonds from such kimberlites or more precisely from the diamond
source region where the ilmenite megacrysts might have formed. There is a rough correlation between the
'oxidation state' of megacrystic ilmenites and the diamond grade of a particular kimberlite pipe (e.g.
Gurney & Zweistra, 1995). However, many exceptions from this general rule exist. In general, the Fe2O3
content of ilmenites correlates negatively with the MgO content, which has led several researchers to state
that kimberlites become more oxidizing during progressive crystallization and/or ascent. However,
experimental studies (mostly at low pressures, see chapter 1.2) indicate that the Fe2O3 contents of
ilmenites increase with increasing FeTiO3 component at constant fO2 at a given temperature (Woermann
et al, 1970).
-1.Introduction-
6
1.2 Previous experimental studies on ilmenite-bearing assemblages
Fe-(Mg)-Ti-O systems
Ilmenites have been the target of a numerous experimental studies. Ilmenite, a rhombic oxide with the
general formula A2O3, is an important structural type in Earth and material sciences. In petrology,
ilmenites occur as accessory minerals in a wide variety of igneous and metamorphic rocks. The Fe-Mg-
Ti-O quaternary has been extensively studied in the past, however most studies have been concerned with
relatively high temperature up to, and including the liquidus. Johnson et al. (1971) studied the FeO-MgO-
TiO2 join at liquidus and solidus temperatures with fO2 = 10-8 bar, and at 1300oC in equilibrium with
metallic iron (Fig. 1.5, c) and calculated qualitative activity composition relations for (Fe,Mg)2TiO4
spinels and (Fe,Mg)TiO3 ilmenite. A systematic study of phase relationships in the ternary MgO - Fe-
oxide – TiO2 at 1 bar in air has been performed by Woermann et al. (1969). At low pressure (and high
fO2), the join MgTiO3 (geikilite) – Fe2O3 (hematite) is characterized by a large miscibility gap; only
compositions close to the endmembers are stable. Intermediate compositions are represented by the
paragenesis MgTiO3-FeTiO3 solid solution (pseudobrookite) - Mg2TiO4 – MgFe2O4 solid solution
(spinels). Interestingly, the miscibility gap shrinks with decreasing temperature (Fig 1.5 a,b).
In two abstracts, Woermann et al. (1970) and Ullmann and Woermann (1990) report additional
experiments at higher pressures (6 - 15 kbar) showing that the ferro-pseudobrookite -armalcolite - karroite
solid solution phases are not stable at high -pressure and are replaced by the paragenesis ilmenitess + rutile
(confirmed by Friel et al., 1977). The miscibility gap in the MgTiO3- Fe2O3 system decreases and
disappears above 6 kbar (at 1300°C). Likewise, the size of the miscibility gap decreases with decreasing
fO2 (at 1 bar) (Fig. 1.5 d); FeTiO3-MgTiO3 solid solutions containing less than approximately 15 mol%
Fe2O3 are fully miscible at 1300°C and fO2 < 10-6 (i.e. at or below NNO). The Fe2O3 content of ilmenites
at constant temperature and fO2 increases with increasing FeTiO3 substitution in MgTiO3. Muan et al.
(1971, 1972) have performed 1 bar experiments under very reducing conditions (fO2 buffered by Fe-FeO
equilibrium): They observed complete miscibility in the FeO-MgO-TiO2 system (with very low Fe2O3)
along the ilmenite-geikilite join. Pownceby et al. (1999) as well determined detailed phase relations in the
system FeO-MgO-TiO2 and Fe2O3-MgO-TiO2 at temperatures 900-1200°C and reported results in
agreement with previous studies (Woermann, Johnson).
-1.Introduction-
7
0.2
0.40.6
0.0
0.6
0.8
Fe2O3
FeTiO3
Sp+Pb+Ilm
Sp+Pb
10-3
10-4
10-5
10-6
10-7
10-8
10-9
MgTiO3
log fO2 at 1300oC
0.0 0.2 0.4 0.6 1.0
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.6
0.0
0.2
0.4
0.6
0.8
TiO2
MgTiO3
Mg2TiO4
Fe2TiO5
Fe2O3MgO
Mg2TiO5
1300oC (Air)
Sp+MW
Sp
Hem+Sp
Gk+Sp
Pb+Gk
R+Pb
Pb
Pb+Sp
Hem+Pb
Gk+Pb+Sp
Hem+Pb+Sp
Hem
0.0 0.2 0.4 0.6 1.0
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.6
0.0
0.2
0.4
0.6
0.8
TiO2
MgTiO3
Mg2TiO4
Fe2TiO5
FeOMgO
Mg2TiO5
1300oC (Metallic iron)
Sp+MW
Ilm+Sp
MFPb+ilm
R+MFPb
FeTiO3
Fe2TiO4
MW
Sp
0.0 0.2 0.4 0.6 1.0
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.6
0.0
0.2
0.4
0.6
0.8
TiO2
MgTiO3
Mg2TiO4
Fe2TiO5
Fe2O3MgO
Mg2TiO5
1000oC (Air)
Sp+MW
Hem+Sp
Gk+Sp
Pb+Gk
R+Pb
Pb
Pb+Sp
Hem+Pb
Gk+Pb+Sp
Hem+Pb+Sp
Hem
a) b)
c) d)
Figure 1.5 Experimental data for the Fe-Mg-Ti-O system. Rhombohedral oxide solid solution shows a large miscibility gap at 1300oC (a) that is reduced at 1000oC in air (b) (Woermann et al., 1969). Solid solutions are complete in contact with metallic iron at 1300oC (c) (Johnson et al, 1971). The ilmenite plane at different oxygen fugacities is shown in (d) at 1300oC (Woermann et al., 1970). Abbreviations: Sp - spinel, Pb - pseudobrookite solid solution, Gk - geikilite solid solution, Hem - hematite solid solution, R – rutile, MFPB - magnesian-ferro-pseudobrookite, Ilm- rhombohedral solid solution. A classical application of ilmenite mineral chemistry is the 2-oxide (ilmenite-hematite solid solution
(rhombic oxides) and magnetite-ulvöspinel solid solution (cubic oxides)) thermometry - oxybarometry,
pioneered by Buddington and Lindsley (1964) with many subsequent modifications (e.g. Spencer and
Lindsley, 1981; Andersen et al., 1991; Ghiorso and Sack. 1991; Sauerzapf et al., 2004), This is an
important thermo-barometric tool for igneous (mostly volcanic) and metamorphic rocks. The calibration
and subsequent thermodynamic treatments of this oxy-thermobarometer base on a large experimental
dataset obtained nearly exclusively at low pressures (1 bar to 1 kbar) in the system Fe-Ti-O with later
additions for Mn bearing systems (Pownceby et al., 1987). Sauerzapf et al. (2008) presented new
thermodynamic models for titanomagnetite - ilmenitess pairs and derived a revised version of the thermo-
oxybarometer which yields much better T-fO2 estimates for temperatures above 800°C under reduced or
moderately oxidized conditions. However, for oxides with high concentrations of additional elements
(MgO, Cr2O3, Al2O3>6 wt%, which is the case for kimberlite) their model is not suitable.
-1.Introduction-
8
A limited number of experimental studies have been performed to measure the partitioning of Fe2+ - Mg
between ilmenite and the Fe-Mg silicate mantle phases olivine, cpx, opx, and garnet (Akella and Boyd,
1971; Andersen and Lindsley, 1979; 1981; Bishop, 1980; Green and Sobolev, 1975) to calibrate potential
geothermometers using ilmenite-silicate Fe-Mg partitioning relationships. The studies by Bishop (1980)
(pyx-ilmenite) and Andersen and Lindsley (1979, 1981) (olivine-ilmenite) where performed in simplified
systems at rather low fO2 (graphite or even iron capsules); pressures were mainly 13 kbar with a few
experiments at 36 kbar to explore the effect of pressure on the Fe-Mg partitioning and the activity
relationships of Fe-MgTiO3 solid solutions. The olivine-ilmenite and pyroxene-ilmenite studies provide
the thermodynamic basis for the formulation of activity models of MgTiO3-FeTiO3, solid solutions and
calibration of the ilmenite-silicate geothermometers. Application of these thermometers have mainly been
directed towards lunar rocks, but applied to the megacryst assemblages and pyroxene-ilmenite
intergrowth they result in relatively high temperatures of 1100-1400°C compared with other thermometric
methods (e.g. 2 -pyroxene, garnet-cpx).
Cr-Al-bearing system
Very limited information is available for Fe-Mg-Ti-O systems containing trivalent cations other than Fe3+.
Grey & Mumme (1972), Grey & Reid (1972) and Grey et al. (1973) have synthesized various oxides in
the system Cr2O3-Fe2O3-TiO2 (-ZrO2) at 1 bar in air (high fO2, basically all Fe3+). They obtained Fe-Ti-
Cr-oxides that are intermediate or combinations of common rutile with the α-PbO2 structure. Zr-
substituted compounds that simulate high-pressure behavior (similar to Ge for silicates) indicate that
increasing pressure (increasing ZrO2 substitution tor TiO2) favors α-PbO2 structured types. This might be
relevant for Cr-bearing systems because rare rutiles from the megacryst suite contain significant amount
of Cr2O3 (in addition to Fe2O3, Nb2O5 and some A12O3).
Muan et al. (1971, 1972) have performed 1 bar experiments under reducing conditions (Fe-crucibles), in
the MgO-TiO2-A12O3 and MgO-TiO2-Cr2O3 systems. Pronounced immiscibility on the rhombic oxide
joins MgTiO3-Al2O3 and MgTiO3-Cr2O3 are observed; at 1300°C only very limited Cr and Al solubility in
MgTiO3 is possible. Intermediate compositions are dominated by the assemblage pseudobrookite + cubic
oxide (spinel). They have investigated in more detail the phase relations of cubic oxides (FeAl2O4-
FeCr2O4-Fe2TiO4 and the equivalent MgO systems). Both cubic oxide systems (Cr and Al) display large
miscibility gaps (increasing with decreasing temperature) between the Al and Ti endmembers that
decrease with increasing Cr-content. The Cr-bearing systems become fully miscible above approximately
30% substitution with the Cr-endmember. Crystal chemical considerations probably imply similar
behavior on the rhombic oxide joins (that will only be stable at high pressures).
-1.Introduction-
9
0.6
0.0
0.6
0.8
Mg2TiO4
MgCr2O4
MgAl2O4
0.6
0.0
0.6
0.8
Fe2TiO4
FeCr2O4
FeAl2O4
1000oC
1000 oC1200oC1300oC
1150oC1300oC
one spinel one spinel
Figure 1.6 Approximate extend of the spinel miscibility gap in the system FeAl2O4-FeCr2O4-Fe2TiO4 (left) and MgAl2O4-MgCr2O4-Mg2TiO4 (right) in the temperature range 1000 - 1300oC and at one bar (after Muan et al., 1972). Recently, Lattard et al (2008) pointed out the importance of chromium for the iron-titanium thermometry
and performed experiments in the Fe-Ti-Cr-O and Fe-Ti-Cr-Mg-O systems at 1 bar in the sub-solidus
temperature range 900-1300°C at low to moderate oxygen fugacity values (ΔNNO between -4 and -1).
The run products are polycrystalline assemblages of titanomagnetite and ilmenite solid solutions with
Cr2O3 contents between 12 and 18 wt.% for the spinels and between 0.7 and 4 wt.% for the ilmenites.
Green and Sobolev (1975) present ilmenite compositions in equilibrium with garnet, olivine and
pyroxenes from experiments performed on (natural) peridotite (Al and Cr-bearing) and olivine-basanite
bulk compositions in the range 21-40 kbar. The fO2 of this study is not specified but must be relatively
high (around NNO according to the authors). Their study implies that the Kd(Mg-Fe) ilmenite-garnet
(=Mgilm*Fe2+gar) / (Fe2+
ilm*Mggar)) is most probably dependant on the Fe2O3 content of the ilmenite (and
garnet?) as well as on pressure. Kd slightly increases with pressure in the range 21-40 kbar but it is not
sensitive to temperature in the observed range. Their final statement is: ' ...the fO2-dependant substitution
of Fe2O3 in ilmenite markedly affects Cr2O3 solubility relationships and may affect the Fe2+-Mg
partitioning relation relationships'. They finish by stating that further study and experimental projects
should be designed to specifically investigate ilmenite solid solutions under controlled physical
conditions.
High-pressure structures and stabilities of ilmenites and rutile
The Ti-oxide phases, ilmenite and rutile (excluding CaTiO3, perovskite that only occurs as a groundmass
phase in kimberlites), which are stable under upper mantle conditions exhibit phase transformations to
higher-pressure polymorphs. TiO2, stable as rutile under low pressure conditions, converts to TiO2-II (α-
PbO2 structure) between 6 and 9 GPa at 700-1200°C (Akaogi et al., 1992; Withers et al., 2003; Bromiley
et al., 2004). This was also observed in the experimental study on a group II kimberlite by Ulmer and
Sweeney (2002) at 8 GPa and 1200°C and in a preliminary study on olivine - enstatite - ilmenite - rutile
-1.Introduction-
10
relationships by Ulmer and Trommsdorff (1998) at 9.5 GPa between 1200 and 1400°C (Fig. 1.7). The
data indicate a lower transition pressure (by approx. 1 GPa) than the data provided by Withers et al.
(2003); this is most probably related to the presence of Fe and/or Cr in the rutiles synthesized in the
studies conducted at ETH Zürich.
TiO2 (II)
rutile
Ol - enst - ilmenite
Ol - enst - rutile
Fo90 - ExperimentsOl(90) - RutileEn(92)- ilm
Temperature (oC)
Pres
sure
(GPa
)
10.0
7.5
5.0
2.5
0.0900 1100 1300 1500 1700
Figure 1.7 Pressure- temperature diagram showing the reaction olivine + rutile = opx + ilmenite (data from Ulmer & Trommsdorff, 1998).
Recent support for this interpretation is provided by experiments reported by Bromiley et al. (2004).
Ilmenite - geikilite solid solutions transform to the perovskite structure at 14-24 GPa at 800°C through a
continuous reaction (FeTiO3 at 14 GPa, MgTiO3 at 24 GPa, Liu, 1975; Linton el al., 1999). The
previously reported phase transition of FeTiO3 ilmenite to FeTiO3 with Li-niobate structure (Syono et al.,
1980) proved to be metastable with respect to the ilmenite - perovskite transition (Mehta et al., 1994). The
inferred phase boundary between FeTiO3 ilmenite and perovskite has a negative Clapeyron slope. At the
potential megacryst formation temperatures of 1000-1400°C the transition in pure FeTiO3 will occur at 12
to 8 GPa, i.e. in the uppermost pressure range accepted for formation of the megacryst suite. Addition of
MgTiO3 component to pure ilmenite will further increase this transition pressure. Therefore, perovskite
structured (Fe,Mg)TiO3 should not be stable under the conditions inferred by most studies for the
generation of the megacryst suite. An exception is Ringwood and Lovering (1970), who infer pressures in
excess of 13 GPa for the formation of primary kimberlite and ilmenite - pyroxene intergrowth
megacrysts.
-1.Introduction-
11
Crystallization of Fe-Ti oxides from ultramafic CO2-bearing kimberlitic liquids
Ilmenite megacrysts predominantly occur in group I (basaltic) kimberlites. They are only rarely described
from group II (micaceous) kimberlites (now also called orangeites, Mitchell, 1995). Experimental studies
on kimberlite crystallization/differentiation under upper mantle (to transition zone) conditions are
relatively rare and often do not report the compositions of Fe-Ti-oxides (if present at all). Studies on an
aphanitic group Ib (Wesselton) kimberlite (Edgar et al., 1988: Edgar and Charbonneau, 1993) and on a
group la kimberlite by Girnis et al. (1995) produced Fe-Ti-oxide-bearing assemblages (coexisting with ol-
cpx-gar±opx ±magnesite). However, they used mostly noble metal (Pt, Au) containers and the resulting
Fe-Ti-oxide phases are typically highly oxidized spinels. The group Ib kimberlites (Edgar and
Charbonneau, 1993) are strongly silica undersaturated, and do not saturate with opx at any pressure and
the Fe-Ti-oxide phases are dominated by (oxidized?) spinel and perovskite. Ulmer & Sweeney (2002)
performed phase equilibria experiments from 1-10 GPa on a group II kimberlite. They obtained ilmenites
partly coexisting with TiO2 (in a-PbO2 structure) at 7.5 and 8 GPa and 1150-1200°C in an assemblage
with olivine + opx + garnet + magnesite ±cpx. Experiments at 8 GPa (1200°C) were performed in
graphite capsules; the compositions of the phases closely match the compositions of the megacryst suite
including ilmenite. Mitchell (2004) studied liquidus and subliquidus phase relationships of the hypabyssal
kimberlite at pressures 5-12 GPa. He described the effect of graphite versus platinum capsules on oxygen
fugacity of the experimental charges and compositions of the phases, especially garnets rhombohedral Fe-
Ti oxides (ilmenite-geikilite-hematite solid solution). This study proposed that kimberlite magmas form
by extensive partial melting of metasomatized mantle and that lamellar ilmenite-clinopyroxene
intergrowths represent the products of non-equilibrium growth in kimberlite magma
-1.Introduction-
12
1.3 Aims of this study
The targets of this study are to quantify compositional variations of rhombic oxides coexisting with upper
mantle phases as a function of pressure, temperature, oxygen fugacity and compositional variables. The
experimentally derived data should/will allow
(1) to constrain thermodynamic properties of rhombic oxide solid solutions at high pressures and
develop model for ilmenite in complex multi-component system;
(2) to interpret chemical variations of natural picro-ilmenites in terms of pressure, temperature or
oxygen fugacity variations during the formation of the picro-ilmenites; and
(3) to use these results to examine the potential of using picro-ilmenite to evaluate the diamond
potential of a given population of picro-ilmenite megacrysts from a kimberlite or associated rock
type.
1.4 Organization of the thesis
This thesis consists of six chapters. Chapter one includes a general overview of ilmenite occurrence and
properties with rationalization of the project. Chapter two describes analytical and experimental methods
used in this investigation, including a description of starting materials employed in the study. Chapters 3
to 5 are designed as manuscripts for upcoming publications: Chapter three presents experimental data on
compositional variations of ilmenite and coexisting phases as a function P-T-bulk-composition. Chapter 4
presents the thermodynamic evaluation of the experimental dataset and derived thermodynamic properties
of rhombic Fe-Ti-Mg oxides solid solution at high pressure. Chapter 5 presents applications to natural
assemblages, comparison of the experimental and thermodynamically derived relations with natural
ilmenites. Chapter 6 summarizes the principal results and conclusions of this work. The appendix
contains data with additional information used in other parts of the thesis.
-1.Introduction-
13
1.5 References Akella J., Boyd F.R. (1971) Partitioning of Ti and Al between pyroxenes, garnet, and oxides.
Carnegie Institution of Washington Year Book, 71, 378-389.
Andersen D. J., Bishop F. C., and Lindsley D. H. (1991) Internally consistent solution models for Fe-
Mg-Mn-Ti oxides: Fe-Mg-Ti oxides and olivine. American Mineralogist, 76, 427-444.
Andersen D. J., Lindsley D. H. (1981) A valid Margules formulation for an asymmetric ternary
solution: revision of the olivine-ilmenite thermometer, with applications. Geochimica et
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Arculus R.J., Dawson J.B., Mitchell R.H., Gust D.A., and Holmes R.D. (1984) Oxidation states of
the upper mantle recorded by megacryst ilmenites in kimberlites and type A and B spinel
lherzolites. Contribution to Mineralogie and Petrology, 85, 85-94.
Bishop F. C. (1980) The distribution of Fe2+ and Mg between coexisting ilmenite and pyroxene with
applications to geothermometry. American journal of science, 280, 46-77.
Boyd F.R., Dawson I.B., (1970) Kimberlite garnets and pyroxene-ilmenite intergrowths.
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Boyd F.R., Nixon P.M. (1975) Origin of the ultramafic nodules from some kimberlites of Northern
Lesotho and the Monastery Mine, South Africa. Physics and Chemistry of the Earth, 9, 431-
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Buddington A.F., Lindsley D.H. (1964) Iron-titanium oxide minerals and synthetic equivalents.
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the Wesselton mine, Kimberley, South Africa. American Mineralogist, 73, 524-533.
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Eggler D.H., and Baker DR. (1982) Reduced volatiles in the system C-O-H. Implications to
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Friel J J., Harker R.I., and Ulmer G C (1977) Armalcolite stability as a function of pressure and oxygen
fugacity.Geochimica et Cosmochimica Acta, 41, 403-410.
Garanin V.K., Kudryavtseva G.P., and Lapin A.V. (1980) Typical features of ilmenite from
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Ghiorso M. S. and Sack R. O. (1991) Fe- Ti oxide geothermometry: thermodynamic formulation and
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Green D.H., and Sobolev N.V. (1975) Coexisting garnets and ilmenites synthesized at high pressures
from pyrolite and olivine basanites and their significance for kimberlite assemblages.
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Grey I.E. and Mumme W.G. (1972) The structure of CrFeTi2O7. Journal of Solid State Chemistry, 5,
168-173
Grey I.E. and Reid A.F. (1972) Shear structure compounds (Cr,Fe)2Tin-2O2n-1 derived from the α-PbO2
structural type. Journal of Solid State Chemistry, 4, 186-194.
Grey I.E., Reid, A.F., and Allpress, J.G. (1973) Compounds in the system Cr2O3-Fe2O3-TiO2-ZrO2
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Griffin W.L., Moore R.O.. Ryan C.G., Gurney J.J., and Win T.T. (1997) Geochemistry of
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Gurney J. J. and Zweistra P. (1995) The interpretation of the major element compositions of mantle
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Haggerty S.E. (1975) The chemistry and genesis of opaque minerals in kimberlites. Physics and
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Haggerty S., Hardie III R. McMahon M. (1979) The mineral chemistry of ilmenite nodule from the
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Haggerty S. E. and Tomkins L. A. (1983) Redox state of Earth's upper mantle from kimberlite
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Haggerty S.E. (1991) Oxide mineralogy of the upper mantle. In D.H. Lindsley, Ed, Oxide Minerals,
25, 355-416. Mineralogical Society of America.
Harte B., Winterburn P.A., and Gurney J.J. (1987) Metasomatic and enrichment phenomena in
garnet peridotite facies mantle xenoliths from the Matsoku kimberlite pipe, Lesotho. In M.A,
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15
Hearn B.C. (1994) Composite megacrysts and megacryst assemblages from the Williams
kimberlites, Montana, USA: Multiple products of mantle melts. In H.O, Meyer, and O.H.
Leonardos, Eds. Kimberlites, related rocks, and mantle xenoliths, 388-404.
Johnson R.E., Woermann E., and Muan A. (1971) Equilibrium studies in the system MgO-FeO-TiO2.
American Journal of Science, 271,278-292.
Jones A.P., Smith J .V . , and Dawson J.B. (1982) Mantle metasomatism in 14 veined peridotites
from Bultfontain Mine, South Africa. Journal of Geology, 90, 435-453.
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Element? Geological Society of America Abstracts with Programs, 40, 6, 515.
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Liu X. and O'Neill H. S. C. (2004) The effect of Cr2O3 on the partial melting of spinel lherzolite in the
system CaO–MgOAl2O3–SiO2–Cr2O3 at 1.1 GPa. Journal of Petrology, 45(11), 2261-2286.
Mehta A., Leinenweber K., Navrotsky A., and Akaogi M. (1994) Calorimetric study of high
pressure polymorphism in FeTiO3: Stability of the perovskite phase. Physics and Chemistry
of Minerals, 21, 207-212.
Meyer H.O., Tsai, H.-M., and Gurney, JJ. (1979) A unique enstatite megacryst with coexisting Cr-
poor and Cr-rich garnet, Weltvreden Floors, South Africa.; Proceedings of the Second
International Kimberlite Conference: The mantle sample; inclusions in kimberlites and
other volcanics,AGU, 279-291.
Mitchell R.H. (1973) Magnesian ilmenite and i t s role in kimberlite petrogenesis. Journal of
Geology 81(3), 301-311.
Mitchell R. H. (1986) Kimberlites: Mineralogy, Geochemistry and Petrology. Plenum Press, New York
and London, 440 p.
Mitchell R. H. (1995) Kimberlites, orangeites, and related rocks. Plenum Press.
Moore A.E., and Lock N.P. (2001) The origin of mantle-derived megacrysts and sheared
peridotites -evidence from kimberlites in the northern Lesotho - Orange Free State
(South Africa) and Botswana pipe clusters. South African Journal of Geology, 104, 23-38.
Moore R.O., Griffin W.L., Gurney J.J., Ryan C.G., Cousens D.R., Sie, S.H., and Suter, G.F.
(1992) Trace element geochemistry of ilmenite megacrysts from the Monastery kimberlite.
South Africa. Lithos, 29, 1-18.
Moore A. E. (1987) A model for the origin of ilmenite in kimberlite and diamond: implications for the
genesis of the discrete nodule (megacryst) suite. Contributions to Mineralogy and Petrology,
95, 245-253.
Muan A,, Hauck J., and Lofail T. (1972) Equilibrium studies with a bearing on lunar rocks.
Proceedings of the Third Lunar Science Conference, 1, 185-196.
Muan A., Hauck J., Osborn E.F., and Serialrer J.F. (1971) Equilibrium relations among phases
occurring in lunar rocks. Proceedings of the Second Lunar Science Conference, 1, 497-505.
-1.Introduction-
16
Nowell G.M., Pearson D.G., Kempton P.D., Noble S.R. Smith C.B (1999) Origin of kimberlites: A Hf
isotope perspective. Eds. 7th International Kimberlite Conference, 2, 616-624.
Pownceby M. I. and Fisher-White M. J. (1999) Phase equilibria in the systems Fe2O3-MgO-TiO2 and
FeO-MgO-TiO2 between 1173 and 1473 K, and Fe2+-Mg mixing properties of ilmenite, ferrous-
pseudobrookite and ulvöspinel solid solutions. Contributions to Mineralogy and Petrology,
135, 198-211.
Powell B.N., Weiblen P. W. (1972) Petrology and origin of lithic fragments in the Appollo 14 regolith.
Proceedings of the Third Lunar Science Conference, 1, 837-852.
Rawlinson P.J. Dawson J. B. (1979) A quench pyroxene-ilmenite xenolith from kimberlite: Implication
for Pyroxene-ilmenite intergrowth. Proceedings of the Second International Kimberlite
Conference, The mantle sample: Inclusions in kimberlites and other volcanics, AGU, 292-295.
Ringwood A.E., Lovering J.F. (1970) Significance of pyroxene-ilmenite intergrowth among kimberlite
xenolith. Earth and Planetary Science Letters, 7, 371-375.
Sauerzapf U., Lattard D., Burchard M., and Engelmann R. (2008) The Titanomagnetite-Ilmenite
equilibrium: New experimental data and thermooxybarometric application to the crystallization
of basic to Intermediate rocks. Journal of petrology, 49(6), 1161-1185.
Sobolev N.V, Kaminsky, F.V., Griffin, W.L., Yefimova, E.S., Win, T.T., Ryan, C.G., amd Botkunov,
A.I. (1997) Mineral inclusions in diamonds from the Sputnik kimberlite pipe, Yakutia. Lithos,
39, 135-157.
Schulze D. J., Anderson P.F.N., Hearn B.C. Hetman C.M. (1995) Origin and significance of ilmenite
megacrysts and macrocrysts from kimberlite. International Geology Review, 37, 780-812.
Spencer K. J. and Lindsley D. H. (1981) A solution model for coexisting iron-titanium oxides.
American Mineralogist 66, 1189-1201.
Truckenbrodt J., Ziegenbein D., Johannes W. (1997) Redox conditions in piston-cylinder apparatus; the
different behavior of the boron nitride and unfired pyrophyllite assemblies. American
Mineralogist, 82, 337-344.
Viljoen K. S., Phillips D., Harris JW., and Robinson D.N. (1999) Mineral inclusions in diamonds from
the Venetia kimberlites, Northern Province, South Africa Eds. 7th International Kimberlite
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Waters F. G. (1987) A suggested origin of MARID xenoliths in kimberlites by high pressure
crystallisation of an ultrapotassic rock such as lamproite. Contributions to Mineralogy and
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Woermann E., Brezny, B., Muan, A. (1969) Phase equilibria in the sytem MgO-iron oxide-TiO2 in air.
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Woermann E., Hirschberg A., Lamprecht A. (1970) Das System Hämatit-Ilmenit-Geikielith unter hohen
Temperaturen und hohen Drucken. Fortschritte der Mineralogie, 47, 79-80.
Withers A.C., Essene E.J., Zhang Y. (2003) Rutile/TiO2 II phase equilibria. Contribution to Mineralogy
and Petrology, 145, 199-204.
-1.Introduction-
17
Ullmann S., Woermann E. (1990) Das System MgO-FeO-SiO2-TiO2 im Druckbereich von 10-30 kbar.
Berichte der Deutschen Mineralogisches Gesellschaft, 1, 266.
Ulmer P., and Trommsdorff V. (1998) TiO2 solubility in mantle olivines as a function of
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Ulmer P. and Sweeney R. J. (2002) Generation and differentiation of group II kimberlites: Constraints
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mineralogy and geochemistry of oxide minerals in polymict xenoliths from the Bultfontain
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Zhao D., Essene E.J., and Zhang Y. (1999) An oxygen barometer for rutile-ilmenite
assemblages:oxidation state of metasomatic agents in the mantle. Earth and Planetary
Science Letters, 166, 127-137.
-2.Experimental setup-
18
2. Experimental and analytical methods 2.1 Experimental apparatus
Experiments were performed at pressure from 2.5 to 7 GPa and temperatures ranging from 1000 to
1400°C employing end loaded piston cylinders for experiments below 4 GPa and a multi-anvil device for
experiments at 5 and 7 GPa. All experiments were performed at ETH Zurich.
2.1.1Boyd and England type end-loaded piston cylinder
Experiments at 2.5 and 3.5 GPa were conducted in end-loaded solid-media apparatus (Fig. 2.1A), with
design similar to that of Boyd and England (1960). Piston diameter is 14 mm, maximum accessible
pressure 4 GPa. NaCl-pyrex assemblies were employed and a friction correction of -3% to the nominal
pressure was applied. Pressure was calibrated at 1000°C against the reaction fayalite + quartz =
orthoferrosilite (1.41 GPa, Bohlen and Boettcher, 1982) and the quartz-coesite transition (3.07 GPa, Bose
and –Ganguly, 1995). The assemblies were first pressurized to 0.4 GPa at room temperature, afterwards
heated to 500oC until the Pyrex glass softened, followed by concomitant pressure and temperature
increase to the desired target values. The temperature was increased with a rate of 50°C/minute.
Temperatures were measured with Pt94Rh6-Pt70Rh30 (B-type) thermocouples with an approximate
accuracy of +/- 5oC; no pressure effect on the EMF was taken into account. Quenching was achieved by
turning off the power supply to the furnace, resulting in a temperature drop to less than 200oC within 10
seconds.
metal frame
railAluminium/Stealcylinderthermocouple protection platetop pressure platepressure vessel(bomb)pistonbottom part 22 mmtop part 14 mmbottom presssure plate(bridge)
Boyd ram (90 tons)with WC-pushing piece
Enh-load ram(320 tons)
CO
OLI
NG
WAT
ER
HY
DR
AU
LIC
OIL
BN rod
pyrex glass cylinder
graphite cylinder
pyrex-glass cylinderNaCl cylinder
brass ringsteel cylinder (base plug)pyrophillite cylinderthermocouple sleeve (mullite)Pt-Rh thermocouple
crushable alumina
noble metal capsule
graphite disks
ruby discBN powder
A) B)
Figure 2.1 A) Cross-section of the Boyd and England type end-loaded piston cylinder. B) Cross-section of the NaCl-Pyrex-BN assembly employed in the experiments.
-2.Experimental setup-
19
The NaCl-Pyrex-BN assembly is illustrated in Figure 2.1 B. A pressed NaCl cylinder was placed around
an outer Pyrex sleeve and a cylindrical graphite heater containing an inner Pyrex sleeve filled with (i) a
crushable alumina cylinder surrounding the thermocouple and (ii) BN powder and a BN rod surrounding
the capsule and filling space below the capsule. A thin ruby disk was placed between the thermocouple
and the noble metal capsule containing the sample to avoid the rigid two-hole ceramic tube (made of
mullite) containing the thermocouple wires from penetrating the capsule. BN was used because it is
nearly impermeable to hydrogen (1GPa, 900°C) and prevents hydrogen loss from the noble metal capsule
to the surrounding atmosphere as it was established by Truckenbrodt at al. (1997). In addition, BN exerts
a low fO2 on the sample assembly avoiding oxidation of graphite containers mostly employed in this
study. The capsules were run vertically with a flat bottom facing the thermocouple. 2.1.2 Walker-type multi-anvil apparatus
Pressure plates
Pressure plates
Containment Ring(hardened tool steelAISI 13-Rc49)
Safety ring(mild steel)
Scatter shield(polycarbonate (makrolon))
Wedges(hardened tool steelAISI M2-Rc62)
Tungesten carbite cubeswth edge truncation(Hertel Grade KMY (6%CO)polished 1st edge lenght)
MgO-octahedron(with fins- Aremco584compaund)
Figure 2.2 Cross-section of the 6/8 multi-anvil module employed at the high-pressure laboratory at ETH-Zurich.
The Walker-type multi-anvil device (Walker et al. 1990) consists of a cylindrical containment ring
accommodating six wedge shaped steal anvils (1st stage anvils) compressing the faces of a large cube that
is in turn assembled from eight small (25 or 32 mm edge length) tungsten carbide cubes with triangular
truncations at the edges of 11 mm in lengths (=TEL, truncation edge length). The truncated cubes leave
an octahedral cavity in the center containing the pressure-transmitting medium. Ceramic octahedron of
18mm edge length, fabricated from a two component MgO-based castable ceramic (Aremco 584
compound) was used. In order to build up pressure the cubes are separated by gaskets, which in this
assembly are an integral part of the ceramic octahedron and, thus consist of MgO. The assembly parts,
which fit into the central, 3.5mm diameter hole of the ceramic octahedron drilled with a WC-drill bit, are
illustrated in Figure 2.3. A straight graphite cylinder (3.5 mm OD, 3.1 mm ID) is used as furnace,
supplemented with a second shorter and smaller (3.1 mm OD, 2.7 mm ID) graphite cylinder in the center
in order to decrease the electrical resistance in the center and lessen the temperature gradient. A boron
-2.Experimental setup-
20
nitride cylinder isolates the capsule from the graphite furnace. Two magnesium oxide rods are placed at
the top and at the bottom of the capsule. To allow stable electrical contact between the furnace and the
WC cubes, and to avoid electrical erosion, two molybdenum disks are placed in direct contact with the
graphite furnace.
GraphiteMolybtemum 2x
Graphite
BN
MgO
3.103.60
1.00
3.103.50
3.10
2.70
1.70
3.10
13.50
3.00
4.40
3.00
5.40
2.70
sample capsule
graphite cylinder
MgO rod
graphite cylinderBN cylinder
MgO rod
Mo disk
Mo disk
thermocouplewith Cu-coils
Figure 2.3 Graphite-MgO-BN assembly used in experiments
Temperature was measured with a Pt94Rh6-Pt70Rh30 thermocouple inserted axially into the assembly, in
direct contact with the capsule. The electromotive-force (emf) of the thermocouple was not corrected for
pressure effects. The experiments were terminated by quenching (turning off the power supplied to the
furnace); measured quenching rates are in the range of 500-700°C/sec.
2.1.3 Pressure calibration of the multi-anvil apparatus
The pressure calibration is based on relationship between applied oil pressure generating the force acting
on the multi-anvil module and the pressure acting on the sample. At room temperature conditions, such a
calibration can conveniently be done by utilizing known pressure-sensitive phase changes in metals such
as Bismuth that are characterized by sudden changes in the electrical resistance when phase
transformations are encountered. In the case of Bismuth, the transition of Bi(I) to Bi(II) occurs at 2.55
GPa, Bi(II) to Bi(III) at 3.15 GPa and the transition from Bi(III) to Bi(IV) occurs at 7.7 GPa at room
temperature (Lloyd, 1971).
-2.Experimental setup-
21
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400 500
RAM LOAD (bars)
PRES
SUR
E (k
bar)
Bi transitionCaGeO3 transition
Linear Pressure
TiO2 transitionSiO2 transition
Figure 2.4 Pressure – load diagram depicting the calibration of the 18-11 castable ceramic octahedron assembly utilized in this study
High temperature calibrations were based on the following phase transitions:
SiO2: quartz-coesite (3.2 GPa, 1200°C, Bose and Ganguly 1995);
CaGeO3: garnet-perovskite (6.1 GPa, 1200°C, Susaki et al. 1985);
TiO2: rutile-PbO2-structure (7.7 GPa, 1100°C, Akaogi et al. 1992).
