Experimental Deformation of Forsterite, Wadsleyite and Ringwoodite: Implications for Seismic Anisotropy of the Earth’S Mantle Hélène Couvy

Home , Ringwoodite, Seismic anisotropy

Experimental deformation of forsterite, wadsleyite and ringwoodite: Implications for seismic anisotropy of the Earth’s mantle Hélène Couvy

To cite this version:

Hélène Couvy. Experimental deformation of forsterite, wadsleyite and ringwoodite: Implications for seismic anisotropy of the Earth’s mantle. Geophysics [physics.geo-ph]. Université des Sciences et Technologie de Lille - Lille I, 2005. English. tel-00008992

HAL Id: tel-00008992 https://tel.archives-ouvertes.fr/tel-00008992 Submitted on 12 Apr 2005

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés.

Experimental deformation of forsterite, wadsleyite and ringwoodite: Implications for seismic anisotropy of the Earth’s mantle

presented by Hélène Couvy

of the Fakultät für Biologie, Chemie und Geowissenschaften der Universität Bayreuth and of the Université des Sciences et Technologies de Lille

A dissertation submitted in fulfilment of the requirement for the degrees of:

Doktor der Naturwissenschaften (Dr.rer.nat.) and Docteur de l’Université de Lille 1 (Spécialité: Sciences de Matériaux)

1st March 2005, Bayreuth (Germany)

Experimental deformation of forsterite, wadsleyite and ringwoodite: Implications for seismic anisotropy of the Earth’s mantle

Von der Fakultät für Biologie, Chemie und Geowissenschaften der Universität Bayreuth und der Université des Sciences et Technologies de Lille

zur Erlangung der Würde eines

Doktors der Naturwissenschaften (Dr.rer.nat.) und Docteur de l’Université de Lille 1 (Spécialité: Sciences des Matériaux)

genehmigte Dissertation

vorgelegt von Hélène Couvy

Bayreuth, im März 2005

Prüfungsausschuss

Prof. J. Breu (Universität Bayreuth) Vorsitzender

Prof. F. Langenhorst (Universität Bayreuth) deutscher Gutachter Prof. P. Cordier (Universität Lille) französicher Gutachter

Prof. D. C. Rubie (Universität Bayreuth)

Prof. H. Leroux (Universität Lille)

N° d’ordre: 3603 bis

Thèse en co-tutelle

présentée

à l’Université des Sciences et Technologies de Lille et à la Fakultät für Biologie, Chemie und Geowissenschaften der Universität Bayreuth

pour l’obtention des grades de: Docteur de l’Université de Lille 1 (Spécialité: Sciences de Matériaux) et Doktor der Naturwissenschaften (Dr.rer.nat.)

par Hélène Couvy

Experimental deformation of forsterite, wadsleyite and ringwoodite: Implications for seismic anisotropy of the Earth’s mantle

soutenue le 1 Mars 2005 à Bayreuth, Allemagne

Jury

Prof. J. Breu (Université de Bayreuth) Président

Prof. F. Langenhorst (Université de Bayreuth) Rapporteur Prof. D. Mainprice (Université de Montpellier) Rapporteur

Prof. D.C Rubie (Université de Bayreuth) Examinateur

Prof. H. Leroux (Université de Lille) Examinateur

Prof. P. Cordier et F. Langenhorst Directeurs de Thèse

The thesis has been co-directed by Prof. Falko Langenhorst (Bayerisches Geoinstitut, University of Bayreuth, Germany) and by Prof. Patrick Cordier (Laboratoire des Structures et Propiétés de l’Etat Solide, University of Lille, France) from September 2001 and January 2005.

Manuscript given the 1st December 2004 Defense passed the 1st March 2005 (Bayreuth, Germany)

I was supported by the Visiting Scientist Program of the Bayerisches Geoinstitut (17.09.2001 – 16.11.2002 and 17.11.2003 – 16.01.2004), by the EU-program “Marie Curie Host Fellowship/ Training Sites” (Contract N° HPMT-CT-2001-00231) (17.11.2002 – 16.11.2003) and by the Deutsche Forschungsgemeinschaft (Project N°: FR 1555/2-1) (17.01.2004-16.01.2005). Moreover, travels have been also funding by the French-Bavarian cooperation program (CCUFB-BFHZ) and by the German Academic Exchange Service within the bilateral French–German Procope Program. All these financial supports are gratefully acknowledged.

Je voudrais remercier tout d'abord Patrick Cordier, initiateur de ce passionnant sujet et Falko Langenhorst pour avoir encadrer cette thèse à Bayreuth. Votre confiance et votre soutient m’ont permis d’évoluer et de m’épanouir dans mon travail. Un grand merci à Stephen Mackwell pour m'avoir accueilli au BGI. Ce travail expérimental a été possible avec à l’aide de Dan Frost et Florian Heidelbach. Merci à vous. Danke schön ! à Hubert Schulze, le magicien des lames minces et autres coupes à 45°, Georg Herrmannsdörfer et Heinz Fischer pour la réparation des pannes en tout genre et l’usinage des précieux assemblages. Un grand merci à Stefan Keyssner, Petra Ständner et Lydia Kison-Herzing pour votre grande générosité et tous les services rendus. Le plaisir de la co-tutelle ne se limitant pas aux joies administratives, elle m’a permis de travailler dans deux labos bien différents mais qui m’ont accueillis aussi chaleureusement l’un que l’autre. Je les en remercie. Je tiens à remercier vivement David Mainprice et Andréa Tommasi de l’université de Montpellier pour les simulations VPSC et le calcul de propriétés sismiques ainsi que pour leur précieux soutient. Mon travail m’a amené à découvrir le monde du synchrotron et ses nuits blanches. Je voudrais remercier William Durham et Yanbin Wang pour leur aide lors les expériences menées à APS ainsi que Don Weidner, Jiuhua Chen et Paul Raterron pour celle mené à NSLS. Merci à Tamás Ungár et Krisztián Nyilas de l’université de Budapest pour leurs mesures effectuées sur mes échantillons. Enfin, ces trois années n’auraient pu être ce qu’elles ont été sans Sylvie, Tiziana, Florian, Burkhard, Fabrice, Christian ein und zwei, Julian, Fabrizio, Julien (un merci spécial pour toi qui m’a fait une place dans ton bureau et qui a supporté la rédaction), Philippe ... Merci à David Rubie, Joseph Breu, David Mainprice et Hugues Leroux pour avoir accepté de juger ce travail. A vous tous qui avez rendu cette thèse non seulement possible mais aussi qui l’avez transformée en un agréable moment (de plus de trois ans !), je vous remercie. Merci à toi, Makram, pour ton immense patience ...

Table of contents

Summary...... 1 Zusammenfassung...... 2 Résumé...... 3

Introduction...... 7

Chapter I. Forsterite, wadsleyite and ringwoodite: structural and rheological data I – Forsterite: pure magnesium end-member of olivine...... 13 II – Wadsleyite...... 15 III – Ringwoodite...... 17

Chapter II. Experimental techniques and developments. I – High pressure techniques: presentation of apparatus and developments...... 21 I.1 – Deformation-DIA (D-DIA)...... 21 I.2 – Kawai-type multianvil apparatus...... 22 I.2.1 – Presentation of the press...... 22 I.2.2 – Using the multianvil press as a deformation apparatus...... 25 I.3 – Experimental developments and calibration performed during this study...... 27 I.3.1 – Developments performed for the D-DIA press...... 27 I.3.2 – Developments performed for deformation in the Kawai-type multianvil press.... 30

I.4 – Presentation of the starting materials (Mg2SiO4)...... 32 II – In situ measurements in the D-DIA...... 33 II.1 – Technical setup...... 33 II.2 – Strain measurement...... 34 II.3 – Lattice strains analysis...... 35 III – Technical analyses on recovered samples...... 36 III.1 – Scanning Electron Microscopy (SEM) and Electron BackScaterring Diffraction (EBSD).... 36 III.1.1- Sample preparation for SEM and EBSD...... 36 III.1.2 – SEM and imaging...... 36 III.1.3 – Electron BackScattering Diffraction technique...... 37 III.2 – Transmission Electron Microscopy (TEM)...... 38 III.2.1 – Sample preparation for TEM...... 38 III.2.2 – Presentation of the microscope...... 38 III.2.3 – Diffraction mode: Selected Area Electron Diffraction (SAED)...... 38 III.2.4 – Imaging mode and observation of dislocations...... 39 III.3 – Other analytical methods...... 40 III.3.1 – Micro-Raman spectroscopy...... 40 III.3.2 – Fourier Transform InfraRed spectroscopy (FTIR)...... 40

Chapter III. Results I – Deformation of forsterite at high pressure...... 43 I.1 – Deformation experiments using the Kawai-type multianvil apparatus...... 43 I.1.1 – Strain marker rotation and piston displacement...... 44 I.1.2 – Microstructural characterisation: SEM and EBSD...... 45 I.1.3 – Microstructural characterisation: X-ray peak broadening...... 50 I.1.4 – Microstructural characterisation: TEM...... 51 I.1.5 – InfraRed spectrometry characterisation...... 52 I.2 – Deformation experiments using the D-DIA apparatus...... 54 I.2.1 – Starting material...... 54 I.2.2 – Annealing experiments under hydrostatic pressure in the D-DIA...... 55 I.2.3 – Deformation experiments performed at the Bayerisches Geoinstitut...... 56 I.2.4 – Deformation experiments performed at APS...... 58 I.2.5 – Deformation experiments performed at NSLS...... 61 II – Deformation on wadsleyite...... 63 II.1 – Phase identification...... 64 II.2 – SEM and EBSD characterisation...... 64 II.3 – TEM investigation...... 70 II.4 – InfraRed spectrometry characterisation...... 71 III – Deformation of ringwoodite...... 71 III.1 – Phase identification...... 72 III.2 – SEM and EBSD characterisation...... 72 III.3 – TEM characterisation...... 73 IV – Influence of a phase transformation on plastic deformation: the case of the forsterite-wadsleyite transformation...... 76 IV.1 – SEM and ESBD characterisation...... 76 IV.2 – TEM characterisation...... 79

Chapter IV. Discussion I – Deformation experiments at high pressure and temperature: progresses and limits...... 83 I.1 – Deformation in the D-DIA...... 83 I.1.1 – Sample preparation...... 83 I.1.2 - Deformation history in D-DIA experiment...... 83 I.2 – Deformation in the Kawai-type multianvil apparatus...... 85 I.2.1 – Starting material...... 85 I.2.2 – Deformation history in a shear deformation experiment...... 86 1.3 – Conclusion on deformation techniques under high pressure and temperature...... 88

II – Deformation of Mg2SiO4 polymorphs under upper mantle and transition zone...... 89 II.1 – Deformation mechanism of forsterite at 11 GPa and 1400°C...... 89 II.1.1 – Changing the deformation mechanisms with pressure...... 89 II.1.2 – Physical origin for a pressure sensitivity of the olivine slip system...... 93 II.1.3 – Linking microscopic to macroscopic: crystallographic preferred orientation...... 94

II.1.4 – Conclusion and open questions...... 97 II.2 – Deformation of wadsleyite and ringwoodite under pressure –temperature conditions of the transition zone...... 97 II.2.1 – Deformation of wadsleyite at 16 GPa-1400°C and effect of the phase transformation forsterite wadsleyite on deformation...... 97 II.2.1.1 – Deformation of wadsleyite at 16GPa and 1400°C...... 98

II.2.1.2 – Influence of the forsterite Îwadsleyite phase transformation...... 102 II.2.2 – Deformation of ringwoodite at 22 GPa and 1300°C...... 104

II.3 – Main conclusions on the deformation of the Mg2Si4 system...... 107 III – Implications for the seismic anisotropy of the Earth’s upper mantle and the transition zone...... 107 III.1 – Pressure sensitivity of olivine slip systems: implications of the seismic anisotropy of the lowermost upper mantle...... 107 III.2 – Predicting strain-induced seismic anisotropy in the upper part of the transition zone...... 111 III.3 – Conclusion...... 114

Conclusions and open questions...... 117

Appendix Appendix I – Strain calculation from the strain marker rotation...... 121 Appendix II – X-ray diffraction peak broadening analysis technique and evaluation of strain anisotropy 123 Appendix III – Crystal preferred orientation modelling: ViscoPlastic Self Consistent (VPSC) method...... 125

References...... 129

Erklärung...... 141

Articles...... 143

Summary

The rheological properties of the major minerals of the Earth’s mantle are still not well constrained. However, these properties are crucial for the understanding of a wide range of processes in the Earth’s interior such as mantle convection. The purpose of this work is to address the issue of the rheology of the lowermost upper mantle and of the transition zone through the mechanical properties at high pressure of olivine (with forsterite composition Mg2SiO4) and of its high-pressure polymorphs wadsleyite and ringwoodite. Indeed, the properties of the Earth’s mantle can be inferred as a first approximation from the mechanical properties of those polymorphs which volumetrically dominate the mineralogy of the region of concern. Deformation experiments have been performed on hot-pressed forsterite samples and on pre- synthesized wadsleyite and ringwoodite samples under pressure conditions of the Earth’s mantle and at 1300- 1400°C. The possible influence of the phase transformation from forsterite to wadsleyite on rheology has been also investigated. Deformation has been achieved by shear using the Kawai-type multianvil apparatus. Complementary experiments on forsterite have been performed in the newly developed Deformation-DIA. Some of them have been carried out on a synchrotron beam line to perform in-situ stress and strain measurements. In order to gain a maximum of information on the deformation mechanisms and on the Crystallographic Preferred Orientation (CPO), a special attention has been devoted to the microstructural characterisation of the samples. Electron BackScattering Diffraction (ESBD) and Transmission Electron Microscope (TEM) have been mainly used. An important pressure-induced change in deformation mechanism is shown in forsterite. The deformation of forsterite at high pressure and temperature is dominated by the [001]{hk0} slip system rather than the [100](010) glide which is extensively observed at low pressure and high temperature.. Concerning the high-pressure polymorphs, their plastic behaviour has been studied with a strong emphasis on the formation of CPO. ViscoPlastic Self Consistent (VPSC) modelling is used to link the CPO with known elementary deformation mechanisms of these phases. The main features of the CPO of wadsleyite are characterized by the alignment of the [100] axes parallel to the shear direction and the alignment of the [001] axes toward the normal to the shear plane. Too many uncertainties remain on the ringwoodite CPO for them being used to interpret seismic anisotropy. Finally, we suggest that strain-induced CPO might be responsible for the seismic anisotropy observed in the lowermost upper mantle and in the upper part of the transition zone. The low seismic anisotropy of the lowermost upper mantle can be explained from the slip system change in forsterite and the CPO of wadsleyite point toward a dominant tangential flow in the upper part of the transition zone.

. 1 .

Zusammenfassung

Die rheologischen Eigenschaften der Hauptminerale des Erdmantels sind derzeit nahezu unbekannt. Die Kenntnis dieser Eigenschaften ist aber entscheidend für das Verständnis vieler Prozesse und Eigenschaften des Erdmantels wie Konvektion, Entwicklung seismischer Anisotropien oder Festigkeit subduzierter Lithosphäre. Ziel dieser Arbeit ist es, die Rheologie des unteren Bereichs des oberen Erdmantels und der Übergangszone über die mechanischen Eigenschaften von Olivin und seiner Hochdruckpolymorphe

Wadsleyit und Ringwoodit (Mg2SiO4) – die volumenmäßig wichtigsten Phasen dieses Regimes – abzuleiten. Die Eigenschaften des Erdmantels können nämlich in erster Näherung aus den mechanischen Eigenschaften dieser Polymorphe berechnet werden. Deformationsexperimente wurden bei Drucken des Erdmantels und bei Temperaturen von 1300- 1400°C an gesintertem Forsterit und zuvor synthetisierten Wadsleyit- und Ringwoodit-Proben durchgeführt. Der mögliche Einfluß der Phasenumwandlung von Olivin in Wadsleyit auf das rheolohische Verhalten wurde ebenso untersucht. Die Deformation wurde durch Scherung der Proben in einer Vielstempelpresse vom Typ Kawai erreicht. Komplementäre in-situ Experimente wurden mit einer neu entwickelten Deformations-DIA- Apparatur an Forsterit durchgeführt. Der thermomechanische Verlauf der Deformation wurde erstmals in den Hochdruckpressen durch zeitaufgelöste Experimente dokumentiert. Um ein Maximum an Information über die Deformationsmechanismen und die kristallographische Vorzugsorientierung (CPO) zu erhalten, wurde auf die Charakterisierung der zurückgewonnenen Proben besonders Wert gelegt. Beugung rückgestreuter Elektronen (EBSD) und Transmissionselektronenmikroskopie (TEM) kamen hierbei zum Einsatz. Die Hochdruckexperimente an Forsterit belegen eine druckinduzierte Änderung des Deformationsmechanismus. Die Deformation von Forsterit ist bei hohen Drucken und Temperaturen durch das [001]{hk0} Gleitsystem geprägt, während bei niedrigen Drucken und Temperaturen üblicherweise [100]- Gleitung vorherrscht. Bei den Hochdruckpolymorphen wurde die plastische Deformation im wesentlichen über die Ausbildung von kristallographischen Vorzugsorientierungen (CPO) erfasst. Viskoplastische eigen-konsistente Modellierung (VPSC) wurde genutzt, um die kristallographische Vorzugsorientierung (CPO) durch bekannte elementare Deformationsmechanismen zu erklären. Die Hauptmerkmale der kristallographischen Vorzugsrichtungen von Wadsleyit sind die Ausrichtung der [100]-Achsen parallel zur Scherrichtung und die Ausrichtung der [001]-Achsen senkrecht zur Scherebene. Im Gegensatz dazu entwickelte sich in Experimenten mit Ringwoodit keine deutliche kristallographische Vorzugsrichtung (CPO). Die deformationsbedingten kristallographischen Vorzugsrichtungen (CPO) liefern schließlich eine Erklärung für die beobachteten seismischen Anisotropien im unteren Teil des oberen Erdmantels und in der Übergangszone. Die geringe seismische Anisotropie des unteren Teils des oberen Erdmantels kann durch eine Änderung des Gleitsystems in Forsterit erklärt werden, während die kristallographische Vorzugsrichtung von Wadsleyit auf tangentiales Fließen im oberen Teil der Übergangszone hindeutet.

. 2 .

Résumé

L’étude de la plasticité des minéraux du manteau terrestre sous pression joue un rôle majeur dans la compréhension et la modélisation des grands processus actifs à l’intérieur de la Terre tels que la convection mantellique. Cependant, les propriétés des minéraux du manteau sont toujours, à ce jour, mal connues. L’objectif de ce travail est d’étudier la rhéologie de la partie inférieure du manteau supérieur et de la zone de transition, à travers l’étude des propriétés mécaniques de la forsterite (Mg2SiO4) et de ses deux polymorphes de haute pression (wadsleyite et ringwoodite). En effet, ces phases sont les constituants principaux des zones étudiées et on peut considérer, en première approximation, qu’elles contrôlent les propriétés du manteau. Des échantillons de forsterite frittés et de wadsleyite et de ringwoodite synthétisés sous pression ont été déformés dans les conditions de pression du manteau et à 1300-1400°C. L’influence de la transformation de phase forsterite-wadsleyite sur la rhéologie a également été étudiée. Les expériences de déformation en cisaillement ont été menées dans la presse multi-enclumes de type « Kawai ». Quelques expériences complémentaires sur la forsterite ont été menées dans la nouvelle presse Deformation-DIA. Certaines ont été réalisées sur synchrotron afin de mesurer contraintes et déformations in situ. Les microstructures des échantillons obtenus ont été caractérisées par Microscopie Electronique en Transmission et leurs textures ont été déterminées à l’aide de la technique de diffraction des électrons rétrodiffusés. En ce qui concerne la forsterite, nous avons mis en évidence un important changement de système de glissement induit par la pression. A haute pression et température, la déformation de la forsterite est dominée par le glissement [001]{hk0} alors que le glissement [100] a largement été observé à basse pression et haute température dans les travaux antérieurs. La plasticité de la wadsleyite et de la ringwoodite a été étudiée principalement aux travers des textures. La méthode de simulation ViscoPlastic Self Consistent a été utilisée pour faire le lien entre les textures et les mécanismes de déformation supposés pour ces deux phases. Les grandes caractéristiques des textures de la wadsleyite sont l’alignement des axes [100] avec la direction de cisaillement alors que les axes [001] sont normaux au plan de cisaillement. Pour la ringwoodite, aucune texture fiable ne peut être proposée. Enfin, les textures produites par la déformation plastique des trois polymorphes peuvent être proposées comme étant à l’origine de l’anisotropie sismique du manteau supérieur et de la zone de transition. Le changement de système de glissement dominant de la forsterite permet d’expliquer la faible anisotropie sismique observée dans la partie inférieure du manteau supérieur et la texture de la wadsleyite indique un écoulement horizontal dominant dans la partie supérieure de la zone de transition.

. 3 .

Introduction

G G pGGGGG G GGGGGGGGGlGGG G G G G G G G UG kG G G G G SGGGGGGSGG UUUUG{GGGGGG GGGGGGlUGtGGGGGGGGG GGG l˅GGGGGGGGG¡¡GGGG UG{GGGG GGGGGGGGGGGGGGGGGGG GGGG GGGGUG G {GGGGGlGG GGGGGUGhGGG GGOwGGGzGPGGGGGO G GGGPSG G GGGGlGGGGGGGGGGGGGGUG zG G G G G G G G G lUG {G G G G wyltG Ow G yG lG tSG k¡G G hSG X`_XPG G G mG XUG ~G G G G GG GGGGGGGGGGSGG ¡GGGGOGGGGSGGGGGGGPUG G

G mGXGTzGGG GGGUGwyltGGk¡GGhGOX`_XPUG G G hSGGGGGGGGGGGSG GG GGGGUGhGG GGGGG GG GGG GGGGSGG GGGGGGGGUGG G hGGGGGGGGGGGGGG GnGGyG OX`]ZPaGGGG UG{GGG GGGGGGGG GG GGGGGG GUGmGG GSG G G G G G G OmG YPG G G UG {G G G G G G

G OtSmPYzv[SG G OjStSmPOtSmShPOzhPYv]G G G OjStSmPZOtSmShPYOzhPZvXYGG OG hG OX``_PPUG hG UG [XWG SG G G G T G UG pG G G ¡SG . 7 . G Introduction

G G G G UG kG OG UG \YWG PSG G G G G UG

{SGGGGGGGGGGGOtSGmSGhPOzSGhPvZGGjzvZGG GĂGOtSGmPvUGG G

G mGYGˀGzGGGGGl˅GUG G G {GGGGGG G GGGXWWGG_WWGG GGGGGwGGzG GGGGGOmGZPUG{SGG G GGGGGGGGGGGGl˅GGUG G

G mGZGˀGjG GOwTPGGGGG G GGG GGwyltGGOGhGOX``_PG

. 8 . G Introduction

G hGG GGG G G UG pG G G G G G G G G¡G GOmG[PUG{GGGGG GGGGGGXWWWG GGGGGGkˉG SGOGG GGGTG PUGzG GGG G G G G G G G G G G UG pG G G G G G G G G G G G OzG wG vPG G G G G G G G GOj GwGvPUGGpGGGGGGGGGGG G G G G G G G G jwvG G G G G G UG pG G G G G G G G G UG oSG G G G G G YYWG G G GGGGG GGGGGGGG GGGG GG GGGG¡UG G

G mG[GˀGlGGGGGGGGGG¡GG GOG zw]TmGGtGGrGOX``]PG G G {GGGG GGGGG GGGG G G G G G ¡SGGGGGGG GGGGGGGGGG GUG{GGGGG GGGGGGSG GG SGGG GGGGGGGGGG¡UG|GGSG GGGG GUGlGGG GGGUGoSG GGGGGTGGGGl˅GGGG

GGGGUGpGG SGGGGGGOtYzv[PGGUGmG \G G G G G G G G G G G TG G G G tYzv[UGzGGG GGGGUG G

. 9 . G Introduction

G G mG \G ˀG wG G G G tYzv[GGG GUG{GGGG GGGG UG G

G {GGGGGGGtYzv[G GGGGGjGpUG{SG GGGGGG GGGGGGGGGG GGGGGOjGppPUG{GGGGGGGGG G G G G G G jG pppUG {G G G Op}PG G G G G G G G G G G TG G G G G G G tYzv[G UGm GGGGGGG GGGGG GG Gl˅GUG G G G G G G G G G G G G G G G G G G G G . 10 . G

Chapter I Forsterite, wadsleyite and ringwoodite: structural and rheological data

The goal of the present study is to investigate the rheology of the lowermost upper mantle and of the transition zone through the mechanical properties of olivine at high pressure and of its high-pressure polymorphs wadsleyite and ringwoodite. As a first approximation, we have used pure forsterite compositions

(Mg2SiO4) either for the olivine phase or for the high-pressure polymorphs. While deformation of olivine has been extensively studied at high temperature, studies on olivine at high pressure as well as on wadsleyite and ringwoodite in their stability fields are still insufficient. This is a consequence of difficulties in deforming minerals at high pressure and high temperature. Significant progress have been achieved in this field since a decade, they are presented Chapter II. Some data on these three phases relevant for the present study are exposed here.

Forsterite, wadsleyite and ringwoodite pGˀGmaGGGTGGG

G vG G G G G G G TG aG G OtYzv[PG G G

OmYzv[PUG{GGGGGGGGGGTG G UG {G iGGGGGGGGG wUGGmGpUXGGGGGGGGG UG{GGGGGGGdG[U^\GËSGGdGXWUX`GËGGGdG\U`^GËUGvGGGG

GGUG{GGGGGGOzv[PGGGGGG GG

GaGGtXGGtYUGtXv]GGGGGGGGGGGzW[G YR GGtYW]GGGGGGGGGGGGUGm G

YR t GG GGGtXGGtYUGvGGGGDTUGG G

G mGpUXGˀG{GGGUGzv[GGGtGGGUG G G vGG GGGGGGGGGUGpGGGGGGGG GGGGGG GGGGUGmGGSGGGGGGGGG GGGGGGGGG[WWGGGGlNGGGGGGG GGGGUGt GGGGGGGGGG GGGGUGGGG G yGOX`]_PGGGGGGGGO\GPSGGGGGXWWW¶jG GGGGGXWTYGGXWT]TXUG|GXWWW¶jGGGGGSGGGWWXGGG¢XXW¤SG OWXWPG G OXWWPUG pG G G G SG G G G G G G G G G G XWW¢W¤UG{GGGGGGGGGGUGzG GG G SGOUUGjGGhNSGX`^WbGjGGwSGX`_XSGX`_[bGrGGUSGX`_]bGoGG rSGX``\SGbGtGGrSGYWWWSGPGGGGGG GOUUGw GGUSGX`^YbGiG GjSGX`^ZbGrGGn¡SGX`^[bGkGGn¡SGX`^^bGkSGX`_WbGkGGnSG X`_XbGrGGUSGX`_YbGtGGUSGX`_\bGiGGUSGX``XbGiGGrSGX``YSGSGX``ZPGG GGG GGGXWWGGGGGGTGGWWXGGG G G G G G G TUG kG G G G G G G GGGGG UG| GGG GGGGXXWGOUUGG XWWG G G OWXWPG PSG WXXG G XWXUG mG G G G SG G G G G G

. 13 . G Forsterite, wadsleyite and ringwoodite

GGGGGG GGGGGGGGOSGGG GGUUUPUGG G mGGGSGGGGGGG GGGGG XWWG G G G aG OWXWPSG ¢WZX¤SG ¢WYX¤SG ¢WXX¤G G OWWXPG OmG pUYPUG jG G G G GGGUGkGGGG GGGGG GSGGGGUGpGOWXWPSGGGGGGGGGG UG {G G G G G G OnSG X`^`PG G G G G G OkSG X`^\bG qGGUSGX`^`PUGlGXWWGGGGOWWXPGGGGGG¡T¡GG GGGGGGcXXWeGUG~GGG GXWWOWPGG GGGGGGGGGXWWGGGOkSGX`^\bGnSG X`^`PUGhGGGGGSGGGGWWXGGOXWWPSG¢XXW¤GGOWXWPGOmGpUYPUG WWXGGGG GGGG GG GGGGG GGGUG{GGG GbG GG GGGXWWGG WWXGGUG G

G mGpUYGˀGvaGGGGGXWWGGOPGGGWWXGGOPUG G G oGGGGGGG GGGGG G G G G G G TG G G G G G G | ZU\G G G GG GGGGUG G j G G G G G G SGGGG G G G G G SG G G G G G G G OiG põG G tSG X``_G G G PUG {G G G G G G G SG TG G G G XXWG G G G G jwvG ¡G G G XWWG G G G G G UG {G G G G G G G G G G G XWW¢W¤G OG G G G G G OWXWPG G G G OWWXPPUG vG G G G G G OG G rSGX``\bGi GGUSGYWWWbGGGUSGYWWWPGGGGGGGjwvGG GGGGGGG GGGGGO{SGX``_bG{GG USGX```bG~GG{ïSGX```PUGjwvG¡G GGWWXGGGGGGGG GGGGGG GqGGrGOYWWXPGGGGGOmGGUSG YWWZbGt¡GGUSGYWW[PGGGGGGGGGUGhGGjwvG¡G G G XWWG G G G WWXG G G G G G G G G G G G O}¡GGUSGYWWZPUG

. 14 . G Forsterite, wadsleyite and ringwoodite

G hG G G G G TG G G GGGGSGG GGGGGGO GXGGGGGTPUGv G G G G G G G G Oi GGUSG YWWWbG GGUSG YWWWPG G TG OrG G ySG X``^bG qG G rSG YWWXbG rG G qSG YWWZbG sGGUSG YWWZbG sGGUSG YWW[bG yGGUSG YWW[PG G UG wG G G G G G G G G G G G G GOGGG PGGIIGGOtGGUSGX`_\bGtGGrSG YWWWSG bG qG G rSG YWWXPUG lG G G G G G _G nwG G G G X[^\G rG G G G G G G G G G G ¡G G G G OsGGUSG YWWZPUG oSG G G G OG SˎPG G G G GGGGGG GUG G ppGTG~ G

GG G ~ GOGETPGG GGGGGGGG¡SGG [XWG G \YWG G G UG {G G G G G G G G UG {G iG G G

GGGGGGpUG{GGGGGzW[GGGOmGpUZPGG

G G G G G G G tXSG tYGGtZUG tXv]GGtYv]GGGGGG

UGtZv]GGGGGGUGzGGGGGGGGG

GGGGGUG{GGGGtYzv[G GGGdG\U]`_GËSGGdGXXU[Z_GËG GGdG_UY\]GËGOoGGzSGX`_XPUG G

G mGpUZGˀG{G GGUGzv[GSGtGGO PGGvGGOPGGUG G G {GGGGGGGUGpGGG GGGGG GyG G tG OX`]]PG G G G G G G G wG yG G OwSG X`_ZPUG mG GGG GGGGGGGOwGyGGjPG

X X G GGGG V[WXWOWXWPGG VYcXWXeOWXWPGOtGGwSGX`_ZbGwSGX`_ZPUGtG

X GwGOX`_ZPGGGGG V[WXWGGG GGGUG{GGG GGGG GGGGOGjGppPUGzGGUGOX``[PGG kGGUGOX``_PGGGGzGjGGGG G GGGX[\W¶jGG

. 15 . G Forsterite, wadsleyite and ringwoodite

G`WW¶jG UGhGGGGGGGGGX[\W¶jGGGGGG G G SG G G G G G G G G G UG XWWG G GGGGGGGGGGGGOWXWPGGG

X X GOzGGUSGX``[PUG V[WXWOWXWPGG VYcXWXeOWXWPGGGGGGUGkGG UG OX``_PG G G G G G G UG pG SG G G XWWG G

X VYcXXXeG iG G G UG XWWG G G G G G UG {G G G GGGG G GGGGGG GG`WW¶jUGG G y G G G G G G G G ¡G ¡G G G G GGOX[GnwGGXXWWTXYWW¶jPG GGkGGUGOX``[PUGhG GGGGOWXWPSGGG G G G G G G G G G WWXG G UG {G G G GGGGGGGGGGUG{GGG GG

