The origins of olivine fabric transitions and their effects on seismic anisotropy in the upper mantle

The origins of olivine fabric transitions and their effects on seismic anisotropy in the upper mantle Dissertation Zur Erlangung des Grades eines Doktors der Naturwissenschaften -Dr. Rer. Nat.- Bayreuther Graduiertenschule für Mathematik und Naturwissenschaften der Universität Bayreuth „Experimental Geosciences“ vorgelegt von Sushant Shekhar Int. M.Sc. (Exploration Geophysics) Aus Kharagpur ( Indien ) May 2011 Prüfungssausschuß: Prof. F. Langenshorst, Universität Jena (1. Gutachter) Prof. David Rubie, Universität Bayreuth (2. Gutachter) Prof. L. Dubrovinsky, Universität Bayreuth Dr. Henri Samuel, Universität Bayreuth Prof. Jurgen Senker, Universität Bayreuth Prof. Ludwig Zöller, Universität Bayreuth Prof. S. Peiffer, Universität Bayreuth Table of Contents Acknowledgements ............................................................................................................................................................................. I Abstract .................................................................................................................................................................................................. II Zusammenfassung ....................................................................................................................................................................... V List of Images ........................................................................................................................................................................................X List of Tables .................................................................................................................................................................................... XVI 1 Introduction .................................................................................................................................................................... 1 1.1 Seismic anisotropy in the earth ...................................................................................................................... 3 1.2 CPO in Olivine ........................................................................................................................................................ 6 1.3 CPO relationship with microstructure ...................................................................................................... 10 1.4 CPO, mantle flow and anisotropy ................................................................................................................ 12 1.5 Mineral description - Olivine ......................................................................................................................... 15 1.5.1 Crystal-chemistry ..................................................................................................................................... 15 1.6 Aim of the thesis ................................................................................................................................................. 17 2 Methodology ................................................................................................................................................................. 19 2.1 Deformation experiments under extreme conditions ........................................................................ 19 2.1.1 High pressure deformation apparatus ............................................................................................ 20 2.2 Sample Preparation ........................................................................................................................................... 36 2.2.1 Hot pressing San Carlos olivine .......................................................................................................... 36 2.2.2 Placing platinum Shear strain marker ............................................................................................. 36 2.3 Analytical Methods ............................................................................................................................................ 37 2.3.1 Measurement of crystallographic preferred orientation using Electron backscatter diffraction technique (EBSD) ................................................................................................................................. 38 2.3.2 Study of dislocation structure using Transmission electron microscope (TEM)........... 44 2.3.3 FTIR ................................................................................................................................................................ 49 2.3.4 Piezoelectric measurements of stress in the Multianvil apparatus ..................................... 53 3 Results ............................................................................................................................................................................. 58 3.1 Deformation experiments on San-Carlos olivine using the D-DIA ................................................. 58 3.1.1 Simple shear deformation experiments on dry San Carlos olivine ...................................... 58 3.2 Characterization of the starting material ................................................................................................. 59 3.3 Measurement of sample strain ..................................................................................................................... 61 3.4 SEM and EBSD characterization ................................................................................................................... 67 3.4.1 LPO determinations of dry San Carlos olivine samples ............................................................ 67 3.4.2 Estimation of the mean grain size ..................................................................................................... 74 3.4.3 TEM characterization .............................................................................................................................. 77 3.4.4 Measurement of sample stress ........................................................................................................... 79 3.5 Experiments under wet condition .............................................................................................................. 83 3.5.1 Measurement of water content using FTIR ................................................................................... 85 3.5.2 NMR spectroscopy on hydrous Forsterite ..................................................................................... 88 3.5.3 General microstructures ........................................................................................................................ 92 3.5.4 SEM and EBSD characterization ......................................................................................................... 95 3.5.5 TEM characterization ........................................................................................................................... 100 3.6 Deformation experiment on Peridotite modal composition ......................................................... 103 In-situ measurement of stress using piezoelectric sensor ........................................................................... 104 4 Discussion ................................................................................................................................................................... 107 4.1 Effects of stress and pressure on the slip systems in olivine: Evidence from deformation experiments on “dry” olivine .................................................................................................................................... 109 4.2 Fabric types under water rich conditions ............................................................................................. 116 4.3 Physical basis for slip system changes in olivine ............................................................................... 117 4.3.1 Dominance of (010)[001] slip system at higher stresses ..................................................... 118 4.3.2 Higher (100)[001] activity at higher water content ............................................................... 125 4.4 Viscoplastic self consistent modelling of fabric development in olivine .................................. 130 4.4.1 Modelling the pole fabric for dry specimen DD455 ................................................................ 131 4.4.2 Modelling the pole fabric for dry specimen DD456 ................................................................ 134 Seismic anisotropy in the upper mantle – Implications from this study ............................................... 136 Seismic anisotropy in the upper mantle ......................................................................................................... 137 Olivine LPO transitions and changes in seismic anisotropy with depth ........................................... 138 5 Conclusion ................................................................................................................................................................... 143 References .............................................................................................................................................................................. 145 Appendix ................................................................................................................................................................................. 152 Erklärung ............................................................................................................................................................................... 165 [X] LIST OF IMAGES FIGURE 1-1: PYROLITIC MANTLE MINERALOGY AS A FUNCTION OF MINERAL VOLUME FRACTION AND DEPTH VARIATION. (FIGURE COURTESY: DAN FROST) .................................................................................................................................................................................................................................................................... 2 FIGURE 1-2: A WAVE TRAVELLING THROUGH A ELASTICALLY ANISOTROPIC MEDIA SPLITS INTO TWO ORTHOGONALLY POLARIZED WAVE. MAGNITUDE OF THE SHEAR WAVE SPLITTING IS GIVEN BY THE TIME DELAY (ΔT) BETWEEN THE FAST WAVE AND THE SLOW WAVE. FIGURE SOURCE: - ED GARNERO - HTTP://GARNERO.ASU.EDU/RESEARCH_IMAGES ........................................................................................................................................................................... 4 FIGURE 1-3: PHYSICAL AND CHEMICAL STRUCTURE AND RADIAL SEISMIC ANISOTROPY OBSERVED IN THE EARTH. SOURCE OF SIGNIFICANT ANISOTROPY IN THE UPPER MANTLE IS BELIEVED TO BE THE CRYSTALLOGRAPHIC PREFERRED ORIENTATION OF MANTLE MINERAL, MAINLY OLIVINE (COURTESY: D. MAINPRICE). ................................................................................................................................................................................................................ 5 FIGURE 1-4: CRYSTALLOGRAPHIC PREFERRED ORIENTATION DEVELOPMENT IN OLIVINE DUE TO SHEARING NATURE OF THE MANTLE FLOW. CPO OF ELASTICALLY ANISOTROPIC MINERALS IS THE PRINCIPAL CAUSE FOR SEISMIC ANISOTROPY OBSERVED IN THE UPPER MANTLE. ................................... 7 FIGURE 1-5: DOMINANT SLIP SYSTEMS IN OLIVINE AS A FUNCTION OF STRAIN RATE AND TEMPERATURE (AT P = 1.5 GPA) (FROM CARTER & AV´E LALLEMANT 1970). RESULTS SHOWN HERE SUGGEST STRESS-INDUCED TRANSITIONS IN THE DOMINANT SLIP SYSTEMS. (B) A COMPARISON OF CREEP STRENGTH FOR DIFFERENT ORIENTATIONS OF SINGLE CRYSTAL AND POLYCRYSTAL AT ˙Ε ≈ 10−5 S−1 (FROM GOETZE 1978). THE [110]C ACTIVATES THE [100] (010) SLIP SYSTEM, THE [101]C ORIENTATION, THE [100] (001) AND [001] (100) SLIP SYSTEMS, AND THE [011]C AND [001] (010) SLIP SYSTEMS. FIGURE SOURCE: KARATO (2008) .................................................................................................................................................. 8 FIGURE 1-6: DOMINANT SLIP SYSTEM IN OLIVINE AS A FUNCTION OF STRESS AND WATER CONTENT [T = 1400 TO 1570K]. AS EVIDENT FROM THE PLOT, HIGHER CONTENT OF WATER PROMOTES (100)[001] SLIP WHEREAS AT HIGHER STRESS PROMOTES (010)[001] SLIP SYSTEM. FIGURE SOURCE: JUNG & KARATO (2001) ....................................................................................................................................................................................................................... 9 FIGURE 1-7: LIKELY DISTRIBUTION OF OLIVINE FABRICS IN THE UPPER MANTLE AS A RESPONSE TO CHANGING STRESS, TEMPERATURE AND WATER CONTENT OF THE PARTS OF UPPER MANTLE (FIGURE SOURCE: KARATO 2008). .................................................................................................................... 12 FIGURE 1-8: IDEALIZED FORSTERITE STRUCTURE PROJECTED ON (100) PLANE (REDRAWN FROM DEER ET AL., 1997). SI ATOMS ARE AT THE CENTRE OF THE TETRAHEDRONS. SMALL BLACK CIRCLE, SI; LARGER GRAY CIRCLE, OXYGEN; BLACK CIRCLE, M1; DIAGONALLY HATCHED CIRCLE, M2 ................... 16 FIGURE 1-9: FORSTERITE STRUCTURE PERPENDICULAR TO (100) SHOWING THE APPROXIMATELY HEXAGONAL CLOSE-PACKING STRUCTURE (REDRAWN FROM DEER ET AL., 1997) .................................................................................................................................................................................................................. 16 FIGURE 2-1: SCHEMATIC DIAGRAMS OF ORIGINAL DIA AND DEFORMATION-DIA. A) ORIGINAL DIA CONSISTS OF UPPER AND LOWER GUIDE BLOCKS, FOUR WEDGE SHAPE SIDE WEDGES AND SIX TUNGSTEN CARBIDE ANVILS. B) A DEFORMATION-DIA HAS TWO ADDITIONAL HYDRAULIC ACTUATORS CALLED DEFORMATION RAMS WHICH PROVIDES A MEAN TO ACHIEVE CONTROLLED DEFORMATION. (SOURCE: Y. WANG) ........................................... 22 FIGURE 2-2: A VERTICAL CROSS-SECTION OF D-DIA SHOWING THE TWO SIDE WEDGES AND THE DIFFERENTIAL RAM. PRESENCE OF DIFFERENTIAL RAMS PROVIDES CONTROLLED DEFORMATION OF THE CUBIC SAMPLE AT A CONSTANT PRESSURE. ................................................................................................ 22 FIGURE 2-3: PRESSURE-TEMPERATURE-STRAIN PROFILE OF TYPICAL EXPERIMENTAL RUN IN D-DIA PRESS. AFTER COMPRESSING THE PRESSURE CELL TO THE REQUISITE PRESSURE, SAMPLE IS HEATED UP TO THE DESIRED TEMPERATURE AND IT IS ALLOWED TO HEAT FOR AT LEAST 30 MIN TO RELEASE THE INITIAL STRESS BUILD-UP, IF ANY PRESENT IN THE SAMPLE. THEN, THE SAMPLE IS DEFORMED AT A CONSTANT STRAIN RATE. ONCE THE TARGET AMOUNT OF STRAIN IS ACHIEVED, DEFORMATION IS STOPPED AND THE SAMPLE IS QUENCHED RIGHT AFTER THAT. THEREAFTER THE PRESSURE IS RELEASED SLOWLY. ....................................................................................................................................................................................................... 23 FIGURE 2-4: CARTOON COMPARING DEFORMATION BY PURE SHEAR AND SIMPLE SHEAR .................................................................................................................. 26 FIGURE 2-5: ORIENTATION CONTRAST IMAGE OF AN EXCESSIVELY DEFORMED SAMPLE AT 8GPA (SAMPLE NO. DD407). ALUMINA PISTONS HAVE FAILED, OWING TO THE LARGE SHEARING STRESS ACTIVE ON THE WEDGE SHAPED ALUMINA PISTONS. THE APPLIED SHEAR STRAIN WAS MORE THAN 200%. ..................................................................................................................................................................................................................................................... 28 FIGURE 2-6: SCHEMATIC DIAGRAM OF AN 8/6 MM D-DIA ASSEMBLY. ................................................................................................................................................... 29 FIGURE 2-7 : A SCHEMATIC DIAGRAM OF A 4/6 MM D-DIA ASSEMBLY SHOWING ITS MAJOR COMPONENTS ................................................................................. 30 FIGURE 2-8: SCHEMATIC OF ASSEMBLY USED FOR PRESSURE CALIBRATION USING BISMUTH AND MANGANIN ............................................................................. 31 FIGURE 2-9: CALIBRATED CELL PRESSURE HAS BEEN PLOTTED AS A FUNCTION OF OIL PRESSURE. ROOM TEMPERATURE CALIBRATION HAS BEEN DONE BY USING PHASE TRANSITIONS IN BISMUTH AND MANGANIN RESISTIVITY METHOD. HIGH TEMPERATURE (1000°C) PRESSURE CALIBRATION WAS DONE USING PHASE TRANSITION IN QUARTZ (QUARTZCOESITE AND COESITESTISHOVITE). 700 BAR OIL PRESSURE IS EQUIVALENT TO 500 TONNE LOAD FOR D-DIA PRESS AT BGI. .......................................................................................................................................................................................... 33 FIGURE 2-10: MEASURED TEMPERATURE ALONG THE SAMPLE LENGTH. CENTER OF THE SAMPLE RECORDED THE HIGHEST TEMPERATURE WITH APPROX. 85°C/MM TEMPERATURE GRADIENT AS WE MOVE TOWARDS THE EXTREMITIES. .................................................................................................................. 34 FIGURE 2-11: EMPLACEMENT OF PLATINUM STRAIN MARKER FOR SHEAR STRAIN MEASUREMENT. APPROXIMATELY 100 NM THICK PLATINUM-LAYER IS SPUTTER COATED ON THE SIDES OF THE TWO CUT HALVES OF THE HOTPRESSED SAMPLE. ROTATION OF THE STRAIN MARKER IS DIRECTLY RELATED TO THE SHEAR STRAIN ........................................................................................................................................................................................................ 37 FIGURE 2-12: FORMATION OF BACKSCATTERED KIKUCHI PATTERNS BY EBSD IN THE SEM. (A) ORIGIN OF KIKUCHI LINES FROM THE EBSD (I.E., TILTED SPECIMEN) PERSPECTIVE. (B) EBSD PATTERN FROM OLIVINE (ACCELERATING VOLTAGE 20 KV)..................................................................................... 39 FIGURE 2-13: SCHEMATIC SETUP OF AN EBSD SYSTEM SHOWING ITS PRINCIPAL COMPONENTS ..................................................................................................... 40 FIGURE 2-14: DIAGRAM ILLUSTRATING THE EVALUATION OF AN EBSD PATTERN. SAMPLE COORDINATE HAS BEEN REPRESENTED BY SUPERSCRIPT “S” WHERE AS SCREEN COORDINATE HAS BEEN REPRESENTED BY SUPERSCRIPT “SCREEN”. SPECIMEN-TO-SCREEN DISTANCE IS . (X*I,Y*I) ARE COORDINATES OF THE CENTER OF THE PATTERN AND (XPC,YPC ) ARE THE COORDINATES OF THE CENTER OF THE SCREEN. ................................ 42 FIGURE 2-15 : SCHEMATIC ILLUSTRATION OF DIFFRACTION AROUND A DISLOCATION CORE. IN THIS CASE THE ELECTRON BEAM IS DIFFRACTED MORE STRONGLY TILED LATTICE PLANES TO ONE SIDE OF THE DISLOCATION CORE THAN IN THE UNDISTORTED PARTS OF THE CRYSTAL. THE TRANSMITTED BEAM IS DEPLETED AROUND THE DISLOCATION LINE, AND IN A BRIGHT-FIELD IMAGE THE DISLOCATION LINE WILL APPEAR DARKER [XI] THAN THE REST OF THE CRYSTAL. ON THE OTHER HAND, THE DIFFRACTED INTENSITY IS GREATER AROUND THE DISLOCATION LINE AND IN A DARK FIELD IMAGE USING THE DIFFRACTED BEAM; THE DISLOCATION LINE WILL APPEAR LIGHTER THAN THE REST OF THE CRYSTAL. UNDER WEAK BEAM (WBDF) CONDITION, THE OVERALL INTENSITY OF THE IMAGE IS REDUCED IN COMPARISON TO A DARK FIELD IMAGE. ..................................... 45 FIGURE 2-16: ILLUSTRATION OF EDGE AND SCREW DISLOCATIONS IN A HYPOTHETICAL CRYSTAL. BURGERS VECTOR “B”, THE LATTICE VECTOR THAT CLOSES THE CIRCUIT AROUND THE DISLOCATION CORE AND DISLOCATION LINE HAS BEEN REPRESENTED BY “DL”, A). IN CASE OF EDGE DISLOCATION, BURGERS VECTOR IS NORMAL TO THE DISLOCATION LINE. IN THIS CASE, SLIP PLANE IS DEFINED AS THE PLANE CONTAINING THE DISLOCATION LINE AND THE BURGERS VECTOR, B). IN CASE OF SCREW DISLOCATION, THE DISLOCATION LINE AND BURGERS VECTOR ARE PARALLEL. ............................................................................................................................................................................................................................................... 49 FIGURE 2-17: DETAILS OF THE FTIR MICROSCOPE (REDRAWN FROM BOLFAN-CASANOVA, 2000) .............................................................................................. 50 FIGURE 2-18: PIEZOELECTRIC CRYSTAL CONFIGURATIONS SHOWING DIFFERENT ORIENTATIONS OF THE APPLIED FORCE WITH RESPECT TO THE CHARGE POLARIZATION. ...................................................................................................................................................................................................................................... 54 FIGURE 2-19: A SIMPLIFIED CIRCUIT DIAGRAM OF THE CHARGE AMPLIFIER PRODUCED BY COMBINING AN OPERATIONAL AMPLIFIER WITH AN RC NETWORK. ............................................................................................................................................................................................................................................... 55 FIGURE 2-20: FINAL ASSEMBLY DESIGN FOR PIEZOELECTRIC EFFECT MEASUREMENTS AT HIGH PRESSURE IN THE D-DIA AND 6-AXIS MULTIANVIL PRESSES. CUBE IS 8 MM IN EDGE LENGTH AND IS COMPRESSED USING 6 MM EDGE LENGTH TRUNCATIONS. THE CRYSTAL IS 1.2 MM IN DIAMETER AND 0.4 MM THICK AND IS COATED WITH AU USING VAPOUR DEPOSITION. .............................................................................................................................. 57 FIGURE 3-1: TOP: SPECIMEN ID B206 – POLE FIGURE FOR POLYCRYSTALLINE OLIVINE SAMPLE HOT-PRESSED AT 1 𝑮𝑷𝒂 AND 1200°C USING PISTON CYLINDER PRESS (TALC-PYREX ASSEMBLY). WE FOUND NO LPO IN THIS SPECIMEN. BOTTOM: SPECIMEN ID H3115 – POLE FIGURE FOR OLIVINE SAMPLE HOT PRESSED AT 8.5 𝑮𝑷𝒂 AND 1200°C USING AN 8-6 MULTI-ANVIL APPARATUS. THIS HOT PRESSED SPECIMEN EXHIBITS A WEAK LPO RESULTING FROM THE ACTIVITY OF THE (𝟎𝟏𝟎)[𝟏𝟎𝟎] SLIP SYSTEM. ........................................................................................................................................ 60 FIGURE 3-2: PLATINUM SHEAR MARKER IN THE SAMPLE DD402 IS SHOWN. A). SIDEWISE DISPLACEMENT (140 µM) OF THE ALUMINA PISTONS CAN BE SEEN. B) FAINTLY VISIBLE PLATINUM MARKER IS SHOWN FOR THE SAME ASSEMBLY. C). A CLOSE-UP LOOK AT THE PLATINUM AND ITS AVERAGE ROTATION DUE TO SAMPLE SHEAR (16.4°); NOTE THAT THE ROTATION OF THE MARKER IS MORE PRONOUNCED NEAR THE PISTON. ...................... 