Temperatures for calibration experiments were measured with Pt94Rh6-Pt70Rh30 (B-type) thermocouple
and run products analyzed by X-ray powder diffraction analysis.
2.2 Capsule design
The majority of the experiments were conducted under relatively reducing conditions by employing
graphite containers sealed into Pt-capsules. Graphite containers were used to minimize Fe-loss and to
constrain the fO2 close to the C-CO-CO2 buffer (Ulmer and Luth, 1991, Frost and Wood, 1995). The
starting material was densely packed into graphite containers machined from graphite rods that are
composed of a crucible shaped lower part and a tight fitting lid. The graphite containers were in turn
placed into Pt-capsules that were welded shut by arc-welding. Pt-tubes with outer diameter (OD) of 4 mm
-2.Experimental setup-
22
(ID 3.5mm) for piston cylinder and 1.6 mm (ID 1.4 mm) for multi-anvil experiments were used for
preparing the capsules. An equivalent capsule configuration was applied for experiments with Mo-
capsules. For runs under oxidizing conditions, a double capsule technique was used. The inner Au80Pd20
capsule with OD 2.3mm was filled with starting material, welded shut and placed into outer Pt-capsule
(OD 4mm) that contains the same starting material (Figure 2.5), following the strategy of Kägi et al.
(2004) to constrain fO2 by the intrinsic fO2 of the pre-conditioned (Fe3+/Fe2+) starting material.
Pt capsule
starting material
graphite/Mo capsule
AuPd capsule
Figure 2.5 Schematic cross-sections of the double capsule techniques used in the present study: Left – Graphite or molybdenum capsule contained in a Pt outer capsule; right – AuPd – Pt double capsule arrangement for higher fO2 experiments. In order to facilitate reaction and to promote synthesis of Fe-Ti-oxide and silicate minerals during the
experiments, moderate amounts of H2O (approximately 5 wt.%) was contained in the starting material as
a hydroxide component. Capsules were weighted before and after welding to control potential H2O-loss
during welding. To prevent evaporation of water from the capsule during welding the capsules were
wrapped with tissues soaked with deionized water. Welded capsules were weighted and placed into
acetone to check for leaks for at least 15 minutes, and then weighted again.
Every capsule contained approximately 10 mg of starting material for piston cylinder and 1-2 mg for
multi-anvil runs.
-2.Experimental setup-
23
2.3 Composition and synthesis of starting material
TiO2
FeOMgOSiO2
SiO2
ilm
opx ol
ru
A
B
C D
A: SM 2 XMg=0.73, YCr=1 (Al-free) SM 7 XMg=0.73, YCr=0.5 (Al-bearing) SM 9 XMg=0.73, YCr=0.3 (Al-bearing) SM 3 XMg=0.85, YCr=1(Al-free) SM 13 XMg=1, YCr=1 (Fe-free, Al-free)B: SM 5 XMg=0.85, YCr=1 (Al-free) SM 4 XMg=0.85, YCr=0.5 (Al-bearing) C: SM 6 XMg=0.85, YCr=1 (Al-free) SM 8 XMg=0.85, YCr=0.5 (Al-bearing) SM 12 XMg=0.73, YCr=1 (Al-free) SM 11 XMg=0.73, YCr=0.5 (Al-bearing) SM 14 XMg=1, YCr=1 (Fe-free, Al-free)D: SM 10 XMg=0.83, YCr=1 (Al-free, Si-free)
Figure 2.6 Starting compositions in the system TiO2-SiO2-(MgO+FeO), projected from Cr2O3 (Al2O3).
Starting compositions representative for ultramafic, peridotite like compositions were chosen, aiming to
access ilmenite coexisting with olivine and pyroxene at variable Fe/Mg ratios and variable fO2. The
system Mg-Fe-Ti-Cr-Si-O-H contains 7 components (assuming carbon to be nearly inert when graphite
capsules are employed), with 5 phases present in a mantle-like paragenesis: olivine, opx, spinel, ilmenite
or rutile (depending on bulk composition) and a liquid/fluid phase when H2O is present. This leaves 1
degree of freedom at fixed pressure, temperature and fO2 (set by buffering via capsule material) that
might be fixed by the Fe/Mg ratio of the bulk system. Therefore, invariant mineral composition will be
obtained in a 5 phase assemblage. For Al-bearing systems, the additional compound increases the degree
of freedom by one that can be fixed by holding the Cr/Al ratio constant.
Starting materials were prepared from pure synthetic oxides (SiO2, TiO2, Fe2O3, MgO, Cr2O3, Al2O3).
Oxides were dried at 1000oC mixed in appropriate molar proportions to obtain compositions with
different Fe/Mg ratio. Oxide mixtures were preferred over pre-synthesized mineral assemblages as they
produce considerably less zoning, in particular when fluxed by hydrous melt/fluid that are also required to
buffer fO2. Table 2.1 represents weight proportion of oxides of the starting materials employed in
different runs. For some runs iron was introduced as Fe2+ in the form of pre-synthesized fayalite to
-2.Experimental setup-
24
ensure reducing conditions. Moderate amount of water (5 w t%) were added to the starting material as
Mg(OH)2 to enhance crystallization and equilibration through a finite amount melt/fluid present at the
experimental run conditions. The oxide mixes were homogenized in an agate mortar under acetone for at
least 1 hour to obtain grain size <5µm. Table 2.1 Composition (in wt.%) of starting material used in experiments
SM2 SM7 SM3 SM4 SM5 SM6 SM8 SiO2 30.61 28.41 31.71 30.39 24.95 18.39 18.01 TiO2 11.48 11.48 12.03 11.75 21.56 30.40 30.10 MgO 26.11 26.05 31.43 30.60 29.68 27.65 27.22 FeO 16.80 16.80 9.83 10.00 8.80 8.56 8.28
Cr2O3 15.00 10.33 15.00 10.33 15.00 15.00 9.81 Al2O3 - 6.93 - 6.93 - - 6.58
100.00 100.00 100.00 100.00 100.00 100.00 100.00 XMg 0.73 0.73 0.85 0.85 0.85 0.85 0.85 Ycr 1.00 0.50 1.00 0.50 1.00 1.00 0.50
SM9 SM10 SM11 SM12 SM13 SM14 SiO2 28.41 - 17.28 17.66 33.50 19.00 TiO2 11.48 29.40 28.89 29.40 12.63 31.95 MgO 26.25 40.88 23.15 23.22 38.87 34.05 FeO 16.80 14.72 15.14 14.72 0.00 0.00
Cr2O3 6.65 15.00 9.30 15.00 15.00 15.00 Al2O3 10.41 - 6.24 - - -
100.00 100.00 100.00 100.00 100.00 100.00 XMg 0.73 0.83 0.73 0.73 1.00 1.00 Ycr 0.30 1.00 0.50 1.00 1.00 1.00
2.4 Factors controlling oxygen fugacity
In natural systems fO2 is often regarded as an independent parameter, in contrast to equilibrium
experiments (closed system), where fO2 is dependent on the water dissociation constant of the reaction
H2O=H2+1/2O2, linking the fO2 of an experimental charge to the hydrogen fugacity fH2. The ability of H2
to diffuse through noble-metal capsules has successfully been applied to control the fO2 in fluid saturated
experiments using a double capsule technique (Eugster 1957, Sisson and Grove 1993). In the absence of
an O2 and H2 buffering technique, the assembly surrounding the noble metal capsules exerts an important
control on fH2 (thus fO2), strongly influencing phase stabilities, in particular the oxidation state in Fe-
phases. However, estimates from various studies for comparable experimental setups differ significantly,
demonstrating the strong dependence of pressure and temperature on fO2. For graphite-NaCl assemblies,
estimates for fO2 range from 0.5 log units above the Ni-NiO (NNO) buffer (Carroll & Wyllie, 1989,
1990; Wolf & Wyllie, 1994) to QFM or 2 log units below the quartz-magnetite-fayalite (QFM) buffer
(Patino Douce & Johnston, 1991; Patino Douce & Beard, 1994, 1995, see also Gardien et al., 2000). The
effects of different assemblies and Fe-pre-conditioning of capsules on the fO2 and redox state in piston
cylinder experiments was discussed e.g. by Kägi et al. (2005) and Truckenbrodt et al (1997). The latter
-2.Experimental setup-
25
study concluded that boron nitride assemblies are nearly impermeable to H2 (at 1.0 GPa and 900 °C),
preventing hydrogen loss from the material in the noble-metal capsule to the surrounding assembly. Thus,
the fO2 is dominated by the "intrinsic" fO2 of the starting material rather than by the assembly. This
approach was selected to simulate very oxidizing conditions by employing oxidized starting materials (all
Fe as Fe2O3) in Au80Pd20 – Pt double capsules similar to Kägi et al. (2005).
The fO2 imposed on the charge by the graphite capsules is controlled by the equilibrium between graphite
and the sample. If a fluid phase is present, thefO2 is equal to the equilibrium value at that pressure and
temperature. If no fluid phase is present, the fO2 of the graphite-C-CO-CO2 (CCO) equilibrium is a
maximum value for the fO2 of the system.
As graphite crucibles were employed, the fO2 is constrained close to C-CO-CO2 equilibrium or more
precisely for H2O-undersaturated experiments in between the fO2 delimited by the C-CO-CO2 equilibrium
and the H2O-max on the C-COH buffer equilibria, i.e. between C-CO-CO2 and about 1 log unit below
(Ulmer and Luth 1991). Oxygen fugacity calculated by Ulmer and Luth for C-CO-CO2 at 25 kbar and
1200oC amounts to fO2=-7.92 corresponding to NNO - 1. In most experiments in graphite capsules we
employed an oxidized starting material with all Fe contained as Fe2O3 leading to reduction during the
experiment resulting in the production of CO2 (and CO) from reaction of ferric iron with graphite
according to the reaction 2Fe2O3 + C = 4FeO + CO2. This strategy, adding H2O plus employing an
oxidized starting material should actually ensure that the equilibrium fO2 during the experiments is
confined to with the relatively narrow band between the C-CO-CO2 equilibrium and H2Omax on the
graphite-COH surface that is located about 1 log unit below the CCO.
In the case of Molybdenum-Pt double capsules, experiments were conducted starting from reduced (all Fe
as Fe2+ by adding fayalite) and oxidized (all Fe as Fe3+ added as Fe2O3) in order to test the approach to
equilibrium from both sides. The fO2 for this experimental setup should be closely constrained by the Mo
+ O2 = MoO2 equilibrium located about 0.25 log units above the iron-wustite (IW) equilibrium at 1200°C
and 25 kbar.
2.5 Analytical Techniques
All recovered charges were embedded in epoxy resin and ground to expose longitudinal cross sections.
Intermittent impregnation with low viscosity epoxy resin under vacuum was done to avoid losing parts of
the fine grained charge. After grinding charges were polished with diamond paste of different grading
finishing with 1 µm
2.5.1 Electron microprobe
After inspection of the run products under the reflected light microscope they were coated with a ≈20 nm
thick carbon layer and analyzed with a JEOL JXA-8200 electron microprobe equipped with 5 wavelength
dispersive spectrometers and an energy dispersive analyzer. Acquisition parameters for quantitative
analysis were 15 kV acceleration voltage and 20 nA sample current. Natural and synthetic oxides and
-2.Experimental setup-
26
silicates were used as standards. Ten analyses were carried out for each phase in all charges Textural
relationships between the phases were studied using secondary (SE) and backscattered electron imaging
(BSE) and characteristic X-ray distribution maps
2.5.2 Powder X-ray diffraction (XRD)
Phase identification for calibration multi-anvil runs was performed by X-ray powder diffraction (XRD)
analysis. The recovered powders very finely ground and suspended with alcohol on single crystal Si-
wavers and run with a Brukker D8 powder-diffractometer. XRD patterns of calibration runs are given in
the appendix. Due to the small amount of material no XRD analyses have been attempted for the
experimental charges on the Ti-oxide - silicate experiments
2.5.3 Micro-Raman spectroscopy
Raman spectroscopy was conducted on several charges to identify mineral species, in particular to verify
the potential presence of clinohumite or other humite-type phases in charges were olivines resulted
exceptionally high TiO2 or low SiO2 concentrations and totals. Raman spectroscopy was performed with a
confocal Dilor LabRam II instrument using an external laser with a wave length of 514 nm. Spectra were
acquired for 60 to 240 s in the range 200 – 1500 cm-1 and 2800 – 3800 cm-1, the latter range
corresponding to bands related to OH-groups in the target minerals that occur around 3500 cm-1 for
clinohumite. Acquired Raman-spectra were compared with existing spectra for (hydrous) Mg-silicates
and Fe-Ti-oxides to identify the mineral species. As reported in chapter 3, we could indeed identify rare
clinohumites present in addition to olivine (and opx?) in a few experiments.
-2.Experimental setup-
27
2.6 References
Akaogi M, Susakt J.-I., Vagi T.. Matsui M., Kikegawa T., Yusa H., and Ito E. (1992) High-pressure-
temperature stability of α-PbO2-type TiO2 and MgSiO3 majorite; calorimetric and in situ
diffraction studies. In Y. Syono, and M.H. Manghnani, Eds. High Pressure Research:
Application to Earth and Planetary Sciences, 67, 447-455.
Bohlen S., R. Boetcher A.L. (1982): The quartz - coesite transformation: a precise determination and the
effects of other components. Journal Geophysics Research., 87, 7073-7078.
Bose K. Ganguly J. (1995) Quartz-coesite transitions revised: Reversed experimental determinations at
500-1200°C and retrieved thermochemical properties. American Mineralogist, 80, 231-238
Boyd F.R., England J.L. (1960) The quartz-coesite transition. Journal Geophysics Research, 65, 749-756.
Bromiley G.D., Hilaret N., and McCammon C.A. (2004) H and Fe3+ solubility in rutile and TiO2 ( I I ) :
Phase assemblages during UHP metamorphism and the role of silica polymorphs in the
lower mantle. Supplement to Lithos, 73(1-2). S34.
Carroll M.R., Wyllie P.J. (1990) The system tonalite-H2O at 15 kbar and the genesis of calc-alkaline
magmas. American Mineralogist, 75, 345-357.
Eugster H.P. (1957) Heterogeneous reactions nvolving oxidation and reduction at high pressures and
temperatures. Journal of Chemical Physics, 26, 1760-1761.
Kägi R., Muntener O. Ulmer P. Ottolini L (2005) Piston-cylinder experiments on H2O undersaturated Fe-
Bearing systems: Am experimental study approaching fO2 conditions of natural calc-alkaline
magmas. American Mineralogist, 90, 708-717.
Lloyd E.C. (1971). Accurate characterization of the high pressure environment. NBS Special Publication,
326, 1-3.
Patino Douce A.E., Beard J.S. (1994) H2O loss from hydrous melt during fluid absent piston cylinder
experiments. American Mineralogist, 79, 585-588.
Patino Douce A.E., Beard J.S. (1995) Dehydration-melting of biotite gneiss and quartz amfibolite from 3
to 15 kbar. . Journal of petrology, 36, 707-738.
Patino Douce A.E., Johnston A.D.. (1991) Phase equilibria and melt productivity in the politic system:
implication for the origin of peraluminous granitoids and aluminous granulites. Contributions to
Mineralogy and Petrology, 107, 202-218.
Sisson T.W., Grove T.L. (1993) Experimental investigation of the role of H2O in calc-alkaline
differentiation and subduction zone magmatism. Contributions to Mineralogy and Petrology,
113(2), 143-166.
Susaki J.-I., Akaogi M., Akimoto S., and Shimomura O. (1985) Garnet-perovskite transformation in
CaGeO3. In situ X-ray measurement using synchrotron radiation. Geophysical Research Letters,
12, 729-732.
-2.Experimental setup-
28
Ulmer P., Luth R.W., (1991) The graphite-COH fluid equilibrium in P, T, fO2 space; an experimental
determination to 30 kbar and 1600°C. Contributions to Mineralogy and Petrology, 106(3), 265-
272.
Walker D., Carpenter M. A., Hitch C. M. (1990). Some simplification to multianvil devices for high
pressure experiments. American Mineralogist, 75, 1010-1028.
Wolf M.B., Wyllie P.J. (1994) Dehydration melting of amphibole at 10 kbar. The effect of temperature
and time. Contributions to Mineralogy and Petrology, 115, 369-383.
-3. An experimental study-
29
3. An experimental study of picro-ilmenites in the system
TiO2-Cr2O3-FeO-Fe2O3-MgO-SiO2±Al2O3 at 2.5-7.0 GPa and 1000-1400°C
3.1 Introduction
Magnesian ilmenite (picroilmenite) is one of the prominent accessory minerals of kimberlites.
Picroilmenite occurrences and diagnostic chemistries are an important tool in prospecting of potential
diamondiferous kimberlite and lamproite pipes. The amount of ilmenite present in kimberlite varies
widely from trace quantities up to 10 wt% and the different paragenetic types can be distinguished
(Mitchell, 1986). It commonly occurs as megacrysts (>1 cm) and macrocrysts (grains significantly large
than matrix minerals and typically >0.2 cm). Ilmenite-rich xenoliths and ilmenite macrocrysts abound in
type I, non-micaceous kimberlites. These xenoliths are relatively robust in fluvial environment and are
widely used in kimberlite exploration programs because their unusual mineral chemistries can readily be
distinguished from ilmenites that area widespread in other igneous and metamorphic rocks.
The chemistries of upper-mantle derived ilmenites reflect their ultramafic source rocks: magnesium in
ilmenite is moderate to high (5-15 wt% MgO) and occurs at the expense of ferrous iron; chromium varies
as a function of depletion (<0.5-5 wt% Cr2O3) or reaction (2-12 wt% Cr2O3); and ferric iron is moderately
low in primary ilmenites (5-15 wt% hematite component) but varies considerably in reacted ilmenites (5-
30 wt % Fe2O3) (Haggerty, 1983).
Ilmenite, FeTiO3, forms a solid solution with geikielite MgTiO3 that provides the basis for
geothermometers based on the Fe2+-Mg exchange between pyroxene and ilmenite and olivine and
ilmenite.
Ilmenite megacrysts have been successfully used to constrain the oxygen fugacity through their relatively
evaluated hematite component (0.05-0.40 mole fractions, c.f. Haggerty. 1991). Haggerty & Tomkins
1983) and Arculus et al. (1994) have used ilmenites to determine the oxygen fugacity of the assemblage
that crystallized the ilmenite megacrysts. Both studies based on two different techniques (thermodynamic
phase equilibrium and intrinsic oxygen fugacity measurements using electrolyte cells respectively),
resulted in rather oxidizing conditions around the reference equilibria Ni-NiO (NNO) and fayalite-
magnetite-quartz (FMQ). Such fO2 conditions are above the (calculated) stability limit of
graphite/diamond under upper mantle conditions (3-6 GPa, 900-1200°C) that is delimited for peridotitic
rocks by the oxygen fugacity of the reaction enstatite + magnesite = olivine + diamond/graphite + O2
(EMOD/G, Eggler and Baker 1982). These results have considerable consequences for the role of the
megacrystic ilmenites in kimberlites and diamond grade evaluation: It has been suggested that the
presence of 'oxidized' ilmenites in the megacryst suite (e.g. Gurney & Zweistra, 1995) or in MARlDs (e.g.
Zhao et ah, 1999) is indicative for a rather oxidizing environment during transport or during a
metasomatic event in the cratonic root that is inferred to be the major source area of diamonds (e.g.
Mitchell, 1995).
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30
A classical application of ilmenite mineral chemistry is the 2-oxide (ilmenite-hematite solid solution
(rhombic oxides) and magnetite-ulvoespinel solid solution (cubic oxides)) thermometry - oxybarometry,
pioneered by Buddington and Lindsley (1964) with many subsequent modifications (e.g. Spencer and
Lindsley, 1981; Andersen et al., 1991; Ghiorso and Sack, 1991; Sauerzapf et al., 2004), This is an
important thermo-barometric tool for igneous (mostly volcanic) and metamorphic rocks. The calibration
and subsequent thermo dynamic treatments of this oxy-thermobarometer bases on a large experimental
dataset obtained nearly exclusively at low pressures (1 bar to 1 kbar) in the system Fe-Ti-O with later
additions for Mn bearing systems (Pownceby et al., 1987). Mantle ilmenites, i.e. megacrysts in
kimberlites, however, are Mg- and Cr-rich. Only limited information is available for the Mg-Fe-Ti-O
system containing trivalent cation other then Fe3+; high pressure data are extremely rare. However, to
extract crucial petrologic information from compositional variations observed in picro-ilmenite
megacrysts originating from kimberlites and associated rocks, it is essential to include Cr (and Al) in such
studies. Therefore, we have conducted a high-pressure experimental study to determine some of the
fundamental parameters that control occurrence and composition of oxide accessory phases in ultramafic,
but Ti and Cr-rich system.
The system Fe-Mg-Ti-Cr-(Al)-Si-O provides a useful simplification for phase equilibrium studies applied
to the Earth mantle. The experimental study reported here is conducted in peridotite like, Ti-rich systems
to specifically evaluate the behavior of Cr3+ in oxide – silicate mantle-like systems. The prime target is to
investigate the phase relations and composition of the oxide phase, in particular ilmenite, as a function of
pressure, temperature and bulk composition.
3.2 Experimental set up
3.2.1 Experimental apparatus
Experiments were performed at pressure from 2.5 to 7 GPa and temperature from 1000 to 1400 °C. All
experiments were conducted at ETH Zurich.
Experiments at 2.5 and 3.5 GPa were performed in end-loaded solid-media apparatus, with design similar
to that of Boyd and England (1960). Piston diameter is 14 mm, maximum accessible pressure 40 kbar. A
NaCl-Pyrex-BN assembly was used as it was established by Truckenbrodt at al. (1997) that BN is nearly
impermeable for hydrogen (1GPa, 900°C) and prevents hydrogen loss from the noble metal capsule to the
surrounding atmosphere. A friction correction of -3% to the nominal pressure was applied. Pressure was
calibrated at 1000°C against the reaction fayalite + quartz = orthoferrosilite (1.41GPa, Bohlen and
Boettcher, 1982) and the quartz-coesite transition (3.07 GPa, Bose and Ganguly, 1995). Temperatures
were measured with Pt94Rh6-Pt70Rh30 (B-type) thermocouples. The assemblies were first pressurized to
0.4 GPa at room, afterwards temperature was increased to about 550°C until the softening point of Pyrex
glass was reached and thereafter pressure and temperature were increased simultaneously to the desired
value The temperature was increased with a rate of 50°C/minute. Quenching was achieved by turning off
the power supply to the furnace, resulting in a temperature drop to less than 200oC within 10 seconds.
-3. An experimental study-
31
All experiments at pressure >3.5 GPa were performed in a Walker type multi-anvil apparatus (Walker et
al., 1990; Walker, 1991). The multi-anvil experiments were performed with WC cubes with truncated
edge lengths of 11 mm. The pressure transmitting octahedron and gasket fins were fabricated from MgO-
based castable ceramics (Ceramcast 584). All runs were performed with 3.5-mm outer diameter graphite
furnace assemblies. Stepped graphite heaters were used to minimize thermal gradients. Temperatures
were measured with Pt94Rh6-Pt70Rh30 (B-type) thermocouples. Pressure calibration experiments were
performed by means of the following phase transitions: quartz–coesite (3.2 GPa at 1200°C, Bose and
Ganguly, 1995; fayalite-γ-Fe2SiO4, 5.0 GPa at 1000°C, Yagi et al., 1987; CaGeO3 garnet-perovskite
transition, 6.1 GPa at 1000°C, Susaki et al., 1985; coesite-stishovite, 9.2 GPa at 1200°C, Yagi and
Akimoto, 1976; Zhang et al., 1996).
3.2.2.Analytical Techniques
All charges were embedded in epoxy resin and ground to expose longitudinal cross section. Intermittent
impregnation with low viscosity epoxy resin under vacuum was done to avoid losing parts of the fine
grained charge. After inspection of the run products on the reflected light microscope they were analyzed
with JXA-8200 electron microprobe equipped with 5 wavelength dispersive spectrometers. Acquisition
parameters were 15 kV acceleration voltage and 20 nA sample current. Natural and synthetic oxides and
silicates were used as standards. Back scattered electron (BSE) images and characteristic X-ray
distribution maps were acquired to characterize the textures of the charges.
3.2.3 Starting material and capsule design
Starting materials were prepared from pure synthetic oxides previously dried at 1000oC (SiO2, TiO2,
Fe2O3, MgO, Cr2O3, Al2O3). Table 1 represents weight proportions of oxides in the different starting
materials. Moderate amount of water (ca.5%) were added to the starting material as Mg(OH)2 to enhance
crystallization and equilibration through the presence of fluid/melt phase at the run conditions. Material
was homogenized in an agate mortar under alcohol.
Two different capsule setups were used: double graphite-Pt or Mo-Pt and Au/Pd-Pt capsules. Most of the
experiments were run under relatively reducing conditions by employing graphite containers sealed into
Pt capsule that also minimize Fe-loss resulting from alloying with the Pt and other noble metals at high
temperatures. Starting material powders were placed into graphite capsule that were put into Pt-capsule
that were closed by arc-welding. Pt-tubes with outer diameter of 4 mm for piston cylinder and 1.6 mm for
multi-anvil were employed. For experiments with Mo-capsules (more reducing conditions close to the Mo
– MoO2 equilibrium) the same technique as for graphite was applied. Au/Pd-Pt double capsules were used
for run with more oxidizing conditions: the inner Au80Pd20 capsule with 2.3OD mm was filled with
starting material, welded shut and placed into outer Pt-capsule (OD 4mm) that contains the same starting
material to minimize chemical potential gradients, in particular in hydrogen, in order to maintain fO2
conditions close to the value defined by the ferrous/ferric ration of the starting material.
-3. An experimental study-
32
Table 3.1 Starting materials used for ilmenite experiments. Iron was recalculated to Fe2O3 and added as hematite.
SM2* SM7 SM3 SM4 SM5 SM6* SM8 SiO2 30.61 28.41 31.71 30.39 24.95 18.39 18.01 TiO2 11.48 11.48 12.03 11.75 21.56 30.40 30.10 MgO 26.11 26.05 31.43 30.60 29.68 27.65 27.22 FeO 16.80 16.80 9.83 10.00 8.80 8.56 8.28
Cr2O3 15.00 10.33 15.00 10.33 15.00 15.00 9.81 Al2O3 - 6.93 - 6.93 - - 6.58
100.00 100.00 100.00 100.00 100.00 100.00 100.00 XMg 0.73 0.73 0.85 0.85 0.85 0.85 0.85 Ycr 1.00 0.50 1.00 0.50 1.00 1.00 0.50
SM9 SM10 SM11 SM12 SM13 SM14 SiO2 28.41 - 17.28 17.66 33.50 19.00 TiO2 11.48 29.40 28.89 29.40 12.63 31.95 MgO 26.25 40.88 23.15 23.22 38.87 34.05 FeO 16.80 14.72 15.14 14.72 0.00 0.00
Cr2O3 6.65 15.00 9.30 15.00 15.00 15.00 Al2O3 10.41 - 6.24 - - -
100.00 100.00 100.00 100.00 100.00 100.00 XMg 0.73 0.73 0.73 0.73 1.00 1.00 Ycr 0.30 1.00 0.50 1.00 1.00 1.00
* two different mixtures, iron added as 1) hematite Fe2O3 and 2) fayalite Fe2SiO4
3.3 RESULTS
3.3.1 Attainment of equilibrium
Phases are generally homogeneously distributed over the entire charge and homogeneous within the
crystals. Consistency between different experiments shows that most experimental products are at or
close to equilibrium. Relicts of starting material were not found. All experiments contained various
amounts of quenched liquid that could not be measured quantitatively as is forms very fine grained
feathery crystals. Table 3.2 Microprobe analyses of time-series experiments (SM12, 1200°C, 25 kbar)
Duration Run SiO2 TiO2 Cr2O3 Al2O3 FeO MgO Total xMg 12 hours NS 87 ol 39.76(27) 0.66(19) 0.59(21) 0 12.37(10) 46.73(34) 100.12 0.87 opx 55.24(359) 2.82(523) 1.25(135) 0 7.43(56) 32.82(137) 99.57 0.89 ilm 0.042(9) 51.19(70) 10.57(52) 0 24.47(13) 13.36(9) 99.63 0.49 spi 0.08(12) 7.68(58) 55.34(184) 0 24.26(54) 11.18(33) 98.55 0.45 ru 0.05(14) 90.86(36) 6.53(4) 0 0.82(7) 0.14(9) 98.41 0.24 48 hours NS 44 ol 40.12(22) 0.56(10) 0.51(10) 0 13.14(14) 48.78(31) 103.11 0.87 opx 57.12(53) 1.05(43) 0.61(10) 0 8.07(13) 34.97(37) 101.83 0.89 ilm 0.07(7) 52.91(20) 13.03(10) 0 25.21(13) 14.03(11) 105.24 0.50 spi 0.09(3) 9.29(30) 55.74(33) 0 26.10(19) 12.35(16) 103.57 0.46 ru 0.03(1) 95.99(24) 6.46(6) 0 0.74(9) 0.11(2) 103.34 0.21 96 hours NS 88 ol 39.73(46) 0.56(9) 0.49(6) 0 10.78(33) 47.92(90) 99.48 0.89 opx 56.62(39) 0.92(19) 0.68(14) 0 6.79(25) 34.54(23) 99.56 0.90 ilm 0.01(1) 50.66(22) 14.31(32) 0 21.49(10) 13.89(10) 100.36 0.54 spi 0.02(2) 8.72(41) 55.43(55) 0 22.25(13) 13.02(7) 99.44 0.51 ru 0.00(0) 93.33(43) 5.83(3) 0 0.60(10) 0.09(3) 99.87 0.22
-3. An experimental study-
33
In order to further constrain attainment of equilibrium in our experiments, time-series experiments were
conducted. The run duration were selected as 12, 48 and 96 hours (Table 3.2). The same mineral
paragenesis was obtained in all runs. The 96-hour run is characterized by slightly higher xMg, probably
as result of moderate iron loss to the Pt outer capsule through micro-cracks in the inner graphite
container. All phases show very similar composition that confirms close approach to equilibrium in our
experiments.
Additionally, we repeated an experiment by employing the resulting mineral assemblage as starting
material for a subsequent experiment. After microprobe analysis, the experimental charge was ground,
reloaded and re-run at identical experimental conditions. This approach can be regarded as an attempt to
attain equilibrium from different directions: the first experiment started from an oxide mix, the second
one used already synthesized minerals. Olivine and ilmenite reveal, within error, identical major element
compositions and Mg#, spinel slightly changed its composition (Table 3.3). The second “repeat”
experiment is characterized by higher amount of quenched liquid. This can be explained by the fact that
amount of water could not be controlled, as it was not added directly and was not measured in the initial
experiment.
In summary, above experiments confirm close attainment of equilibrium by the experimental approach
employed in our study. Table 3.3 Mircoprobe analyses of “repeat” experiments (SM6, 1200°C, 25 kbar, 49 hours)
Run Phases SiO2 TiO2 Cr2O3 Al2O3 FeO MgO Total XMg NS17 ol 40.79 0.72 0.38 0 3.15 55.78 100.82 0.97
ilm 0.02 61.03 4.52 0 8.92 26.81 101.30 0.84 spi 0.05 23.34 36.41 0 13.99 27.06 100.85 0.78
NS 71 ol 39.82 0.96 0.47 0 3.18 54.78 99.21 0.97 ilm 0.00 60.91 4.54 0 9.02 26.78 101.25 0.84 spi 0.01 19.51 42.72 0 13.15 25.63 101.02 0.78 liquid 0.01 21.41 9.07 0 3.97 41.90 76.34 0.95
3.3.2 Bulk composition and phase relations
Variable phase parageneses were observed in our experimental products. Mineral compositions of the run
products together with experimental conditions are given in Tables 3.3 and 3.4. Bulk composition has a
significant effect on phase parageneses; in particular the Mg# of the system exerts strong control on phase
stabilities.
Experiments were conducted with different bulk compositions characterized by variable Mg/Fe and Cr/Al
ratios, and different SiO2-contents. Figure 3.2 shows a ternary diagram illustrating the different starting
compositions employed in this study. A first set of experiments was conducted with a composition
corresponding to point A on Figure 3.2. For an XMg of 0.73 (SM1 and SM7, Table 3.1), the stable
paragenesis at 2.5 – 3.5 GPa is ol+opx+ilm+sp (+liquid) At 5 GPa ilmenite is no longer stable; the stable
oxide paragenesis is represented by a rutile+spinel assemblage with garnet forming an additional phase in
the Al-bearing composition (SM7). Changing XMg of the system to 0.85 (SM3, SM4) resulted in the
-3. An experimental study-
34
absence of ilmenite for both starting compositions (Al-free and Al-bearing) observed coexisting phases
are rutile + olivine + opx + spinel. The same paragenesis is observed for Fe-free compositions (SM 13).
Figure 3.1 Back scattered electron (BSE) image of one of the run products (SM2, 1200, 25); the same area is shown twice with different contrast and brightness to distinguish silicate phases (left) and oxides phases (right) respectively.
Composition A:
SM3, SM4: XMg=0.85, YCr=1, 0.5olivine, opx, spinel, rutile
SM9: XMg=0.73, YCr=0.3 (Al-bearing)P=25 kbar: olivine, opx, spinel, ilmeniteP=35 kbar: opx, garnet, spi, rutile
SM7: XMg=0.73, YCr=0.5 (Al-bearing)P=25, 35 kbar: olivine, opx, spinel, ilmeniteP>50 kbar: olivine, opx, garnet, spi, rutile
SM2: XMg=0.73, YCr=1 (Al-free)P=25, 35 kbar: olivine, opx, spinel, ilmeniteP=50 kbar: olivine, opx, spi, rutile
Composition B:SM5: XMg=0.85, YCr=1 (Al-free)olivine, opx, spinel, rutile
Composition C:SM6: XMg=0.85, YCr=1 (Al-free)P=25-70 kbar:olivine, ilmenite, spinelSM8: XMg=0.85, YCr=0.5 (Al-bearing)olivine, opx, spinel, rutile
SM12: XMg=0.73, YCr=1 (Al-free)P=25, 35, 50, 70 kbar: olivine, opx, spinel, ilmenite, rutile(P>50 kbar material without H2O)SM11: XMg=0.73, YCr=0.5 (Al-bearing)P=25 kbar: olivine, opx, rutile, ilmeniteP=35, 50 kbar: olivine, opx, garnet, spi, rutile, ilmeniteSM14: XMg=1, YCr=1 (Fe-free, Al-free)olivine, ilmenite, spinel, rutile
SM13: XMg=1, YCr=1 (Fe-free, Al-free)olivine, opx, spinel, rutile
Composition D:SM10: XMg=0.83, YCr=1 (Al-free, Si-free)P=25 kbar: spinel, MgOP=35, 50 kbar: spinel, ilmenite, MgO
FeOMgOSiO2
ilm
opx ol
ru
A
B
C D
SiO2
TiO2
Figure 3.2 Ternary diagram illustrating the starting compositions employed in the different runs, projection from Cr2O3 and Al2O3. In order to stabilize ilmenite, bulk compositions were changed toward the SiO2-poor, TiO2-rich side (Fig.
3.2, point B, SM5); however, the stable coexisting oxides paragenesis was still spi+ru. Only with a
starting material containing more than 20 wt% TiO2 and less than 20 wt% SiO2 (comp. C, SM6
(XMg=0.85)) ilmenite was observed as a stable phase. For this composition, however, opx is not stable
anymore but is replaced by the phase assemblage olivine+spinel+ilmenite that forms the stable
assemblage at all investigated pressures (2.5-7.0 GPa).
35
Table 3.4 Microprobe analyses (wt%) and experimental conditions of runs employing Pt-graphite capsules.