X G¡aGXWW¢WYX¤GOGGPGG VYcXXXe¢XWX¤UG G tG G G G G G G {G OYWWXPSG {G G UG OYWWZbG YWWZPUG wG G G T ¡G G G OG PG G G G G G G GGGGGOjGGySGYWWXGGGjGppPGGX\TX`GnwGG G G G X_WW¶jUG jG G G G G G G G G

X G G G G UG mG G G G aG VYcXXXe¢XWX¤SG XWWOWXWPSG XWWOWWXPSG XWW¢WXX¤SGXWW¢WYX¤GGGGGGGGGGGG aGWXWOWWXPSG WXW¢XWX¤GGcXWXeOWXWPUGlGG¢WYX¤SGGGGGGGGGGGG

G G zv[GUGpGGGGGGGWWXGGG G UG kG GGGWXWGGcXWXeGGGUGcXWXeGGGGGG

X X OWXWPG G G G VYcXWXeUG WXWG G G G G G VYcXXXeG G X OGPGGG¢XWX¤GGGGGG V[WXWGGUGzGGG GGGTG UGpSGGGGGGGGGG G G G G SG G G SG G G G G G G G G G ¡G G G UG {G G G SG G G G G G G G T ¡G G G G G G G GG GrGGyGOX``^PGOGjGppPUG{GGGGGGG G G G G G TG G G G TG UG

X lGGGX[GnwSGXZWW¶jGG GGm`WGGGG VYcXXXe¢XWX¤SG XWWOWXWPG G XWW¢WXX¤G OmG pU[PG G G G G G G G G G G O{SGYWWXbG{GGUSGYWWZPUG{GjwvGGG¡GGGUGG G

. 16 . G Forsterite, wadsleyite and ringwoodite

G mGpU[GˀGl GG GG GGGGGGUG G GG pppGTGyG

G G mGG\XWGGGSG GGGG GGaGGOGJT PUGyGGGGG G G G TTG G G G G

UGyGGGGG GOGGmZPUG{Gzv[GGGGG G G G UG {G G G G G G tYRGGmYRG G G G G G G

GUG{GGGGtYzv[GGG GyGGtGOX`^WPG GGdG_UW^XGËUG{GGGGGGGOmGpU\PUG G

G mGpU\GˀG{GGGUGzv[GGGtGGGUG G G {GGGGGGGGGGGOUUGiGGUSGX`]`bG zGGtSGX`^WbGjSGX`^^PUGG G pGGGSGGGGG GGGGGGGcXXWeGGG

X GGGGGOtSGX```PUG VYcXXWeGGGGGGiGUGvGGG SGGGGGGGGGGGGG GUG{GGG GGG¢XXX¤GG¢XXW¤SGG¢XWW¤GGGGGSGGSGGG OtSGX```GGGPUG G {GGG¡GG GGGGGGGGG UG tG G wG OX`_WbG X`_ZPG G G G G G G G G G . 17 . G Forsterite, wadsleyite and ringwoodite

X {UG { G G G G G G G G G G ¢XXW¤G G G G G VYcXXWeG X GGG]W¶GG GG¢XXX¤GUG{GGGGGaG VYGXXWGG

GX V[GXXWGGGGUG

G wG G G G G OtSG mPYzv[G G G G G G T SG TG G rG G UG OX``_PUG z G G G G G G G G G G G X]G nwG G G G G G X[WWTX]WWG rUG hG TG G O|GWU\G»PGGGGT G G SG TG G OG ZG »PG G G G UG {ltG G G G G G G G G G

X VYcXXWeGGG¢XXXPGGG¢XWW¤GGGUGpGGG SG{GOYWWXPGG

G tYzv[G G G G G G OjG G ySG YWWXPG G YYG nwG X X GXWWWTX[WW¶jUG{G GGG VYcXXWe¢XXX¤GG VYcXXWe¢XXW¤GGGG UGpG GSGGGGGGGGGG GGOSG [\¶SG]W¶GGPGGGGGGTGTG{ltGUG GGGUGOYWWZPGGGGGGGGGGYWGnwGGGGXZ\W¶jUG{ G G G G XWWW¶jSG G G G G G G TG G G G G G G | ZU\GGGGUG G G y GGjwvGGGGG GG G~G GUOYWW[PGG TG GGGGUG{ GGGGGGGGGGYWT[WG nwGGGjwvG¡G GcXXWeGGGGGGUG{GGG GcXXWeGGGUG{GGGG¢XXX¤GG¢WXX¤GG\WGnwGG¢WXX¤GG[ZGnwUGG G G G G G G G G G G G G G G G G G G G

. 18 . G

Chapter II Experimental techniques and developments

Achieving plastic deformation experiments under pressure-temperature conditions of the Earth’s mantle is one of the most challenging issues in mineral physics. This field is then evolving very rapidly. It is now possible to perform deformation experiments to ca. 10 GPa using the newly developed Deformation-DIA where differential stress is controlled independently from pressure and where relatively large strains (several tens of %) can be reached. A D-DIA has been installed in the Bayerisches Geoinstitut in 2000. The geometry of this apparatus allows coupling with a synchrotron light source in order to measure stress and strain in situ during this experiment. For pressures above 10 GPa, it is necessary to use conventional high-pressure experiments such as the Kawai-type multianvil press or the diamond anvil cell. In the course of the present study, only large-volume multianvil apparatus have been used. Plastic deformation can be achieved with this apparatus provided modified assemblies are developed. In this chapter, the principles of the techniques used in this study are presented as well as the technical developments achieved. Most experiments were performed in Bayreuth without in situ measurements of mechanical data. Our strategy was to perform detailed microstructural characterisations on recovered samples. The various analytical techniques used are also presented in this chapter.

Experimental techniques and developments pGˀGoGGaGGGGGG

G G vGGGGGG GTGGGGTGG UGmGppUXGGGGGGGGGGGGGG UG{GkTkphSGGGi SGG GGGG GGGGUG jGGG ¡SGGG GGGGGG GGGG G G G G G UG ~G G G G G G G rT G GGGGGinpGG GGUG{GGGGGGG GGGG GGGGGGUG G

G mGppUXGˀGwˀGGG GGGUG{G GGGG UG G G

G pUXGˀGkTkphGOkTkphPG

G G {GGGGTGGGGGGaGGG GGG GGGGGGGGUG|G SGG GGaGGnGGGwGUG G {GnGGGGGG GGOnGGUSGX`]WPUG{GGG G G G G G TG G G G G G G G G G UG yG GGGGGOUUGnGppGGiSGX`_`bGnGG{SGX``ZbGy GGUSG X``_PGGGGGGGGGGGGGGUG[GnwUG G hGGGGGG GwGOX`^WPUGmGGG GGG G G G UG kG G G G G G G G OSG GGPGGGGUGmG GSGGGGGGGZWWG twG G XZWW¶jUG {G G G G G G G G G G G G G G GGGGGGGXWWGUG . 21 . Experimental techniques and developments

G {G G G G G G G G G XWG nwGGYWWW¶jGGG G GTGGaGGTkphGO~GGUSGYWWZPGOmGppUYPUG{G G G G G G G kphG TG G OvGGUSG X`][PSG G G G G G TG G UG {G G G G G G G T G GGGGGiuGG~jGUG{GGGGG GG

GGGGsjvZGGGG~ZLyT~Y\LyGGGGUG{G G GGGGGGGGGGGUG pG G kTkphSG G G G G G SG G G G G G G G G G G G G GGGGGGGGGGGGGGGGGG GGGUG} GGGGGGSGGGGGGGwG G G UG iG G G G G G G G G G G G UGG G hGGkTkphGGGGGGGi GnSGGGGGGGG GGGGGGGGGGG UG{GGG GGGGG OGpUZUXPUGGGG

G mGppUYGˀGzGGGGkTkphUGhGXGGGGGGGYGGGG UG G G

G pUYGˀGrT GGG G

GGpUYUXGˀGwGGGGG G

G {G rT G G SG G G qG G G G X`_WG OUUG rG G lSG X`^WbGpGGUSGX`_[PSGGGGG GGGGGGGGwT{GUG{G G G G G TG G G G G G G G G G Y\G nwG G G

. 22 . Experimental techniques and developments

GYWWW¶jUG{GGGGGGG GGGGGGGGG GGGG UG{GGGGGGGG GGGGOmGppUZPUGG G

G mGppUZGˀGrG GaGGGGGGGGGGGGUG G G {G G G G G G G G G G G G G UG {G G G G G G G TG G G G G G G GGGGGUG{GGGGGGtvGGGG\LGG jYWZUGGGGGGG GG GGGGOmGppU[PUGG

G {GGGGGGOmGppU\PGGG GGG GGOsjvZG GGSGGGGGPUGpGGG GSGGGGGGGGG GGGGGGGGUG{GGGGGGGGG GG GGGGGGGGGGGGUG{GGGG GG GGG

G G G UG hG vYG G G G G G G G G G G G tvG G G G G G sjvZG G G G G G UG {G G G G G G G G G G G O~ZLyT~Y\LyG G G PG G G hYvZGUG G

G mGppU[GˀGrT GGaGGGGGGGGGGG UG GG G . 23 . Experimental techniques and developments

G oGGGGGGGUGw GGGGG GGGGGGGGGUGjGG{GGGGG GGGGGGGGGG GGGGGGGG GGGGUGG G

G mGppU\GˀGrG GaGTGGGGX_VXXG UG G G {G G G G G G G UG {G G G G G G G G G GTGO{lsPGGG~jGGGGGGTGOvlsPGGGGG GGGGGGGGTGGGGGOsGG~SGX``YPUG kGGGGGGGGGGaGvlsV{lsGGUG{GppUXG GG G G G G G G G G G G G XWWWTYWWWG G G UG pGGvlsV{lsGGGGGGGGG ¡G G G G G G G G UGG G

vlsV{lsG zGGOZPG wGGOnwPG

X_VXXG XYG [TXYG X[V_G \T_G XXTX^G XWV[G XG YYTY]G

G {GppUXGˀGzGGGGGGGGGGGGrT GG G G {GGGGTGGGGrT GGGG GGGG GGGGGGGGGGGGUGvGGGGGG GGGGGGGGGGGGGGvlsV{lsGUG{GGGG UGhGGSGGGG GGGGGGGG G G G G UG mG SG G G iTpG G iTppG G iTpppG G iTp}G GGYU\YGnwGG^U^GnwG GOs SGX`^XbGnSGX``_PUGhGGSGGG GGGGGGGGUG}GGGGGGG G G G G G G G G G G G G G UG mG SG GGGGGGGGGGGGGUG{SGG G G G G G G G G G UG {G G G G G G G

GGGGGGGTGOGGUSGX``]PSGDTtYzv[GGET tYzv[GOtGGUSGX``[PGGEtYzv[GGJTtYzv[GOz¡GGUSGYWWWPGSGUGmG . 24 . Experimental techniques and developments ppU]G G G G G G G G i G nG OG G G PUG {G GGGGGGGGGG·GWU\GnwbGGGG G G G G G G G G G G G G UG pG G G G GGGGGGGGGGGGGGGUG oSG G GG GGGGGOySGX```PUGG G

G mG ppU]G ˀG {aG G G G G zG G OXYWWPUG jG G X_VXXG OPG G GGX[V_GO PUGhGGGSGGGGWU]GGGGGGGGGG o G G OXWWWPUG iaG G G G G G G O\WWWPUG yG O PG G T GOPGOGmGGUOYWW[PPUG mG TG SG G G TG G GGGGG GG GGGG UG G

GGpUYUYGˀG|GGGGGGGG

G {G GGGGGGGGT GUGzG GG GG GGGGGGT GUGhGGrT GGGGGGGGGGGGSGGGG GGGGGGGGT GGUGl GG G mGGUSGOX`_XPSGGGGGGGGGGGGG GOnGppGG

. 25 . Experimental techniques and developments iSGX`_`bGsGG~SGX``YbGiGGUSGX``ZbGzGGUSGX``[bG~SGX``_bGjGG ySG YWWXbG jGGUSG YWWYbG {G G jSG YWWZbG {GGUSG YWWZPUG {G G G G G G G G G G G G G OmG ppU^PUG kG G SG G G GGGUG~GGGSGGGGGGG GGGGG GGGGG GGGGG GGUGpGGGGG G G G G G G G G SG G G G G G G G G G G UG hG G SG G G G G SG SG G UG {G G G G G G UG pG G G G G SG rG G yG OX``^PG GGGGGOmGppU^PUG{GGG GGGGGGGGG GGGGG[\¶UG{GGGGGGGO GYWW»PGGGGUGoGT GGGGGGGGGGGGGGGGOG XWWLbGGGrGGyGOX``^PPUGhGGGGGGGGGGG GGGGUG G

G mGppU^GTGjTGGGGOPGGGOPGGUG G G pGG SGGGGGGGGGGGGG G GGGGGGGOrGGySGX``^PUG G G vG G TG G G G G G G SG G G G G G G GGG GOmGppU_PGGGGGGGGGGGG GGGGUGhGSGGGGGG GO\W¶TXWW¶jVGPUG{GXWGG X\G G G G G G X[WW¶jSG G G G G UG {G G G G G UGhGGGGGSGGG GGGGGGGGOGGG G¡PGGGGGGGGGGGUG{GGGGG G G XWTYWG G G G G G ~jG UG {G G G G G G G GGGGUG G G

. 26 . Experimental techniques and developments

G mG ppU_G ˀG { G G G G rT G G UG iaG G G GUGn aGGGUG G G

G pUZGˀGlGGGGGGG G

GGpUZUXGˀGkGGGGkTkphGGG

G hGGkTkphGGG G GGGGi GnSGGGGGG GGGGGGGGG UGzGGO{GppUYPGG GGGG GGGGGGGGUGtGGGGGGG\GnwGG XXWWTXZWW¶jUG{GGGGGGG GGGGGrT GGOGmGppU\PUGG G

yGJG rGGGTGtG wGG kkW^G vGGGGG GGGG kkX]G w GG¡GTGwGG wGGGVGjGGG kkX^G uGGGTGwGG wGGGVGjGGG wG G G G VG wG kkX`G uGGGTGwGG GG kkYWG {GGGGGGGG wGGGG uG G G G G G G TG wGGGVGwGG kkYXG {GGGGhYvZGGGwG G TG G G wG G GG G kkYYG {GwGG w GGGG

kkYZG jGhYvZGGGw G oGGGTGtGGG kkY[G nGGGwGG p GGGG nG GGGG G kkY]G uGGGGG GGGhYvZGG jG h v G G G G G kkY^G Y Z oGGG w G kkY_TY`G kGG nG G {GppUYGˀGlGGGGGGGGGGGGGUG wdGG G G mG ppU`G G mG ppUXWG G G G G G G G G G G G G GGG UG{GGGGGGGGGGGUG . 27 . Experimental techniques and developments

G {GGGGGGGsjvZGG GGG G G G G G G T UG hG G G G G G ¡G G G UG {G G G G GGGGGGGOGmGppU\PGGG GG GGaGG GGGGUGiGGGGSGGGGGbG GG GGGGGGGGUGG G {G G G G G G G G Ow PG UG wG G G G

¡GGGGGGGUGjGhYvZGGGbGSGGGG G GGGGGGGGGGOkkYZTY[PUGhGGG w G G G G G G G G G G G G G G G G UGG

G mGppU`GˀGGjTGGGkTkG GGGGi GnG G

G mGppUXWGˀGPGjGGGGGGG G GGGGGGGGPGkGGkkX`aGGw GGGGGGGG GGGGGGGGGGGGGGGGGGGPGkGGGkkX]aGGGG¡GGGGGO{jPG GG

G hGGGGhYvZGGGGGGGGGGGGw GG GGOkkY^PGOmGppUXWPUGG

G {GGGG GGGhYWZGGGGGGGGbGGGGG G G UG kG G G G G G G OkkX]TX^TX`TYWTYXPG G G GGGGGGGG¡GGGGGOmGppUXWPUGG . 28 . Experimental techniques and developments

G jG hYvZG G G G G G G G G GGG G G¡UGkGGGGGGGGGGGGGG

GGGGGSGGGGGhYvZGGGGGUGG G {GGGGGGGT GG GGGGG GGG

GGhYvZUG G {G¡GGGGGGG aG]V_GG[V]GOTGGGVTGGG GGPUG{GppUZGGGGGGGGGGGGGGG UGG G

G zGGOZPG wGGOnwPG

]V_G YTZG XT[G [V]G WU\TXG YTG]G

G {GppUZGTGzGGGGGGGGkTkphGUG G GG G wGGGGGGGGG GGGDEGGG tYnW[GGGG[U^GnwGGXXWW¶jGOtGGUSGX`]`PUG{GGGGGG mGpppUXXUGG

G mGppUXXGˀGwGGGGGkTkphGGGi UGmG aGGGSG G aGGGGGGGUGzGaG[V]GG SGGaG ]V_GG UG GG G vG G G G G G G SG G G G G GGGGGG GGGGGGGOmGppUXYSGGGPUG{GGGGGG GO\W¶T XWW¶jVGPGGGGGO GGPUG{GGGGGGGGGGG G G G G G G UG {G G G G SGGGGGGGOGGPGGGGGGGGGGG UG~GGGGGGGGGGSGGGGGGGGGOG GaGGGGGGGGGGPGGGGGGG GGGGUGkGSGGGGGGGGGG

. 29 . Experimental techniques and developments

GGGUG~GGGGGSGGGGGGGG G G G G G G G G G G G G G G G G G G GGGUG{GGGGGGGGGGGGGG GG GGG~jGGGGGGGGGGGGGUG G

G mGppUXYGTGlGGGkTkphGUGzGGGUG G G G G pUZUYGˀGkGGGGGGrT GGG

G pGG SGGGGGGG GGtYzv[GOSG GG PG G G G G X[WW¶jG OG mG \PUG zG G G G G G G GGGOGXXGnwGGGGYYGnwGGPSGG¡GGGGG GG GGGG UGG G mGGGXXGnwGGSGGX_VXXG GGGGGGGG GOG{GppUXPUGhGrGGyGOX``^PGGGG GGGX[V_G G SG GGGGGGGGX_VXXG GOmGppUXZPUG{GGGGGGGG GUGpSGGGGGGGGGGGGGGG GGG G GG GGGGGGGGGGGGUGG G mGGG SGGX[V_G GGGGGGGGG GGG GGOmGppUXZPUG{GXWWWGOo PGGXYWWGOzPGGGGGGG GGGUGG G {GGGGGSGGGGGGXWV[G GGGGG G G UG {G G G G G G G GG\WWWGGGGi G nGOmGGUSGYWW[PUG{GGGGTGGGXWWWTYWWWGGUGpGG G G G G i G nG G G G G G G G G G G G G G G G G G G UG pG G SG G G G G G G G G G OX`G G Y[G nwG G X[WW¶jPG G G X_V_G UGvGGGGGGGGGGGGGGOmGppUXZPUG G

. 30 . Experimental techniques and developments

G mGppUXZGTGjTGGGX_VXXSGGX_V_GGGX[V_GGGGOGG GPUG G G pG GGGG SGGGGGGGGGGGGGGG G G G G UG pG G G G G G G G G G G G G G GGGGGGGGGGGUG{GGG GrG

GyGOX``^PGGGGGGG GhYvZUG G {G G G G G G G G G G G G G G G UG pG GGG GGGGGGUGpGGGGGGGOySG X```PUG {G G G G G G G X_VXXG G X[V_G G OG G G GPSGGGXaXGTGGG G GGGGtGGjG G G G G OuGGUSG X`_\PUG {G G G G G G qlvsG qhT_YWWG GGGGi GnUG{GGGGGGGG G G G G G G G G G G G G UG |G G izlG G G G SG G G G G G G G ¡UG {G G G T G G GG GuGGUGOX`_\PSGGGGGGGGUGmGppUX[GGG G G G G G G UG {G G G G G G G G G G XZWW¶jG OG G G X[V_G G G G {dG X\WW¶jPUG {G G G G GGG^\·XW¶jVGGGTGGGGGGGOGGGGGGG G G G G G PUG mG G G G G G G G G GGGGGGGGbGGGGGG\W·YW¶jUG

. 31 . Experimental techniques and developments

G mG ppUX[G ˀG {G G G G X_VXXG G X[V_G G G G G G OTPGUG{GGGGGGGGUGn GGGXXWW¶jGOPGG X]WW¶jGOPUGpaG\W¶jUGzGaGY\G»UG GG G m SGGGGGG GGGG GX[V_GG GG GTGGGGGzGOX\U\PGnwUG{GGGGGGGG GGGGYWGnwGGY][GGGGo GOXWWWPGUG G

G pU[ˀGwGGGGGOtYzv[PG G

G mGGGGGGGGtvGGzvYGGGUGhGG GGGXWWW¶jGGGGGGGSGGGGGGGX[WW¶jGGG GGG GGOc\»PUG{GGGGGGGGGaGmXG

. 32 . Experimental techniques and developments

G mYUG T G G G G mXG G G G G mYG G G G tvG G zvYG UG G G ppGˀGpGGGGGkTkphG

G G vGGGGGGTG GGG GGGGGG GGG GGGG GGGOUUG~GGUSGX``_bGkGGUSG YWWYbGjGGUSGYWW[bGsGGUSGYWW[PUG{G GGGkTkphGGGGGGUG zG SG G G G G G G G G G G G G G GGGGGGGGGGGGGGG G UG {G G G G G G G G T G SG G G G G i G nUG {G G G G G G G G G G G G G hGuGs GOjSG|zhPGGiGuGs GOuGSG|zhPGGG kTkphGGGGGGGUG{GGGGGGGGGG UG G G ppUXGˀG{GG G

G {G GGGkTkphGGGGGGGT GGGGUGvGGG GGGGGGGGG SGG GGGGGG G G G G OG G aG UUG iuPUG pG G SG G G G G G G z G iG G G G G G G G G G G G GO~SGX``_bG~GGUSGX``_bGjGGUSGYWW[bGsGGUSGYWW[UG G pGGGGG SGGGGGGGGGGGkTkphG G G G G G nzlG G G G hG wG zG OhwzSG hG uG s SGjPGGGGX^iYGGGGuGz GsGzGOuzszSGiG uGs SGuGPUGG G lGGGGG GGT GUGhGGGGGG¡GG G T G G G G UG {G G G G G G G G G G G G G G GGGGGGGGGG¡GG G G G G UG {G G G ¡G G G G G YG G YG G G G G G XWW»G G XWW»G G ¡G G T G UG {G G G G G G SG G ]G ~jG G G G G G ]G G G GGUG{GiuGGGT GGGGGT GGGGGG GG GGGGGUG G hG uzszSG G G G G G G G G G OmG ppUX\PG G G GGGUGhGGGGGGjGGUOYWW[PUGpGGG SGG¡GGGGGGGGGGGGGGG G G G ¡G G OmG ppUX]PUG {G G G G G G G G G G G G

. 33 . Experimental techniques and developments

GGGGGGGGUGhGjjkGGGGGGGGGG hnG GGGOmGppUX]PUG

G mGppUX\GˀGT GGGGG GGuzszGOGjGGUGOYWW[PPG GG G hGhwzSG GGGGGGGGGGGG¡GGGG GGGGGGGGhnG GGGGGGjjkGUG

G mGppUX]GˀGn GGT GGGGGGkTkphGUGTGGiGGGGT GGOGjGGUGOYWW[PPUG G G

G ppUYTGzGG G

G hGGGGGGGGGGGGGGGGGGGGGG UG pSG yG G G G T G G G G G G G G G G G OmG ppUX^PUG {G G G G G G G G UG {G G G G G G G G G G G G G G G G G G G G UG mG G SGGGGGGGGG GGXWT]TXUG G . 34 . Experimental techniques and developments

G mGppUX^GˀGyGGGGGGmvyYXGGUG{GGGGG GGGGGGGGGGiuGUG{GyGGGGGGUGG G G

G ppUZGˀGsGG G G

G h GGGGGGGGSGGGGGGGGT G

UGpGGkTkphGSGVZGGGGGGGSGUUGGGSGVXGG

VYGGGGGGSGGG¡GGOmGppUX]PUGtSG G GG

G G G VXG GGG VYUG h G G G G G G G G G GGGUG{GGGGGGaG G

§V 0 0 · §V 0 0 · § t 3 0 0 · ¨ 1 ¸ ¨ p ¸ ¨ ¸ V ij ¨ 0 V 2 0 ¸ ¨ 0 V p 0 ¸ ¨ 0 t 3 0 ¸ G ¨ 0 0 ¸ ¨ 0 0 ¸ ¨ 0 0 2t 3¸ © V 3 ¹ © V p ¹ © ¹

GV p GGG GGOGGPGG t GGGGaG

V p 1 3 V 1 2V 3 GGGG t V 3 V 1 G

G pG G G G G d G SG d m (hkl) SG G G G G G G G G G

G aG

d(hkl) m d(hkl) P H hkl GGGGGGOXPG d(hkl) P

G d(hkl) P GGGGGGG V p UGmGzGGUGOX``_PSGGGGGG

GaG

2 d m(hkl) d p (hkl) 1 (1 3cos \ )Q(hkl) GGGGGOYPG

. 35 . Experimental techniques and developments

G\ GGGGGV 3 GGGGSGG Q(hkl) GaGG

1 Q(hkl) (t / 3)(2*G(hkl) ) GGGGGGGOZPG

G G(hkl) GGGGGGGGG G GGG (hkl) GGG

GGGOzGGUSGX``_PUGmGOXPSGOYPGGOZPSGGG t GGGaG G

d(hkl)V d(hkl) H t 2*G(hkl) * G d(hkl) P

G d(hkl)V GG d(hkl) H GGG d GGGGGT GGGGGG

G¡GSG UGG G G pppGˀGh GGGGGG

G G tG G G G G G G ¡G TUG hG G G G G G G G G ¡G G G G G G GGGGGGGGG G G G G G G G UG {G G G G G G UG zG G ¡G G G G G G G G G G UG G

G pppUXGTGzGlGt GOzltPGGlGizGkGOlizkPG G

GGpppUXUXGˀGzGGGzltGGlizkG G

G jTGGGGOGGGGPGGGGGG G GG GGGZ»UG{GGGGGGi GnG GoGz¡UGhG GlizkGGG GGGG GGGGSGGGGGG G G G G G G SG G G G G G G G G G G UG G

GGpppUXUYGˀGzltGGG

G hG G zltG G G G G G i G nG G G sG nG X\ZWG zltGGGGGGGOmlnPGGGlizkGUG{GGGGGGG G G G G G G G G YWG }SG G G G G UG YWG G G G G GGZU\GhUG

. 36 . Experimental techniques and developments

G GjTGGGGGGGGGG G G zltG G G G GGG¡GGGGGGGGGGGUG{GGGG G G iG zG lG OizlPG G vG jG OvjPUG {G G G G G GGGGGizlGG G GGGUG{G GGGGGG GTGGGGGGGGGGGGUG G

GGpppUXUZGˀGlGizGkGG

G j G G G OjwvPG G G G G G lizkG G Ok SGX`_[PUGpGGzltGSGGGGGG^W¶GGGGOmGppUX_PUG~GGG GGGGGGGGGGGSGGGGGTG G G G G G G G G G G G G TG rG G G GG UG{GlGizGwGOlizwPGGGGGG G G G G SG G G G G G G G G G G UG{GGGGGOhGGUSGX``YPSGGGGGGGG GGGUGoSGGGGGGGGGGG GG G G G G G TUG w G TG G G G G G G G G G G G G TG G G G G G G GUGmGGGGGGGGGGTGTGG GGGTGGGGGGTUGtGGGrGGGG G G G G G OG jG pppSG ppUYPUG pG G G G G SG XWWG GGG GGGGOiGpõGGtSGX``_PUGmGGSGG G G G G G G G G G G G G G G UG {G GGGGGGG GGGGG\¶GGGGG GGnGGGGX\¶Gm~otUG{GG GGGGGUGG G hG G G G G G G johuulsG \G OorsG { PG G G G GGGGwm\SGGG GkGtGOsGG{ SG | GGtGppSGmPUG G

G mGppUX_GˀGlizkaGGGGGGGGGGGGGGzltGUG G G G . 37 . Experimental techniques and developments

G pppUYGˀG{GlGt GO{ltPG

GGpppUYUXGˀGzGGG{ltG

G k G G G OY\G »PG G G G G G G G G {ltG UG{GGGGGGGi GnG GoGz¡G{GG GGGGGjGGGGGG[U\G}GGGG G G G X\¶G G G GGUGG G G

GGpppUYUYGˀGwGGGG

G {ltGGGGGGsGGGGwGjtZWGGGGZWWG}G GGYWWG}GqGYWWjGGGi GGGwGjtYWGmlnGUG G hG {ltG G G G G G G G G G SG G G G G G G G G G OmG ppUX`PUG {G G G G G G G UG {G G GGGGGGGGGGGGG GGGGGGG GGUG

G mGppUX`GˀGzGGGG{ltUG G G

GGGpppUYUZGˀGkGaGzGhGlGkGOzhlkPG

G {GGGGGGGGGGUG{GGGGG GGGGGGGUGwGGGGGGG GGGG

. 38 . Experimental techniques and developments

G G iG UG {G G G ¢¤G G G iG G G TdTi TG G G G G G

OPGGGGGPGGTiG GGi˅GaG

2u d hkl u sinT B n u O G

GOGGGGGGUG{GGGGGGGGGGGGG

YTiGGGGUG{GGGGGGGGGGGGGG GGGGGGGUG

G G

GGpppUYU[GˀGpGGGGGG

G {GGGGGGGGGGGGGGGGGG GGGGGUGmGGSGGG G G G G G G GGGGGGGGUG| SGGG GGGGGGG G GGGGOPGGGiGUG{GGGGˈTˉUGG G pG G G G G SG G TG ˈG ˉG G G UG pG G SG G G G G G G G G G G G GGUG{GGGGG ±GGGÁGGGGGGGGUGpGGSGGGGG GGGTGGGUG G G j GGGGGGGG GGGGGUG{ GG GGGGGGG{ltGGGGGG¡GUG~GGGG GGGiGGGGG SGGGGGG GGGGG GGGGGGGUG{GGGGG GUGhGG GGGGGGGGGGG GTGTGUGpGGSG GGGTSGGGGGGGGGGTGGG GG GGGGiGGGGQUGv GGG GGGGGG OGGGGPGGGGGiGGGGGGGGGOmG ppUYWPUG{GGGGGGGGGGGGGGGGGG G UG {G G G G G G G G G G G G G G G GGG UG G

G mGppUYWGˀGvGGGGGGGG vGGSGGG GGGiGGˀGiGUGG vG G SG ~TG TG SG G G ¡G OG PG G G G G G GGGGGGGGUG

. 39 . Experimental techniques and developments

& G hG GGG¡G GGGG R SGGGGGG D GGG GaG & & D 2S u g R G & G g GGGGUG & G mGGGSGGGGGGGGiGG b UG{GGG GGGGGGGGG aG & & g b 0 bG & {GGGGGG¡GGUGpGGG GGGGGG g G

GGGGGGGUGpGGGGGSGGGGG G GUG{GGGGaG & & & & & g b 0 bGG g (b u) 0 G & G u GGGGGGGGGUGG G G

G pppUZGˀGvG GGG G

GGpppUZUXGˀGtTyG G

G pG G SG G G G G G G G G G yG UGyGGGGGGXWWTXXWWGTXGGGGsyGGG G oTuG G O]ZYG PUG zG G G YG TXUG oTG G OXWWPG G TG G GGGGG\G»UG G

GGpppUZUYGˀGmG{GpyG GOm{pyPG

G {G GGGGG GGGGGGi˞GpmzGXYWG oyGTGm{pyGGGGGi˞GpyGUGtGGG

G G G G G SG G jmYG TG G G T SG TG tj{G UG {G G G G G G G UG kG G SG G G G G

GGGGGGGGGGGGoYvTGGjvYTGGUG ~GGGG¡GGXWWG»GGGGGGGUGtGGGGG G G m{pyG G G G G tG GGGGzGG USG OYWWYPUG |¡G m{pyG G G G G G G G G G UG {G G G GG GGGGGSGGGGGGGZ]Y\GG ZZWWGTXSGGGG GGGGGGGvoGUG{GGGG GGGGG GwGOX`_YPUG G G G G . 40 .