62 FIGURE 3-3: ROTATION OF PLATINUM STRAIN MARKER Θ AND AMOUNT OF SHEAR ∆L FOR A STRAIN MARKER INITIALLY ORIENTED AT 45° TO THE BASE OF THE SPECIMEN. DOTTED PARALLELOGRAM DEPICTS THE INITIAL ORIENTATION OF A HYPOTHETICAL PLANAR ELEMENT OF THICKNESS “T” THAT UNDERGOES SHEARING DUE TO THE SIDEWISE MOVEMENT OF THE ALUMINA PISTONS. SOLID LINES INDICATE THE NEW ROTATED POSITION OF THE SAME ELEMENT AFTER THE SHEAR STRAIN OF Γ. ............................................................................................................................................................................ 63 FIGURE 3-4: VARIATION IN STRAIN EXPERIENCED BY THE SAMPLE DD402 ALONG ITS THICKNESS. TOP-LEFT: THE PARTS CLOSER TO THE ALUMINA PISTON ARE STRAINED MORE THAN THOSE ARE CLOSE TO THE NEUTRAL LINE N´N. LOCAL ORIENTATION OF THE PT STRAIN MARKER IS SHOWN USING A SOLID WHITE LINE WHEREAS ORIGINAL ORIENTATION OF PT-MARKER IS SHOWN USING A DOTTED RED LINE. SENSE OF SHEAR IS AS INDICATED BY THE TWO RED ARROWS ON THE TOP AND BOTTOM. TOP-RIGHT: LOCAL INCREASE IN THE SHEAR STRAIN IN THE SAMPLE NEAR ALUMINA PISTON HAS BEEN MARKED BY A CURLY BRACKET. BOTTOM (LEFT AND RIGHT): THESE IMAGES SHOW THE DIFFERENCE IN THE ROTATION ANGLE AS WE MOVE AWAY FROM THE NEUTRAL LINE TOWARDS THE ALUMINA PISTON. ....................................................................................................... 64 FIGURE 3-5: REACTION OF OLIVINE WITH ALUMINA FORMS A LAYER OF SPINEL AND GARNET AT THEIR INTERFACE. THIS MAY ENHANCE THE COUPLING BETWEEN THE PISTON AND THE SPECIMEN MATERIAL (OLIVINE) .............................................................................................................................................. 65 FIGURE 3-6: DRY SAMPLES DEFORMED AT 3 GPA AND 1300°C. SAMPLE DEFORMED AT LOWER STRAIN RATE (TOP) SHOWS DOMINANT SLIP SYSTEM TO BE (𝟎𝟏𝟎)[𝟏𝟎𝟎]. OLIVINE A-AXES ARE PREFERENTIALLY ALIGNED SUB-PARALLEL TO THE SHEAR DIRECTION WHEREAS B-AXES ARE ALIGNED SUBNORMAL TO THE SLIP PLANE. (BOTTOM) SAMPLE DEFORMED UNDER HIGHER STRAIN RATE ALSO SHOW THE PRESENCE OF (𝟎𝟏𝟎)[𝟏𝟎𝟎] SLIP SYSTEM ALONG WITH (𝟎𝟏𝟎)[𝟎𝟎𝟏] SLIP SYSTEM. ......................................................................................................................................................................... 67 FIGURE 3-7 : DRY SAMPLES DEFORMED AT 5 GPA AND 1300°C. SAMPLE DEFORMED AT LOWER STRAIN RATE (TOP) SHOWS DOMINANT SLIP SYSTEM TO BE (𝟎𝟏𝟎)[𝟏𝟎𝟎]. OLIVINE A-AXES ARE PREFERENTIALLY ALIGNED SUB-PARALLEL TO THE SHEAR DIRECTION WHEREAS B-AXES ARE ALIGNED SUBNORMAL TO THE SLIP PLANE. (BOTTOM) SAMPLE DEFORMED UNDER HIGHER STRAIN RATE ALSO HAS BOTH (𝟎𝟏𝟎)[𝟏𝟎𝟎] SLIP AND (𝟎𝟏𝟎)[𝟎𝟎𝟏] SLIP SYSTEM ACTIVE. 20° GAUSSIAN SMOOTHING WAS APPLIED TO THE POLE FIGURE OF SPECIMEN DD350. ...................................... 68 FIGURE 3-8: DRY SAMPLES DEFORMED AT 5 GPA AND 1400°C. SAMPLE DEFORMED AT LOWER STRAIN RATE (TOP) SHOWS HAS AN LPO RESULTANT OF SIGNIFICANT STRAIN CONTRIBUTION FROM BOTH (𝟎𝟏𝟎)[𝟏𝟎𝟎] AND 𝟎𝟏𝟎𝟎𝟎𝟏 SLIP SYSTEM. (BOTTOM) SAMPLE DEFORMED UNDER HIGHER STRAIN RATE HAS (𝟎𝟏𝟎)[𝟎𝟎𝟏] SLIP SYSTEM DOMINANT. .......................................................................................................................................................... 69 FIGURE 3-9: DRY SAMPLES DEFORMED AT 8.5 GPA AND 1300°C. SAMPLE DEFORMED AT SLOWER STRAIN RATE (BOTTOM) SHOWS DOMINANT SLIP SYSTEM TO BE (𝟎𝟏𝟎)[𝟏𝟎𝟎] AND (𝟎𝟏𝟎)[𝟎𝟎𝟏]. OLIVINE A-AXES AND C-AXES ARE PREFERENTIALLY ALIGNED SUB-PARALLEL TO THE SHEAR DIRECTION WHEREAS B-AXES ARE ALIGNED SUBNORMAL TO THE SLIP PLANE. (BOTTOM) SAMPLE DEFORMED UNDER HIGHER STRAIN RATE SHOW THE PRESENCE OF (𝟎𝟏𝟎)[𝟎𝟎𝟏] SLIP SYSTEM. 20° GAUSSIAN SMOOTHING WAS APPLIED TO THE POLE FIGURE OF DD335. ..................................... 70 FIGURE 3-10: SUBSETS OF POLE FIGURES INDICATED A PARTICULAR CRYSTALLOGRAPHIC AXIS PARALLEL TO A SELECTED SPECIMEN AXIS. [100] || X0 IMPLIES THAT THE SUBSET CONTAINS ONLY THE DATA POINTS SUCH THAT OLIVINE [100] AXES ARE ALIGNED PARALLEL (OR SUB-PARALLEL) TO XAXIS OF THE SPECIMEN. ........................................................................................................................................................................................................................ 71 FIGURE 3-11: DRY SAMPLES DEFORMED AT 8GPA AND 1500°C. NO RECOGNISABLE LPO IS PRESENT IN THESE SAMPLES. .................................................... 73 FIGURE 3-12 : TOP: EBSD MAP FOR SPECIMEN DD350 WITH NON-INDEXED DATA POINTS; GRAINS HAVE BEEN ASSIGNED COLOUR ACCORDING TO THEIR EULER ANGLES 1 TO 3; BOTTOM: EBSD MAP AFTER GRAIN RECONSTRUCTION USING THE NEAREST NEIGHBOUR NOISE-REDUCTION METHOD...... 74 FIGURE 3-13: TOP -TEM MICROGRAPH FOR SPECIMEN D384 THAT WAS DEFORMED AT 8.5 GPA AND 1300°C. C-DISLOCATIONS (ONLY EDGE SEGMENTS ARE VISIBLE) ARE VISIBLE IN THE TOP-LEFT IMAGE (𝒈= [𝟎𝟎𝟒]). NO A-DISLOCATION COULD BE SEEN FROM 𝒈= [𝟏𝟏𝟎] IMAGING DIRECTION, WHICH IMPLIES THAT C-SLIP WAS THE DOMINANT SLIP SYSTEM. BOTTOM – TEM MICROGRAPHS FOR SPECIMEN DD391 DEFORMED AT 8.5 GPA AND 1500°C. BOTH AAND C-DISLOCATIONS CAN BE SEEN IN THE LEFT IMAGE. RIGHT IMAGE SHOWS ONLY THE C-DISLOCATION FOR THE SAME SPECIMEN. WHITE DOUBLE-ARROWS IN THE PICTURE INDICATE THAT SENSE OF SHEAR FOR THE BULK SAMPLE............................................................ 78 FIGURE 3-14: TEM MICROGRAPHS FOR THE DRY SAMPLE DD455 DEFORMED SLOWLY AT 1300°C. ACTIVE SLIP SYSTEMS ARE (010)[100], (100)[001] AND (010)[001]. FIGURE ON THE LEFT SIDE SHOWS LARGE NUMBER OF B = [100] DISLOCATIONS PRESENT IN ONE GRAIN. WHITE DOUBLEARROWS IN THE PICTURE INDICATE THAT SENSE OF SHEAR FOR THE BULK SAMPLE. ............................................................................................................. 79 [XII] FIGURE 3-15: DISLOCATION DENSITY VERSUS STRESS RELATIONSHIP [JUNG AND KARATO, 2001A]. THE SOLID LINE IS THE STRESS VERSUS DISLOCATION DENSITY RELATIONSHIP FOR A SINGLE CRYSTAL WITH THE SCHMIDT FACTOR = 0.5 [KOHLSTEDT ET AL., 1976B]. ....................................................... 80 FIGURE 3-16: LEFT-DURING ARGON MILLING PROCESS, ARGON STREAM BOMBARDS THE SAMPLE FROM TOP AND BOTTOM (ONLY TOP STREAM IS SHOWN IN THE FIGURE). THIS GIVES THE MILLED GRAIN SHAPE OF A WEDGE (MARKED BY THE PRESENCE OF THICKNESS FRINGES) WITH HALF-ANGLE BEING EQUAL TO THE ANGLE OF INCIDENCE OF ARGON STREAM (~5°). APPROXIMATE THICKNESS OF THE PLATEAU OF THE GRAIN CAN BE CALCULATED FROM THIS SIMPLE MODEL. RIGHT-WEDGE SHAPED PART AND PLATEAU TOP (REGION ENCLOSED BY WHITE RECTANGLE) OF ARGONMILLED OLIVINE GRAIN FOR SPECIMEN DD384 IS SHOWN HERE. THIS SAMPLE WAS DEFORMED AT 8.5 GPA AND 1300°CNOTE THAN BASE (B) OF THE WEDGE PART IS APPROXIMATELY 2 µM. .................................................................................................................................................................................... 81 FIGURE 3-15 SHOWS THIS RELATIONSHIP FOR DRY AND WET SPECIMENS [JUNG AND KARATO, 2001B]. FIGURE 3-17: STRESS VERSUS RECRYSTALLIZED GRAIN-SIZE RELATIONSHIP FROM JUNG AND KARATO 2001. STRESS MAGNITUDES IN THE SAMPLES FROM THIS STUDY WERE ESTIMATED FROM DISLOCATION DENSITIES. THE SOLID LINES INDICATE THE RESULTS OF THE LEAST SQUARE FIT FOR THE ‘DRY’ AND ‘WET’ CONDITION. THE SIZE OF RECRYSTALLIZED OLIVINE DEFORMED UNDER ‘WET’ CONDITIONS IS SIGNIFICANTLY LARGER THAN THAT UNDER ‘DRY’ CONDITIONS AT THE SAME STRESS. .................................................................................................................................................................................................................................................... 82 FIGURE 3-18: BACKGROUND CORRECTION OF THE RAW FTIR DATA. A BASELINE WAS CREATED USING PIECEWISE CUBIC INTERPOLATION METHOD. WATER SOLUBILITY VALUES ARE SENSITIVE TO THE CHOICE OF THE BASELINE AND RANGE OF WAVENUMBER USED FOR INTEGRATION (2950 TO 3780 CM-1 IN OUR CASE). .................................................................................................................................................................................................................... 85 FIGURE 3-19: FTIR SPECTRA OF HYDROUS OLIVINE SPECIMEN AFTER THE EXPERIMENTS. ABSORBANCE OF THE SPECTRA WAS NORMALIZED FOR 1 CM THICK SPECIMEN. ................................................................................................................................................................................................................................... 86 FIGURE 3-20: WATER SOLUBILITY IN SAN CARLOS OLIVINE (MODIFIED AFTER KEPPLER AND BOLFAN-CASANOVA [2006]). OUR RESULTS ARE SHOWN ALONG WITH THE EXPERIMENTAL DATA FROM MOSENFELDER ET AL. (2006; BLUE DIAMOND) AND KOHLSTEDT ET AL. (1996; RED SQUARES). THE H2O CONTENTS FROM THIS STUDY EMPLOY THE PATERSON CALIBRATION SO AS TO COMPARE THEM DIRECTLY WITH THE WORK OF KOHLSTEDT ET AL., 1996 WHERE OLIVINE WAS SATURATED WITH EXCESS H2O.THIS COMPARISON INDICATES THAT THE OLIVINE FROM THIS STUDY HAD H2O CONTENTS LESS THAN THE SATURATION LEVEL (25-35%). THE STUDY OF MOSENFELDER ET AL (2006) REPORTED HIGHER H2O CONTENTS MAINLY BECAUSE OF USING THE NEWER BELL ET AL CALIBRATION. ............................................................................................................ 87 FIGURE 3-21: NMR SPECTRA FOR GYPSUM AND SYNTHETIC FORSTERITE SAMPLE. GYPSUM WITH ITS KNOWN WATER CONTENT HAS BEEN USED AS THE STANDARD. SYNTHETIC FORSTERITE WAS SYNTHESIZED BY ADDING SMALL AMOUNT OF EQUIMOLAR MIXTURE OF BRUCITE AND SILICA WITH FORSTERITE (SEE TABLE 3-2) AT 11 GPA AND 1150°C USING 8-6 TYPE MA APPARATUS. SAMPLE Z769 WAS ADDED WITH 4 TIMES MORE BRUCITE-SILICA MIXTURE THAN Z771. CHEMICAL SIFT FOR PEAKS ARE MARKED BY THE ARROW. THE VALUE IN THE PARENTHESIS FOR Δ 6.73 IS THE CORRESPONDING VALUE OF THE ORDINATE. ........................................................................................................................................................................... 89 FIGURE 3-22: LEFT: RELATION BETWEEN O-H STRETCHING FREQUENCY AND D (O...O) [LIBOWITZKY, 1999]. OPEN SYMBOLS REPRESENT STRAIGHT H BONDS, SHADED SYMBOLS MARK BENT H BONDS, AND FILLED ONES DENOTE COPPER COMPOUNDS; CIRCLES - SILICATES, SQUARES - (OXY)HYDROXIDES, HEXAGONS - CARBONATES, DIAMONDS - SULFATES, TRIANGLES - PHOSPHATES AND ARSENATES. RIGHT: ISOTROPIC CHEMICAL SHIFTS VERSUS O – H...O DISTANCE FOR VARIOUS CRYSTALLINE COMPOUNDS (ECKERT ET AL. 1988)............................................................................. 90 FIGURE 3-23: FTIR SPECTRA OF THE SPECIMEN Z769 CONTAINING FE-FREE SYNTHETIC FORSTERITE WITH TWO WT. PERCENTAGE BRUCITE-SIO2 EQUIMOLAR MIXTURE. WATER CONTENT IN THIS SAMPLE WAS MEASURED USING FTIR IS 559 WT. PPM USING CALIBRATION BY PATERSON (1982) .................................................................................................................................................................................................................................................... 91 FIGURE 3-24: SEM ORIENTATION CONTRAST IMAGES OF THE SPECIMENS DEFORMED UNDER WET CONDITION. IN GENERAL, THE AVERAGE GRAIN SIZES IN THE HYDROUS SPECIMENS ARE SMALLER IN COMPARISON TO THEIR DRY COUNTERPARTS IN TERMS OF P-T CONDITIONS. GRAINS IN WET SPECIMENS HAVE SERRATED BOUNDARIES. ...................................................................................................................................................................................... 93 FIGURE 3-25: WET SAMPLES DEFORMED AT 3 GPA AND 1300°C. SAMPLE DEFORMED AT LOWER STRAIN RATE (TOP) SHOWS TWO ACTIVE SLIP SYSTEMS – (010)[100] AND (100)[001]. (BOTTOM) SAMPLE DEFORMED UNDER HIGHER STRAIN SHOWS ONLY (100)[001] SLIP SYSTEM TO BE ACTIVE. .................................................................................................................................................................................................................................................................. 96 FIGURE 3-26: WET SAMPLES DEFORMED AT 5 GPA AND 1300°C. BOTH THE HIGH STRAIN RATE AND LOW STRAIN RATE SAMPLE EXHIBIT ONLY ONE ACTIVE SLIP SYSTEM – (100)[001]. ................................................................................................................................................................................................. 96 FIGURE 3-27: WET SAMPLES DEFORMED AT 5 GPA AND 1400°C. SAMPLE DEFORMED AT LOWER STRAIN RATE (TOP) SHOWS MAINLY ONE ACTIVE SLIP SYSTEMS – (100)[001]. WHEREAS, (BOTTOM) SAMPLE DEFORMED UNDER HIGHER STRAIN HAS TWO (010)[001] AND (100)[001] SLIP SYSTEMS ACTIVE. ................................................................................................................................................................................................................................... 97 FIGURE 3-28: WET SAMPLES DEFORMED AT 8.5 GPA AND 1300°C. IRRESPECTIVE OF THE STRAIN RATE, BOTH THE SPECIMENS DEFORMED AT 8.5 GPA AND 1300°C SHOW TWO ACTIVE SLIP SYSTEMS –(010)[100] AND (100)[001]. THIS OBSERVATION IS CONSISTENT WITH ACTIVITY OF (010)[001] SLIP SYSTEM AT RELATIVELY HIGHER STRESSES AND (100)[001] SLIP SYSTEM UNDER HYDROUS CONDITION. ..................................... 98 FIGURE 3-29: WET SAMPLES DEFORMED AT 5 GPA AND 1500°C. SAMPLE DEFORMED AT LOWER STRAIN RATE (TOP) SHOWS TWO ACTIVE SLIP SYSTEMS – (010)[100] AND (100)[001]. (BOTTOM) SAMPLE DEFORMED UNDER HIGHER STRAIN SHOWS ONLY (100)[001] SLIP SYSTEM TO BE ACTIVE. .................................................................................................................................................................................................................................................................. 99 FIGURE 3-30: TEM MICROGRAPHS FOR THE WET SPECIMEN DD456. DEFORMATION EXPERIMENT WAS CARRIED OUT AT 8.5 GPA AND 1300°C WITH A STRAIN RATE OF 5X10-4. TOP FIGURE SHOWS THE PRESENCE OF C-DISLOCATIONS. (100)[001] DISLOCATIONS ARE MOSTLY OF EDGE NATURE WHERE AS THE [001] SCREW DISLOCATIONS ARE MOST LIKELY FROM (010)[001] DISLOCATION. EVIDENCE OF CROSS-SLIP CAN BE ALSO SEEN AS INDICATED BY MARKER 1 IN TOP IMAGE AND WHITE ARROW IN THE BOTTOM-LEFT IMAGE. BOTTOM-RIGHT FIGURE ALSO SHOWS STRAIGHT CSCREW DISLOCATION FROM (010)[001] SLIP SYSTEM. ............................................................................................................................................................. 101 FIGURE 3-31: A TYPICAL HRTEM IMAGE (UPPER AND LOWER RIGHT) AND THE FAST FOURIER TRANSFORMED IMAGE (LOWER RIGHT) OF THE DISSOCIATED C-EDGE DISLOCATION VIEWING ALONG THE {110} ZONE AXIS OF A DEFORMED HYDROUS OLIVINE. THE IMAGE CONTRAST IN THE DISLOCATION CORE REGIONS IS DIFFERENT FROM THAT IN THE SURROUNDING BULK, WHICH INDICATES THAT THE CORE IS EXPANDED. .............. 102 FIGURE 3-32: PERIDOTITE SAMPLES DEFORMED AT 8.5GPA AND 1300°C. OLIVINE IN THE SLOWLY DEFORMED AGGREGATE LIKELY HAS BOTH (010)[100] AND (010)[001] SLIP SYSTEMS ACTIVE WHEREAS IN THE EXPERIMENT CONDUCTED AT HIGHER STRAIN RATE THE SLIP SYSTEM IS (010)[001]. PYROXENE IN BOTH THE CASES SHOW (100)[001] SLIP SYSTEM .................................................................................................................. 103 [XIII] FIGURE 3-33: OUTPUT VOLTAGE FROM THE CHARGE AMPLIFIER AS A FUNCTION OF TIME FOR AN EXPERIMENT WHERE A GAPO4 CRYSTAL WAS COMPRESSED TO 2 GPA AND THEN HELD AT CONSTANT STATIC PRESSURE FOR 80 MIN. ................................................................................................... 104 FIGURE 3-34: OUTPUT VOLTAGE AS A FUNCTION OF TIME FOR AN EXPERIMENT HELD STATICALLY AT 2 GPA AND THEN DEFORMED BY DRIVING OUT THE ANVILS IN THE HORIZONTAL DIRECTION SIMULTANEOUSLY AFTER APPROXIMATELY 60 S BY 20 MICRONS. THE DRIFT BEFORE 60 S IS LINEAR AND IS REMOVED BY SUBTRACTING A LINEAR BACKGROUND AS SHOWN IN B. ............................................................................................................................... 105 FIGURE 3-3-35: STRESS AND ANVIL DISPLACEMENT VERSUS TIME FOR 4 DEFORMATION EVENTS PERFORMED AT 2 GPA. .................................................... 106 FIGURE 4-1: SUMMARY OF FABRICS OBSERVED IN SAN-CARLOS OLIVINE DEFORMED UNDER DRY AND WET CONDITION AT DIFFERENT STRAIN RATES. EXPERIMENTS WERE PERFORMED BETWEEN 3 TO 8.5 GPA AND 1300°C TO 1500°C. WIDTH OF EACH COLOUR BAR IS PROPORTIONAL TO THE APPROXIMATE NUMBER OF GRAINS THAT WERE PRESENT IN THE SUBSET CONTAINING DATA POINTS FOR THAT SLIP SYSTEM. REFER TO SECTION 3.4.14 FOR MORE DETAILS. AS SHOWN IN THE TABLE AT TOP-RIGHT CORNER OF THE PAGE, THE LOWER ROW IN THE 2X2 MATRIX CONTAINS RESULTS FROM DRY EXPERIMENTS WHILE UPPER ROW CONTAINS RESULTS FROM WET EXPERIMENTS. THE LEFT COLUMN IN 2X2 MATRICES HAS RESULTS FROM SLOWLY DEFORMED SAMPLES WHEREAS SAMPLES DEFORMED AT RELATIVELY HIGHER STRAIN RATE HAVE THEIR FABRICS SHOWN IN THE RIGHT COLUMN. ..................................................................................................................................................................................................................... 111 FIGURE 4-2: POLE FIGURES FOR TWO POLYCRYSTALLINE OLIVINE SPECIMEN HOTPRESSED AT 8.5 GPA (H3115) AND 11 GPA (H3354). SPECIMENS WERE ANNEALED AT 1400°C. BOTH POLE FIGURES RESEMBLE A-TYPE FABRIC WHICH IS OFTEN OBSERVED UNDER LOW STRESS AND DRY DEFORMATION ENVIRONMENT. PRESENCE OF A-TYPE FABRIC IN THESE HOTPRESSED SPECIMEN IS INDICATIVE OF (010)[100] SLIP SYSTEM ACTIVITY. .............................................................................................................................................................................................................................................. 113 FIGURE 4-3: DEFORMATION DATA FROM THIS STUDY AND OTHER STUDIES ARE SHOWN AS A FUNCTION OF STRESS AND WATER CONTENTS (T ∼ 1470– 1670 K). LARGER SYMBOLS WITH BLACK BOUNDARIES REPRESENT DATA FROM THIS STUDY WHEREAS REST OF DATA ARE FROM KATAYAMA ET AL. 2004. EXCEPT, ONE OF THE DATA FOR D-TYPE FABRIC IS FROM BYSTRICKY ET AL. (2001). WATER CONTENT WAS ESTIMATED USING THE PATERSON (1982) CALIBRATION. BROKEN GRAY LINES INDICATE THE LIKELY TRANSITION LINE BETWEEN TWO DIFFERENT FABRIC TYPES (MODIFIED AFTER KARATO ET AL., 2008) ................................................................................................................................................................................... 115 FIGURE 4-4: CRITICAL RESOLVED SHEAR STRESSES (CRSS) OF THE (010)[100] AND (010)[001] SLIP SYSTEMS AS A FUNCTION OF TEMPERATURE. DATA (CORRESPONDING TO A STRAIN RATE OF 10-5 S-1) FROM EXPERIMENTS PERFORMED ON SINGLE CRYSTALS ORIENTED ALONG [011]C (BLACK-FILLED SYMBOLS) TO PROMOTE [001](010) GLIDE AND ALONG [110]C (OPEN SYMBOLS) TO PROMOTE [100](010) GLIDE. (SOURCEPHD THESIS – HELEN COUVY, 2005) ............................................................................................................................................................................................ 118 FIGURE 4-5: TEMPERATURE DEPENDENCE OF THE CRITICAL SHEAR STRESS ΤC(T) OF COVALENT CRYSTALS MEASURED UNDER HIGH OR ATMOSPHERIC PRESSURE. THE DATA ARE TAKEN FROM THE REFERENCES: LAGERLOF ET AL. (1994) FOR Α-AL2O3, CASTAING ET AL. (1981B) FOR SI AND BOIVIN ET AL. (1990) FOR GAAS OF INTRINSIC AND P-TYPE. (FIGURE SOURCE: KOIZUMI ET AL., 1994) ..................................................................... 119 FIGURE 4-6: LEFT IMAGE SHOWS A KINK (DARK LINE) LYING ACROSS A POTENTIAL VALLEY. BROKEN LINES INDICATE THE POTENTIAL MAXIMA WITH MINIMA REPRESENTED BY THE SOLID LINES. RIGHT: A KINK IN THE PRESENCE OF EXTERNAL STRESS HAS ITS EQUILIBRIUM POSITION DISPLACED AWAY FROM THE UNSTRESSED POSITION. SIZE OF THE KINK IS REPRESENTED BY KINK HEIGHT H AND WIDTH 2K+L IN CASE OF A TRAPEZOIDAL KINK MODEL. (SOURCE: SUZUKI ET AL. 1995) ............................................................................................................................................................................. 120 FIGURE 4-7: ENTHALPY CHANGE ASSOCIATE WITH THE CONTRIBUTION FROM THERMAL PERTURBATION AT TEMPERATURE T AND MECHANICAL WORK DONE BY STRESS Σ. ............................................................................................................................................................................................................................. 121 FIGURE 4-8: THE FUNCTION G(X) GIVING THE SHAPE OF THE PEIERLS POTENTIAL. IT IS SINUSOIDAL FOR A = 0, DAM-LIKE WITH A ROOF TOP FOR A=0.5, AND CAMEL-HUMP SHAPED, WITH AN INTERMEDIATE MINIMUM FOR A = 0.8. (SOURCE: KOIZUMI 1994) ................................................................... 122 FIGURE 4-9: PREDICTED CRSS VALUES FOR A-SLIP AND C-SLIP USING DOUBLE KINK NUCLEATION THEORY. AT AROUND 1300°C, 300 MPA STRESS WOULD BARELY ACTIVATE C-SLIP WHEREAS AT AROUND 600 MPA, BOTH C-SLIP AND A-SLIP ARE ACTIVE. IN THIS CASE, ACTIVITY OF (010)[001] SLIP SYSTEM WOULD BE HIGHER BECAUSE THIS SLIP SYSTEM HAS EXTRA THERMAL ENERGY AVAILABLE AT ITS DISPOSAL. ....................................... 124 FIGURE 4-10: (001) PROJECTION OF THE OLIVINE STRUCTURE. ONLY THE OXYGEN IONS ARE SHOWN, BUT THE POSITIONS OF THE SILICON IONS ARE INDICATED BY THE SI 04 TETRAHEDRA. PERIODIC JOGS IN A (100) PLANE ARE INDICATED BY THE BROKEN LINE. THE ATOM POSITIONS ARE THOSE OF THE PAPER BY HANKE (1965). (FIGURE SOURCE: OLSEN AND BIRKELAND, 1973) ..................................................................................................... 127 FIGURE 4-11: FTIR SPECTRA FOR HYDROUS SAMPLES SHOW PEAKS AT 3477, 3448, 3629 AND 3676 CM-1. THESE PEAKS COULD BE ARISING FROM HYDROGEN ASSOCIATED WITH VACANT SILICON SITES. .............................................................................................................................................................. 128 FIGURE 4-12: DRY SAMPLES DEFORMED AT 8.5 GPA AND 1300°C. SAMPLE DEFORMED AT SLOWER STRAIN RATE SHOWS DOMINANT SLIP SYSTEM TO BE (𝟎𝟏𝟎)[𝟏𝟎𝟎] AND (𝟎𝟏𝟎)[𝟎𝟎𝟏]. ............................................................................................................................................................................................. 