Run T, oC P, kbar Duration Phases SiO2 TiO2 Cr2O3 Al2O3 FeO MgO Total XMg SM2 NS4 1000 25 140 ol 39.60(18) 0.20(4) 0.44(6) 0 13.21(21) 47.15(40) 100.60 0.86
opx 56.67(31) 0.36(5) 0.60(7) 0 8.04(31) 34.14(37) 99.80 0.88 ilm 0.19(26) 53.79(102) 4.82(21) 0 28.39(55) 12.48(14) 99.67 0.44 spi 0.11(4) 4.76(46) 57.90(110) 0 26.93(32) 8.52(13) 98.22 0.36 ru 0.13(9) 92.20(86) 5.16(69) 0 1.15(7) 0.14(5) 98.78 0.17 NS7 1000 35 120 ol 39.30(16) 0.31(10) 0.57(16) 0 14.52(58) 45.31(52) 100.01 0.85 opx 56.38(62) 0.54(57) 0.65(12) 0 8.60(49) 33.13(33) 99.30 0.87 ilm 0.08(2) 54.21(27) 5.16(16) 0 28.61(32) 11.66(19) 99.73 0.42 spi 0.15(5) 4.68(57) 59.97(103) 0 25.05(68) 7.72(28) 97.59 0.35 NS3 1100 25 90 ol 39.40(19) 0.29(6) 0.56(7) 0 13.73(17) 47.00(20) 100.97 0.86 opx 56.15(36) 0.53(16) 0.63(10) 0 8.37(16) 33.96(28) 99.64 0.88 ilm 0.04(2) 51.62(26) 8.43(12) 0 26.72(15) 12.93(12) 99.74 0.46 spi 0.08(2) 6.64(88) 55.78(217) 0 26.46(75) 9.99(19) 98.96 0.40 NS9 1100 35 78 ol 38.60(32) 0.30(5) 0.57(9) 0 14.39(28) 44.94(34) 98.79 0.85 opx 55.99(37) 0.43(3) 0.61(9) 0 8.37(38) 33.15(29) 98.55 0.88 ilm 0.08(4) 52.40(77) 8.44(30) 0 26.78(47) 11.77(40) 99.48 0.44 spi 0.14(4) 6.83(35) 55.63(66) 0 25.95(67) 8.74(45) 97.29 0.38 ru 0.09(2) 89.27(119) 7.42(52) 0 0.70(9) 0.14(3) 97.62 0.26 NS1 1200 25 46 ol 39.83(12) 0.28(5) 0.41(6) 0 13.89(9) 47.14(19) 101.53 0.86 opx 56.89(19) 0.68(8) 0.47(7) 0 8.59(23) 34.29(16) 100.91 0.88 ilm 0.08(2) 49.40(41) 12.52(15) 0 25.00(11) 12.70(6) 99.70 0.48 spi 0.15(3) 9.28(21) 51.23(35) 0 26.53(15) 11.64(9) 98.83 0.44 NS6 1200 35 50 ol 39.52(31) 0.31(5) 0.51(7) 0 12.97(10) 46.65(21) 99.96 0.87 opx 56.59(20) 0.57(10) 0.59(10) 0 7.87(19) 33.87(22) 99.50 0.88 ilm 0.10(7) 48.04(36) 13.61(26) 0 25.53(25) 11.93(11) 99.21 0.45 spi 0.13(2) 7.03(140) 54.36(295) 0 25.64(120) 10.81(37) 97.97 0.43 NS2 1300 25 17 ol 39.21(17) 0.25(6) 0.54(8) 0 13.89(19) 46.74(21) 100.63 0.86 opx 56.04(17) 0.75(12) 0.69(11) 0 8.24(10) 34.09(16) 99.81 0.88 ilm 0.07(4) 46.21(46) 17.14(109) 0 24.17(20) 11.34(27) 98.94 0.46 spi 0.16(9) 10.22(33) 49.62(64) 0 26.71(31) 11.97(9) 98.68 0.44
36
Table 3.4 Continued.
Run T, oC P, kbar Duration Phases SiO2 TiO2 Cr2O3 Al2O3 FeO MgO Total XMg SM2 NS8 1300 35 26 ol 39.37(24) 0.29(5) 0.45(6) 0 12.24(13) 46.97(19) 99.31 0.87
opx 56.25(22) 0.66(8) 0.65(16) 0 7.40(12) 33.98(14) 98.94 0.89 ilm 0.11(3) 45.71(34) 23.57(31) 0 19.14(20) 10.73(7) 99.26 0.50 spi 0.16(4) 9.08(12) 54.52(51) 0 22.16(27) 12.56(15) 98.48 0.50 NS35 1200 50 30 ol 40.22(25) 0.31(10) 0.41(32) 0 7.36(117) 52.22(119) 100.51 0.93 opx 56.99(36) 0.47(17) 0.55(14) 0 6.28(99) 35.79(74) 100.08 0.91 spi 0.25(7) 6.84(364) 62.10(240) 0 16.74(104) 14.60(67) 100.54 0.61 ru 0.11(3) 87.04(43) 11.31(19) 0 0.64(10) 0.39(6) 99.49 0.52
SM7 NS31 1000 25 120 ol 39.69(57) 0.25(6) 0.34(8) 0.02(1) 14.53(32) 47.48(30) 102.31 0.85 opx 54.99(152) 0.42(4) 0.82(16) 2.63(127) 9.04(16) 33.19(62) 101.09 0.87 ilm 0.06(2) 56.10(28) 2.89(18) 0.56(2) 30.96(29) 13.05(18) 103.61 0.43 spi 0.19(20) 2.86(46) 38.00(303) 25.95(398) 23.26(120) 13.16(74) 103.42 0.50 ru 0.05(2) 95.41(106) 3.56(45) 0.54(7) 1.38(34) 0.17(12) 101.09 0.18 NS32 1000 35 110 ol 40.02(42) 0.24(5) 0.31(9) 0.02(1) 14.87(107) 47.44(85) 102.90 0.85 opx 56.14(30) 0.36(6) 0.72(13) 2.27(38) 9.29(48) 33.33(39) 102.12 0.86 ilm 0.06(3) 56.73(40) 3.00(19) 0.50(2) 32.32(33) 12.08(20) 104.67 0.40 spi 0.10(3) 2.53(30) 39.27(289) 25.81(317) 23.33(85) 12.30(60) 103.34 0.48 ru 0.06(3) 97.56(361) 1.94(210) 0.77(6) 1.50(31) 0.27(17) 102.10 0.24 NS20 1100 25 96 ol 39.41(23) 0.20(5) 0.32(7) 0.02(1) 14.99(18) 46.11(22) 101.06 0.85 opx 54.50(60) 0.64(4) 0.92(5) 2.91(76) 8.98(13) 32.45(25) 100.41 0.87 ilm 0.14(1) 52.70(26) 5.54(16) 1.03(2) 28.77(21) 12.92(10) 101.11 0.44 spi 0.10(3) 4.55(40) 36.92(173) 23.18(271) 22.33(88) 13.42(54) 100.49 0.52 NS23 1100 35 90 ol 39.51(60) 0.24(9) 0.46(48) 0.10(24) 13.13(19) 47.82(42) 101.26 0.87 opx 54.99(48) 0.61(41) 0.98(19) 2.32(33) 8.00(20) 33.75(50) 100.66 0.88 ilm 0.03(21) 54.85(51) 4.00(44) 0.85(10) 27.97(40) 13.09(35) 100.79 0.45 spi 0.19(17) 3.41(29) 38.43(268) 23.37(294) 22.68(72) 13.88(51) 101.95 0.52 ru 0.04(3) 92.76(70) 4.26(78) 0.97(17) 1.69(20) 0.16(6) 99.88 0.14 gar 39.16(255) 1.29(14) 10.81(145) 7.15(204) 11.75(51) 30.35(75) 100.51 0.82 NS29 1200 25 52 ol 40.50(30) 0.23(8) 0.26(5) 0.08(7) 14.77(20) 48.40(28) 104.25 0.85 opx 55.31(23) 0.74(5) 1.07(12) 3.11(17) 9.11(16) 33.77(21) 103.12 0.87 ilm 0.05(1) 55.17(21) 6.15(19) 1.21(2) 27.57(11) 14.50(9) 104.65 0.48 spi 0.13(2) 6.27(47) 37.97(180) 19.75(229) 23.75(33) 14.86(22) 102.73 0.53
36
37
Table 3.4 Continued.
Run T, oC P, kbar Duration Phases SiO2 TiO2 Cr2O3 Al2O3 FeO MgO Total XMg SM7 NS30 1200 35 44 ol 38.77(37) 0.23(5) 0.36(9) 0.06(2) 14.33(10) 48.20(36) 101.95 0.86
opx 53.01(187) 0.75(46) 1.12(15) 3.56(89) 9.05(66) 33.33(48) 100.83 0.87 ilm 0.05(1) 52.42(32) 8.39(10) 1.79(2) 28.29(11) 13.50(14) 104.44 0.46 spi 0.22(9) 5.69(15) 37.17(120) 20.46(129) 24.38(34) 14.84(19) 102.75 0.52 NS21 1300 25 38 ol 40.32(10) 0.23(4) 0.31(10) 0.07(1) 14.42(20) 47.33(23) 102.67 0.85 opx 54.38(43) 0.99(16) 1.22(22) 3.51(28) 8.96(28) 32.68(22) 101.73 0.87 ilm 0.14(14) 52.67(36) 9.36(23) 2.00(3) 25.31(11) 13.68(10) 103.16 0.49 spi 0.34(42) 8.68(14) 38.15(123) 16.64(98) 23.63(14) 15.10(34) 102.53 0.53 NS26 1300 35 38 ol 40.89(31) 0.23(4) 0.27(3) 0.07(1) 13.73(8) 48.74(22) 103.94 0.86 opx 55.50(34) 0.77(7) 1.22(8) 3.48(14) 8.63(8) 33.31(31) 102.90 0.87 ilm 0.09(1) 48.78(37) 13.70(31) 3.04(7) 25.40(17) 12.53(13) 103.54 0.47 spi 0.30(15) 7.68(16) 37.25(109) 18.77(88) 23.42(18) 16.11(19) 103.53 0.55 NS41 1200 50 27 ol 41.22(29) 0.25(2) 0.18(2) 0.03(1) 9.02(77) 50.98(85) 101.66 0.91 opx 56.67(38) 0.63(19) 1.10(29) 1.78(27) 6.17(100) 35.13(72) 101.48 0.91 spi 0.17(2) 4.35(70) 54.16(78) 11.87(22) 14.87(61) 17.30(41) 102.71 0.67 ru 0.10(6) 86.91(25) 10.70(9) 0.83(2) 0.74(4) 0.39(2) 99.67 0.49 gar 42.38(19) 0.96(17) 5.62(36) 19.32(32) 9.68(63) 23.54(58) 101.49 0.81
SM6 NS27 1000 25 90 ol 41.73(81) 0.79(52) 0.29(8) 0 2.16(12) 55.88(43) 100.85 0.98 ilm 0.01(1) 62.19(50) 1.24(31) 0 8.43(35) 28.54(25) 100.41 0.86 spi 0.02(2) 16.97(186) 42.55(387) 0 14.94(81) 25.40(98) 99.88 0.75 NS28 1000 35 100 ol 34.38(79) 5.78(130) 0.63(24) 0 2.42(17) 54.24(70) 97.46 0.98 ilm 0.00(0) 64.64(18) 0.90(34) 0 9.10(36) 28.23(26) 102.87 0.85 spi 0.02(1) 18.01(107) 44.50(200) 0 14.98(60) 25.14(53) 102.65 0.75 NS18 1100 25 72 ol 41.76(37) 0.79(6) 0.40(11) 0 3.01(11) 56.38(25) 102.34 0.97 ilm 0.01(1) 63.18(11) 2.51(10) 0 9.25(15) 28.09(17) 103.03 0.84 spi 0.02(1) 19.79(79) 40.81(136) 0 14.63(15) 26.09(44) 101.35 0.76 NS25 1100 35 93 ol 38.89(89) 1.49(129) 0.59(19) 0 2.93(16) 57.19(71) 101.08 0.97 ilm 0.01(1) 63.51(48) 2.85(64) 0 8.71(32) 28.36(43) 103.44 0.85 spi 0.04(2) 18.99(190) 44.56(340) 0 12.73(77) 25.76(71) 102.07 0.78 NS17 1200 25 49 ol 40.79(51) 0.72(13) 0.38(11) 0 3.15(7) 55.78(41) 100.82 0.97 ilm 0.02(1) 61.03(15) 4.52(10) 0 8.92(8) 26.81(31) 101.30 0.84 spi 0.05(1) 23.34(129) 36.41(224) 0 13.99(39) 27.06(59) 100.85 0.78
38
Table 3.4 Continued.
Run T, oC P, kbar Duration Phases SiO2 TiO2 Cr2O3 Al2O3 FeO MgO Total XMg SM6 NS22 1200 35 42 ol 41.07(28) 0.74(12) 0.38(7) 0 2.69(5) 56.28(24) 101.16 0.97
ilm 0.03(2) 61.86(23) 4.14(14) 0 8.10(12) 27.94(24) 102.06 0.86 spi 0.05(1) 21.44(114) 38.70(195) 0 13.44(39) 27.78(53) 101.42 0.79 NS19 1300 25 38 ol 34.67(147) 3.46(103) 0.90(9) 0 4.22(14) 54.05(147) 97.30 0.96 ilm 0.02(1) 60.35(29) 6.36(10) 0 7.79(6) 26.76(17) 101.28 0.86 spi 0.07(2) 26.34(41) 32.94(69) 0 11.95(12) 29.73(17) 101.03 0.82 NS24 1300 35 35 ol 40.33(84) 2.45(161) 0.40(8) 0 2.69(11) 55.46(42) 101.34 0.97 ilm 0.15(29) 60.87(119) 4.83(59) 0 7.49(17) 28.22(28) 101.57 0.87 spi 0.17(15) 29.29(119) 27.84(86) 0 12.85(19) 31.54(15) 101.68 0.81 NS81 1300 50 23 ol 39.25(94) 0.63(9) 0.33(10) 0 2.76(12) 56.29(82) 99.27 0.97 ilm 0.05(2) 55.93(41) 12.19(72) 0 8.26(8) 24.94(30) 101.37 0.84 spi 0.16(2) 18.66(109) 44.18(172) 0 10.73(52) 27.40(22) 101.13 0.82 NS37 1200 50 30 ol 41.19(31) 0.43(10) 0.12(3) 0 1.66(27) 56.58(39) 99.98 0.98 ilm 0.01(1) 61.49(47) 9.07(53) 0 3.74(13) 28.79(24) 103.10 0.93 spi 0.07(3) 10.78(278) 60.11(443) 0 4.60(28) 25.91(131) 101.47 0.91 NS49 1200 70 24 ol 41.20(18) 0.53(9) 0.26(6) 0 2.75(7) 55.87(31) 100.61 0.97 ilm 0.02(1) 54.05(86) 13.89(118) 0 9.65(14) 23.43(34) 101.05 0.81 spi 0.10(2) 16.18(231) 52.75(323) 0 10.25(70) 21.29(82) 100.57 0.79
SM3 NS11 1100 25 90 ol 39.39(104) 0.23(6) 0.39(11) 0 8.97(35) 52.39(52) 101.36 0.91 opx 59.30(55) 0.56(17) 0.58(5) 0 6.02(74) 38.08(72) 104.52 0.92 spi 0.06(4) 4.31(58) 63.92(146) 0 19.76(71) 12.67(35) 100.71 0.53 ru 0.22(35) 92.57(73) 6.60(52) 0 0.64(7) 0.25(32) 100.28 0.41 NS12 1300 25 44 ol 41.03(73) 0.33(12) 0.59(8) 0 8.09(16) 54.63(38) 104.66 0.92 opx 58.88(76) 0.81(4) 0.66(6) 0 4.93(14) 39.06(21) 104.34 0.93 spi 0.20(25) 10.20(301) 56.72(430) 0 16.38(143) 16.30(86) 99.80 0.64 ru 0.08(2) 91.69(34) 7.65(16) 0 0.41(6) 0.21(2) 100.03 0.48 NS14 1200 35 48 ol 41.02(23) 0.29(5) 0.45(9) 0 9.30(17) 50.76(14) 101.82 0.91 opx 58.31(24) 0.43(8) 0.61(12) 0 5.61(26) 36.33(27) 101.28 0.92 spi 0.08(2) 3.84(78) 64.09(222) 0 20.08(88) 11.77(28) 99.86 0.51 ru 0.06(2) 88.67(39) 8.23(14) 0 0.72(7) 0.15(2) 97.84 0.28
SM4 NS13 1200 25 48 ol 38.24(85) 0.19(6) 0.47(7) 0.04(1) 8.34(7) 52.26(27) 99.53 0.92 opx 53.28(91) 0.81(9) 1.42(20) 3.45(40) 5.04(7) 35.53(28) 99.54 0.93 spi 0.12(3) 3.96(29) 41.55(156) 25.13(119) 12.25(26) 18.09(28) 101.10 0.72 ru 0.04(3) 92.62(36) 5.19(29) 0.68(2) 0.43(4) 0.17(3) 99.13 0.41
38
39
Table 3.4 Continued.
Run T, oC P, kbar Duration Phases SiO2 TiO2 Cr2O3 Al2O3 FeO MgO Total XMg SM5 NS15 1200 25 49 ol 41.20(22) 0.40(19) 0.65(27) 0 7.00(8) 52.19(19) 101.44 0.93
opx 58.27(21) 0.85(12) 0.61(11) 0 4.46(20) 36.94(14) 101.14 0.94 spi 0.15(16) 7.45(33) 61.21(52) 0 14.75(23) 16.10(34) 99.66 0.66 ru 0.04(1) 89.11(24) 8.23(12) 0 0.38(4) 0.18(3) 97.93 0.46 NS16 1200 35 38 ol 40.13(21) 0.41(14) 0.48(11) 0 8.34(10) 52.14(40) 101.49 0.92 opx 57.08(29) 0.77(25) 0.69(11) 0 4.91(9) 36.91(17) 100.36 0.93 spi 0.13(12) 5.98(35) 62.43(66) 0 17.55(17) 13.90(11) 99.99 0.59 ru 0.03(1) 88.35(39) 9.29(9) 0 0.51(5) 0.22(1) 98.41 0.44
SM8 NS33 1200 25 50 ol 38.67(28) 0.22(4) 0.26(5) 0.06(1) 17.18(25) 46.01(18) 102.40 0.83 opx 52.04(78) 0.96(20) 1.02(6) 4.94(43) 10.38(19) 31.48(24) 100.82 0.84 ilm 0.06(2) 55.73(47) 3.77(12) 1.45(2) 29.97(17) 13.50(13) 104.48 0.45 spi 0.24(15) 4.26(22) 24.71(101) 35.24(127) 21.54(39) 16.32(30) 102.30 0.57 NS42 1200 35 48 opx 55.84(33) 0.53(5) 1.02(11) 3.30(37) 7.42(33) 34.21(35) 102.32 0.89 gar 42.95(22) 0.87(20) 3.28(30) 21.37(20) 10.25(57) 24.08(38) 102.79 0.81 ru 0.05(2) 93.06(36) 6.41(3) 0.77(2) 0.89(6) 0.14(1) 101.32 0.21 spi 0.12(2) 3.35(32) 44.61(78) 20.69(34) 18.59(26) 16.37(15) 103.72 0.61
SM9 NS34 1200 25 52 ol 40.85(30) 0.57(15) 0.35(6) 0.07(3) 9.41(11) 51.26(32) 102.53 0.91 spi 0.18(4) 6.22(89) 37.87(80) 23.92(61) 15.97(25) 18.58(25) 102.74 0.67 ru 0.05(3) 95.78(37) 4.18(6) 0.58(4) 0.61(5) 0.17(6) 101.38 0.34 NS40 1200 35 47 ol 40.89(21) 0.52(15) 0.28(8) 0.05(2) 9.03(10) 51.25(54) 102.02 0.91 spi 0.14(1) 4.26(26) 36.45(256) 27.55(272) 15.33(58) 18.80(44) 102.52 0.69 ru 0.04(1) 93.02(56) 5.62(11) 0.92(2) 0.89(6) 0.28(2) 100.76 0.35
SM10 NS38 1200 25 50 spi 0.00(1) 32.77(326) 19.77(546) 0 15.79(52) 34.46(149) 102.79 0.80 MgO 0.00(30) 0.77(61) 1.23(30) 0 12.32(17) 88.59(75) 102.91 0.93 NS39 1200 35 44 ilm 0.00(1) 64.48(30) 1.69(27) 0 8.41(47) 28.98(34) 103.56 0.86 spi 0.00(1) 30.05(194) 23.50(373) 0 17.43(183) 32.62(86) 103.59 0.77 MgO 0.00(5) 0.68(11) 1.64(7) 0 14.41(43) 84.17(122) 100.91 0.91 NS36 1200 50 25 ilm 0.00(0) 64.03(17) 3.08(13) 0 8.06(16) 28.74(12) 103.91 0.86 spi 0.00(1) 23.36(315) 37.74(551) 0 11.67(197) 30.18(115) 102.94 0.82 MgO 0.00(1) 0.62(15) 2.07(8) 0 13.09(67) 87.06(87) 102.84 0.92
SM12 NS56 1000 25 120 ol 39.78(16) 0.62(15) 0.40(6) 0 12.28(62) 47.30(55) 100.38 0.87 opx 56.84(25) 0.68(9) 0.55(13) 0 7.57(21) 33.99(43) 99.63 0.89 ilm 0.06(7) 54.56(65) 5.43(12) 0 27.01(43) 13.52(73) 100.57 0.47 spi 0.06(2) 4.28(166) 64.64(402) 0 22.78(194) 8.65(39) 100.40 0.40
40
Table 3.4 Continued.
Run T, oC P, kbar Duration Phases SiO2 TiO2 Cr2O3 Al2O3 FeO MgO Total XMg SM12 NS56 1000 25 ru 0.03(2) 93.89(220) 4.09(232) 0 1.00(21) 0.17(6) 99.17 0.23
NS55 1000 35 110 ol 39.85(59) 0.69(31) 0.60(29) 0 11.51(14) 49.42(77) 102.07 0.88 opx 57.23(85) 0.94(65) 0.68(47) 0 6.78(43) 35.59(27) 101.22 0.90 ilm 0.20(26) 51.47(109) 7.03(38) 0 27.45(52) 13.58(56) 99.73 0.47 spi 0.07(10) 4.65(134) 63.47(244) 0 23.88(129) 8.99(55) 101.05 0.40 ru 0.08(13) 90.87(228) 5.63(234) 0 1.42(29) 0.24(13) 98.25 0.23 NS61 1000 50 50 ol 39.87(18) 0.66(23) 0.44(11) 0 10.38(13) 49.54(18) 100.88 0.89 opx 57.18(12) 0.56(15) 0.51(9) 0 6.14(38) 35.28(29) 99.67 0.91 ilm 0.12(10) 51.51(134) 9.11(145) 0 25.97(30) 13.62(38) 100.33 0.48 spi 0.21(13) 4.75(92) 61.40(206) 0 23.98(130) 9.92(37) 100.26 0.42 ru 0.32(74) 91.73(300) 4.31(330) 0 1.58(35) 0.45(51) 98.39 0.34 NS57 1100 25 100 ol 37.62(87) 0.52(11) 0.41(7) 0 12.45(16) 48.13(14) 99.13 0.87 opx 54.77(72) 0.68(57) 0.65(16) 0 7.00(14) 35.21(54) 98.41 0.90 ilm 0.05(3) 53.09(173) 8.50(21) 0 25.03(86) 13.81(36) 100.49 0.50 spi 0.06(2) 5.91(140) 59.88(305) 0 24.27(118) 10.44(27) 100.56 0.43 ru 0.04(2) 92.78(36) 5.33(6) 0 0.71(10) 0.10(2) 98.95 0.20 NS59 1100 35 48 ol 38.14(38) 0.67(20) 0.41(8) 0 11.42(18) 48.91(22) 99.54 0.88 opx 54.41(78) 1.37(9) 0.82(18) 0 6.92(13) 35.11(34) 98.63 0.90 ilm 0.07(3) 50.34(25) 10.54(13) 0 25.58(18) 13.36(22) 99.88 0.48 spi 0.09(2) 6.39(56) 57.73(45) 0 25.29(20) 10.41(13) 99.91 0.42 ru 0.05(1) 89.77(41) 7.22(15) 0 0.94(10) 0.15(2) 98.12 0.22 NS44 1200 25 48 ol 40.12(22) 0.56(10) 0.51(10) 0 13.14(14) 48.78(31) 103.11 0.87 opx 57.12(53) 1.05(43) 0.61(10) 0 8.07(13) 34.97(37) 101.83 0.88 ilm 0.07(7) 52.91(20) 13.03(10) 0 25.21(13) 14.03(11) 105.24 0.50 spi 0.09(3) 9.29(30) 55.74(33) 0 26.10(19) 12.35(16) 103.57 0.46 ru 0.03(1) 95.99(24) 6.46(6) 0 0.74(9) 0.11(2) 103.34 0.21 NS45 1200 35 48 ol 39.88(77) 0.72(25) 0.78(87) 0 12.82(14) 49.08(31) 103.28 0.87 opx 57.92(76) 0.78(25) 0.81(18) 0 7.74(23) 35.68(27) 102.93 0.89 ilm 0.09(15) 52.07(43) 13.51(23) 0 26.18(41) 13.51(50) 105.35556 0.48 spi 0.09(2) 7.48(28) 59.03(89) 0 25.91(44) 11.40(31) 103.90633 0.44 ru 0.04(1) 93.93(26) 7.96(28) 0 0.82(12) 0.12(3) 102.8732 0.21
40
41
Table 3.4 Continued.
Run T, oC P, kbar Duration Phases SiO2 TiO2 Cr2O3 Al2O3 FeO MgO Total XMg SM12 NS65 1300 35 28 ol 40.59(13) 0.49(11) 0.35(7) 0 9.34(11) 50.17(12) 100.9277 0.90
opx 57.55(44) 0.73(9) 0.45(9) 0 5.44(19) 35.84(39) 100.012 0.92 ilm 0.04(3) 45.07(171) 20.74(157) 0 20.67(50) 13.20(43) 99.715 0.53 spi 0.85(46) 6.33(210) 58.44(261) 0 20.54(96) 13.63(163) 99.77453 0.54 ru 0.04(2) 93.57(40) 5.11(12) 0 0.57(9) 0.06(6) 99.36244 0.16 NS52 1200 50 24 ol 40.58(38) 0.61(13) 0.54(9) 0 10.36(58) 49.58(64) 101.66313 0.90 opx 57.58(53) 0.93(36) 0.67(18) 0 6.23(44) 36.13(34) 101.54728 0.91 ilm 0.10(15) 45.67(98) 25.75(79) 0 17.83(93) 11.40(66) 100.75496 0.53 spi 0.16(5) 9.78(345) 57.91(289) 0 21.89(201) 11.58(151) 101.32267 0.49 ru 0.05(4) 85.70(42) 11.12(29) 0 0.67(5) 0.24(10) 97.77427 0.39 NS62 1200 70 27 ol 39.78(61) 1.01(99) 0.59(58) 0 8.47(35) 50.81(136) 100.66602 0.91 opx 57.17(29) 0.56(10) 0.52(6) 0 5.30(19) 36.66(15) 100.21804 0.93 ilm 0.12(8) 41.58(232) 24.02(357) 0 21.83(70) 12.04(81) 99.58939 0.50 spi 0.31(17) 4.30(59) 63.65(155) 0 19.98(36) 12.47(37) 100.7117 0.53 ru 0.09(1) 86.13(28) 10.01(21) 0 1.41(3) 0.36(3) 98.01 0.32 NS60 1300 25 48 ol 37.75(38) 0.50(8) 0.51(5) 0 10.00(10) 50.33(16) 99.09 0.90 opx 54.60(44) 1.12(6) 0.55(4) 0 6.01(5) 36.19(12) 98.47 0.91 ilm 0.07(2) 47.02(29) 23.27(15) 0 17.30(12) 12.73(10) 100.39 0.57 spi 0.13(2) 9.88(13) 55.59(34) 0 19.97(22) 14.74(15) 100.30 0.57
SM11 NS66 1200 25 48 ol 38.98(28) 0.46(10) 0.35(12) 0.05(3) 12.35(10) 48.00(27) 100.20 0.87 opx 53.22(27) 0.92(13) 1.12(10) 3.56(26) 7.48(8) 33.11(18) 99.40 0.89 ilm 0.01(1) 54.74(31) 5.80(21) 1.28(3) 23.04(14) 14.93(15) 99.79 0.54 ru 0.01(2) 92.48(26) 4.48(7) 0.66(3) 0.53(7) 0.15(3) 98.31 0.33 liq 24.48(289) 1.20(33) 0.26(11) 15.15(102) 11.59(72) 11.75(71) 64.43 0.64 NS67 1200 35 44 ol 40.07(22) 0.57(13) 0.32(5) 0.08(4) 9.88(11) 49.72(22) 100.63 0.90 opx 55.08(34) 0.73(5) 1.12(11) 3.33(14) 6.29(32) 33.75(40) 100.31 0.91 ilm 0.04(2) 52.97(39) 7.86(26) 1.92(2) 22.06(21) 15.83(22) 100.68 0.56 spi 0.16(3) 4.30(29) 38.12(91) 24.06(76) 17.27(32) 17.02(20) 100.93 0.64 ru 0.02(2) 93.33(33) 4.26(8) 0.71(2) 0.84(8) 0.12(3) 99.27 0.63 gar 41.99(0) 0.86(0) 3.13(0) 21.46(0) 8.38(0) 24.25(0) 100.07 0.84 NS70 1200 50 28 ol 40.76(102) 0.59(9) 0.32(4) 0.06(6) 8.53(24) 50.71(93) 100.97 0.91 opx 56.44(36) 0.73(20) 1.02(19) 1.36(20) 5.75(13) 35.14(22) 100.44 0.92 ilm 0.04(2) 41.80(305) 21.12(356) 2.14(48) 21.96(36) 12.58(97) 99.63 0.51 spi 0.16(3) 6.07(203) 51.23(158) 9.51(44) 19.11(16) 14.99(20) 101.07 0.58
42
Table 3.4 Continued.
Run T, oC P, kbar Duration Phases SiO2 TiO2 Cr2O3 Al2O3 FeO MgO Total XMg SM11 NS70 1200 50 ru 0.04(1) 92.52(14) 5.10(17) 0.35(3) 0.73(10) 0.07(4) 98.81 0.14
gar 41.66(61) 1.33(67) 4.84(60) 19.46(53) 8.28(74) 24.28(90) 99.85 0.84 SM13 NS47 1200 25 48 ol 42.92(16) 0.22(6) 0.48(7) 0 0 56.78(61) 100.39 1
opx 59.87(37) 0.58(5) 0.67(8) 0 0 39.36(33) 100.48 1 spi 0.12(9) 3.17(25) 74.48(47) 0 0 23.58(16) 101.34 1 ru 0.08(9) 91.36(24) 9.29(7) 0 0 0.19(9) 100.92 1 NS48 1200 35 48 ol 42.77(38) 0.27(9) 0.56(13) 0 0 57.72(22) 101.31 1 opx 60.18(17) 0.45(4) 0.75(8) 0 0 40.04(32) 101.42 1 spi 0.10(3) 3.31(101) 74.45(110) 0 0 23.29(39) 101.15 1 ru 0.26(61) 90.71(109) 8.90(34) 0 0 0.20(26) 100.06 1 NS46 1200 50 27 ol 42.62(28) 0.45(34) 0.48(8) 0 0 57.28(50) 100.83 1 opx 59.99(35) 0.41(9) 0.78(41) 0 0 40.19(45) 101.37 1 spi 0.42(50) 4.50(239) 72.87(206) 0 0 23.25(127) 101.04 1 ru 0.06(2) 82.17(86) 15.91(64) 0 0 0.32(11) 98.46 1 NS53 1200 70 23 ol 42.31(122) 0.25(7) 0.39(4) 0 0 56.82(121) 99.78 1 opx 58.85(38) 0.35(8) 0.69(12) 0 0 39.86(60) 99.74 1 spi 0.13(5) 17.91(217) 71.61(366) 0 0 9.37(113) 99.03 1 ru 0.20(20) 83.58(102) 12.83(62) 0 0 0.46(48) 97.07 1
SM14 NS51 1200 25 48 0l 41.06(29) 0.52(13) 0.32(4) 0 0 58.47(19) 100.36 1 ilm 0.06(6) 59.02(79) 11.98(30) 0 0 30.16(54) 101.22 1 spi 0.08(1) 6.53(68) 69.03(95) 0 0 25.91(55) 101.54 1 ru 0.03(1) 90.17(33) 7.69(4) 0 0 0.28(4) 98.16 1 NS68 1200 35 48 ol 40.72(15) 0.54(7) 0.31(5) 0 0 57.27(12) 98.84 1 ilm 0.06(9) 58.43(36) 11.20(15) 0 0 29.53(48) 99.22 1 spi 0.05(3) 5.50(49) 69.66(58) 0 0 24.24(30) 99.45 1 ru 0.01(1) 88.00(27) 8.63(20) 0 0 0.34(5) 96.98 1 NS54 1200 50 20 ol 41.90(18) 0.54(5) 0.35(7) 0 0 57.94(16) 100.72 1 ilm 0.08(11) 59.07(58) 12.46(82) 0 0 29.97(47) 101.59 1 spi 0.11(5) 4.91(93) 72.58(145) 0 0 24.61(75) 102.21 1 ru 0.05(7) 86.77(83) 11.58(63) 0 0 0.61(9) 99.01 1
Total iron reported as FeO. XMg=Mg/(FeO+MgO) (molar) Units in parentheses indicate standard errors (2σ) from average analysis. Accordingly, 59.07(5) should be read as 59.07 wt%±0.05.
42
-3. Experimental study-
43
The same low-SiO2 composition but with a lower XMg (0.73) (SM12) is characterized by the presence of
three oxides: ilmenite + rutile + spinel coexisting with olivine and opx. This assemblage is, again, stable
over the entire pressure range. However, for pressures higher than 5 GPa H2O-free starting material was
employed because the use of H2O-bearing starting materials at high pressures resulted in strong zonation
of the charges (Fig. 3.3), even using the “shaking” multi-anvil device (Schmidt & Ulmer, 2004), and, in
addition, ilmenite was not stable in the H2O-bearing runs.
Figure 3.3 Backscattered electron images of run products of experiments employing H2O-bearing SiO2-poor starting materials resulting in strong zonation: SM12, 1200oC, 50 kbar, left panel - experiment conducted in the “shaking” multi-anvil device; right panel – static multi-anvil experiment. In an Al-bearing, silica-poor, TiO2-rich system (SM11) garnet is observed at pressures of 3.5 and 5 GPa.
For Al-bearing starting material with an XMg=0.85 (SM8, composition C) ilmenite is not stable; the
observed paragenesis is ol + opx + spi + ru.
In SiO2-free experiments (composition D, SM10) ilmenite is only stabilized at pressure exceeding 3.5
GPa. Additional phases are spinel and periclase with high iron contents (ferripericlase).
3.3.3 Effect of different oxidizing condition on phase assemblages
In order to test the effects of variable oxygen fugacity on phase assemblages and mineral compositions,
experiments were conducted in Pt-Mo and Pt-Au/Pd capsules employing two different starting materials,
SM 2 and SM 6 (Table 3.1) representing high and low SiO2 and TiO2 contents and XMg of 0.73 and 0.85
respectively. In order to impose high and low fO2 conditions and/or to approach equilibrium from
oxidizing and reduced conditions, starting materials with the same proportion of compounds was prepared
but iron was added as fayalite instead hematite resulting in only Fe2+ instead of Fe3+ in the starting
material. The results of these series of experiments targeted to investigate the effect variable oxygen
fugacity are listed in Table 3.5.
-3. Experimental study-
44
Table 3.5 Electron microprobe analyses of run products of experiments conducted in Mo and Au/Pd capsules , at 1200°C and 25 kbar, duration ≈48 hours (results of experiments conducted in graphite capsules are listed for comparison). FeO and XMg: all Fe as a Fe2+.