Chapter III Results

Through the present experimental study on the mechanical properties of olivine at high pressure and of its high-pressure polymorphs, we address the rheology of the Earth’s mantle down to 670 km depth. For sake of simplicity and to allow comparison, most experiments have been carried out at 1400°C. Besides the intrinsic mechanical behaviour of each phase, the possible role on rheology of a phase transformation at the olivine-wadsleyite transition has been investigated. Given the pressure range in the mantle transition zone and in the lowermost upper mantle, the Kawai- type multianvil apparatus appears to be the most well adapted technique. As a complex thermo-mechanical history is associated with this kind of experiments, a special attention has been devoted to the evolution of deformation with time duration. For this purpose, detailed characterisations of the samples recovered after the experiments have been performed at different scales. Although its pressure range does not give a direct access to the transition zone conditions, the Deformation-DIA, which possesses very attractive possibilities on the control of deformation parameters, has been used here to extend the range of the experiments performed on forsterite. These experiments as well as the results of these microstructural characterisations are presented in this chapter and will be discussed in the next chapter.

results pGˀGkGGGGGGG G

G pUXGˀGkGGGGrT GGG GG G {G G G G G G G G G SG G G SG G G G G G G G G G G G G UG nG G G G G G G G G SG G G G G G G G G G G G G GGGGUG G G kG G G G rT G G G G G G G G GGmXUG{GGGGTGGGGX_VXXG GG\GnwGGXXWW¶jGG[G UG {G OYWW»PG G G G G G [\¶G G G TG UG hG G G G G GGGGGGGGGGGGGGGGGGG G G G UG {G G G G G G G G G X_VXXG UG {G GGGGG{GpppUXUG G

zGJG uG zGG wG OoT vGG { kG yGJG G G G G OPG O¶jPG OPG OnwPG OUPG O»PG PG zY`][OXPG zY`XXG Z]WG XXG TG TG ]GO[PG _WGGOXWPG zY`^WOXPG zY`[^G Z]WG XXG TG TG `GOZPG _`GOXWPG zZWY[OXPG zZWX^G Z]WG XXG TG TG XWGOXXPG YWWGO[WPG zY``]G zY`]XG Z]WG XXG X[WWG XG `GOZPG `ZGOZWPG zY``^G zY`]XG Z]WG XXG X[WWG XG XWGO[PG `ZGO\WPG zY`X^G zY_`^G Z]WG XXG X\WWG ]WG \GOZPG XX`GOYWPG zY`\[OYPG zY`XWG Z]WG XXG X[WWG ]WG _GOYPG X[YGO[WPG zY`\\OYPG zY`XXG Z]WG XXG X[WWG ]WG XZGO\PG X[\GOYWPG zY``ZG zY`[^G Z]WG XXG X[WWG ]WG XXGO]PG XYZGOZWPG zY``[G zY`]XG Z]WG XXG X[WWTX\WWG ]WG ]GOYPG XZ^GO[WPG zY`_[G zY`[^G Z]WG XXG X[WWG [_WG X\GO_PG XZZGOYWPG zY``_G zY_`^G Z]WG XXG X[WWG [_WG _GO[PG XWWGGOYWPG zZW^`G zZWX^G Z]WG XXG X[WWG [_WG XZGOX[PG ^^GOYWPG

G {G pppUXG ˀG lG G G G G G G G G OzaG zG PUGXPGzGTGGGGTGGYPGzGGGGGGGOGG GPUG G G lGGGGGXXGnwGGX[WW¶jGGGSGGGGGG G G G G G G G G G TUG zG G G G G GG GGGGGGGGGGG

. 43 . G results

G G G UG zG G G G G G G G G G G GGGUGG GG

GGpUXUXGˀGzGGGGGG

G hG G SG G G G G G G G G G G G UG hG G SG mG pppUXG G G G G G TG G G G G G G G G XXG nwUG mG pppUXG GGGGGG G G G G G G G G G G G G G G G G UG hG G G G G G G G G mG pppUXG G G G G G G G G GG GGGGGGGGGGGGUG{GGGG GGmGpppUXUGuGGGGGGGGUG{GGGGGGGG GGGGG GGGOrGGySGX``^PGGGGGG G GGGUGG G

G mGpppUXGTGvGGGTGGGGGUG PGjGGGGUGjGGGOzY`^WPUG PGlGGGGUGuGGGGGGUGhGGGGX[WW¶jT XXnwGOzY``[PGG PG jG G G G G G G G UG hG G G G G G X[WW¶jG XXnwG OzY``^PUG G G zG G G G G G G G G zltG G G G UG {G GGG{GpppUXGGGGGGGGGGGSG GGGXW¶UG pSGGGGGGGGGGT¡GGGGG]¶G G XW¶UG uG G G G G G IG IG G IGIGUGhGG G SG G G G G G G G G G G G UG {G G G G G {G pppUXUG hG G G G SG G G G G G G G G

. 44 . G results

GGGGGTUGhSGGGGGGGSG G G G G OrG G ySG X``^bG rGGUSG X``_PSG G G G G G UG mG G SG G G G G G G G G G G G G GGGXXGnwSGX[WW¶jGGGJGdWUZGOGhGpGGGGGGG G G G PUG uG G G G G GGGGSG G G GGGGGGGUG G

GGpUXUYGˀGtGaGzltGGlizkG

G l GGGGGGGzltUGmGpppUYGG GGG GUGG G

G mG pppUYG TG zltG G G G G G G UG jG SG G G ¡GGGGUG PGhGTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGPGhGGGGXXnwGGGX[WW¶jGOzY`\\PG PGhGGGGXXnwGOzY`][PGGGGGGGGGGGGGGGGGGGGPGhGGGGXXnwGGX[WW¶jGOzZW^`PG PGhGGGGXXnwhGGX[WW¶jGOzY``]PG G

. 45 . G results

G {GGGOGGPGGGGmGpppUYUGpGGGGG G G G ¡G G XWG »UG hG G G OmG pppUYPSG G G G G G GGGGGGOPGOGGGmGpppUYPUG{GGGG GGGGG GGGGGX[WW¶jGOmGpppUYPUGmGGGGOG GGaGmGpppUYTPSGG GGGGGGGGGG¡UG GG G {G G ¡G G G G G G zltG G G p{G G O| G G {G oG zG jSG zG hPSG G G G G G G G G G G zltG UG{GGGGGGGGGGGGGGUG{GG GG GXU\]GGGGGZkTG¡GOjGGr SGX`_`PUGmGpppUZGGG GGG¡GGGmGpppU[G GGGGGG¡GGUG{G GG¡GGTGGGGGGGGXXTX]G»UGhGGGGSG GGGG¡GGSGGGGGGGX[GGX^G»UGhGGGGSGG GGGOGG¡aGYXG»PGGGGGUG G

G mG pppUZG ˀG mG G ¡G G G G zZWY[G OG PSG zY``]G OG PSG zY`\\GOGPGGzZW^`GOGPUG G

. 46 . G results

G mG pppU[G ˀG mG G G G G G ¡G G G G G UG iG G G GOYVGGPUG GG G {G G G lizkG G G G G mG pppU\G G mG pppU_UG mG G G G OTPG zY_`^SG G G G G G G G G G G TG UG mG G GGGGSGGGGGGGGGGGGGGGUG{G GGGUGG G {GGGOGTaGzY_`^PGGGGGGOzZWY[PG GG GjwvbGGGGGXWWGGGGGGGWXWGGGG GWWXGGOmGpppU\PUGGG G

G mG pppU\G TG lizkG G G G G G G G TG G G G G G G G OzY_`^PG G G G G OzZWY[PUG mG zY_`^SG G G G G G G G G G GUGmGzZWY[SGGGGGGGGGGGGGGGbGG G G G UG sG G TG SG G G G G WUYG G G G GUG

. 47 . G results

G hGGGGGOmGpppU]PSGGXWWGGGWWXGGGGGGGG GGGGGGGGGUGiGGGGXWWGGGGGG GGWWXUGWXWGGGGGGGGGGGGUGG G

G mGpppU]GTGlizkGGGG GGGGGGGGGGOzY``]GG zY``^PUG{G GGGG GGGG GGGGGbGGGGG UG sG G TG SG G G G G WUYG G G G G UG GG G v G G G SG G G G G jwvG OmG pppU^PUG mG G zY`\[SG zY`\\G G zY``[SGGWWXGGGGGGGUGjGGGGzY``[GGG G G G G WWXG G G G G G GGGGUG{G GGWWXGGGzY`\[GGzY`\\GGGGGGGGSGG GG GGGGUGvGGSGGzY``ZSGGWWXGGGGGGGGG GGUGpGzY`\[SGzY`\\GGzY``ZSGGXWWGGGGGGGGGGG GGSGGGGGGGGUGzY`\[SGzY`\\GGzY``ZGGGG G GXWWGGGGGGGGGGUGzY``[G GGXWWG G G G G G G G G G G UG mG G G ˈG ˉG SG WXWG GGGGGWWXSGGGGGGGGGGSGGGG GOzY`\[GGzY``ZPGGGGGGGGGGOzY`\\GGzY``[PUG G mGGGGGzY``ZGOGGGjwvGGGPGGjwvGGGG GGWWX¢W¤UG G

. 48 . G results

G mGpppU^GTGlizkGGGG GGGGGGGGGGOzY`\[SGzY`\\SG zY``ZGGzY``[PUG{GGGGGGGGGGGGGGbGGG GGUGsGGTGSGGGGGWUYGGGGG UG G G hGGGGGOmGpppU_PSGzY``_GGzZW^`GGGWWXGGGGGG GGGGOUZW¶PGGWXWGG GGGGGGGGUG{G XWWG G G G G aG G G G G G G G G G G G GGG GGGGGGGGGGGGGGGGG GUG{GjwvGGˈGˉGGGSGGGGGGSGGjwvGUG G

. 49 . G results

G mGpppU_GTGlizkGGGG GGGGGGGGGGOzY``_GG zZW^`PUG{G GGGG GGGG GGGGGbGGGGG UG sG G TG SG G G G G WUYG G G G G UG G G uGGGGGSGGGGG G SG G XUY^G G XU_WG GGGGUG G

GGpUXUZGˀGtGaGT GGG

G {GGG GGGGGGGGGT GGG GOUUGjGGUSGYWWXbGzGGUSGYWWXbG|çGGUSGYWWXPUG{GGGG G G G G G {UG |çG G rUG u G OkG G nG w SG | G iSG o PUG {G G SG G G G G G SG G G G ~G OX`^WPbG |çG G UG OX```PG G |çG G UG OYWWXPG G UG mG G SG G G G G G G G GOGhGppGGPUGG G zG G G G G OzY`][PSG G G G G G OzY``]PSG G G GGGOz`\[SGzY`\\GGz```ZPGGGGGGGOzY``_PGGGG G T GUGmGGGGGG aG¢WYX¤SG¢XWX¤SG¢WWY¤SG¢XZW¤GG¢YYW¤UG { GGGG¢XWX¤GGGGGGGGGGGGGGmG pppU`UG pG G G G G G G G G GGGGGGG G G G G G G G UG {G G G G G G G G G G G G O|çGGUSG YWWXPG G G G G G G G

G ceG OoSG X`_YPG G G SG SG G G SG VSG G G TG ¡G G GO~SGX`^WPUG{G¡GGGG¡GGGGGGGG UG {GGGGGGG¡GGGGUUGGG{ltGUG G {GGOGGGPGGGGGGGG{GpppUYUG {GGGGGGGGGGGGGGGGG {ltGUG

. 50 . G results

G mGpppU`GˀGPG{ GGGXWXGiGGGGGGGUG{GGG GGGGGGGUG GGGGGGGGGGGGGGGGGGGPG kG G G G G G G G X[WW¶jUG {G G G G WUWXG G GGGGGUG{GGGGGGG G UG G {G G OG G PG G G G G G G G G G G mG pppU`UG {G G GG GOGGGGG GGaGX]ÝXWX[GTYPGG GGGGGGGGGYÝXWX[GTYGGGG GGGGG UG {SG G G G G G TG G G XWX[GTYSG G G GUGG G

X[ TY zGJG GG V ceGG UGGXW G GG

zY`][GOGPG \\GO\PG WUZ_GOWUW\PG _WGO\PG X]GO[PG zY``]GOGXGGGPG X]XGOXWPG WUWXGOWUWXPG X]WGOXWPG YUYGOWU\PG zY`\[GOGXGGGPG `[GOXWPG WUX`GOWUW\PG XW\GOXWPG YUYGOWU\PG zY`\\GOGXGGGPG ]ZGO\PG WUZ]GOWUW\PG `WGO\PG YU_GOWU\PG zY``ZGOGXGGGPG XX_GOXWPG WUW]GOWUWYPG XYWGOXWPG WUW[GOWUWYPG zY``_GOG_GGGPG XYYGOXWPG WUXYGOWUW\PG XZWGOXWPG WUW`GOWUWYPG

G {GpppUYGˀGmGaGGGT GGG UGtSGGGSGVG G G ¡G G SG TG G G SG ceSG G G GSGUGGGGGGGUGtGGGGGUG G G

GGpUXU[GˀGtGaG{ltG

G {GGGG GGGGG{ltGGGGGGWWXG UG oSG G G G G G G G G G G G T UGhGGSGGGGGGGSGG GG GT GGUG{GSGGWWXGiGSGGGGGG G G G G OmG pppUXWPG G G G G G G G G UG } G G G G G G G G GGGGG GGG GGGUGhGGSGGGG GGGG GGG WWXG G OmG pppUXWPUG vG G G G G G G G G G G G G . 51 . G results

G G OmG pppUXWPUG zG G G G G G G G GG¢WYX¤GOmGpppUXWPUGpGGGGGSGGGGUGzGSG SGGGWWXGGGGGGGGGOmGpppUXWPUGG

G mGpppUXWGTG{ltGGGGUG~TGTG PGzGzZWY[SGGGGXXGnwGGGUGWWXGGGGUGuGG GGGGGUGaYYYUG PGzGzY`\[SGGGGGGXXGnwSGX[WW¶jUGWWXGGUGaWW[UG PGzGzY``[SGGGGGGXXGnwSGX[WW¶jUGlGGUGG {aGGUGaYY[G iaGGTUG{GGGGGGOWYXPUGaWYXG PGzGzY`_[SGGGGGGXXGnwSGX[WW¶jUGzGGGWWXGUG aWW[UG G G

GGpUXU\GˀGpyG GG

G hGGGG±GGÁGGGGGG GGGG SGG GGGGGGGGGGGGG GG G OGGG GTGGGGWToGGGGGGPUG zGGGOzZWY[PGGGGGGOzY``]PSGGGOzY``\\GGzY``ZPGGG . 52 . G results

G OzZW^_PG G G UG {G G G G G G G G G {G pppUZUGG

G G {GGGGGGGGGTGG GUG{GGG{G pppUZG G G G G G UG pG G G G G G G G GGG GGGGoVXW]zGUGpGGGGG GGG GGGUGkGG SG{GpppUZGGGGGGG G G GGGGGGGGGGGGGGGGG oVXW]zGGGUGmGpppUXXGGGGGG GaGG GGG G G G G G G G G OzZWY[PG G G ˈG ˉG G OzZW^`PUGmGGSGGGGGGGGUG G

zG o GGOoVXW]zPG

zZWY[GOGPG X`WYGO__[PG zY``]GOGXGPG X___GOY^]PG zY`\\GOGXGPG YY[_GO[]_PG zY``ZGOGXGPG _\ZGO[[]PG zZW^_GOG_GPG Y_`GOZ[PG

G {G pppUZG TG o G G G G G G SG G G G G UG G

G mGpppUXXGˀGpGGGGGGGGOzZWY[PGGGGGGG OzZW^`PUGG GG G G

. 53 . G results

G pUYGˀGkGGGGkTkphGG G

G kG G G G G rT G G G G XXnwG G X[WW¶jG G G GGGG GWWXGUG| GOUUGGGPSGG G G WWXG G G G G G G G G TG G OG jGpPUG{GGGGGGGGGGGGGG GGGGGGGjGpppUG{GGGGGGGG SG G G G G G G G G G G OUUG G XXG nwG G G PUG {G G G TkphG G G G G G G G G G G G UG mG G SG G kTkphG G G G G G G G G GGGGGOGjGpPUGpGGGGGGGGGG UGm SGGGGGGGG GGGGGG GGG GGUGlGGGGGGUGi GG GGi GGGGGG GGGSGGGGG GGGGhwzGGuzszGT G GUGG G

GGpUYUXGˀGzGG

G vGGGGGGGGGGGT GGGGG ¡GGG GGGG¡UG{GG¡GGGGGGGGGGG GGGGGGGGXWWGÝGXWWG»YGO¡GGGGPUG{GG¡GGG GGGGGG GGT GGUGG G pGGGGGGGGGGGSGGG GGmYGGGGGGwGUGG G hG G TG G OwWZZYPG G G G G ZWWtwG G XXWW¶jG OG G G PGGGi GnG GqGtUGzltGGGGGGG G G ¡G G G OXWG »PG G G OmG pppUXYPUG {G G G G G G GGGGT GUGoSGGGGGTGGOGG i PGGGG¡GGGGGGGGUG G

G mGpppUXYGˀGoTGUGzltGGGGUGzGaGYWG»G PGwWZZYGGTSGGmYG PGwWZZZGGTSGGmYGGGG

. 54 . G results

G mYGGGGGGGGGTGOwWZZZPGGGGGG | GGtGOkGGlGzPG GqGtUG{GGG G G G wWZZYUG {G G TG G OwWZZZPG G G G OG [T\G »PG G GGGGGGGGT GGGOmGpppUXYPUGG GG G wWZZYGGwWZZZGGGGGGGG GXU[GGGGXU[GGGG GG]V_G GGG GXGGGGXGGGGGG[V]G SG UG G {G G G G G G G G SG G G G G GGXWWW¶jGGGGGGGG TGUG{G G G G G G G pG UG j G G wWZZYG SG G SG G G G Z]`·[[G oVXW]zGGG GGGG GGwWZZZGGG G GGGGGGGGGUG G

GGpUYUYGˀGhGGG GGGGkTkphGG

G {GGGGGGG]V_GkTkphG GGGi GnGG GTGGwWZZYUG{GGGGGGGGGGGGGkTkphG G G G G G G G G G G G G G UG{GGGGYGnwSGXZWW¶jGGGGGGGGG{G pppU[UG G

zGJG vGG uGG {G oGG yGJG oTG G OnwPG O¶jPG OPG

kkXWG wWZZYG ^WGG YG XZWWG Y[WG kkX[G wWZZYG ^WGG YG XZWWG XYWG

G {GpppU[GˀGlGGG GGGGGGGkTkphGGG i GnUG GG G {G G G G kTkphG G G G OXZWW¶jPG G G G G GGrT GGGGGUGG G tGGkkXWGGkkX[GGGG¡G GG GGzltG UG{GG¡GGGGGGGGGGGp{UGhG G G G SG kkX[G G G G G ¡G G G ][G »G OZ_»G G G PG G GGGGSGGGG¡GGkkXWGGUGXXWG»GO^X»GGGPUGG G {ltGGGkkXWGGGGGG_WLGGG G G G G UG G hG G G G G G G G G G G G G G GGGGGGUG{GGGGGGGGGGGG GUG G

. 55 . G results

G {G G G OZ[^·X\G oVXW]zPG G G G G G G OkkX[PG G G GGGGGGGGUG G

GGpUYUZGˀGkGGGGGi GnG

G {GGGGGGi aGGGwWZZYGGYGnwGGXZWW¶jGGG GwWZZZGG]GnwGGXZWW¶jUG{GGGG¡GG{GpppU\UG G

zGJG vG uG {G {GGG tGGG yGJG oT G G O¶jPG OLPG OXWT\TXPG G OPG OnwPG

kkXYG wWZZYG ^WG YG XZWWG Y[OWU\PG _OXPG kkXZG wWZZYG ^WG YG XZWWG Y\OWU\PG [OXPG kkZXG wWZZZG XYWG ]G XZWWG Y\GOWU\PG \GOXPG

G {GpppU\TGlGGGGGGGkTkphGGGi GnUG G G {GGGGGGGGGGG GUG G {GGGGGGGGGGO{G pppU\PG G G G G G UG {G G G G G GGGGGGG GGGGUGtGGGGGGGGGGSGG G G G G G G G G G G G G G UG {G GGGGGGGGGGGGGGUGG{GGG GGGGGGGGXWT\TXGGGGGGGUGY\LUG G {GjwvGGkkXYGGkkZXGGGG GlizkUG{ GGGGmGpppUXZUGG G

G mGpppUXZGˀGlizkGGGGGaGkkXYSGGGY[LGGYGnwSGXZWW¶jGG_ÝXWT\TXG GGGkkZXGGY\LGG]GnwSGXZWW¶jGG\ÝXWT\TXUG{GGGGGGUGsG GTGSGGGGGWU\GGGGGUG . 56 . G results

{GGGGGGUGiGjwvGG¡G G G G G G WXWG G GGGGGGGGGXWWGGGWWXGGGGGGG GWXWGUG{GXWWGGGGGGGGGGGGGOGUGZW¶PG GGGUG{GXWWG GWWXGGGG GUG{GGGG GGGGGGGG UG G mG pppUX[G G G G G G G{ltGGkkXZUG{GGG G GGXWXZTYUGXWWGGWWXGGGG GGGGG GGGmGpppUX[SGGGGGGGGGGG[WWGGWW[UG{ G GGGUG{GGGGGGG GGGGGGG GUGmGGGGGUGG G

G mGpppUX[GTG{ltGGGGUGkkXZGGGY[LGGYnwGXZWW¶jGG[ÝXWT\TXUG ~TGTGUG GGGG G . 57 . G results

GGpUYU[GˀGkGGGGhwzGG

G {GGGGGhwzGGGGGGkTkphGGGGG G G UG {G G G G G wWZZZG G UG {G G GGGG{GpppU]UGlGGGGG~jGUG G

zGJG uG sG {G {GG tGGG yGJG OoT G OPG O¶jPG OLGPG OXWT\TXPG PG OnwPG

wWZZZG maXU\OWU\PG maYOXPG kW\W[G RG ^WG ¥ZG XZWWG tvaXZGOWU\PG tva`OXPG tvRiuG kW\WXG wWZZZG ]WG ¥YU^G XZWWG ]OWU\PG XOXPG

G {GpppU]GˀGlGGGGGGGkTkphGGGhwzG G G kW\W[GGGGGGGGGGkTkphGGhwzUG{GGGkW\W[GG GGG aGGOY\WG»GPGGTGGOwWZZZPGGGGGO^\WG»GPGG GGZaYGGtvGGGGGOmGpppUX\PUG{G GGG GwGGG GGGGUGiGGGtvGGGGGG GGT GUG{G GGGG^WGGGGXZWW¶jUGpGGGGGGGXZWW¶jGG GUGG G kW\WXGGGGG]WSGGGXYWW¶jGGGGGGG GUG {GGGGGGXZWW¶jGGUGG G

G mG pppUX\G ˀG vTG G G G kW\W[G OG G G G hwzPUG {G G GGGGGGGG~jGUG G G {G TG G G G G G G G G G G G G UG G kW\WXGGGGG]LGGGTGGXWT\TXUGmGpppUX]GGGGG GkW\WXGG]WGGXZWW¶jSGGGGGGG_[GGGGGXWT\TXUG~G GGGGGGGGGG[]G»UG{GGGGGG . 58 . G results

GGGUGpGGGGGGGGGbGG~jGGGT GG UG {G G G G G G TG G OmG pppUX\PG G G G GGGUGG G pG kW\W[SG G G G G G G G XU\LG G YÝXWT\TXG G tvG G G GGXZLGG`ÝXWT\TXUG GG

G mG pppUX]G TyG G G kW\WXG G ]WG G XZWW¶jG XPG G G G YPG G UG G G {GGGkW\W[GGGGGGGGGtvUGpGhwzSG GG GGGGGGT GGG¡G GGGGG GGUG{G¡G GGTGG GGGSG GG G G G G G G OG mG ppUX]G jG ppPUG zG G G G G G G G G SG G G G G G TUG oG G GGGGGGGG GGGGSGGGGG GOjGGUSGYWW[PUG{GGGGG¡GGGGGGGG UG G sG G G G G G G G G G G G G G GUG¢WYX¤SG¢XWX¤SG¢XYW¤SG¢WWY¤SG¢XZW¤SG¢XZX¤SGG¢XXY¤GGGGGG¢XXX¤SG ¢YWW¤GG¢YYW¤GGGGtvUGG G {GGGGGkW\W[GGGmGpppUX^UG{GGGGG GGtvGOGPGGGGGGO GPUG{GGGGGUG {GGGG^WGGGGGGGtvGGGGGGG G G G \U\G nwG G [U\G nwG UG {G G G G G tvG G G G G GG\WW¶jGGGZGnwGGXZWW¶jUG{GGGGGGGGG GGGGGUG

. 59 . G results

G {GGGGGGGGGSGG\WW¶jSGGG\U^GnwG GG GG[U\GnwGG`WW¶jSGGGGGGGGGGUG{G GGGGGGGGGGGGG GGGT GGG GGGGUG G

G mGpppUX^GˀGhGGGGkW\W[GGT GGGGGO GPGGG tvGRiuGGOGPUG G G ~GGGGGGGGG GGGGGGGGGG tvRiuGGGXZWW¶jUGhG^WGGXZWW¶jSGGGGGkTkphGGGhwzGGUGZGnwUGmG GGSGkW\WXGGGGGGGGYU^GnwUG{GGGG GGGhwzGGGGGGGG¡GUG G G {GGGGGGGkW\WXGGGG G{ltUGtGG G G G UG oSG G G G G G G G OXWXYG TYPG G XWWG G WWXGGGGGOmGpppUX_PUG G

G mG pppUX_G TG{ltGGGUGkW\WXGGG]GLGGYU^GnwG XZWW¶jG G XÝXWT\TXUG ~TGTGGGWWXGUG G G G G . 60 . G results

GGpUYU\GˀGkGGGGuzszG

G vG G G G G G G uzszG G G kTkphG G G G G G UG {G G G G G G G wWZZZUG {G G GGGG{GpppU^UG{GGGGGGiuGUG G

zGJG sG uG tGG {G {GG yGJG OoT OPG G G O¶jPG OLPGG PG G OnwPG OXWT\TXPG

mvyYXG wWZZZG \WG ¥[G XZWWG XWGOWU\PG YU\GOXPG

G {GpppU^TGlGGGGGGGkTkphGGGGG G GuzszUG G G mvyYXGGGGG\WSGGGXWWW¶jGGGGGGGGG GXZWW¶jUG{GGGGGGGG G G G G G G G UG{GGGGGSGG]WW¶jGGGXWWW¶jGGGGGGG GOmGpppUYWPUGG G {GTGGGGGGGG GGGGGUG mvyYXG G G G G XWLG G G TG G YU\ÝXWT\TXUG mG pppUX`G G G G GGmvyYXGG\WGGXZWW¶jUG{GGGGGG GGGGGGG GGG^XGGGGGYU\ÝXWT\TXUG{GGGG^ZG»UG{GGG GGGGGGGGGGGGiuGUG{ GGGT GGG G GGGGGGGG~jGGOGmGpppUX]PG G

G mGpppUX`GˀGyGGGmvyYXGG\WGGXZWW¶jGXPGGGGYPGGUG {GGGGGGyGGGGGG GGGUG G

. 61 . G results

G wGGGGGGGGGGGGOzGGUSG X``_bGjGGUSGYWW[SGGGppGGppUZPGGGGGOmGpppUYWPUG{GGG G¢WYX¤SG¢XWX¤SG¢XYW¤SG¢WWY¤SG¢XZW¤SG¢XZX¤SGG¢XXY¤GGGGGGGUGG GG {GGGGG¡GGGGT GGGGG¡G GGGGG GSG UGG G vGmGpppUYWSGG GGGGGGGGGUG{G GGGGGGGGGGGGG GGUG G hG\WGGGSGGGGGGXU\TYGnwUG{G GGG GGG[U\GnwUGhGGGGGGGGXWWW¶jSGGGGG G GWU\GnwUG{GGG GGWU\GnwGGGGXZWW¶jGGGGGG YU\ÝXWT\TXUG{G GGGG[GnwGG GGGUG G

G mG pppUYWG ˀG wG G G G G G G G G G G UG o GGaGGUGkGaGGUGpGG GSGGGUG {GGGGGGGGGGGGGGGGUGlG GGGGGGGGGUG G G {GGGlizkGGGmvyYXGGGGmGpppUYXUG{GGGG G G UG {G WXWG G G G G G G G G G XWWG G WWXG G GGGGGGWXWUGWXWGGGGGGGjwvGOkkXYGGkkZXPUG G

. 62 . G results

mGpppUYXGˀGlizkGGGG GGGGGOmvyYXPGGXWLGG[GnwSGXZWW¶jG GYU\ÝXWT\TXUG{GGGGGGUGsGGTGSGG GGGWU\GGGGGUG GGG G ppGˀGkGG G G G G

G ~ GGtYzv[GGGGGGGGGGG GGGGGGGGGGGGGGGGGGGG GjwvGGGGGGGGGGUGG G G ~ G G G G mXG G G X[V_G G G X]G nwG G X\WW¶jG G ZG UG {G OYWW»PGGGGGG[\¶GGGTG UGhGGGGGGGG G G G G G G G G G G G G G G G G G G GUG{GGGGGGGGG X[V_G UG {G G GGGG{GpppU_UG G

zG zGJG vG uG wG {G kG G yGJG Oz G G G G O¶jPG OPG G GmXPG OPG OnwPG O»PG OUPG

oX`\XOXPG oX`[`G Y][G X]G TG TG TG ZY]OX\PG oX`^_OXPG oX`]^G Y][G X]G TG TG TG YYYO\WPG oX`\ZG oX`[`G Y][G X]G X[WWG XG X\OYPG Z\ZOZYPG oX`\[G oX`[`G Y][G X]G X[WWG XG WG Y_`OZYPG oX`^`G oX`]^G Y][G X]G X[WWG XG TG Z_XO_]PG oX`_XG oX`]^G Y][G X]G X[WWG XG X\O[PG YYXOX[PG oX__YG zZXZ^G Y][G X]G X[WWG ]WG YZGOZPGG TG oX`[\G oX`[XG Y][G X]G X[WWG ]WG ^GOYPG Z`^OZZPG oX_][OYPG zZXX]G Y][G X]G X[WWG [_WG XZOYPG \X\O[\PG zZYXZG oX`Z`G ZWWG X]G X[WWG [_WG Y\G Z\[OZYPG