131 FIGURE 4-13: POLE FIGURES FOR MODELS DESCRIBED IN THE TABLE 5-3. MODELS WHICH ASSUME VERY SIMILAR CRSS VALUE FOR (010)[100] AND (010)[001] AND AT LEAST THREE TIMES HIGHER CRSS VALUE FOR OTHER TWO SLIP SYSTEMS CAN MIMIC THE EXPERIMENTAL POLE FIGURE. 133 FIGURE 4-14: NORMALIZED ACTIVITY VERSUS EQUIVALENT STRAIN PLOT FOR VARIOUS MODEL. MODEL 1 TO 6 IS SHOWN HERE. ACTIVITY OF SLIP SYSTEMS CAN CHANGE WITH INCREASING STRAIN BECAUSE OF GEOMETRICAL CONSTRAINTS. IN THIS SENSE, MODEL 4 AND 5 APPEAR VERY STABLE ............................................................................................................................................................................................................................................................... 134 FIGURE 4-15: WET SAMPLES DEFORMED AT 8.5 GPA AND 1300°C. THE SPECIMENS SHOWS TWO LIKELY ACTIVE SLIP SYSTEMS – (010)[100] AND (100)[001] WHICH HAS ALSO BEEN CONFIRMED BY TEM STUDY ON THIS SAMPLE........................................................................................................... 135 FIGURE 4-16: POLE FIGURES FOR MODELS DESCRIBED IN THE TABLE 5-4. MODELS WHICH ASSUME (100)[001] TO BE THE EASIEST AND (010)[100] AS SLIGHTLY HIGHER THAN THE FORMER ALONG WITH VERY HIGH VALUE OF CRSS FOR (010)[100] AND (001)[100] I.E. FOR A-SLIP CAN REPRODUCE WELL THE POLE FIGURE FOR THE SPECIMEN DD456. ......................................................................................................................................... 135 FIGURE 4-17: LEFT: SHEAR WAVE ANISOTROPY IN THE UPPER MANTLE AS A FUNCTION OF DEPTH. RIGHT: P-WAVE ANISOTROPY AS A FUNCTION OF DEPTH (SOURCE: PHD THESIS – HELEN COUVY, 2005). .......................................................................................................................................................... 138 FIGURE 4-18: VARIATION OF WATER CONTENT OF MAJOR MINERAL PHASES IN THE UPPER MANTLE. CHANGES IN THE WATER CONTENT ARE RESULT OF VARIATION IN THE PORTIONING COEFFICIENT OF WATER FOR VARIOUS PHASES WITH DEPTH. ......................................................................................... 140 FIGURE 4-19: VARIATION IN OLIVINE FABRIC WITH CHANGES IN WATER CONTENT AS A FUNCTION OF DEPTH. PRESENCE OF C-TYPE FABRIC CAN EXPLAIN THE NATURE OF THE SEISMIC ANISOTROPY IN THE LOWER PARTS OF THE UPPER MANTLE. NUMBERS IN THE PARENTHESIS ARE THE VSH/VSV RATIOS (FROM KARATO ET AL., 2008) THAT ARE OBSERVED IN NATURAL OLIVINE SPECIMENS EXHIBITING CORRESPONDING FABRIC TYPES. ..... 141 LIST OF TABLES TABLE 1-1: FABRIC TYPE AND NATURE OF SLIP SYSTEM (JUNG AND KARATO, 2001) .............................................................................................. 9 TABLE 1-2: SUMMARY OF SLIP SYSTEM (DURHAM AND GOETZE, 1977) ................................................................................................................. 11 TABLE 1-3: SHEAR WAVE SPLITTING (DIRECTION OF THE POLARIZATION OF THE FASTER, VERTICALLY TRAVELING SHEAR WAVES) (FROM KARATO, 2008) .................................................................................................................................................................................................. 13 TABLE 1-4: VSH/VSV ANISOTROPY (FROM KARATO, 2008) .................................................................................................................................... 13 TABLE 1-5: LATTICE CONSTANTS AND DENSITIES OF OLIVINES (DEER ET AL., 1997) ........................................................................................... 16 TABLE 2-1: LIST OF DEFORMATION DEVICES AND PROPERTIES (MODIFIED AFTER KARATO 2008) .................................................................... 21 TABLE 2-2: LIST OF EXPERIMENTS AND THE END PRODUCTS - CALIBRATION OF CELL PRESSURE AT 1000°C USING PHASE TRANSITION IN QUARTZ ................................................................................................................................................................................................................ 32 TABLE 2-3 : OPTICS SETTINGS FOR DIFFERENT FREQUENCY RANGES USED TO ANALYZE WATER SPECIES ............................................................. 50 TABLE 3-1: EXPERIMENTAL CONDITIONS AND RESULTS OF DRY SAN CARLOS OLIVINE EXPERIMENTS .................................................................. 59 TABLE 3-2: MEASUREMENT OF STRESS USING RECRYSTALLIZED GRAIN SIZE ........................................................................................................... 76 TABLE 3-3: LIST OF EXPERIMENTS AND EXPERIMENTAL CONDITIONS UNDER WET CONDITION ............................................................................. 83 TABLE 3-4: STARTING MATERIAL FOR DEFORMATION EXPERIMENTS ON HYDROUS OLIVINE .................................................................................. 84 TABLE 3-5: DESCRIPTION OF THE STARTING MATERIAL AND WATER CONTENT FROM 1H MAS NMR AND FTIR MEASUREMENTS ................ 89 TABLE 3-6: O – H...O DISTANCE FOR DIFFERENT STRETCHING FREQUENCIES PRESENT IN THE FTIR SPECTRA OF THE HYDROUS FORSTERITE (Z769) AND OLIVINE SAMPLE USING RELATION CORRELATION PROPOSED BY LIBOWITZKY (1999). CHEMICAL SHIFT VALUES OBSERVED USING 1H MAS NMR AND CORRESPONDING O – H...O DISTANCE IN THE HYDROUS FORSTERITE SAMPLE (ECKERT,1988) HAS BEEN SHOWN IN THE BOTTOM TWO ROWS. ............................................................................................................................................... 90 TABLE 3-7: DEGREE OF RECRYSTALLIZATION AND RECRYSTALLIZED GRAIN SIZE FOR WET SPECIMENS ................................................................ 93 TABLE 3-8: EXPERIMENTAL CONDITIONS FOR PERIDOTITE DEFORMATION EXPERIMENTS AND LIKELY ACTIVE SLIP SYSTEMS ........................ 103 TABLE 4-1: FABRIC TYPE AND NATURE OF SLIP SYSTEMS (JUNG AND KARATO, 2001) ........................................................................................ 110 TABLE 4-2: VALUE OF CONSTANTS THAT DESCRIBE WELL THE CRSS-TEMPERATURE RELATION FOR THE TWO SLIP SYSTEMS IN OLIVINE ... 123 TABLE 4-3: CHOICE OF RELATIVE CRSS VALUES USED FOR VARIOUS MODELS IN ORDER TO SYNTHETICALLY GENERATE THE POLE FIGURE FOR SPECIMEN DD455 ............................................................................................................................................................................................ 131 TABLE 4-4: CHOICE OF RELATIVE CRSS VALUES USED FOR VARIOUS MODELS IN ORDER TO SYNTHETICALLY GENERATE THE POLE FIGURE FOR SPECIMEN DD456 ............................................................................................................................................................................................ 135 TABLE 4-5: VSH /VSV ANISOTROPY FOR VARIOUS OLIVINE FABRICS AS A FUNCTION OF MANTLE FLOW DIRECTION (FROM KARATO, 2008) ............................................................................................................................................................................................................................. 137 [VII] wird argumentiert, dass der Rückgang der seismischen Anisotropie, der in den obersten 300 km des oberen Mantels beobachtet wird, nicht durch eine druckinduzierte Änderung des dominanten Gleitsystems in Olivin verursacht wird. Stattdessen wird vorgeschlagen, dass Änderungen im H2O-Gehalt des Olivins mit der Tiefe eine Verschiebung der Textur von Typ A nach Typ C bewirken, mit einem möglichen Umweg über die Textur des Typs E (charakterisiert durch das Gleitsystem (001) [100]), die in dieser Studie jedoch nicht beobachtet wurde. Modellierungen wurden durchgeführt, um zu zeigen, dass diese Änderung im dominanten Gleitsystem die Verringerung der seismischen Anisotropie mit der Tiefe im oberen Erdmantel verursachen kann. Der H2O-Gehalt von Olivin steigt von unter 100 ppm bei 50 km Tiefe auf 250 ppm bei 300 Kilometern Tiefe an. Allerdings wird nicht argumentiert, dass der gesamte H2O-Gehalt des Mantels mit der Tiefe ansteigt, sondern, dass diese Änderung im H2O-Gehalt des Olivins durch die Änderung des Verteilungskoeffizienten von H2O zwischen Olivin und Pyroxen mit der Tiefe bei einem konstanten H2O Konzentration von 200 ppm im oberen Erdmantel verursacht werden kann. Ähnliche Verformungsexperimente wurden mit einer Probe peridotitischer Zusammensetzung bei 8.5 GPa und 1300 ° C durchgeführt und ergaben identische Olivintexturen wie die monomineralischen Experimente. Texturen für Diopsid und Enstatit in diesen Experimenten sind ähnlich mit denen, die zuvor in Experimenten bei niedrigerem Druck produziert wurden. Experimente mit einem piezoelektrischen Einkristall aus GaPO4 wurden in der D-DIA und der 6-Stempel MAVO Presse bei hohen Drücken durchgeführt, um die elektrische Ladungen zu messen, die durch die deviatorischen Spannungen erzeugt werden. Die elektrische Ladung des Kristalls wurde mithilfe eines Operationsverstärkers gemessen. In Experimenten bei Raumtemperatur wurden unter Verwendung der kubischen Zelle erfolgreich quantifizierbare elektrische Ladungen gemessen, die bei absoluten Bewegungen der Deformationsstempel von weniger als 0,5 µm erzeugt wurden. Obwohl [VIII] die piezoelektrische Konstante für GaPO4 bei hohen Drücken noch nicht kalibriert ist, konnten aus den gemessenen elektrischen Ladungen mechanische Spannungen im Bereich von 4-350 MPa abgeschätzt werden. [1] 1 Introduction Only rocks of the earth’s outer crust are directly accessible to analysis but this surface reservoir accounts for less than 1% of Earth's total volume. Clues to the chemical and physical state of the Earth’s underlying mantle can be obtained through the study of xenoliths i.e. rocks brought to Earth's surface in basalt flows or by more exotic magmas such as diamond-bearing kimberlite pipes. In addition larger sections of the oceanic lithospheric mantle can become tectonically attached to the continental crust during mountain building episodes and meteorites also provide some clues about the likely chemical composition of the bulk Earth and its metallic core. The deep interior of the Earth remains directly inaccessible, however, and it can only be studied indirectly, using tools provided by geophysics – such as analysis of seismic waves and the measurement of gravity, heat flow, and magnetism. Seismology has been the most important tool for the determination of the Earth’s deep structure and likely chemical composition. Seismic body wave data has been employed to produce one dimensional global model for S and P wave velocities in the Earth [Dziewonski and Anderson, 1981]. These one-dimensional profiles have been compared with mineral seismic velocities determined as a function of pressure, temperature and composition in the laboratory in order to determine the likely mineralogy and composition of the mantle as a function of depth [Frost, 2008; Stixrude and Lithgow-Bertelloni, 2005]. Such comparisons are generally consistent with an ultramafic upper mantle composed of olivine, orthoand clinopyroxene and garnet to depths of approximately 410 km. The velocities for the mantle at greater depths are consistent with a bulk mantle of similar composition to the upper mantle, although undergoing phase transformations to denser mineral polymorphs with increasing depth. Seismic discontinuities at 410, 520 and 660 km, where waves are reflected and converted at sharp boundaries in mineral elastic properties, are consistent with experimental studies that show phase transformations of olivine to higher pressure [2] structures at pressure corresponding to these depths. Seismic observations are therefore consistent with the upper mantle being comprised dominantly of olivine, ∼60 volume % (Fig 1-1), which is also in agreement with the majority of mantle xenoliths which show the upper mantle to be olivine dominated. Figure 1-1: Pyrolitic mantle mineralogy as a function of mineral volume fraction and depth variation. (Figure courtesy: Dan Frost) Velocities of seismic body waves in the Earth increase with depth as a result of both the effect of pressure on mineral elastic properties and phase transformations to denser mineral structures. While the former effect causes a gradual increase in velocity with depth the later introduces discontinuous changes in velocity. However, seismic wave velocities [3] also change as a function of the direction of propagation in some regions of the mantle. This anisotropic behaviour is a phenomenon of great significance because it results from the development of fabric in mantle rocks caused by convective flow driven by heat flow in the earth. Convection in the earth’s mantle has a direct bearing on the motion of tectonic plates, which in turn governs the evolution of the most prominent geological features on the earth’s surface, such as mountains, oceans, volcanoes etc. The study of seismic anisotropy can therefore be used to understand the direction of mantle convection, to investigate the coupling between the lithosphere and the asthenosphere and to delineate structures in the interior such as continental roots. 1.1 Seismic anisotropy in the earth Seismic anisotropy arises from anisotropic elastic properties of rocks and minerals and can result from two main processes in the Earth, both related to deformation. Shape preferred orientation (SPO) arises from layering, caused, for example, by mineral banding or melt channelling, while crystallographic preferred orientation (CPO) arises from the alignment of elastically anisotropic minerals. Seismic anisotropy due to SPO would infer banding of minerals into layers with strongly different elastic properties. Most mantle mineral, however, do not have sufficiently different elastic properties to cause strong seismic anisotropy through SPO [Shearer, 1999]. The exception would be banding involving melt layers, although these could only occur in the very top of the mantle, potentially beneath ridges, or possibly in the D’’ layer. Anisotropy in the bulk of the mantle is generally attributed to CPO. Seismic anisotropy is measured using two main techniques: 1. Azimuthal anisotropy is the variation in wave velocity, both S and P waves, with the direction of wave propagation. This was first detected from the azimuthal dependence of waves (a P wave that travels along the boundary between the crust and mantle) in the oceanic lithosphere, beneath the Pacific Ocean [Hess, 1964]. This type of anisotropy is measured by determining the directional dependence of wave velocities through a region of the earth. For this purpose a series of different [4] sources (e.g. earthquakes) are required to send waves to one or more receivers so that suitable directional coverage of the region in question is obtained. The differences in velocity as a function of the direction that the wave travelled through the region of interest are then analyzed. The main drawbacks in studying azimuthal anisotropy are that many source-receiver pairs are required and heterogeneities can also cause apparent anisotropy because rays travel through different regions on their way to the region of interest. Azimuthal anisotropy can also be studied using Surface waves (Rayleigh and Love waves). 2. Polarization anisotropy is similar to birefringence in optical mineralogy and leads to shear-wave splitting in seismograms. S-wave particle motion is normal to the propagation direction and the velocity is therefore a function of the material elastic properties in directions normal to the propagating direction. In an anisotropic medium S-waves therefore become polarized with a fast S-wave direction orthogonal to a slow one. The velocity difference between the polarized S-waves causes shear wave splitting, where the two polarized waves develop a delay time. At a single receiver station the polarization direction (φ) of the fast shear wave and the time delay (𝛿𝑡) between the two pulses can be measured (Fig. 1-2). Figure 1-2: A wave travelling through a elastically anisotropic media splits into two orthogonally polarized wave. Magnitude of the shear wave splitting is given by the time delay (δt) between the fast wave and the slow wave. Figure source: - Ed Garnero - http://garnero.asu.edu/research _images In addition to these different measurement techniques, seismologists often model anisotropy in the mantle assuming transverse isotropy, which considers an elastic medium to have a [5] symmetry axis normal to the propagation direction. In most instances the symmetry axis is considered to be vertical and this type of anisotropy is therefore often termed radial anisotropy. Differences in properties are implied in the horizontal and vertical directions. P waves are then resolved into PH and PV components in the horizontal and vertical directions and SH and SV are the corresponding polarized S-waves. The first reference model for seismic structure of earth, PREM (Dziewonski and Anderson, 1981), includes this kind of anisotropy in the top 220 km of the Earth (Fig 1-3). The value VSH/VSV or VSH2/VSV2 or inequalities such as VSH>VSV are frequently used to quantify anisotropy in the mantle as shown in figure 1-3. Figure 1-3: Physical and chemical structure and Radial seismic anisotropy observed in the earth. Source of significant anisotropy in the upper mantle is believed to be the crystallographic preferred orientation of mantle mineral, mainly olivine (Courtesy: D. Mainprice). Significant seismic anisotropic is observed in the upper mantle and the D’’ layer (between lower mantle and the outer core) (Fig 1-3). Major source of the seismic anisotropy in the upper mantle is the CPO of major mineral phases e.g. olivine and [6] pyroxene. Out of these two mineral phases, olivine has much larger contribution to the overall anisotropy in the upper mantle because of its larger intrinsic anisotropy and the volume. Anisotropy in the crustal regions is generally caused by the shaped preferred orientation and presence of melts and fluids. 1.2 CPO in Olivine Creep within the earth’s convecting mantle results in the non-random distribution of crystallographic orientations of major mantle minerals such as olivine, pyroxene and garnet because these minerals have anisotropic mechanical properties (Karato, 1989). As these minerals, particularly olivine, also have intrinsic elastic anisotropy the development of CPO makes the mantle seismically anisotropic in places. Therefore, seismic anisotropy in the mantle reflects the strain field prevailing in the past (frozen-in anisotropy) within the lithosphere or present convective processes in the asthenosphere and deeper mantle. As shown in Figure 1-3, the bulk of mantle below 200 km appears seismically isotropic, which could be interpreted as a result of diffusion creep or superplastic flow (Karato, 1995), because such diffusive processes do not lead to CPO development. CPO results from dislocation glide which acts to rotate the orientation of a crystal to match the imposed deformation regime. CPO depends on the deformation geometry and the active dislocation slip systems of the crystal. A slip system is related to the motion of the dominant dislocations active in the mineral. Natural olivine –bearing rocks show a deformation fabric dominated by alignment of the [100] axis parallel with the direction of apparent shear deformation, abbreviated as a-slip, while the (010) plane is parallel to the shear plane (Fig 1-4). [7] Figure 1-4: Crystallographic preferred orientation development in olivine due to shearing nature of the mantle flow. CPO of elastically anisotropic minerals is the principal cause for seismic anisotropy observed in the upper mantle. The olivine fabric database compiled by (Ben Ismaїl and Mainprice 1998) indicates that up to 50% of naturally deformed samples possess this (010)[100] CPO olivine fabric. Apart from the most common (010)[100] slip system, other known slip systems in olivine are (001)[100], (010)[001] and (100)[001] [Carter and Ave'lallemant, 1970]. In the past, experimental studies have been performed on natural and synthetic samples in order to understand the effect of deformation conditions on the CPO development in olivine and other minerals (Carter and Ave'Lallemant 1970, Nicolas et al. 1973, Zhang & Karato 1995). Initial works on experimental deformation on San Carlos olivine indicated that slip systems in olivine change with changing stress and temperature [Carter and Ave'lallemant, 1970; Goetze, 1978]. At lower stresses (or higher temperatures) (010)[100] slip system was found to be most active where as higher stresses (or lower temperatures) (010)[001] slip system was most active. Under intermediate stress and temperature conditions, {0kl}[100] slip system was the easiest (Fig. 1-5). Later works by Karato and co-workers [8] also proposed a change in slip system at from (010)[100] to (010)[001] slip system at higher stresses [Jung and Karato, 2001a]. Change in slip system has also been observed with change in water content of olivine [Jung and Karato, 2001a; Katayama et al., 2004]. At moderate water content (less than 60 wt. ppm), (001)[100] slip system was found to be dominant slip system while it changed to (100)[001] slip system at higher water contents (Fig. 1-5). Figure 1-5: Dominant slip systems in olivine as a function of strain rate and temperature (at P = 1.5 GPa) (from Carter & Av´e Lallemant 1970). Results shown here suggest stress-induced transitions in the dominant slip systems. (b) A comparison of creep strength for different orientations of single crystal and polycrystal at ˙ε ≈ 10−5 s−1 (from Goetze 1978). The [110]c activates the [100] (010) slip system, the [101]c orientation, the [100] (001) and [001] (100) slip systems, and the [011]c and [001] (010) slip systems. Figure Source: Karato (2008) Previous works at Bayerisches Geoinstitut [Couvy et al., 2004] indicated that at higher pressures (11 GPa), the deformation was mainly caused by slip of dislocation with [001] burgers vectors, indicating that c-slip was easier under these conditions. Deformation of single crystal olivine specimens also reaffirmed this conclusion where [001]-slip over [100]-slip progressively becomes easier with increasing pressure [Raterron et al., 2007]. Theoretical modelling of dislocation core structure by first principal calculations indicated that this change in slip system with pressure can be explained by change in dislocation core structure with pressure [Durinck et al., 2005]. [15] 1.5 Mineral description - Olivine Mg-rich olivine is a common mineral of mafic and ultramafic rocks, and is generally considered to be the major constituent of the Earth’s upper mantle (40-80% in volume) with a composition close to (𝑀𝑔0.9𝐹𝑒0.1)2𝑆𝑖𝑂4 based on analyses of olivine in mantle xenoliths. 