Sample Phase SiO2 TiO2 Cr2O3 FeO MgO Total XMg SM 6 NS-17 ol 40.79 0.72 0.38 3.15 55.78 100.82 0.97
Pt-graphite ilm 0.02 61.03 4.52 8.92 26.81 101.30 0.84 spi 0.05 23.34 36.41 13.99 27.06 100.85 0.78 NS-80-6 ol 40.43 0.71 0.36 2.78 55.10 99.38 0.97 Pt-Mo ilm 0.01 61.85 3.25 7.41 27.49 100.01 0.87 Fe as hematite spi 0.04 24.31 33.13 11.52 28.13 97.13 0.81 NS-83-16 ol 39.70 0.39 0.36 7.35 52.18 99.99 0.93 Pt-Mo spi 0.07 8.79 55.71 17.20 15.63 97.40 0.62 Fe as fayalite ru 0.07 70.83 4.69 0.45 0.21 76.24 0.46 NS-74 ol 41.40 0.24 0.04 1.58 56.23 99.49 0.98 Pt-Au/Pd ilm 0.03 61.23 3.54 6.94 28.76 100.50 0.88 spi 0.07 20.54 36.11 14.11 29.07 99.90 0.79
SM 2 NS-1 ol 39.83 0.28 0.41 13.89 47.14 101.53 0.86 Pt-graphite opx 56.89 0.68 0.47 8.59 34.29 100.91 0.88 ilm 0.08 49.40 12.52 25.00 12.70 99.70 0.48 spi 0.15 9.28 51.23 26.53 11.64 98.83 0.44 NS-80-2 ol 38.53 0.15 0.55 16.06 44.21 99.51 0.83 Pt-Mo opx 55.68 0.50 0.58 9.16 32.93 98.85 0.87 Fe as hematite spi 0.13 9.65 46.87 27.30 9.85 93.79 +Mo 0.39 ru 0.05 53.58 5.54 1.08 0.15 60.40 +Mo 0.20 NS-83-15 ol 38.51 0.24 0.58 16.11 45.07 100.51 0.83 Pt-Mo opx 55.90 0.56 0.59 9.56 33.11 99.72 0.86 Fe as fayalite spi 0.23 10.16 46.67 27.80 10.11 94.96 +Mo 0.39 ru 0.10 59.77 5.90 2.02 0.42 68.21 +Mo 0.27 NS-72 opx 57.59 0.43 0.38 4.35 36.78 99.52 0.94 Pt-Au/Pd ilm 0.03 34.13 23.08 29.97 10.18 97.40 0.38 spi 0.08 4.24 53.09 26.60 14.11 98.12 0.49
The bulk XMg has a significant effect on the influence of the oxygen fugacity on the stability of the
phases. The composition with lower Mg# (XMg=0.73), i.e. the containing more iron, is more sensitive to
change of the oxidizing environment. More oxidizing condition (Pt-Au/Pd capsules compare to Pt-
graphite) result in the disappearance of olivine and increasing Mg# of opx (from 0.87 to 0.94). In contrast,
the (apparent) XMg of ilmenite decreases but it becomes more Cr-rich (23 wt%) (NS72). Spinels are
characterized by slight increase of XMg; other components stay almost the same. Analysis of capsule walls
close to the charge indicates that iron contents do not exceed 0.2 wt% FeO consistent with very oxidizing
conditions
-3. Experimental study-
45
Figure 3.4 Backscattered electron (BSE) images of run products in Mo-capsules (NS83, 1200oC, 25 kbar)
Experiments in Mo-capsules exerting oxygen fugacities close to the Mo-MoO2 equilibrium exhibit
disappearance of ilmenite and appearance of rutile, silicate phases stay generally the same. Low Mg
(higher Fe) starting composition turns out to be reactive to the Mo capsule material: spinels contain up to
7 wt% of MoO2 and rutile (or another TiO2-polymorph/solid solution) – up to 40 wt% MoO2. On Figure
3.4 the growth of Mo crystals is clearly recognizable. These experiments could not be used to evaluate the
effect of reducing conditions on the mineral chemistry. However, this problem was not encountered for
starting compositions with the higher XMg of 0.85 (SM6). No contaminations with capsule material were
observed and phase paragenesis did not change. Spinel slightly changed composition towards the more
magnesian side; olivine and ilmenite remain the same. In experiments with Pt-Au/Pd capsules, phase
paragenesis remained constant and only ilmenite characterized by slightly increased XMg changed its
composition: changes in other components were negligible. For Mo-capsules there is a distinct effect of
bulk Fe2+- Fe3+.
Generally, different oxidizing conditions (different capsule material) did not have significant effects, but
we have to keep in mind that in addition we have external fO2 control imposed by the assembly
surrounding the noble capsule (BN) that tends to result rather low fO2 conditions and might have strongly
affected the results of the AuPd-Pt double capsule experiments.
3.3.4 Phase compositions
3.3.4.1 Ilmenite
Ilmenite obtained in the experiments is characterized by compositions corresponding to kimberlitic
ilmenite. In Figure 3.5 ilmenites from experimental runs employing different starting materials are plotted
together with natural ilmenites obtained from kimberlites using divalent (FeO+MgO), trivalent
(Fe2O3+Cr2O3 (+Al2O3)) and tetravalent (TiO2) oxides. Ilmenites from starting materials with XMg=0.73
completely overlap with natural data. Experimental ilmenites obtained from experiments employing
starting material with higher Mg# (0.85) are characterized by more magnesian ilmenite.
-3. Experimental study-
46
0.0 0.2 0.4 0.6 1.0
0.6
0.8
1.0 0.0
0.2
0.6
0.0
0.2
0.4
TiO2 MgTiO3 FeTiO3
R2O3
RO0.8
R2O3 SM 12SM 6SM 2Monastery Diatreme(Haggerty et al., 1979)kimberlitic ilmenite(Wyatt, 1979)Frank Smith Mine(Pasteris, 1979)
Figure 3.5 Ternary diagram illustrating the composition of experimental and natural ilmenites expressed as major elements using combined divalent (FeO+MgO), trivalent (Fe2O3+Cr2O3 (+Al2O3)) and tetravalent (TiO2) oxides in wt.%.
Ilmenite compositions systematically exhibit high and increasing Cr contents with increasing temperature
and pressure, reaching up to 25 wt% in experiments with XMg=0.73 in Al-free systems, values not
commonly observed in natural picro-ilmenite samples from kimberlites and other mantle xenoliths (Fig.
3.6). The incorporation of Cr is counter-balanced by decreasing Ti contents (Fig. 3.6) implying a coupled
substitution: (Fe2+,Mg)Ti = 2 Cr. Figure 3.7 clearly indicates that this exchange mechanism is dominating
in the absence of Al; Fe3+ (recalculated) is nearly constant and does not really contribute to the exchange
reaction. For compositions with high XMg (0.85) ilmenites are enriched in Ti and contain considerably
lower concentration of Cr. The pressure effect is negligible in the range 25-35 kbar. However, for
experiments at 50 and 70 kbar, a positive effect of pressure on Cr concentrations is observed, whereas Ti
concentrations decrease with increasing pressure.
-3. Experimental study-
47
ilmeniteXMg=0.73
ilmeniteXMg=0.85
ilmeniteXMg=0.73
ilmeniteXMg=0.85
ilmeniteXMg=0.73
ilmeniteXMg=0.73
a)
b)
c)
Figure 3.6 Compositional variations of ilmenites in Al-free systems as a function of temperature and pressure: a) SM2, b) SM12, c) SM6.
-3. Experimental study-
48
Fig 3.7. Compositional variation of ilmenite for SM2 as a function of pressure and temperature in cations per formula unit (p.f.u.) iluustrating the Cr-Ti substitution mechanism
In Al-bearing systems, the concentration of aluminum in ilmenites is positively correlated with pressure
and temperature; it however, amounts to less than 3 wt% (Fig. 3.8) and the pressure effect on the
concentration of Al is minor in the range 25 to 35 kbar. Addition of Al to the system results in decreased
amounts of Cr in the ilmenite solid solution (max. 14 wt% at the highest pressure as opposed to 23 %
Cr2O3 in the corresponding Al-free system) but the Cr concentration became distinctly pressure sensitive
(Fig. 3.8). Ferric iron content was calculated from electron microprobe analysis assuming perfect
stoichiometry and charge balance. As our experiments were conducted under reducing conditions Fe2O3
does never exceed 6 wt% and results 0 for some experiments.
Figure 3.8 Al and Cr concentrations of ilmenites for the Al-bearing composition SM7. In general, increasing temperature results in enrichment of trivalent cations. This feature is very well
illustrated in the ternary diagrams using calculated end-member compositions for ilmenites (Fig. 3.9).
This diagram also illustrates that increasing pressure results in decreasing MgTiO3 component.
-3. Experimental study-
49
XMg=0.73,YCr=0.5
0.0 0.2 0.4 0.6 0.8 1.0
0.6
0.8
1.0 0.0
0.2
0.4
MgTiO3FeTiO3
Fe2O3+Cr2O3+Al2O3 Fe2O3+Cr2O3+Al2O3
0.0 0.2 0.4 0.6 0.8 1.0
0.6
0.8
1.0 0.0
0.2
0.4
MgTiO3FeTiO3
Fe2O3+Cr2O3 Fe2O3+Cr2O3
25 kbar35 kbar
XMg=0.73,YCr=1
Figure 3.9 Ilmenite compositions expressed as endmember components as a function of pressure and temperature for compositions SM2 and SM7 (arrows indicate temperature increasing). 3.3.4.2 Spinel.
Spinels are present in all experimental products. They are represented by Ti-bearing to Ti-rich chromites
in the Al-free experiments and by Ti-bearing picotites in the Al-bearing systems. The general
characteristic is decreasing Cr and increasing Ti contents with increasing temperature. There is, however,
no simple correlation with pressure. For the composition with XMg=0.73 and high SiO2 content (SM2, Fig
3.10(a)) 25- and 35- kbar isobars are distinguished, but for the composition with identical XMg but lower
SiO2 concentration (SM12, Fig 3.10(b)), we observe a cross over for 25 and 35 kbar with increasing
temperature and the effect at even higher pressures (50 and 70 kbar) is not so pronounced. For a
composition with XMg =0.85 (SM6, Fig 3.10(c)) the effect of high pressure is more evident: with
increasing pressure spinel contains less Ti and more Cr. The one experiment at 70 kbar, however, does
not conform to this general trend and it is not clear to date if this is an experimental artifact or does indeed
reflect the real behaviour of spinel coexisting with olivine and ilmenite. .
Bulk XMg clearly exerts a strong control on the composition of spinel; for a composition with XMg=0.85
spinel contains higher amounts of Ti and lower amounts of Cr at any given pressure and temperature. Its
composition is actually close to the ulvoespinel - chromite join and can be identified as qandelite with the
general formula (Mg,Fe2+)2(Ti,Cr)O4, but with large amounts of Cr instead of ferric iron due to the Cr-
rich nature of the system and the low fO2 of these experiments not allowing for appreciable amounts of
ferric iron.
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50
In presence of Al (SM7), the Cr contents of spinels remain nearly constant over the investigated
temperature range at 25 and 35 kbar coexisting with olivine, opx, ilmenite ± rutile , the Al-content
decreases with increasing temperature and appears slightly pressure dependant with increasing Al-content
at the highest temperatures from 25 to 35 kbar. The decrease of Al is counterbalanced by an increase in
Mg+Ti implying a coupled exchange Al2O3 = Ti + Mg. At 50 kbar, spinel coexists with rutile and no
longer with ilmenite and results much higher Cr-content, whereas the Al, Ti and Fe-contents are
decreased (Fig. 3.11).
spinelXMg=0.73
spinelXMg=0.73
spinelXMg=0.73
spinelXMg=0.73
spinelXMg=0.85
spinelXMg=0.85
a)
b)
c)
Figure 3.10 Compositional variations of spinels with pressure, temperature and XMg, a) SM2, b) SM12, c) SM6
-3. Experimental study-
51
Figure 3.11 Composition of spinels from Al-bearing starting material (SM7). 3.3.4.3 Rutile.
Rutiles are characterized by high Cr contents - 5-10 wt% - other components are usually present in
concentrations of less than 1 wt%. Figure 3.12 illustrates variations of rutile compositions as a function of
pressure and temperature for starting material SM12. It is evident, that increasing pressure (at least to 50
kbar) leads to a decrease of the Ti and an increase of the Cr content. Recalculated ferric iron (Fe3+)
contents likewise increase with increasing pressure, but decrease with temperature: this might be related
to increasing fO2 on the C-COH equilibrium with increasing pressure and decreasing temperature relative
to metal – oxide equilibria like Ni-NiO or FeO-Fe3O4 resulting in increasing Fe3+ content in the
assemblage. It should, however be noted that all iron is recalculated as Fe3+ clearly influenced by the fact
that these rutiles must be non-stoichiometric or more likely contain appreciable amounts of OH in their
structure. The substitution of Ti by Cr and basically nothing else (the ratio of Cr / (Sum of all other
cations except Ti and Cr) is in the order of 3-7, Cr is responsible for 80-88% of the “missing” Ti. The Cr
– Ti exchange is not isovalent, hence a simple mechanism cannot be inferred in the absence of any penta-
valent (5+) cation and the most probably exchange that we can envisage is the substitution of TiO2 by
CrO(OH) or Ti + O2 = Cr + O + OH. The Cr substitution in rutile seems to be rather dependent on bulk
composition and, can, thus, at the moment not be easily utilized as a geobarometer, despite the fact that
the potential undoubtedly exists.
-3. Experimental study-
52
a) b)
c)
Fig 3.12. Compositional variation of rutile for SM12 as a function of pressure and temperature: a) Ti; b) Cr; c) Fe3+ all values in cations per formula unit (p.f.u.) 3.3.4.4 Olivine.
Olivines present in the runs are close to ideal stoichiometry calculated on a 3-cations basis. The
Mg/(Mg+Fe) ratio of olivines are generally high (0.85-0.9) and correlate with the bulk XMg of the starting
material; the highest values are observed for runs with bulk XMg of 0.85. Cr contents of olivines do not
exceed 0.8 wt.% and commonly vary between 0.3-0.6 wt.%. Olivines from runs employing a starting
composition enriched in TiO2 (SM6) contain considerable amounts of TiO2, we measured up to 5 wt.%.
Figure 3.13 shows a plot of TiO2 versus SiO2 wt% of olivines. Some high TiO2 contents encountered in
olivine may represent analytical artifacts due to secondary X-ray fluorescence that, however, could be
account for only small part of TiO2 in small grains or at the edge of grains. In some runs where we
observed a negative dependence of the SiO2 and TiO2 we additionally analyzed the specimen with
Raman-spectroscopy for the presence of OH-group that where indeed identified in some samples (NS28,
NS19). In addition, in these samples peaks identified in the 800 – 900 cm-1 range are characteristic for
humite group minerals. This would indicate that some of our samples are actually within the stability field
of OH-clinohumite.
-3. Experimental study-
53
Figure 3.13 TiO2 contents of olivines versus SiO2, assuming Ti replacement of Si on the tetrahedral sites as possible substitution mechanism. 3.3.4.5 Orthopyroxene.
The occurrence of ortho- pyroxene is bulk compositionally dependant. The Mg# of orthopyroxene varies
between 0.86 and 0.93. They contain normally less than 1 wt% of Cr2O3 and TiO2. In Al bearing systems,
opx contains 2-3 wt% of Al2O3 and is characterized by slightly higher Cr2O3 content; a positive
correlations of Al-, Ti- and Cr-contents with temperature are observed (Fig. 3.14). The atomic fraction of
Cr is always lower than that of Al, suggesting that Cr possibly enters as the MgCrAlSiO6 endmember and
that additional tetrahedrally coordinated Al is used for the incorporation of Ti. Over the investigated
pressure range, increasing pressure does not strongly influence the solubility of Cr and Al. There is no
correlation observed for the distribution of Al between the M1 and the tetrahedral sites as a function of
pressure or temperature.
a) b)
Figure 3.14 Compositional variation of opx with pressure and temperature for Al-bearing compositions, a) Ti versus Cr contents, arrow indicates increasing temperature; b) Al content versus temperature.
-3. Experimental study-
54
3.3.4.6 Garnet
Garnet is observed only in Al-bearing systems and at pressures of 35 kbar and higher in a few runs. They
are characterized by XMg=0.76-0.85, Al2O3 ranges between 19 and 22 wt.% wt.% and Cr2O3 content are
2.6 – 5.6 wt.%. These values correspond to 78-86% Mg-endmembers (pyrope, knorringite and very minor
koharite (Mg3Fe2Si3O12) and 7-16% Cr-endmembers. The limited number of samples that actually contain
garnet does not allow a comprehensive treatment of the garnet compositions as a function of pressure,
temperature and/or bulk composition. 3.3.5 Iron – Magnesium partitioning
3.3.5.1 Ilmenite-silicates
A rather complex dependency on pressure and temperature is observed for the Fe-Mg distribution
coefficient between ilmenite-olivine and ilmenite-opx pairs, indicating that the incorporation of Cr into
ilmenite considerably complicates the existing ilmenite-silicate Fe-Mg geothermometers. Figure 3.15
illustrates the temperature, pressure and composition dependence of Fe-Mg KD. The distribution
coefficient was expressed in the common way as:
silFe
ilMg
silMg
ilFesililm
MgFeD XXXX
K =−− )(
Similar behaviour is observed for ilmenite-olivine and ilmenite-opx mineral pairs. Partitioning of Fe and
Mg shows negative correlation with temperature between 1000 and 1200 oC. However, between 1200 and
1300°C (XMg = 0.73) we observe an inversion of the temperature dependence most probably related to
strongly increasing Cr-contents in the ilmenite in this temperature interval resulting in strong non-ideality
of the Fe2+-Mg incorporation into ilmenite. A positive pressure effect is observed for compositions with
XMg =0.73. For compositions with XMg=0.85 (only containing one silicate phase, olivine) a negative
temperature effect is more clearly evident and a crossover for the 25 and 35 isobars is observed. The
effect of higher pressure is not clear as the data set is too limited to draw decisive conclusions.
-3. Experimental study-
55
1000 1050 1100 1150 1200 1250 13000
2
4
6
8
10
K D (Fe
-Mg)
1000 1050 1100 1150 1200 1250 13000
2
4
6
8
10
1000 1050 1100 1150 1200 1250 13000
2
4
6
8
10
T,oC1000 1050 1100 1150 1200 1250 1300
0
2
4
6
8
10
K D (Fe
-Mg)
1000 1050 1100 1150 1200 1250 13002
4
6
8
10
K D (Fe
-Mg)
T,oC
ilm-olXMg=0.73
ilm-olXMg=0.73
ilm-olXMg=0.85
ilm-opxXMg=0.73
ilm-opxXMg=0.73
25 kbar
70 kbar50 kbar35 kbar
a)
b)
c)
Figure 3.15 Distribution of Fe2+ and Mg for ilmenite-silicate pairs for different bulk compositions. a) SM2, b) SM12, c )SM6
-3. Experimental study-
56
3.3.5.2 Spinel-silicates
Partitioning of Fe and Mg between spinel and silicate phases correlates negatively with temperature. Fe-
Mg distribution between spinel and silicates is more temperature sensitive than between ilmenite-silicate
pairs. Pressure does not have an obvious effect, but some positive correlation is observed for experiments
with bulk XMg= 0.73. For a bulk XMg = 0.85, as well as for ilmenite, cross-over at low pressures is
observed.
1000 1050 1100 1150 1200 1250 13002
4
6
8
10
12
14
16
K D (Fe
-Mg)
T,oC
1000 1050 1100 1150 1200 1250 13002
4
6
8
10
12
14
16
K D (Fe
-Mg)
1000 1050 1100 1150 1200 1250 13002
4
6
8
10
12
14
16
T,oC
1000 1050 1100 1150 1200 1250 13002
4
6
8
10
12
14
16
K D (Fe
-Mg)
1000 1050 1100 1150 1200 1250 13002
4
6
8
10
12
14
16
25 kbar
70 kbar50 kbar35 kbar
spi-olXMg=0.85
spi-olXMg=0.73
spi-olXMg=0.73
spi-opxXMg=0.73
spi-opxXMg=0.73
a)
b)
c)
Figure 3.16 Distribution of Fe2+ and Mg for spinel-silicate pairs for different bulk compositions. a) SM2, b) SM12, c) SM6
-3. Experimental study-
57
3.3.5.3. Ilmenite - spinel
The temperature effect is slightly positive on the Fe-Mg distribution between the two oxide phases. The
pressure effect in the range 25 to 35 kbar is almost negligible. For bulk systems with high XMg (0.85) the
variation is less consistent, but neglecting the data point at 3.5 GPa and 1300°C (experiment NS 24) still a
slightly positive dependence of KD is observed.
1000 1050 1100 1150 1200 1250 13000.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
K D (Fe
-Mg)
1000 1050 1100 1150 1200 1250 13000.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
T,oC
1000 1050 1100 1150 1200 1250 13000.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
K D (Fe
-Mg)
T,oC
ilm-spiXMg=0.73
ilm-spiXMg=0.73
ilm-spiXMG=0.85
Figure 3.17 Distribution of Fe2+ and Mg for ilmenite – spinel pairs, a) SM2, b) SM12, c) SM6
-3. Experimental study-
58
3.4 Discussion
The principle parameters controlling ilmenite occurrence are bulk XMg and pressure, whereas temperature
mainly controls composition of the coexisting phases. Ullmann and Woermann (1990) reported
experiments in the system MgO-FeO-SiO2-TiO2 at pressures of 10-30 kbar showing that the stable oxide
paragenesis under these conditions is rutile + ilmenitesss. In the presence of additional Cr in the system,
spinel becomes a stable phase and rutile is present variably. In our experiments, ilmenite is stable in all
charges run with starting material having an XMg = 0.73, but for bulk XMg= 0.85 its stability depends on
the amount of SiO2 and TiO2 in the system. Ilmenites incorporates significant amount of Cr, but
generally significantly less than spinel
Figure 3.18 MgO versus Cr2O3 content of experimental ilmenites from different starting materials. Pressure and temperature are not specified, but generally increasing temperature is positively correlated with increasing Cr content, pressure does not result a straightforward correlation. Ilmenites can be separated into distinct groups according to their Cr2O3-MgO relationships (Fig. 3.18). A
first group with lower concentration of MgO is obtained from starting material with lower XMg (0.73) that
can incorporate larger amounts of Cr; a second group with a higher amount of MgO (bulk XMg of the
starting material of 0.85 and 1.0) contains lower concentrations of Cr2O3. These two groups might
represent the two limbs of ‘Haggerty’s parabola’ and can possibly be explained by (1) solvus relationship
(Haggerty and Tomkins, 1983) in the Cr-Fe-Mg-Ti-O system between Fe2O3-rich rhombic oxides and
(Mg,Fe)TiO3-rich rhombic oxides that closes with increasing FeTiO3 and/or Cr2O3 component or (2) by
igneous crystallization of rhombic oxide coexisting with different silicate assemblages, e.g. garnet-
bearing at high pressures that depletes Cr and Mg and garnet/pyroxene free (olivine - carbonate) that is
responsible for the high Mg- high Cr limb of the parabola (at lower pressures) (e.g. Boyd and Dawson,
1970; Boyd and Nixon, 1975; Haggerty et al., 1979; Hearn, 1994; Moore and Lock, 2001).
Figure 3.19 illustrates the compositions of ilmenites coexisting with spinels expressed in major element
oxides, combining divalent (FeO+MgO), trivalent (Fe2O3+Cr2O3 (+Al2O3)) and tetravalent (TiO2) oxides.
-3. Experimental study-
59
Ilmenite compositions lie between MgTiO3 and FeTiO3 and move toward the Mg-endmember in Mg-rich
systems. The content of trivalent cations of ilmenite increases with increasing temperature and is
counterbalanced by decreasing Ti content. Ilmenites enriched in Ti contain considerably lower
concentrations of Cr.
25 kbar
70 kbar50 kbar35 kbar
0.0 0.2 0.4 0.6 1.0
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.6
0.0
0.2
0.4
0.6
0.8
TiO2
MgTiO3
FeTiO3
Mg2TiO4
Fe2TiO4
MgCr2O4FeCr2O4Fe3O4 R2O3RO
0.0 0.2 0.4 0.6 1.0
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.6
0.0
0.2
0.4
0.6
0.8
TiO2
MgTiO3
FeTiO3
Mg2TiO4
Fe2TiO4
MgCr2O4FeCr2O4Fe3O4 R2O3RO0.0
TiO2
0.0 0.2 0.4 0.6 1.0
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.6
0.2
0.4
0.6
0.8
MgTiO3
FeTiO3
Mg2TiO4
Fe2TiO4
MgCr2O4FeCr2O4Fe3O4 R2O3RO
0.0 0.2 0.4 0.6 1.0
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.6
0.0
0.2
0.4
0.6
0.8
TiO2
MgTiO3
FeTiO3
Mg2TiO4
Fe2TiO4
MgCr2O4FeCr2O4Fe3O4 R2O3RO
a) b)
c) d)
Figure 3.19 Ternary diagram illustrating the composition of ilmenite-spinel pairs expressed as major elements using combined divalent (FeO+MgO), trivalent (Fe2O3+Cr2O3 (+Al2O3)) and tetravalent (TiO2) oxides in wt.%, arrows indicate increasing temperature. a) SM2, XMg=0.73, b) SM7, XMg=0.73, Al-bearing system, c) SM12, XMg=0.73, d) SM6, XMg=0.85.
Spinel is the principal Cr-bearing phase (35-60 wt% Cr2O3 in spinel). The composition of spinels
observed in the experiments exhibits similar features as for example spinels from the Apollo 11 and 12
lunar missions (Haggerty, 1970). Spinels from the Apollo 12 mission samples fall into separate groups
along join Fe2TiO4-FeCr2O4 and analysis of spinels from the Apollo 11 mission samples are located
between these two groups (Fig. 3.20). Because of the distribution of the Apollo 12 spinels located on
opposite sides of the Apollo 11 spinels, a miscibility gap was suggested along the ulvospinel-chromite
join. Muan et al (1971, 1972) however, reported the presence of continuous solid solution between the
(Mg,Fe)2TiO4 and (Fe,Mg)Cr2O4 end members and the presence of an extensive miscibility gap between
(Mg,Fe)2TiO4 and (Fe,Mg)Al2O4.
-3. Experimental study-
60
0.0 0.2 0.4 0.6 1.0
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.6
0.0
0.2
0.4
0.6
0.8
TiO2
MgTiO3
FeTiO3
Mg2TiO4
Fe2TiO4
MgCr2O4FeCr2O4Fe3O4 R2O3RO
APOLLO XIAPOLLO XIISM6SM12
Figure 3.20 Spinel analyses from Apollo 11 and Apollo 12 missions (from Haggerty, 1970) in comparison with experimental spinel. Spinel from our experiments can be divided in two groups according to the bulk XMg of the starting
material: Spinels from starting compositions with XMg=0.73 are close to isotropic spinels from the Apollo
12 samples (Fig.3.19, c, Fig. 3.20) and lie near to the join FeCr2O3-Fe2TiO4, close to the Cr-endmember;
spinels obtained from experiments with XMg=0.85 corresponds to spinels obtained from the Apollo 11
samples (Fig 3.19, d, Fig 3.20) and spinel composition displaced toward the Mg-, Ti-rich endmember. A
general feature is the depletion in trivalent cations with increasing temperature.
Addition of the Al does not exert strong control on the phase stability but due to the limited number of
Al-bearing experiments run at high pressure, the spinel-garnet transition is not fully described by this
experimental data set. The appearance of garnet at 35 kbar is, however, consistent with other studies
(Grütter et al, 2006, Klemme, 2004) in Cr-bearing systems
For coexisting ilmenite and spinel solid solutions the Fe/Mg ratio is higher for spinel in Al-bearing
system while in the absence of Al ilmenite is characterized by the higher magnesium numbers.
Rutiles, when present, are rather Cr-rich, up to 10 wt%, which is common feature for kimberlitic rutiles in
association with ilmenite (Mitchell, 1986).
Fe-Mg partitioning between ilmenite and silicates, as well as between spinel and silicates, is not strongly
pressure sensitive, but can be evaluated in terms of temperature dependency (see next chapter).
-3. Experimental study-
61
3.5 Conclusion The present experimental study provides constrains on phase equilibria and composition of coexisting
minerals in the system Fe-Mg-Ti-Cr-(Al)-Si-O at high pressure, high temperature conditions.
Phase parageneses and compositions of the phase are, as anticipated from not being fully buffered, bulk
compositionally controlled. Olivine and spinel are present in most of the runs, but the stability of opx and
ilmenite are highly dependent on bulk XMg and SiO2 content of the system.
The pressure stability of ilmenite is, as well, bulk compositionally dependant: in SiO2-rich, low MgO
compositions ilmenite is stable at pressure up to 50 kbar, whereas for more magnesian compositions
ilmenite is stable only in starting compositions with low SiO2 and high TiO2 contents at any pressure
investigated
The solubility of Cr2O3 in ilmenite increases with increasing pressure and temperature and is bulk
compositionally dependant.
Fe2+ and Mg partitioning data reveal that the incorporation of Cr in ilmenite considerably complicates
existing ilm-olivine and ilm-opx geothermometers. Generally, a slightly negative temperature dependence
of the Fe-Mg KD between ilmenite and olivine is observed that is more obvious for coexisting spinel–
silicate pairs.
-3. Experimental study-
62
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66
4. Thermodynamic modeling of Fe2+-Ti-Cr-Fe3+-Mg±Al ilmenite solid solution
as a function of pressure and temperature
4.1 Introduction
The system Fe-Mg-Ti-Cr-Al-Si-O provides a useful simplification for phase equilibria in the Earth
mantle. Cr has pronounced effects on the phase associations in ultramafic, peridotite-like compositions.
Most of the studies on Cr-bearing assemblages considered garnet and spinel as major hosts of chromium
(Klemme 2000, Brey et al., 1999, Doroshev, 1997) but no attention was given to picroilmenite as a
chrome-bearing phase. Kimberlitic picroilmenites display unique features not observed in any other
terrestrial ilmenites (but partly in common with some ilmenites occurring in lunar rocks in particular in
the anorthosites and the KREEP basalts, e.g. Powell and Weiblen, (1972). They are MgO-rich (XMg varies
between 0.2 - 0.6) and variably Cr- and Nb-rich (e.g. Moore et al., 1992; Griffin et al., 1997; Griffin and
Ryan. 1995). Haggerty (1975) observed a 'peculiar' parabolic (more rarely hyperbolic) trend of
megacrystic ilmenites in a Cr2O3 versus MgO diagram. Such relationships have been observed for many
megacryst suites worldwide (e.g. Eggler et al., 1979; Moore, 1987; Schulze et al, 1995).
A classical application of ilmenite mineral chemistry is the 2-oxide (ilmenite-hematite solid solution
(rhombic oxides) and magnetite-ulvöspinel solid solution (cubic oxides)) thermometry - oxybarometry,
pioneered by Buddington and Lindsley (1964) with many subsequent modifications (e.g. Spencer and
Lindsley, 1981; Andersen et al., 1991; Ghiorso and Sack. 1991; Sauerzapf et al., 2004). This is an
important thermo-barometric tool for igneous (mostly volcanic) and metamorphic rocks. The calibration
and subsequent thermodynamic treatments of this oxy-thermobarometer base on a large experimental
dataset obtained nearly exclusively at low pressures (1 bar to 1 kbar) in the system Fe-Ti-O with later
additions for Mn bearing systems (Pownceby et al., 1987). Sauerzapf et al. (2008) presented new
thermodynamic models for titanomagnetite - ilmenitess pairs and derived a revised version of the thermo-
oxybarometer which yields much better T-fO2 estimates for temperatures above 800°C under reduced or
moderately oxidized conditions. However, for oxide phases with appreciable amounts of additional
components (MgO, Cr2O3, Al2O3>6 wt%, which is the case for kimberlite) their model is not suitable.
A limited number of experimental studies have been performed to measure the partitioning of Fe2+ - Mg
between ilmenite and the Fe-Mg silicate mantle phases olivine, cpx, opx, and garnet (Akella and Boyd,
1971; Andersen and Lindsley, 1979; 1981; Bishop, 1980; Green and Sobolev, 1975) to calibrate potential
geothermometers using ilmenite-silicate Fe-Mg partitioning relationships. The studies by Bishop (1980)
(pyx-ilmenite) and Andersen and Lindsley (1979, 1981) (olivine-ilmenite) were performed in simplified
systems at rather low fO2 (graphite capsules or even iron capsules); pressures were mainly 13 kbar with a
few experiments at 36 kbar to explore the effect of pressure on the Fe-Mg partitioning and the activity
relationships of Fe-MgTiO3 solid solutions. The olivine-ilmenite and pyroxene-ilmenite studies provide
the thermodynamic basis for the formulation of activity models of MgTiO3-FeTiO3, solid solutions and
-4. Thermodynamic modelling-
67
calibration of the ilmenite-silicate geothermometers. Application of these thermometers have mainly been
directed towards lunar rocks, but applied to the megacryst assemblages and pyroxene-ilmenite
intergrowth they result in relatively high temperatures of 1100-1400°C compared with other thermometric
methods (e.g. two-pyroxene, garnet-cpx).
Recently, Lattard et al (2008) pointed out the importance of chromium for the iron-titanium thermometry
and performed experiments in the Fe-Ti-Cr-O and Fe-Ti-Cr-Mg-O systems at 1 bar in the sub-solidus
temperature range 900-1300°C at low to moderate oxygen fugacity values (ΔNNO between -4 and -1).
The run products are polycrystalline assemblages of titanomagnetite and ilmenite solid solutions with
Cr2O3 contents between 12 and 18 wt.% for the spinels and between 0.7 and 4 wt.% for the ilmenites.
Using experimental data presented in chapter III thermodynamic models were developed for Cr-bearing
picroilmenite basing on data on Fe-Mg partitioning with olivine and spinel and Cr-Ti partitioning with
spinel. .
The goal of this study is to understand the behaviour of Cr and its influence on the Fe-Mg substitution
mechanisms between ilmenite and coexisting phases.
4.2 Gibbs free energy of solid solution
The free energy of solution can be written as
Gtotal = G* - TSconf (1)
where G* denotes the non-configurational free energy, including both ideal and non-ideal or excess
contributions to the free energy,
G*= Gideal + Gexcess (2)
Gexcess is modeled as an expansion around the composition for each individual case. The most common
expansion is the Maclaurin series, which for a binary, 1-site crystalline solution between X1 and X2 takes
the form:
G excess = A+ BX2+ CX22 +DX2
3+… (3)
There are two ways how this expansion is used in geological literature. The first is to truncate the
expression after the third term:
G excess = A+ BX2+ CX22 (4)
which gives rise to a symmetrical distribution of Gexcess around X1 and X2 and is called a symmetrical
solution model. The second way is to truncate after the forth term:
G excess = A+ BX2+ CX22 +DX2
3 (5)
which gives rise to an asymmetrical distribution of Gexcess around X and is called an asymmetrical solution
model. Asymmetry occurs only when there is a large difference in ionic radius of the mixing cations. By
evaluating the behavior of Gexcess in the limits of pure X1 or pure X2 it is defined in terms of WG-
interaction parameter (recall that non-ideal behavior arises from interaction between molecules or atoms).
Gexcess=X1X2WG, for symmetric solution (6)
Gexcess=X1X2 (WG12 X2+WG21 X1), for asymmetric solid solution. (7)
-4. Thermodynamic modelling-
68
WG is the difference between Henry’s law standard state chemical potential and the Raoult’s law standard
state chemical potential. The effects of the temperature for Gexcess can be accommodated by splitting up
the parameter of the power series into temperature and pressure dependant terms. The WG term then is
expressed as:
WG = WH - TWS+ PWv (8)
where WG is derived from experiments on real crystals or, alternatively, inferred from natural
parageneses. WG may be dependent on temperature and pressure but is a constant, independent of
composition, under fixed P, T conditions.
Addressing the problem of finding activity coefficient that express the departure of activities from the
ideal solution, we can write
µi = µio+ RTln(ai) (9)
ai=Xi γi (10)
where γi is the activity coefficient and ai is the activity. If the Gexcess =0, then it follows for a binary
solution that γi is equal to 1 and ai=Xi; in such case, the solution in is ideal.
µi = µideal +µexcess (11)
µexcess = (1-Xi)2WG (12)
⎥⎦
⎤⎢⎣
⎡ −=
RTWX Gi
i
2)1(expγ (13)
for a symmetric model and
⎥⎥⎦
⎤
⎢⎢⎣
⎡ −+−=
RTXWWXWW jGjiGijjGijGji
i
32 )(2)2(expγ (14)
for an asymmetric solution where j=2 when i=1 and vice versa. Another important point is that µi is
independent from the free energy of formation of the other component j.
Since any complex solid solution can be considered as a set of binary solid solutions, the formulation for
the thermodynamics of a complex solid solution can be derived from the binaries at the appropriate
composition. A generalized asymmetric Margules expression for a 1-site crystal with nc components
mixing on the site has been presented by Berman and Brown (1984):
∑∑∑−
= =≠=
=1
1
nc
i
nc
ij
nc
ikjk
Gijkkjiexcess WXXXG (15)
For a ternary solution this results in
Gexcess= X1X1X2 WG21 + X1X2X2 WG12 + X1X1X3 WG31 + X1X3X3 WG13 + X2X2X3 WG32 +
X2X3X3 WG23 + X1X2X3 WG123 (16)
The term WG123 is called ternary interaction term and describes a symmetrical interaction within the
ternary solution. As it was established by Hellfrich et al. (1989), ternary mixing parameters exist
independently of their component binaries. It is, therefore, impossible to estimate ternary interaction
coefficients having knowledge only of the mixing properties of the binaries. Ternary interaction
parameters, in general, may be negligible because pair-wise interaction dominates. Because the Margules
-4. Thermodynamic modelling-
69
expansion is truncated after the third term, there are no Margules parameters of higher order than the
ternary interaction term, regardless of the number of components.
The configurational entropy for mixing can be written as
∑−=i
iiconf XXRS )ln(α (17)
where Xi is the mole fraction of the component i and the α is a constant related to the site multiplicity. For
a multisite phase with random mixing of cations on each site, the configurational entropy can be written
as (Thompson, 1969, 1970):
∑∑−=i
sisiss
conf nnbRS )ln( ,, (18)
where b is the number of sites (s) per formula unit and ni,s is the fraction of ni on the site s.