G {GpppU_GTGlGGG GGGGGGOzaGSG oaGo GPUGXPGGSGGYPGUG . 63 . G results

G kGGGGGGX]GnwGGX[WW¶jGGGSGGGG G UG zG G G G G G UG zG G G G G GGGGGG GGGUG G

G ppUXGˀGwGG

GG G {GGGGGGGGGGGGGGTyG UG G jGGGGGGGGGGGGGGG G OmG pppUYYPUG {G yG G G G OoX`[\PGGG GGGGG ^YYGG`X_GTXGOsGGUSGX``[PUGoSGGGGGGGGGGX[WW¶jGGG SG G G G G T ¡G G G G OmG pppUYYPUG {G yG GGGOoX`_XPGGG GGGGG_Y]GG_\]GTXGOnGGUSGX``^PUG{G GG GGGˈGˉGUGuGGGG GG GGGGG GyG UG G

G mGpppUYYGˀGyGGG GOoX`[\SGG PGGGOoX`_XSGGPUG G

G ppUYGˀGzltGGlizkGG

GG G {GGGGGGGGGzltUGmGpppUYZGG G G G G G UG {G G G OG aG mG pppUYZPG G G GGGGGG¡UGjGGGGGGGGG GGGGGGGGGGGGGGGG G GGOmGpppUYZPUGmGpppUYZGGG GGGGˈGˉGSG G TG G UG {G G G G G G G G GG UG{GG¡GGGGGGGGUG{G¡G G GGGUGhGGGGGGGOmGpppUYZTPSG G . 64 . G results

GG GGG¡GGGGG GGOG GGPUGGG

G mG pppUYZG ˀzltG G G G OG PUG jG SG G G ¡G G GGUG{GGGGGGYW»G PGhG GOzZXZ^SG PGGGGGGGGGGGGGGGGGGGGG PGhGGGGX]GnwOoX`^_SG PGG PGhGGGGX]GnwGGX[WW¶jGOoX`\ZSGPGGG PGhGGGGX]GnwGGX[WW¶jGOGoX`[\SG PG PGhGGGGX]GnwGGX[WW¶jGOzZYXZSG PGG G G G {G G ¡G G G G G G G G p{G UG mG pppUY[G G mGpppUY\GG GGG¡GGGGG¡GUGkGGGGG G G TeG G TeG SG G G ¡G G G UG {G G GGGGGG GGGG¡GUGhGTG GSGGG¡GUGmGGG GGGG¡UGmG GGGGGSGGGG¡GGGX\G»GGY\G»UGG

. 65 . G results

G mG pppUY[G ˀG ~ aG G ¡G G G G G oX`^_G OG PSG oX`\ZG OG PSGoX__YGOGPGGzZYXZGOGPG G

G mG pppUY\G ˀG lG G G G ¡G G UG iG G G G OYVG G PUG iGaG UGn GaGUG G G zGGGGGGGGGGGG GGzltG G O{G pppU_PUG {G G G G G G G G G G oX`\XG G oX`^_G GGGGGGGO GGGGGGGPUGhGGGGG oX`^`G G G G SG G G G G UG {G G G G G G G G GGWGGX\¶GGGGGGOTGPGGG^G GY\¶GGGGGGGUGpGGGGGGGGG GGG GGUGtSGGGGGG G G G G G G G G G G G G OG Z\[G »G G \X\G »PG G G G G G G G G GOGYYXG»GGZ_XG»PUGoSGGGGGGGGGG GTeGGTeG GGGGGGGUG . 66 . G results

G G ~ G jwvG G G G G lizkUG hG G G jG ppG OpppUXUZPSG G G GGGGGGGTGGGG UGmGpppUY]GGGGGG G G G G G OG oX`[\PUG mG pppUY]G G G G lizwG G G GlizwGG GjG\UG{G¡GGGGGG G G G G cWXXeG G G UG{GGGGGGGGXYW¶GGGGGlizwGGG ¡GUGv GGXGGUGpGGYSGGGGGOGPGGGGG G G G G G G UG {G TG G G G ¡G G G G OG G G SG G G G G G G G G UUUPUG pG G G GGGGG UG G

G mGpppUY]GˀG~ aGGGGGlizkGGOPGGGGG G GjG\UG G G mGpppUY^G GmGpppUY_G GGGG lizkGGG GUG mGG GSGGGGGGGGGGGTGUGmGGG GOGGPGGGGGGGGGGGGGUG{GG GGUGkGGGGGGGGGGGGSGGrG GGGG GUG{SGG GGGGGGUGG G {GjwvGGGGGGG ¡GGOmGpppUY^PUG G hGGGOmGpppUY^PSGGGGoX__YGGoX`[\GG¡G GGXWWGG GGGGGGWXWGGGGGGGGGGGUG WWXGG GGGGGGGGGGGGGUGZW¶GGGGG GGGGGoX`[\GGGGGGG[\¶GGGGGGoX__YUG G

. 67 . G results

G mGpppUY^GTGlizkGGGG GGG GaG GGOzZXZ^PGGGG GOoX__YG GoX`[\PUG mGzZXZ^SGGGGGUGmGGGGOGGPSGG G GGGGGGGGGG G G G G G bG G G G G UG sGGTGSGGGGGWU\GGGGGUG G G hGGGGGOmGpppUY_PSGoX_][GGzZYXZGGGXWWGGGGGOUG XW¶PG G G G UG WXWG G G G G G G G G G G G UG {G WWXG G G G G G G G G G G G G G G G OXW¶PG G G GGGoX_][UGjGGWWXGGGGGzZYXZUG G {GjwvGGGGGGGGGGGGGGUGG G {G G G G G G SG G ZUW[G G \U[\G G G G G UG

. 68 . G results

G mGpppUY_GTGlizkGGGG GGG GaGGGOoX_\[GGzZYXZPGG UG{GGGGGGGGGGGG GGGGGbGG G G G UG sG G TG SG G G G G WU\G G G G GUG G G mG pppUY`G G G jwvG G G G G TG G OˈG ˉPUG {G GGGGGGGGGGGGGGUGGGGG GGGGGGGGGGGGGUGoX`\ZGGGGXWWGG GGGGGGGSGGWXWGGGGGGGGGGG WWXG G G G G G UG {G G G G G UG mG oX`\[SG XWWG G GGGGSGWXWGGGGGGGGWWXGGGGGG XWWUG

G mGpppUY`GTGlizkGGGG GGGGGTGGGOoX`\ZGG oX`\[PUG{GGGGGGGGGGGG GGGGGbGG G G G UG sG G TG SG G G G G WU\G G G G GUGG . 69 . G results

G ppUZGˀG{ltGG

GG G mG pppUZWG G G G G G G {ltUG hG G SG G G G G G G G OmG ppUZWPUG uG G G G GGGGUGhGGGGSGyG GGlizkGGGG GGGTGGUGoSG{ltGGGGGGG G GGGGGGGGGGGG GGUG{GGG GGGGGGGGGGGGUGG G hGGGGSG GG G GGGGGOmG pppUZWPUG tG G G G ¡G G G G XWWG G OG G G G G G GaWXWPUGoGGGG GGGGG GGGGG GGGGUG} GGGGGGGGGG GUG{GG GGGGXWXZGTYGGGGGUGhGGGGSG GGGGGGG GGGGGGGGGG XWXZGTYUGv GGGGGGGGGGGGGUG G

G mGpppUZWGTG{ltGGGG G PGzGoX`\XSGGGGX]GnwGGGG PG zG oX`\[SG G G G G G X]G nwSG X[WW¶jUG tG G G G G G G PGzGoX__YSGGGGGGX]GnwSGX[WW¶jUGXWWGGUG~TGTG . 70 . G results

G ppU[GˀGpyG GG G

G {G G G G G G G G G G pG UG {G GGGGGGGGGOoX`^_PSGGGGGOoX__YPG G G G G G OoX_][PUG {G G G G G G G G G {G pppU`UG {G G G G G G G G G G G G G G G G GGGGˀGGUGG G

zG o GGOoVXW]zPG

oX`^_GOGPG ZX`YGOZWZPG oX__YGOGXGPG ZZ_WGOZZ`PG oX_][GOG_GPG ^[]GOXZ\PG

G {GpppU`GTGo GGG GGGGSGGGGG UG G G pppGˀGkGGG

G {GGGGtYzv[GGGGGGGrT GG G O\WWWG G PUG yG G G G mXG G G X_V_G G G YXG nwG G XYWW¶jGGZGUG{GOYWW»PGGGGGG[\¶GGG UGkGGG GGG G G G G G G G SG G G GGGGGGUG{G GGGGGGGX_V_G UG{GGGGGG{G pppUXWUG G

uG zGJG vGG {G kG yGJG G z G OPG O¶jPG OPG OnwPG

Z]^G Z]]G Y`\G YYG XZWWG XG Z[XG ZY_G Y`\G YYG XZWWG X_WG

G {GpppUXWGˀGlGGGGGGGGUGOaG¡GPG G G kG G G G G G YYG nwG G XZWW¶jG G G G G G UG G G G G

. 71 . G results

G pppUXGˀGwGG

GG G {GGGGGGG GGGGGGG GTyG UGmGpppUZXGGyGGGZ[XGOPGGZ]^GO PUG{ G G GGGG^`WGTXGG_Y\GTXGGGGGGGGOsG GUSGX``[PUG G

G mGpppUZXGˀGyGGGGGZ]^GOG PGGZ[XGOGPUG G

G pppUYGˀGzltGGlizkGG GG G mGpppUZYGGGGGGGGUG{GGG TG G G G G G ¡UG {G G G G G G GGGGGGUG{GG¡GGGZXG»GOX`G»GGGPGG Z]^GG\\G»GOY\G»GGGPGGZ[XGOG¡GGGp{GPUG G

G mG pppUZYG TG zltG G G G G OG PUG jG SG G G ¡GGGGUG{GGGGGGYWG»G PGhGGGGYYGnwGGXYZWW¶jGOZ]^PGTGGPGhGGGGYYnwGGXZWW¶jGOGZ[XPG GG . 72 . G results

G {G G G lizkG G G G G mG pppUZZUGGGGGGG GGGGGGGGGGGUG{GGGGUGG G hG G G G SG G T G G G G G G lizkG UG hGGGGSGGGG GGjwvUG{GcXWWeGGGGGG G GGaGGGGGGGGGGGGGGGGGG G G UG zG G G G G G GGGGGGG GGGGGGUGcXXXeGG¡GGGGGGGGGGUGpG GGGGGGGGUGcXXWeG GGGTG GbGG GGGGGGGGGGGGG UG[\¶GGGGGGGG UG{GjwvGGGGGGGG GGGGGGGUG{G cXWWeGG GGGGGGGGGGGGGGGGUG[\¶G GGGUG{GcXXXeGGGGGGGGGGGGGGGG UGZW¶GOGGPGGGGGGGUG{GcXXWeGG G GG TG GbGGGGGGGGGGGGGGGGUG[\¶G GGGUGG G

G mGpppUZZGTGlizkGGGG GGGGGGGGGGGYYnwG GXY\W¶jGOZ]^PGGGGGGGGYYnwGGXZWW¶jGOZ[XPUG{GGGGG GGGGGGG G G G G G bG G G G G UG sG GTGSGGGGGWU\GGGGGUG G G

G pppUZGˀG{ltGG G

G mG pppUZ[G G G G G G G G G G G G G G XZWW¶jUG {G G G G G G G G G ¡G G G G

. 73 . G results

GG UGmGp}UZ[GGGGGGGGGGG GGUGG {G G G G G G G G G G G G G G GGG GGGUG{GGGGGGGGG GGG GUGuGGGGGUG G

G mG pppUZ[G ˀG {ltG G G G UG zG Z[XG G ZG G G YYnwG G XZWW¶jUG PG{ GUGiGG PGGPGlGGGUG~TGTUG zGGGPGGGG G G p}G ˀG pG G G G G G G aG G G G G GˀG GUG

G G {GGG¡GGGGGSG GGGTG GGUG{GG GG GGGGGGGjwvG GG UGpGGGGGGGGGGGSGGG GGGUGz SGG GGGGGGGGUGpG GSGGGGGGGGGG GGTSG TGGGUG

. 74 . G results

G lG G G G G G rT G G UG mG G G GGTGGmXGGGGX[V_G GGXXGnwGGX[WW¶jGG[GUG{GOYWW»PG GGGGG[\¶GGGTG UGhGGGGGGGGG G G G G G G G G G G G G G G G G G GUG{GGGGGGGX_VXXGGG UG G pGGGGGG GGSGGGGGGG GG GG GGGGUG{GGGGGG G SG G G G G G G G UG {G G G G G G G G {GpppUXXUG G

vGG uG wG zG zGJG {G kG yG yGJG G G G G oTG O¶jPG OPG G OPG OnwPG O»PG O»PG

zZY\ZG zZY[[G \WWG X]U\G X[WWG ZWG D ZYZO]PG X`[OYPG

zZ[XYG zZ[XXG \WWG X]U\G X[WWG [\G E Z[[O_PG X]^OXZPG

zZY\[G zZY[[G \WWG X]U\G X[WWG ]WG E [X]O^PG XYYO]PG

G {G pppUXXG TlG G G T GGGGGGG GGOzaGzGPUG G G {GGGGGGGGGGGTyG UG hG GGGSGGGGGGGUGhG GGGGGGG SGGGGGG GOmGpppUZ\PG G

G mG pppUZ\G ˀG wTTG G G G G zZY\ZG OX]nwSG X[WW¶jSG ZWG PSG zZ[XYGOX]nwSGX[WW¶jSG[\GPGGzZY\[GOX]nwSGX[WW¶jSGGPUG G G G

. 75 . G results

G p}UXGTGzltGGlizkGG

GG G yG G G G G G G zltUG {G G G G G G G G G GGGUGpGGSGGGGGGGGGmGpppUZ]UG uGGGGGGGGGGGGGGGGUGhGGSG GGGGGGGGGGGGGGGGGGUG {G G G G G {G pppUXZUG hG G G G G G G aG G G GGZYZG»GG GGGGOzZY\ZPGGGGG[X]G»GGGGG GOzZY\[PUGtSGGGGGGGGGUG{GG G GGYWWG»GG GUG{GGGGGGGGGGG X`[»GG GGGGOzZY\ZPGGXYYG»GGGGGUG{GGG GGGGGGGGGGGGGGUG G

G mGpppUZ]GˀGvGGGGGGGzZY\[UG{GGGGGGGGUG {GGGGG GG G G {G G ¡G G G G G G G G G zltG G OmG pppUZ^PG G p{GUG{GGGGG¡GGGGGGGmGpppUZ_UGmG G G G G G G G G G G G G G G G GG¡GOmGpppUZ^PUG{GGGGGUG\WG»GGGGGG XX\G »G G G G G G OmG pppUZ_PUG hG G G G G SG G SG G G SG G G G G OUG \WG »PUG {G G G G G GGGG¡GOmGpppUZ_PUGhGGGGSGG GGGGOGG UG ^WG »PUG {G G ¡G G G OmG pppUZ^PG G G G G G G GGGUG G

. 76 . G results

G mG pppUZ^G ˀG mT G G G aG zltG G OG PUG jG SGGG¡GGGGUG {GGGGGGYWG»G PGhG GGGX]nwGGX[WW¶jGOzZY\ZSGPG PGhG GGGGGGX]GnwGGX[WW¶jGOzZ[XYSG PG PGhGGGGGGX]GnwGGX[WW¶jGOzZY\[SG PGG GG G {G G G lizkG G G G G mG pppUZ`UG {G G G G G GGGGGGGGGGGGUG{GGGGUG G hG GGGSGGGG GGGjwvUG{GWWXGG GGGGGGGGGGGGGGGGGGG UGXWWGG GGGGGGGGGGWXWGGGGGG GGGGGUG G

. 77 . G results

G mGpppUZ_GˀGmT GGGaGGGGG¡GGUGiG GGGOYVGGPUG G G hG GGGGSGG GGG GGjwvUGXWWGGGG GGGGGGOUGZW¶PUG{GWXWGGWWXGGGGGGGGXWWUG{ G GGGGGGOUGZW¶PGGGGGGGGGGGGGG WWXGUGG G hGGGGSGGGjwvGGGUG{GXWWGGGG GGGGGGUGWXWG GGGGGGSGGGGGGG GGGGUG{GWWXGGGGGGGOUGZW¶PGGGGGG G UG {G jwvG G G G G G G G G G G G G GGOGGppGGGPG G {G GGG GGGGGGGGGGGGG GGGGGGUG G

. 78 . G results

G mGpppUZ`GˀGmT GGGaGlizkGGGG GGGG GOzZY\ZPGG GGOzZ[XYGGzZY\[PUG{GGGGGGGGG G G G G G G G G bG G G G G UG sG G TG SGGGGGWU\GGGGGUG G

G p}UYGˀG{ltGG

GG G mG pppU[WG G G G G G G G zZY\ZUG hG yG G G lizkG G G G SG G G G G G G G G G G G G G G G OmG pppU[WG G PUG mG G G G WWXG G G G G UGuGGGGGGG GGGGUG~G GGG GGGGGGG GUG{G pppUXYG G G G G G XSG YG G ZG G G mG pppU[WG G G G G UG hGG GGGGG SGG GGG GGG GGGGG GGGUG G G G G G

. 79 . G results

GGG GGG pGJG GGGGG GGGGG

TXWWG YWTXG XG OWYXPG OWXWPG

TXWWG TZXWG YG OWYZPG OWWXPG

XWWG XWTXG ZG OWXXPG OXXXPG

WTXWG XXTXG [G OWWXPG OXWXPG

YTXWG WXZG \G OXYXPG OXWWPG

G {G pppUXYG ˀGwGG¡GGGGGGGGG ¡G G G G UGpGXSGYGGZGGGmGpppU[WUG G G

G mGpppU[WGˀGmT GGGaGGG{ltGGGzZY\ZGOG G GGX]GnwGGX[WW¶jPUG{GGGGGG GUGG mGPSGWWXGGUGaWW[G~GGG G G G G G G G G G G . 80 . G

Chapter IV Discussion

As the techniques used in the course of this study are not used in routine, some developments were needed. Our detailed microstructural characterisations have provided new insights on the behaviour of samples during deformation in those experiments. This aspect of our work is presented in this section. Then, we address the issue of the plastic deformation of the Mg2SiO4 polymorphs under pressure and temperature conditions from the upper mantle to the transition zone. The first major result to be discussed is the pressure- induced change in deformation mechanism. The plastic behaviour of the three Mg2SiO4 polymorphs is studied with a special emphasis on the formation of crystallographic preferred orientations. VPSC modelling is used to link the CPO with known elementary deformation mechanisms of these phases. Finally, implications on seismic anisotropy of the lowermost upper mantle and of the upper part of the transition zone are derived based on our results.

Discussion pG TG kG G G G G G aG G G

GG G zGGSGGGGGGGGGGG UG xT G G OG G rT G G G G G G G PG G G G G GGGkTkphGGGGyGkGhGOykhbG¡GGrSGYWWXPGG GG GGGGGGGGlGGGGG G G G G UG kG G G SG G G G G G G GGTG GGG GGUG G {GG GG GGGGGGGGGGTG GGGGGGG GGGGGGGG¡UG{GG G G G G UG {G G G TkphGGGG GGG GGGTGGUGhGGGOGGGG¡GG PSGGG GGGGrT GGGGGGGGGG G UG {G G G G G G G G G G GGGGSGGSGGSGGGGUGG G

G pUXGˀGkGGGkTkphG

GGpUXUXGˀGzGG

G zGGG GGGkTkphGUGvGGGGGT GGGGG GGGGTG GUGpSGTGG G G G G G G G G G G G G G G G UG nG ¡G G G G G G G G G G G T G G G G GGGUGhGGG¡GGGGGGGGGGG T GGGGGGGGGGGGGGGOTG GXWWÝXWWG»YPUGhGGGGGG¡GG\GGXWG»UGG G

GGpUXUYGˀGkG GGkTkphGG

G lG G G G G uzszG OmvyYXPG G G G G G G GGGGOGGGGXU\TYGnwPGGGGGUGhGGG G G G G G G G G SG G G G G G G G G G G UG kG G G SG G G G G G G G G G GGGGGGGGUG{GGGGG G G G G G G UG {G G G G G G G G G GG¡GGGGUGpSGGGOzY`][SGzY`^WG GzZWY[PGGGGGG GGGGGGGGGUG| SG G {ltG G G G G G G G G G G kTkphG G UG {G kTkphG G G G G G G G G G G G G G G G UG pG

. 83 .

G Discussion

G G TG G i G OkkXYG G kkXZPG G G G G G G G XZWW¶jGGGUGtGGGGGGG GG G GGGGX[WW¶jGOGmGpppU`PUGpGGGGGGGG GG G G G G G G ¡G G UG lG kkX[G G G G G G wWZZYSG G G ¡G G G XWG G UG ]WG »G G G G UG {ltG G G G G G G G G OkkXWPG G G G G G UG tG G G G G UG zG G G G G G G G G GGGUG{GGGG G GGGGGG OG mvyYXSG mG pppUYWPG G G G \WWG twUG {G G G G G G G G G GGGGUGG G G {GGGGGGGGGGGGGGGG GUGzGGGGGGGGGGGGTGG GGGGGGGGUGzGGG GG GGGGG GUGhGGGG GGGGGGGGGGGG UGhGGGGG GGGG GGUGkGSGGG GGGGGGGGGGGGG GGTGUG { GG GGGGGGGGGGGGGGUG lG G G G G G SG G G G G G G G G G GGGGGG GGGGGGOGYG»GG]WGGGGG GXWT\TXPUGG G G kGSGGGGGGGGGG\WWGtwGGGGGGXWT\TXUG {G G G G G G G G G G G G G G G G G UG{GGGOGPGGGGGGGGGGGGG mGpppUYWUGkGGGGGGGGUGpGGG GGG G G G G G Y\G LUG vG G G G G SG G G G G G G GG GUGG G kGGGGUGiGGGGGGGGGGG GGG GGGGGGGGGUG{GGGGGGGG G G G GVG GGGGGGGG G G G G GUG GGG G {G G G G G G G G G G XZWWTX[WW¶jGGGGGG G GGGOGGGGGPUG|GGSGGGGGGG GGkTkphGSGGGGGGG GGGGUG{G GGGGGGGGGGGGGGUG{GGG G GGGGGGGGG GUGoSGGGGG G G G G G G G T UG {G G G G G G G G G SG GGGGUGjGGGGGGGGG GGGUGkGG SGGGGGGG GGGG ^GnwGG~jGGG\GnwGGiuGUG{GG GGGGGGGG

. 84 .

G Discussion

G G T G G G G G G G G OsG sSG G PUG {G GGGGG GGGGGGOzGGUSGX``YPG GGGGO~GGUSGX``_PUGwGGGGGGGGGG GUGm SGGGGGGGGGw GGGGGG G G G G G G G G G G UG pSG G G G kkX[G G G G G OwWZZYaG Z]`G oVXW]zPG G G G G G G G Z[^G oVXW]zGGGGGXZWW¶jGGYGnwUGG G G kTkphG G G G G G G G G jwvG G G G G lizkUG nGG GGGSGGjwvGGGGGGOkkXYSGkkZXGG mvyYXPUG{GGGjwvGGGGG GGGUG{GGGGGGGG G G G G G OUUG {SG X`[_PUG oSG G G G G G G G GGGjwvGGGGUGG G G

G pUYGˀGkGGGrT GGG

G G m SG G rT G G G G G G G UG {G G G G G G G G G G UG ~G G G G G GGGTGGOGGGjGppPGGGGGGG GGGGGGUG{GGGGGrT GGGGG GG GGGGGT¡GGGGGGXWTY\GnwUGpGGGGG GG GGGGG GGGGGG¡UG G pG G G G G G G G G G G G G G rG G yGOX``^PGGGGjGppGTGpUYUYUGpGGGGGG GGtYzv[SGGG G GGGGGX[V_GGGGX_VXXGGX_V_GGUG{GG GGGG¡GOGYWWG»GSGGSGGaGXU\GPGGGGGGG G UG{GGGGG GGGX_V_G GGG\WWWGGGG GGi GnUG G

GGpUYUXGˀGzGG

G {GGGGGGGGGGGGTGGGGGG T GGTG UG{GGGGGG GGGG UG m SGGGG GGGGGGGGSGYWWG»GSGGG GGG[\¶UGz SGGGGGGG GGGGG GGGGGGGGUG{ SGGGG¡GGGG GGUG{GG¡GGG GlizkGUGhGGGXWWTX\WGGG G GGGGGGjwvGOiGpõGGtSGX``_PUGpGGGG GGGGG GG¡GGXWTYWG»UGG

. 85 .

G Discussion

G pGGGTG SGGGGT GGGGGGG GGGGGGGGUGpGSGGGGG GGGGGGGGGGGG GGGGUG~GG GOoX`\ZSGX`\[SGoX`^`GGoX`_XGGG GGGPGGGGG G GGGGSG GG GGTGGUGG G

GGpUYUYGTGkG GGGGGGG

G {GG GGGG G GGGG G GGGGG GGGGGGGrT GGUGG G hGGkTkphGSGGGGGGGGGGUG{GGUG OYWWZPG G G G G G G G G G G G G G G G G G G G G UG ~G G G G G G G G G G G G G kTkphG G G G G G G G UG pG SG G G GGGGGGGG GGGGGGUGvG G G G G G G G G SG G G SG G G G GGGGGGUGkG GGGGG GT GG GGG GXU]ÝXWX\GTYGGG GGGG GG GGG XWX]TXWX^GTYGOG{ltGPUG~GGSGSGSGGGGGGG GGGGGGGG{ GaG G

1 2 V 1 V 3 D b P U G

G D GGGGGG SG b G G G iG SG P G G G G G U G G

G UG{GGGGGOmSGX`]^PGGGG G G G OrG G n¡SG X`^[bG rGGUSG X`^]bG ~GGUSG X`__PG G ˈˉG G GGG GGUGmGrGGUGOX`^]PSGD GGGGGGZUG hGGGGSG{ GGGGGGGGGGXU\GnwSG GG G G G G G G G G kTkphG OmG pppUYWPUG {G G G G G T G G G G SG G G G G G G UG kG G G G G SG lizkG G G G G G G jwvG G G G G GG GUGG G G wGGGGGX[V_G GGGGGGGGG GYWGnwGGGGGGGGY][GGGGGGGGGGX]GnwG GGGGX[V_G UG{GGGGG GGGGGGGG GGGGGGGG GGGUGG G G vGGGGGSGGGGGUG{GGGGGX[WW¶jG GXYGGX\GUGpGGGGGGGGGGSGGG . 86 .

G Discussion

GGUGpGGGGGSGGGGGGX[WW¶jGGGG G GGGGGGYGGZGUG{GGGGGGGGGG GGG GGGGGGG~jGUGpGGGSGGGG G G G G G G X[WW¶jSG G G G G G G G G G GGOGXU]ÝXWX\TYGGYÝXWX[TYPUGmGGG SGGGGGG G\WW·YWWGtwUGuGjwvGGGGGGSGGGGGGG GGGGGGGGGOmGpppU\PUG{GGGGGGG GjwvGGGGGGGGGGUG~ G GGGGGUGwGGGGyG GG G SG G G G G G TSG TG G OGoX`\ZSGoX`\[SGoX`^`GGoX`_XPGGUG{ltGGGGoX`\[GG GGG GGGGGGGGGOmGpppUZWPUG G {G G G G G SG G SG G G G G G G G G G GUGmG GGGGGGX[V_G GOmGppU\PSGG GSGGGGGSGGGGGGGGGGGG G G UG pSG G G o G G G G SG G G G G Y][G G G GGX]GnwGGXYWW¶jGGGXZGnwG GGGUG{GGGG GGGGGTGGUGpSGGGGGGG G\WWWGGGGGGGGGGGGGX[WW¶jGGGGGG G G Y`\G UG oSG G G G G G G G G G G G G G G G G SG G G G G SG G G G G G G GGGOjGppGpUZUYPUGm SGGGGGGG GGGG G G G G G G G G G G G G G G G UGpG GSGG GGGGGGGGGGGGT G GGGTUG G kG G G rT G G G G G G G OrG G ySGX``^PUGhGGGGGGSGGG GGGGGG G GGGGUG{GGGGGGGGGGG GGGGGGGGGGGGGkTkphUGhGGG G G G G G G UG mG G G G X[WW¶jSGGGGGGGG G G G G G G G TG G UG zG GGGGGGGG{ltUGzGGGGGG GGGG GG GGGGUG{GGGGGGGGG GGGXWW·\WtwGGUGvGGGGGGGkTkphGGGGT GGGUGlizkGGGGGGjwvGGGGGGG OzY`X^SGzY``[SGzY``\SGzY``ZGGzY``[PGGGGGGGGGOzY``_GGzZW^`PG G jwvG G G G G G G G G G G G G OoX_][G G zZYXZPG G G G G G G OoX__YG G oX`[\PUG tSG G G G G G G G G G G G G G G G G G G G G G G G G G G G UG {G G G

. 87 .

G Discussion

GGGGGGGGG GGGGSGGG GGG GGGGGGGUG G {GGGGGGGGGGGGGGGG GGGG UG{GGGSGGSGGGGGWUZGGG G G G G G XG G G G rG G yG OX``^PG G rG G UG OX``_PUG {G G G G G G G G G G G G G G G [\¶G G G G G G G GGGGGGG G G G UG pG G [\¶SG G G G G G G GGG GGGGG GSGGGGGGUGvG G GGGGGSGGGGG G GGGGSGGG GG GGGGGGGGGGUGG G jG SG G G OG jG ppSG XUZUYG G mG ppUX[PG G G G G G G G G G G G G G G G G G G GGGGGGXWW¶jGGGGGGGGGG\W¶jUGvGGG G G G G G G G G G G G UG wG G G G

GGGGGGUGpGG SGGGG GGGhYvZG

GtYzv[GGGGGOGXWWGGGmGp}UXPG GGGGOG GG GGzltPUG{GG GGGGGG GGGGGG GGGGGGGUGpSGGGGGGGGG GGGGG GGGGGGGGGGGGUG G

G mGp}UXGˀGpGTGGGGG UGzltGGGTUG{GG G G G G G G G G G G G G G G OzY`X^SG X[WW¶jSGXXGnwGGXGPUGzGaGXWWGG G G m SG G G G G G G G TG G G GGGGGGrT GGGGGG GG UG G G

G pUZGˀGjGGGGGGGGG G

G ~GGkTkphGGGGG GGGGGGlGG GTGGGGGGGZWWGUGpGGGGGG

. 88 .