1.5.1 Crystal-chemistry Olivine is an orthosilicate [Deer et al., 1997], and a solid solution between the two endmembers, 𝑓𝑜𝑟𝑠𝑡𝑒𝑟𝑖𝑡𝑒,(𝑀𝑔)2𝑆𝑖𝑂4 (𝐹𝑜100𝐹𝑎0) and 𝑓𝑎𝑦𝑎𝑙𝑖𝑡𝑒,(𝐹𝑒)2𝑆𝑖𝑂4(𝐹𝑜0𝐹𝑎100). Olivine crystal lattice has an orthorhombic symmetry (space group: Pbnm). The important crystallographic parameters of olivine are shown in Table 1-5. The structure consists of independent 𝑆𝑖𝑂4 tetrahedra linked by divalent cations (M1 and M2) in six fold coordination (Fig 1-8). The oxygen anions are arranged in sheets nearly parallel to the (001) plane and closely resemble a hexagonal close-packed structure (Fig. 1-9). Each oxygen atom is bonded to one silicon cation and three divalent cations (e.g. Mg2+, Fe2+) with octahedral co-ordination. However, since the oxygen atoms are not perfectly close-packed, the M1 and M2 polyhedra are irregular shaped, and in such a way that the M2 site is slightly larger than the M1 site. The adjacent M1 sites share edges to form bands parallel to the [001] axis. These bands are connected to the next M1 bands in the upper layer (or lower layer) by the M2 octahedral sites. There is apparently no complete ordering in the Mg/Fe2+ distribution between the M1 and M2 sites, but Fe2+ has a preference for the M1 site. M1 and M2 may also be occupied by other cations such as Ni2+, Mn2+, Ca2+, Cr3+ [Deer et al., 1997] or B3+ [Sykes et al., 1994]. In particular, olivines from Xenoliths often contain a small amount of nickel (Frey and Prinz, 1976). [16] Table 1-5: lattice constants and densities of Olivines (Deer et al., 1997) Forsterite Mantle olivine Fayalite Chemical Formula Mg2SiO4 (Mg0.9,Fe0.1)2SiO4 Fe2SiO4 a (Å) 4.754 4.755 4.8211 b Å 10.197 10.21 10.4779 c (Å) 5.9806 5.985 6.0889 Density (g/cm 3 ) 3.222 3.4 4.392 Figure 1-8: Idealized forsterite structure projected on (100) plane (Redrawn from Deer et al., 1997). Si atoms are at the centre of the tetrahedrons. Small black circle, Si; larger gray circle, oxygen; black circle, M1; diagonally hatched circle, M2 Figure 1-9: Forsterite structure perpendicular to (100) showing the approximately hexagonal closepacking structure (redrawn from Deer et al., 1997) [17] 1.6 Aim of the thesis Principal goal of this PhD work is to determine the origin of changes in the dominant slip systems at high pressure and high temperature environment prevalent in the upper mantle. For this purpose, we plan to conduct simple shear deformation experiments on San Carlos olivine and Peridotite modal composition, using Deformation-DIA. Experiments are designed to delineate the influences of pressure, temperature, strain rate and H2O content on slip systems in olivine. At the initial stages of this PhD work, a new high pressure assembly will be designed which should allow us to reliable conduct deformation experiments at pressures above 8 GPa under high temperature conditions. Deformed specimens are to be analyzed using a variety of analytical tools that includes SEM & EBSD, TEM, FTIR and NMR. 1. Effect of stress and pressure on slip systems in olivine A range of experiments has been conducted at various pressure and temperatures to explore the effect of stress on the slip systems in olivine. In this way, we also ascertained the role played by pressure on changes in olivine slip systems. Pressure has been varied between 3 to 8.5 GPa at temperatures between 1300 to 1500°C. Determination of stress in the sample, for some experiments, has been performed Ex-Situ using dislocation densities obtained by Transmission electron microscopy. Alternatively, stresses have also been measured using recrystallized grain size data obtained by EBSD technique and comparing them with known recrystallized grain size versus stress calibration. TEM studies were also be employed for detailed study of dislocation microstructure. 2. Effect of water on slip systems in olivine A similar range of experiments have been performed on “wet” olivine specimens to determine the effect of H2O on slip systems in olivine. Water content of the hydrous specimens has been analyzed using FTIR spectroscopy. Some of these [18] specimens have also been studied by TEM to understand the role of water on dislocations. 3. Olivine is the most voluminous phase in the upper mantle rocks. Other important mineral phases in the upper mantle are Pyroxenes, Spinel and Garnet. Deformation studies have been performed on Peridotite modal composition, which represents the upper mantle rock composition, to understand the role of other mineral phases e.g. pyroxenes on the overall fabric development in a upper mantle. 4. Stress is the most crucial parameter in a controlled deformation experiment. Yet, it is one of the most poorly constrained. In-situ measurement of stress, in most cases, is either performed using externally (external to the pressure cell) placed load cell or using x-ray radiography. The former method often gives a measured value of stress that can be far off from the actual value experienced by the sample material. This difference is caused by the frictional forces active throughout the pressure cell. Other method of stress measurement using the x-ray radiography relies upon synchrotron based radiation source. This approach is not suitable for day-to-day use in a standard laboratory environment. Therefore, attempt has been made to develop a stress sensor based upon piezoelectric property of GaPO4 crystal. Once this technique has fully developed, it should provide us a mean to make in-situ stress measurements. [19] 2 Methodology 2.1 Deformation experiments under extreme conditions Many types of equipment have been used to deform mineral assemblages at ambient and high pressure and temperature conditions. For many years the gas media Paterson rig and the Griggs apparatus were the main devices used to deform samples but could only be employed at conditions equivalent to the crust and very shallow mantle (see table 1). However the need to investigate rheological properties at higher pressures resulted in initial attempts using the 6-8 Kawai-type multianvil, DIA and diamond anvil cell [Karato, 2008a]. These devices were not designed for applying controlled deformation at high pressure but they could expose samples to high deviatoric stresses as a result of anisotropic compression. In the diamond cell this occurs quite normally when a poorly hydrostatic pressure medium is employed, while in multianvil devices deviatoric stresses can be applied by placing harder materials in the sample column direction compared to the perpendicular direction. In these devices high deviatoric stresses then develop during compression. Once high pressures are reached the application of temperature softens the pressure medium and the stresses relax. The need to provide a better control over the sample deformation environment, however, lead to the development of new high pressure deformation devices such as the Rotational Drickamer device (Karato, 2008) and the deformation DIA apparatus. In order to study the development of Crystallographic preferred orientation (CPO) of mineral assemblages at mantle conditions, deformation experiments must be able to satisfy the criterion given below: 1. The method must provide the ability to generate and maintain extreme states of pressure (for upper mantle 1-14 GPa) and temperature (above 1000-1600°C) conditions prevalent in the earth’s mantle, for time durations that allow fabrics to develop at suitable strain rates (1-48 hours). [20] 2. Such a method should also provide control over strain rate (or stress) which is essential for any meaningful understanding of the fabric development. 3. The ability to measure strain rate and stress. 4. Provide control over chemical environment e.g. water and oxygen fugacity is also required. 5. Allow recovery of the sample for fabric and textural analysis. And, 6. Ensure that the sample does not deform during compression and decompression phase of the experiment. 2.1.1 High pressure deformation apparatus Understanding the role of deviatoric stress (and several other physical & chemical parameters) on the development of texture in material is a prerequisite to the understanding of anisotropic behaviour of minerals. Material scientists also use such studies for establishing relations between various manufacturing processes and the mechanical performance of the product material. The immense scope of such studies has led to the development of a series of high pressures apparatuses with each having a unique set of advantages and drawbacks. Simple dead weight loading experiments are an effective way to perform precise deformation experiments under ambient pressure condition [Carter et al., 1980] whereas at the other extreme of pressure diamond-anvil cells can be used to deformed materials up to 200 GPa pressure but with poor control over strain rate and stress distribution [Kinsland and Bassett, 1977]. At intermediate pressures, a range of devices exist which all tend towards a compromise in terms of maximum pressure and the control over deformation and sample environment. Some salient features of various deformation apparatus are given below in the table 2-1. For experiments to address olivine fabric development pressures of between 1-15 GPa are required. Though, the 6-8 multianvil configurations can achieve these pressures, only stress relaxation experiments can be performed and no control over strain rate is possible [Bussod et al., 1993; Karato and Rubie, 1997]. The Rotational Drickamer device (e.g. [Yamazaki and Karato, 2001] can provide control of strain rate over the pressures of interest, however, it is very limited in sample size and control over [21] pressure and temperature is limited accept when used in conjunction with in situ X-rays. Consequently the deformation-DIA appears to embody a suitable compromise between allowing control over strain rate, pressure and temperature and also achieving a range of pressure of interest to the study of olivine fabric development in the upper mantle. Table 2-1: List of deformation devices and properties (Modified after Karato 2008) Type of apparatus Max. P (GPa) Max. T(K) In-situ Stress measurement Comment Dead-weight creep apparatus 10-4 2000 From applied load Low ƒH 2 O Gas-medium apparatus (e.g. Paterson rig) 0.5 1600 Internal load cell Limited ƒH 2 O Griggs-type apparatus 3 1600 External load cell Limited strain Deformation-DIA 23 1700 X-ray diffraction Limited strain Rotational Drickamer apparatus 18 2000 X-ray diffraction Unlimited strain 6-8 Multianvil stressrelaxation 23 2000 X-ray diffraction Non-steady state, relaxation experiments only Diamond anvil 200 1000 X-ray diffraction Non-steady state, very high stress, Study of LPO difficult due to small sample size 6ram cubic press 25 2000 X-ray diffraction Limited strain Deformation-DIA The Deformation-DIA (or D-DIA) is a modified form of DIA cubic-anvil apparatus [Osugi et al., 1964]. The D-DIA incorporates two additional hydraulic actuators; here referred to as differential rams, which provide independent control of the displacement of two vertically opposing anvils [Wang et al., 2003]. The original DIA consists of upper and lower guide blocks, four wedge-shaped side wedges, and six tungsten carbide anvils. The six anvils of the D-DIA define a cubic volume due to their square shaped truncation. Four out of six anvils are attached to the side wedges whereas one each of the other two anvils is mounted to the upper and lower guide blocks. [22] Differential Ram Side Wedge Displacement Transducer Main load From Press Hydraulic Oil line Sample Guide Block Anvil Figure 2-2: A vertical cross-section of D-DIA showing the two side wedges and the differential ram. Presence of differential rams provides controlled deformation of the cubic sample at a constant pressure. Original DIA Deformation DIA Figure 2-1: Schematic diagrams of original DIA and Deformation-DIA. A) Original DIA consists of upper and lower guide blocks, four wedge shape side wedges and six tungsten carbide anvils. B) A deformationDIA has two additional hydraulic actuators called deformation rams which provides a mean to achieve controlled deformation. (source: Y. Wang) [23] As the main guide block of the DIA is compressed the vertically opposing anvils are advanced. The 45° surfaces of the side wedges, however, ensure that a component of the vertical displacement is converted to a horizontal displacement which advances the 4 horizontal anvils. Once high pressure has been achieved through the advancement of the main ram, the vertical differential rams can be advanced thus applying a principle stress on the cubic sample assembly. D-DIA’s unique design provides a way to advance the differential rams into the sample assembly without raising the confining pressure in the process. A typical experimental run in the D-DIA is illustrated below in Figure 2-2. One starts by hydrostatically compressing the sample assembly, with differential rams fully withdrawn to maintain the oil pressure in the main ram at a constant value. The action of the guide block transfers the vertical compressional force into horizontal compression via the side wedges. Then the sample is heated up to the requisite temperature and kept in this state for approximately 30 min, with a view to achieve thermal equilibrium. Then the differential rams are advanced so as to bring a non-cubic shape change to the assembly while simultaneously withdrawing the main ram at an appropriate rate. This ensures that total force exerted by the main ram stays constant and hence the volume of the sample assembly is also conserved (Wang et al., 2003). Figure 2-3: PressureTemperature-Strain profile of typical experimental run in DDIA press. After compressing the pressure cell to the requisite pressure, sample is heated up to the desired temperature and it is allowed to heat for at least 30 min to release the initial stress buildup, if any present in the sample. Then, the sample is deformed at a constant strain rate. Once the target amount of strain is achieved, deformation is stopped and the sample is quenched right after that. Thereafter the pressure is released slowly. [24] The onset of movement of the differential rams occurs only when the differential ram pressure is sufficient enough to overcome the confining force and the friction. Hence, the higher the confining pressure, higher is the initial differential ram pressure required to move the differential rams. This imposes a limit to the maximum confining pressure at which deformation can be achieved without breaking the anvils. Using the 500 tonne Voggenreiter D-DIA press available at the Bayerisches Geoinstitut with 4 mm square truncations tungsten carbide (WC) anvils, it is possible to perform deformation experiments up to 10 GPa confining pressure, at temperatures as high as 1500°C. The displacement of the two differential anvils is measured relative to the guide block using displacement transducers. The transducers employ a magnetic response to measure displacement to a precision of 0.2 µm. Sample assembly design As stated earlier, in the D-DIA a wide range of pressure and temperature conditions can be achieved (up to 10 GPa and 1700°C). In order to access higher pressures the truncation size on the tungsten carbide anvils can be reduced, however, this also reduces the sample size as the dimensions of the cubic pressure assembly must also be reduced. For the work performed in this thesis two assembly configurations were developed. The 6/8 assembly employs 6 mm edge length square faceted tungsten carbide anvil truncations with a cubic sample assembly that is 8 mm in edge length. It was used to achieve pressures up to 3.5 GPa. The 4/6 assembly, used between 3.5 and 10 GPa, employs 4 mm anvil truncations and a 6 mm edge length cube. The experimental set-up for deformation experiments consists of a cubic pressure medium composed of fired or unfired pyrophyllite. The cube is drilled out along one axis for the insertion of a furnace separated by a thermally insulating sleeve. The resistive materials graphite and rhenium are used as furnaces, while zirconia is used as a thermally insulating sleeve around the furnace to make the experimental set-up thermally efficient. A number of attempts were made to employ lanthanum chromite as a furnace material, [31] Pressure and temperature calibration of the Sample assembly Pressure calibration at room temperature The sample pressure must be calibrated in each D-DIA assembly against the oil pressure using phase transitions that occur at well-determined pressures. Initially room temperature calibrations were employed to identify the approximate pressure range for further high temperature calibrations and to define the gradient of the pressure calibration. Bismuth undergoes phase transitions at 2.54 GPa (Bi I-II), 2.7 GPA (Bi II-III) and 7.7 GPa (Bi III-IV) which causes a change in the resistivity of bismuth [Getting, 1998; Lloyd, 1971], whereas the resistivity of Manganin wire (Cu86/Mn12/Ni2) changes linearly with pressure. In order to calibrate the pressure achievable with the 6 mm pyrophyllite pressure cell, a thin wire of Bismuth was placed between two AgCl disks as shown in Fig 2-8. Thin copper foils which served the purpose of electrode, were placed at the two ends of the Bismuth wire. A constant current was supplied through the bismuth wire and the voltage across the Cu-electrodes was measured during the compression. Bi I-II transition was observed at around 17 bar oil pressure. For obtaining the pressure-resistivity relationship of Manganin, the same setup was used but with Manganin wire replacing the Bismuth wire. The change in Manganin resistivity with the confining pressure can be expressed as the pressure coefficient of the resistance change given by �𝛿𝑅𝑅0 ���1𝑃 � �=(2.322 ± 0.008)×10−2 𝐺𝑃𝑎−1 where 𝛿𝑅 is the change in resistance and R is the resistance at any given pressure P measured in GPa (Robert J. Zeto and H. B. Vanfleet). The pressure dependence of resistivity must be Figure 2-8: Schematic of assembly used for pressure calibration using Bismuth and Manganin [32] calibrated using a known pressure point, for which we used the Bi I-II transition. As shown in Fig 2-8 the pressure at room temperature determined using Manganin wire reaches a plateau just over 7 GPa, consistent with the observation that we were unable to observe the Bi III-IV transition at 7.7 GPa. This plateau is typical of most multianvil assemblies and results from the gasket supporting an ever-increasing proportion of the load. Figure 2-9 shows that data from calibration experiments at room temperature and 1000°C. The assembly is more efficient at generating pressure at 1000°C than at room temperature as shown by the Coesite/Stishovite transition, which occurs at approximately 110 bars oil pressure (78.6 tonnes of applied load). Pressure calibration at high temperature Phase transition in quartz to its high pressure polymorphs, coesite and stishovite, is pressure and temperature dependent. At 1000°C, quartz transforms to coesite at ~ 2.95 GPa; whereas the coesite to stishovite transition pressure at 1000°C is at ~9.25 GPa (Akaogi & Navrotsky, 1984). A fine grained mixture of fibrous quartz was placed in the standard assembly (but in pure shear configuration). The sample assembly was brought up to the requisite pressure and then it heated at 1000°C for ~5 hours. After quenching and decompression, the end product was sectioned and polished and analyzed using Raman spectroscopy to identify the SiO2 polymorph in the run products. Table 2-2: List of experiments and the end products - Calibration of cell pressure at 1000°C using phase transition in Quartz Experiment Run Oil pressure(bars) Observation DD451 17.1 Quartz DD452 19.6 Quartz and Coesite coexist DD387 78.6 Coesite DD400 85.7 Stishovite [33] Figure 2-9: Calibrated cell pressure has been plotted as a function of oil pressure. Room temperature calibration has been done by using phase transitions in Bismuth and Manganin resistivity method. High temperature (1000°C) pressure calibration was done using phase transition in Quartz (quartzcoesite and coesitestishovite). 700 bar oil pressure is equivalent to 500 tonne load for D-DIA press at BGI. Temperature calibration of the sample assembly The sample temperature distribution within the 4/6 deformation cell assembly was measured using a two-pyroxene thermometer assemblage, employing the calibration of Nickel & Brey, (1984). An equimolar powdered mixture of Al-free enstatite and diopside were placed between the alumina deformation pistons at 45° to the axial direction. 4 wt% PbO was added to the sample as a flux. The sample powder was compacted before the second deformation piston was placed on top, but the sample was not hot pressed. The experiment was heated at 1300°C (thermo-couple temperature) and 8 GPa pressure for approx. 6 hrs. No deformation was applied. Chemical compositions of fully reacted neighbouring pairs of enstatite and diopside grains were measured using a JEOL JXA – 8200 electron microprobe at BGI. [34] The recovered sample slice was approximately 200 µm thick in the axial direction. The calibration employs the distribution of Ca and Mg between the two-pyroxene minerals. The determined mean temperature in the central portion of the sample slice was approximately 150°C higher than the temperature measured at the thermocouple. The difference between the mean temperature at the middle of the sample and at the extreme points of the sample was found to be ~75°C (Fig 2-10). This results in a temperature gradient of 84° C/mm along the sample length. The variation in temperature likely reflects the thermal gradient along the furnace; with the centre of the sample, therefore, placed will in the hottest part of the furnace, while the thermocouple and sample extremities next to the furnace are slightly out of the hot spot. Figure 2-10: Measured temperature along the sample length. Center of the sample recorded the highest temperature with approx. 