4.3 Structures and thermodynamic formulation of minerals
4.3.1 Ilmenite
Ilmenite crystallizes in a trigonal structure that consists of hcp (hexagonally closed-packed) layers of
oxygen ions parallel to (001). The cations occupy octahedral sites, which lie halfway between the hcp
oxygen layers. Two thirds of the octahedral sites are filled. The structure of ilmenite is closely related to
hematite (Fe2O3) and consists of alternating layers of symmetrically related cations that are octahedrally
coordinated by essentially close-packed layers of oxygen anions. MgTiO3 – geikilite has the ilmenite
structure with the space group 3R . Alternating cation layers are arbitrarily designated as A- and B-site
layers. In hematite, Fe3+ cations occupy both layers and the structure is described by the space
group cR3 . In chemically disordered ilmenite or geikilite structures Fe2+ and Ti4+ or Mg2+ and Ti4+
cations are randomly distributed over the two layers, and the hematite space group is preserved. As either
cation develops preference for an A-site or B-site layer, the symmetry of the two fold axes is lost, and the
3R structure results.
Down the [001] direction, the ordering sequence corresponds to (-Fe-Ti--Ti-Fe--), generating a unit
cell composed of six cation and six anion layers. In the (001) plane, the arrangement of cations forms
connected six-fold rings which are shifted with respect to the adjacent upper and lower neighboring
layers. The incorporation of Fe3+ and Mg causes a decrease in cell dimension of pure ilmenite, especially
along the c-axis.
-4. Thermodynamic modelling-
70
a b cABABABABABAB
ABABABA
a) b)
c)
Figure 4.1 Ilmenite and hematite structure and cation distribution: a) Cation arrangement on close-packed anion layers. b) Stacking sequence of cations in ilmenite (open circles Ti, filled Fe2+). c) Cation distribution scheme for hematite (circles denote Fe3+).
The ilmenite solid solution coexisting with olivine and pyroxenes was experimentally investigated by
Bishop (1976, 1979) and Anderson and Lindsley (1979, 1981, 1988). Bishop conducted experiments at
high temperatures (895-1436°C, 13 kbar) and fitted FeTiO3-MgTiO3 as a strictly regular solution ignoring
effects of Fe3+. Anderson and Lindsley conducted experiments at lower temperatures 700-900 °C and
pressures of 1 and 13 kbar respectively. They found a temperature dependency of distribution coefficient
developed a geothermometer and also presented a solution model to account for the non-ideality of
olivine and ilmenite in the ternary system ilmenite-geikielite-hematite accounting for the effect of Fe3+.
The solution model is constructed on the assumption that the phases remain fully ordered over the
temperature-composition range of interest, and that the excess Gibbs free energy of mixing may be
expressed in terms of temperature dependant asymmetric regular solution parameters. Their expression
differs from equation (15) used in Berman and Brown (1984) in that it includes an additional summation
of Xk/2 in the coefficients for Wij.
∑∑ ∑ ∑∑ ∑≠ ≠ ≠ ≠
++=i ijj jikk i ijj jikk
kjiijkkjjiijexcess XXXWXXXXWG, ,, , ,
)2/( (19)
Another solution model of activity-composition relations in ilmenites is presented by Ghiorso (1990,
2008) and Ghiorso and Sack (1991). The model of Ghiorso describes the solution in the system (Fe2+, Mg,
Mn2+)TiO3 – Fe2O3, and makes explicit provision for convergent cation ordering. In addition, it
accommodates excess Gibbs energies of mixing by temperature independent, symmetric regular solution
parameters between the joins of the composition ordering space. Ordering is accounted for by considering
the ilmenite solid solution as a mixture between “species” rather than thermodynamic components. The
excess Gibbs energy is constructed by treating mixing along each binary “species” join as a symmetric
regular solution with temperature independent coefficients. Other studies on ilmenite by O’Neill (1998)
and Pownceby et al. (1987) investigated Fe-Mn partitioning between ilmenite and silicate phase (olivine,
garnet) and developed activity models for the FeTiO3-MnTiO3 join.
-4. Thermodynamic modelling-
71
At high temperatures, there is complete solid solution between ilmenite and hematite.
Ilmenites obtained in our experiments contain essential amounts of chromium, the ilmenite solid solution
is, therefore, considered to be a quaternary solution between FeTiO3, MgTiO3, Fe2O3 and Cr2O3. As
hematite forms a solid solution with eskolaite (Cr2O3) and both exhibit similar structural (lattice)
parameters (Blake, 1966, Chaterjee et al 1982), Cr2O3 was incorporated into solution in the same way as
ferric iron, i.e. a symmetric geikilite-eskolaite and an asymmetric ilmenite-eskolaite join, assuming
ilmenite-geikilite and geikilite-hematite joins to be symmetric and ilmenite-hematite to be asymmetric.
The set of binary joins used to represent ilmenite solid solutions is illustrated in Fig. 4.2. In this study, we
considered ilmenite close to the FeTiO3-MgTiO3 join, that should crystallized in the ordered 3R form.
FeTiO3 MgTiO3
Fe2O3 Cr2O3
sym
sym
asym
sym
asym sym
Figure 4.2 Details of the solution model for ilmenite considered in this study
As a simplifying assumption, we ignored ternary interaction parameters by setting them equal to zero.
Gexcess of ilmenite solution following the formulation of Andersen et al. (1981) based on equation (19) can
then be written as:
))21
21()
21
21((
))21
21()
21
21((
hemgkililesk
Ghemgkeskeskil
Geskil
eskgkililhem
Geskgkhemhemil
Ghemil
eskhemGeskhem
gkeskGgkesk
gkilGgkil
gkhemGgkhemex
XXXWXXXWXX
XXXWXXXWXX
WXXWXXWXXWXXG
++++++
++++++
+++=
−−
−−
−−−−
where are defined as
ilCr
ilMg
ilFe
ilFe
ilFe
il XXXXX
X22 32
2
+++=
++
+
(21)
ilCr
ilMg
ilFe
ilFe
ilMg
gk XXXXX
X22 32 +++
=++
(22)
ilCr
ilMg
ilFe
ilFe
ilFe
Hem XXXXX
X22
2
32
3
+++=
++
+
(23)
ilCr
ilMg
ilFe
ilFe
ilCr
esk XXXXX
X22
232 +++
=++
(24)
The activity coefficients for FeTiO3, MgTiO3 and Cr2O3 may be calculated from equation (20) using
numerical differentiation and the definition of activity:
(20)
-4. Thermodynamic modelling-
72
ilhemGhem
ileskGesk
eskilGeskgk
ilgkGgk
ilgkGgk
eskilGesk
gkilGgk
ileskGeskgk
hemilGhem
gkilGgkhem
eskilGeskhem
ileskGeskhem
gkilGeskgk
hemilGhemgk
ileskGeskhem
eskilGhemesk
ilhemGeskhem
ilgkGeskgk
ilhemGhemesk
hemilGhemesk
ileskGeskgk
ilgkGgkesk
gkilGhemgk
hemilGhemesk
ilhemGhemgk
hemilGeskhemgk
eskilGeskhemgk
gkilGeskhemgk
ilgkGeskhemgk
ilhemGeskhemgk
ileskGeskhemgk
gkilGgkesk
ilhemGhemgk
eskilGeskgk
ilgkGgkhem
hemilGhemgk
ilhemGhem
hemilGgkhem
hemilGhem
eskilGgkesk
gkeskGeskgk
ileskGhemesk
gkhemGhemgk
ileskGgkesk
eskilGhemesk
ilhemGeskhem
hemilGeskhem
ilhemGgkhem
eskhemGeskhem
ilgkGhemgk
gkilGhemgk
ileskGesk
eskilGesk
gkilGgk
ilgkGhemgk
gkilGeskgk
ilgkGeskgkil
WXWXWXXWXWXWXWXWXXWXWXXWXX
WXXWXXWXXWXXWXX
WXXWXXWXXWXXWXX
WXXWXXWXXWXXWXXX
WXXXWXXXWXXXWXXX
WXXXWXXWXXWXXWXX
WXXWXWXXWXWXXWXX
WXXWXXWXXWXXWXX
WXXWXXWXXWXXWXX
WXWXWXWXXWXXWXXRT
−−−−−
−−−−−−
−−−−−
−−−−−
−−−−−
−−−−
−−−−−
−−−−−−
−−−−−
−−−−−
−−−−−−
−+++−++−+++
+−+−−
++−−+
−−+++
++−−
−+−−−
−++−+−
−−−+−
+−−++
−−−−+−=
32223
332322
22
2
22
222
2222
2222
222
322222
2232222323
23
2133
21
23
233
21
23
3213
232
22
233213
212
23
2ln γ
gkhemGhemil
ileskGeskil
eskilGeskil
gkilGilesk
gkilGeskil
gkilGhemil
ilgkGhemil
eskilGilesk
ilgkGilesk
gkilGilhem
ilgkGeskil
gkeskGeskil
ilgkGhemil
ilgkGilesk
hemilGilhem
ileskGeskil
gkilGeskil
ilgkGilhem
gkeskGhemesk
ilhemGhemil
hemilGhemil
ilhemGhemil
ilhemGilhem
hemilGilhem
ileskGilesk
gkilGhemil
eskilGeskil
gkhemGhemesk
gkeskGesk
gkilGil
ilgkGil
gkilGil
ilgkGil
gkilGeskhemil
ilgkGeskhemil
gkhemGhem
eskhemGeskhemgk
WXXWXXWXX
WXXWXXWXXWXX
WXXWXXWXXWXXWXX
WXXWXXWXXWXXWXX
WXXWXXWXXWXXWXX
WXXWXXWXXWXXWXX
WXXWXWXWXWXWXWXXXWXXXWXWXXRT
−−−
−−−−
−−−−−
−−−−−
−−−−−
−−−−−
−−−−−−
−−−−
+−−
−−+−
++−++
+−−++
+++−−
−+−−−
++−++−−++−=
21
323
21
3321
21
23
32121
22222ln
2
22
2222
22
222
2222
23322
2γ
ileskGhemil
eskilGhemil
ileskGgkil
eskilGgkil
ileskGilhem
eskilGilhem
ileskGilgk
ileskGil
eskilGil
ileskGil
eskilGil
eskhemGhem
eskilGilgk
ileskGhemil
eskilGhemil
ileskGgkil
eskilGgkil
eskhemGilhem
eskhemGgkhem
gkeskGgkil
gkeskGgkhem
ilhemGilhem
ilhemGhemil
ilhemGilhem
hemilGilhem
hemilGhemil
hemilGhemil
ilgkGgkil
ilgkGgkil
ilgkGilgk
gkilGilgk
gkilGgkil
gkilGgkil
ileskGgkhemil
eskilGgkhemil
gkeskGgk
gkhemGgkhemesk
WXXWXXWXXWXXWXXWXXWXXWXWXWXWXWXWXX
WXXWXXWXXWXXWXX
WXXWXXWXXWXXWXX
WXXWXXWXXWXXWXX
WXXWXXWXXWXXWXX
WXXXWXXXWXWXXRT
−−
−−−−−
−−−−−−
−−−−−
−−−−−
−−−−−
−−−−−
−−−−
+−+−+−++−−++−
−+−++
++++−
−+−−+
−−+−−
+−+−=
22
22222
332222
2
2222
222
2
3332223
21
23
21
23
21
21
21
21
22lnγ
Existing modeling parameters for ilmenite solid solutions are listed in Table 4.1. Most of these parameters
(except WGhem-esk) were derived and discussed by Andersen and Lindsley (1988, 1991). WG
hem-esk was
derived from Eremin et al. (2007) who presented minimum mixing enthalpies for the hematite-eskolaite
system. Due to the close values of the electronic radii and electronegativities of atoms, they observed
complete miscibility even at room temperature. This supports our assumption of incorporating the
(27)
(25)
(26)
-4. Thermodynamic modelling-
73
eskolaite component into ilmenitess in the same way as hematite. WGhem-esk is, therefore, assumed to be
independent of temperature.
Table 4.1 Parameters for ilmenite used as input to our solution model (Andersen et al., 1988; Eremin et al, 2007).
Parameter Join WH (J/mole) WS (J/mol·K) WV (J/bar)
WGhem-gk hematite-geikilite 76086 75.6
WGil-gk ilmenite-geikilite 8405.5215 3.0423203 0.0108
WGgk-il geikielite-ilmenite 7363.5693 3.495958 0.0108
WGil-hem ilmenite-hematite 44204.801 12.274
WGhem-il hematite-ilmenite 126342.5 100.6
WGhem-esk hematite-eskolaite -20000
4.3.2 Olivine
The structure of olivine is characterized by a slightly distorted hexagonally closed-packed (hcp)
arrangement of oxygen atoms parallel to (100). One eighth of the tetrahedral interstices are occupied by
Si cations. The M atoms, i.e., Mg or Fe2+, occupy half of the available octahedral sites and are distributed
in two distinctive lattice positions: Ml with local 1 symmetry and M2 with local m symmetry. The M sites
form chains of edge-sharing octahedra parallel to [001]. Mg and Fe2+, characterized by a similar ionic
radius, can be found in both sites and at upper mantle/lower crust conditions can be considered almost
disordered.
At higher pressure the olivine structure (α-(Mg,Fe)2SiO4) transforms into a distorted spinel structure (β-
(Mg,Fe)2SiO4 or wadsleyite) at ~14GPa/1000°C and to the cubic closed-packed (ccp) spinel structure (γ-
(Mg,Fe)2SiO4 or ringwoodite) at ~17 GPa/1000°C. The α to β transition is limited to Mg-rich olivine with
Mg/(Mg + Fe) >0.85.
The forsterite-fayalite solid solution has extensively been investigated. Olivines found in natural rocks
approximate the Mg-Fe join. Previous studies on solution properties can basically be grouped into two
types: (1) those based on the analysis of Fe/Mg exchange (Kawasali and Matsui, 1977, O’Neill and Wood
1979 O’Neill and Wall, 1987, Wiser and Wood, 1991, Koch, Muller et al., 1992, Von Seckendorff and
O’Neil, 1993) and (2) those from calorimetric measurements (Thierry et al., 1981, Wood and Kleppa,
1981, Kojitani and Akagi, 1994). Despite the fact that Fe-Mg mixing takes place on two energetically
different sites (M1 and M2), all studies agree in assuming that the difference between the Mg-Fe
parameters of the M1 and M2 sites is very small.
Thierry et al. (1981) conclude that no excess enthalpy of solution could be discerned at 1180 K and 1 atm
for the forsterite-fayalite solution. Davidson and Mukhopadhyay (1984) and Davidson and Lindsley
(1989) opted to neglect the Fe-Mg interaction in their models. All other investigations have concluded
that Mg/Fe olivines have small positive derivation from ideal mixing.
Wood and Kleppa (1981) concluded that the forsterite-fayalite solution should be regarded as asymmetric
with respect to composition, in apparent contrast with previous studies (see Table 4.2 for a summary of
-4. Thermodynamic modelling-
74
values adopted in previous works). However, subsequent investigations have not confirmed this
proposition. In the present study, a symmetric regular solution model for olivine has been adopted.
Evaluating the values of Mg/Fe interaction parameters for symmetric models in Table 4.2, it is evident
that they appear to consistently fall within the range of 5±2. The only values that are in clear
disagreement are of Kawasaki and Matsui (1977) and Sack and Ghiorso (1989).
Table 4.2 Mixing parameters for (Fe,Mg)2SiO4 olivines (in kJ)
Value Reference WMg-Fe 11.6 Kawasaki and Matsui (1977) WMg-Fe 4.415 O'Neil and Wood (1979) WMg-Fe 4.1868 Wood and Kleppa (1981) WMg-Fe 8.3736 Wood and Kleppa (1981) WMg-Fe 0 Davidson and Mukhopadhyay (1984) WMg-Fe 5 O'Neill and Wall (1987) WMg-Fe 0 Davidson and Lindsley (1989) WMg-Fe 10.17±0.25 Sack and Ghiorso (1989) WMg-Fe 3.7±0.8 Wieser and Wood (1991) WMg-Fe 7.12±1.8 Koch-Müller et al. (1992) WMg-Fe 5.45±0.574 von Seckendorff and O'Neill (1993) WMg-Fe 6.44±P*0.09 Kawasaki and Ito (1994)
Experimental determinations of activity coefficients in olivine at high temperatures (Nafziger and Muan,
1967; Kitayama and Katsura, 1968; Williams, 1971) have lead to the conclusion that this phase exhibits
small positive deviations from ideality. Although Williams (1972) used a more complex model, Matsui
and Nishizawa (1974) have shown that the data on olivine non-ideality are adequately represented by the
regular solution model (Thompson, 1967): ol
Gfofaex WXXG = (28)
Thus, the activity coefficients for the olivine phase are given by:
olGfofa
olGfafo
WXRTWXRT
2
2
ln,ln
==
γγ (29-30)
The value of olGW was derived by Andersen et al. (1981) from Fe-Mg partitioning between ilmenite and
olivine. They used two kinds of expressions to model the non-ideality of the olivine solid solution: the
symmetric Margules formulation and an asymmetric model that incorporates excess heat capacity terms
that are based on olivine-chloride exchange data and calorimetric data (Engi, 1980). Individual
parameters derived from different models were different but ∆Gexch was very similar within the
temperature range considered. For the present study, we assigned the following value to olGW =5248 –
3.26T that is derived from on a calibration based on the Fe2+-Mg partition between coexisting ilmenite-
olivine pairs assuming that this will be most consistent with our study.
The Ti in olivine was assumed an analytical artifact and ignored.
-4. Thermodynamic modelling-
75
4.3.3 Spinel
The chemistry of the spinels is characterized by a wide range of compositions and can be subdivided into
diverse solid solution series. Spinel minerals are cubic and contain eight formula units per unit cell. Their
structure consists of ccp (cubic close-packed) oxygen layers parallel to (111) with one eight of the
tetrahedral sites (A position) and one half of the octahedral sites (B position) occupied by metal cations.
All spinels contain two different cations, or at least cations with two different valence states in case of the
same element, in the ratio of 2:1. The general chemical formula for spinel is AB2O4 (or A8B16O32 per unit
cell), where A and B are cations of different valence: in the most common cases these are either 2+ and
3+ or 4+ and 2+. In most natural spinels the cations Fe2+, Mg2+, Fe3+, A13+, Cr3+, and Ti4+ make up at least
98 percent of all cations. Spinels are classified as normal or inverse, depending on the distribution of the
more abundant cation among the tetrahedral and octahedral sites. In unary AB2O4 spinels cation
distributions vary between the ordered limits termed "normal" (A cation in tetrahedral site, all B cations
in the octahedral sites; (A)[B]2O4 - e.g. Mg(Fe)2O4) and “inverse” (A and B cations in octahedral sites; B
cation in tetrahedral site; (B)[A,B]2O 4 e.g. Fe3+(Fe2+,Fe3+)2O4). In fact, all distributions falling between
these two extremes may be realized, and to describe this situation it is convenient to define an additional
parameter, x, the degree of inversion, which is the fraction of tetrahedral sites occupied by B ions. Thus x
may vary between 0 for the perfectly normal case and 1 for the perfectly inverse case.
OxigenB-atoms on octahedral siteA-atoms on tetrahedral site
Figure 4.3 Graphical representation of the spinel structure.
The calculation of activity – composition dependences of multi-component spinel is based on the model
of O’Neill and Navrotsky (1984) for binary spinel solution.
The procedure follows three distinct and successive steps:
1. The site occupancy for each cation and hence the contribution of the cation distribution to the free
energy of the solid solution, is calculated using the model of O’Neill and Navrotsky (1984). The free
energy of mixing at this stage is termed ∆Go(ICD), where ICD stands for ideal cation distribution.
-4. Thermodynamic modelling-
76
2. The excess free energy of mixing, which results from the mixing of cations of different sizes (called
SM for size mismatch). This procedure is also described in O’Neill and Navrotsky (1984) for binary
solution.
3. The effect of the simultaneous and potentially independent substitution of Mg and Fe2+ (M cations) on
one hand and Cr, Fe3+ and M+Ti (Y cations) on the other hand, is calculated using reciprocal solution
formalism, the excess free energy of mixing from this stage is termed ∆Go(REC). Fe2TiO4
Mg2TiO4
FeCr2O4
MgCr2O4
Fe3O4
MgFe2O4
(Fe2+) [Cr Cr] O4
(Mg) [Cr Cr] O4
(Fe2+) [Fe2+Ti] O4
(Mg) [Mg Ti] O4
(Fe3+) [Fe2+Fe3+] O4(Fe2+) [Fe3+Fe3+] O4
(Fe3+) [Mg Fe3+] O4(Mg) [Fe3+Fe3+] O4
Figure 4.4 Schematic representation of the spinel solid solution composition space illustrating the endmembers
involved in the solution model adopted in this study
At all stages this approach is based on fitting of the model to the experimental observations. Thus, the
regular solution parameters in stage 2 (SM) are obtained by fitting activities calculated from the ideal
cation distribution to experimentally determined activity-composition relations, and miscibility gaps, on
the relevant binary joins. Hence, any errors introduced in the first stage through the use of inappropriate
site preference energies are compensated for in the next stage.
Ideal cation distribution (in Al-free systems)
The approximation has been made that the site preference energies of Fe2+ and Mg are equal. With this
assumption, the site occupancies in the spinel may be defined as (O’Neill and Navrotsky, 1984):
Cation Tet. Site Oct. Site Sum Fe2++Mg 1 - x NTi + x 1 + NTi
Fe3+ x 2-2NTi-NCr-x 2-2NTi-NCr Cr - NCr NCr Ti - NTi NTi
total 1 2 3 The equilibrium cation distribution may be calculated from the equation:
02)1)(22(
)(ln 2 =++
−−−−+
+−x
xxNNxNx
RT FeMCrTi
Ti βα (31)
-4. Thermodynamic modelling-
77
where α and β are disordering energies. The change in the free energy of the spinel solution from cation
ordering, relative to an idealized standard state of complete order, is:
∑ ++=Δ +−2
2ln xxXXRTGFeMii
odisorder βα (32)
where Xi is the mole fraction of the i- type cations on each site, so that the first term on the right hand site
is the configurational entropy of the solution multiplied by temperature. The free energy of mixing of the
solid solution relative to the endmember component spinel is then:
.2ln)()( 423 RTXOMFeGXGICDG TiodisorderFe
odisorder
o −Δ−Δ=Δ + (33)
Size mismatch
The model of O’Neill and Navrotsky (1984) assumes that the regular solution interaction parameters (the
W terms) are independent of both the composition and the degree of inversion of the spinels.
The regular solution model results:
∑∑ −=ΔYM ji
jiji XXnWSMG, ,
0 )( (34)
and hence
))(()(ln,
∑∑∑ ∑ −−−− −++=j k
jkkjkijiYM j
jijii XXWWWnXXnWSMRT γ (35)
Where n is the number of sites per formula unit on which mixing takes place.
For spinel endmember components
CrTiTiCrTiFeFeCr
TiFeTiFeCrCrFeMgMgTiOMgFe
CrTiTiCrTiFeFeCr
TiFeTiFeCrCrFeMgMgTiOFeFe
FeTiFeTiFeCrTiCr
FeCrFeTiCrTiFeMgMgTiOMgCr
FeTiFeTiFeCrTiCr
FeCrFeTiCrTiFeMgMgTiOFeCr
FeCrFeCrTiFeTiCr
TiFeFeTiCrCrFeMgMgTiTiOMg
FeCrFeCrTiFeTiCr
TiFeFeTiCrCrFeMgMgTiTiOFe
XXWWWWXWXWXXRT
XXWWWWXWXWXXRT
XXWWWWXWXWXXRT
XXWWWWXWXWXXRT
XXWWWWXWXWXXRT
XXWWWWXWXWXXRT
)(222)1)(1(ln
)(222)1(ln
)(222)1)(1(ln
)(222)1(ln
)(222)1)(1(ln
)(222)1(ln
33
33242
33
33242
333
33242
333
33242
333
33242
333
33242
222
222
222
222
222
222
−−−
−−−
−−−
−−−
−−−
−−−
−−−
−−−
−−−
−−−
−−−
−−−
−++++−+=
−+++++=
−++++−+=
−+++++=
−++++−+=
−+++++=
++
+++
++
+++
+++
+++
+++
+++
+++
+++
+++
+++
γ
γ
γ
γ
γ
γ
(36-41)
Any interaction term between M and Y type cations are already implicitly taken care of in the calculation
of the cation disorder, and therefore do not appear in the above equation. Values for the W term are taken
from O’Neill and Navrotsky (1984) and O’Neill and Wall (1987) and are summarized in Table 4.3.
The reciprocal solution effect
The following are the independent reciprocal exchange reactions in the multi-component spinel solution
of interest of this study:
-4. Thermodynamic modelling-
78
MgCr2O4 + Fe3O4 = FeCr2O 4+ MgFe2O4 (REC 1)
Mg2TiO4 + 2Fe3O4 = Fe2TiO4 + 2MgFe2O4 (REC 2)
2MgCr2O4 + Fe2TiO4 = 2FeCr2O4 + Mg2TiO4 (REC 3)
The reciprocal solution model is described in details by Wood and Nicholls (1978). The model gives:
)2()1()1()1()(ln)2()1()(ln
)3()1()1()1()(ln)3()1()(ln
)3()1()2()1()(ln)3()2()(ln
42
42
342
342
342
342
RECGXXRECGXXRECRTRECGXXRECGXXRECRT
RECGXXRECGXXRECRTRECGXXRECGXXRECRT
RECGXXRECGXXRECRTRECGXXRECGXXRECRT
TiMgCrMgOMgFe
TiMgCrMgOFeFe
TiMgFeMgOMgCr
TiMgFeMgOFeCr
CrMgFeMgTiOMg
CrMgFeMgTiOFe
Δ−+Δ−=Δ+Δ=
Δ−+Δ−=Δ+Δ=
Δ−+Δ−=Δ+Δ=
+
+
+
+
γγ
γγ
γγ
(42-47)
The parameters required for the equations are listed in Table 4.3 and were obtained from various
experimental studies and discussed by O’Neill et al. (1987). Table 4.3 Solution parameters for the spinel solid solution model in the system Mg-Fe-Cr-Ti-O
Parameter Value(kJ mol-1) Cation distribution α 20 β -20
Size mismatch WCr-Fe3+ 6.25 WTi-Fe3+ 4.6 WTi-Cr 10
WMg-Fe2+ 1.96 Reciprocal solution
∆G (REC 1) 6.54 ∆G (REC 2) 0 ∆G (REC 3) 13.80
Combining the results of all three stages of the procedure to calculate the activity of spinel components
finally results:
lnγi = ln γi (ICD) + ln γi (SM) + ln γi (REC) (48)
4.4 Ilmenite-olivine exchange
The reaction describing the partitioning of Fe2+ and Mg between olivine and ilmenite is:
FeSi1/2O2 + MgTiO3= MgSi1/2O2 + FeTiO3 (49)
At the conditions of equilibrium, the equilibrium constant for the reaction may be defined as:
KRTGexch ln−=Δ (50)
If the minerals were ideal solid solutions (αi=Xi) then:
olilmMgFeDol
FeilMg
olMg
ilFe K
XXXX
K −−== )( (51)
where KD is the distribution coefficient, X is the mole fraction
79
Table 4.4 Run data as recalculated endmember parameters used for calculation for olivine-ilmenite exchange reactions
Starting Additional
N composition Run T, oC P, kbar Xilm Xgk Xhem Xesk Xcor Xfo Xfa Kd
phases
1 SM2 NS4 1000 25 0.48 0.40 0.04 0.08 - 0.86 0.14 7.53 opx, spi, ru 2 NS7 1000 35 0.52 0.38 0.01 0.09 - 0.85 0.15 7.51 opx, spi 3 NS3 1100 25 0.41 0.40 0.06 0.14 - 0.86 0.14 6.20 opx, spi 4 NS9 1100 35 0.47 0.38 0.01 0.14 - 0.85 0.15 6.96 opx, spi, ru 5 NS1 1200 25 0.37 0.38 0.05 0.20 - 0.86 0.14 5.85 opx, spi 6 NS6 1200 35 0.37 0.36 0.06 0.22 - 0.87 0.13 6.65 opx, spi 7 NS2 1300 25 0.35 0.33 0.05 0.27 - 0.86 0.14 6.36 opx, spi 8 NS8 1300 35 0.32 0.32 0.00 0.37 - 0.87 0.13 6.85 opx, spi, ru
9 SM6 NS27 1000 25 0.08 0.84 0.06 0.02 - 0.98 0.02 4.59 spi 10 NS28 1000 35 0.13 0.83 0.02 0.01 - 0.98 0.02 6.19 spi 11 NS18 1100 25 0.11 0.81 0.04 0.04 - 0.97 0.03 4.52 spi 12 NS25 1100 35 0.11 0.82 0.03 0.04 - 0.97 0.03 4.52 spi 13 NS17 1200 25 0.12 0.78 0.03 0.07 - 0.97 0.03 4.70 spi 14 NS22 1200 35 0.09 0.81 0.04 0.06 - 0.97 0.03 4.39 spi 15 NS19 1300 25 0.11 0.78 0.02 0.10 - 0.96 0.04 3.16 spi 16 NS24 1300 35 0.07 0.81 0.05 0.07 - 0.97 0.03 3.37 spi 17 NS81 1300 50 0.09 0.69 0.04 0.18 - 0.97 0.03 4.81 spi 18 NS37 1200 50 0.06 0.81 0.00 0.13 - 0.98 0.02 4.45 spi 19 NS49 1200 70 0.11 0.65 0.04 0.20 - 0.97 0.03 5.96 spi
20 SM12 NS56 1000 25 0.45 0.43 0.04 0.09 - 0.87 0.13 7.13 opx, spi, ru 21 NS55 1000 35 0.38 0.42 0.09 0.11 - 0.88 0.12 7.06 opx, spi, ru 22 NS61 1000 50 0.38 0.41 0.06 0.15 - 0.89 0.11 7.78 opx, spi, ru 23 NS57 1100 25 0.40 0.43 0.03 0.14 - 0.87 0.13 6.49 opx, spi, ru 24 NS59 1100 35 0.36 0.40 0.07 0.17 - 0.88 0.12 6.91 opx, spi, ru 25 NS44 1200 25 0.36 0.40 0.04 0.20 - 0.87 0.13 6.00 opx, spi, ru 26 NS45 1200 35 0.36 0.38 0.05 0.20 - 0.87 0.13 6.48 opx, spi, ru 27 NS65 1300 35 0.33 0.34 0.05 0.28 - 0.91 0.09 9.30 opx, spi, ru 28 NS52 1200 50 0.29 0.33 0.00 0.39 - 0.90 0.10 7.49 opx, spi, ru 29 NS62 1200 70 0.24 0.33 0.09 0.34 - 0.91 0.09 8.01 opx, spi, ru 30 NS60 1300 25 0.28 0.37 0.00 0.35 - 0.90 0.10 6.84 opx, spi, ru
80
Table 4.4 (Continued)
Starting Additional
N composition Run T, oC P, kbar Xilm Xgk Xhem Xesk Xcor Xfo Xfa Kd
phases 1 SM7 NS31 1000 25 0.47 0.40 0.06 0.05 0.01 0.85 0.15 6.83 opx, spi, ru 2 NS32 1000 35 0.52 0.38 0.05 0.05 0.01 0.85 0.15 7.81 opx, spi, ru 3 NS20 1100 25 0.42 0.39 0.07 0.09 0.02 0.85 0.15 5.84 opx, spi 4 NS23 1100 35 0.46 0.41 0.03 0.07 0.02 0.87 0.13 7.24 opx, spi, ru, gar 5 NS29 1200 25 0.39 0.42 0.06 0.10 0.03 0.85 0.15 5.38 opx, spi 6 NS30 1200 35 0.37 0.38 0.08 0.13 0.04 0.86 0.14 5.77 opx, spi 7 NS21 1300 25 0.38 0.40 0.04 0.14 0.05 0.85 0.15 5.56 opx, spi 8 NS26 1300 35 0.33 0.34 0.06 0.20 0.07 0.86 0.14 6.13 opx, spi 9 SM8 NS33 1200 25 0.44 0.40 0.06 0.06 0.03 0.83 0.17 5.19 opx, spi 10 SM11 NS66 1200 25 0.40 0.47 0.01 0.10 0.03 0.87 0.13 5.89 opx, ru, liq 11 NS67 1200 35 0.32 0.47 0.04 0.12 0.04 0.90 0.10 6.19 opx, spi, ru, gar 12 NS70 1200 50 0.23 0.33 0.10 0.30 0.04 0.91 0.09 7.17 opx, spi, ru, gar
g
gg
80
-4.Thermodynamic modeling-
81
When minerals are not ideal (αi=Xiγi) derivation from ideal solid solution exists and the model requires
knowledge of the activity coefficients γ:
γγγγγ
KKXXXX
K DolFe
ilMg
olMg
ilFe
olFe
ilMg
olMg
ilFe =⋅= (52)
Since K is constant at constant temperature and pressure, evaluation of the variation of KD as a function
of composition provides information on the activity composition relation (Kγ). As exchange reactions
generally involve small amount of free energy, they are sensitive to the activity-composition relations.
For ∆Gexch and WG we can write
∆Gexch = ∆Hexch + P∆Vexch - T∆Sexch (53)
WG=WH+PWV-TWS (54)
The exchange energy (∆Gexch) will be zero if the two phases are in Fe-Mg exchange equilibrium.
Therefore, the complete expression for the reaction is
RTln KD = - ∆Hexch - P∆Vexch + T∆Sexch- RTlnγil + RTlnγgk - RTlnγfo +RTlnγfa (55)
Activity coefficients (25, 26) for ilmenite and (29, 30) for olivine endmembers derived in previous
sections were substituted in equation (55).
Compositions of olivines and ilmenites from experiments (Table 4.4) were fitted to the obtained equation
and solved by the method of least squares, thus we have over-determined system of linear equations: in
matrix notation Ax=B. Least squares solution x minimizes the length of the vector (Ax-B) in L2 metric
space, that is norm of (Ax-B). Solution x was obtained by Matlab back slash operator which is based on
QR decomposition or Cholesky factorization of matrix A depending on the analysis of the matrix A. We
used two models with 8 or 9 unknowns: ∆Hexch, ∆Sexch, ∆Vexch, gkeskHW − , gkesk
SW − , eskilHW − , eskil
SW − ,
ileskHW − , ilesk
SW − . The first model treats ∆Vexch of exchange reaction as a known parameter derived from
other studies (-0.047 J/bar Andersen et al (1981)) which leaves 8 unknown parameters. For the second
model, we took ∆Vexch as an unknown variable to evaluate a potential pressure effect. The resulting
parameters of the least square analysis are listed in table 4.5.
-4.Thermodynamic modeling-
82
Table 4.5a) Parameters for the ilmenite solution model for temperature dependent interaction parameters. Parameters all data Joules/mole V (Andersen) V unknown
∆Hexch -29066 (8405) -28899 7969 ∆Sexch -6.9265 (5.9) -8.12 5.6756
WHesk-gk 42849000 (128551000) 57348000 (122202000)
WSesk-gk -70038 (110870) -69170 (105107)
WHilm-esk 42568000 (128542000) 57165000 (122205000)
WSilm-esk -70232 (110850) -69314 (105088)
WHesk-ilm 43134000 (128566000) 57686000 (122224000)
WSesk-il -69829 (110860) -68920 (105098)
∆Vexch -0.11 (0.04) Table 4.5 b) Parameters for the ilmenite solution model for temperature independent interaction parameters (full and reduced data set). Parameters all data excluding some experiments Joules/mole V (Andersen) V unknown V (Andersen) V unknown
∆Hexch -13748 (6258) -13365.00 (7686) -11713 (3612) -12154 (4318) ∆Sexch 3.4619 (4) 3.65 (5) 5.21 (2) 4.991 (2)
WGesk-gk -29344000 (142544000) -29945000 (145755000) 122790000 (77100000) 123600000 (79120000)
WGilm-esk -29350000 (142540000) -29950000 (145750000) 122770000 (77100000) 123590000 (79110000)
WGesk-ilm -29360000 (142550000) -29961000 (145751000) 122780000 (77100000) 123600000 (79110000)
∆Vexch -0.05 (0.04) -0.042613 (0.02) Table 4.5 c) Regularized parameters for the ilmenite solution model for temperature independent interaction parameters (reduced data set)
ParametersJoules/mole
regularized
∆Hexch -12164 (2941) ∆Sexch 5.02 (2)
WGesk-gk 13933 (4119)
WGilm-esk 1612 (6531)
WGesk-ilm 6357 (5798)
By fitting all our experimental results directly to the equation we obtained parameters listed in the first
part of Table 4.5. Taking the obtained parameters, we rearrange the equation for temperature and
calculated temperatures for each of our experiments employing the experimental phase composition (Fig.