G Discussion

G G G G G G G G G G G G G GGGaG TGGGGG GGG TGGGGGGGaGGTSGGG TG GGGOGGZWLPGGGGGG TGSGGGGGGGGGGGGGGGGG G GGUG {GGGGGGGGGGGGGGGGGGOG GGGGGGG GGGGGGUGX\GnwPUG{GG G G G G ¡SG G rT G G G G G G G G G G G G G G G G G G G ¡G UG pG G GSGGGGGGGY]GnwGOjGGySGYWWXbGjG G USG YWW[PUG oSG G G G G G G G G G G G G GrGGyGOX``^PGUG{G G GGGGX[V_G GGG GGX^GnwGGGGGGX_VXXGGX_V_GGGG UG{GGGG GGGYYGnwGGGUG{GGGGGG GGGGG \WWWGGGGGi UG~GGGGGGGGGGGG GTGGG GGGGUGG G G ppG ˀG kG G tYzv[G G G G G G G ¡G G

G G tGGGG GGGGGi GGrT GGGkT kphG G OG G G G G PG G G G G G G G G G G G UGpGGGGSGGG GGGGGGhwzGGiusUG vGGGGGGGjwvGG GGGGGGGGG

GG GGtYzv[UG{GGGGGGG GGGGG G G G G ¡UG {SG G G G G G ¡G G GGGGGGGGGGGGGGG GGGGGGGjwvUG G

G ppUXGˀGkGGGGGXXGnwGGX[WW¶jG G

GGppUXUXGTGjGGGGGG

G {GGGGGGGGGGGGGG G rT G G G G G G G G GjwvGGOmGpppU^PGGGG G G G G G {ltG OmG pppUXWPUG l G G G G G OG zY``ZPGGjwvGGGGGWWXGGGGSGGGGGWWXG

. 89 .

G Discussion

UG pSG {ltG G G G G G G G G WWXG UG sG G G G G G G SG GGGGGGGrT GGGXXGnwUG G G {ltGGGGGG GGGOzY`][SGzY`^WGGzZWY[PGG GGG GGWWXGGGGGGGGGUGpGGGGGG G G G G G G G G UG {G G SG G G SGGWWXGGGGGGGGGGGUGG G pG G G G G G G G G G X[WW¶jG OzY`X^SG zY`\[SG zY`\\SG zY``ZG G zY``[PSG{ltGGGGGG GGGWWXGUGG GG mGGGGGGGO_GPSGGGGGGGG GGGGUG{GGGGGGGGGG_G GOGmGpppUXWPGGG GGOG GPGGUGpGGG G G G G G G G G G G G G G GGGGGG GOGGXWWGGGPUG{GGGGGWWXGGG SGGGGGGG GXGUG G G {ltGGGGGGGkTkphGOkkXZGGkW\WXSGmGpppUX[GGX_PGG G G OYG G ]G nwPG G G G WWXG G G XWWG G G G G G G G G G G G OG G G {ltG G G G G G GGGG GGGGG PUG G WWXGGGGGGGGUGpGGG GGGT GGGGGG GOUUGrGGn¡SGX`^[bGkGGnSG X`_XPUG {G G G G XWWG G WWXG G G G G G G TUG kG G G G G G G G G G G G jG yG zG zG OjyzzPGG G G G G G G G UG hG G SG mG p}UYG G GGjyzzGGXWWGGWWXGGGOWXWPGGGGGGTGGXWT\TXUGpG GGGGGWWXGGGGGGGSGGXWWGGGG GGUG{GGGTGG GG GGGGG G G OG G G G G G G G G G G G G sG OYWWXPGGGPGGGG GWWXGUG G G

. 90 .

G Discussion

kGGn¡SGX`^^G w GGUSGX`^YG tGGUSGX`_\G kGGnSGX`_XG rGGn¡SGX`^[G kGGn¡SGX`^^G w GGUSGX`^YG tGGUSGX`_\G kGGn¡SGX`^^G rGGUSGX`_YG kGGnSGX`_XG G

G mGp}UYGˀGvaGGGGGGG GXWWOWXWPGGWWXOWXWPGGGG GUGkGOGGGGGGXWT\TXPGGGGGG G GGWXXGOTG PGGGWWXOWXWPGGGGXXWGOG PGG GXWWOWXWPGUG G G wGGG GGGGWWXGGGTGUGmG SGWWXGGG GGG GyGGUGOYWW[PGGsGGUGOYWWZPGG_T`GnwGG \WWT_`W¶jUG iSG G G G SG WWXG G G G SG G G G mG p}UYUG zGGGX\GnwGG`WW¶jGGZWGG GkTi¡GGUGOX``_PGGGG GGGGGGWWXGGGGGGUG GG G {GGGWWXGGGTGGG GGGGGG GUGpGGGGSGSGGGGGOGGGGPGG GG GGTGGGUGG G vGGGGGGG OXU\GnwPGGGGG GGGGTG GGG GWWXGGGGGG UG h G G G G G X[WW¶jG G G G G G G G G G G G GGGGGGGGGGOjwvPUG{GjwvG GGGGGG GGGGGGGGGG GGG X[WW¶jG G G G G UG \WWG twUG {G G G G OmG p}UYPG G SG G G SG XWWG G G G G G G G G UG vG G G G GGGGjyzzGGXWWGGWWXGGGGmGp}UYUG{GGGG GSGGGGGGXWWGGGGGGGGGGGWWXG G G G G UG {G G G G GGGGGGXWWGG G G G G G WWXG UG pSG WWXG G G ¢W¤G G G G G G G G G G G }G tG UG nG G GGGGGGX[WW¶jGG G G UG pG G G G G G XWWG G G G G G UG {G GGGGGGXWWGGGkTkphGGGGGGG GGGGGGSGGGGGGGOG]GGY\LPUG . 91 .

G Discussion

G i G G G SG G G G G G G G G UG pG G SG jwvGGGGGGGWWXGGGOXWWPGOzY`\[SGzY`\\GGzY``ZPGG G G G OWXWPG OzY`\\G G zY``[PUG {G G G G G G G G G G G G G UG{GGjwvGGGGGGGGGGGGUGpGG GGGGGGGGGGGGGG{ltGGGGG G G G G G G UG tG G G G G G kTkphG G G G G G G G UG {G G G G G G G GjwvGGGGUGoSGGGGGGGGGG GGSGGGGUGlGkkZXGO]GnwPGGjwvGGWXWGGG GGGGGXWWGGWWXGGGGGGGGGSGG GGGGGOmGpppUXZPUGhGGSGGGGGGGG GGG OXWWGVGWWXGGGPUGoSGOWXWPGGGGGGGUG G hGGGGGGGGGGGG GGGG G G G G G G G G G G wG yG OG PG G uzszGGGkTkphGGGG GGGGGG UGzGGGG G G SG G G G G G G G G UG {G kTkphG TG G G G G UG vG G G G WXXG OG G WWXOWXWPG PG G G G G GGXXWGGGXWWOWXWPGUGhGGGGGGGG GGG GGGGGUGzGGGGGGYU^GnwGGG^UYGnwGGG GOXXWWTX[WW¶jPGGGGGUGhGYU^GnwGGX[WW¶jSGGG GG G XXWG G G G G G G [ÝXWT]TXG G G G G G G WXXG G G G G G G XU[ÝXWT]TXUGhG^UYGnwGGX[WW¶jSGGGGGGG G G G XXWG G G G G G G G WXXG G G G G G XZÝXWT]TXGGX^ÝXWT]TXG UGhGTGGGG GOGXWWOWXWPG G WWXOWXWPPG G G G G G G UG } G G G TG G G G G G G G G G G G G G G G UG hG G GGGGGGGGGGGrGGGGmGp}UZUG G

G mG p}UZG TlG G G G G G G G G G G G G XXWG G WXXG G G G G UG {G G G G G G G G kTkphG G X[WW¶jG G G GG\WWGtwGOj GGwUGyPUG

. 92 .

G Discussion

GGppUXUYGTGw GGGGG GGGGG G

G {G G G G G G G G G G G G G G G G GGG UG{GGGGGTGGGGGG GSGUUGGGGUGzGGGGG G G G G G G GGG{GOGGUSGYWWXbGGGUSGYWWXPSGGGGGG GGGGG GUG{GGGSGGGGGGGGGGGGG | G G sG G qG kG OG PUG hG G G G G G GSGGGGGGGGSGGGGGGSGGGG UG hG SG G G G G G G G G G G G G UG qUG k˅GGGGGGGSGUUGGGG GG G G G G G G G G G G G G G G UG {G G G GGGGGGG GGGGGGGGGGG GGGUGpGGGGGGG¡GGGG G GGG G G G G OG kG G UGOGPGGGG G G G G PUG jG G }G OX`^WPG G G G G wG G G G G G G G G G G G G G G wTuG G OUUG qøG G k SG X``^PUG {G G G G G G G G WWXOWXWPG G XWWOWXWPG G G G G T GG}hzwGGOrGGoSGX``ZbGrGGmĂSGX``]PUGmGGGG SGGGGGGGGGGGGGGGG GGUG {GGGGGmGp}U[UGhG¡GSGG GGGXWWOWXWPGGWWXOWXWPG G GGGGGGGGYWWWGqVYGOGGGXWWGG GGGG GGWWXPUG{GGGGG GGGGXWGnwUGhGG GGG WWXGGGGGSGGGGXWWGGG GGOG\WLPUG{GG G G G G G G G G G G XWWG G G G G G G G G G G G UG {G G G G G G G G G GGGGGGGGGUGpGGGGGXWWG GGGGGGWWXGUG G

G mGp}U[GˀGl GGGGGGGGGXWWOWXWPGOPGGWWXOWXWPG OPUGjGGGGGGWGnwGOG PGGXWGnwGOG PGOj G GqUGkPUG GGG

. 93 .

G Discussion

GGppUXUZGTGsGGGaG GGG

G wGGG GG GGGGG UGpGG SGGGG G G G G TG G TG G G G G G G G GG jwvUGjwvG GGGGGGGGGG SGGG G G UG pG G SG G G G G G G G G G GOG{ltG¡PGGGGGjwvGOGlizkPUG{GGGGGGG GGGGGGGG GGUGmGSGGjwvGGGGGG GGGGGUG{GGGGG G hG {G G kG tG OsG G { SG | G G tSG mPG GG}wGzGjGGOtGGUSGX`_^bGsGG{ïSGX``ZPGOGhG pppG G G G G G PUG {G G G G G G G G G G T GGGGGOGGGGpppUXPUG GG G }wzjGGGG GGGGOUG~GGUSGX``XbG{GGUSGX```bG ~GG{ïSGX```bG{GGUSGYWWWPGGGG GGOUUGiGGUSG YWWYbGjGGUSGYWW[bGtGGUSGYWW[PUG{GGGGG GGGjwvGGG G GUGpGGGSGGGjwvGGGG\WWG GG G G G UG vG {ltG G G G G G G G G G G GGGGGGGGGGGG GOjyzzPGGGG UG }wzjG G G G G G G G jyzzG G XWWOWXWPSG XWWOWWXPSG WWXOWXWPSGWWXOXWWPSGXWW¢WXX¤SGXWW¢WYX¤SGWWXG¢XXW¤GG GGGGGZaXa]GGO{Gp}UXPG GGGGWU\GOGGGGGGGGPGGGXUG G

WWXOWXWPG XWWOWXWPG XWWOWXXPG zG G WWXOXWWPG XWWOWWXPG XWW¢WYX¤G WWX¢XXW¤G

yGjyzzG ZG XG ]G

G {Gp}UXGTGyGGGGGGGG GGGGGG}wzjG UG G G z GGGGGSGGGGGdZGGGGGUGpSG }wzjGGGG GGGGGGZGG \G G G G G G G GGGbGGGGGGGGGGGGjwvGGGGGUG mGp}U\GGGGG}wzjGGGGGGWU\GGXUGzkGGuzwGGG GGGGGGGGG UGhGGGGGWU\SGXWWGGWXWG GGGGGGGGGGGGGGGGGGGGGGGG GGGGGGWWXGGGGGGGGGGGGGG GGGGGUGtG GOUGZW¶PGGG GGGGGG UG{GGGGGGjwvGG GGGG GGjwvG OGmGpppU^PUGjwvGGGGGGGGGXWWSGWXWGGWWXGGG . 94 .

G Discussion

GGWWXUGzGjwvGGGGGGGjyzzGGGGG GGGGWWXG GG GGGGXWWG UG G

G mGp}U\GTGmG GGGGG}wzjGGG\WWGGGG GGWU\GGXUGsGGTGSGGGWU\GGGGG UGkGGUGzkdGGGuzwdGGGGUGpGGGGG UG G G {G G G G G G G G G G G G G G G G G G mGp}U]UGhGG GGGWWXG GGG`WLGG_WLGGGGGGWU\GG XGGSG SGGGGGGGWWXGGGGXWWGGWXWG UGh GGXWWOWXWPGG GGWUW\GLGGYWLGGWGGXGGGGGG G G G WWXG G G UG {G G G G G G G G G G G G G G G UGhGGWWXG SGG GG WWXGGG¢XXW¤GG GGGGGGUGG{GGGGGWWXG GG¢XXW¤GGGGGjwvGGUG G

. 95 .

G Discussion

G mGp}U]GˀGlGGG GGGGGGGGGGG}zwjGG OG{Gp}UXGGPUGiG aG GGXWWG GvG aG GGWWXG UG GG G {G SG }wzjG G G G G G TG G G G GG GGGjwvGGGGGXXGnwGGX[WW¶jGGG GGOmGpppU^PUG G G oSGG GGjwvGGUGjGjwvGGGGGGG GGGYWWGGOGG]GnwPGGGGGG¡G GXWWGGGGGUG h GGG GGOUUGuGGUSGX`^ZbGuGGjSGX`_^bG~GGUSG X``YbGiGpõGGtSGX``_bGiGpõGGUSGYWWXPSGG GGOGG rSGX``\bGi GGUSGYWWWbGGGUSGYWWWPGGGGGGGjwvGGG G G O{SG X``_bG {GGUSG X```bG ~G G {ïSG X```PG G G G jwvG ¡G G XWWG G WXWG G G G G G G G G G G G G UG G {GGGGGjwvG¡G GWWXGGGGGG G G G G G G G G G qG G rG OYWWXPUG ~TG G GGGGGGYGnwGGX[WWTX\^W¶jGGGGOX]WGG[]WGtwPUG {G GGjwvGGGGGGGGWWXGGOGGXWWGPGGGGG G G G UG mG qG G rG SG jwvG GWWXGGGGGSG G G G G G G G G G G OmGGUSG YWWZbG t¡GGUSG YWW[PG G G G G G G G G G UG jG jwvG ¡G G WWXG G G G G G G G G G G G G G G G G `G G [ZG nwG G G G O~GGUSG YWW[PUG {G GGGGGGWWX¢W¤GG GGGGGGGGG G G G G WWXG G G G G G G G G G G OUG

. 96 .

G Discussion ySGX`]_bGGpppSGX`]`bGw GGUSGX`^YPUGwTGGOGGGZGnwG GGGPGGG GG GGjwvG¡G GWWXGGG GGGGGOXXGnwGGX[WW¶jPGGGG GGGGUG |GGjwvGGG GGGGGGGG GGsGG O}¡GGUSGYWWZPUG{GjwvGG¡G GGGGGGXWWGGWWXGG GGGUG{GGGGGGGGG[U[GnwTXY]`¶jGG[U]G nwTXZZ]¶jUG{ GGGGGGGGWWXGGGGGGG G[U\GnwGGXZWW¶jUGG G

GGppUXU[GTGjGGGG

G G mGGGGGGGG GSGG GGGG GGG GGG GGGG GGGGGG GUG{G G G G G G G jwvG G G G G G G G G G UGpGGGGGGGGG GGGGOG pppUXPUG pG G SG G G G G G G G G G G G G G G G G G G G G UG tG G G G G G G G GGG GGGGGGGGGUG G {G G G G G G G G G G G G G G UG {GGGGWWXGGGGGGGOUUGsSGYWWXPGG GGGGGGGGGUGpGGGGGGGGGG UG G kG GGGGGGGGGG GGG GGGGqGMGrGOqGGrSGYWWXPGGGYGnwGGTGUGoSG qGMGr˅GGGGGGGG GGGSGUUG GXWWGGGWWXGGGGGGGGOzTGrSG G PUG j SG G G G G G G G SG G G G G bG G G G SG G G G G UG tG G G G GG GGUG G

G ppUYG ˀG kG G G G G G TG G G

GG¡G

GGppUYUXG ˀG kG G G G X]G nwTX[WW¶jG G G G G G GTG GGG

GG G {GGGGG G GG GUGG GUGhGGGGG GGGSGGGGG GGGT GG GGGGUGuGGOkGGUSGX``[bGzGGUSGX``[bGjGG

. 97 .

G Discussion

USGX``_bGkTi¡GGUSGX``_bG{GGjSGYWWZbG{GGUSGYWWZbG{GGUSGYWWZPG G G G G G G G G G G TG UG oSG G G G G G SG G G G G G G G G ¡SGGG GUG G

GGGppUYUXUXGˀGkGG GGX]GnwGGX[WW¶jG

G kG G G G G G G G X]G nwG G X[WW¶jG G G G G GGGGGjwvUGhGGGGGGGGG GGGGGOoX`[`GGoX`]^PUG{GGGGG{ltGGG GGGGGXWX]TXWX^GTYUG{G GGGGGGGGG G G TG G OXU]ÝXWX\TYPUG {G G G G G TG G G G G G G lizkUG pG G G G G G G G G jwvG G G GGGUGG ~GGGOGGpUYUYPGGGGGGOGXYTX\GPGGGGGG G G X[WW¶jG G G G G SG G G G TG G G OoX`\ZSG oX`\[SG oX`^`G G oX`_XPUG hG G SG G G G G G G G G G G G G G G G OmG pppUYZG G mG pppUY\PUG tSG G G G G G G jwvG OmG pppUY`PUG jwvG G oX`\ZG G oX`\[G G G G G UG WWXG G G G G G G G XWWG G WXWG G G G WWXSG G G WXWG G XWWG G G G G UG {G jwvG G G G G G G G G G G G G G G G X[WW¶jG G XXG nwG OG G ppUXPUG pSG {ltG G G G GGG GWWXGUGoSGGjwvGGGGGG GGGGGGUGiGGGGGGGG G GGGGGGG GUGhGlizkGGG GGG GGGSG{ltGGG GGG GOGWUY\GGXG»GGPG GGGGGGGGGGGGOmGpppUZWPUGkGGG GG ¡G G G SG G G G G G G G G G G UG G hG G G G X[WW¶jSG G G G G G G OoX__YG G oX`[\PUG {ltGGGGGUG{G GGGGGG GGGGXWXZGTYUGzGXWWGGGGGOmGpppUZWPUG{G G GGGGGGGGUGG G pGGGGGOzZYXZGGoX_][PSGGG GGUG{GGG G G G G G G G G G G G G G UG uG G GGGUGpGGGG GGGGGGGGG G G G G UG {G G G G G G G {G G UG OYWWZPUG pG SG G{ltGGGG GOGGG GPGG GGGGGGOWXWPGOUUGwSGX__ZbGtGGwSGX`_ZbGzGGUSGX``[bG{G GUSGYWWZPUG{G GGGGGGGGGOkTi¡GGUSGX``_PGGG GGG GGGG GGGGGGG G{GGUGOYWWZPGOG . 98 .

G Discussion

GTPGGGGGGGG GGGUGhGG G{GG

UGOYWWZPSGGGGGGGOtSmPYzv[G UGG G sG G G G G G G G G G G G G GG GGGUGoSG{ltG GGGG GGG G G G G G OG G G G G G G G G PUG{GGGGGGGGGGG{GGUG OYWWZbG YWWZPG G G G G G G G UG vG G G G GGGGkTi¡GGUGOX``_PGGGGGGG GGG `WW¶jUGG G G lizkGGGGGjwvGGGG GUG{GjwvGG GGGGGGGGOmGpppUY^GGmGpppUY_PUGpGGGGG GOoX__YGGoX`[\PSGGGjwvGGUGXWWGGGGGGGGG GGGGGSGWXWGGGGGGGGGGGGG WWXG G G G G G G G G G G UG pG G G G G G OoX_][GGzZYXZPSGGjwvGG GGUG{ G GGGG GGG GGGGGoX_][GG GGGGGWWXGGGGUGG G G iG G {ltG G G G lizkG G G G G G G G GjwvGG GGGGGGUGoSGGGGG GG GGGUGpGGGGGGGGGG G G G jwvUG pG G G G G SG jwvG G G G G G GGGGGGGGGGGUG~GGGG G G G G G OppUXUZPSG }wzjG G G G G G hG {G G kG tGOsGG{ SG| GGtSGmPUGG G hGGSGGGGGG GGG jwvG G G G UG pG G G SG G G jwvG G G G \WWG G G G G G UG sGSGGGG GGGGGGGGjwvUG{GG G G G G G G {ltG G G G G G G G G O{G G jSG YWWZbG {GGUSG YWWZPUG zG G G G G SG

X aG XWWOWXWPSG XWWOWWXPSG XWW¢WXX¤SG XWW¢WYX¤SG VYcXXXe¢XWX¤SG WXWOWWXPSG WXW¢XWX¤SG G cXWXeOWXWPUGoSGGGGiGGOWXWGGcXWXePGG GGGGG G G G G G SG G G G G G G G GGG GG GOG G GGG pUYUYPUGpSG{G GUGOYWWZPGG

X G G G G G SG G G XWWGG VYcXXXeG G G G G G TUG hG G G TG G G G G G G G SG {G G UG OYWWZPG G G G G G G G G G G G G G G G G G UG {G G G G G G G T G G G GGGGGGGGG GOjyzzPUG{ltGGGG

X G G XWWG G VYcXXXeG G G G G G G G GGGG

. 99 .

G Discussion

UG ~G G G SG G G G }wzjG G G G G G G

X GjyzzGG VYcXXXeGGXWWGG GGGGGGXa\GOG\aXPGO{Gp}UYPGGG GGGGXUGz SGGGGGGGGG UG{GG GGGGGGUGzGGGGUGz GGGGG SGGGGdZGGGGGUGpSG}wzjGGGG GGGGG GZGG\GGGGGGGGGGbGGGGGGGG GGGGjwvGGGGGUGG G

G XWWGOWWXPG GXWWOWXWPG GXWW¢WXX¤G GXWW¢WYX¤G cXXXe¢XWX¤G

GXG XG XG XG XG XG GYG XG \G \G \G XG GZG XG \G \G \G \G G[G YG \G \G \G XG

G {Gp}UYGTGzG GGGGGGGGGGGGUG G G mG G G OmG p}U^PSG G XWWG G G G G G G G G G SG G G G GGGGGGGGWWXGGGGGGGGGGGGG SGGGGG GGGGGUGiGGG GGOcYW¶GG GGGGWU\PGGGGSGG GGGGGUGG G ~GGGSGGXWWGGGGGGGSGGGWWXGG G GGGGGGGGUGG G GG

. 100 .

G Discussion

G mGp}U^GˀGj GGGG GG G}wzjGUGjGGG X GGXWWGG VYcXXXeGG GGGGXGG[GGGGGGGGGG UG sG G TG SG G G G G WU\G G G G G UGkGGUGzGGG¡GO GPSGGOGPGGG UGzGGaGWU\G G G } GGjyzzGSGSGG GGGGG GOmGp}U_PG GG GGGGXWWGGWWXGUGoG GGXWWG SGGGGGXGGZGG SG SG G G GUG\\LGG]WLGG G G G SG G G GGGGXWWGGGGWWXGGWXWUGvGGGSGGGGG

X VYcXXXe¢XWX¤SGGGGGYGG[GOUG]\GLPSGGGGGGGGUG {GGGGGGGGGGWXWGGUGoG GGXWWGG G OG XG G ZPG G G G G G G WXWG G G G G G G G

X GGGGGGGUGkG GG VYcXXXe¢XWX¤GSGGSGGG G G G WXWG G G G G G G G G G UG XWTZW¶G G G G UG

. 101 .

G Discussion

G mG p}U_G ˀG}wzjGGGGGG aGG G G G G G G GGGGUG G G uG G G G G G G G G G G G jwvG OmGpppUY^GGmGpppUY_PUGpGSGGGGWXWGGGGGGG G G G G G G G G G G G }wzjG UG zG G G G G G G G G G UG{GGGGGGGGG GG GGGGGGGGUGwGGGG G GGGUG{GGGGGGGGGGG UG h SG G G G G G G G G G G G GGG UGoSGGGGGGG GGSGG GG GGGGGjwvGOGGPGGGGGGG aGGGGXWWGGGGGGG WWXGGGGGGGUG vG G G G G G G G G G G jwvUG { G G G G G GGGGGOpppUYPUG G

GGGppUYUXUYGTGpGGGGoG GGGG

G pGGGGG GGGGGGGGGGUG mGGSGGTGG GGGGGGGGG GGGG G jwvG G G G UG oSG G G G G G G G ¡G G G GGGGGGGlGGGGGGGG GGG UG{G GGGGGGGGUG{GGGG G G G G G G G G G G G UG pG G G G G G GGGGGGSGSGGGOUUGrGG~SGX`^WbGqGGUSGX`^\bG GGwSGX`_ZbGkGGUSGYWWXbG{GGUSGYWWXPUGz SGGGGGG

. 102 .

G Discussion

SG G G G G G G G G G G UG {G G G G G G G GGGG GGT G SGGGGGGG G G G G G G G G G G G G G G G GOGjGpppSGp}PUGG G G mGGGOzZY\YSGzZ[XYGGzZY\[PGTGGGGGGG GUG{GGGGGGGGGG G GG G G G X[WW¶jG G G G OzZY\ZPSG G G G OzZ[XYPG G G G OG mG pppUZ\PUGyG GGGGGGGGGGUGhG GG GX[WW¶jSGGGGGGGGOzZY\ZPGG{ltGGGGG G G GUG jGGGG GG GG GGG G GGX[WW¶jGGX]U\GnwUG{GzltGGGGGGOmGpppUZ^PGG G GGGGG¡UG{GG¡GGGGGG T GGGGGGGGG GUGG G G {GGjwvGGGGGOmGpppUZ`PGGGGGGGG GGXXGnwSGX[WW¶jGGGGOmGpppU^PGGGGGGGGG WWXG G OG G ppUXUXPUG {G G G G jwvG G G zZY\ZG G G G GG GGGGUGhGGSGGjwvGG G GGGGG GGG GGGX]GnwGGX[WW¶jGGG G G G OmG pppUY^G G G pppUY_PUG vG SG G G G G G jwvG G G GGGGGGGGGUGG GG G {ltG G G G G G OzZY\ZPG G G G OmG pppU[WPUG {G G G G G G G G G G G X[WW¶jUG {G G G G GGGGGGGUGuG G GGGGG GGG GGO{GpppUXYPUGmGSGGXGGYGGmGpppU[WG G {G pppUXYSG G G G G G bG SG G G G G G G UG tSGGGGGGGGGGGGO GGWWXG GSGmGpppU[WPGGGUG{GGGGG GG G G G G G G UG {G G G G G G G G GGGGGG GGGOUUGn GGUSGX``XbGi GG USG X``YbG i G G ySG X``[PUG {G G G G G G G G G G G UGG G G ~GGGGGGGGGGGGGUG{GG G G G G G G G G G G G G G G G G G G G GGGGGSGGGGGUG{GGGGGGGG GGGGGGGGGT GGGGG GGGGGGO{GpppUXXPUG{GGGGG GGGG

. 103 .

G Discussion

G G G G G G G OmG pppUZ^PUG tSG G G G G G G G G G G G G G GGGUGm SGGGG GGGGSGGGGGGGGT GG G G G G G G G UG hG G G SG G G G OmG pppUY\PGGGG¡GGGGGGGGGGT G UGoSGGGGGPGGGT¡GGGSGPGG G GOGG G PSG G G G ¡G G UG wG G G G G G G G G GGG¡GGGGGGG SGGGSGGG GG G¡GGGGGG GO PGOUUGrSGX``\bGyGGrSG X``^PUGvGGGGGG GGGT GUG GGG

G ppUYUYGˀGkGGGGYYGnwGGXZWW¶jG

GG G hG G SG G G G G G G G G G G G G G TG GGOX_TY[GnwGGXZWW¶jPGGGOUUGjGGUSGX``_bGrGG USGX``_bGrGGk SGYWWXbG{SGYWWXbGjGGUSGYWWYbGrSGYWWZbGGGUSGYWWZbG~GG USG YWW[PUG uG G G G G G G G G G G G G GGUG G vG G G G G G G G G jwvG G G G YYG nwG G XZWW¶jG G G GGGGGGGGGGGGGGG¡UG G wT G G G G G G G G G G G YYG nwG G XZWW¶jUG{GGGGG GGGGGG GGG G G G G G TG G G G G GGOGmG_PUGhGG GOZ]^PGGGGGGGXZWW¶jGGG GGGGXYTX\GUG wGGGGGGGGGGGGGGG OmGpppUZXPUG{GTGGG GGGGUG{GGG OZ[XPGGGGGZGGGGXZWW¶jUGG G {GlizkGGGGGG GjwvGOmGpppUZZPUGhGGGG SGGjwvGGG GGGGGGGcXXWeGGGGGGG GGGUGhGGSGGjwvGGGGGGcXWWeGGGGG GGGGcXXWeGGGGGGGGGGUG{G GGjwvGG GcXWWe¢XXW¤GG GGUG{GG{ltGGOmGpppUZ[PGGGG GGGUG GG {G jwvG G G G SG G G G G SG G G G G G G G GGGGOzGGoTtSGX`_\bGtGGUSGYWWYbG¡GGrSGYWWYbG oGGUSG YWWZPUG {G jwvG G G G G cXXWeG G G G G G G GOGGGGPGGGcXXXeGGGGGGGUGGtSGG G G G G G G G jwvG G G khjG G YWG G \WG nwG G G GGGGcXXWeGGGGGGGGGO~GGUSGYWW[PSGG GcXXWeGGGUGwG{ltGGGGOtGGwSGX`_ZbGrG . 104 .

G Discussion

G USG X``_bG {SG YWWXPSG G G G OUUG tGGUSG X`^]bG } îGGUSG X`^_bG kT

X i¡GGUSGX``_bGtSGX```PGGG VYGcXXWeGGGGGGiGGGGG GGG GGG¢XXX¤SG¢XXW¤GG¢XWW¤GOGPUGG G G hGGGG SGGGjwvGGGGGG G}wzjG OkGtGG hG{SG sG G{ SG| GGtSGmPUG {GGGGG GGGjwvGGG GUGpGGGSGG GjwvGGGGXWWWG GG GGGUG{GGGGG G G T G G G G G GGGGGGG G OjyzzPUG ~G G G SG G }wzjG G G G G G G G G

X X X jyzzGaG VYcXXWe¢XXX¤SG VYcXXWe¢XXW¤GG VYcXXWe¢XWW¤GG GGGGGO{G

X X p}UZPGGG}wzjGGGGGGGGjyzzGaG VYcXXWe¢XXX¤SGG VYcXXWe¢XXW¤SGG

X VYcXXWe¢XWW¤G G cXWWe¢XXW¤G G G G G G G YaXG O{Gp}UZPUGuGGGG G cXWWe¢XXW¤GGGGGGUG{GGGGGYGOmGp}U`PUG G

X X X G VYcXXWe¢XXX¤G G VYcXXWe¢XXW¤G G VYcXXWe¢XWW¤G GcXWWe¢XXW¤GG

GXG XG XG XG uGG GYG YG YG YG XG

G {Gp}UZGˀGzG GGGGGGGGGGGGUG G G z GG SGGGGGGGGSGGG GGGGGGUGhGGGdZGGGGGUG G

. 105 .