85°C/mm temperature gradient as we move towards the extremities. Oxygen fugacity of the experiments The oxygen fugacity is an important parameter in deformation experiments as it controls the concentration and mobility of point defects in Fe-bearing minerals [Demouchy and Mackwell, 2006; Kohlstedt and Mackwell, 1998]. The oxygen fugacity is not controlled 1300 1350 1400 1450 1500 1550 -0.85 -0.65 -0.45 -0.25 -0.05 0.15 0.35 0.55 0.75 Temperature (°C) Distance from the center of the sample (mm) Temperature (°C) along the sample length Standard Deviation = 43° [35] in D-DIA experiments but it is influenced by the type of furnace employed and by the nature of the starting material. The use of graphite or metal furnaces generally leads to more reducing conditions because the furnaces can only be oxidized during the experiment and has no mechanism to release oxygen or oxidized species. The oxygen fugacity can be measured in the experiment however particularly in the region of the Pt capsule or Pt strain markers where the proportion of Fe alloying with the Pt can be measured. 𝐹𝑒2𝑆𝑖𝑂4 = 𝐹𝑒𝑆𝑖𝑂3 + 𝐹𝑒 + 𝑂2 𝑂𝑙𝑖𝑣𝑖𝑛𝑒 𝑒𝑛𝑠𝑡𝑎𝑡𝑖𝑡𝑒 𝐴𝑙𝑙𝑜𝑦 The equilibrium can be used to determine the oxygen fugacity from the thermodynamic relationship 24 3 2 log log log 2log ln(10) olivine orthopyroxene metal Fe SiO FeSiO Fe o G fo RT aa a −∆ =+− − Where, 24 olivine Fe SiO a , a metal Fe and 3 orthopyroxene FeSiO a are the activities of the Fe2SiO4 component in olivine, Fe in the Pt-Fe alloy and FeSiO3 in pyroxene respectively. ∆G0 is the free energy of the end-member equilibrium, which was taken from thermodynamic data reported by [Stagno et al., 2011]Stagno and Frost (2011). In some deformation experiments where pyroxene was observed and the Fe content of Pt foil or strain marker was measured it was possible to calculate the oxygen fugacity in the experiment. For this activity composition relations for Fe in Pt alloy were required, which were taken from Mann et al. (submitted). The determined oxygen fugacity at 8 GPa and 1500°C was -0.8±0.5 log units or approximately at the fayalite-magnetite-quartz (QFM) oxygen buffer. This value is within the range found for mantle rocks, although it may be considered slightly more oxidised than many samples from the deep mantle, >100 km, which are in general closer to QFM –2 [Frost and Mccammon, 2008]. [36] 2.2 Sample Preparation 2.2.1 Hot pressing San Carlos olivine A fine grained powder of (𝑀𝑔0.9,𝐹𝑒0.1)2𝑆𝑖𝑂4 San Carlos olivine with grain size below 10 µ𝑚 was loaded into a 12 𝑚𝑚 long and 5 𝑚𝑚 outer Diameter cylindrical Platinum capsule. Using ¾” Talc-Pyrex glass assembly and 200t piston cylinder press at Bayerisches Geoinstitut, the assembly was cold pressed to 10𝑘𝑏 confining pressure. Thereafter it was heated to a temperature of 1100°𝐶 and kept as such for 30 𝑚𝑖𝑛. Then the assembly was slowly decompressed over 12 ℎ𝑜𝑢𝑟𝑠 period along with simultaneously cooling to room temperature. Slow decompression with simultaneous cooling was performed in order to avoid decompression cracks. Hydrous olivine samples were prepared by adding an equimolar mixture of Brucite and Silica to the powdered olivine and then hotpressed in the 6-8 multianvil device. In some instance, Brucite-Silica aggregate was added to the pre-hotpressed samples while assembling process before the experiment. 2.2.2 Placing platinum Shear strain marker After hot pressing the sintered samples were carefully removed from the high-pressure assembly and the top and bottom of the capsule removed. 1.2mm diameter cylindrical cores were prepared from these samples in the thin section laboratory by H. Schulze. Using a diamond wire saw, 200µm thick elliptical slices of hot pressed olivine sample were then cut from the core each of which were oriented at 45° to the core axis. Each olivine slice was then cut into two symmetrical halves, with the direction of cutting oriented parallel to the original cylindrical core (Fig 2-11). The exposed surfaces of this cut were then sputter coated with a ~100nm Pt layer. Putting a Pt marker in this way, on a cross-section cut parallel to the cylindrical axis minimizes the marker rotation due to axial compression of the sample. [37] 0.2 mm Sample Pt Strain Marker Alumina Piston Pt capsule Figure 2-11: Emplacement of platinum strain marker for shear strain measurement. Approximately 100 nm thick Platinum-layer is sputter coated on the sides of the two cut halves of the hotpressed sample. Rotation of the strain marker is directly related to the shear strain 2.3 Analytical Methods As the central theme of this thesis has been to study of the effects of physical and chemical parameters on the crystallographic preferred orientation of olivine, electron backscatter diffractometer (EBSD) has been the primary analysis technique. It is also crucial however to relate the determined CPO, or lack thereof, to the underlying deformation mechanism and active slip system in the crystal and for this purpose Transmission electron microscope (TEM) has been a vital analysis technique. Water content in the starting sample and the recovered sample has been measured using Fourier Transform Infrared (FTIR) spectroscopy. A brief introduction to these three important instruments is provided in the next paragraphs. The Electron probe micro-analyzer (EPMA) was used for analyzing the chemical composition of recovered samples and to examine the equilibrium distribution of Ca and Mg between enstatite and diopside aggregates employed in experiments to calibrate the temperature in the pressure cell. Raman spectroscopy has also been utilized for phase [38] identification in the run products from experiments performed to calibrate cell pressure using quartz-coesite and coesite-stishovite phase transformations. 2.3.1 Measurement of crystallographic preferred orientation using Electron backscatter diffraction technique (EBSD) Electron backscattered diffraction (EBSD); sometimes also referred to as backscatter Kikuchi diffraction (BKD) is a technological add-on to a scanning electron microscope. It provides an SEM with a microstructural-crystallographic analysis capability. Primarily, EBSD is used to study texture or preferred orientation of any crystalline or polycrystalline material. This is achieved by indexing and identifying the crystal systems. Apart from structure and orientation information, EBSPs (Electron back scatter patterns; See figure No. 2-12 for an example of such a pattern in mineral olivine) contain additional information on crystal lattice perfection, local strain, deformation, and grain boundaries. Traditionally these types of studies have been carried out using x-ray diffraction (XRD), neutron diffraction and/or electron diffraction in a TEM. [39] Figure 2-12: Formation of backscattered Kikuchi patterns by EBSD in the SEM. (a) Origin of Kikuchi lines from the EBSD (i.e., tilted specimen) perspective. (b) EBSD pattern from olivine (accelerating voltage 20 kV). EBSD system consists of a phosphor screen, compact lens and low light CCD camera attached to a Scanning Electron Microscope (SEM) (Fig. 2-13). A polished sample specimen is placed into the normal position in the specimen chamber, and is tilted to ~70° from the normal position. Doing so boosts the contrast of EBSPs. EBSPs are generated if a stationary beam interacts with the surface of a crystal [Alam et al., 1954],[Venables and Harland, 1973]. The electrons while interacting with an atom undergo inelastic scattering. It results in a fraction of the electrons losing a small part of their energy. This process creates a divergent source of electrons close to the surface of the sample. Some of these electrons are incident on atomic planes at angles which satisfy the Bragg equation. For each given plane, these electrons emanate in diffraction cones from both the front and back surface of the plane. When these cones intersect the phosphor screen, the Kikuchi lines are formed. The Kikuchi lines appear as almost straight lines because the cones are very shallow as the Bragg angle is of the order of 1°. Small Bragg angle results from the fact that incident electrons have very high energy and hence very small wavelength (λ ≈ 8 pm for a 25 KeV electron beam). Hence, Kikuchi bands are effectively the trace of the plane from which they are formed and the EBSD pattern is therefore a gnomonic projection of the crystal structure. [40] Figure 2-13: Schematic setup of an EBSD system showing its principal components Thus, the whole Kikuchi pattern consists of pairs of parallel lines where each pair, or “band,” has a distinct width and corresponds to a distinct crystallographic plane. The intersection of bands corresponds to a zone axis (pole), and major zone axes are recognized by intersection of several bands. The Kikuchi pattern therefore essentially embodies all the angular relationships in a crystal—both the - and inter-planar angles— and hence implicitly contains the crystal symmetry. Figure 2-12 shows an EBSD Kikuchi pattern from mineral San-Carlos olivine. The orientation of the pattern and hence of the volume from which it has arisen is evaluated by “indexing,” that is, identifying the poles and bands in the pattern, and calculating the relationship between these and some chosen reference axes. From Kikuchi bands to pole figure Automated identification of a crystal orientation involves identifying the kikuchi lines in the gray scale image containing EBSPs. First step towards this process involves the preprocessing stage of edge detection. This is a non-trivial task because contrast normal to the kikuchi lines rarely change abruptly. The pattern of Kikuchi lines on the phosphor screen is electronically digitized and processed to recognize the individual Kikuchi lines. These data are used to identify the phase, to index the pattern, and to determine the orientation of the [47] In an Ar ion-milling device the sample is loaded on a stage and lowered into a vacuum chamber. In this vacuum there are two argon ion guns, on opposing sides of the sample. Each gun consists of an anode inside of a cathode tube with small hole in it. The anode is connecting to an Ar supply, and since there is a several kV difference between the anode and cathode, Ar is ionized and accelerated through a hole in the cathode tube and directed at the specimen. As the accelerated Ar ions hit the surface of the specimen, they sputter the top surface layer of then specimen away, by which the specimen is thinned. Ion milling usually results in two kinds of damage to the specimen, creation of topography on a initially flat surface and secondly the creation of an amorphous layer of material on the surface (Barna et al., 1999). The first kind of damage can be reduced by rotating the sample while thinning and using a low incidence angle of the ion beam on the specimen, however due to the geometry of the holder, the lowest incidence angle that can be used for thinning in the ion milling device is 12 degrees. Rotation of the specimen reduces the creation of topography since the sputtering rate is dependent on the orientation of the incident ion beam relative to the crystal lattice of the crystallites in an aggregate [Barna and Menyhard, 1994]. Rotation of the specimen thus averages out (or at least reduces) the orientation dependent sputtering rate. Creation of a damaged or amorphous layer is harder to reduce. Typical operating conditions of ion miller are 2 – 5 kV, in this range ionization of the target can happen by electron exchange between the incident electron and specimen, and thus modifying the direct surface layer of the specimen (Malherbe, 1994). As the incident ions impinge on the surface, the ion will lose its energy in two different way, either through electron interactions with atoms of the specimen, or by nuclear interaction (momentum transfer) with specimen atoms before it finally becomes trapped (implanted) within the specimen. Electronic interaction results in the ionization of specimen atoms. Nuclear interaction, or collision, between the incident ion and atoms of the specimen result in a momentum or energy transfer from the impinging ion to a specimen atom. Momentum transfer sets the atoms of the specimen in motion and leads to sputtering of the specimen atoms if the atoms is freed from the surface, or otherwise may lead to a cascade of collisions inside the specimen. If the impinging ion transfers enough energy, not a single cascade of collision will occur, but a group of atoms will be set simultaneously in motion, a so-called 'spike', which may completely amorphize a portion of the lattice (Malherbe, [48] 1994). The above mentioned processes are dependent on the incident angle, charge, mass and energy of the incident ion, and the properties of the target (Barna and Menyhard, 1994; Barna et al., 1999). The thickness of the damaged or amorphized layer thus will also vary with these variables. A higher energy of the incident ion increases penetration depth and thus the thickness of the damaged layer, whereas as higher mass of the incident ion decreases it penetration depth. A lower incident angle will decrease the thickness, though below an incident angle of 10° the dependence on incident angle becomes very weak (Barna et al., 1999). A multiply ionized incident ion will have a higher energy and thus create a thicker damage layer. Next to this, energy transfer of the incident ion to the specimen may also result in heating of the specimen, which may also damage or modify the specimen, cooling therefore is required for some specimens. Screw and edge dislocations Strain is defined by the displacement of an atom from its position that would be expected from the ordinary periodicity of the crystal. Causes of such a strain field can be dislocations, planar defects or other imperfections in the crystal lattice. In the case of dislocations two different types, or end types since most dislocations have a mixed character, of dislocations can be distinguished, i.e. screw and edge dislocations. Edge dislocations can be seen as the insertion of an additional lattice half plane in the otherwise regular crystal lattice. At the place where this additional half plane ends, the lattice will be distorted around the end of the edge dislocation, called the dislocation core, due to relaxation of the lattice around the core (Figure 2-16a). Screw dislocation the lattice is sheared on a plane such that part of the lattice above this plane has an offset to the lattice below the plane, the direction of the offset also lies in this plane (figure 2b). Dislocation are described by the Burgers vector b, the lattice vector that closes the circuit around the dislocation core (figure 2-16), and the dislocation line (direction DL) around which the lattice is deformed strongest. For an edge dislocation the dislocation line and the Burgers vector are perpendicular, for a screw dislocation they are parallel. [49] The distortion of the lattice around the dislocation core may alter the lattice is such a way that diffracted beams that are in the undistorted lattice not excited, become exited in the distorted lattice. Figure 2-16: Illustration of edge and screw dislocations in a hypothetical crystal. Burgers vector “b”, the lattice vector that closes the circuit around the dislocation core and dislocation line has been represented by “DL”, a). In case of edge dislocation, burgers vector is normal to the dislocation line. In this case, slip plane is defined as the plane containing the dislocation line and the burgers vector, b). In case of screw dislocation, the dislocation line and burgers vector are parallel. 2.3.3 FTIR The hydroxyl distribution within the samples were analyzed with unpolarized Fourier transform infrared (FTIR) using a Bruker™ IFS 120 HR high-resolution FTIR spectrometer with a Bruker™ IR microscope. A schematic picture of the interferometer is shown in fig 2-17. The spectrometer is coupled with a Brucker IR microscope containing all reflecting Cassegrain optics that allows measurements of small areas with apertures down to 10 µm. Measurements in the near infrared region were carried out using tungsten light source, CaF2 beam/splitter and high sensitivity, narrow-band MCT detector. The standard optic settings for the different frequency ranges of interest for analyzing water species are also shown in table 2-3. [50] 1. IR beam in transmission mode 2. Condenser mirror 3. Sample holder 4. Cassegranian objective 5. Objective 6. Aperture 7. Moving mirror 8. Ocular 9. MCT detector Figure 2-17: Details of the FTIR microscope (Redrawn from Bolfan-Casanova, 2000) Table 2-3 : Optics settings for different frequency ranges used to analyze water species Optic parameter Frequency Range Near infrared Mid Infrared Beam splitter setting CaF2 KBr Detector setting MCT microscope MCT microscope Source setting W lamp Globar Several hundred scans were accumulated for each spectrum with 1 or 4 cm-1 resolution. During the measurements, the optics of the spectrometer was evacuated and the microscope was purged with a stream of H2O and CO2—free purified air. Polarized infrared [51] radiation was generated using a metal-strip polarizer on a KRS-5 substrate. Background corrections of absorbance spectra were carried out by a piecewise continuous cubic fit of the baseline defined by points outside the OH-stretching region. Calculation of the water content The measurement of water content by IR spectroscopy is based on the Beer Lambert law: 𝐴= 𝜀 × 𝑐 × 𝑡 Where, 𝐴 is the absorbance, 𝜀 is the extinction coefficient, in cm-1 /(mol/L), 𝑐 is the concentration of the absorber, in mol/L, and 𝑡 is the sample thickness, in cm. Thus, to obtain quantitative data the extinction coefficients of the OH bands must be known. These are determined by the calibration of the infrared data with an independent analytical method. For most of the mantle phases, however, 𝜀 is not precisely known because its calibration is difficult for two reasons: Analytical techniques, such as Karl Fisher titration and gas extraction manometry, are limited to high water contents and thus require a large amount of homogeneous material, which, for high pressure synthetic samples, is extremely difficult to obtain. 1H MAS NMR (Magic-Angle-Spinning Nuclear magnetic resonance) spectroscopy is an intrinsically quantitative technique which has recently been used for the study of water in mantle NAMs (Kohn, 1996). The main disadvantage of this technique, however, is that the samples must be iron-free. H2O bound to mineral surfaces and contained in inclusions can lead to inaccurate values. Thus the water content of the sample can easily be overestimated by such bulk techniques. [52] In the present study, because of the absence of specific calibration for most highpressure phases, the concentration of hydroxyl groups were determined by integrating the absorption using the calibration of extinction coefficients by Paterson (1982). 𝐶=𝑋𝑖 150𝜉�𝐾(𝜈) (3780 −𝜈)𝑑𝜈 Where, 𝐶 is the concentration of hydroxyl (in H/106 or ppm wt H2O), 𝜉 is an orientation factor, equal to 13 � for unpolarized measurement on olivine [Mackwell and Kohlstedt, 1990], 𝐾(𝜈) is the absorption coefficient (in cm-1) for a given wavenumber 𝜈 , and 𝑋𝑖 is a density factor. Its value is chemical composition dependent. 