4.6) in order to check the consistency of the results. Obtained parameters have rather high values and
correlation with experimental temperature is rather poor. Furthermore, the WH and WS terms of the
interaction parameters are interrelated and it is most probably not possible or practical to extract them
separately from our experiments. For further thermodynamic modeling, we assumed interaction parameter
to be temperature independent, which decreased the number of unknown parameters to solve in the
equations from 8 to 5 or from 9 to 6. There is no significant difference between the two models (V-fixed,
V-free) employed and the value obtained for ∆Vexch is close to that determined by Andersen.
In order to improve the fits, we evaluated the experimental set carefully realizing that for some
experiments we obtained strong deviations from the experimental temperature when performing the back-
calculations. Consequently, we consider these points as outliers and removed them from the data set for
-4.Thermodynamic modeling-
83
the regression. In detail: point 27 (corresponding to experiment NS 65) is characterized by slightly lower
Fe-content of the olivines (higher XMg) and was performed at highest temperature of our experimental
range; experiment NS37 (point 18) has suffered evident iron loss from the experimental charge and is
most probably not equilibrated over the entire charge; olivines in experiments NS19 and NS 28 (points
15 and 10) contain essential amounts of Ti and are most probably not olivine but clinohumite or olivine-
clinohumite polysomatic intergrowth. The fitting procedure was redone with the curtailed sample set:
Margules parameters remain rather high, but the correlation of the calculated with the experimental
temperature results much improved (Fig. 4.6, c). However, ∆Vexch becomes slightly different and some
distinction between the models is observed, the model with not fixed ∆Vexch gives slightly lower
temperatures; further exclusion of data points did not result any improvement.
The solution of our model evidently depends on small errors introduced by input parameters that result in
big errors for the obtained solution parameters. Errors of the obtained parameters calculated for a
confidence interval of 95% reveal large uncertainties by straight fitting of the data. In least square
modeling, there is the implied assumption that the distribution of errors around the constant vector is
normally distributed, which is not the case for exchange experiments; instead, it is some unknown
function of the starting composition, reaction path, diffusion rates and duration of the experiment. In
addition, if we have a closer look at the obtained parameters it is apparent that the first unknowns (∆Hexch,
∆Sexch) that are providing the principal input to the solution of the matrix are characterized by rather
compatible values. The contribution of W-parameters to the global solution of the matrix is smaller and
they have unrealistically high values as well as uncertainties. The problem is that our matrix data set is ill-
conditioned. We considered our dataset as ill-posed and applied regularization methods for computing
stabilized solutions. The matrix set up for the least square analysis was regularized by the Tikhonov
method with regularization parameters obtained by the l-curve or gcv (generalized cross-validation
function) method that provides valid parameters in order to obtain more stable solutions (see appendix).
1 2 3 4 5 6 7 8 9 10 11
0.5
1.0
1.5
2.02.20 3.24 2.36 2.28
2.96 2.83 2.48Z(s)
S Figure 4.5 illustrates a literature example of spectral composition reconstruction taken from the book of
Tikhonov “Solutions of ill-posed problems”. Mathematically, it is similar to our problem of solving over
determined systems of linear equations. Reconstruction of spectra by direct fitting of experimental results
Figure 4.5 Reconstruction of spectra by solving over-determined system of linear equations. Direct fitting of experimental data results a “saw-tooth” distribution which has nothing common with real spectra, but after applied the regularization procedure solution drastically improved.
-4.Thermodynamic modeling-
84
gives a “saw-tooth” distribution, which has nothing common with a real spectrum, but after applying the
regularization procedure the solution drastically improved.
Uncertainties were calculated with the “bootstrap” method. The reduced dataset omitting evidently
outlying experiments (26 equations) and with the exchange volume of the reaction taken from Andersen
was accepted as the base describing the exchange reaction and was taken for further processing.
T experimental
T calc (V free)T calc (V fix)
a)
b)
c)
Figure 4.6 Comparison of experimental and calculated temperatures employing the parameters listed in Table 4.5. a) all experiments, b) all experiments with temperature-independent interaction parameters, c) excluding some experiments. Experiments (runs) are given in the same order as listed in Table 4.4 (first column).
-4.Thermodynamic modeling-
85
Al-bearing system
Ilmenites in experiments from Al-bearing systems exhibit up to 3 wt% Al2O3 in solid solution. Therefore,
we attempted to evaluate the modeling parameters including corundum (Al2O3) in the ilmenite solid
solution. The same procedure as for chromium was applied to alumina in order to evaluate the activity
coefficients for corundum in ilmenite. Results of the linear least square fitting and of the further
regularization are provided in Table 4.6. Calculated errors for the direct computing method completely
overlap the obtained parameters (not given). In Figure 4.7 calculated and experimental temperatures are
shown, the values are in a good agreement.
Table 4.6 Parameters obtained for alumina-bearing system.
Parameters Joules/mole
data regularized
∆Hexch -14665 (2891) -16961 (4461) ∆Sexch 3.7 (2) 0.91 (3)
WGcor-gk -192240000 (63990000) 41888 (12976)
WGilm-cor -192610000 (64010000) -44011 (10029)
WGcor-ilm -192170000 (63990000) 2120 (10934)
T experimentalT calculated
0 1 2 3 4 5 6 7 8 9 10 11 12 13
1000
1200
1400
1600
1800
2000
Runs
Tem
pera
ture
, K
Figure 4.7 Experimental temperatures and temperatures calculated with the parameters listed in Table 4.6. Runs correspond to numbers (first column) in Table 4.4 4.4 Spinel - ilmenite exchange.
Prior to calculating element partitioning between ilmenite and spinel, the olivine–spinel Fe2+-Mg
exchange proposed by the model of O’Neill and Wall (1987) is examined: These authors presented an
exchange geothermometer that we applied to our experimental data in order to compute temperatures of
equilibration at experimental pressures. Figure 4.8 presents a comparison of the calculated and
experimental temperatures respectively. Results are generally in a good agreement indicating that the
-4.Thermodynamic modeling-
86
adopted solution model for spinel (O’Neill and Navrotsky, 1983, 1984) is suitable to treat our
experimental spinels. Some of the experiments clearly fall outside the general correlation; the possible
reasons will be discussed later for the corresponding mineral pairs.
0 5 10 15 20 25 30 35600
800
1000
1200
1400
1600
1800
2000
Tem
pera
ture
, K
experimental temperaturecalculated from O'Neill (1987)
Figure 4.8 Comparison of experimental temperature and temperatures calculated with the O’Neill and Wall (1987) olivine – spinel geothermometer.
For a given pressure, temperature and bulk Fe/Mg ratio equilibrium spinel compositions coexisting with
ilmenite can be represented by the following exchange reactions:
- Fe-Mg exchange spinel-ilmenite
- Cr-Ti exchange spinel-ilmenite
- Fe3+ exchange with Cr and Ti spinel-ilmenite
The last reaction involving Fe3+ was not taken into consideration for modeling because ferric iron was not
directly determined and its content in spinel and ilmenite was calculated from charge balance. In addition,
as discussed in chapter 3, ferric iron contents of oxide phases are generally low and nearly invariant for
most but a few samples.
4.4.1 Fe-Mg exchange between spinel and ilmenite
The exchange of Fe2+-Mg between ilmenite and spinel can be represented by three different reactions
among the following mineral endmembers:
2MgTiO3 + Fe2TiO4 = 2FeTiO3 + Mg2TiO4 (I) (56)
MgTiO3 + FeCr2O4 = FeTiO3 + MgCr2O4 (II) (57)
MgTiO3 + FeFe2O4 = FeTiO3 + MgFe2O4 (III) (58)
where
87
Table 4.7 Run data given as recalculated endmember compositions used for calculation of spinel-ilmenite exchange reactions.
XMg XFe2+ XCr XTi XFe3+ Additional Run T, oC P, kbar spinel spinel spinel spinel spinel
Xilm Xgk Xhem Xesk Kd(Fe-Mg)
Kd(Cr-Ti) phases
1 SM2 NS4 1000 25 0.40 0.60 0.87 0.07 0.06 0.48 0.40 0.04 0.08 1.28 0.007 opx, ol, ru 2 NS7 1000 35 0.37 0.63 0.91 0.07 0.02 0.52 0.38 0.01 0.09 1.29 0.007 opx, ol 3 NS3 1100 25 0.44 0.56 0.84 0.10 0.06 0.41 0.40 0.06 0.14 1.25 0.019 opx, ol 4 NS9 1100 35 0.40 0.60 0.87 0.07 0.06 0.47 0.38 0.01 0.14 1.21 0.013 opx, ol, ru 5 NS1 1200 25 0.48 0.52 0.80 0.14 0.07 0.37 0.38 0.05 0.20 1.12 0.046 opx, ol 6 NS6 1200 35 0.47 0.53 0.83 0.10 0.07 0.37 0.36 0.06 0.22 1.07 0.037 opx, ol 7 NS2 1300 25 0.48 0.52 0.78 0.15 0.06 0.35 0.33 0.05 0.27 1.01 0.076 opx, ol 8 NS8 1300 35 0.52 0.48 0.84 0.13 0.02 0.32 0.32 0.00 0.37 0.93 0.086 opx, ol, ru 9 SM6 NS27 1000 25 0.84 0.16 0.65 0.25 0.10 0.08 0.84 0.06 0.02 1.91 0.008 olivine
10 NS28 1000 35 0.81 0.19 0.67 0.26 0.07 0.13 0.83 0.02 0.01 1.55 0.006 olivine 11 NS18 1100 25 0.82 0.18 0.64 0.29 0.07 0.11 0.81 0.04 0.04 1.67 0.019 olivine 12 NS25 1100 35 0.81 0.19 0.69 0.28 0.04 0.11 0.82 0.03 0.04 1.76 0.019 olivine 13 NS17 1200 25 0.80 0.20 0.60 0.37 0.03 0.12 0.78 0.03 0.07 1.68 0.047 olivine 14 NS22 1200 35 0.84 0.16 0.61 0.32 0.07 0.09 0.81 0.04 0.06 1.62 0.037 olivine 15 NS19 1300 25 0.83 0.17 0.56 0.42 0.02 0.11 0.78 0.02 0.10 1.47 0.084 olivine 16 NS24 1300 35 0.84 0.16 0.48 0.48 0.03 0.07 0.81 0.05 0.07 2.13 0.084 olivine 17 NS81 1300 50 0.87 0.13 0.68 0.27 0.05 0.09 0.69 0.04 0.18 1.17 0.092 olivine 18 NS37 1200 50 0.94 0.06 0.83 0.14 0.03 0.06 0.81 0.00 0.13 0.81 0.026 olivine 19 NS49 1200 70 0.79 0.21 0.77 0.23 0.00 0.11 0.65 0.04 0.20 1.64 0.079 olivine 20 SM10 NS39 1200 35 0.85 0.15 0.40 0.48 0.12 0.10 0.84 0.03 0.03 1.47 0.034 MgO 21 NS36 1200 50 0.87 0.13 0.59 0.35 0.06 0.10 0.82 0.03 0.05 1.19 0.030 MgO 22 SM12 NS56 1000 25 0.41 0.59 0.93 0.06 0.01 0.45 0.43 0.04 0.09 1.39 0.007 ol, opx, ru 23 NS55 1000 35 0.41 0.59 0.92 0.06 0.01 0.38 0.42 0.09 0.11 1.56 0.010 ol, opx, ru 24 NS61 1000 50 0.45 0.55 0.90 0.07 0.04 0.38 0.41 0.06 0.15 1.34 0.014 ol, opx, ru 25 NS57 1100 25 0.46 0.54 0.88 0.08 0.04 0.40 0.43 0.03 0.14 1.24 0.016 ol, opx, ru 26 NS59 1100 35 0.46 0.54 0.86 0.09 0.05 0.36 0.40 0.07 0.17 1.31 0.023 ol, opx, ru 27 NS44 1200 25 0.49 0.51 0.82 0.13 0.05 0.36 0.40 0.04 0.20 1.15 0.041 ol, opx, ru 28 NS45 1200 35 0.47 0.53 0.85 0.10 0.05 0.36 0.38 0.05 0.20 1.18 0.033 ol, opx, ru 29 NS65 1300 35 0.52 0.48 0.86 0.09 0.05 0.33 0.34 0.05 0.28 0.97 0.050 ol, opx, ru 30 NS52 1200 50 0.49 0.51 0.86 0.14 0.00 0.29 0.33 0.00 0.39 1.21 0.095 ol, opx, ru 31 NS62 1200 70 0.51 0.49 0.87 0.13 0.00 0.24 0.33 0.09 0.34 1.26 0.091 ol, opx, ru 32 NS60 1300 25 0.58 0.42 0.84 0.14 0.02 0.28 0.37 0.00 0.35 0.93 0.088 ol, opx, r
88
Table 4.7 (Continued)
XMg XFe2+ XCr XTi XFe3+ Additional Run T, oC P, kbar spinel spinel spinel spinel spinel Xilm Xgk Xhem Xesk Kd(Fe-Mg)
Kd(Cr-Ti) phases
33 SM14 NS51 1200 25 1 0 0.92 0.08 0.00 0.00 0.70 0.00 0.30 - 0.019 ol, ru 34 NS68 1200 35 1 0 0.93 0.07 0.00 0.00 0.71 0.00 0.29 - 0.015 ol, ru 35 NS54 1200 50 1 0 0.94 0.06 0.00 0.00 0.69 0.00 0.31 - 0.014 ol, ru
88
-4.Thermodynamic modelling-
89
uspgk
ilqanexch aa
aaRTIG
⋅
⋅−=Δ 2
2
ln)( (59)
chrgk
ilpchexch aa
aaRTIIG
⋅
⋅−=Δ ln)( (60)
maggk
ilmgfexch aa
aaRTIIIG
⋅
⋅−=Δ ln)( (61)
with ai corresponding to the activity of the respective endmembers for every reaction. The abbreviations
are il - ilmenite, gk - geikilite, usp – ulvospinel (Fe2TiO4-spinel), qan – qandelite (Mg2TiO4-spinel), chr –
chromite (FeCr2O4-spinel), pch – picrochromite (MgCr2O4), mag – magnetite (Fe2+Fe3+2O4), mgf –
magesioferrite (MgFe3+2O4).
The general algorithm for calculating the parameters is identical to the ilmenite-olivine mineral pairs. The
calculations were essentially performed in the same order of treatment and simplifications as exemplified
for the ilmenite-olivine exchange, i.e. (1) all samples with temperature dependent interaction parameters;
(2) all samples with temperature independent interaction parameters; (3) reduced data set with
temperature independent interaction parameters; (4) additionally, the 3 considered reactions were solved
simultaneously instead of individually; and (5) regularization was performed on the results.
Correlation between calculated and experimental temperatures for the entire data set employing either
temperature dependent or independent interaction parameters is not satisfying (Table 4.8a) and b), Fig.
4.9). Consequently, a number of experiments that were responsible for the largest deviations were
excluded from the data set. In detail this concerns experiment NS37 (point 18), that results unrealistically
high temperatures most probably related to the evident iron loss; this experiment was as well excluded
from the calculation of the ilmenite-olivine exchange and resulted out of correlation when the O’Neill and
Wall olivine-ilmenite thermometer was applied. Data point 9 (NS27) was also excluded from the general
fit: Ilmenite observed in this run is characterized by relatively low Cr content (Table 4.7), that was not
crucial for ilmenite-olivine exchange but probably for the exchange with spinel were Cr is an essential
component that becomes important. Data points 20 and 21 (NS 39 and NS36) were excluded as well.
These experiments were performed in a silica-free system and the coexisting phase is magnesiowustite
(Mg,Fe)O that might be the cause for this inconsistently. After those data were discarded, the correlation
of the experimental and calculated temperatures improved considerably (Table 4.8c), Fig. 4.9 c) and
values obtained from all three reactions for temperature independent interaction parameters became more
concord.
This reduced data set was taken for further calculations. As the 3 reactions considered are not independent
of each other, we treated the reactions simultaneously instead of solving them individually and finally
applied the aforementioned regularization procedure to them (Table 4.8d).
-4.Thermodynamic modelling-
90
Table 4.8a) Modeling parameters for the Fe-Mg exchange between ilmenite and spinel for temperature-dependent interaction parameters, in Joules/mole. Parameters all data Joules/mole usp-qand chr-pch mag-fmg ∆Hexch 26752 (21376) -12326.00 (14151) -3796.60 (17122) ∆Sexch 43.67 (15) -4.78 (10) 1.98 (12) ∆Vexch 0.01 (0.1) 0.03 (0.07) 0.04 (0.08)
WHesk-gk -30843000 (165963000) 77477000 (219733000) 22030000 (265880000)
WSesk-gk 81010 (142840) 53420 (189120) 63932 (228838)
WHil-esk -31635000 (165955000) 76844000 (219736000) 21539000 (265881000)
WSil-esk 80536 (142814) 53011 (189089) 63613 (228797)
WHesk-il -30605000 (165985000) 77558000 (219772000) 21981000 (265919000)
WSesk-il 81082 (142828) 53463 (189107) 63887 (228823)
Table 4.8b) Modeling parameters for the Fe-Mg exchange between ilmenite and spinel for temperature-independent interaction parameters, in Joules/mole. Parameters all data simple Joules/mole usp-qand chr-pch mag-fmg ∆Hexch 18024 (17504) -17836 (10722) -14467 (12710) ∆Sexch 35.64 (11) -9.62 (7) -6.67 (8) ∆Vexch -0.09 (0.09) -0.02 (0.06) -0.02 (0.06)
WGesk-gk -246340 (176576340) 109760000 (216330000) 79839000 (256431000)
WGil-esk -317720 (176567720) 109750000 (216320000) 79850000 (256420000)
WGesk-il -116300 (176576300) 109770000 (216330000) 79851000 (256419000)
Table 4.8c) Modeling parameters for the Fe-Mg exchange between ilmenite and spinel for temperature-independent interaction parameters on the reduced data set, in Joules/mole . Parameters excluding experiments Joules/mole usp-qand chr-pch mag-fmg ∆Hexch 30982 (14787) -12730 (7741) -12000.00 (7539) ∆Sexch 41.81 (9) -7.25 (5) -6.10 (5) ∆Vexch -0.20 (0.07) -0.08 (0.04) -0.08 (0.04)
WGesk-gk 58447000 (124123000) 174530000 (129960000) 151110000 (126560000)
WGil-esk 58390000 (124120000) 174530000 (129960000) 151120000 (126560000)
WGesk-il 58569000 (124121000) 174540000 (129960000) 151120000 (126570000)
Table 4.8d) Modeling parameters for the Fe-Mg exchange between ilmenite and spinel for temperature independent interaction parameters on the reduced data set for simultaneous regression (left side) and optimized through regularization (right side), in Joules/mole
Parameters all reactions together regularized Joules/mole usp-qand chr-pch mag-fmg usp-qand chr-pch mag-fmg ∆Hexch 26419 (18182) -6070 (14102) -9532 (14102) 28204 (11803) -3904 (9923) -7137 (10001)∆Sexch 33.97 (12) 2.01 (9) 0.32 (9) 34.72 (8) 3.25 (6) 1.71 (7) ∆Vexch -0.21 (0.09) -0.08 (0.08) -0.06 (0.08) -0.23 (0.06) -0.09 (0.06) -0.07 (0.06)
WGesk-gk 93237000 (140203000) -19190 (3252)
WGil-esk 93201000 (140199000) -43696 (10381)
WGesk-il 93323000 (140197000) 62896 (8186)
-4.Thermodynamic modelling-
91
experimental temperaturereaction I, usp-qandreaction II, chr-pchrreaction III, mag-fmg
a)
b)
c)
Figure 4.9 Comparison of calculated and experimental temperatures for Fe2+-Mg exchange between ilmenite and spinel. Temperatures were calculated with the parameters listed in Table 4.8, experiments are in the same order as listed in Table 4.7 - a) for all experiments with temperature-dependent interaction parameters, b) all experiments with temperature-independent interaction parameters, c) reduced data set with temperature-independent interaction parameters.
4.4.2 Cr-Ti exchange between spinel and ilmenite
In order to further constrain the ilmenite solid solution parameters, we considered the distribution of
chromium and titanium between coexisting spinel and ilmenite that can be represented by the following
-4.Thermodynamic modelling-
92
two reactions, where the first (I, 62) reaction describes the exchange for iron endmembers and the second
(II, 63) for magnesium endmembers:
FeTiO3 + FeCr2O4 = Cr2O3 + Fe2TiO4 (I) (62)
MgTiO3 + MgCr2O4 = Cr2O3 + Mg2TiO4 (II) (63)
The data set utilized for these calculations is provided in Table 4.7. The last three experiments in this
table originate from an iron free system and where not considered in the general calculation. Our attempt
to include them to the computation resulted in considerable increase in the uncertainties for calculated the
parameters.
In the calculations of the Cr-Ti exchange only one experiment was excluded from data set (point 20, NS
39), further reduction of the data set did not lead to any significant improvement of the correlation. The
experiment NS 28 (points 10) exhibiting a low Cr content of the ilmenite that was excluded for Fe2+-Mg
exchange reactions is in good agreement with the entire data set, probably due to the fact that in this
exchange reaction set, the activity coefficient for eskolaite is evaluated directly.
The same fitting procedure as for Fe-Mg olivine-ilmenite and spinel-ilmenite exchange was performed.
At first we fitted the entire data set with temperature dependant W parameters and then simplified the
model by taking Wg temperature independent. Thereafter, we evaluated the results and excluded some
experiments and fitted the reaction simultaneously and finally applied regularization to this results. It is
worth to note that the obtained parameters, even without regularization, are more physically reasonable in
comparison with the parameters obtained from the Fe-Mg exchange reaction between spinel and ilmenite
Table 4.9a) Modeling parameters for the Cr-Ti exchange between ilmenite and spinel for temperature-dependent interaction parameters, in Joules/mole.
Parameters all data Joules/mole I - Fe II - Mg ∆Hexch -33904 (130133) -113730.00 (108860) ∆Sexch -15 (88) -69.37 (72) ∆Vexch 0.08 (0.08) 0.08 (0.05)
WHesk-gk 97273 (145737) 192040 (109420)
WSesk-gk 16 (101) 83 (73)
WHilm-esk 151130 (565640) 298280 (526110)
WSilm-esk -2 (381) 80 (353)
WHesk-ilm 204960 (182720) 156240 (98660)
WSesk-il 148 (134) 101 (72)
-4.Thermodynamic modelling-
93
Table 4.9b) Modeling parameters for the Cr-Ti exchange between ilmenite and spinel for temperature-independent interaction parameters for all data and the reduced data set, in Joules/mole.
Parameters all data excluding 1 experiment Joules/mole I - Fe II - Mg I - Fe II - Mg ∆Hexch 3405.00 (18139) -5709.9 (17540) 16540 (14883) 5693 (16806) ∆Sexch 1.33 (9) -2 (6) 6.28 (8) 1.64 (6) ∆Vexch 0.01 (0.07) 0.011 (0.05) -0.02 (0.06) -0.02 (0.05)
WGesk-gk 61883.00 (8324) 63618 (9658) 55281 (6875) 56880 (9323)
WGilm-esk 114000.00 (33870) 165630 (43990) 94779 (27441) 139750 (41780)
WGesk-ilm 4892.50 (14169) -1164.2 (9827) 5792 (11239) -690 (8943)
Table 4.9c) Modeling parameters for the Cr-Ti exchange between ilmenite and spinel for temperature-independent interaction parameters on the reduced data set for simultaneous regression (left side) and optimized through regularization (right side), in Joules/mole
Parameters all reactions together regularized Joules/mole I - Fe II - Mg I - Fe II - Mg ∆Hexch 15602 (13296) 9990.1 (10352) 28451 (4812) 16156 (4826) ∆Sexch 3.6049 (6) -1.31 (5) 3.06 (3) -4.92 (3) ∆Vexch -0.015 (0.06) -0.038 (0.04) -0.10 (0.04) -0.07 (0.03)
WGesk-gk 49909 (4864) 38271 (1487)
WGilm-esk 90007 (21463) 33281 (4664)
WGesk-ilm 11375 (6807) 24354 (3682)
-4.Thermodynamic modelling-
94
a)
b)
c)
experimental temperaturereaction I, Fe-endmembersreaction II, Mg-endmembers
Figure 4.10 Comparison of calculated and experimental temperatures for the Cr-Ti exchange between ilmenite and spinel. Temperatures were calculated with parameters listed in table 4.9; experiments are in the same order as in Table 4.7: a) for all experiments temperature-dependent interaction parameters; b) all experiments with temperature-independent interaction parameters; c) reduced data set with temperature-independent interaction parameters.
4.5 Internally consistent solution
In order to obtain a set of parameters that is consistent with all investigated exchange reactions involving
ilmenite, we simultaneously solved all equation derived above. The resulting set of free energy and
interaction parameters are listed in Table 4.10
-4.Thermodynamic modelling-
95
Table 4.10 Parameter set derived by simultaneous treatment of all exchange reactions
Parameters all reactions regularized ∆Hexch
ilm-ol -3021 (15310) -1035 (3031) ∆sexch
ilm-ol 15.6 (10) 15.5 (2)
∆Hexchusp-qan 4990 (17692) 325 (2956)
∆Sexchusp-qan 14.9 (11) 8.5 (2)
∆Vexchusp-qan -0.159 (0.097) -0.167 (0.076)
∆Hexchchr-pch -16785 (15092) -4502 (3028)
∆Sexchchr-pch -7.5 (10) -0.8 (3)
∆Vexchchr-pch -0.054 (0.087) -0.069 (0.076)
∆Hexchmag-mgf -20247 (15092) -5340 (3089)
∆Sexchmag-mgf -9.2 (10) -0.7 (2)
∆Vexchmag-mgf -0.034 (0.087) -0.052 (0.07)
∆HexchI-Fe -22580 (17844) 5221 (2921)
∆SexchI-Fe -28.1 (10) -16.2 (3)
∆VexchI-Fe 0.026 (0.084) -0.049 (0.07)
∆Hexch
II-Mg -15529 (20317) 7538 (2820) ∆Sexch
II-Mg -28.1 (11) -17.8 (2) ∆Vexch
II-Mg -0.017 (0.091) -0.079 (0.07)
WGesk-gk 33678 (6175) 23141 (2002)
WGilm-esk 85748 (7605) 50461 (3164)
WGesk-ilm 1505 (22439) 5436 (2633)
Using the obtained parameters we recalculated temperatures of experiments for three phase assemblages.
The correlation is shown in Figure 4.11. Application of these parameters for selected mineral pairs gives
improper results (negative temperatures). Combination of all exchange reactions makes parameters
dependant on all phases present and does not allow separate treatment.
Figure 4.11 Comparison of calculated and experimental temperatures for the three phase assemblage. Temperatures were calculated with parameters listed in table 4.10; experiments are in the same order as in Table 4.4
-4.Thermodynamic modelling-
96
4.6 Calibration for pressure
In an attempt to evaluate our models for barometry we rearranged our equations and solved them for
pressure and calculated the experimental pressure utilizing the modeling parameters obtained before in
the same way as we did for temperature. Figure 4.12 illustrates the correlation between experimental and
calculated pressures. The results are not very consistent; a considerable number of calculated pressures
plot rather far away from the experimental ones. Excluding some specific experiments as previously done
for temperature and recalculating the interaction parameters did not result in significant improvement.
Most probably, pressure has a different effect on the exchange mechanisms than temperature and cannot
be derived in the same way. Further calibrations for barometry were, therefore, not carried out.
experimental pressurecalculated pressure
c)
b)
a)ilmenite-olivine
Fe-Mg ilmenite-spinel
Cr-Ti ilmenite-spinel
Figure 4.12 Comparison of calculated and experimental pressure for mineral pairs; pressure was calculated using the parameters presented in the foregoing sections: a) ilmenite-olivine Fe-Mg exchange (Table 4.5c); b) ilmenite-spinel Fe-Mg exchange (Table 4.8d); and c) Cr-Ti ilmenite spinel exchange (Table 4.9d).
-4.Thermodynamic modelling-
97
4.7 Discussion Model parameters were derived by least square fitting of experimental data and their subsequent
regularization for olivine – ilmenite and spinel – ilmenite solid solution pairs. As the data were fitted for
different exchange reactions separately, we obtained three groups of modeling parameters for Cr2O3 in
ilmenite. The largest data spread for experimental and calculated values for the obtained parameters as a
function of temperature are observed for the Fe-Mg ilmenite-spinel exchange. It was already pointed out
by Anderson et al. (1991) that the relative insensitivity of Fe-Mg partition between ilmenite and spinel
strongly limits the usefulness in geothermometry. The smallest values for the interacting parameters
(closer to ideality) were obtained for the exchange of ilmenite with olivine whereas the Cr-Ti exchange
with spinel results larger numbers that might be more realistic as parameters for eskolaite were evaluated
directly from the Cr exchange reactions. Table 4.11 Modeling parameters for Cr2O3 in ilmenite solid solution, extracted from previous tables. Parameters Joules/mole
ilmenite-olivine Fe-Mg spinel-ilmenite Cr-Ti spinel-ilmenite simultaneous fitting
WGesk-gk 13933 (4119) -19190 (3252) 38271 (1487) 23141 (2002)
WGilm-esk 1612 (6531) -43696 (10381) 33281 (4664) 50461 (3164)
WGesk-ilm 6357 (5798) 62896 (8186) 24354 (3682) 5436 (2633)
The obtained parameters were utilized to evaluate the activity-composition relationships through
equations 25-27 for FeTiO3 – Cr2O3 and MgTiO3 – Cr2O3 binaries respectively. Activities and free energy
of mixing calculated for the joins are shown in Figures 4.13 - 4.15.
The W term for the geikielite-eskolaite join is characterized by values that differ significantly from each
other for exchange reactions with spinel and olivine exchange reactions. The binary is characterized by
non-ideality that is larger close to the eskolaite endmember and considerably larger for the ones derived
from the Cr-Ti exchange reaction with spinel whereas Fe-Mg distribution with spinel predicts close to
ideal behaviour. The plots for Gmix reveal that the ∆Gmix curve is convex upward for intermediate
composition for the spinel Cr-Ti exchange reaction, and, hence, the existence of solvus is interfered.
According to this model, we can incorporate ≈15% of eskolaite component into geikielite, which
corresponds to the limits observed in our experiments for the iron free system. In contrast, the parameters
derived from the Fe-Mg exchange reaction with olivine and spinel infers complete solution between
geikilite and eskolaite.
The ilmenite-eskolaite join (FeTiO3-Cr2O3) was modeled as asymmetric and shows large inconsistency
for different exchange reactions: Nevertheless, generally a positive deviation from ideality is observed. A
different behaviour is observed for ∆Gmix, for the olivine-ilmenite exchange, the curve is conclave
downward over the entire range predicting complete miscibility; for the Cr-Ti exchange with spinel, the
curve is slightly asymmetric towards the ilmenite site, and Fe-Mg spinel-ilmenite exchange shows strong
asymmetry close to ilmenite endmember with the existence of a solvus for Cr-rich compositions. These
differences become apparent probably due to the different exchange mechanisms. For the reaction with
-4.Thermodynamic modelling-
98
olivine we are strictly looking at an Fe2+-Mg exchange, whereas the exchange with spinel reflects a
combination of more than one reaction. In addition, the amount of ferric iron in both spinel and ilmenite
is only calculated from the charge balance and hence not tightly constrained. Sobolev et al. (1999) found
that the charge-balancing procedure tends to overestimate the Fe3+ content of a sample and results in
rather big uncertainties for spinel. This not really controllable aspect might indeed introduce large
deviations from ideality into the exchange magnetite-magnesioferrite (Fe3O4-MgFe2O4). In addition, the
Fe2+-Mg exchange between spinel and ilmenite is not likely to be suited to derive interaction parameters
for eskolaite because spinel contains considerable amount of Cr-component as well. This aspect was
already addressed in the discussion of the excluded experiments where ilmenite with low Cr-contents did
not correlated with the entire dataset. Overall, we observe, that the general behaviour of the ilmenite-
eskolaite join is similar to the geikielite-eskolaite join.
a) b) c)
Figure 4.13 Variation of the activity and free energy of mixing for the geikilite-eskolaite solid solution for temperatures ranging from 1000 to 1400°C. Temperature is increasing downwards. a) Fe-Mg olivine-ilmenite exchange, b) Fe-Mg spinel ilmenite exchange, c) Cr-Ti spinel-ilmenite exchange. The dashed line in the activity plots indicates ideal behaviour.
-4.Thermodynamic modelling-
99
Xil Xil
a) b) c)
Figure 4.14 Variation of activity and free energy of mixing for ilmenite-eskolaite solid solution temperatures ranging from 1000 to 1400°C. Temperature is increasing downwards. a) Fe-Mg olivine-ilmenite exchange, b) Fe-Mg spinel ilmenite exchange, c) Cr-Ti spinel-ilmenite exchange. The dashed line in the activity plots indicates ideal behaviour. In order to obtain internally consistent parameters, all exchange reactions were fitted together and the
plots for these parameters are shown in Figure 4.15. For the geikielite-eskolaite join, complete solid
solution is predicted at higher temperatures, whereas at lower temperatures miscibility appears. The
ilmenite-eskolaite join is similar to the one obtained for Fe-Mg spinel-ilmenite exchange - strongly
asymmetric with miscibility close to the ilmenite endmember. This is consistent and can be explained by
long-range ordering in rhombohedral oxides, as transition from partially ordered R3 to fully disordered
R 3 c structure contributes significantly to the configuration entropy and consequently to the activity
composition relation of each endmember.
In the introductory part of the chapter, we pointed out describing structure of ilmenite that our model
considered ilmenites in the ordered R 3 form. The extrapolation of compositions to the Cr2O3 endmember
requires large uncertainties but the general behaviour can clearly be seen.
-4.Thermodynamic modelling-
100
a) b)
Figure 4.15 Variation of the activity and free energy of mixing for a) geikielite-eskolaite and b) ilmenite-eskolaite solid solutions with temperature ranging from 1000 to 1300°C and the free energy and interaction parameters obtained from simultaneous fitting of all exchange equilibria. Temperature is increasing downwards. The dashed line in the activity diagrams indicates ideal behaviour. We calculated activity composition relations for the FeTiO3-Cr2O3 and MgTiO3-Cr2O3 joins adding
hematite and geikielite or ilmenite components respectively (Fig. 4.16, 4.17). For the MgTiO3-FeTiO3-
Cr2O3 ternary, compositions towards the MgTiO3-FeTiO3 join behave closer to ideality with decreasing
temperature. The addition of Fe2O3 does not strongly change the general behaviour as the incorporation of
hematite moves the join further away from the ordered state.
-4.Thermodynamic modelling-
101
Ilm 0Hem 0.1 Ilm 0.1
Hem 0.1Ilm 0.2Hem 0.1
Ilm 0Hem 0
Ilm 0.1Hem 0
Ilm 0.2Hem 0
Figure 4.16 Activity-composition relations for the geikielite-eskolaite join with ilmenite and hematite components added to the solution. The dashed line in the activity diagrams indicates ideal behaviour.
Gk 0Hem 0.1
Gk 0Hem 0
Gk 0.1Hem 0.1
Gk 0.1Hem 0
Gk 0.2Hem 0
Gk 0.2Hem 0.1
Figure 4.17 Activity-composition relations for the ilmenite-eskolaite join with geikielite and hematite components added to the solution. The dashed line in the activity diagrams indicates ideal behaviour.
The large majority of experiments utilized in this study were performed exclusively at relatively low
oxygen fugacities corresponding to the C-O-H equilibrium close to the C-O join; therefore, the coexisting
phases have Fe3+ poor compositions. According to Sauerzapf et al. (2008), Mg preferentially enters the
rhombohedral phase (ilmenite-geikilite); with decreasing temperature this partitioning behaviour is even
more pronounced.
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102
4.8 Conclusion
The present chapter is the part of the study on Cr-rich picro-ilmenite and is followed by testing of the
obtained parameters and reformulated geothermometers for natural assemblages. The thermodynamic
model for the ilmenite solid solution coexisting with olivine and spinel has been developed and is based
on quaternary Margules solution with temperature independent interaction parameters (WG). The model
provides a satisfactory fit to the experimental data used in the refinement. Exchange parameters were
obtained for (1) ilmenite-olivine Fe2+-Mg exchange; (2) ilmenite-spinel Fe2+-Mg exchange; (3) Cr-Ti
ilmenite-spinel exchange and (4) for combination of all exchange reactions listed above. The comparison
of parameters for ilmenite-olivine and spinel-olivine pairs shows different behaviour due to the unlike
distribution mechanisms but existence of miscibility gap for Cr2O3-(Fe,Mg)TiO3 solution is evident. The
predicted miscibility gap is in accord with natural picroilmenites containing less than 10 wt% of Cr2O3.