G Discussion

G mGp}U`GTGPGj GGGGGG G}wzjGUGjGG GGGG GGGGXGGYGGGGGGGGGGUGsG G TG SG G G G G WU\G G G G G UG kG GUGzGGG¡GO GPSGGOGPGGGUGzGGaYG GGGGGGGGGGGGGGGGGGPG mG SG lizkG G G G G G G GGOZ[XPGGG GGGOGmGpppUZ[PUGG G G G{G jwvG G G G G XG G G cXXXeG G G TG G bG G GGGGGGGGGGGGGUG[\¶GGGUGcXXWeG GGG TG GGGGGGGGGGGGGGGUG[\¶G GGGGGGUGG G {G jwvG G G G G YG G UG {G cXWWeGGGbGGGG G G G G G G G G G G G G OUG ZW¶PG G G G UG cXXWeG GGGGGGGGGGGGGGGGGGGGGGG GGGUGcXXXeG GGTG GbGGGGGGGGG GGGGGGUG[\¶GGGUG G G {G G XG G G G G G G G G jwvG G G OmG p}UXWSGZ[XPSGGGGGGGGGGjyzzUG{GGGcXWWe¢XXW¤GG GGGGG GGGGGGGjwvUGoSGG{ltGGGG GGGGG GGUGuGGjwvGGGGGGG GGGGUG G G G

. 106 .

G Discussion

G ppUZGˀGtGGGGGGGtYzv[G G GG G kG G G SG G G G G G G G XXG nwG G X[WWjG G G G G G G G G G G G G G G UG hG G SG WWXG G G G G G XWWG G G G G G UG {G G G G G G G UG kG G G G G G G G G G G G G G G G G UG kG G G G G G G G TG G G GGG UGkGG G G jwvG G G G G SG G G G G G G G GGGGGjwvGUG{G GGGGGGG jwvGGGGOGG PGGGGGUGvGGGG G G G VG G G G G G G G G G G G G G G jwvUG {G G G G G G G G G GGGUG{GGTGGGG GGGG GGGGGGG¡GGGG GUGm SGGGGGSGG G G G G G G G G G SG G TG G G GGGGGGGGGGGGGG UG G pppG TG pG G G G G G l˅G G G G G

G¡G

G G vGGGGGGG GGG GGGG GG UG{GGG GGG GGGG GGG GGGGG GGGUGpGGGSGGGGGG jwvGGGG GGGGGG GGGUG G G

G pppUXGwG GGGG aGGGGG GGG GGG

GG G {GGGG GGjwvGGGGGGGGGG G GGXWWOWXWPGSG G GGGGGG GG G GGGGGGY\WGGGOUUGzSGX``]bG{SGX``_PUGXWWOWXWPGGG jwvG¡G GXWWGGGGGSGWXWGGGGGUG{G GG jwvGGGGGGGGGUUGuGGUSGX`^ZbGGGrSGX``\bGiG põGGtSGX``_bGiGpõGGUSGYWWXPGGGGGGGOUUG{GGUSG X```bG~GG{ïSGX```bG{GGUSGYWWWPUGpG GGGGG GGG G G G G G G G GGGXWWGSGUGGGG GSGGGGGGGWXWGSGUUGGGGGUGpGG

. 107 .

G Discussion

G G G G UG {G G G G G G G G G G G G GGGGXWWGGGGG GGGGGGGGG GGGGGXWWGGWXWGUG GG G {GGGGGGGXXGnwGGX[WW¶jSGGGGG GGGZZWGSGGGGGGGGG GGGXWWGG GWWXGGOppUXPUGjwvGGGGGGWWXGGG¡G GGG G WWXG G G G G G G G XWWG G WXWG G G G G G OmG pppU^PUG kGWWXGGGGGGGGTGGGGGG GUG G {G SG G G SG G G G G G XWWG G WWXG G G G G G UG vG kTkphG G G G G G XWWG G WWXG G G G G GUGpGGGGG GwGyGGTGGG G G G G G XWWOWXWPG G WWXOWXWPG UG |G G SG G GGGGG^GnwGOmGp}UZPUG{GGGG GyGGTG GSGGGSGGGGGGGGGGaG ZWWTZ\WGUGpGGGGGGGWWXGG GGGGGG G G UG hG SG WWX¢XXW¤G G G G G G G WWXOWXWPG G WWXOXWWPUG mG G G G G G G G G G G UG jG G G G G G G G G G G G G G G G jwvG G G G GGGOiGpõGGtSGX``_PUGzTGGGGG^WGG SG G G jwvG G G XWWG UG {G jwvG G G G G TG T GGzGhGGG^WGGX\WGGOiGpõGGUSGYWWXPUGjwvGG GGGGGGTGGGGGGTGG GGG{¡GGrGGGGUGX[WGGGO}¡GGUSGYWWZPUG {GGGXWWGGGGGGGX\WGGG G G zGGGGGGG GGGGGGGUGtG

GTGGOwyltSGphzwSGhrXZ\GGhrZWZPGG¡ GGwGGO}woPG

GGGGO}w}PGOmGp}UXWPSGGGGG GGGSGGG

GGGZ\WGGOtGGrSGX``]PUGzGGOhrXZ\GGZWZPGGG}w}G

GGG}woGGZ\WGUG{GzGGG GGG GG

GGGGGGY\WGUGmG¡ TGzGSG¡ GGO}zoPG

GGGG GG GGO}z}PGGGGGY\WGUGiGZWWGG

G [WWG G }z}GGGG}zoSGG GGGGGGGGGUG oT GGGGGGzGGGOlGGkSGX``_PGGGGG GTGGG GGGOnGGUSGYWWZPGGGGGG

G G ¡G G }zoe}z}G G Y\WG G UG hG G SG G G G G GGG GGGGGZWWGGUGzGGGGGGG G

G}z}GeG}zoGGGGGGGGGGGwGGwTjGGOlG GkSGX``_PUGG

. 108 .

G Discussion

G mGp}UXWGˀGlGGGGGGGG GOPGGGGG GG GOPGGGTG GGO GGqUwUGtPG GG G yGGGGGGwGGpGGGGGG GG

G G G G G G Y\WTZWWG G G }zoG G G G }z}G OtSG X`_\bG jG G sïîSG X`__bG uG G m SG X`_`bG sïðGGUSG X``_PUG h G G TG G G GGGwGGwGG GGGG GGGGX]WGGGG GOn GGUSGX``]UGzrzGGGGGGGGG SGGGG GGGGG¡GGGGGGGGG GG GG˺G YGOzSGX``]PGGGzrzGGGGGGYWWTY\WGGGGUG G m SG G G G SG G sG G OsSG X`\\PSG G G GGGYYWGG GGGGOSGGSGzzGGGwGG zG PG G G UG {G G G G G G G G G G G GG GGGGGGG¡GGGGGGG GGGOyGGqSGX``XPGGGGGGGGG G G G G SG G G G jwvG G SG G G G G G G G G SG G G G G jwvG OrSGX``YPUGoSGGGGG G G G G G G G G G XXnwG G X[WW¶jG G G G G T SG TG G OsGGUSG YWWZbG sGGUSG YWW[PG G G G G TG G O¥YWTZWG »PSG G G G G G G G G G GGGGGZWWGGUG GG G {G TG G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G UG {G G G G G G kG tGGhG{GOsGG{ SG| GGtSGmPUGzG GOmGp}UXXPGGGGGGG GGO]ZLGSGX^LGSGYWLG

. 109 .

G Discussion

PGGGGGXXU_GnwGGGGXZ_WG¶jSGGGZ\\GGSGG GGGGGGGGOhGGUSGX``^PSG TGGOjG GUSGX``^PSGGOjGGiSGX``_PUGmGGjwvSGGGjwvGGGGppUXUZGG GGGGGGGGG GGWWXGGGGGGGOmG p}U\PUGnGGGGjwvSGGGGGG}wzjGGGGG TG TG G G G G G jwvG G G G G OtGGUSG YWW[PUG~GGGGGGGGGGGTGGGGGG UGoSGGGGGjwvGGGGGGGGGGGG G OiGGUSG YWWYPSG G G G G G G G G G G G OtGGUSGYWWWPUGG G pGmGp}UXYSGGGGGG GG aG WU`LG G XU`LG UG{GGGGGGGGGGGGUG{GGG GGGGGGGOzkPGG G UG {G G G G G G

¡GGGG¡GGG}wGGGGG GGwGG G G G G G G ¡G UG zG G ¡G G G ¡G G G G G G ¡G G G G G G G G G G G G G G GGGGGGGGGGUGmGGGGGGG

GzGGGGGGGGUGoSGG¡GSG}z}GGGG}zoUGG G

G mG p}UXXG ˀG tG TG G G G G G G G SGGGGGGGGGG]ZLGGGSGX^LGG GGGYWLGGGGGXXU_GnwSGXZ_W¶jGGGGGGXUGzGG G UG sG G TG SG G G WUXG VG G G G SGWUWYGVGGGGGGWU\LG GG G G G G UG tG wG G G zG G G G WU`LG G XU`LG UG{GGG GGGUG G G hG G G G G G G G G G G G G G G OtSG X`_\bG jG G sïîSG X`__bG uG G m SG X`_`bG tG G rSG X``]bG lG G kSG X``_bG sïðGGUSG X``_bG nGGUSG YWWZPG G G G G GOcYLPGGY\WGGGwGGzGUG{GGzTG SGGSGGXU`LSG GGGGGG GGwGGGGGGGOtGGrSGX``]PUG h G G G G G G OG G G G G G PG G G G G ¡G UG mG G G G SG G G G G G wG G . 110 .

G Discussion

GGG¡GGGGG¡ GGzGG}z}GGGG}zoSGG G G G G G G G G G G ZWWG UG pG SG G GGGGGG UG GG {GSGGG GGWWXGGGGGGGG GG GGGGGGGG GGGGGGZWWGUGpGGGG G G G G G G G wG G zG G G G G G UG {G GGGGGGGGG GGGGGY\WGGG G G G G G G G G G G G G G [WWG G UG {G GGGGGGlGGGG GGGGG¡GGG G G G G G G G G SG G G G G G G OG GGGOUUGrSGX``YbGrGGUSGX``ZPPGGGGjwvGGG GG GGTGGG GWWXGGGGGGUGpSGG GGXWWGGWWXGGGGG GGGGGGGwGGzGG G G G G G G G G G G G G G ¡G G GGGGGG GGTGGGGSGGGl˅GUG G

G pppUYGTGwGTGG GGGGGGGG¡G

GG G hGGGGppUYUXUXSGGGGjwvGG GGGGGUGuGGG jwvG G G G G }wzjG G G G G G UG oSG G G G G G GGGGGjwvaGGGGXWWGGGGGGGWWXGGG GGGGUG{GGGGSGGGGSGGGGG G jwvUG hG G G G G G G G G G G G G G G G¡GGGGGGGUG G G hGGSGGTGGGGGOmGp}UXYPGGGG G G XWWLG G OmG p}U^SG G YPG G G G G G ¡G G G G GO]WLG GOmGp}U^GGYPGGG[WLGPGGGGGGG GGG GOGGUSGX``^bGzGGUSGX``_PGGG TGGOjGG USGX``^PUGhGGGGSGGGGGjwvGG G GGOtGGUSGYWW[PUG tSGGG G GGGGGGGGGGG UG{G GGGGmGp}UXYSGGGG GGGGGGGG G G G G G XWWLG G G G G G]WLG GTG[WLGGGG G G UG zG TG G G G G G G SG GGGGGG¡GSGGGUGG G pG mG p}UXYSG G G G G G G G SG YU[LG G XLSG G G G G G G UG jG G G G G G G G G G G G G G G SG G G G G G G G G G G G G G G UG zG G ¡G G G ¡G G GGGG¡GGGGGGGGOzkPGGGG GGG . 111 .

G Discussion

G G G G G G G G G G G G G UG hG G G GGGG GGGGGGGGGGGGGG GGGGOuzwPUGzGG¡G GG¡G G G G G G GGGGGGG¡UGoSGGG¡GGGGGG GGOzXPG GG GGGGGGG GGGGGG GGSGGG¡GGGGGGGGG GGGGG GGGUG{SGGGGGG G G G G G G GGGGGGGGG¡SGGGGGOzXPSGG G¡GGGGGGGSG GGG¡G SGGGG GOzYPGGG GOXLPUGpGSGGGGGGGSGG G ¡G G G G G G OzXPG G G ¡G bG G G ¡G G G G OzYPG G G ¡G UG pG G G G G G G GGG GjwvGGGjyzzGGOppUYUXUXGGmGp}U^PSGGG GG TGGGG GGGGGGGGGUG G

mG p}UXYG ˀG tG TG G G G G G G G G GGGGGG GXXWLGG GG GGGG]WLGG G G G [WLG G G UG zG G G XUG zG G G UG sG G TG SG G G WUXG VG G G G SG WUWYG VG GGGGGWU\LG GGGGGG UG{GGG GGGUG G G {G TG G G G G G G G G G G GG SGGGGGGGWXWGGGGGGjwvG OmGp}UXZPUG{GGGGGGzZY\[GOGGGGGGGGG T GPUGlGGGGGGGG GjwvGG G UG G . 112 .

G Discussion

G mGp}UXZG ˀG{TGGGGG GGGGGG G jwvG G zZ[\[G G G X]U\G nwG G X[WW¶jUG zG G G UG sG G TG SG G G WUXG VG G G G SG WUWYG VG G G G G G WU\LG GGGGGG UG{GGGGGGUG G G jG G G G G G G G G mG p}UXYSG G G G G GGGUG{GGGGGGwGGGGGGGG UG[W¶GGGGGGGGUGpGGSG¡GGGGGGG G UG zG G G G G G SG G G G G ¡ T ¡GGUG} GG GGG G TGGUG{SGG G G jwvG G G G G G T G G G jwvG G G GGwGGUGG GG G jGGGGGGGGGG GG GG¡GGGGG GGGGGGG¡UGpSG G I¡ISG UUSG G G G G G G G G ¡ TG

GGOwoPGGG¡ T¡GGGOzoPGOtGGrSGX``]PSGG

G G G ¡G G G T¡G G G Oz}PG G G G G G G G

¡ T¡GGGOzoPGO{GGGoSGYWWYPUGh¡G GGz}TG G G G G OXLPG G G G G G G GsGGGOGGYLPUGoG G G G G G G G SG G jwvGGGGGGG G GGGGUGpGSG GGGG¡G GGG G GGGGsGGGOqUG{SGGPUGtG G G G G G G G G G G G G G G G G G G G ¡UG m SG G ¡ TG G G ¡G G G G G G G G G TGGGSGGGzrzUGjGGGGGGGG GGG¡G GGGGGGGGGGG¡G G zrzG G G G wG G ¡G OmG G mSG X``]PUG pSG G G G SGGG GGGGGzrzGGG G G G SG G G G G G G G UG }G SG G G G SG G G G G G ¡G G G G G UG kG ¡G G G G G G ¡G G G GG GGGGGGGGG¡GGGG G G GGGGGGGGUGzGG GGGGG SG G G G T G G G G GG GGGGG GGGGGG GGGGO{GGUSGX``\PUG{G . 113 .

G Discussion

GGGGGGGGGGG GGGGGGG GGGGG¡SGGGGG GGG GGG]^WGGUG sG G G G G G G G G G G ¡G G G G G G GGGGGGGGGGG¡GOiGGtSGX``_PGG GG GGGGGGG GGGGGG ¡SGGqSGy SGGp¡TiSGGGG¡GOnGGrSGYWWZPUG G

G pppUZGTGjG

GG G {G¡SGTGjwvGGGGGTG GGWWXGG

X GG GG GGGGXWWGG VYGcXXXeGGGGGGGG GGGGGGGGGG¡UGjGGGG GG GGGGGG GGZWWGUGkGGG GG G G G G G G G G G G jwvG G G G G GGGGGGGGG¡UGhGGjwvGGGGGG GGGGGGGG¡GG UG G G G G G G G G G G G G G G G G G G G G G G G G . 114 .

Conclusions and open questions

In this study, the mechanical properties of forsterite, wadsleyite and ringwoodite have been studied with a view to understand development of their crystallographic preferred orientations. These data are important to decipher our observations of seismic anisotropy which are one of the few relics of past convection in the Earth’s mantle.

Various points have been highlighted from this study:

1) The D-DIA offers a new possibility to perform deformation experiments up to 10 GPa with capabilities comparable to standard deformation experiments at low pressure (control on strain rate, strain, in-situ measurement of stress and strain). The deviatoric stress is controlled independently from pressure and different kinds of test can be performed. Moreover, the damage introduces during the cold compression can be annealed before deformation. However, for higher pressures, the Kawai-type multianvil is still the only tool to deform millimeter-size samples up to 26 GPa at high temperature. We have seen in this study that, taking advantage of the 5000t press available at the Bayerisches Geoinstitut, shear deformation experiments have been performed at 22 GPa. We show that this possibility of exploring the mechanical behavior of Earth’s minerals at conditions corresponding to depths down to ca. 700 km is not yet a routine. In particular, we show that detailed microstructural characterizations are necessary to check for the active mechanisms.

2) One of the salient information brought from this study is the occurrence of a pressure-induced change in the deformation mechanisms of forsterite. With pressure increase, [001] glide takes over [100] glide as dominant deformation mechanism. More work is needed to have a more precise understanding on the sensitivity of the various slip systems (including the actual planes) to this pressure effect. We also need to have more information on the transition pressure and on whether this transition is gradual (as suggested by our D-DIA experiments) or not.

3) The change of dominant slip system of olivine is determinant to explain the weak seismic anisotropy observed in the lowermost upper mantle. VPSC simulations and calculation of seismic anisotropy have shown that the variation of the P and S waves anisotropy patterns are fully compatible with the transition from [100] to [001] glide.

4) Deformation experiments on wadsleyite have shown that back-transformation occurs at the beginning of the deformation experiment. The influence of this phase transformation on the CPO development is uncertain. However, the comparison of experimental CPO with those from VPSC simulations allows to extract robust features characterized by the alignment of [100] axes parallel to the shear direction and by the alignment of [001] axes normal to the shear plane. More experimental work on wadsleyite is necessary to constrain the alignment of [010] axes.

. 117 .

Conclusions and open questions

5) The comparison between seismic anisotropy observed in the transition zone and the seismic properties calculated from wadsleyite CPO is compatible with a dominant tangential flow in the upper part of the transition zone.

6) The influence of the phase transformation from forsterite to wadsleyite on the rheology has been studied more precisely from dedicate experiments. Wadsleyite grains nucleate as incoherent precipitates either inside the grains or at the grain boundaries of forsterite with no influence of the defect microstructure of deforming forsterite on wadsleyite nucleation. The phase transition does not seem to strongly enhance the plasticity of the aggregate (no marked flattening or elongation of wadsleyite grains for instance). Moreover, the phase transition does not induce significant grain size reduction that could affect rheology.

7) The deformation experiments on ringwoodite have shown that the back-transformation observed in wadsleyite is not systematic. The CPO observed in ringwoodite cannot be simulated with VPSC taking

1 into account known /2<110> slip systems only. The CPO can only be reproduced numerically if <100>{110} slip systems (that have never been reported) are introduced in the simulation. Our preliminary TEM observations on deformed ringwoodite cannot support this assumption (nor can we rule it out…). More work is needed on ringwoodite to link microscopic deformation mechanisms and CPO before those are used to model seismic anisotropy

To conclude, we show that although they are still very challenging, deformation experiments under high pressure and high temperature represent one of the most exciting issues in minerals physics. Impressive progresses have been made in the last years. No doubt that many more must be awaited in the next ones.

. 118 .

Appendix

In this appendix are presented the strain calculation from the rotation of the strain marker as well as the complementary techniques used through collaborations with other groups:

- X-ray diffraction peak broadening techniques (T.Ungár and K. Nyilas from the Department of General Physics, University Budapest, Hungary).

- ViscoPlastic Self Consistent modelling (Andrea Tommasi and David Mainprice from the Laboratoire de Tectonophysique, University of Montpellier, France).

Appendix

hGpG

zGGGGGGG

G G {GGGGGGGGGGGGGGGGGGUG{G GGGGGGDG|[\¶GGGGGGGG UG G

G mGhUXGˀGn GGGGGGGGUG G {G G G G G G G G G G G G G G jG G OXSG YSG ZPG OmGhUXPUGpGGSGGGGGGGOmGhUYPUG G

G mGhUYGˀGyGGGGGGGGGGGG G pGGGGmGhUYGGGGGUGv GGGGG¡aG T ! 0

E 21 0 G

wu1 E 21 tgT a with a ! 0 wx2

G G G . 121 . G Appendix

{GGGGaG §0 a 0· ¨ ¸ E ¨0 0 0¸ G ¨ ¸ ©0 0 0¹ {GGGGGGG GGGGGGOG GGG GT GaG § 0 a 2 0· ¨ ¸ H ¨ a 2 0 0¸ G ¨ ¸ © 0 0 0¹ G hG G G G G SG G G G G G G G G G D' G G G OXPUG {G

GGGGGOUUG D D' PGGGGGGGGOX˅SGY˅SGZ˅PGGGG

GGOX˅PGGGGGGGOmGhUXPUG{GGGGD D' GGG

GGG E1'2' GOmGhUZPUG G

G mGhUZGˀGzTGGGGjGGOX˅SGYSGZ˅PUG G

{GGGGGGGGGGGHXYGGGGGGaG

E1'2' tg D'D G

1' /2 ! 2'/1! E21

sinD sinD E21 G sin2 D a 2 sin D 2H12 G {GGGGGGGGTGG aG G tg D'D J 2 u H G 12 2sin2 D

. 122 . G Appendix

hGppG T G G G G G G G G G G GG

G hppUXGTGT GGGG G

G kG G G G G TG G G G G G G G G G iG UG jG G G G G G ~G MG oG OX`\ZPG G ~GMGhGOX`\WPGGGG GGGGGGGGGG

GGO|çGGiï SGX``]PUG{GGSG C SGGGGGG hkl GGGG

SGGiGGGGGGSG b GG l SGGGGGGG GG

GG GGG{ltUG C GGGGGGGG UG{GGGGG GGGGGGGG GGGT GGGGGG G GO|çGGUSGX```bG|çGG{ SGX```bG|çGGUSGYWWXPUGoGGGG G G G G UG {G G G G G G {ltG G G G G GGGGGGGGGG GGGGGGGGG G SG UUG XWX_GTYUG iG G G ~ToG G ~ThG G O|çGGUSG YWWXPG G G G G OyçGGUSG YWWXbG yçGGUSG YWW[PG G G GGGGGGGGGGGGGGUG G {GGGGGGmGpppUXGOTPUGj SGGGGG GGGGGUG{GGGGGGGGGGG G G G G G G G UG pG G G G G G G G G GGaG¢WYX¤SG¢XWX¤SG¢WWY¤SG¢XZW¤SG¢YYW¤UGtGjrDGGGGG G G OuG myG \YXPSG G G [W}SG ^WG hG G UG{GGGGGGG G G WUXWU_UG {G G G G G GGGGGGG G OvlkG \WG iSG tPG G G G G X[WG G GUG{GGGGG GGG_WGPUG{GGGGGGGGG GTG GGT GGGG¡GGGGGGGGGGT GG GGUGG G

G hppUYGTGlGGG G

G zG G G T G TG G G G G G TG G G G Om~otPGGGGGGGmGGGG~ThGGGG

2 GGGGGGGSG g GG g UGpGGGG GGGG

SG C SG SG G G G G G G G G G G G G G G G O~SG X`^WbG |çG G iï SG X``]bG |çGGUSG YWWXPUG pG G G G G G GGGGGGGGGGGGGGGGGG

G hkl GGGGGGGGGGGO|çGG{ SGX```PUGzGG GGGGG SGGGGGGGUGmGGGG

. 123 . G Appendix

G G G G G G G G G G G G G O|çG G { SGX```bGkGG|SGYWWYPUGmGG SGGGGGaG G

§ § 2 2 2 2 ·· ¨ 4 4 4 2 2 2 2 2 2 ¨§ h k l · ¸¸ C D E u h a1k a2l a3h k a4h l a5l k / ¨ ¸ G ¨ ¨¨ a2 b2 c2 ¸ ¸¸ © ©© ¹ ¹¹ G

G a S b GG c GGGGSG h SG k GG l GGGtGGG ai SGdXT\SGGG

GGGGG GGGGGGG UG D GG E GG G

GGG GGGGG C SGGGGGG hkl GGGGO|çG GUSGYWWXPUG{GGGGGG GGG G GGG G G G G G OrG G r¡SG X`__bG |çG G { SG X```PUG {G G

GGG ai GGGGGGG GVGGGSGSG

G GUGpGGGSGG ai GGGGG GGGm~otGGG

GGGGGGG~ToGSGOUUSGlGO`PGG|çGGUSOYWWXPPUG mG G ai G SG G SG G G G G G SG C *G G UG hG G

G G G O~SG X`^WbG |çGGUSG YWWXPG G G G G G G G G

GGGGaGc C e#WU[UG{GGGG C *GGGGG UG~GG

GGG C GGGGGGG GGGGGG Ot~wPG G G G G G G G G G G G ¡G G G SG GOyçGGUSGYWWXPUG G G G G G G G G G G G

. 124 . G Appendix

G hGpppG j GGGaG}wGzGjGO}wzjPGG GG

G j G G G G G G G G G G G G T G G O}wzjPG OtGGUSG X`_^PSG G G G G G G G sG G{ïGOX``ZPUG{GGGGlGzGG~GGTGOUUSG~GGUSGX``XPG GGGGGGGGSGGGGGGG G G G G G G G G UG pG G G G G G G G G OjGGUSG X``]PSG G O{GGUSG YWWWPSG GOiGGUSGYWWYPGGGOtGGUSGYWW[PUGpGGGGGGG G SG G G G G G OzSG X`Y_PG G G O{ SG X`Z_PG GGSGG}wzjGGGGGGGGGGGGGG G G UG zG G G G G G G G G G GUG G hG G G SG G G G G G G bG G G GGGG GGG G ¡GGGGGUG{GG

GGGG G s GGGGGGGGG s G GGTGaG

s s s n s n . . . § rij s · §W r · ij J J ¨ ¸ J ¨ ¸ G s 0 ¨W s ¸ 0 ¨ W s ¸ © 0 ¹ © 0 ¹ . TX s s G J 0 GGGGGSGGGX SGG SGW r SGW 0 GGG GGGSG

GGGSGGGjyzzGGG G s SGGGGGGGG

s GG GGzGG r UGG

. G {GGGGGGGGGGOS H PGGGSGGGG

G G G G G G O 6SG D PUG {G ˈXTˉG G OtGGUSG X`_^bG sGG{ïSGX``ZPGGGGGG}wzjGbGGGG GGGGGGUGpGGGGGGGG G G GGGGGGGGGGGGGG GGOoltPSGGGGGGGGGGUG{GGaG . ~ H ij D DM S 6 G ij ijkl ijkl kl

G M˜ GGGGGGDGGGGGG¡GGGGGG G oltUG DGdGWG G G G G G G OG PSDGdGXG G G G T G G OG G G G G G G G G PG DGdG G G G GGGOGPUGGG G . 125 . G Appendix

G G {GG GGG GGGGG GGGsbGG GGGOGG GG~dWU`PGGaG ª0 1 0º ª0 1 0 º « » « » L 0 0 0 GGG L 0 .237 0 G « » « » ¬«0 0 0¼» ¬«0 0 0.237¼» SGGGGSG dW SGGGGGGGGWUWY\GGGGUG {GGGGGaG

H D W dW G eq ³ eq GG}GtGGGGaG

Deq 2 / 3Dij Dij G

GG G {G GGGGGGGG GGGSGGjyzzGGG SGGGGSGGGGGG G G G G G oltSG G GGGDUG{GGGGG GGGjwvGGG GUGG G G G G G G G G G G G G G G G G G G G G G G G G

. 126 . G

References

Abramson, E. H., M. Brown, L. J. Slutsky and J. Zaug (1997). The elastic constants of San Carlos olivine up to 17 GPa. J. Geophys. Res. 102: 12,252-12,263.

Adams, B. L., S. I. Wright and K. Kunze (1992). Orientation imaging: The emergence of a new microscopy. Metallurgical Transactions A 24A(819-831).

Agee (1998). Phase transformations and seismic structure in the upper mantle and transition zone. in Ultrahigh-pressure mineralogy: Physics and chemistry of the Earth's deep interior. R. J. Hemley. Washington, D.C. 37: 165-203.

Bai, Q. and D. L. Kohlstedt (1992a). High-temperature creep of olivine single crystals III. Mechanical results for unbuffered samples and creep mechanisms. Philosophical Magazine A 66(6): 1149-1181.

Bai, Q. and D. L. Kohlstedt (1992b). High-temperature creep of olivine single crystals, 2. Dislocation structures. Tectonophysics 206: 1-29.

Bai, Q. and D. L. Kohlstedt (1993). Effects of chemical environment on the solubility and incorporation mechanism for hydrogen in olivine. Phys. Chem. Miner. 19: 460-471.

Bai, Q., S. J. Mackwell and D. L. Kohlstedt (1991). High-temperature creep of olivine single crystals 1. Mechanical results for buffered samples. Journal of Geophysical Research 96(B2): 2441-2463.

Bascou, J., A. Tommasi and D. Mainprice (2002). Plastic deformation and development of clinopyroxene lattice preferred orientations in eclogites. J. Struct. Geol. 24(8): 1357-1368.

Ben Ismaïl, W., G. Barruol and D. Mainprice (2001). The Kaapvaal craton seismic anisotropy: petrophysical analyses of upper mantle kimberlite nodules. Geophysical Research Letters 28(13): 2497-2500.

Ben Ismaïl, W. and D. Mainprice (1998). An olivine fabric database: an overview of upper mantle fabrics and seismic anisotropy. Tectonophysics 296: 145-157.

Binns, R. A., R. J. David and S. J. B. Reed (1969). Ringwoodite, natural (Mg,Fe)2SiO4 spinel in the Tenham meterorite. Nature 221: 943.

Blacic, J. D. and J. M. Christie (1973). Dislocation substructure in experimentally deformed olivine. Contrib. Mineral. Petrol. 42: 141-146.

Brearley, A. J. and D. C. Rubie (1994). Transformation mechanisms of San Carlos olivine to (Mg,Fe)2SiO4 E- phase under subduction zone conditions. Physics of the Earth and Planetary Interiors 86: 45-67.

Brearley, A. J., D. C. Rubie and E. Ito (1992). Mechanisms of the transformations between the D, E and J polymorphs of Mg2SiO4 at 15 GPa. Physics and Chemistry of Minerals 18: 343-358.

Brunet, D. and P. Machetel (1998). Large-scale tectonic features induced by mantle avalanches with phase, temperature, and pressure lateral variations of viscosity. J Geophys Res Solid Earth 103: 4929-4945.

Bussod, G. Y., T. Katsura and D. C. Rubie (1993). The large volume multi-anvil press as a high P-T deformation apparatus. Pageoph 141(1): 142-161.

Bystricky, M., K. Kunze, L. Burlini and J.-P. Burg (2000). High shear strain of olivine aggregates: rheological and seismic consequences. Science 290: 1564-1567.

. 129 .

References

Cara, M. and J. L. Lévèque (1988). Anisotropy of the asthenosphere: The higher mode data of the Pacific revisited. Geophys. Res. Lett. 15: 205-508.

Carter, N. L. and H. G. Ave'lallemant (1970). High temperature flow of dunite and peridotite. Geological Society of America Bulletin 81: 2181-2202.

Castelnau, O., M. Drakopoulos, C. Schroer, I. Snigireva, A. Snigirev and T. Ungár (2001). Dislocation density analysis in single grains of steel by x-ray scanning microdiffraction. Nuclear Instruments and Methods in Physics Research A467-468: 1245-1248.

Castelnau, O., P. Duval, R. A. Lebensohn and G. R. Canova (1996). Viscoplastic modelling of texture development in polycrystalline ice with a self-consistent approach: comparison with bound estimates. J. Geophys. Res. 101(B6): 13851-13868.