𝑋𝑖= 4.39 × 104 𝐻106𝑆𝑖 ⁄ or 2695 wt ppm H2O for olivine (Fo90). [53] 2.3.4 Piezoelectric measurements of stress in the Multianvil apparatus Quantitative rheological measurements and the determination of mineral and rock flow laws rely on the ability to measure deviatoric stresses in materials under well-defined conditions. In room or low pressure devices stress measurements are achieved through the use of a load cell which must be mechanically coupled to the loaded sample but which resides outside of the sample environment or high pressure chamber. A load cell uses the strain response of a calibrated material to measure force, with strain converted into variations in electrical conductivity using a strain gauge. In the Griggs solid media deformation apparatus, which operates to pressures of approximately 3 GPa, the stress in the deformation piston is measured by means of a load cell in mechanical contact with the sample through the piston and hard alumina rods [Holyoke and Kronenberg, 2010]. However, at pressures higher than 3 GPa where multianvil devices are employed stress measurements are extremely challenging. Ex-situ measurements can be made to determine average stresses using sample specific calibrations of dislocation densities or recrystallization grain size. However, such methods can only be calibrated at lower pressures with devices that use load cells and their application at high pressure is uncertain and limited. In situ x-ray diffraction measurements to examine the distortion of diffracted Debye Scherrer rings can be used to determined lattice strain from which stresses can be determined. However, the accuracy of such measurements is currently of the order of at least 100 MPa and a rigorous internally consistent treatment of such diffraction data has yet to be demonstrated [Durham et al., 2009]. A load cell that can be used internally in solid media pressure assemblies would be a significant advantage, particularly if it could preserve the accuracy in stress demonstrated by low-pressure devices. Mechanical strain gauges placed internally in a solid media devise would be extremely difficult to calibrate and to separate changes in pressure from those of deviatoric stress. The calibration of the charge developed on the surface of piezoelectric crystals as a function of force, however, may be one promising alternative. A piezoelectric charge develops on the surface of a non-centrosymmetric crystal in response to the application of mechanical strain. Piezoelectric crystals and ceramics find [54] uses in an enormous range of devices such as transducers, microphones, igniters and micro-actuators. One of the most common piezoelectric crystals employed is quartz, which is used for example as a piezoelectric resonant oscillator to produce an electric signal with a precise frequency. The charge polarization of a crystal caused by the application stress is related to the applied force through the piezoelectric charge constant, dab, where “a” is the direction of the polarization and b is the direction of the applied stress. It is convention to describe the crystallographic directions x, y, z with subscripts 1, 2, 3, with shear about one of these axes being referred to by 4, 5, 6. Piezoelectric crystals have different responses depending on the direction of stress with respect to the direction of charge polarization as shown in figure 2-18. Figure 2-18: Piezoelectric crystal configurations showing different orientations of the applied force with respect to the charge polarization. The relationship between change Q and force F varies with the configuration but only for transverse operation is it a function of crystal shape. Longitudinal 𝑄 = 𝐹𝑑11 2.a Transverse Q= 𝐹𝑑13𝐿𝑇 � 2.b Shear Q = 𝐹𝑑14 2.c [55] d11 for quartz, for example, is –2.3x10-12 C/N. The charge developed on a crystal can be determined by measuring the voltage; however, as the charge is very small the discharge time would be of the order of nano-seconds. A method of amplification is required in order to convert the charge on the crystal into a measurable voltage. This can be performed by constructing a charge amplifier or integrator amplifier. An integrator amplifier uses an operational amplifier circuit with a resistor and capacitor in series, a so called RC network. The circuit produces an output voltage, which is proportional to the integral of the input voltage as a function of time. A charge of equal magnitude to that on the piezoelectric crystal builds up on the range capacitor and the output voltage is a function of the range capacitance and the charge. Op amp V C = 10 nF r Piezoelectric Crystal Cables Cc Rc Ri Vo Charge Amplifier Figure 2-19: A simplified circuit diagram of the charge amplifier produced by combining an operational amplifier with an RC network. In figure 2-19, Cr is the range capacitor, Ri is an insulating input resistance and Rc and Cc are the resistance and capacitance of the cables connecting the crystal to the charge amplifier. The output voltage 𝑉𝑜 is Shear 𝑉0=−𝑄𝐶𝑟 � 2.d [56] An important aspect in the use of a charge amplifier in the measurement of small charges is the elimination of drift, which is an undesirable change in the output signal over time. Drift originates from leakage of current or charge through the cabling (Cc,Rc), the crystal itself or the operational amplifier (although modern MOSFET op amps have an extremely high gain that eliminates drift). If a piezoelectric charge is to be measured from within a high pressure multianvil assembly, then the cabling within the cell assembly needs to have a very high Rc. As many ceramics can contain H2O or C extreme caution has to be taken to ensure the resistance across the cables remains extremely high in order to eliminate drift. Choice of Piezoelectric crystal For high pressure and potentially high temperature measurements in a multianvil assembly a piezoelectric crystal needs to be selected with a suitable thermodynamic stability. Although quartz is stable to at least 15 GPa at room temperature, at 573°C it transforms to β-quartz and the piezoelectric effect is lost. GaPO4 is isomorphic with quartz but has a piezoelectric coefficient (𝑑11 =– 4.5𝑥10 −12 𝐶/𝑁) that is twice as large [Krempl et al., 1997]; [Damjanovic, 1998]. The comparable β-quartz high temperature phase transition occurs at 930°C at room pressure, enabling GaPO4 to be used as a piezoelectric material to much higher temperatures than quartz. High pressure studies have indicated that at room temperature GaPO4 is stable in the quartz structure to at least 9 GPa [Sowa, 1994]; [Badro et al., 1998] Two x-plates of GaPO4 single crystal (a plate with the thickness in x-direction to measure d11 in the longitudinal configuration) were kindly donated by Piezocryst GmBH. The plates were 0.4 and 1 mm thick and could be cored to any diameter. High pressure sample assembly for piezoelectric measurements The main consideration in the development of a high pressure cell assembly for piezoelectric measurements is eliminating or minimizing drift by ensuring that no current can leak across the piezoelectric crystal through the assembly material. Drift causes the output voltage to rise steadily and often rapidly with time. Once the saturation voltage of 10 V is reached Cr is fully charged and is discharged automatically by the closing of the switch across Cr. Many different assembly and cable configurations were tested in order to [63] Figure 3-3: Rotation of platinum strain marker θ and amount of shear ∆l for a strain marker initially oriented at 45° to the base of the specimen. Dotted parallelogram depicts the initial orientation of a hypothetical planar element of thickness “t” that undergoes shearing due to the sidewise movement of the alumina pistons. Solid lines indicate the new rotated position of the same element after the shear strain of γ. 𝐶𝑎𝑠𝑒 𝐼:𝑖𝑓 𝜃 ≤45° 𝛾=�∆𝑙 𝑡�= 1 −tan (45°−𝜃) 3.a. 𝐶𝑎𝑠𝑒 𝐼𝐼∶𝑖𝑓 𝜃>45° 𝛾=�∆𝑙 𝑡�= 1 + tan (𝜃−45°) 3.b. 𝐻𝑒𝑛𝑐𝑒,𝑖𝑛 𝑔𝑒𝑛𝑒𝑟𝑎𝑙,𝑠ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑎𝑖𝑛 𝛾=�∆𝑙 𝑡�= 1 −tan(|45°−𝜃|) 3.c. 𝑤ℎ𝑒𝑟𝑒 |𝑥| 𝑖𝑠 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 𝑜𝑓 𝑥. In a reference frame attached to the alumina piston, rotational component of the strain matrix is absent. Hence, the equivalent strain matrix can be represented as: �𝜖 𝑖𝑗 �=�0𝜀12 0 𝜀 21 0 0 0 0 0� 3.d. 𝑤ℎ𝑒𝑟𝑒 𝜀12 =−𝜀21 = 𝛾2 ⁄ [64] Figure 3-4: Variation in strain experienced by the sample DD402 along its thickness. Top-Left: The parts closer to the alumina piston are strained more than those are close to the neutral line N´N. Local orientation of the Pt strain marker is shown using a solid white line whereas original orientation of Pt-marker is shown using a dotted red line. Sense of shear is as indicated by the two red arrows on the top and bottom. Top-Right: Local increase in the shear strain in the sample near alumina piston has been marked by a curly bracket. Bottom (Left and Right): These images show the difference in the rotation angle as we move away from the neutral line towards the alumina piston. The platinum strain marker also preserves evidence that in most instances the sample experiences non-uniform strain along its thickness. The shear strain close to the alumina piston is generally slightly larger than the strain near the centre or neutral line of the [65] sample, N´N in Figure 3-4. This occurs because the polycrystalline specimen, unlike a single crystal, does not behave as a perfect rigid body. Transference of shear force between two adjacent flow layers occurs via the interlayer friction, similar to a fluid column. This variation in shear strain should be more marked when grains are polygonal shaped and have straight edges. In this case, grains can easily slip past each other with lesser effect of inter-granular friction than in the case of irregular shaped grains (as is the case with hydrous olivine sample). Employing the Pt strain marker and equation 3.c the shear strain determined for the edge of the sample is calculated from, 𝛾𝑚𝑎𝑥 = 1 −tan(45°−26.7°)= 0.67 However in the centre of the sample the angle of the strain marker is only 16.4° and the determined shear strain is 0.44. Inhomogeneities in shear strain of the order of 30% occur through most samples and the shear strain reported is the maximum value recorded. Figure 3-5: Reaction of olivine with alumina forms a layer of spinel and garnet at their interface. This may enhance the coupling between the piston and the specimen material (olivine) It is also possible to estimate shear strain from the sidewise displacement of the alumina pistons. This assumes that the pistons are mechanically coupled to the sample because slip at the sample pistons interface would result in erroneously large maximum strain estimates. The maximum shear strain experienced by sample DD402 can be calculated from the piston displacement from: 𝛾𝑚𝑎𝑥 =𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑛𝑣𝑖𝑙 𝑆𝑎𝑚𝑝𝑙𝑒 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 ≅140 µ𝑚 200 µ𝑚= 0.7 [66] This is in excellent agreement with the strain marker estimate and implies good mechanical coupling between the sample and pistons. The shear strain imparted to the sample decreases as the distance from the piston increases even though there is no appreciable sliding between the alumina piston and the sample material, unlike in other studies ( [Zhang et al., 2000] ) where loss of strain has been observed quite frequently. We have made no special attempts at enhancing the coupling between the piston and the specimen material. All alumina pistons were cut using diamond wire saw. In our case, the better coupling could be result of higher confining pressures (3 to 8.5 GPa) which should ensure a much better frictional contact by localized deformation of the alumina pistons and the olivine sample along their interface. Reaction between olivine and alumina leading to the formation of layer of spinel and garnet at the olivine-alumina interface could be another factor that might be responsible for a better coupling (Figure 35).In some instances it was not possible to place a Pt strain marker in the sample due to the sample being too fragile. In these cases it was also possible, to estimate the shear strain by measuring the lateral displacement of the top and bottom alumina pistons (Figure 3-2B). [67] 3.4 SEM and EBSD characterization Recovered samples were cut and polished for SEM observations to determine the grain size distribution and lattice-preferred orientation. 5° cluster size and 15° Gaussian smoothing has been applied for generating the pole figures from EBSD data, unless otherwise specified. 3.4.1 LPO determinations of dry San Carlos olivine samples 3 𝑮𝑷𝒂 pressure and 1300°C Strain-rate: 2.5x10-5; No. Of grains: 1835; Shear strain ≈ 1.5 Figure 3-6 : Dry samples deformed at 3 GPa and 1300°C. Sample deformed at lower strain rate (Top) shows dominant slip system to be (𝟎𝟏𝟎)[𝟏𝟎𝟎]. Olivine a-axes are preferentially aligned subparallel to the shear direction whereas b-axes are aligned subnormal to the slip plane. (Bottom) Sample deformed under higher strain rate also show the presence of (𝟎𝟏𝟎)[𝟏𝟎𝟎] slip system along with (𝟎𝟏𝟎)[𝟎𝟎𝟏] slip system. EBSD patterns from samples recovered from experiments performed at 3 GPa and 1300°C are shown in Figure 3-4 for fast and slow strain rates. The experimental shear direction is indicated horizontal to the page. The sample deformed at a slower strain rate of 2.5x10-5 s-1 exhibits alignment of olivine a-axes sub-parallel to the shear direction whereas the olivine (010) is aligned sub-parallel to the shear plane, as evident from the alignment of olivine [010] axes normal to the shear direction. The specimen deformed at a higher strain rate of 50x10-5 s-1 also shows a strong fabric originating from the (010)[100] slip system. [68] However, there is also an evidence for a weaker texture originating from slip on (010)[001] slip system as indicated by the partial alignment of [001] axes sub parallel to the shear direction. Observation of (010)[001] along with (010)[100] is in line with the observation of Jung and Karato (2001) where they found (010)[001] slip system to be dominant at higher stresses. 5 𝑮𝑷𝒂 pressure and 1300°C The sample deformed at 5 GPa and 1300°C at a strain rate of 2.5x10-5 has (010)[100] as the dominant slip system, similar to experiments at 3 GPa. Whereas the sample deformed under similar condition but with a faster strain rate of 50x10-5 appears to have the (010)[001] slip system also making an important contribution to the overall deformation. In this case, the overall LPO in the sample becomes weaker. This weakness may result from the competing actions of more than one slip system. Strain-rate: 2.5x10-5; No. Of grains: 1675; Shear strain ≈ 1.1 Strain-rate: 40x10-5; No. Of grains: 1520; Shear strain ≈ 0.7 Figure 3-7 : Dry samples deformed at 5 GPa and 1300°C. Sample deformed at lower strain rate (Top) shows dominant slip system to be (𝟎𝟏𝟎)[𝟏𝟎𝟎] . Olivine a-axes are preferentially aligned sub-parallel to the shear direction whereas baxes are aligned subnormal to the slip plane. (Bottom) Sample deformed under higher strain rate also has both (𝟎𝟏𝟎)[𝟏𝟎𝟎] slip and (𝟎𝟏𝟎)[𝟎𝟎𝟏] slip system active. 20° Gaussian smoothing was applied to the pole figure of specimen DD350. [69] 5 𝑮𝑷𝒂 pressure and 1400°C Samples deformed at 5 GPa, but at a slightly higher temperature of 1400°C show a similar mix of the two slip systems as found at lower temperatures. While at the slower strain rate both (010)[100] and (010)[001] slip systems are sub equally active, at the higher strain rate of 50x10-5, the (010)[001] slip system appears to dominant deformation. Interestingly, the LPOs at this temperature appear to be stronger than at 1300°C. This may be a result of slightly higher strains in these samples. 8.5 𝑮𝑷𝒂 pressure and 1300°C The LPO for the sample deformed at 8.5 GPa, 1300°C and a strain rate of 2.5x10-5 shows evidence for contribution from (010)[100], (010)[001] and (100)[001] slip system. Presence of (010)[100] and (010)[001] slip system is consistent with deformation under moderately high stress (285 MPa). Presence of (100)[001] may be result of the activation of harder slip system as per the Von Mises criteria. Strain-rate: 4x10-5; No. Of grains: 2320; Shear strain ≈ 1.4 Strain-rate: 50x10-5; No. Of grains: 1980 ; Shear strain ≈ 1.5 Figure 3-8: Dry samples deformed at 5 GPa and 1400°C. Sample deformed at lower strain rate (Top) shows has an LPO resultant of significant strain contribution from both (𝟎𝟏𝟎)[𝟏𝟎𝟎] and (𝟎𝟏𝟎)[𝟎𝟎𝟏] slip system. (Bottom) Sample deformed under higher strain rate has (𝟎𝟏𝟎)[𝟎𝟎𝟏] slip system dominant. [70] Specimen DD335, which was also deformed at 8.5 GPa and 1300°C but at a higher strain rate (50x10-5) indicates that the (010)[001] slip system was predominately active. This observation is also consistent with the reports of (010)[001] being easy slip system under higher stresses (395 MPa). Specimen DD455 and active slip systems HKL Channel™ 5 program which has been used for EBSD data analysis allows for selection of subsets of a few data points. A new data file is created by using an elliptical subset selection tool shows by red-dotted like in figure 3-10-A. Such a subset can be created in a way to include grains with a particular orientation. Figure 3-10-A shows selection where only the grains with their [010]-axes oriented sub-parallel to the specimen Y0 axis. The selected data points marked by red-dotted ellipse are used for drawing a new EBSD pole-figure as shown in figure 3-10-B. The purpose of analyzing such subsets is to establish the simultaneous activity of more than one slip system. Strain-rate: 2.5x10-5; No. Of grains: 1850 ; Shear strain ≈ 1.4 Strain-rate: 5x10-4; No. Of grains: 2500 ; Shear strain ≈ 1.2 Figure 3-9: Dry samples deformed at 8.5 GPa and 1300°C. Sample deformed at slower strain rate (Bottom) shows dominant slip system to be (𝟎𝟏𝟎)[𝟏𝟎𝟎] and (𝟎𝟏𝟎)[𝟎𝟎𝟏] . Olivine a-axes and c-axes are preferentially aligned sub-parallel to the shear direction whereas b-axes are aligned subnormal to the slip plane. (Bottom) Sample deformed under higher strain rate show the presence of (𝟎𝟏𝟎)[𝟎𝟎𝟏] slip system. 20° Gaussian smoothing was applied to the pole figure of DD335. [71] Subset selection – Only grains oriented sub-parallel to b-axis [010] || y0 No. of data points in the subset; N = 46918 [001] || x0 N = 43663 [100] || x0 N = 22546 [100] || z0 N = 27094 [001] || z0 N = 28081 [100] || y0 N = 2733 Figure 3-10: Subsets of pole figures indicated a particular crystallographic axis parallel to a selected specimen axis. [100] || x0 implies that the subset contains only the data points such that olivine [100] axes are aligned parallel (or sub-parallel) to x-axis of the specimen. X Y A B C D E F G [72] Taking the example of DD455, the [010] || y0 subset i.e. a subset consisting of grains with their b-axes aligned (sub-)parallel to the y0 specimen axes, we observe that some of these grains have their a-axes aligned sub-parallel to x0 –specimen direction or shear direction. This particular subset also includes grains with their c-axes aligned sub-parallel to shear direction. This observation can be construed to be indicative of comparative activity of the two slip systems – (010)[100] and (010)[001]. A more refined understanding of slip system activity can be obtained by analyzing several such subsets and counting the number of grains (or data points) present in those subsets. Figure 3-10-E shows mostly the grains with dominant slip system being (010)[001]. We can make such an assumption because all such grains with their a-axes aligned parallel to z0-axis of the specimen also have their b-axis aligned sub-normal to the shear direction and c-axis aligned sub-parallel to the shear direction. Such a configuration develops due to the dominant activity of (010)[001] slip systems with number of data points being 27094. On the other, figure 3-10B shows the pole figure for those grains who are neither deformed preferably either in (010)[100] slip system or (010)[001] slip system and the number of data points in this case is 46918. Hence, the number of data points indicative of (010)[100] slip system is (46918 – 27094) = 19824. Hence, we can say that the relative activity of (010)[100] to (010)[010] is 19824/27094 = 0.73:1. Similarly, from figure 3-10-D the relative activity of (001)[100] to (010)[100] is (22546 – 19824)/19824 = 0.137:1. From figure 3-10-G, we can derive the relativity activity of (100)[001] slip system with respect to (010)[100] which is equal to (2733 / 19824 ) = 0.138:1. Hence, the activity of 4 major slip systems is as follows: Slip system (010)[100] (010)[001] (100)[001] (001)[100] Activity 1 1.37 0.138 0.137 [79] Figure 3-14: TEM micrographs for the dry sample DD455 deformed slowly at 1300°C. Active slip systems are (010)[100], (100)[001] and (010)[001]. Figure on the left side shows large number of b = [100] dislocations present in one grain. White double-arrows in the picture indicate that sense of shear for the bulk sample. 3.4.4 Measurement of sample stress Dislocation density method In this work, we have taken two different approaches for measuring flow stress in the sample. The first approach is based upon the relationship between dislocation density and flow stress, whereas the second approach relies upon the fact that the recrystallized grain size in materials that have deformed plastically, is a function of stress as has been discussed in the last section. Wherever, TEM micrographs are available, stress has been estimated using the Taylor’s equation (Eq. 3.f), which relates flow stress to the dislocation density in the specimen [Kohlstedt et al., 1976b]. 𝜎1−𝜎3=𝛼𝑏𝜇𝜌12 � 3.f. Where; 𝛼≈3 𝑏=𝑏𝑢𝑟𝑔𝑒𝑟′𝑠 𝑣𝑒𝑐𝑡𝑜𝑟 𝜇=𝑠ℎ𝑒𝑎𝑟 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 𝜌=𝑑𝑖𝑠𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 [80] Figure 3-15: Dislocation density versus stress relationship [Jung and Karato, 2001a]. The solid line is the stress versus dislocation density relationship for a single crystal with the Schmidt factor = 0.5 [Kohlstedt et al., 1976b]. The critical step in adopting this procedure is the estimation of dislocation density, ρ, which in turn is defined as the total length of dislocation in a unit volume of the specimen. Several methods have been proposed for the measurement of total length of dislocation which involve manual processing of the micrographs [Bailey and Hirsch, 1960; Ham, 1961]. It is also noteworthy that the dislocation density in polycrystalline aggregate may differ from a single crystal because of heterogeneous deformation near grain-boundaries [De Bresser, 1996] and grain boundary migration [Jung and Karato, 2001b]. Jung and Karato 2001) have proposed a new calibration curve for the relationship between dislocation densities and stress (Fig 3-16). Measurement of the sample thickness: As described in the last chapter, our TEM specimens have been thinned using Argon milling process. This process results in a wedge shaped grain with a plateau top as shown in Figure 3-15 for the specimen DD384 deformed [81] at 8.5 GPa and 1300°C. Wedge shaped region can be identified easily by the presence of thickness fringes at the edge of the grain. Figure 3-16: Left-During argon milling process, argon stream bombards the sample from top and bottom (only top stream is shown in the figure). This gives the milled grain shape of a wedge (marked by the presence of thickness fringes) with half-angle being equal to the angle of incidence of argon stream (~5°). Approximate thickness of the plateau of the grain can be calculated from this simple model. Right-Wedge shaped part and plateau top (region enclosed by white rectangle) of argon-milled olivine grain for specimen DD384 is shown here. This sample was deformed at 8.5 GPa and 1300°CNote than base (b) of the wedge part is approximately 2 µm. Argon milling has been done at varying voltage with an angle of incidence of Argon stream being ~5°. From figure 3-14, we have: 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑙𝑎𝑡𝑒𝑎𝑢,𝑡= 2𝑏tan𝜃 𝐹𝑜𝑟 𝑏≅2µ𝑚 𝑎𝑛𝑑 𝜃= 5°; 𝑠𝑎𝑚𝑝𝑙𝑒 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠≈350 𝑛𝑚 Total length of dislocations: Projected length of dislocation in the area of interest (white rectangular region marked in Figure 3.14-right) can be estimated manually or using an image processing program. Assuming that dislocations are a straight line and are inclined to the surface of the micrograph (Figure 3.14-left), the true length of a [82] dislocation, 𝑙 = �(𝑙𝑝)2+ (𝑡)2 where 𝑙𝑝 is the projected length of a dislocation and 𝑡 is the thickness of the grain. Total length in this case, as measured from the 2-D micrograph, turns out to be ~17.34 µ𝑚. Dislocation Density: Now the dislocation density in the volume corresponding to the white rectangular area in the Figure 3.14 is 𝑙(𝑎𝑟𝑒𝑎×𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠)=17.34 µ𝑚 12.92 µ𝑚2×0.35 µ𝑚= �3.84 µ𝑚−2= 3.84 ×1012 𝑚−2 𝐻𝑒𝑛𝑐𝑒,𝑓𝑟𝑜𝑚 𝐸𝑞.3.