We suggest using parameters obtained from fitting of all reactions for the three phase assemblage and for
specific mineral pair – parameters from respective fitting. Our preference is for the Cr-Ti spi-ilm
exchange as it is based on the straightforward evaluation of the Cr2O3 activity in the oxide phases.
Application of the obtained geothermometers to natural systems is directed towards the kimberlitic-
ultramafic assemblage where Cr-rich picroilmenite occur. It should be noted that our models were
calibrated at relatively high temperatures and extrapolation to low-temperatures assemblages may
introduce large uncertainties. It not possible to compare directly our model estimates with other
experimental studies because of low attention to Cr in ilmenite in previous studies.
-4.Thermodynamic modelling-
103
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5. Application of ilmenite-oxide-silicate exchange equilibria to the genesis of
picroilmenite bearing assemblages
5.1 Introduction
Magnesian ilmenite is an important constituent of most kimberlites worldwide.
The chemical and physical resistance of Mg-ilmenite makes it one of the key kimberlite indicator
minerals. Magnesian ilmenites occur as megacrysts in many kimberlites. Because of its distinctive
appearance and its resistance to weathering it is an important indicator mineral in diamond exploration.
Numerous attempts have been made to devise empirical parameters relating the geochemistry of these
ilmenites to diamond occurrence and grade of individual kimberlites. In general these attempts have been
unsuccessful, because the relationship between ilmenite occurrence and composition to the kimberlites
and to diamond formation is not understood (Griffin, 1997).
It is commonly accepted, that most of the ilmenite mega crystals and their associated silicate phases are
the products of extended fractional crystallization from a single batch of mafic/ultramafic carbonate-rich
kimberlitic magma.
Ilmenite is extremely uncommon as an inclusion in diamonds. The abundant megacrysts and macrocrysts
of ilmenite yield no information on the extent to which a kimberlite has sampled diamond bearing region
of the upper mantle (most likely the lowermost part of the lithospheric keel of cratonic areas). The
importance of ilmenite in diamond exploration, in addition to simply being an indicator of the presence of
kimberlites, is that its composition is thought to contain information on the oxidation state of the
kimberlite, the host magma that transports diamonds from the upper mantle to the surface of the Earth.
Ilmenites with high Fe3+/Fe2+ ratios (enriched in hematite component Fe2O3) are thought to be indicative
of oxidizing conditions in the magmas that would cause entrained diamonds to be substantially resorbed
(oxidized to CO2 or CO) to the extent that they are completely dissolved into the carbonate-rich
kimberlitic magma.
Because magnesian ilmenite commonly is used as an indicator mineral in diamond exploration,
considerable effort has been pursued in order to utilize ilmenite chemistry as a guide for the diamond
potential, as well as for the presence of kimberlites. Following the general recognition that diamond is a
xenocryst, (commonly) not genetically related to the kimberlite, and that the megacrysts suite to which
ilmenite belongs may be only indirectly related to the kimberlite, attention turned to the use of ilmenite as
an indicator of the P-T-fO2 conditions prevailing in the mantle (lithosphere). Gurney and Zweistra (1995)
describe the use of ilmenite composition as an index of diamond preservation, arguing that low-Mg
hematite-rich ilmenites indicate a high oxidation state in the mantle that (partly) equilibrated with
kimberlites during their passage and ascent. This high oxidation state would be detrimental to the
preservation of diamonds during the ascent of the kimberlite to the surface and its subsequent cooling.
The ilmenite suits obtained from most of the significantly diamondiferous kimberlites pipes and dikes
contain 10% hematite component on average; the weakly diamondiferous kimberlites may have either
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110
lower or higher average hematite contents. Barren kimberlites pipes generally contain high hematite
ilmenite suits; those with low hematite suites are generally restricted to off-craton kimberlites where
diamonds would not be expected to occur in any case (not sampling deep enough lithospheric mantle
sections, e.g. Mitchell, 1995).
Ilmenite suites from significantly diamondiferous pipes tend to be dominated by high-Mg, high-Cr
ilmenites, while the weakly diamondiferous and barren on-craton pipes tend to have predominantly
lower-Mg, low- to high-Cr ilmenites, representing the low-Mg side of the parabolic Mg-Cr distribution
presented and discussed in section 1.1.
Although monomineralic (single phase) ilmenites can occur anywhere in the Cr2O3-MgO compositional
range of the ‘Haggerty’s parabola’ in most kimberlites (Schulze, 1987), ilmenites intergrown with
silicates (commonly pyroxenes and/or olivine) are typically located on the Mg-rich limb or in the ‘trough’
and the Mg-poor limb consists of the monomineralic ilmenites.
Two contrasting geological environments have been suggested for the formation of the discrete nodule
suite: Boyd and Nixon (1973) and Pasteris et al. (1979) envisage the megacrysts as being phenocrysts in a
chemically zoned crystal magma mush, occurring over a depth interval of some 50 km between the
sources inferred for the derivation of deformed and undeformed xenoliths recovered from the Lesotho
pipes. Magma and megacrysts are considered to have been incorporated into a later, essentially unrelated
kimberlite liquid. Deformation of the discrete nodule suite is not readily explained by such a model
however. A further drawback is that an upward zonation from Mg-rich to more Fe-rich liquids is required
– representing a gravitationally unstable configuration which is difficult to envisage. An alternate model,
put forward by Harte and Gurney (1980), is that small volumes of kimberlitic liquid were injected into a
fracture network in the lithosphere surrounding the main volume of kimberlite magma at depth. In these
fracture network, the kimberlites would crystallize as pegmatitic veins down the temperature gradient
(thermal aureole) surrounding the kimberlite magma over a narrow vertical and lateral distance. Limited
experimental studies position of kimberlites phase equilibria as a function of pressure and temperature
indicate the ilmenite occurs at variable stages within the in the crystallization sequence of kimberlites,
related to its bulk composition and volatile content (Green et. al, 1975, Medvedev et al. 2000).
5.2 Formulations of ilmenite – oxide and ilmenite – silicate geothermometers.
Two different approaches have been applied recently for modeling solid solution properties in the system
ilmenite-geikielite-hematite (Ghiorso, 1990, 2008, Andersen et al, 1981, 1991). The starting point of
Andersen´s treatment of the Fe-Mg exchange equilibria between ilmenite-olivine and ilmenite-spinel
corresponds to a completely ordered ilmenite-geikilite solid solution, while Ghiorso et al.´s used a
convergent cation ordering model, which assumes disordering of Fe2+, Mg and Ti, as well as Fe3+, on
structurally equivalent sites.
In this work, we adopted the sub-regular solution model for ilmenite similar to the one used by Andersen,
treating ilmenite as a quaternary solid solution between FeTiO3, MgTiO3, Fe2O3 and Cr2O3.
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111
Partitioning of elements between ilmenite and olivine and ilmenite and spinel was preferred for modeling
as these phases were present in most but a few experiments containing ilmenite. The following exchange
reactions were defined:
1) Fe-Mg exchange ilm-ol: FeSi1/2O2 + MgTiO3= MgSi1/2O2 + FeTiO3
2) Fe-Mg exchange ilm-spi: 2MgTiO3 + Fe2TiO4 = 2FeTiO3 + Mg2TiO4
MgTiO3 + FeCr2O4 = FeTiO3 + MgCr2O4
MgTiO3 + FeFe2O4 = FeTiO3 + MgFe2O4
3) Cr-Ti exchange ilm-spi: FeTiO3 + FeCr2O4 = Cr2O3 + Fe2TiO4
MgTiO3 + MgCr2O4 = Cr2O3 + Mg2TiO4
The reactions 1) and 2) were investigated by Andersen (1991) and he noted relative temperature
insensitivity of the Fe-Mg partitioning. In contrast, Knecht et al. (1977) have pointed out that there is
considerable temperature sensitivity of the Cr-Ti exchange for iron end-members. This reaction is
somewhat similar to another exchange reaction that is widely adopted as a geothermometer:
4) FeTiO3 + Fe3O4 = Fe2O3 + Fe2TiO4
that is going along and is often combined with the oxidation reaction:
5) 4Fe3O4 +O2 = 6Fe2O3
Together forming the well known Fe-Ti-oxide oxybarometers originally formulated by Buddington and
Lindsley (1964).
Ferric iron contents of our experimental oxides were calculated from charge balance and resulted
generally low, close to or even amounting to 0 in most cases. This clearly limits application of the above
thermometers (eqn. 1-3) to oxybarometry, but considering the same substitution mechanism for Cr3+ as
for Fe3+ (Fe2++Ti4+=2Fe3+) Cr-Ti exchange was assumed to provide sensitive estimation of temperatures.
5.3 Application to natural assemblages
In this section we applied thermodynamic models for Cr-bearing ilmenites derived in the previous
chapters to natural assemblages and compared our results with other existing thermometers for the
respective mineral assemblages
Limeira I and Indaia I (Meyer et al. 1995) are Mesozoic alkaline intrusions that occur 20 km north of
Monte Carmelo and 25 km west of Coromandel, Brazil. Petrographically these rocks resemble hypabyssal
macrocrystal kimberlites (for a comprehensive description of kimberlites nomenclature and textures
associated with kimberlites and orangeites see Mitchell, 1995, 1997). They consists of rounded
macrocrysts and subhedral phenocrysts of olivine, macrocrysts of green diopside, Mg-ilmenite, altered
phlogopite and chromite spinel, set in a groundmass composed of serpentine, calcite, perovskite, apatite,
monticellite and spinel. This mineral assemblage is typical of Group I kimberlites (or archetypical or
basaltic kimberlites, depending on the authors).
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Macrocrystal olivine (2-6 mm) is angular, whereas smaller olivines ranging in size between 1 and 0.15
mm are often euhedral. There appears to be no difference in forsterite content between macrocrystal and
microphenocrystal olivine. Olivine constitutes about 30-35 % of the rock. Magnesian ilmenite is common
and ranges in size between 1 and 0.1 mm. Most grains appear rounded but when examined in details
reveal ragged margins due to replacement by perovskite and spinel. The spinel is present as a groundmass
phase which averages 0.05 mm in size and may be either euhedral or rounded. It differs in chemical
composition from the aluminous magnesian chromite macrocrysts (however, only analyses of
groundmass spinels are given in the publication). The overall compositional trend of spinels is from
titanian chromites to magnesian ulvoespinel-ulvoespinel-magnetite (MUM).
Table 5.1 Mineral compositions of Limeira I and Indaia I kimberlites (Meyer et al. 1995) together with temperatures calculated by a variety of geothermometers
Sample Limeria Indaia Phase ol ilm spi ol ilm spi SiO2 39.6 0.24 0.27 39.7 0.05 0 TiO2 0 52.9 19.4 0.05 51.9 22.8 Cr2O3 0 2.13 7.48 0.03 2.16 10.3 Al2O3 0 0.14 0.76 0 0.47 0.79 Fe2O3 30.7 22.8 FeO 11.2 30.4 27.9 15.4 30.5 21.7 MgO 48.5 12 11.8 45.2 12.7 18.4 Total 99.9 98.4 100.2 100.9 99.1 98.7
O'Neill 1987 1239 2023 Andersen 830 945
ilm-ol 839 1212 Cr-Ti spi-ilm 816 871 Fe-Mg il-spi 650 285
all react. 120 450
We calculated temperatures using our thermometer formulations and compared them to the olivine-spinel
thermometer of O’Neill (1987) and the ilmenite-olivine thermometer of Andersen (1981). The values
obtained from the Fe-Mg spinel-ilmenite distribution and the combination of all reactions are too low,
probably due to the high, recalculated Fe3+ content of spinels that was not the case in our experiments
from which the models were calibrated. There is a general agreement among the calculated temperatures
for the Limeria sample but for Indaia the obtained temperatures differ very significantly.
Rudnick et al. (1991) reported the petrography and mineral chemistry of xenoliths from the Lashaine and
Olmani volcanoes in northern Tanzania: Sample 89-671 is a xenolith defined as a dunite exhibiting a
granoblastic equant texture that contains a mineral assemblage suitable for thermometry. Olivines are
fresh and unzoned, with forsterite contents ranging from 86.6 to 93.9. Chromites occur as inclusions in
olivine and have a very high #Cr (0.85) and low TiO2 contents (5%). The pressure and temperature
estimated from different mineral assemblages result 3.8-5.0 GPa and 950-1250 oC.
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Table 5.2 Mineral compositions of Lashaine xenolith (Rudnick, 1991) with calculated temperatures.
Sample 89-671 Phase ol ilm spi SiO2 39.8 0 0.08 TiO2 0 53.36 4.72 Cr2O3 0.06 4.06 51.6 Al2O3 0 0.07 7.12 Fe2O3 5.35 FeO 11.9 26.6 19 MgO 47.7 14.3 11.9 Total 100 100.1 100.5
O’Neill 1987 1300 Anders 940 ilm-ol 1130
Cr-Ti spi-ilm 894 Fe-Mg il-spi 245
all react. 811
For this example our olivine-ilmenite thermometer results a temperature almost 200oC higher than the
Andersen geothermometer; the temperatures obtained from Cr-Ti exchange are 50oC lower and the Fe-
Mg spinel-ilmenite distribution gives inconsistent temperature.
Olivine and ilmenite intergrowths in kimberlites (Thaba Patsoa, Lesotho) were reported by Boyd and
Nixon (1973). The pressure estimate is that given by Boyd and Nixon (1973) based on the Al2O3 contents
of orthopyroxene (coexisting with garnet). Boyd and Nixon (1973) estimated that the coexisting
pyroxenes in these rocks had equilibrated at 1120°C (sample 1582) and 1080°C (sample 1680B).
Andersen and Lindsley (1981) tested their thermometer on this particular assembly. However, we found
errors in their calculations of ilmenite endmembers and, consequently, our re-assessment resulted that
their published temperatures are higher than those recalculated with the correct formulation of the
thermometer. Revised temperatures from Anderson and from our olivine-ilmenite thermometer are
provided in Table 5.3: the results from our formulation of the geothermometer are only slightly lower
than the values obtained from Andersen & Lindsley´s (1981) corrected thermometer. Table 5.3 Composition of kimberlitic ilmenites and olivines from Boyd and Nixon (1973) with calculated temperatures.
Sample 1582 (57 kbar) 1680B (50 kbar) Phase ol ilm ol ilm SiO2 38.94 0.19 40.39 0.07 TiO2 0.05 49.61 <0.05 56.63 Cr2O3 <0.05 2.17 <0.05 1.4 Al2O3 <0.05 0.69 <0.05 0.47 Fe2O3 <0.05 8.97 <0.05 2.93 FeO 15.22 25.7 10.88 26.65 MgO 45.45 10.49 48.58 13.52 Total 100.24 98.24 99.97 101.9
Andersen 969 951 ilm-ol 913 939
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Solovyeva et al (1997) presented compositions of mantle-derived xenoliths from the Udachnaya
kimberlites (Siberia) that contain ample evidence of mantle metasomatism and melting (Table 5.4). Two
groups of rocks with primary or texturally equilibrated mica (phlogopite) are distinguished: The first
group includes common granuloblastic lherzolites, harzburgites, pyroxenites and websterites of the
spinel- and garnet-peridotite facies; the second group contains texturally equilibrated mica that is believed
to be of possible magmatic origin.
Although, calculated temperatures are not likely to be correct due to the uncertainty in equilibration of the
observed mineral assemblages, the presented analyses clearly demonstrate the limits of application of the
developed thermometers. For the UV-303 and G10 samples, the authors gave temperatures calculated by
the Spenser and Lindsley (1981) formulation. For UV-303 we obtained temperatures that are much lower
with a much larger difference in the Mg-Fe partitioning between spinel and ilmenite. Low temperatures
obtained in this calculation may well indicate that these phases did not reach equilibrium or were re-
equilibrated at lower temperatures. It should be noted that our models were calibrated at relatively high
temperatures and extrapolation to the low-temperatures assemblies may introduce large uncertainties.
Another important point to consider is that spinel coexisting with ilmenite in the natural assemblage is an
Al-rich, “classic” spinel, but our solution models were calibrated (mostly) on Al-free compositions that
will naturally introduce additional uncertainty. The ilmenite analysis from the G-10 sample does not only
contain a high Cr content (6-10 wt.% ), but is additionally characterized by high amounts of hematite 23-
29 %, shifting the rhombohedral oxide far from the ordered state and obtained temperatures are probably
completely out of scale. Temperatures for samples 218/87 and 76/749f calculated with the olivine-
ilmenite Fe-Mg partitioning are in agreement with calculations obtained with Andersen´s (1981)
thermometer with differences in the order of 20-50oC; calculation with the spinel-olivine exchange
thermometer of O’Neill (1987) results higher temperatures for sample 218/87 but is in agreement for
sample 76/749f.
115
Table 5.4 Compositions of minerals from the Udachnaya kimberlite (Solovyeva et al., 1997) with calculated temperatures.
Sample Phase SiO2 TiO2 Cr2O3 Al2O3 Fe2O3 FeO MgO Total Solov. Andersen O'Neill Mg-Fe spi-
ilm Cr-Ti spi-
ilm ol-ilm all reactilm 0.23 51.4 1.44 0.83 6 2.9 10.1 99.5 spi1 0.18 0.69 9.04 49 9.04 13.4 16.6 98.3 641 361 526 spi2 0.38 0.55 7.1 49.4 10.1 14.4 15.9 98.2 622 382 482
UV-303
spi3 0.19 0.38 5.1 56.5 5.87 11.5 18.7 98.5 630 346 505 ilm8 0 34.6 6.08 0.94 27.5 24.1 5.28 98.7 spi1 0.13 6.9 22.5 11.7 27.6 21.2 8.29 99.0
1074
1877 -4396.8
ilm7 0.12 35.9 8.31 1.05 23.2 24.5 4.98 98.5 spi2 0 5.66 28.2 9.54 26.8 19.9 7.47 98.2
1007
1785 -447.35
ilm9 0 32.7 7.51 0.76 29 23.5 4.9 98.5 spi3 0.05 6.37 19.5 5.24 29.8 30.2 6.83 98.4
1006
2001 19163
ilm6 0.01 35.1 10.1 1.25 22.7 23.9 4.95 98.4
G-10
spi10 0.85 4.88 22.9 15.9 9 34.6 9.47 98.6 1156
341 1875
ol 40.6 0 0 0 0 7.44 51.9 100.4
ilm 0.02 57.2 1.06 0.13 2.2 23.6 15.8 100.6 1209
1191
spi1 0 0 22.7 46.3 1 10.9 18.3 99.6 2236 -321 573
218/87
spi2 0 17 1 4 63 15 100.0 1505 9 1956 ol 42 0 0 0 0 10.2 49 101.3
ilm1 0 53.7 3.95 0.24 29.7 11.2 99.0 1087 333 1009 1154 735 ilm2 0 54.8 4.07 0.42 27.8 12.9 100.2 1325 506 1025 1355 838
76/749f
sp 0.4 12.3 30.9 2.75 39.7 10.4 97.8 1302 ol 41.1 0 0 0 0 9.04 49.9 100.5 555/80 il 0 52.8 1.25 0.95 26.1 16.76 98.0
1031
875
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Scott (1979) described a suite of kimberlite and potassic lamproite dykes occurring in the area of
Holsteinsborg, Central West Greenland that form narrow intrusions, which have fairly consistent strike
directions. The kimberlites have macrocrysts of olivine, phlogopite, picroilmenite and rare pyrope garnet
in a matrix composed of olivine, clinopyroxene, carbonate, apatite and spinel.
Table 5.5 Mineral compositions from kimberlite dykes from Central West Greenland (Scott,1979) with calculated temperatures.
Sample 5518G Phase ol ilm spi SiO2 41.78 0.04 0.3 TiO2 0.01 52.12 20.87 Cr2O3 0.03 1.87 0.93 Al2O3 0 0.99 1.86 Fe2O3 6.75 29.13 FeO 8.06 26.91 34.91 MgO 50.56 11.06 10.19 Total 100.98 99.51 96.9
O'Neill 1987 1196 Anders 842 ilm-ol 810
Cr-Ti spi-ilm - Fe-Mg ilm-
spi 804 all react. 156
Temperatures obtained from the Fe-Mg spinel-ilmenite and olivine-ilmenite partitioning are close to
temperatures calculated with Andersen´s (1981) thermometer; the combined all reaction thermometer is
not reliable in this case as it is strongly affected by the low Cr (<1wt%) content of the spinel and, hence,
absence of a significant Cr-Ti distribution between the oxide phases. The high Fe2O3 content of the spinel
(29 wt%, based on charge balance calculation) in this case does not affect the Mg-Fe distribution between
spinel and ilmenite causing a problem in the Limeira I and Indaia I (Meyer et al. 1995) examples. This is
most probably related to the observation that the change of the site preferences of Fe3+ and the extent of
the miscibility gap in the Fe3O4-FeCr2O4 join is associated with an increasing Cr/(Cr+Fe3+) ratio (Sack,
1991) and, in addition, the observed spinel is Cr-poor.
Akella (1979) studied the Lattavaram kimberlite from Wajrakharur area, Southern India and presented
mineral analyses of coexisting Mg-rich olivine and ilmenite. Chemically, there are two types of ilmenites,
one of which is six times richer in chromium compared to the other one (Table 5.6). The chrome-rich
ilmenite contains ~50 % geikielite component, whereas the chrome-poor variety has ~32 %. It is
presumed that the earlier formed ilmenites are more iron-rich and relatively poor in chromium, and as
crystallization progressed, the later formed ilmenites have become magnesian with higher concentration
of Cr. It is not understood whether the assumed progressive crystallization took place during the process
of kimberlite formation or during its ascent before emplacement.
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Table 5.6 Compositions of olivines and ilmenites in Lattavaram-2 kimberlite (Akella, 1979) with calculated temperatures
Sample Lattavaram-2 Phase ol ilm ilm SiO2 41.28 0.24 0.16 TiO2 0.05 53.37 53.18 Cr2O3 0.06 4.03 0.79 Al2O3 0.02 0.3 0.38 Fe2O3 FeO 11.23 23.73 35.48 MgO 48.23 16.43 10.08 Total 101.49 99.04 100.39
Anders 2775 957 ilm-ol 3050 981
The calculated temperatures clearly show that Cr-rich ilmenite is not in equilibrium with olivine, whereas
the low-Cr, high-Fe variety results temperatures in a good agreement with Andersen (1981) and might
indeed represent pre-eruption conditions
Eggler et al. (1979) described megacryst assemblages from kimberlite pipes in the State Line district,
Colorado-Wyoming, and the Iron Mountain district Wyoming, which contain coexisting ilmenite and
olivine. Pressure was assumed to be 50 kbar corresponding to a depth of 150 km that is within the range
of orthopyroxen equilibration pressures obtained by Eggler. Temperatures obtained with our model for
ilmenite-olivine partitioning are slightly different than ones calculated with the model of Anderson (1981)
and the difference becomes larger for more Cr-rich ilmenites and Fo-rich olivines but the displacement to
the lower- or higher- temperature side is not clear (Table 5.7).
Table 5.7 Composition of megacrysts assemblages from kimberlite (Eggler, 1979) with calculated temperatures.
Sample SD2-118 SD2-116 Phase ilm ol ilm ol SiO2 0.00 40.30 0.17 40.00 TiO2 48.60 0.03 52.90 0.04 Cr2O3 10.60 0.04 2.80 0.01 Al2O3 1 0 0 0.02 Fe2O3 9 0 8 0.00 FeO 15 10 21.50 12.00 MgO 15.50 49.50 14.20 48.20 Total 99.60 99.89 99.51 100.3
Anders 1242 1080 ilm-ol 1285 1069
Wyatt (1979) studied picroilmenites with intergrowth of titanian chromite and rutile from kimberlites
(location is not given by author). Ilmenite macrocrysts are exceptionally high in Cr2O3 (up to 13 wt%,
Table 5.8). The spinels are rich in both Ti and Cr and correspond to titanian chromites, similar Ti-Cr-
spinels are commonly found in lunar rocks and are, actually, similar to our experimental spinels, most
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probably reflecting rather low oxygen fugacities The assembly was suspected to contain armalcolite
((Mg,Fe2+)Ti2O5) that is unstable below 1010±20oC at atmospheric pressure, but with increasing pressure
breaks down to the Mg-armalcolite, rutile and ilmenite.
Table 5.8 Composition of picroilmenite-spinel-rutile intergrowth (Wyatt, 1979) with calculated temperatures.
Sample Phase SiO2 TiO2 Cr2O3 Al2O3 Fe2O3 FeO MgO TotalMg-Fe spi-ilm
Cr-Ti spi-ilm
ilm 0.01 48.46 11.18 1.02 7.35 18.48 13.96 100.7 1179 1234 ilm 0 54.7 4.14 0.27 5.4 19.84 16.3 100.9 638 1055 LI/10/33 spi 0.16 8.11 41.56 11.4 4.93 19.25 14.22 99.89
ilm 0 56.31 3.31 0.35 2.42 20.07 16.86 99.8 LI/10/14 spi 1.34 13.34 25.22 10.4 10.03 22.83 15.43 99.18
544 1071
ilm 0 51.09 8.62 0.9 4.53 21.07 13.8 100.3LI/10/39 spi 0.06 7.37 40.8 12.35 60.07 18.23 14.32 99.56
772 856
ilm 0 48.99 10.64 1.12 6.23 19.01 13.92 100.1LI/10/35 spi 0.08 6.78 42.17 12.34 7.3 16.56 15.4 100.9
835 1158
ilm 0.02 49.42 10.22 1.05 5.96 19.19 14.04 100.1LI/10/2 spi 0.38 15.29 36.86 10.29 0 20.08 17.18 100.4
877 1441
ilm 0 47.24 13.06 1.02 5.43 19.48 13.81 100.6LI/10/12 spi 0.02 10.89 36.45 9.03 6.95 20.46 14.38 98.44
1211 1352
ilm 0 49.3 11.23 1.16 5.43 19.48 13.81 100.6LI/10/19 spi 0.22 8.42 43.38 10.41 3.57 18.71 14.64 99.65
990 1266
ilm 0.02 52.49 1.64 0.04 6.25 29.71 9.62 100.1LI/10/192 spi 0.01 16.31 23.21 0.67 16.31 36.82 6.13 99.84
915 698
The computed temperatures (assuming a pressure of 20 kbar) reveal that the Cr-Ti partitioning results
higher temperatures than Fe-Mg, except for sample LI/10/192. Overall, Cr-Ti temperatures span a
considerably lower temperature range and are, probably, closer to mantle/igneous temperatures than the
Fe-Mg partitioning that is commonly much more susceptible to low temperature re-equilibration.
5.4 Comparison with ilmenite-spinel intergrowths.
The ilmenite-spinel-rutile intergrowths described in the last example in the previous chapter were
compared with experiments containing the respective three oxide assemblages (experiments conducted on
starting composition SM12) (Figure5.1). Experimental and natural ilmenites fall exactly in the same
compositional range, whereas natural spinels have compositions slightly richer in Ti than the
experimental ones. Temperatures calculated for natural samples employing the Cr-Ti ilmenite-spinel
thermometer are generally in agreement with our experimental trends: enrichment in three-valent cations
with increasing temperature for ilmenite and depletion for spinel. The data from this study do not confirm
the model proposed by Wyatt (1979) that the boundaries of the spinel-ilmenite-rutile three-phase
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0.0
0.2
0.0 0.2 0.4 0.6 1.0
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.6
0.0
0.2
0.4
0.6
0.8
TiO2
MgTiO3
FeTiO3
Mg2TiO4
Fe2TiO4
MgCr2O4FeCr2O4Fe3O4 R2O3RO
1071
697
8421351
12351266
11571441
842
697
1071
1441
1351
11571266
1235
0.0 0.2 0.4 0.6 1.0
0.0
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
0.6
0.0
0.2
0.4
0.6
0.8
TiO2
MgTiO3
FeTiO3
Mg2TiO4
Fe2TiO4
MgCr2O4FeCr2O4Fe3O4 R2O3RO
1300
12001100
1000
10001100
13001200
Figure 5.1 Ternary diagram for coexisting ilmenite and spinel, upper panel: natural assemblages (Wyatt, 1979) with temperatures calculated using the Cr-Ti ilmenite-spinel thermometer; lower panel: experimental paragenesis obtained at 25 kbar, starting composition SM12.
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field moves toward the RO-TiO2 join with decreasing temperature. According to our results, the three-
phase field will expand, but the breakdown reactions proposed by Wyatt (1979) are actually confirmed
(Figure 5.2). Although, in our experiments exsolution textures were not produced and rutile, spinel and
ilmenite are discrete phases, the displacement mechanism is similar to the one proposed : I) Cr-ilmenite
→ Cr-ilmenite + spinel; II) Cr-ilmenite → Cr-depleted ilmenite + spinel + rutile; III) Cr-depleted ilmenite
→ Cr-spinel + rutile. The breakdown of ilmenite is dependent on the Mg# of the system, pressure and
silica activity. According to our experiments, the change from the spi+ru to spi+ilmenite assemblage is
confined to pressures <50 kbar for a bulk XMg=0.73. With decreasing silica activity and increasing Mg#,
the stability field of ilmenite increase up to pressure of 70 kbar.
0.6
0.2
0.4
0.6
0.8
TiO2
RO
ilm
usp
chr
0.6
0.2
0.4
0.6
0.8
TiO2
RO
ilm
usp
chr
0.6
0.2
0.4
0.6
0.8
TiO2
RO
ilm
usp
chr
0.6
0.2
0.4
0.6
0.8
TiO2
RO R2O3
ilm
usp
chr
decreasind temperature
decreasind temperature
R2O3
R2O3
R2O3
R2O3
R2O3
Figure 5.2 Schematic diagrams illustrating the changes in composition in the three-phase (ilmenite-spinel-rutile) field with decreasing temperature. Upper panel presents the interpretation of Wyatt (1979) that three phase boundary would move toward the RO-TiO2 join with decreasing temperature. Lower panel: according to our experimental results the three phase boundary becomes wider such that Cr-rich spinel and rutile are possible breakdown products.
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5.5 Crystallization of ilmenite
Figure 5.3 Back scattered electron (BSE) image of one of the experimental charges (NS 19, 1300°C, 25 kbar, SM6) with textures displaying the crystallization sequence.
Some of experiments demonstrate clear textural evidences that allow to determine the crystallization
sequence. Figure 5.3 shows a backscattered electron (BSE) image of one of the runs with high Mg-
number (XMg=0.85) and low SiO2 (~18 wt.%) composition (SM6); the observed assemblage is ilmenite –
spinel – olivine. The first phase to crystallize is spinel that is followed by ilmenite. Olivine forms
interstitial grains and is the last phase in the crystallization sequence. This is consistent with the
hypothesis of Mitchell (1973) that ilmenites from (South-) African kimberlites crystallized before silicate
minerals and is used as an argument to explain the lower Cr- content of ilmenites (as compared to SiO2-
richer compositions) that first crystallized spinel resulting in a depletion in Cr. For more SiO2-rich (~30
wt.%) compositions, higher silica activity will possibly fist stabilize silicate phases. This is also the case
for low-SiO2 but at the same time low-Mg-number composition (SM12, XMg=0.73) where the
paragenesis olivine – opx – ilmenite – spinel – rutile is observed. This is consistent with the interpretation
of Eggler et al. (1979) that Cr-rich ilmenites crystallized concomitantly with olivines and orthopyroxenes.
In case the silicate phases precipitated first, by the time of crystallization of the oxide phases, the melt is
depleted in Mg and Fe and the concentration of Ti becomes too high to be completely incorporated into
ilmenite and spinel, thus rutile is stabilized in addition. For starting compositions with XMg=0.85, the first
oxides that crystallize are rather Ti rich and rutile is not present.
The observed crystallization sequences indicate that the position of ilmenite in the crystallization
sequence is depending on magma composition, specifically on the Mg and Si content. It should, however,
be clearly pointed out that the crystallization sequences observed in experimental charges are strongly
dependant on the nature of the starting material; we utilized sintered oxide mixes containing a moderate
amount of volatiles (both H2O added and CO2 derived from reduction of ferric iron with graphite forming
CO2) and hence a mobile phase (liquid or fluid depending on temperature). The crystallization paths
might well be dependent on the exact nature of these mixes. In case of gel-like starting materials and/or
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pre-synthesized mineral mixes the order of crystallization might vary considerably. A clearly visible order
of crystallization in experimental charges, in any case, reflects kinetically driven processes and is, thus, to
a certain extent the expression of non-equilibrium thermodynamics at the initial stages of an experiment
linked to the strong oversaturation of certain components/phases with respect to the equilibrium
assemblages. Crystallization sequences are, thus, driven by a combination of oversaturation, activation
energies (nucleation and crystal growth) and diffusion of species in the mobile phase (liquid / fluid
present in the charges during re-crystallization from oxide mixes to mineral phases). The observation that
some of the crystallization sequences observed in the experimental charges also seem to operate in natural
kimberlitic systems indicates that (1) either similar kinetically driven processes operate in natural silicate-
carbonate magmas or (2) that the temperature driven crystallization (the common processes in natural
magmas) is somehow mimicked during the crystallization of a synthetic counterpart.
5.7 Conclusion
Thermometers derived in previous chapters were applied to natural assemblages and compared with other
published formulations of thermometers. The olivine-ilmenite Fe-Mg partitioning is in general agreement
with other formulations. The application of the three-phase thermometer (ilm-ol-spi) usually results much
lower temperatures, meaningful results are only expected if all three phases were in equilibrium and, thus,
the thermometer actually provides a useful tool to access the extent of equilibration among the three Fe-
Ti-oxide phases. As these thermometers included the magnetite-magnesioferrite (Fe2+Fe3+2O4 –
MgFe3+2O4) join in spinel and, thus, require exact knowledge of the Fe3+ content in sample; this might
introduce their inaccuracy when applied to system containing considerably higher amount of ferric iron
than encountered in the experimental study. The Cr-Ti spinel-ilmenite distribution, however, provides
rather promising results but will require additional calibration for spinel with higher Fe3+ content, i.e.
experiments conducted at considerably higher fO2 conditions and/or in less Cr-rich but Fe-rich systems
Furthermore, to date, the application of our model(s) is restricted to rhombohedral oxides having ordered
R 3 structure. Although our models were calibrated at temperatures above 1000°C, temperatures obtained
in the 800-900°C range for (some) assemblages are in reasonable agreement with other thermometric
formulations.
The composition of ilmenites containing exsolutions (and/or intergrowths) of spinel and rutile match the
composition of the oxides obtained in the experiments and the formation of exsolutions and/or
intergrowth textures is consistent with the inferred stability of ilmenite coexisting with spinel and/or
rutile also providing reasonable temperature estimates for the Cr-Ti exchange reactions.
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5.8 References Akella J, P. S. Rao, R. H. McCallister, F. R. Boyd, H. O. A. Meyer (1979), Mineralogical study on the
diamondiferous kimberlite of the Wajrakharur area, Southern India, Proceedings of the Second
International Kimberlite Conference, Kimberlites, Diatremes and Diamonds: their geology,
petrology and geochemistry, AGU, 172-177
Akella J., Williams R. J., and Mullins O. (1976) Solubility of Cr,Ti, and Al in co-existing olivine, spinel,
and liquid at 1 atm. Proceedings of Lunar Scientific Conference 7th, 1179-1194.
Andersen D. J., Bishop F. C., and Lindsley D. H. (1991) Internally consistent solution models for Fe-Mg-
Mn-Ti oxides: Fe-Mg-Ti oxides and olivine. American Mineralogist 76, 427-444.
Andersen D. J. and Lindsley D. H. (1979) The olivine-ilmenite thermometer. Proceedings of Lunar
Scientific Conference 10th, 493-507.
Andersen D. J. and Lindsley D. H. (1981) A valid Margules formulation for an asymmetric ternary
solution: revision of the olivine-ilmenite thermometer, with applications. Geochimica et
Cosmochimica Acta 45, 847-853.
Andersen D. J. and Lindsley D. H. (1988) Internally consistent solution models for Fe-Mg-Mn-Ti oxides:
Fe-Ti oxides. American Mineralogist 73, 714-726.
Aranovich L. and Kawasaki T. (2007) Si-in-spinel geobarometry for ultramafics. Geophysical Research
Abstracts 9, 823-824.
Aranovich L. Y. and Bergman R. G. (1996) Optimized standard state and solution properties of minerals
II. Comparisons, predictions, and applications. Contributions to Mineralogy and Petrology 126,
25-37.
Arculus R. J., Dawson J. B., Mitchell R. H., Gust D. A., and Holmes R. D. (1984) Oxidation states of the
upper mantle recorded by megacryst ilmenite in kimberlite and type A and B spinel lherzolites.
Contributions to Mineralogy and Petrology 85, 85-94.
Ashchepkov I. V. and Vishnyakova E. V. (2006) Monomineral ilmenite thermo- and oxybarometry and
its application to reconstruction of magmatic systems and metasomatism within mantle columns
of Siberian platform. Geophysical Research Abstracts 8, 921-922.