Chai, M., J. M. Brown and L. J. Slutsky (1997). The elastic constants of a pyrope-grossular-almandine garnet to 20 GPa. Geophys. Res. Lett. 24(5): 523-526.

Chen, J., L. Li, D. J. Weidner and M. Vaughan (2004). Deformation experiments using synchrotron X-rays: in situ stress and strain measurements at high pressure and temperature. Physics of the Earth and Planetary Interiors 143-144: 347-356.

Chen, J. H., T. Inoue, D. J. Weidner, Y. J. Wu and M. T. Vaughan (1998). Strength and water weakening of mantle minerals, olivine, wadsleyite and ringwoodite. Geophysical Research Letters 25: 50.

Chiang, Y. and W. D. Kingery (1989). Grain boundary migration in nonstoichiometric solid solution of magnesium aluminate spinel: I, Grain growth studies. J. Am. Ceram. Soc 72: 271.

Chopra, P. N. and M. S. Paterson (1981). The Experimental Deformation of Dunite. Tectonophysics 78: 453- 473.

Chopra, P. N. and M. S. Paterson (1984). The role of water in the deformation of dunite. J Geophys Res Solid Earth 89: 7861-7876.

Christian, J. W. and V. Vitek (1970). Dislocations and staking faults. Rep. Prog. Phys. 33: 307-411.

Coleman, L. C. (1977). Ringwoodite and majorite in the Catherwood meteorite. Canadian Mineralogist 15: 97- 101.

Collins, M. D. and J. M. Brown (1998). Elasticity of an upper mantle clinopyroxene. Phys. Chem. Minerals 26: 7-13.

Cordier, P., D. Mainprice and J. L. Mosenfelder (2004). Mechanical instability near the stishovite-CaCl2 phase transition: implication for crystal preferred orientations and seismic properties. European Journal of Mineralogy 16: 387-399.

Cordier, P. and D. C. Rubie (2001). Plastic deformation of minerals under extreme pressure using a multi-anvil apparatus. Materials Sciences and Engineering A309-310: 38-43.

Cordier, P., E. Thurel and J. Rabier (2002). Stress determination in multianvil deformation experiments based on dislocation curvatures measurements: Application to wadsleyite and ringwoodite. Geophysical Research Letters 29(9): 101029-101033.

. 130 .

References

Darot, M. (1980). Déformation expérimentale de l'olivine et de la forsterite. PhD Dissertation, Université de Nantes.

Darot, M. and Y. Gueguen (1981). High-temperature creep of forsterite single crystals. Journal of Geophysical Research 86(B7): 6219-6234.

Dingley, D. (1984). Diffraction from sub-micron areas using electron backscattering in a scanning electron microscope,. Scanning Electron Microscopy II: 569-575.

Dragomir, I. C. and T. Ungar (2002). Contrast factors of dislocations in the hexagonal crystal system. J. Appl. Cryst. 35: 556-564.

Dunand, D. C., C. Schuh and D. L. Goldsby (2001). Pressure-induced transformation plasticity of H2O ice. Physical Review Letters 86(4): 668-671.

Dupas, C., N. Doukhan, J. C. Doukhan, H. W. Green II and Y. T.E. (1994). Analytical electron microscopy of a synthetic peridotite experimentally deformed in the E olivine stability field. Phys. Chem. Minerals 25: 501-514.

Dupas-Bruzek, C., T. G. Sharp, D. C. Rubie and W. B. Durham (1998a). Mechanisms of transformation and

deformation in Mg1.8Fe0.2SiO4 olivine and wadsleyite under non-hydrostatic stress. Physics of the Earth and Planetary Interiors 108: 33-48.

Dupas-Bruzek, C., T. N. Tingle and H. W. Green II (1998b). The rheology of olivine and spinel magnesium

germanate (Mg2GeO4): TEM study of the defect microstructures. Phys. Chem. Minerals 25: 501-514.

Durham, W. B. (1975). Plastic flow of single crystals of olivine. PhD dissertation, M.I.T, Cambridge, Massachusetts.

Durham, W. B. and C. Goetze (1977a). A comparison of the creep properties of pure forsterite and iron- bearing olivine. Tectonophysics 40: T15-T18.

Durham, W. B. and C. Goetze (1977b). Plastic flow of oriented single crystals of olivine 1. Mechanical data. Journal of Geophysical Research 82(36): 5737-5753.

Durham, W. B., D. J. Weidner, S.-i. Karato and Y. Wang (2002). New developments in deformation experiments at high pressure. in Plastic deformation of minerals and rocks. S.-i. Karato and H.-R. Wenk. Washington, D.C., MSA. 51: 21-49.

Durinck, J., A. Legris and P. Cordier (in press). Influence of the crystal chemistry on ideal shear strength in forsterite: First-principle calculation. American Mineralogist.

Dziewonski, A. M. and D. L. Anderson (1981). Preliminary reference Earth model. Physics of the Earth and Planetary Interiors 25: 297-356.

Ekstrom, G. and A. M. Diewonski (1998). The unique anisotropy of the Pacific upper mantle. Nature 394: 168- 172.

Fouch, M. J. and K. M. Fisher (1996). Mantle anisotropy beneath northwest Pacific subduction zones. J. Geophys. Res. 101: 15987-16002.

. 131 .

References

Frese, K., V. Trommsdorff and K. Kunze (2003). Olivine [001] normal to foliation: lattice preferred orientation

in prograde garnet peridotite formed at high H2O activity, Cima di Gagnone (Central Alps). Contrib. Mineral Petrol. 145: 75-86.

Friedel, F. (1967). Dislocations. Oxford, Pergamon.

Frost, D. J., B. T. Poe, R. G. Tronnes, C. Liebske, A. Duba and D. C. Rubie (2004). A new large-volume multianvil system. Physics of the Earth and Planetary Interiors.

Fujimura, A., S. Endo, M. Kato and M. Kumazawa (1981). Preferred orientation ofE-Mn2GeO4.

Gaherty, J. B., T. H. Jordan and L. S. Gee (1996). Seismic structure of the upper mantle in the central Pacific corridor. J. Geophys. Res. 101: 22,291-22,309.

Getting, I. C. (1998). New determination of the bismuth I-II equilibrium pressure: A proposed modification to the practical pressure scale. Metrologia 35: 119-132.

Gillet, P., I. Daniel and F. Guyot (1997). Anharmonicity of Mg2SiO4-forsterite measured from the volume dependence of the Raman spectrum. European Journal of Mineralogy(9): 255-262.

Gleason, G. C. and J. Tullis (1993). Improving flow laws and piezometers for quartz and feldspar aggregates. Geophysical Research Letters 20: 20,2111-20,2114.

Gorbatov, A. and B. L. N. Kennet (2003). Joint bulk-sound and shear tomography for Western Pacific subduction zones. Earth Planet. Sci. Lett. 210: 527-543.

Green, D. H. and A. E. Ringwood (1963). Mineral assemblages in a model mantle composition. J Geophys Res Solid Earth 68: 937-945.

Green II, H. W. and R. S. Borch (1989). A new molten salt cell for precision stress measurement at high pressure. European Journal of Mineralogy 1: 213-219.

Griggs, D. T., F. J. Turner and H. C. Heard (1960). Deformation of rock at 500°C and 800°C. Men. Geol. Soc. Am. 79: 39-104.

Gueguen, Y. (1979a). Dislocations in naturally deformed terrestrial olivine: classification, interpretation, applications. Bulletin de minéralogie 102: 178-183.

Gueguen, Y. (1979b). Les dislocations dans l'olivine des péridotites. PhD Dissertation, Université de Nantes.

Gung, Y., M. Panning and B. Romanowicz (2003). Global anisotropy and the thickness of continents. Nature 422: 707-711.

Guyot, F., G. D. Gwamnesia and R. C. Liebermann (1991). An olivine to beta phase transformation mechanism

in Mg2SiO4.

Heidelbach, F., I. Stretton, F. Langenhorst and S. J. Mackwell (2003). Fabric evolution during high shear strain

deformation of magnesiowüstite (Mg0.8Fe0.2O). Journal of Geophysical Research 108(B3): 2154-2168.

Hinds, W. C. (1982). Aerosol Technology: Properties, behavior and measurement of airbone particles. NewYork, Wiley. . 132 .

References

Hirth, G. and D. L. Kohlstedt (1995a). Experimental constraints on the dynamics of the partially molten upper mantle. Diffusion in the diffusion creep regime. J. Geophys. Res. 100: 1981-2001.

Hirth, G. and D. L. Kohlstedt (1995b). Experimental constraints on the dynamics of the partially molten upper mantle. Diffusion in the dislocation creep regime. J. Geophys. Res. 100: 15441-15449.

Horiuchi, H. and H. Sawamoto (1981). E-Mg2SiO4: single-crystal X-ray diffraction study. American Mineralogist 66(568-575).

Ito, E., E. Takahashi and Y. Matsui (1984). The mineralogy and chemistry of the lower mantle: An implication

of the ultrahigh pressure phase relations in the systeme MgO-FeO-SiO2. Earth and Planetary Science Letters 67: 238-248.

Jaoul, O., M. Michaut, Y. Gueguen and B. Ricoult (1979). Decorated dislocations in forsterite. Phys. Chem. Miner. 5: 15-19.

Johnson, C. A., R. C. Bradt and J. H. Hoke (1975). Transformational plasticity in Bi2O3. Journal of American Ceramic Society 58(1-2): 37-40.

Joòs, B. and M. S. Duesbery (1997). The Peierls stress of dislocations: an analytic formula. Physical Review Letters 78: 266-269.

Jung, H. and S.-i. Karato (2001). Water-induced fabric transitions in olivine. Science 293: 1460-1463.

Karato, S., M. S. Paterson and J. D. FitzGerald (1986). Rheology of synthetic olivine aggregates: influence of grain size and water. J. Geophys. Res. 91: 8151-8176.

Karato, S.-i. (1992). On the Lehmann discontinuity. Geophysical Research Letters 19(22): 2255-2258.

Karato, S.-i. (1995). Phase transformations and rheological properties of the mantle minerals. in Earth's deep interior. D. Crossley and A. M. Soward. New York, Gordan and Breach:: 223-272.

Karato, S.-i., C. Dupas-Bruzek and D. C. Rubie (1998). Plastic deformation of silicate spinel under the transition-zone conditions of the Earth's mantle. Nature 395: 266-269.

Karato, S.-i. and H. Jung (2003). Effect of the pressure on high-temperature dislocation creep in olivine. Philosophical Magazine 83(3): 401-414.

Karato, S.-i. and D. C. Rubie (1997). Toward an experimental study of deep mantle rheology: A new multianvil sample assembly for deformation studies under high pressures and temperature. Journal of Geophysical Research 102(B9): 20111-20122.

Karato, S.-i., D. C. Rubie and H. Yan (1993). Dislocation recovery in olivine under deep upper mantle conditions: implications for creep and diffusion. Journal of Geophysical Research 98(B6): 9761-9768.

Kashima, K., I. Sunagawa and K. Sumino (1982). Plastic deformation of olivine single crystals. Science Report of Tohoku University series III 15: 218-407.

Kavner, A. (2003). Elasticity and strength of hydrous ringwoodite at high pressure. Earth and Planetary Science Letters 6783: 1-10.

. 133 .

References

Kavner, A. and T. S. Duffy (2001). Strength and elasticity of ringwoodite at upper mantle pressures. Geophysical Research Letters 28(14): 2691-2694.

Kawai, N. and S. Endo (1970). The generation of ultrahigh hydrostatic pressures by a split sphere apparatus. Rev. Sci. Instruments 41: 1178-1181.

Klimanek, P. and J. R. Kuzel (1988). X-ray diffraction line broadening due to dislocations in non-cubic materials. 1. General considerations and the case of elastic isotropy applied to hexagonal crystals. J. Appl. Cryst. 21: 59-66.

Kohlstedt, D. L. and C. Goetze (1974). Low-stress high -temperature creep in olivine single crystals. Journal of Geophysical Research 79(14): 2045-2051.

Kohlstedt, D. L., C. Goetze and W. B. Durham (1976). Experimental deformation of single crystal olivine with application to flow in the mantle. in The Physics and Chemistry of Minerals and Rocks. R. G. J. Strens, John Wiley and Sons:: 35-49.

Kot, R. A. and V. Weiss (1970). Transformation plasticity in iron-nickel alloys. Metallurgical Transactions 1: 2685-2693.

Kresse, G. and J. Furthmüller (1996). Efficiency of ab-initio total energy calculation for metals and semiconductors using a plane-wave basis set. Comput. Mat. Sci. 6: 15-50.

Kresse, G. and J. Hafner (1993). Ab inition molecular dynamics for liquid metals. Physical Review B47: 558.

Lebensohn, R. A. and C. N. Tomé (1993). A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystal: application to zirconium alloys. Acta Metall. Mater. 41: 2611-2624.

Lehmann, I. (1955). The times of P and S in northeastern America. Ann. Geofis. 8: 351-370.

Leroux, H. (2001). Microstructural shock signatures of major minerals in meteorites. European Journal of Mineralogy 13: 253-272.

Lévêque, J. J., E. Debayle and V. Maupin (1998). Anisotropy in the Indian Ocean upper mantle from Rayleigh and Love waveform inversion. Geophys. J. Int. 133: 529-540.

Li, L., P. Raterron, D. J. Weidner and J. Chen (2003). Olivine flow mechanisms at 8 GPa. Physics of the Earth and Planetary Interiors 138: 113-129.

Li, L., D. J. Weidner, J. Chen and M. Vaughan (2004). Stress measurements of deforming olivine ay high pressure. Physics of the Earth and Planetary Interiors 143-144: 357-367.

Liebermann, R. C. and Y. Wang (1992). Characterization of sample environment in a uniaxial split-sphere apparatus. in High-Pressure Research; Application of the Earth and Planeraty Sciences. Y. Syono and M. H. Manghnani. Washington D.C., American Geophysical Union. 67: 19-31.

Liu, L., T. P. Mernagh and T. Irifune (1994). High-pressure Raman spectra of E-Mg2SiO4, J-Mg2SiO4, MgSiO3- ilmenite and MgSiO3-pervoskite. Phys. Chem. Minerals 55(2): 185–193.

. 134 .

References

Lloyd, E. C. (1971). Accurate characterization of the high pressure environment. in NBS Special Publication. Washington DC. 326: 1-3.

Mackwell, S. J., D. L. Kohlstedt and M. S. Paterson (1985). The role of water in the deformation of olivine single crystals. Journal of Geophysical Research 90(B13): 11319-11333.

Madon, M. and J. P. Poirier (1980). Dislocation in spinel and garnet high pressure polymorphs of olivine and pyroxene: implicatins for mantle rheology. Science 207: 66-68.

Madon, M. and J. P. Poirier (1983). Transmission electron microscope observation of DE and J (Mg,Fe)2SiO4 in shocked meteorites: planar defects and polymorphic transitions. Physics of the Earth and Planetary Interiors 33: 31-44.

Mainprice, D., G. Barruol and W. Ben Ismaïl (2000). The seismic anisotropy of the Earth's Mantle: From single crystal to polycrystal. in Earth's deep interior: Mineral physics and tomography from the atomic to the global scale. S.-i. Karato, A. M. Forte, R. C. Liebermann, G. Master and L. Stixrude. Waschington, D.C., American Geophysical Union. 117: 237-264.

Mainprice, D., J. Bascou, P. Cordier and A. Tommasi (2004). Crystal preferred orientations of garnet: Comparison between numerical simulations and electron back-scattered diffraction (EBSD) measurements in naturally deformed eclogites. J. Struct. Geol. 26: 2089-2102.

Mei, S. and D. L. Kohlstedt (2000a). Influence of water on plastic deformation of olivine aggregates 1. Diffusion creep regime. J. Geophys. Res. Solid Earth 105: 21457-21469.

Mei, S. and D. L. Kohlstedt (2000b). Influence of water on plastic deformation of olivine aggregates 2. Dislocation creep regime. J. Geophys. Res. Solid Earth 105: 21471-21481.

Merkel, S., H. R. Wenk, J. Shu, G. Shen, P. Gillet, H.-k. Mao and R. J. Hemley (2002). Deformation of polycrystalline MgO at pressures of the lower mantle. Journal of Geophysical Research 107(B11): 2271-2288.

Mitchell, T. E. (1999). Dislocations and mechanical properties of MgO-Al2O3 spinel single crystal. J. Am. Ceram. Soc 82: 3305-3316.

Mitchell, T. E., L. Hwang and A. H. Heuler (1976). Deformation in spinel. Journal of Materials Science 11: 264- 272.

Mizukami, T., S. R. Wallis and J. Yamamoto (2004). Natural examples of olivine lattice preferred orientation patterns with a flow-normal a-axis maximum. Nature 427: 432-436.

Molinari, A., G. R. Canova and S. Azhy (1987). A self-consistent approach of the large deformation crystal polycrystal viscoplasticity. Acta Metall. 35: 2983-2994.

Montagner, J. P. (1985). Seismic anisotropy of the Pacific Ocean inferred from long-period surface waves dispersion. Physics of the Earth and Planetary Interiors 38: 28-50.

Montagner, J. P. and B. L. N. Kennett (1996). How to reconcile body-wave and normal-mode reference Earth models? Geophys. J. Int. 125: 229-248.

Morimoto, N., S. Akimoto, K. Koto and M. Tokonami (1969). Modified spinel, beta-manganous orthogermanate: Stability and crystal structure. Science 165: 586-588. . 135 .

References

Morishima, H., T. Kato, M. Suto, E. Ohtani, S. Urakawa, W. Utsumi, O. Shimomura and T. Kikegawa (1994). The

phase bounbary between D and E-Mg2SiO4 determined by in situ X-ray observation. Science 265: 1202-1203.

Nickel, K. G., G. P. Brey and L. Kogarko (1985). Orthopyroxene-clinopyroxene equilibria in the system CaO-

MgO-Al2O3-SiO2 (CMAS): new experimental results and implications for two-pyroxene thermometry. Contrib. Mineral Petrol. 91: 44-53.

Nicolas, A., F. Boudier and A. M. Boullier (1973). Mechanism of flow in naturally and experimentally deformed peridotites. American Journal of Science 273: 853-876.

Nicolas, A. and N. I. Christensen (1987). Formation of anisotropy in upper mantle peridotites - A review. in Composition, structure and dynamics of the lithosphere-astenosphere system. K. Fuchs and C. Froidevaux. Washingtown, D.C., AGU. 16.

Nishimura, C. E. and D. W. Forsyth (1989). The anisotropic structure of the upper mantle in the Pacific. Geophysical Journal 96: 203-230.

Osugi, J., K. Shimizu, K. Inoue and K. Yasunami (1964). A compact cubic anvil high pressure apparatus. Review of Physical Chemistry of Japan 34(1): 1-6.

Paterson, M. S. (1970). A high-pressure, high-temperature apparatus for rock deformation. Int. J. Rock Mech. Min. Sci. 7: 517-526.

Paterson, M. S. (1982). The determination of hydroxyl by infrared absorption in quartz, silicates glasses and similar materials. Bulletin de minéralogie 105: 20-29.

Phakey, P., G. Dollinger and J. Christie (1972). Transmission Electron Microscopy of Experimentally Deformed Olivine Crystals. in Flow and fracture of rocks. H. C. Heard, I. Y. Borg, N. L. Carter and C. B. Raleigh. Washington, D.C., American Geophysical Union. 16: 117-138.

Price, G. D. (1883). The nature and significance of stacking faults in wadsleyite, natural E-(Mg,Fe)2SiO4 from the Peace River meteorite. Physics of the Earth and Planetary Interiors 33: 137-147.

Price, G. D. (1983). The nature and significance of stacking faults in wadsleyite, natural E-(Mg,Fe)2SiO4 from the Peace River meteorite. Physics of the Earth and Planetary Interiors 33: 137-147.

Raleigh, C. B. (1968). Mechanisms of plastic deformation of olivine. Journal of Geophysical Research 73(14): 5391-5406.

Raterron, P., Y. Wu, D. J. Weidner and J. Chen (2004). Low-temperature olivine rheology at high-pressure. Physics of the Earth and Planetary Interiors 145: 149-159.

Revenaugh, J. and T. Jordan (1991). Mantle layering from ScS reverberations 3. The upper mantle. J. Geophys. Res. 96: 19,781-19,81009.

Ribárik, G., J. Gubicza and T. Ungár (2004). Correlation between strength and microstructure of ball milled Al- Mg alloys determined by X-ray diffraction. Mater. Sci. Eng. A In press.

Ribárik, G., T. Ungár and J. Gubicza (2001). MWP-fit: a program for multiple whole-profile fitting of diffraction peak profile by ab initio theoretical functions. Journal of Applied Crystallography 34: 669-676.

. 136 .

References

Riedel, M. R. and S.-i. Karato (1997). Grain-size evolution in subducted oceanic lithosphere associated with the olivine-spinel transformation and its effects on rheology. Earth and Planetary Science Letters 148: 27-43.

Ringwood, A. E. and A. Major (1966). Synthesis of Mg2SiO4-Fe2SiO4 spinel solid solutions. Earth and Planetary Science Letters 1: 241-245.

Ringwood, A. E. and A. Major (1970). The sytem Mg2SiO4-Fe2SiO4 at high pressure and temperatures. Physics of the Earth and Planetary Interiors 3(89-108).

Rubie, D. C. (1999). Characterizing the sample environment in multianvil high pressure experiments. Phase Transitions 68: 431-451.

Rybacki, E., J. Renner, K. Konrad, W. Harbott, F. Rummel and B. Stöckhert (1998). A servohydraulically- controlled deformation apparatus for rock deformation under conditions of ultra-high pressure metamorphism. Pure and Applied Geophysics 152: 579-606.

Sachs, G. (1928). Zur Ableitung einer Fliessbedingung. Z. Ver. Dtsch. Ing. 72: 734-736.

Schafler, E., M. Zehetbauer and T. Ungár (2001). Measurement of screw and edge dislocation density by means of x-ray Bragg profile analysis. Materials Sciences and Engineering A319-321: 220-223.

Sharp, T. G., G. Y. A. Bussod and T. Katsura (1994). Microstructures in E-Mg1.8Fe0.2SiO4 experimentally deformed at transitions-zone conditions. Physics of the Earth and Planetary Interiors 86: 69-83.

Shimomura, O., W. Utsumi, T. Taniguichi, T. Kikegawa and T. Nagashima (1992). A new high pressure and high temperature apparatus with sintered diamond anvils for synchrotron radiation use. in High pressure research: Application to Earth and planetary sciences. Y. Syono and M. H. Manghnani. Tokyo, Terra Scientific Publishing Compagny. 3: 3-11.

Siemes, H. and C. Hennig-Michaeli (1985). Ore minerals. in Preferred orientation in deformed metals and rocks: an introduction to modern texture analysis. H. R. Wenk, Academic Press.

Siesler, H. M., Y. Ozaki, S. Kawata and H. M. Heise (2002). Near-infrared spectroscopy, principles, instruments, applications. Weinheim, Wiley-VCH.

Silver, P. G. (1996). Seismic anisotropy beneath the continents: Probing the depths of geology. Ann. Rev. Earth Planet. Sci 24: 385-432.

Singh, A. K., C. Balasingh, H.-k. Mao, R. J. Hemley and J. Shu (1998). Analysis of lattice strain measured under nonhydrostatic pressure. Journal of Applied Physic 83(12): 7567-7575.

Sinogeikin, S. V., T. Katsura and J. D. Bass (1998). Sound velocities and elastic properties of Fe-bearing wadsleyite and ringwoodite. J. Geophys. Res. B. 103: 819-825.

Smith, J. V. and B. Mason (1970). Pyroxene-garnet transformation in Coorara meteorite. Science 168: 832- 833.

Suzuki, A., E. Ohtani, H. Morishima, T. Kubo, Y. Kanbe and T. Kondo (2000). In situ determination of the phase

boundary between wadsleyite and ringwoodite in Mg2SiO4. Geophysical Research Letters 27: 803-806.

. 137 .

References

Taleb, L., N. Cavallo and F. Waeckel (2001). Experimental analysis of transformation plasticity. International Journal of plasticity 17: 1-20.

Taylor, G. I. (1938). Plastic strain in metals. J. Inst. Met. 62: 307-324.

Thoraval, C., P. Machetel and A. Cazenave (1995). Locally layered convection inferred from dynamic models of the Earth's mantle. Nature 375: 777-780.

Thurel, E. (2001). Etude par microscopie electronique en transmission des mécanismes de déformation de la wadsleyite et de la ringwoodite. PhD Dissertation, Université des Sciences et Technologies de Lille.

Thurel, E. and P. Cordier (2003a). Plastic deformation of wadsleyite: I. High-pressure deformation in compression. Phys. Chem. Minerals 30: 256-266.

Thurel, E., P. Cordier, D. J. Frost and S.-i. Karato (2003b). Plastic deformation of wadsleyite: II. High- pressure deformation in shear. Phys. Chem. Minerals 30: 267-270.

Thurel, E., J. Douin and P. Cordier (2003c). Plastic deformation of wadsleyite: III. Interpretation of dislocations and slip systems. Phys. Chem. Minerals 30: 271-279.

Tommasi, A. (1998). Forward modeling of the development of seismic anisotropy in the upper mantle. Earth and Planetary Science Letters 160: 1-13.

Tommasi, A., D. Mainprice, G. Canova and Y. Chastel (2000). Viscoplastic self-consistent and equilibrium- based modeling of olivine lattice preferred orientations: Implications for upper mantle seismic anisotropy. Journal of Geophysical Research 105: 7893-7908.

Tommasi, A., B. Tikoff and A. Vauchez (1999). Upper mantle tectonics: Three-dimensional deformation, olivine crystallographic fabric and seismic properties. Earth and Planetary Science Letters 168: 173- 186.

Trampert, J. and H. J. van Heijst (2002). Global anisotropy, azimuthal anisotropy in the transition zone. Science 296: 1297-1299.

Turner, F. J. (1948). Mineralogical and structural evolution of the metamorphic rocks. Mem. geol. Soc. Am. 30.

Ungár, T. and A. Borbély (1996). The effect of dislocation contrast on X-ray line broadening: a new approach to line profile analysis. Appl. Phys. Lett. 69: 3173-3175.

Ungár, T., I. Dragomir, A. Révész and A. Borbely (1999). The contrast factor of dislocations in cubic crystals: The dislocation model of strain anisotropy in practice. Journal of Applied Crystallography 32: 992- 1002.

Ungár, T., J. Gubicza, P. Hanak and I. Alexandrov (2001a). Densities and character of dislocations and size- distribution of subgrains in deformed metals by x-ray diffraction profile analysis. Materials Sciences and Engineering A319-321: 274-278.

Ungár, T., J. Gubicza, G. Ribarik and A. Borbely (2001b). Crystallite size distribution and dislocation structure determined by diffraction profile analysis: principles and practical application to cubic and hexagonal crystals. Journal of Applied Crystallography 34: 298-310.

. 138 .

References

Ungár, T. and G. Tichy (1999). The effect of dislocation contrast on X-ray line profiles in untextured polycrytals. Phys. Stat. Sol. A 147: 425-434.

Vauchez, A., F. Dineur and R. Rudnick (2003). Microstructure, texture and seismic anisotropy of the lithospheric mantle above a mantle plume. Insights from the Labait volcano xenoliths (Tanzania). submitted.

Veyssière, P., J. Rabier, H. Garem and J. Grilhé (1978). Influence of temperature on dissociation of dislocation and plastic deformation in spinel oxides. Philosophical Magazine A 38(1): 61-79.

Wang, Y., W. B. Durham, I. C. Getting and D. J. Weidner (2003). The deformation-DIA: A new apparatus for high temperature triaxial deformation to pressures up to 15 GPa. Review of Scientific Instruments 74(6): 3002-3011.

Wang, Y., I. C. Getting, D. J. Weidner and M. Vaughan (1998). Performance of tapered anvils in a DIA-type, cubic-anvil, high -pressure apparatus for X ray diffraction studies. in Properties of Earth and planetary materials at high pressure and temperature. M. H. Manghnani and T. Yagi. Washington, American Geoohysical Union. 101: 35-39.

Wang, Y., R. C. Liebermann and J. N. Boland (1988). Olivine as in situ piezometer in high pressure apparatus. Physics and chemistry of minerals 15: 493-497.

Warren, B. E. and B. L. Avenbach (1950). The effect of cold work distortion on X-ray pattern. J. Appl. Phys. 21: 595-610.

Wedel, A., W. Skrotzki and K. Weber (1992). Microstructure and texture in peridotite xenoliths from the Hessian Depression. Geotektonische Forschungsheft 78: 89-125.

Weidner, D. J. (1998). Rheological studies at high pressure. in Ultrahigh-Pressure Mineralogy. R. J. Hemley. Washington, DC, Mineralogical Society of America. 37: 493-524.

Weidner, D. J., Y. Wang, G. Chen, J. Ando and M. T. Vaughan (1998). Rheology measurements at high pressure and temperature. in Properties of Earth and Planetary Materials at High Pressure and Temperature. M. H. Manghnani and Y. Syono. Washington D.C., American Geophysical Union:: 473-482.

Wenk, H. R., K. Bennett, G. R. Canova and A. Molinari (1991). Modelling plastic deformation of peridotite with the self-consistent theory. J. Geophys. Res. 96: 8337-8349.

Wenk, H.-R., I. Lonardeli, J. Pehl, J. Devine, V. Prakapenka, G. Shen and H.-K. Mao (2004). In situ observation of texture development in olivine, ringwoodite, magnesiowustite and silicate perovskite at high pressure. Earth and Planetary Science Letters 226(3-4): 507-519.

Wenk, H. R. and C. N. Tomé (1999). Modeling dynamic recrystallisation of olivine aggregates deformed in simple shear. J Geophys Res Solid Earth 104: 25513- 25527.

Wilkens, M. (1970). The determination of density and distribution of dislocations in deformed single crystals from broadened X-ray diffraction profiles. Phys. Stat. Sol. A 2: 359-370.

Williamson, G. K. and W. H. Hall (1953). X-ray line broadening from filed aluminium and wolfram. Acta Metall. 1: 22-31.

. 139 .

References

Xu, Y., D. J. Weidner, J. Chen, M. T. Vaughan, Y. Wang and T. Uchida (2003). Flow-law for ringwoodite at subduction zone conditions. Physics of the Earth and Planetary Interiors 136: 3-9.

Yamazaki, D. and S.-i. Karato (2001). High-pressure rotational deformation apparatus to 15 GPa. Rev. Sci. Instruments 72(11): 4207-4211.

Yamazaki, D. and S.-i. Karato (2002). Fabric development in (Mg,Fe)O during large strain, shear deformation: implications for seismic anisotropy in Earth's lower mantle. Physics of the Earth and Planetary Interiors 131: 251-267.

Yang, L. H., P. Söderlind and J. A. Moriarty (2001a). Accurate atomistic simulation of (a/2)<111> screw dislocations and other defects in bcc tantalum. Philosophical Magazine A 81: 1355.

Yang, L. H., P. Söderlind and J. A. Moriarty (2001b). Atomistic simulation of pressure-dependent screw dislocation properties in bcc tantalum. Materials Science and Engineering A 309-310: 102-107.

Young III, C. (1969). Dislocations in the deformation of olivine. American Journal of Science 267: 841-852.

Zamora, M. and J. P. Poirier (1983). Experiments in anisothermal transformation plasticity: the case of cobalt. Geophysical implication. Mechanics of Materials 2: 193-202.