𝑓; 𝑭𝒍𝒐𝒘 𝒔𝒕𝒓𝒆𝒔𝒔,𝜎1−𝜎2=𝟐𝟕𝟐 𝑴𝑷𝒂 𝑎𝑡 8.5 𝐺𝑃𝑎 𝑎𝑛𝑑 1300°𝐶. Measurement of stress using recrystallized grain size piezometer As has been discussed in the previous sections, mean recrystallized grain size in a deformed specimen varies with flow stress. Figure 3-15 shows this relationship for dry and wet specimens [Jung and Karato, 2001b]. Figure 3-17: Stress versus recrystallized grain-size relationship from Jung and Karato 2001. Stress magnitudes in the samples from this study were estimated from dislocation densities. The solid lines indicate the results of the least square fit for the ‘dry’ and ‘wet’ condition. The size of recrystallized olivine deformed under ‘wet’ conditions is significantly larger than that under ‘dry’ conditions at the same stress. Referring back to the same sample DD384 (See figure 3-14 for a TEM micrograph of the same sample), recrystallized grain size in this sample has been found to be ~7.6 𝜇𝑚 . The stress corresponding to this value of recrystallized grain size is ~230 𝑀𝑃𝑎 . This value is 40 𝑀𝑃𝑎 lower than the calculated value from the dislocation density method in the last section. The source of this discrepancy in the flow stress value could be the error in estimating grain sizes from EBSD measurement or due to the error in the thickness measurement of the grain from TEM micrograph. In this case, a step size of 4 µ𝑚 has been used for data collection whereas the mean grain size is 7.6 𝜇𝑚. [83] 3.5 Experiments under wet condition Deformation experiments on wet olivine samples were performed at 3, 5 and 8.5 GPa pressures with the maximum value of the pressure corresponding to ~250 KM of depth in the upper mantle (Table 3-2). At least two experiments were performed at each pressuretemperature condition with the strain rate differing by an order of magnitude. For each of the three pressure points, experiments were carried out at 1300°C. Additionally, experiments were also performed at 1400°C at 5GPa and 1500°C at 8.5GPa. The starting material for each deformation experiment consisted of polycrystalline San Carlos olivine powder mixed with equimolar mixture of brucite and silica as the source of water (Table 3-3). After achieving the desired pressure, the assembly was heated up and left to anneal for 2-3 hours at 1150°C, a temperature value less than the target temperature, to avoid excessive grain growth during annealing. This period also provides sufficient time for hydration of the olivine sample because of the breakdown of brucite during heating. Thereafter, the temperature was raised to the final target level for that experiment and deformation commenced through the advancement of the deformation anvils. Table 3-3: List of experiments and experimental conditions under wet condition Run ID Pressure (GPa) Temperature (°C) Strain rate (x10 -5 s -1 ) Shear1 Strain Water Content2 (wt. ppm) Stress3 (MPa) DD430 3 1300 3.2 1.2 90 250 DD477 3 1300 55 1.3 74 340 DD463 5 1300 4 1.1 279 210 DD461 5 1300 50 0.9 214 325 DD462 5 1400 5 2.4 168 310 DD466 5 1400 50 1.0 189 365 DD457 8.5 1300 2.5 1.1 419 310 DD456 8.5 1300 50 1.2 461 370 DD473 8.5 1500 15 1.1 401 300 DD460 8.5 1500 60 1.3 340 325 1 Shear strain has been determined using sidewise displacement of the pistons. 2 Estimation of water content is based upon calibration by Paterson (1982). 3Stress has been determined using recrystallized grain size versus stress relation except for DD456 which has been calculated using the dislocation-density obtained from TEM micrograph. [84] The shear strain for each experiment was calculated from the sideward displacement of the top and bottom alumina shear-pistons from post-mortem observation of the deformed assembly. This method had to be employed because hot pressed H2O-bearing olivine aggregates proved to be far too fragile to cut into slices or added Pt strain markers. The totally strain applied to the cubic assembly, measured using the transducers attached to the independent deformation anvils, was always greater than that determined from the sideward displacement of the alumina shear pistons. This implies that the strain rate initially applied to the cubic assembly was actually moderately faster than those experiences by the sample. This difference results from the minor deformation of assembly parts other than the sample material. Hence, the nominal target strain on the cubic assembly was accordingly replaced by the determined sample strain and then the true strain rate experienced by the sample was calculated and given in Table 3-1. The corrections in strain between those measured on the entire cubic assembly and those actually experienced by the sample where generally within 10% of each other. This is in better agreement with what was observed for the dry samples and likely results from significant softening of the samples in the presence of H2O. Table 3-4: Starting material for deformation experiments on hydrous olivine Sample ID Starting material DD477 Hotpressed San Carlos olivine (1 GPa) + 0.1 wt % Brucite+SiO2 equimolar mixture DD466 Hotpressed San Carlos olivine (1 GPa) + 0.5 wt % Brucite+SiO2 equimolar mixture Others Polycrystalline olivine aggregate + 0.5 wt % Brucite+SiO2 equimolar mixture [85] 3.5.1 Measurement of water content using FTIR The water content of each deformed specimen has been analyzed using FTIR spectroscopy. Two hundred scans are collected for each spectrum at a resolution of 1 cm-1. Background correction has been made using a baseline obtained by piecewise cubic interpolation method (Fig. 3-16). Absorbance values for each specimen are normalized for hypothetical specimen of 1 cm thickness. Integration has been performed between wavenumbers 2950 to 3780 cm-1. The calibration proposed by Paterson (1982), instead of the relatively newer one proposed by Bell et a. (2003), has been employed to relate the total integrated absorbance with wavenumber to the water content. This choice of calibration makes it possible to compare our water content data with results from Kohlstedt et al. (1996) and also directly compare with results from previous deformation studies (Jung et al. 2001; Karato et al., 2008) which have routinely employed the Paterson calibration. Figure 3-18: Background correction of the raw FTIR data. A baseline was created using piecewise cubic interpolation method. Water solubility values are sensitive to the choice of the baseline and range of wavenumber used for integration (2950 to 3780 cm-1 in our case). The Bell et al. (2003) calibration most likely provides a better estimate of the H2O content of olivine because it was performed specifically on olivine. The Bell calibration would imply H2O contents that are approximately 3 times higher in comparison to that 250030003500400045005000 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 Wavenumber (cm -1 ) Absorbance (for 100 µm thick specimen) Background corrected data Baseline Raw data (DD461) [86] measured by the Paterson calibration for H20 content. However, rather than correcting data previous studies using an arbitrary correction parameter the H2O contents are simply reported using the older calibration. Ultimately, the absolute H2O contents are less important than the degree of saturation, which can be determined from comparison with the study of Kohlstedt et al. (1996), which also used the older calibration. Measurement of water content by either of the above-mentioned approaches, results in solubility values that are sensitive to both the choice of baseline and the range of wavenumber selected for the integration. As shown in the figure 3-17, strong IR absorbance peaks can be observed at wavenumbers (in cm-1) 3612, 3599, 3579, 3568 and 3568 for 8.5 GPa experiments (DD456, DD457 and DD460). Minor peaks at 3504, 3475 and 3450 cm-1 can also be seen. In the 5 GPa run products (DD461, DD463 and DD462), peaks at 3579 cm-1 and 3568 cm-1 are not so well resolved. IR spectra for neither of the samples exhibit any recognizable presence of group II bands that has been reported to occur below 3450 cm-1 [Bai and Kohlstedt, 1993; Matveev et al., 2001]. Figure 3-19: FTIR spectra of hydrous olivine specimen after the experiments. Absorbance of the spectra was normalized for 1 cm thick specimen. 3400 3450 3500 3550 3600 3650 0 50 100 150 200 250 Wavenumber (cm-1) Absorbance (cm-1) DD456 DD457 DD460 DD461 DD462 DD463 DD466 DD430 DD473 DD477 3568 3504 3475 3450 3612 3548 3599 3579 [87] Figure 3-20: Water solubility in San Carlos olivine (modified after Keppler and Bolfan-Casanova [2006]). Our results are shown along with the experimental data from Mosenfelder et al. (2006; blue diamond) and Kohlstedt et al. (1996; red squares). The H2O contents from this study employ the Paterson calibration so as to compare them directly with the work of Kohlstedt et al., 1996 where olivine was saturated with excess H2O.This comparison indicates that the olivine from this study had H2O contents less than the saturation level (25-35%). The Study of Mosenfelder et al (2006) reported higher H2O contents mainly because of using the newer Bell et al calibration. Comparison of our water solubility results with previous works indicates that solubility values observed in our samples are lower than the saturation level reported by Kohlstedt et al. (1996) from 1100°C (Fig. 3-18). The water content in olivines recovered from this study varies between 25 and 35 % of the saturation level. Saturated H2O olivine contents are expected to rise slightly with temperature but then drop at higher temperatures due to the presence of silicate melting. Some idea of how temperature may influence H2O saturation levels can be gained by examining experiments performed by Smyth et al. (2006) on forsterite. The H2O saturation limit in pure forsterite at 1250°C is almost double the value at 1100°C but it drops to almost half of the 1100°C value by 1500°C. The H2O contents reported for San Carlos olivine in this study from 1500°C are lower than the saturated values reported by Kohlstedt et al. (1996) at 1100°C but may still be close to the [88] saturation limit, which may be lower at this higher temperature. Data from Mosenfelder et al. (2006) yield saturated H2O contents for temperatures between 1100-1300°C are 2-4 times higher than the water contents from Kohlstedt et al. (1996), but most of this increase can be attributed to the use of the newer FTIR H2O calibration proposed by Bell et al. (2003). 3.5.2 NMR spectroscopy on hydrous Forsterite Positions of the resonance peaks obtained from 1H MAS (magic angle spinning) NMR are extremely sensitive to the minute differences in the chemical environment around a nucleus. Differences in the position of the resonance peaks are referred as chemical shift, which is measured in ppm. A known weight of powdered sample material is loaded in a ceramic rotor of length 1.2 cm and inner diameter 1.5 mm. After being placed in the NMR probe, such that the angle between the direction of the external magnetic field and rotor axis is 54.7° (the magic angle), the rotor is spun at very high speed (30 KHz). This choice of angle coupled with high rotation speed, minimizes the broadening of resonance peaks. In nominally anhydrous minerals, H should be strongly bonded to the adjacent oxygen [Kohn, 2006]. Results from hydroxyl containing minerals and other materials indicate that a strong correlation exists between not only between chemical shift (𝛿) and 𝑂−𝐻 distance (𝑟𝑂𝐻) [Brunner and Sternberg, 1998] but also between 𝛿 and 𝑂−𝐻. . 𝑂 distance (𝑟𝑂..𝑂) [Eckert et al., 1988]. Moreover, the area under an NMR resonance curve is directly proportional to the number of resonating nuclei. Hence, position of the resonance peaks, expressed as chemical shift with respect to the resonance peak of reference material Tetramethylsilane ((CH3)4Si, usually referred to as TMS), gives us information regarding the chemical environment of the hydrogen. On the other hand, calculating the area under the resonance curve and comparing it with NMR spectra of a standard material with known water content (e.g. Gypsum), we can find out the absolute number of the H nuclei present in the sample. This approach of measuring water content using 1H MAS NMR has a detection limit as small as 1 ppm of H2O by weight [Kohn, 2006]. Hydrous forsterite samples were prepared at 11 GPa and 1150°C using 6-8 type multianvil apparatus. In case of sample Z771, 2 wt% of equimolar mixture of brucite and silica [95] 3.5.4 SEM and EBSD characterization 3 GPa pressure and 1300°C In the wet sample deformed at 3GPa and at a slower strain rate of 3.2x10-5 evidence can be seen for relatively equal activity of both the (010)[100] and (100)[001] slip systems (Fig.3-23: Top). Interestingly poles to the (100) plane of the (100)[001] slip system are sub horizontal and rotated anticlockwise with respect to the Y0 axis. This rotation is anomalous, as the shear sense should cause anticlockwise rotation only until the maxima are aligned with the Y0 axis. The most likely explanation for this is as a result of additional compressive strain experienced by the powdered starting material. The direction of the compressive strain is at 45° to the shear direction. In the dry experiments, reported in section 3.3.2, (010)[100] was found as the most common slip system. This is also observed to be the most common slip system in natural samples and in previous experiments performed at relatively lower stresses under dry conditions [Carter and Ave'lallemant, 1970; Nicolas et al., 1973; Phakey et al., 1971; Zhang and Karato, 1995; Zhang et al., 2000]. The (100)[001] slip system on the other hand is common in experimentally deformed specimens that contain more than approximately 40 wt. ppm water [Karato, 1995; Karato et al., 2008; Katayama and Karato, 2008], which is therefore quite consistent with this result. The pole figure for the specimen (DD477) deformed under similar pressuretemperature-water conditions but performed at a higher strain rate (5.5x10-4 s-1) (Fig. 323: Bottom) exhibits a fabric developed only through the activity of the (100)[001] slip system. This experiment is therefore also consistent with previous experiments performed at these H2O concentrations at pressures below 2.2 GPa [Karato, 1995; Karato et al., 2008; Katayama and Karato, 2008]. [96] 5 GPa pressure and 1300°C Strain-rate: 3.2x10-5; Water content: 90 wt. ppm; No. Of grains: 3320; Shear strain ≈ 1.2 Strain-rate: 5.5x10-4; Water content: 74 wt. ppm; No. Of grains: 3500; Shear strain ≈ 1.3 Figure 3-25 : Wet samples deformed at 3 GPa and 1300°C. Sample deformed at lower strain rate (Top) shows two active slip systems – (010)[100] and (100)[001]. (Bottom) Sample deformed under higher strain shows only (100)[001] slip system to be active. Strain-rate: 4x10-5; Water content: 279 wt. ppm; No. of grains: 4010; Shear strain ≈ 1.1 Strain-rate: 5x10-4; Water content: 214 wt. ppm; No. of grains: 3800; Shear strain ≈ 0.9 Figure 3-26: Wet samples deformed at 5 GPa and 1300°C. Both the high strain rate and low strain rate sample exhibit only one active slip system – (100)[001]. [97] 5 GPa pressure and 1400°C The (100)[001] slip system is the only active slip system observed in the specimens deformed at 5 GPa and 1300°C irrespective of the strain rate at which they were deformed (Fig 3-24). In this case the [001] axis poles appear in a girdle pattern which likely results from a component of compressive strain of the powdered aggregate sample. Compression causes alignment in the [001] direction but as there is no unique shear direction a girdle develops. Deformation experiments on powdered aggregates often result in a non-zero contribution from compressive strain to the overall deformation during compaction of the sample material. At 5 GPa and slightly higher temperature of 1400°C the slower strain rate experiment exhibits the same fabric as that observed at lower temperature i.e. (100)[001]. At the same conditions but at higher strain rate the fabric of the recovered sample is again dominated by the (100)[001] slip system (Fig 3-25). In addition, however, a weaker fabric resulting from activity of the (010)[001] slip system is also present. While the (100)[001] slip Strain-rate: 5x10-5; Water content: 168 wt. ppm; No. Of grains: 4670; Shear strain ≈ 2.4 Strain-rate: 5x10-4; Water content: 189 wt. ppm; No. Of grains: 3920; Shear strain ≈ 1.0 Figure 3-27: Wet samples deformed at 5 GPa and 1400°C. Sample deformed at lower strain rate (Top) shows mainly one active slip systems – (100)[001]. Whereas, (Bottom) Sample deformed under higher strain has two (010)[001] and (100)[001] slip systems active. [98] system has been previously observed to be active at high H2O content, the (010)[001] slip system has been previously documented under higher stress conditions irrespective of the H2O content. (Karato 1995; Karato et al. 2008; Katayama et al. 2008) report the (010)[001] slip system as dominant over a range of H2O contents at stresses over 300 MPa, from experiments performed at pressures <2.2 GPa. This would again be consistent with the experiments performed at these conditions where evidence for the (010)[001] slip system appears in the experiment performed with a faster strain rate and therefore under higher stresses. 8.5 GPa pressure and 1300°C Fabrics developed in samples deformed at 8.5 GPa and 1300°C (Fig 3-26) are in general very similar to those found in the wet samples at 3 and 5 GPa. The sample at low strain rate shows evidence for the dominant slip system being (100)[001], however either (010)[100] or (010)[001] or both may also be active, albeit with much lower activity than the (100)[001] slip system. Strain-rate: 2.5x10-5; Water content: 419 wt. ppm; No. Of grains: 3850; Shear strain ≈ 2.4 Strain-rate: 5x10 -4 ; Water content: 461 wt. ppm; No. Of grains: 4350; Shear strain ≈ 1.0 Figure 3-28: Wet samples deformed at 8.5 GPa and 1300°C. Irrespective of the strain rate, both the specimens deformed at 8.5 GPa and 1300°C show two active slip systems –(010)[100] and (100)[001]. This observation is consistent with activity of (010)[001] slip system at relatively higher stresses and (100)[001] slip system under hydrous condition. [99] Sample DD456, which was deformed at the same pressure and temperature conditions but at a higher strain rate, has also developed a fabric dominated by the (100)[001] slip system but again a weak contribution from the (010)[001] slip system also seems to be present. This two-slip system combination appears consistent with dislocation activity under higher stresses and hydrous condition as also proposed in previous studies [Karato, 1995; Karato et al., 2008; Katayama and Karato, 2008]. TEM observation on the sample DD456 confirms the presence of these two slip systems (See section 3.1.2). 8.5 GPa pressure and 1500°C Unlike the pole figures for dry experiments deformed at 8.5 GPa and 1500°C, where no appreciable LPO was detected, most likely as a result of deformation occurring in the diffusion creep regime and likely assisted by grain boundary sliding, wet experiments have developed strong fabrics under both slow and fast strain rates. Strain-rate: 1.5x10-4; Water content: 401 wt. ppm; No. Of grains: 1600; Shear strain ≈ 1.1 Strain-rate: 6x10-4; Water content: 340 wt. ppm; No. Of grains: 1920; Shear strain ≈ 1.3 Figure 3-29 : Wet samples deformed at 5 GPa and 1500°C. Sample deformed at lower strain rate (Top) shows two active slip systems – (010)[100] and (100)[001]. (Bottom) Sample deformed under higher strain shows only (100)[001] slip system to be active. [100] At the relatively slower strain rate of 1.5x10-4 the (010)[001] slip system appears to have led to a slightly stronger fabric than the sub equally present (100)[001] slip system. At the faster strain rate of 6x10-4, however, the (100)[001] slip system dominates with only a faint indication that (010)[001] slip may also be present. 