Ballhaus C. (1993) Redox states of lithospheric and asthenospheric upper mantle. Contributions to
Mineralogy and Petrology 114, 331-348.
Berman R. G. and Aranovich L. Y. (1996) Optimized standard state and solution properties of minerals I.
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-6. Summary and Outlook-
128
6. Summary and Outlook In this study, aiming to evaluate properties and compositional dependences of the orthorhombic oxide –
picro-ilmenite as a function of pressure, temperature, composition and fO2, high-pressure, high-
temperature experiments have been conducted.
Experimental results determine ilmenite stability to be dependent on Fe/Mg ratio and SiO2-content of the
system, whereas temperature (over the investigated range) controls compositional changes of ilmenite.
Ilmenite is stable at bulk XMg=0.73 but for higher Mg# (0.85) it is only stable only in low-SiO2 (~18 wt%)
compositions.
The Mg-contents of ilmenites reflect primarily the Fe/Mg ratio of the material from which it was
crystallized.
The silica activity in the experiments is buffering the assemblages containing ol + opx + oxides to ol +
oxides with αSiO2 decreasing and Mg# increasing.
Absence of ilmenite for high silica (30 wt %) systems with XMg=0.73 for pressures exceeding 50 kbar is
consistent with the absence of ilmenite as inclusions in diamonds and, thus, simply reflects the stability of
ilmenite in ultramafic, mantle-like bulk compositions
The solubility of Cr2O3 in ilmenite increases with increasing pressure and temperature and is bulk
compositionally dependant. In general, increasing temperature results in enrichment of trivalent cations.
Ilmenites in two silicate parageneses exhibit smaller XMg but incorporate higher amounts of Cr and,
correspondingly, plot to the left-hand side of the “Haggerty parabola”.
The composition of ilmenite might also depend on the position of ilmenite in the crystallization sequence
that is the function of the chemistry of starting material, which, in turn, corresponds to differences in
source magmas and/or mineral assemblages.
A data set for the mixing properties of ilmenite has been derived from the analysis of the experimental set
in the system Mg-Fe-Ti-Cr-Si-O. Solubility of Cr2O3 in ilmenite was accounted for the Fe-Mg
partitioning between ilmenite with coexisting spinel and olivine, Cr-Ti spinel-ilmenite distribution was
considered as well. Ilmenite was modeled with a quaternary solid solution model incorporating FeTiO3-
MgTiO3-Fe2O3-Cr2O3 endmembers with temperature independent Margules parameters.
The derived thermodynamic model provides approximations for activity – composition relations in multi-
component ilmenite solid-solutions and predicts the existence of a miscibility gap for the MgTiO3-Cr2O3
and FeTiO3-Cr2O3 joins which is decreasing with the addition of FeTiO3 to the binary MgTiO3-Cr2O3.
Addition of Fe2O3 does (should) not have a strong influence because it drives the join further away from
the ordered state.
The derived thermodynamic parameters were utilized to formulate geothermometers based on the Fe-Mg
ilmenite-spinel and olivine-spinel, and the Cr-Ti ilmenite-spinel exchange equilibria, as well as
combination of all this exchange reactions together. These thermo(barom)metric formulation reproduce
well the experimental temperatures , while experimental pressures recalculations results in large scatter of
the data.
-6. Summary and Outlook-
129
Thermometers were, finally, applied to natural assemblages reported in literature from metasomatic
mantle assemblages and macro-/xenocryst assemblages from kimberlites and associated rocks. The results
were compared with previously formulated thermometers and shortcomings are pointed out. Application
of the obtained geothermometers is restricted to “kimberlitic” ultramafic assemblies were Cr-rich picro-
ilmenite occur and the thermometers can be utilized to test potential equilibration of the picro-ilmenites
with the inferred mineral assemblages (which is evidently often not the case as single mineral separates
from kimberlites and lamproites are published with no textural criteria that they actually form an
equilibrium mineral assemblage).
6.1 Outlook
Ilmenite-spinel and ilmenite-olivine pairs were modeled in this study but their relationship to
orthopyroxene was not evaluated because opx not always coexisted with ilmenite; thus existing data from
this study should be combined with some additional experiments to constrain thermodynamic mixing
properties of oxide –silicate equilibria including opx as the second most important mantle phase to extend
potential applications of this study..
Additional information contained in the experiments, but not extracted to date concerns the “Si-in-spinel”
geobarometer suggested by Aranovich (2007, abstract): Aranovich describes the dependency of the SiO2
content of spinel as a function of pressure. However, his calibration suffered from the absence of data on
Cr-bearing spinels that are very common in ultramafic environments. The present experiments could
provide such information and the obtained barometer can theoretically directly be applied to spinel-
bearing inclusions in diamonds.
As additional experimental work it would be useful to do further investigate Al-bearing systems,
especially at higher pressure, which will allow determining the garnet –spinel transition in complex
system and will provide data for the formulation of interaction parameters for Al-bearing spinels that are
more realistic for naturally occurring parageneses. This would, in particular, provide additional
information on the Al-, Cr-contents and partitioning in orthopyroxenes; the Al-free compositions obtained
in the present experiments must represent a minimum Cr-content as the incorporation of Cr in
orthopyroxene is believed to be strongly linked to the presence of tetrahedrally coordinated Al that is,
likewise, the principal control on the incorporation of Ti in opx
As a further extension of the present work, inclusion of Ca into the system would lead to the concomitant
occurrence of low- and high-Ca pyroxene, and Ca-bearing garnet and, thus, would provide information
that is directly relevant for the formation of the megacryst suite in kimberlites and associated rocks
As mentioned above, most studies on Mg –rich ilmenite were exclusively focused on ilmenite and present
only analyses of discrete ilmenite without considering the coexisting mineral assemblage; in addition, the
number of published analysis of Cr-ilmenite bearing assemblages is relatively small. It would, thus, be
essential to conduct a comprehensive field-based study focused on Cr-rich kimberlitic ilmenite evaluating
-6. Summary and Outlook-
130
their occurrence and composition within the entire mineral assemblage present in the kimberlites and their
xenoliths in order to link ilmenite chemistry and occurrence to the formation of the megacryst suite and to
decipher the generation of the megacryst suite that could either be linked to the crystallization of
kimberlitic magmas or to metasomatic events not connected to the host kimberlite transporting them to
the surface.
-Appendix I-
131
Appendix I Gibbs free energy for exchange reactions with ilmenite
1. Ilmenite-olivine Fe-Mg exchange
FeSi1/2O2 + MgTiO3= MgSi1/2O2 + FeTiO3
MgFeD
olGfa
gkilGilhemil
ililhemgkhemgkilhemgkhemgkeskgkhem
ileskgkeskgkeskhemileskileskgkeskhemgk
eskilhemil
Ghemhemhemeskgkhemhemgkeskhem
gkhemhemeskeskhemgkilhemilhemhemililhem
G
hemeskhemeskhemeskhemgkeskhemilhemgkhem
ilhemhemilhemgkhemhemgkgkhem
Ghemeskhem
hemgkilhemilesk
Ggkeskeskileskeskilesk
eskgkhemeskeskileskhemgkeskhemeskgkhemesk
gkeskGeskgkileskeskeskhem
eskilGhemeskeskhemgk
eskileskileskeskhemeskilgkeskgkesk
hemeskeskeskgkilgk
Ggkhemgkeskgkilhem
eskilileskilhemileskhemililileskhemil
eskgkgkeskhemgkeskgkhemgkhemgkolilm
exch
KRTHSTVPWXWXXX
XXXXXXXXXXXXXX
XXXXXXXXXXXXXXX
XXWXXXXXXXXXX
XXXXXXXXXXXXXW
XXXXXXXXXXXXXX
XXXXXXXXXWXXX
XXXXWXXXXXXXX
XXXXXXXXXXXXXXX
WXXXXXXXWXXXXX
XXXXXXXXXXXXX
XXXXXWXXXXXXX
XXXXXXXXXXXXXXX
XXXXXXXXXXXXG
−−
−
−
−
−
−−
−
−
−Δ−Δ+Δ−−+−−
+−+−+−−+
−+−−+−−
−+−++−−−
+−−−−
+−−++++
−−++−+++
+++−−++
+−−++−
++++−−
+−−−+−+
+−−+++−−
+++−++−+
−+++−−=Δ
21
ln)21()23
2323
21
2122
2332
3()22133
212
21(*
)223233
212
23()
()32212
232
233(
)()32213
21
212()2
21
321322
232233
23(
32
222222
232
232222
222
22222
2232
2232
2222
22
22222
32222
222232
322
-Appendix I-
132
2. Spinel-Ilmenite Fe-Mg exchange
2MgTiO3 + Fe2TiO4 = 2FeTiO3 + Mg2TiO4
MgFeDREC
spiCr
spiMgREC
spiCr
spiMg
RECspiFe
spiMg
spiFeMg
spiMg
spiTiREC
spiFe
spiMg
spiFeMg
spiMg
spiTi
eskilGhemeskeskhemgkeskilesk
ileskeskhemeskilgkeskgkeskhemesk
eskeskgkilgk
Ggkhemgkeskgkilhemeskil
ileskilhemileskhemililileskhemil
eskgkgkeskhemgkeskgkhemgkhemgk
gkeskGeskgkileskeskeskhem
gkhemGhemeskhem
hemgkilhemilesk
Ggkeskeskileskeskilesk
eskgkhemeskeskileskhemgkeskhemeskgk
hemeskilhem
Ghemeskhemeskhemeskhemgk
eskhemilhemgkhemilhemhemilhemgkhem
hemgkhemil
Ghemhemhemeskgkhemhemgk
eskhemgkhemhemeskeskhemgkilhemilhem
hemilgkil
Gilhemilililhemgkhemgk
ilhemgkhemgkeskgkhemileskgkeskgk
eskhemileskileskgkeskhemgkeskiluspilm
exch
KRTHSTVPGXXGXXGXXWXXGXX
WXXWXXXXXXXXXXXXXXXXXXXX
XXXWXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXWXXXXXXXWXXX
XXXXWXXXXXXXXXXXXXXXXXXXXX
XXWXXXXXXXXXXXXXXXXXXXXX
XXWXXXXXXXXXXXXXXXXXXXXX
XXWXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXG
−−
−−
−
−−
−
−
−
−
−
−Δ−Δ+Δ−Δ+Δ−−
Δ−−−+−Δ+++−−+−−−+−++
−−+++−−+++−++−+
−+++−−++++++
+++−−+++−−++−
++−−++++−−++
−+−++−−−+−−−−+−−+−+−+−−+−+−
−+−−−=Δ
+
+
21
31231
2
ln)1()1()1)(1(
)1()6422226
42()2246226424
344663()2222()22
22()6442232423
6()2434626224
3()42626242
2()46422632224
43646(
33
22
2
222
2222
322222
22232
322
22
2232
222
222
222223
3222
222
2322222
2223
22
-Appendix I-
133
MgTiO3 + FeCr2O4 = FeTiO3 + MgCr2O4
MgFeD
RECspiFe
spiMg
spiFeMg
spiMg
spiTi
RECspiTi
spiMgREC
spiTi
spiMg
spiFeMg
spiMg
spiTi
RECspiFe
spiMg
eskilGhemeskeskhemgkeskilesk
ileskeskhemeskilgkeskgkeskhemesk
eskeskgkilgk
Ggkhemgkeskgkilhemeskil
ileskilhemileskhemililileskhemil
eskgkgkeskhemgkeskgkhemgkhemgk
gkeskGeskgkileskeskeskhem
gkhemGhemeskhem
hemgkilhemilesk
Ggkeskeskileskeskilesk
eskgkhemeskeskileskhemgkeskhemeskgk
hemeskilhem
Ghemeskhemeskhemeskhemgk
eskhemilhemgkhemilhemhemilhemgkhem
hemgkhemil
Ghemhemhemeskgkhemhemgk
eskhemgkhemhemeskeskhemgkilhemilhem
hemilgkil
Gilhemilililhemgkhemgk
ilhemgkhemgkeskgkhemileskgkeskgk
eskhemileskileskgkeskhemgkeskilchrilm
exch
KRTHSTVPGXXWXX
GXXGXXWXX
GXXWXXXXXXXX
XXXXXXXXXXXX
XXXWXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXXX
WXXXXXXXWXXX
XXXXWXXXXXXXX
XXXXXXXXXXXXX
XXWXXXXXXXX
XXXXXXXXXXXXX
XXWXXXXXXXX
XXXXXXXXXXXXX
XXWXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXXXG
−−
−
−
−
−−
−
−
−
−
−
−
Δ−Δ+Δ−Δ−−−+−Δ+Δ−−++
Δ+−−+−
−−+−++
−−+++−−+
++−++−+
−+++−−
++++++
+++−−++
+−−++−
++−−+
+++−−++
−+−++−−
−+−−−−
+−−+−+−
+−−+−+−
−+−−−=Δ
+
+
21
312
2
31
ln)1()1)(1(
)1()1(
)3221
321
21
2()2213
21322
232233
23(
)()
()32212
232
23
3()2232
33212
23()2
213
3212
21
()232323
21
212
223323(
12
332
122
2222
322222
22232
322
22
2232
222
222
222223
3222
222
2322222
2223
22
-Appendix I-
134
MgTiO3 + FeFe2O4 = FeTiO3 + MgFe2O4
MgFeD
spiFeMg
spiMg
spiTiREC
spiCr
spiMg
RECspiTi
spiMgREC
spiTi
spiMgREC
spiCr
spiMg
spiFeMg
spiMg
spiTi
eskilGhemeskeskhemgkeskilesk
ileskeskhemeskilgkeskgkeskhemesk
eskeskgkilgk
Ggkhemgkeskgkilhemeskil
ileskilhemileskhemililileskhemil
eskgkgkeskhemgkeskgkhemgkhemgk
gkeskGeskgkileskeskeskhem
gkhemGhemeskhem
hemgkilhemilesk
Ggkeskeskileskeskilesk
eskgkhemeskeskileskhemgkeskhemeskgk
hemeskilhem
Ghemeskhemeskhemeskhemgk
eskhemilhemgkhemilhemhemilhemgkhem
hemgkhemil
Ghemhemhemeskgkhemhemgk
eskhemgkhemhemeskeskhemgkilhemilhem
hemilgkil
Gilhemilililhemgkhemgk
ilhemgkhemgkeskgkhemileskgkeskgk
eskhemileskileskgkeskhemgkeskilmagilm
exch
KRTHSTVPWXXGXX
GXXGXXGXX
WXXWXXXXXXXX
XXXXXXXXXXXX
XXXWXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXXX
WXXXXXXXWXXX
XXXXWXXXXXXXX
XXXXXXXXXXXXX
XXWXXXXXXXX
XXXXXXXXXXXXX
XXWXXXXXXXX
XXXXXXXXXXXXX
XXWXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXXXG
−−
−−
−
−−
−
−
−
−
−
−
Δ−Δ+Δ−−++Δ−−Δ−−Δ+Δ+
++−−+−
−−+−++
−−+++−−+
++−++−+
−+++−−
++++++
+++−−++
+−−++−
++−−+
+++−−++
−+−++−−
−+−−−−
+−−+−+−
+−−+−+−
−+−−−=Δ
+
+
21
2
2
ln)1)(1()1(
)1(
)1()3221
321
21
2()2213
21322
232233
23(
)()
()32212
232
23
3()2232
33212
23()2
213
3212
21
()232323
21
212
223323(
21
221
222
2222
322222
22232
322
22
2232
222
222
222223
3222
222
2322222
2223
22
-Appendix I-
135
3. Cr-Ti spinel-ilmenite exchange
FeTiO3 + FeCr2O4 = Cr2O3 + Fe2TiO4 I
CrTiDREC
spiCr
spiMgREC
spiFe
spiMg
spiFeCr
spiFeTi
spiCrTi
spiFe
spiCr
spiFeTi
spiFeCr
spiCrTi
spiFe
spiTi
RECspiFe
spiMg
spiCrTi
spiCr
spiCrTi
spiTiREC
spiTi
spiMg
eskilG
eskeskeskhemgkeskhemilhemgkgkeskhemesk
hemeskhemilgkililgkilgkeskilhemil
gkileskgkhemilgkesk
Ggkhemgkeskgkgkil
hemilGeskhemgkhemilhemgkhemhemeskhemilhem
ilhemgkhemhemgkeskhemhemeskilhem
Ghem
eskhemeskhemeskhemgkhemilhemhemilgkhem
hemeskhemgkhemgkhemililesk
Geskgkilesk
eskhemgkhemeskeskgkgkeskeskhemilhemilhem
ilgkgkilhemililileskhemeskgkgkhemil
gkilGgkeskgkhemeskgkhemgkgkhemgkgkesk
gkilgkeskhemgkgkililgkeskhem
Ghemilhem
hemgkeskhemilgk
Geskgkhemgkgkgkeskeskgk
hemgkgkilgkgkilgkileskhemgkhemgkFeI
exch
KRTHSTVPGXXGXXWWWXXRTWWWXX
GXXWXWXGXXW
XXXXXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXXWXXXXXXX
WXXXXXXXXXXXXX
XXXXXXXXXXWX
XXXXXXXXXXXXXX
XXXXXXXXWXXXX
XXXXXXXXXXXXXXX
XXXXXXXXXXXXXXX
WXXXXXXXXXXXXX
XXXXXXXXXXWXXX
XXXXWXXXXXXXXX
XXXXXXXXXXXXXXG
−−−−−−−
−−−
−
−
−
−
−
−
−
−Δ−Δ+Δ−Δ−Δ−−+−+−++
Δ+−+Δ+
+−++++−
+−−+−−++
+++−−−−+
+−+++−+
+−++−++
−+−−++−
−+−−+−−+
−−−−−−+
−+−+−++−+
−−+++−+
+++−+−−
−−+−−−−
++−++−−=Δ
+
++++++
+
ln)(22ln2)(2
22*
)222321
323
232
212
33()(
)22321
213
21()2
32322
213
23()232
23321
2132
23
232(
)21
2133
2122()
()33223
232
212(
32
122
3
3222
22223
2222
_23222
2222
2322
222322
22222
2223
22222
3222
2232
2222
3
333333
3
MgTiO3 + MgCr2O4 = Cr2O3 + Mg2TiO4 II
CrTiDREC
spiCr
spiMg
RECspiFe
spiMg
spiFeCr
spiFeTi
spiCrTi
spiFe
spiCr
spiFeTi
spiFeCr
spiCrTi
spiFe
spiTiREC
spiFe
spiMg
spiCrTi
spiTi
spiCrTi
spiCr
eskilGeskileskilileskilgk
ilhemilgkililhemhemilgkililgkhemil
gkhemGhemgkhemeskhemilhem
gkeskGgkhemgkil
gkeskileskhemeskilesk
Gileskileskililhemgk
ilhemilhemgkililgkhemilileskgkilil
gkilGeskhemilgkilhemilileskilhemilhem
ilileskeskilililgkgkililgk
Gileskilhem
hemileskilileskilhemilililgkgkil
gkileskhemileskhem
GhemilhemhemgkeskhemMgII
exch
KRTHSTVPGXXGXXWWWXX
RTWWWXXGXX
WXWXWXXXXXXXX
XXXXXXXXXXXXXXX
WXXXXXXXWXXXXXXXXXXWXXXXXXXX
XXXXXXXXXXXXXXX
WXXXXXXXXXXXXX
XXXXXXXXXXWXXXX
XXXXXXXXXXXXXX
XXXXXWXXXXXXXG
−−−−
−−−
−−−
−−
−
−
−
−−
−Δ−Δ+Δ−Δ−−Δ−−−+−
+−++Δ−+
+−+−−+
−−−+++++
++++−−−+++++−−
+−+−−−−−+
−−−++−
−−−+++++
++−−+−−+
++−−−−=Δ
++++
++++
ln)1()1()(2
2ln2)(2)1(
22)21
223
233322(
)()()2
21
213
2132(
)2323
23
23221()
3321
212
21
2()(
3
2
1
22222
22223
2
22222
22223
222
3222222
22322
22
3333
3333
-Appendix II-
136
Appendix II A.II.1 The discrete ill-posed problems and their regularization It is often the case when data available to the researcher cannot be treated by traditional computational approach. This is the case, for example, for ill-posed problems which lack solvability in some natural functional spaces. Moreover, these problems lack stability of the solution with respect to errors of input data. This is significant since we almost never deal with the absolutely exact values of input parameters. The concept of ill-posed problems goes back to Hadamard (1923) in the beginning of this century. Hadamard essentially defined a problem to be ill-posed if the solution is not unique or if it is not a continuous function of the data; if an arbitrarily small perturbation of the data can cause an arbitrarily large perturbation of the solution. Today there is a vast amount of literature on ill-posed problems arising in many areas of science and engineering. The theory for ill-posed problems is well developed in the literature. We can easily illustrate the main difficulties associated with such problems by means of a small numerical example. Consider the following least squares problem
2min bAx
x−
with coefficient matrix A and right-hand side b given by
,29.102,211.017.010.016.0
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
=A ⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
33.325.027.0
b
Here, the right-hand side b is generated by adding a small perturbation to an exact right-hand side corresponding to the exact solution ( )11=Tx :
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛−+⎟⎟
⎠
⎞⎜⎜⎝
⎛
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
=02.003.0
01.0
00.100.1
29.102,211.017.010.016.0
b .
The difficulty with this least squares problem is that the matrix A is ill-conditioned; its condition number is 1.1·103. This implies that the computed solution is potentially very sensitive to perturbations of the data. Indeed, if we compute the ordinary least-squares solution xLSQ by means of a QR factorization of A, then we obtain
⎟⎟⎠
⎞⎜⎜⎝
⎛=
40.801.7
LSQx .
This solution is obviously worthless, and something must be done in order to compute a better approximation to the exact solution ( )11=Tx . The large condition number implies that the columns of A are nearly linearly dependent. One could therefore think of replacing the ill-conditioned matrix A = (a1 a2) with either (a1 0) or (0 a2), both of which are well conditioned. The two corresponding so-called basic solutions are
-Appendix II-
137
⎟⎟⎠
⎞⎜⎜⎝
⎛=
065.1)1(
Bx , ⎟⎟⎠
⎞⎜⎜⎝
⎛=
58.20)2(
Bx
Although these solutions are much less sensitive to perturbations of the data, and although the corresponding residual norms are both small,
031.02
)1( =− bAxB , 036.02
)2( =− bAxB ,
the basic solutions nevertheless have nothing in common with ( )11=Tx . A major difficulty with the ordinary least squares solution xLSQ is that its norm is significantly greater than the norm of the exact solution. One may therefore try another approach to solving the least squares problem by adding the side constraint that the solution norm must not exceed a certain value α,
2min bAx
x− subject to α≤
2x .
The such computed solution xα depends in a non-linear way on α, and for α equal to 0.1, 1, 1.385, and 10 we obtain
⎟⎟⎠
⎞⎜⎜⎝
⎛=
05.008.0
1.0x , ⎟⎟⎠
⎞⎜⎜⎝
⎛=
54.084.0
1x , ⎟⎟⎠
⎞⎜⎜⎝
⎛=
74.017.1
385.1x , ⎟⎟⎠
⎞⎜⎜⎝
⎛−
=60.7
51.610x .
We see that by a proper choice of α we can indeed compute a solution x1.385 which is fairly close to the desired exact solution ( )11=Tx . However, care must be taken when choosing α and the proper choice of α is not obvious. Although the above example is a small one, it highlights the three main difficulties associates with discrete ill-posed problems:
1. the condition number of the matrix A is large 2. replacing A by a well-conditioned matrix derived from A does not necessarily lead to a useful solution 3. care must taken when imposing additional constraints.
The purpose of numerical regularization theory is to provide efficient and numerically stable methods for including proper side constraints that lead to useful stabilized solutions, and to provide robust methods for choosing the optimal weight given to these side constraints such that the regularized solution is a good approximation to the desired unknown solution. The typical manifestations of discrete ill-posed problems are systems of linear equations and linear least-squares problems arising from discretization of ill-posed problems. An interesting and important aspect of discrete ill-posed problems is that the ill-conditioning of the problem does not mean that a meaningful approximate solution cannot be computed. Rather, the ill-conditioning implies that standard methods in numerical linear algebra for solving and, such as LU, Cholesky, or QR factorization, cannot be used in a straightforward manner to compute such a solution. Instead, more sophisticated methods must be applied in order to ensure the computation of a meaningful solution. This is the essential goal of regularization methods. The primary difficulty with the discrete ill-posed problems is that they are essentially underdetermined due to the cluster of small singular values of A. Hence, it is necessary to incorporate further information about the desired solution in order to stabilize the problem and to single out a useful and stable solution. Regularization involves introducing additional information in order to solve an ill-posed problem or prevent overfitting. This information is usually of the form of a penalty for complexity, such as restrictions for smoothness or bounds on
-Appendix II-
138
the vector space norm. A theoretical justification for regularization is that it attempts to impose Occam's razor on the solution. From a Bayesian point of view, many regularization techniques correspond to imposing certain prior distributions on model parameters. The same idea arose in many fields of science. For example, the least-squares method can be viewed as a very simple form of regularization. A simple form of regularization applied to integral equations, generally termed Tikhonov regularization after Andrey Nikolayevich Tychonov, is essentially a trade-off between fitting the data and reducing a norm of the solution. In statistics, the method is also known as ridge regression. It is related to the Levenberg-Marquardt algorithm for non-linear least-squares problems. The idea is to define the regularized solution xλ as the minimizer of the following weighted combination of the residual norm and the side constraint
{ }2
2
22
2)(minarg ∗−+−= xxLbAxx λλ ,
where the regularization parameter λ controls the weight given to minimization of the side constraint relative to minimization of the residual norm. Clearly, a large λ (equivalent to a large amount of regularization) favors a small solution seminorm at the cost of a large residual norm, while a small λ (i.e., a small amount of regularization) has the opposite effect. λ also controls the sensitivity of the regularized solution xλ to perturbations in A and b, and the perturbation bound is proportional to λ-1. Thus, the regularization parameter λ is an important quantity which controls the properties of the regularized solution, and λ should therefore be chosen with care. Besides Tikhonov regularization, there are many other regularization methods with properties that make them better suited to certain problems or certain computers. Like the least squares formulation Regularization methods produce solutions that can be characterized as solutions to minimization problems. A.II.2 Generalized cross-validation The basic idea in cross-validation is following: If any data point yi is left out and a solution xλ,i is computed to the reduced problem of the dimension (m-1)×n, then the estimate of yi computed from the xλ,i must be a good estimate. While ordinary cross-validation depends on the particular ordering of the data, general cross validations is invariant to orthogonal transformation (including permutations) of the data vector y. The GCV function to be minimized is defined by
2
2
2
)))((()(
)( IKKItraceyKxλ
λλξ
−
−≡ ,
where K(λ)I is any matrix that maps the right-hand site y onto the solution x(λ), i.e., x(λ)= K(λ)Iy. Although GCV works well for many problems, there are some situations in which GCV has difficulty finding a good regularization parameter. One difficulty is that the GCV function can have a very flat minimum and hence the minimum itself may be difficult to localize numerically. Another difficulty is that GCV can sometimes mistake correlated noise for a signal. The underlying assumption is that the errors in the right hand side are normally distributed with zero mean and covariance matrix σ2I. GCV is fairly robust against nonhomogenity of variance and non-Gaussian errors; however, the method is quite likely to give unsatisfactory results if the errors are highly correlated.
-Appendix II-
139
A.II.3 L-curve Perhaps the most convenient graphical tool for analysis of discrete ill-posed problems is the so-called L-curve which is a plot for all valid regularization parameters of the (semi)norm
2regLx of the regularized solution versus the corresponding residual norm2
bAxreg − . In this
way, the L-curve clearly displays the compromise between minimization of these two quantities, which is the heart of any regularization method. The L-curve has a distinct L-shaped corner located exactly where the solution xλ changes in nature from being dominated by regularizations errors(i.e., by oversmoothing) to being dominated by errors in the right hand side. Hence the corner of the L-curve corresponds to a good balance between minimization of the sizes and the corresponding regularization parameter λ is the good one. The L-curve for Tikhonov regularization has two characteristic parts, namely, a “flat” part where the regularized solution xλ is dominated by regularization errors and “vertical” part where xλ is dominated by right-hand-side errors magnified by the division by small singular values. The idea of the L-curve criterion for choosing the regularization parameter is to choose a point on this curve that is at the “corner” of the vertical piece. The ideal solution: The L-curve defined by a smooth, computable formula. If the functions ρ̂ and η̂ are defined by some computable formulas, and if the L-curve is twice continuously differentiable, then it is straightforward to compute the curvature κ(λ) of the L-curve by means of the formula
2/322 ))ˆ()ˆ((ˆˆˆˆ
)(ηρ
ηρηρλκ′+′
′′′−′′′=
Lacking a smooth, computable function defining L-curve. In many situations we are limiting to knowing only a finite set of points on the L-curve. In computational sense, the L-curve then consists of a number of discrete points corresponding to different values of the regularization parameter at which we have evaluated ρ̂ and η̂ . In many cases, these points are clustered, giving the l-curve fine-grained details that are not relevant for consideration. We must define a differentiable, smooth curve associated with the discrete points in such way that fine-grained details are discarded while the overall shape of the L-curve is maintained; i.e., we want approximating curve to achieve local averaging while retaining the overall shape of the curve. A reasonable approach is therefore to base the approximating smoothing curve on cubic spines. For our study we used Regularization Toolbox by Per Christian Hansen 2008.
-Appendix II-
140
¨Figure A.2.1 GCV for ilmenite-olivine exchange, the minimum is not found.
Figure A.2.2 L-curve for ilmenite-olivine exchange.
-Appendix II-
141
Figure A.2.3 GCV for ilmenite-olivine exchange for Al-bearing ilmenites, minimum not found.
Figure A.2.4 L-curve for ilmenite-olivine exchange for Al-bearing ilmenites
-Appendix II-
142
Figure A.2.5 GCV for spinel-ilmenite Fe-Mg exchange.
Figure A.2.6 L-curve for spinel-ilmenite Fe-Mg exchange.
-Appendix II-
143
Figure A.2.7 GCV for spinel-ilmenite Cr-Ti exchange, minimum not found
Figure A.2.8 L-curve for spinel-ilmenite Cr-Ti exchange.
-Appendix II-
144
Figure A.2.9 GCV for combination of all reactions, minimum not found
Figure A.210 L-curve combined for combination of all reactions
-Appendix II-
145
A.II.4 The Bootstrap In recent years the statistical literature has examined the properties of resampling as a means to acquire information about the uncertainty of statistical estimators. The bootstrap is a procedure that involves choosing random samples with replacement from a data set and analyzing each sample the same way. Sampling with replacement means that every sample is returned to the data set after sampling. So a particular data point from the original data set could appear multiple times in a given bootstrap sample. The number of elements in each bootstrap sample equals the number of elements in the original data set. The range of sample estimates you obtain enables you to establish the uncertainty of the quantity you are estimating. Bootstrapping is the practice of estimating properties of an estimator (such as its variance) by measuring those properties when sampling from an approximating distribution. One standard choice for an approximating distribution is the empirical distribution of the observed data. In the case where a set of observations can be assumed to be from an independent and identically distributed population, this can be implemented by constructing a number of resamples of the observed dataset (and of equal size to the observed dataset), each of which is obtained by random sampling with replacement from the original dataset. It may also be used for constructing hypothesis tests. It is often used as an alternative to inference based on parametric assumptions when those assumptions are in doubt, or where parametric inference is impossible or requires very complicated formulas for the calculation of standard errors. The advantage of bootstrapping over analytical methods is its great simplicity - it is straightforward to apply the bootstrap to derive estimates of standard errors and confidence intervals for complex estimators of complex parameters of the distribution, such as percentile points, proportions, odds ratio, and correlation coefficients. References Bakushinskiy A., Goncharsly A A. (1994) Ill-posed problems: Theory and Application. Kluwer
Academic Publishers Marie. H. Rasmussen, L. K. Clemmensen (2003) The Effect of Regularizing Matrices and
Norms in Tikhonov Based Image Restorations, Midway project for Professor Per Christian Hansen IMM, DTU
Hansen P.C, D. P. O’Leary (1993) The use of the L-curve in the regularization of the discrete ill- posed problems. SIAM J. Sci. Computers, 14, 6, 1487-1503
Shou G., M. Jiang, Ling Xia, Qing Wei, Feng Liu, S. Crozier (2006) A comparison of different choices for the regularization parameter in inverse electrocardiography models. Proceedings of the 28th IEEE EMBS Annual International Conference
J. Hadamard, (1923).Lectures on Cauchy's Problem in Linear Partial Differential Equations, Yale University Press, New Haven
P. C. Hansen, (1989) Perturbation bounds for discrete Tikhonov regularization, Inverse Problems 5, L41- L44.
Matlab Reference Guide, The MathWorks, Mass., 1996. K. Miller, (1970), Least squares methods for ill-posed problems with a prescribed bound, SIAM J. Math.
Anal. 1 52-74. A. N. Tikhonov & V. Y. Arsenin, (1977) Solutions of Ill-Posed Problems, Winston & Sons,
Washington, D.C. A. N. Tikhonov & A. V. Goncharsky, (1987) Ill-Posed Problems in the Natural Sciences, MIR
Publishers, Moscow.
-Appendix II-
146
-Acknowledgments-
147
Acknowledgments
First I would like to thank my supervisor Prof. Dr Peter Ulmer for giving me opportunity to do
PhD at Institute of Mineralogy and Petrology, for introducing to the world of experiments (where
else I could spoil so much Platinum). Thanks for allowing me freedom in decisions and
conducting research at the lab and not pushing with timing.
My sincere appreciation and gratitude are to Diane Seward who, actually, was my first
supervisor when I came to Zurich as exchange student. She was always ready for help and
advice. Diane introduced me to Swiss life and always carried about me.
As well thanks to ex-co-supervisor Russell Sweeney for taking me to the project, pity we not
finished it together but at least we had one lunch.
I gratefully acknowledge Max Schmidt and Stefan Klemme for considering my work and being
my referents.
Many thanks for Claudia and Ursula for helping with documents and bills and all administration.
Of course a lot thanks to all people that I have meet during the time of being Doktorandin at
IMP, thanks for your friendship and nice time at the parties, Friday bier (when I used to go to
them), conferences and casual coffee breaks. Thanks to Maarten and Alistair for helping with
broken pistons, thanks to Luca and Jessica for help with microprobe, thanks to Christian and
Nene for help with multi-anvils. Thanks to all “former” members: Huong, Elena and Alex,
Zarina, Paola, Adelie, Giulio, Tonny, Dani, Alya, Alessandro, Yulia. Thaks to “still doing” and
“new arrivals”: Remko, Rita, Ester, Ettore, Mattia, Angelika, Ute, Arno, Mark, Tamara, Rohit.
Thanks to my officemates for atmosphere at the office that encourage writing of the thesis. Sorry
to those I didn’t mention I’m just too tired to keep everything in mind.
Thanks to “Russian” community for wonderful time at Russian lunches and nice non-scientific
discussions.
Special thanks to Oleg who always encourage and support me, not only in writing this thesis;
especially for his patience. Your support in many ways was very valuable for me. And for sure
gratitude is to Timur for being a real motivation to finish this thesis.
My most sincere hearty thanks to my family, for their support with decision to go to Switzerland,
continues carry and understanding over all the years. Thank you for everything!
-Acknowledgments-
148
-Curriculum Vitae-
149
CURRICULUM VITAE
Name Semytkivska Nina Date of Birth 3rd August 1983 Nationality Ukraine Address Glattalstr. 188
CH-8153 Rümlang, Switzerland
EDUCATION 2005-2010
PhD study at Institute of Mineralogy and Petrography, ETH. Title of the dissertation: “Picro-ilmenites: An experimental study in simple and complex systems to investigate P-T-fO2-composition relations at high pressures” Supervisor Prof. Dr. P. Ulmer
2004-2005 National Taras Shevchenco University of Kiev Geology Faculty Study of Geochemistry Petrography and Mineralogy, Kiev, Ukraine Diploma thesis: “Fission track dating of cooling history of region Dir, Northern Pakistan, Himalayas”. Supervisor Dr. O.V. Andreev, S.E. Shnyukov
2000-2004 National Taras Shevchenco University of Kiev Geology Faculty, Kiev, Ukraine Bachelor degree
1990-2000 Secondary School, Kirovohrad, Ukraine
WORK / PROFESSIONAL EXPERIENCE 06/2004-02/2005 Exchange trainee, IAESTE studentship
ETH, Zurich
2003-2004 National Taras Shevchenco University of Kiev Geology Faculty Laboratory assistant, MS Windows system administration. Data processing and analysis, Faculty of Geology
06/2003-07/2003 Exchange trainee, IAESTE studentship Martin Luther University, Halle, Germany