Zha, C.-s., T. S. Duffy, H. Mao, R. T. Downs, R. J. Hemley and D. J. Weidner (1997). Single-crystal elasticity of beta -Mg (sub 2) SiO (sub 4) to the pressure of the 410 km seismic discontinuity in the Earth's mantle,. Earth Planet. Sci. Lett., 147: E9-E15.

Zhang, J., B. Li, W. Utsumi and R. C. Liebermann (1996). In situ X-Ray observations of the coesite-stishovite transition: Reversed phase boundary and kinetics. Physics and Chemistry of Minerals 23: 1-10.

Zhang, S. and S.-i. Karato (1995). Lattice preferred orientation of olivine aggregates deformed in simple shear. Nature 375: 774-777.

Zhang, S., S.-i. Karato, J. Fitzgerald, U. H. Faul and Y. Zhou (2000). Simple shear deformation of olivine aggregates. Tectonophysics 316: 133-152.

. 140 .

Erklärung

Hiermit erkläre ich, dass ich die vorliegende Arbeit selbständig verfasst und keine anderen als die von mir angegebenen Quellen und Hilfsmittel verwendet habe.

Ferner erkläre ich, dass ich anderweitig mit oder ohne Erfolg nicht versucht habe, diese Dissertation einzureichen. Ich habe außerdem keine gleichartige Doktorprüfung an einer Hochschule endgültig nicht bestanden.

Bayreuth, 01.12.2004 Hélène Couvy

Eur. J. Mineral. 2004, 16, 877-889

Shear deformation experiments of forsterite at 11 GPa - 1400°C in the multianvil apparatus

HÉLÈNE COUVY1, 2, DANIEL J. FROST1, FLORIAN HEIDELBACH1, KRISZTIÁN NYILAS3, TAMÁS UNGÁR3, STEPHEN MACKWELL1,* and PATRICK CORDIER2,**

1Bayerisches Geoinstitut, Universität Bayreuth, Germany 2Laboratoire de Structure et Propriétés de l'Etat Solide, UMR CNRS 8008, Université des Sciences et Technologies de Lille, Villeneuve d'Ascq, France 3Department of General Physics, Eötvös University Budapest, H-1445 Múzeum krt. 6-8, Budapest VIII, P.O.B. 323, Hungary

Abstract: Synthetic forsterite samples were shear-deformed at 11 GPa, 1400°C in the multianvil apparatus. The deformation microstructures have been characterised by SEM, EBSD, X-ray diffraction peak broadening and strain anisotropy analysis, and TEM. Different time durations have been characterised with a view to follow the evolution of strain and stress in high-pressure deformation experiments. A high density of [001] dislocations is introduced during pressurization at room temperature although no significant macroscopic shear or crystal preferred orientations are induced at this stage. The deviatoric stress is probably on the order of 1.5 GPa. Heating at 1400°C leads to a rapid decrease of the density of these dislocations. The shear deformation at high-temperature leads to measurable strain and development of crystal preferred orientations after one hour. Stress and strain- rate continue to decrease with time, such that eight hour experiments exhibit microstructures where recovery is apparent. At this stage, the stress level is estimated at ca. 100 MPa from dislocation density measurements. Crystal preferred orientations and TEM characterisation show that glide of [001] dislocations on (100) or (010) is the dominant deformation mechanism. Further investigation is needed to determine whether inhibition of [100] glide in these experiments is due to the role of water or whether a physical effect of pressure is also contributing.

Key-words: shear deformation, high-pressure, forsterite, dislocations, core structure.

1- Introduction where A is a constant for each particular slip system. This equation shows that the creep rate ε• exhibits a dependence Olivine is by far the most abundant mineral of the upper on stress (exponent n), oxygen fugacity (exponent m) and mantle. It is also considered to be the weakest phase and orthopyroxene activity (exponent q). Olivine is found to hence to control the rheology of the upper mantle. For this deform mostly along [001] (on (100) and (010)) at low reason, it has been clear for a long time that modelling the temperature and high stress whereas [100] glide (on (010), nature of convection in the outer 400 km of the Earth's (021), (031) and (001)) dominates at high temperature (and mantle requires a good knowledge of the plastic properties low stress). Although a wide range of thermochemical of olivine. Many studies have been conducted to investigate environments have been considered in the past, the physical the deformation mechanisms and flow laws of olivine conditions investigated remained quite narrow (mostly 1 single crystals (Blacic & Christie, 1973; Kohlstedt & atm pressure and high-temperature). Only recently has the Goetze, 1974; Durham & Goetze, 1977a and b ; Darot, influence of large strains (Bystricky et al., 2000; Zhang et 1980; Darot & Gueguen, 1981; Mackwell et al., 1985; Bai al., 2000) and high-pressure (Karato & Rubie, 1997; Jung et al., 1991; Bai & Kohlstedt 1992a and b, 1993) and poly- & Karato, 2001; Li et al., 2003, 2004; Raterron et al., crystals (e.g., Chopra & Paterson, 1981, 1984; Karato et 2003) been considered. Pressure has been shown to have a al., 1986; Hirth & Kohlstedt, 1995a and b; Mei & strong influence on the point defect chemistry (and hence Kohlstedt, 2000a and b). Bai et al. (1991) and Bai & on rheology) under "wet" conditions (Mackwell et al., Kohlstedt (1992a and b) have shown that flow laws in 1985, Mei & Kohlstedt, 2000a and b; Jung & Karato, olivine can be described by an equation of the form: 2001). Experiments performed on olivine powders at 8 GPa ε• = Ασ n f m a q exp(–∆H / RT) (1) and temperatures to 1475 K in a multianvil apparatus have O2 opx

*E-mail: presently at : Lunar and Planetary Institute, 3600 Bay Area Blvd, Houston, TX 77058-1113, USA **[email protected] 0935-1221/04/0016-0877 $ 5.85 DOI: 10.1127/0935-1221/2004/0016-0877 © 2004 E. Schweizerbart’sche Verlagsbuchhandlung. D-70176 Stuttgart JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, B12405, doi:10.1029/2004JB003158, 2004

Strain-induced seismic anisotropy of wadsleyite polycrystals and flow patterns in the mantle transition zone Andre´a Tommasi,1 David Mainprice,1 Patrick Cordier,2 Catherine Thoraval,1 and He´le`ne Couvy2,3 Received 29 April 2004; revised 4 October 2004; accepted 8 October 2004; published 17 December 2004.

[1] We use forward models based on recent high-pressure experimental data on mantle minerals to predict the seismic anisotropy produced by plastic strain of orthorhombic wadsleyite, the dominant mineral in the upper transition zone. These models predict a weak seismic anisotropy for a polycrystal of pyrolitic composition (60% wadsleyite, 40% garnet) at transition zone conditions: 2% for P and 1% for S waves for a shear strain of 1. Both P and S wave anisotropy patterns show an orthorhombic symmetry. P waves propagate faster at low angle to the shear direction and slower at high angle to the shear plane. S wave anisotropy is characterized by faster propagation of waves polarized at low angle to the shear direction. Horizontal shearing results therefore in higher velocities for horizontally propagating P waves (PH ) and horizontally polarized S waves (SH ), as well as in weak azimuthal variation of SV and SH velocities. On the other hand, vertical flow leads to higher velocities for vertically propagating P waves (PV ) and vertically polarized S waves (SV) and to a weak azimuthal variation of SV velocity but to a roughly constant SH velocity. Analysis of global observations of seismic anisotropy in the transition zone in the light of these models supports dominant horizontal flow in the uppermost transition zone, in agreement with predictions of geodynamical models that explicitly introduce phase transitions. INDEX TERMS: 3902 Mineral Physics: Creep and deformation; 8120 Tectonophysics: Dynamics of lithosphere and mantle—general; 8121 Tectonophysics: Dynamics, convection currents and mantle plumes; 7207 Seismology: Core and mantle; KEYWORDS: mantle convection, seismic anisotropy, crystal preferred orientation Citation: Tommasi, A., D. Mainprice, P. Cordier, C. Thoraval, and H. Couvy (2004), Strain-induced seismic anisotropy of wadsleyite polycrystals and flow patterns in the mantle transition zone, J. Geophys. Res., 109, B12405, doi:10.1029/2004JB003158.

1. Introduction explain, for instance, that some slabs, like the Marianas and Java, plunge steeply across the transition zone, penetrating [2] Convection patterns in the Earth’s mantle depend promptly into the lower mantle, whereas others, like the strongly on how physical properties are modified by the Japan, southern Kurile, and Izu-Bonin, are deflected within pressure-induced phase changes that take place in the the transition zone [van der Hilst et al., 1991]. Partially transition zone, i.e., between 410 and 670 km depth. After (or locally) layered convection also reconciles dynamic a long debate on whether mantle convection was double- or topography predicted in mantle circulation models with single-layered, current models tend to favor a single-layer observations [Thoraval et al., 1995; Cadek and Fleitout, convection in which the transition zone behaves as a more 1999]. or less permeable barrier. Indeed, geodynamical models [3] Knowledge of flow patterns within the transition zone show that, because of its negative Clapeyron slope layer is thus essential to constrain the structure of mantle [Akaogi et al., 1989], the ringwoodite to perovskite + circulation. Seismic anisotropy observations are undoubtedly magnesiowustite phase change at the base of the transition the best tool to image flow patterns in the deep Earth, since zone slows material transfer across the transition zone, anisotropy, as in the upper mantle, may result from strain- leading to intermittently layered convection [Christensen induced crystal-preferred orientation (CPO) of elastically and Yuen, 1985; Machetel and Weber, 1991]. This convection anisotropic minerals. Seismic anisotropy in the transition style, in between whole mantle and layered convection, may zone at a global scale was first suggested by a joint analysis of body wave travel times and free oscillation frequencies 1Laboratoire de Tectonophysique, CNRS/Universite´ de Montpellier II, [Montagner and Kennett, 1996], which showed that these Montpellier, France. data may be reconciled by a weak radial anisotropy in the 2Laboratoire Structure et Proprie´te´s de l’Etat Solide, CNRS/Universite´ transition zone. This anisotropy is characterized by higher de Lille, Villeneuve d’Ascq, France. velocities of horizontally propagating compressional waves 3Bayerisches Geoinstitut, Universita¨t Bayreuth, Bayreuth, Germany. (PH) and horizontally polarized shear waves (SH ) relatively Copyright 2004 by the American Geophysical Union. to vertically propagating compressional waves (PV )and 0148-0227/04/2004JB003158$09.00 vertically polarized shear waves (SV ), respectively. Faster

B12405 1of10 letters to nature

Acknowledgements We thank A. Moore and P. T. Atkins for field and laboratory assistance. This Several lines of evidence point to seismic anisotropy decreasing research was supported by grants from the A. W. Mellon Foundation to L.A.D. and O.A.C., and with depth in the upper mantle. Most global one-dimensional from the N.S.F. to L.A.D., O.A.C. and A.C.K. models (PREM, IASP, AK135 and AK303) show horizontally propagating P waves travelling (at velocity v ) faster than vertical Competing interests statement The authors declare that they have no competing financial PH interests. ones (at v PV), but the difference in velocity reduces with depth, resulting in isotropic behaviour at 350 km depth4. Some models Correspondence and requests for materials should be addressed to L.A.D. ([email protected]). (AK135 and 303) even show v PV slightly faster than v PH below 350 km. The S-wave polarization anisotropy also decreases mono- tonically from the surface to become isotropic at 250 km. For horizontally propagating S waves, horizontally polarized waves show a higher velocity (v SH) than vertically polarized waves (v SV) ...... down to about 250 km depth. Between 300 km and 400 km depth, v SV is higher than v SH, but anisotropy is five times lower than in the Pressure sensitivity of olivine slip uppermost mantle. High-resolution global tomographic models based on S-wave data12 or on the inversion of three-component systems and seismic anisotropy surface and body waveform data13 support these general findings, with strong anisotropy characterized by v SH . v SV above 250 km of Earth’s upper mantle depth. At greater depth, these models require a strong decrease in anisotropy, with a minimum around 300 km depth. S-wave data 1 1 2,3 2 . David Mainprice , Andreá Tommasi ,He´le`ne Couvy , Patrick Cordier also call for weak anisotropy, with v SV v SH at the base of the upper & Daniel J. Frost3 mantle beneath the central Pacific and Pre-Cambrian cratons12. Regional surface wave studies in the Pacific and Indian ocean basins 1Laboratoire de Tectonophysique, CNRS/Universite´ de Montpellier II, F-34095 also suggest that anisotropy is present from the surface to ,250– Montpellier cedex 5, France 300 km depth1–3,14, with v being greater than v . Analysis of two- 2 SH SV Laboratoire Structure et Proprie´te´s de l’Etat Solide, CNRS/Universite´ de Lille I, station surface wave profiles in the Pacific and Philippine plates F-59650 Villeneuve d’Ascq, France 3 imply a still shallower anisotropy limited to the upper 160 km of the Bayerisches Geoinstitut, Universita¨t Bayreuth, D-95440 Bayreuth, Germany 15 ...... mantle . SKS studies cannot constrain the depth of the anisotropic The mineral olivine dominates the composition of the Earth’s layer, but the strong correlation of the direction of polarization of upper mantle and hence controls its mechanical behaviour and the fast shear wave with the surface geology and the observed delay # seismic anisotropy. Experiments at high temperature and mod- times 2 s (ref. 14) suggests that SKS splitting occurs in the upper erate pressure, and extensive data on naturally deformed mantle 200–250 km of the mantle. rocks, have led to the conclusion that olivine at upper-mantle Finally, a regional seismic discontinuity, called the Lehmann conditions deforms essentially by dislocation creep with domi- discontinuity, has been detected at about 220 km depth by various nant [100] slip. The resulting crystal preferred orientation has seismic methods (reflection, surface waves, ScS reverberations and P been used extensively to explain the strong seismic anisotropy to S conversions), mainly beneath continents. This discontinuity observed down to 250 km depth1–4. The rapid decrease of aniso- has been interpreted as being due to either (1) a strong anisotropy tropy below this depth has been interpreted as marking the caused by intense deformation of olivine in a zone of mechanical transition from dislocation to diffusion creep in the upper coupling between the lithosphere and the asthenosphere16, or (2) mantle5. But new high-pressure experiments suggest that dislo- the transition between an anisotropic uppermost mantle deforming cation creep also dominates in the lower part of the upper mantle, by dislocation creep (which produces a crystal preferred orien- but with a different slip direction. Here we show that this high- tation, CPO, of olivine) and an isotropic deep mantle deforming by pressure dislocation creep produces crystal preferred orien- diffusion creep (which does not produce CPO)5. However, recent tations resulting in extremely low seismic anisotropy, consistent high-pressure, high-temperature experiments show that even in with seismological observations below 250 km depth. These fine-grained aggregates (,20–30 mm), dislocation creep is the results raise new questions about the mechanical state of the dominant deformation mechanism under conditions equivalent lower part of the upper mantle and its coupling with layers both to those prevailing at 300 km depth9,17,18. above and below. The pressure, or pressure interval, at which the transition from Despite the considerable effort to characterize olivine’s deformation mechanisms over the past 30 yr, it is only recently that deformation experiments could be conducted at pressure– temperature conditions of the entire upper mantle6–8.New simple-shear experiments on olivine aggregates at 11 GPa and 1,400 8C, conditions equivalent to those at depths of 330 km, have shown that deformation takes place by dislocation creep, with dominant activation of [001]{hk0} slip systems9, suggested by the concentration of [001] parallel to the shear direction and of [100] and [010] normal to the shear plane (Fig. 1). Transmission electron microscopy shows the exclusive presence of dislocations with [001] Burgers vectors in a screw orientation, compatible with [001](hk0) slip. Dominant [001] slip in the deep upper mantle Figure 1 Preferred orientation of [100], [010] and [001] crystallographic axes in synthetic requires re-evaluation of the interpretation of anisotropic olivine polycrystal S2954 deformed at 1,400 8C and 11 GPa confining pressure in simple physical properties. For instance, the fastest P-wave velocity will shear9. Lower hemisphere equal-area projection, contours at intervals of 0.5 multiples of no longer parallel the shear direction as in an upper mantle a uniform distribution. 3,269 measured orientations. Dextral shear (top to the right) is deforming by dominant [100](010) slip, which is the assumption indicated by half-arrows; SD, shear direction; NSP, normal to shear plane; X, finite strain traditionally used in relating flow and seismic anisotropy in the extension direction. Shear strain ,0.3. Inclined black line marks the foliation (flattening mantle10,11. plane).

[100](010) to [001](hk0) slip occurs has still not been characterized, pyroxene) at a pressure of 11.8 GPa and temperature of 1,380 8C, but it must be less than 11 GPa, which corresponds to 330 km corresponding to 355 km depth, were calculated using recently depth9. Constraints on the minimum depth for this transition may determined elastic constant tensors of olivine25, pyrope-rich gar- be derived from the analysis of olivine CPO patterns in naturally net26 and diopside27. Olivine displays the modelled CPO (Fig. 2). deformed mantle rocks19. Spinel-peridotites that are equilibrated Garnet has a random CPO; this agrees with predictions of VPSC above 70 km depth display solely CPO characteristic of [100] slip. simulations and observations in naturally deformed garnet-rich This CPO is also dominant in high-pressure garnet-peridotites from rocks that show that garnet CPOs are always very weak28.We South Africa equilibrated between 70 km and 150 km depth20. CPO have assumed that diopside also has a random orientation as suggesting activation of both slip directions at high-temperature high-pressure data are lacking for this mineral. However, if diop- conditions is restricted to rare high-pressure peridotite mylonites side has a CPO similar to that developed under high-temperature/ from the Tanzanian and Kaapvaal cratons equilibrated at ,140 km low-pressure conditions29, it will tend to reduce anisotropy by depth21. This suggests that [100] slip dominates in the mantle above destructive interference with olivine30. Both compressional and 150 km depth. shear waves display weak anisotropies (0.9% and 1.9%, respect- We simulated development of CPOs in olivine polycrystals ively). The fastest compressional waves propagate at a high angle to deformed in simple shear under high-pressure conditions, using a the shear plane. The variation of compressional waves’ velocities viscoplastic self-consistent (VPSC) model22 that has been exten- within the shear plane is very small. Thus in a mantle deforming by sively tested for olivine23,24. In this model, as in all polycrystal horizontal shearing, almost no azimuthal variation of P-wave plasticity approaches, CPO evolution is essentially controlled by the velocity (v P) would be observed and vertically propagating P imposed deformation, the initial texture, and the active slip systems. waves would be only slightly faster than those propagating hori- The last depend on the mineral structure, but also on the tempera- zontally. The polarization anisotropy of shear waves is characterized ture and pressure conditions, which control their relative strength by faster propagation of waves polarized at a high angle to the shear or critical resolved shear stress (CRSS). In Fig. 2, we show the CPO plane, and the largest delay times are observed for propagation at a developed in an aggregate of 500 initially spherical and randomly high angle to the shear direction in the shear plane. For propagation oriented olivine grains after a shear strain of 0.3 and 1.0; [001] axes in the shear plane, the fastest S waves are polarized at a high angle tend to align in-between the stretching and the shear direction, and to the shear plane. Hence, for horizontal flow, v SV is greater than [100] and [010] axes concentrate at high angles to the shear plane. v SH. In this simulation, CRSS for the [001](hk0), [100](001) and All the above predictions are consistent with global and regional [100](010), and [100](011) and [100](021) systems are 1:3:6; that seismic observations1–4,12–14, which show a weak anisotropy (,2%) is, slip on [001](hk0) is three times easier than slip on [100](010) below 250 km depth for P and S waves. The predicted S-wave and six times easier than on [100](021). Yet tests with different anisotropy, although weak (1.9%), is twice as strong as the P-wave CRSS values predict similar CPO for all combinations in which slip anisotropy observed in global models4. Anisotropy patterns in [001] systems is significantly easier than in [100] systems. observed in global models (transverse isotropy with a vertical Comparison with olivine CPO formed in recent high-temperature symmetry axis) are best reproduced for horizontal shearing. For high-pressure experiments in simple shear (Fig. 1) provides evi- such a flow pattern, our simulations predict that vertical P waves dence that these models give good estimates of olivine CPO in the propagate faster than horizontal ones, and that for horizontally lower part of the upper mantle. propagating S waves v SV is greater than v SH, in agreement with The three-dimensional distribution of seismic velocities in a global models of anisotropy patterns for depths greater than polycrystalline aggregate may be estimated by averaging the indi- 300 km. In addition, vertically propagating shear waves will detect vidual grain elastic constant tensors as a function of the crystal- no anisotropy. lographic orientations and mineralogical composition of the We conclude that dominant activity of [001](hk0) in olivine at aggregate. Seismic properties (Fig. 3) of an upper-mantle sample high pressure is entirely compatible with the available seismic data, with pyrolitic composition (63% olivine, 17% garnet, 20% clino- which indicate a weak anisotropy in the upper mantle below 300 km. It is difficult to imagine another scenario that would reproduce the anisotropy patterns of P and S waves in such detail. The interpretaion presented here allows us to consider that the

Figure 3 Modelled three-dimensional compressional velocity and shear wave anisotropy distributions, and fastest shear wave polarization. Data shown for an aggregate composed of 63% anisotropic olivine and isotropic garnet and diopside (17% and 20%, respectively) at 11.8 GPa and 1,380 8C. Lower hemisphere equal-area projections; contours at 0.1 km s21 intervals for compressional waves, 0.02 km s21 intervals for shear waves, Figure 2 Olivine crystal preferred orientations predicted using a viscoplastic self- and 0.5% anisotropy intervals for shear wave polarization anisotropy. Dashed line marks consistent model. Data are shown for a shear strain of 0.3 (top) and 1.0 (bottom). Lower minimum contours. Maximum P-wave and S-wave anisotropy is 0.9% and 1.9%, hemisphere equal-area projection, contours at intervals of 0.5 multiples of a uniform respectively. Black and white lines (for low and high anisotropy, respectively) in right panel distribution, 500 grains. Symbols and abbreviations as Fig. 1. indicate the direction of polarization of the fast shear wave.

732 NATURE | VOL 433 | 17 FEBRUARY 2005 | www.nature.com/nature © 2005 Nature Publishing Group letters to nature weakly anisotropic upper mantle layer below 250 km depth is 30. Mainprice, D., Barruol, G. & Ben Ismaı¨l, W. in Earth’s Deep Interior: Mineral Physics and Tomography from the Atomic to the Global Scale (eds Karato, S.-I., Forte, A. M., Liebermann, R. C., Masters, G. & actively deforming by dislocation creep, and hence the top and Stixrude, L.) 237–264 (AGU, Washington DC, 2000). bottom layers may be strongly coupled down to 400 km depth. Our predictions (that weak seismic anisotropy will develop in olivine- Acknowledgements This Letter is dedicated to the memory of G. Canova, who introduced A.T. rich aggregates deforming by [001](hk0) slip in the deep upper and D.M. to VPSC modelling. H.C. was supported by the Deutsche Forschungsgemeinschaft. mantle) challenge the two traditional interpretations for regions in Competing interests statement The authors declare that they have no competing financial the deep Earth of weak seismic anisotropy; (1) that they represent interests. zones of poor deformation coherence at the seismic length scale, or (2) that the dominant deformation mechanism (for example, Correspondence and requests for materials should be addressed to D.M. diffusion creep) in these regions does not produce CPO. Indeed, ([email protected]). transition from dominant [100] to [001] slip at high pressure may explain the variation with depth of the anisotropy patterns of P and S waves, even if the entire upper mantle deforms coherently with a dominant horizontal shearing component (as expected in a con- vective system with large-scale plates at the surface, like the Earth’s ...... A mantle). Stratigraphic placement and Received 11 August; accepted 30 November 2004; doi:10.1038/nature03266. 1. Montagner, J.-P. Seismic anisotropy of the Pacific Ocean inferred from long-period surface waves age of modern humans from dispersion. Phys. Earth Planet. Inter. 38, 28–50 (1985). 2. Cara, M. & Le´ve`que, J. L. Anisotropy of the asthenosphere: The higher mode data of the Pacific revisited. Geophys. Res. Lett. 15, 205–208 (1988). Kibish, Ethiopia 3. Nishimura, C. E. & Forsyth, D. W. The anisotropic structure of the upper mantle in the Pacific. Geophys. J. 96, 203–230 (1989). Ian McDougall1, Francis H. Brown2 & John G. Fleagle3 4. Montagner, J.-P. & Kennett, B. L. N. How to reconcile body-wave and normal-mode reference earth models. Geophys. J. Int. 125, 229–248 (1996). 1Research School of Earth Sciences, Australian National University, Canberra, 5. Karato, S.-I. On the Lehman discontinuity. Geophys. Res. Lett. 19, 2255–2258 (1992). 6. Karato, S. I. & Rubie, D. C. Toward an experimental study of deep mantle rheology: a new multianvil ACT 0200, Australia 2 sample assembly for deformation studies under high pressures and temperatures. J. Geophys. Res. 102, Department of Geology and Geophysics, University of Utah, Salt Lake City, Utah 20111–20122 (1997). 84112, USA 7. Cordier, P. & Rubie, D. C. Plastic deformation of minerals under extreme pressure using a multi-anvil 3Department of Anatomical Science, Stony Brook University, Stony Brook, apparatus. Mater. Sci. Eng. A 309–310, 38–43 (2001). New York 11794, USA 8. Durham, W. B., Weidner, D. J., Karato, S. I. & Wang, Y. in Plastic Deformation of Minerals and Rocks ...... (eds Karato, S.-I. & Wenk, H.-R.) (American Mineralogical Society, Washington, 2002). 9. Couvy, H. et al. Shear deformation experiments of forsterite at 11 GPa – 1400 8C in the multianvil In 1967 the Kibish Formation in southern Ethiopia yielded apparatus. Eur. J. Mineral. (in the press). hominid cranial remains identified as early anatomically modern 10. Tommasi, A. Forward modeling of the development of seismic anisotropy in the upper mantle. Earth humans, assigned to Homo sapiens1–4. However, the provenance Planet. Sci. Lett. 160, 1–13 (1998). and age of the fossils have been much debated5,6. Here we confirm 11. Silver, P. G. Seismic anisotropy beneath the continents: Probing the depths of geology. Annu. Rev. Earth Planet. Sci. 24, 385–432 (1996). that the Omo I and Omo II hominid fossils are from similar 12. Ekstrom, G. & Diewonski, A. M. The unique anisotropy of the Pacific upper mantle. Nature 394, stratigraphic levels in Member I of the Kibish Formation, despite 168–172 (1998). the view that Omo I is more modern in appearance than Omo 13. Gung, Y., Panning, M. & Romanowicz, B. Global anisotropy and the thickness of continents. Nature II1–3. 40Ar/39Ar ages on feldspar crystals from pumice clasts 422, 707–711 (2003). 14. Le´veˆque, J. J., Debayle, E. & Maupin, V. Anisotropy in the Indian Ocean upper mantle from Rayleigh within a tuff in Member I below the hominid levels place an older and Love waveform inversion. Geophys. J. Int. 133, 529–540 (1998). limit of 198 6 14 kyr (weighted mean age 196 6 2 kyr) on the 15. Gaherty, J. B., Jordan, T. H. & Gee, L. S. Seismic structure of the upper mantle in the central Pacific hominids. A younger age limit of 104 6 7 kyr is provided by corridor. J. Geophys. Res. 101, 22291–22309 (1996). feldspars from pumice clasts in a Member III tuff. Geological 16. Revenaugh, J. & Jordan, T. Mantle layering from ScS reverberations 3. The upper mantle. J. Geophys. Res. 96, 19781–19810 (1991). evidence indicates rapid deposition of each member of the Kibish 17. Li, L., Raterron, P., Weidner, D., Chen, J. & Vaughan, M. T. Stress measurements of deforming olivine Formation. Isotopic ages on the Kibish Formation correspond to at high pressure. Phys. Earth Planet. Inter. 143–144, 357–367 (2004). ages of Mediterranean sapropels, which reflect increased flow of 18. Li, L., Raterron, P., Weidner, D. & Chen, J. Olivine flow mechanisms at 8 GPa. Phys. Earth Planet. Inter. the Nile River, and necessarily increased flow of the Omo River. 138, 113–129 (2003). 40 39 19. Ben Ismail, W. & Mainprice, D. An olivine fabric database: an overview of upper mantle fabrics and Thus the Ar/ Ar age measurements, together with the sapropel seismic anisotropy. Tectonophysics 296, 145–158 (1998). correlations, indicate that the hominid fossils have an age close to 20. Ben Ismail, W., Barruol, G. & Mainprice, D. The Kaapvaal craton seismic anisotropy: petrophysical the older limit. Our preferred estimate of the age of the Kibish analyses of upper mantle kimberlite nodules. Geophys. Res. Lett. 28, 2497–2500 (2001). hominids is 195 6 5 kyr, making them the earliest well-dated 21. Vauchez, A., Dineur, F. & Rudnick, R. Microstructure, texture, and seismic anisotropy of the lithospheric mantle above a plume. Insights from the Labait volcano xenoliths. Earth Planet. Sci. Lett. anatomically modern humans yet described. (in the press). The principal outcrops of the Kibish Formation are along the 22. Lebensohn, R. A. & Tome´, C. N. A self-consistent anisotropic approach for the simulation of plastic Omo River where it skirts the Nkalabong Range (Fig. 1), with the deformation and texture development of polycrystals: Application to zirconium alloys. Acta Metall. Mater. 41, 2611–2624 (1993). highest outcrops close in elevation to that of the watershed between 7,8 23. Wenk, H.-R., Bennet, K., Canova, G. R. & Molinari, A. Modelling plastic deformation of peridotite the Omo and the Nile rivers . Former hydrographic links are with the self-consistent theory. J. Geophys. Res. 96, 8337–8349 (1991). apparent from Nilotic fauna in the Turkana Basin sequence8–10. 24. Tommasi, A., Mainprice, D., Canova, G. & Chastel, Y. Viscoplastic self-consistent and equilibrium- The Kibish Formation (about 100 m thick) consists of flat-lying, based modeling of olivine lattice preferred orientations. Implications for upper mantle seismic anisotropy. J. Geophys. Res. 105, 7893–7908 (2000). tectonically undisturbed, unconsolidated sediments deposited 25. Abramson, E. H., Brown, M., Slutsky, L. J. & Zaug, J. The elastic constants of San Carlos olivine up to mainly in deltaic environments over brief periods. It comprises 17 GPa. J. Geophys. Res. 102, 12252–12263 (1997). the youngest exposed sedimentary sequence in the Omo Basin, and 26. Chai, M., Brown, J. M. & Slutsky, L. J. The elastic constants of a pyrope-grossular-almandine garnet up lies disconformably upon the Nkalabong Formation11,12 or on the to 20 GPa. Geophys. Res. Lett. 24, 523–526 (1997). 12 27. Collins, M. D. & Brown, J. M. Elasticity of an upper mantle clinopyroxene. Phys. Chem. Miner. 26, underlying Mursi Formation . Strata are composed principally of 7–13 (1998). claystone and siltstone, with subordinate fine sandstone, conglom- 28. Mainprice, D., Bascou, J., Cordier, P. & Tommasi, A. Crystal preferred orientations of garnet: erate and tuffs (Fig. 2). Comparison between numerical simulations and electron back-scattered diffraction (EBSD) Butzer et al.13 and Butzer14 divided the Kibish Formation into measurements in naturally deformed eclogites. J. Struct. Geol. 26, 2089–2102 (2004). 29. Bascou, J., Tommasi, A. & Mainprice, D. Plastic deformation and development of clinopyroxene Members I to IV on the basis of disconformities with up to 30 m lattice preferred orientations in eclogites. J. Struct. Geol. 24, 1357–1368 (2002). relief (Fig. 2). The members record discrete times of deposition