3.5.5 TEM characterization In order to relate the observed fabric with the dislocation microstructure a TEM investigation was carried out on sample DD456, which was deformed under a higher strain-rate of 5x10-4 at 8.5 GPa and 1300°C and contained a water content of 958 wt. ppm. It was considered unnecessary to examine multiple wet samples from various conditions using the TEM as EBSD measurements show all wet samples to have essentially similar LPO fabric and therefore should all show evidence for dislocations with [001] Burgers vectors slipping on either the (010) or (100) planes. The LPO for sample DD456 is typical of this wet fabric, which is dominated by the (100)[001] slip system but with evidence for weaker activity of the (010)[001] slip system. TEM micrographs of DD456 show evidence for c-dislocations with slip planes being (010) and (100). Edge segments for the (010)[001] dislocations are more mobile whereas for the (100)[001] slip system dislocations, screw segments are more mobile. Cross-slip is an active process as marked by the pointer 1 in the top image (Fig 3-28) and some of the edge (100)[001] dislocations are kinked (pointer 2 in Fig 3-28). Evidence of cross-slip can also be seen in the bottom-left image as indicated by the white arrows. The bottom-right image shows long and straight screw dislocations from (010)[001] slip system. There is fewer sub grain boundaries observed in comparison to samples deformed under dry conditions. Presence of long and straight screw segments could also indicate resistance to the glide of dislocation. Although potentially also showing the tops of dislocation loops, the structures in the HRTEM image shown in Fig 3-29 seem to be more consistent with being the cores of a weakly dissociated c-dislocations. The Fast Fourier transformed image (Fig 3-29: lower right) of the dissociated c-edge dislocation when viewed along the {110} zone axis, shows a [101] variation in contrast. The image contrast in the dislocation core regions is different from that in the surrounding bulk, indicating the core is expanded. Figure 3-30: TEM micrographs for the wet specimen DD456. Deformation experiment was carried out at 8.5 GPa and 1300°C with a strain rate of 5x10-4. Top figure shows the presence of c-dislocations. (100)[001] dislocations are mostly of edge nature where as the [001] screw dislocations are most likely from (010)[001] dislocation. Evidence of cross-slip can be also seen as indicated by marker 1 in top image and white arrow in the bottom-left image. Bottom-right figure also shows straight c-screw dislocation from (010)[001] slip system. [102] Figure 3-31: A typical HRTEM image (upper and lower right) and the Fast Fourier transformed image (lower right) of the dissociated c-edge dislocation viewing along the {110} zone axis of a deformed hydrous olivine. The image contrast in the dislocation core regions is different from that in the surrounding bulk, which indicates that the core is expanded. [103] 3.6 Deformation experiment on Peridotite modal composition Deformation experiments performed were performed on a peridotite assemblage at 8.5 GPa and 1300°C. In the low strain rate sample, the likely active slip systems are (010)[100] and (010)[001] whereas the dominant slip system in olivine in the high strain rate sample is (010)[001]. In case of pyroxene assemblage (100)[001] slip system is the only likely active slip system in both high and low strain rate sample (Table 3-8). Table 3-8: Experimental conditions for Peridotite deformation experiments and likely active slip systems Run ID Pressure (GPa) Temperature (°C) Strain rate (x10 -5 s -1 ) Stress (MPa) Likely Active slip systems DD495 8.5 1300 5 230 Olivine: (010)[100] and (010)[001] Pyroxene : (100)[001] DD483 8.5 1300 40 325 Olivine: (010)[001] Pyroxene : (100)[001] Strain-rate: 5x10 -5 ; Shear strain ≈ 1.6 Strain-rate: 50x10-5; Shear strain ≈ 1.3 Figure 3-32: Peridotite samples deformed at 8.5GPa and 1300°C. Olivine in the slowly deformed aggregate likely has both (010)[100] and (010)[001] slip systems active whereas in the experiment conducted at higher strain rate the slip system is (010)[001]. Pyroxene in both the cases show (100)[001] slip system [104] These results indicate an identical olivine fabrics to those observed in monomineralic experiments at the same conditions. Fabrics for diopside and enstatite were found to be similar to those found in previously performed lower pressure experiments. In-situ measurement of stress using piezoelectric sensor Piezoelectric stress measurements were made using GaPO4 single crystals within a 8/6 multianvil assembly. Many test experiments were made in the D-DIA however the most successful runs, where drift was minimal, were performed using the 6-axis MAVO press. The success of the MAVO press in these experiments most likely originates from the highly resistive electrical insulation of each individual anvil. In the D-DIA press the top and bottom guide blocks are electrically connected via the oil lines to the deformation rams. Figure 3-33: Output voltage from the charge amplifier as a function of time for an experiment where a GaPO4 crystal was compressed to 2 GPa and then held at constant static pressure for 80 min. The anvils therefore cannot be used as part of the circuit and crystals must, therefore, be connected via separate cables that pass through the gasket. The use of the cables that have to pass through the gaskets that form as the cubic assembly is compressed probably results in current leakage. Figure 3-33 shows the output voltage from the charge amplifier for an experiment compressed to 2 GPa, which remained under static conditions for 80 min. This voltage change would correspond to changes in stress of the order of 5 GPa over this time period and more likely results from drift. The origin of this drift is unclear. Drift is positive for the first 30 min but eventually goes through a maximum and decreases. However, the slope of [111] strain rate (and hence higher flow stress) has a larger proportion of data points indicating the B-type fabric. Figure 4-1: Summary of fabrics observed in San-carlos olivine deformed under dry and wet condition at different strain rates. Experiments were performed between 3 to 8.5 GPa and 1300°C to 1500°C. Width of each colour bar is proportional to the approximate number of grains that were present in the subset containing data points for that slip system. Refer to section 3.4.14 for more details. As shown in the table at top-right corner of the page, the lower row in the 2x2 matrix contains results from dry experiments while upper row contains results from wet experiments. The left column in 2x2 matrices has results from slowly deformed samples whereas samples deformed at relatively higher strain rate have their fabrics shown in the right column. Hence, it can be concluded that under high stress deformation conditions the B-type fabric dominates i.e. the (010)[001] slip system contributes to most of the strain. Although, [112] the proportion of data points with the B-type fabric increases at 5 GPa and 1400°C with respect to 5GPa and 1300°C , this is actually in line with a slightly higher strain rate and hence higher flow stresses in specimens deformed at 1400°C. Equally important is the observation that at 8.5 GPa and 1300°C, the specimen deformed at a slower strain rate shows a larger proportion of data points with the A-type fabric. There have been reports that at higher pressures c-slip, slip with a Burgers vector [001], becomes easier than a-slip. The approximate transition pressure between a-slip and c-slip apparently varies between studies with Jung et al. (2009) reporting this transition at approximately 3.6 GPa whereas Raterron et al. (2007) place the transition at approximately 7.6 GPa. If there was indeed a pressure related easing of the b = [001] slip then it would be hard to reconcile this with the results in Fig. 4-1, which show dominant (010)[100] slip system activity at slower strain rates at 8.5 GPa. These results are rather more in line with the observation that a change from a-slip (b = [100] slip) to c-slip (b = [001] slip) can occur at higher stresses [Jung et al., 2006]. Another piece of strong evidence that a-slip continues to be the dominant slip mechanism at high pressures, comes from analysis of specimens that were hot-pressed in the 6-8 multianvil under pseudo-hydrostatic conditions i.e. without the inclusion of alumina hard parts in the multianvil assembly that can lead to strong deformation (Fig 4-2). In two such hot-pressing experiments, dry olivine powder was hotpressed at 1400°C at pressures of 8.5 GPa and 11 GPa. During cold compression of the multianvil assembly, some dislocations are introduced in the olivine sample. Once, the sample is heated up to high temperatures, dislocation recovery processes start, leading to deformation of the sample and development of a weak LPO. As seen in the pole figures on the next page, the A-type fabric are clearly present both of these specimens. [113] Figure 4-2: Pole figures for two polycrystalline olivine specimen hotpressed at 8.5 GPa (H3115) and 11 GPa (H3354). Specimens were annealed at 1400°C. Both pole figures resemble A-type fabric which is often observed under low stress and dry deformation environment. Presence of A-type fabric in these hotpressed specimen is indicative of (010)[100] slip system activity. The LPO fabrics observed in Fig 4-2 could have only developed in these samples if a-slip was dominant. Interestingly, the first report of a pressure induced transition in olivine LPO was by Couvy et al. (2004) from deformation experiments performed at BGI using a similar multi-anvil apparatus. The assembly setup was in simple shear configuration, however, unlike that reported here where no deliberate attempt was made to deform the olivine sample during hot-pressing. The peak stress that would have developed during the initial stages of annealing must be lower than in the experiments of Couvy et al. (2004). Hence, the hot-pressing fabric in specimens H3115 and H3354 must result from deformation under low stresses and thus it can be concluded that a-slip continues to be the easiest slip mechanism even up to 11 GPa pressure under low stress deformation conditions. The observations in previous studies where a transition of a-slip to c-slip has been attributed to increasing pressure are more likely to result from higher stresses which may inevitably increase in experiments at higher pressures.. Pole figures shown by Jung et al. (2008) do not show strong LPOs despite large amounts of strain that their samples [114] experienced. Results from Raterron et al. [2007] where they observed a pressure related transition in the slip system, are based upon experiments performed at stresses varying between 300 MPa to 1800 MPa. Similarly in the study of Ohuchi et al. [2011] most specimens exhibiting the presence of c-slip have estimated stresses in excess of 350 MPa. Only in one specimen are stresses reported to have been less than 300 MPa but this sample actually indicates dominant activity of the (100)[001] slip-system under dry conditions. Additionally the observation that various studies have placed the pressure of the transition at widely varying values can also be explained if this transition in fact results from increasing flow stresses. Figure 4-3 shows the fabrics observed in this study compared with those reported in previous studies. Larger symbols with black boundaries are data points from this study. The results are in very good agreement with variations in fabric reported by Karato et al. [2008]. At higher stresses, under dry condition the B-type fabric was observed, whereas under lower stresses and dry conditions deformation resulted in the dominance of A-type fabric. Hydrous specimens exhibit C-type fabric which also agrees with previous reports from lower pressure deformation studies. None of the specimens characterized in this study showed evidence of E-type or D-type fabric because experimental conditions in were never entered these regions of stress-water content space. Broken grey lines in the image are the likely transition boundaries between two different fabric types. The main conclusion of the results obtained from deformation experiments under dry condition is that pressure apparently plays no direct role in the slip system transition in olivine. (010)[001] slip system contributes most to the overall strain at higher stresses and the B-type fabric should be observed under such environment. A-type fabric should be the most dominant type fabric that we would expect to see in the lithospheric mantle because stresses are expected to be too low (<10 MPa) to generate B-type fabric. However, in the mantle wedge near subducting slabs it is possible that regions exist where B-type fabric could occur as these regions are most likely deforming at relatively high stresses. [115] Figure 4-3: Deformation data from this study and other studies are shown as a function of stress and water contents (T ∼ 1470–1670 K). Larger symbols with black boundaries represent data from this study whereas rest of data are from Katayama et al. 2004. Except, one of the data for D-type fabric is from Bystricky et al. (2001). Water content was estimated using the Paterson (1982) calibration. Broken gray lines indicate the likely transition line between two different fabric types (Modified after Karato et al., 2008) [116] Lack of LPO in the dry samples deformed at high temperature at 1500°C and 8.5 GPa has likely resulted from diffusion accommodated grain boundary sliding. High grain growth, as evident from grain size measurements made in recovered experiments, points to the dominance of diffusion creep. The presence of straight grain boundaries indicate that conditions were suitable for grain boundary sliding. There were many four-grain junctions present in these samples and these junctions were slightly diamond shaped which is additional evidence that grain boundary sliding may have been the active deformation process. It is well known that diffusion creep does not result in LPO development. Moreover, grain boundary sliding (GBS) also does not favour LPO development because in the presence of GBS, intracrystalline deformation is only weakly dependent on the orientation of grains [Drury and Humphreys, 1988; Karato et al., 1986; Zhang et al., 1994]. Fabric types observed in the olivine deformed as a part of the peridotite modal composition are identical to those observed in monomineralic experiments at the same conditions. The dominant slip system in the pyroxene component of this aggregate had most likely (100)[001] slip system active. 4.2 Fabric types under water rich conditions The hydrous specimens in this study all contain water contents in excess of 50 ppmw. From figure 4-3, it can be seen that the C-type fabric is the most commonly observed fabric in these specimens. However, some of the high stress water-rich samples also indicate the presence of the B-type fabric e.g. DD456. A TEM study on one of the wet samples (DD456) indicates the dominant presence of b = [001] dislocations. The active slip systems in this specimen were observed through TEM to be (100)[001] and (010)[001]. The activity of the (010)[001] slip system in this sample is similar to activity observed in the dry specimens deformed under higher stresses. The (100)[001] slip system is an unusual slip system because glide on the (100) plane most likely involves breaking of SiO4-tetrahedra, unlike glide on (010) where no SiO4 tetrahedra are encountered during glide. Dislocation microstructures in the wet sample (DD456) observed using the TEM show that dislocation loops on the (010) glide plane have longer screw segments than their edge components. There are long edge segments of c-dislocations visible and most of them are part of c- [117] dislocations on the (100) glide plane. Where only screw segments of c-dislocations are visible it is unclear whether glide is also occurring on the (100) plane because determination of the glide plane is not possible when only screw segments are visible. The abundant number of c-dislocation on the (010) slide plane with a screw nature is in clear contrast to the c-dislocations observed in the dry specimens which were mostly of edge nature under similar P-T-stress conditions. Another pertinent observation in the wet sample is the evidence of climb of edge dislocations and cross-slip of screw dislocations. A few prismatic loops lying in the (010) plane can also be observed, which have been associated with the presence of H2O in olivine. A further interesting observation is that the transition line between C-type and B-type fabrics appears to have a positive slope with respect to the olivine H2O content. This is in contrast to the previous study of Katayama et al. 2004 where a negative slope was proposed. In accordance with Fig 4-3 it would require increasingly higher stresses to push olivine from the C-type fabric regime into the B-type regime with increasing water content of olivine. It would also imply that water favours slip on the (100) plane over the (010) plane. 4.3 Physical basis for slip system changes in olivine In the following section an attempt is made to identify a physical basis for changes in slip systems as a function of stress and water content. As mentioned previously, under high stress deformation conditions deformation by b = [001] slip becomes dominant and the slip system changes from (010)[100] to (010)[001]. Slip with b = [001] also becomes dominant in the presence of water. In this case, the dominant glide plane becomes (100) which are not known to be an easy glide plane because of way the SiO4 tetrahedra are arranged in olivine. Based upon the rheological and microstructural data available from previous studies along with results from this study, an attempt is made here to explain the dominance of the (010)[001] slip system under higher stresses and the cause of C-type fabric development in wet specimens due to the likely action of the (100)[001] slip system. [118] 4.3.1 Dominance of (010)[001] slip system at higher stresses Studies on rheology of olivine single crystals point towards a temperature related transition in the olivine slip system (Fig 4-4). Measurements of the critical resolved shear stresses for (010)[100] and (010)[001] slip systems indicates that CRSS for the (010)[001] slip system is lower than the CRSS for the (010)[100] slip system at lower temperature. Whereas, the reverse is observed at higher temperatures where the (010)[100] slip system is initiated at much lower stresses. This transition between CRSS values of the two slip systems occurs at around 1200°C at a corresponding value of 400 MPa CRSS. Figure 4-4: Critical resolved shear stresses (CRSS) of the (010)[100] and (010)[001] slip systems as a function of temperature. Data (corresponding to a strain rate of 10-5 s-1) from experiments performed on single crystals oriented along [011]c (black-filled symbols) to promote [001](010) glide and along [110]c (open symbols) to promote [100](010) glide. (SourcePhD thesis – Helen Couvy, 2005) Interestingly, in this study the fabric transition from A-type to B-type, which is related to the transition between the dominant slip systems (010)[100] and (010)[001], was also observed at around 300 MPa, which given the uncertainty in both determinations puts it in close proximity to the cross-over in the CRSS for the two slip systems shown in Fig 5-4. In the following section, it is argued that the stress related transition in the fabrics is a logical [119] consequence of changes in the CRSS of the two slip systems with temperature. Before this argument is pursued, however, it is worthwhile to review why CRSS changes with stress. The temperature dependence of CRSS has been observed in metals and various ionic and covalent compounds [Castaing et al., 1981]. Also, different slip planes can have different temperature dependency of CRSS as is shown for α-Al2O3 in Fig 4-5. Figure 4-5: Temperature dependence of the critical shear stress τc(T) of covalent crystals measured under high or atmospheric pressure. The data are taken from the references: Lagerlof et al. (1994) for α-Al2O3, Castaing et al. (1981b) for Si and Boivin et al. (1990) for GaAs of intrinsic and ptype. (Figure source: Koizumi et al., 1994) This temperature dependence of the CRSS value is generally explained on the basis of intrinsic resistance to dislocation motion by the process known as the “Peierls process”. It has been suggested that the Peierls process becomes important for the rheology of olivine at higher stresses. Power law creep provides a good description for olivine flow only at lower stresses, whereas at higher stresses the olivine flow law becomes exponential [Goetze, 1978; Katayama and Karato, 2006]. An exponential flow law can be predicted based upon dislocation motion by the Peierls mechanism via nucleation of double kinks. Dislocation motion by the Peierls mechanism may be more important for b = [001] because [120] dislocation lines tend to be straighter for c-dislocations [Karato et al., 2008; Phakey et al., 1971]. Although, the value of critical stress at which the Peierls process starts to dominate the flow behaviour is not yet clear. Peierls mechanism of deformation by double kink nucleation At finite temperatures, dislocations do not move all at once in a plane strain manner but motion occurs through the generation and nucleation of kink-pairs. In this regime, nucleation of kink-pairs is the rate determining step for slip. Once a kink grows above a critical size, further straining takes place by migration of these kinks. A kink on a dislocation line can be envisaged as a dislocation on a dislocation line (Fig 46). According to the Peierls mechanism, a straight dislocation line has its lowest energy when it lies in a potential valley parallel to lines of closest packing of atoms on the slip plane. During the motion of a straight dislocation from one valley towards the next, the atoms in the vicinity of the core of the dislocation change their positions and bond angles, causing the energy of the dislocations to increase. Midway between two adjacent valleys, the dislocation energy reaches a maximum value and any additional displacement will cause the dislocation to fall down the energy maxima into the next valley. The maximum shear stress necessary to promote such forward motion of the dislocation is known as the Peierls stress 𝜏𝑝. Figure 4-6: Left image shows a kink (dark line) lying across a potential valley. Broken lines indicate the potential maxima with minima represented by the solid lines. Right: A kink in the presence of external stress has its equilibrium position displaced away from the unstressed position. Size of the kink is represented by kink height h and width 2K+L in case of a trapezoidal kink model. (Source: Suzuki et al. 1995) [127] segments unlike in dry specimens. It is a known fact that motion of screw dislocation is conservative and it generally does not involve diffusion [Nabarro, 1967]. Glide on (100) plane in hydrous specimens As mentioned earlier (100) plane is not an easily explicable glide for dislocations in olivine because it would appear to involve breaking of Si-O bonds present in the SiO4 tetrahedra (Fig 4-10). There are models of glide on the (100) plane which involve significant contribution from dislocation climb. After observing frequent occurrence of (100)[001] slip system in natural olivine Olsen and Birkelan.T [1973] proposed that such a glide may be possible by periodic occurrence of jogs on the dislocation line shown as the broken line in the figure 4-10. Figure 4-10: (001) projection of the olivine structure. Only the oxygen ions are shown, but the positions of the silicon ions are indicated by the Si 04 tetrahedra. Periodic jogs in a (100) plane are indicated by the broken line. The atom positions are those of the paper by Hanke (1965). (Figure source: Olsen and Birkeland, 1973) Figure 4-10 shows olivine (001) plane parallel to the plane of paper. It is clear that (010) is easier because dislocation line gliding on this plane will experience no obstruction from SiO4 tetrahedron whereas glide on (100) plane would be extremely difficult. However, [128] model proposed by Olsen and Birkelan.T [1973] cannot explain development of CPO in olivine. According to their model ratio of strain by glide to strain by climb 𝑙𝑔𝑙𝑐 ⁄< 1 because for every glide step by a segment of dislocation, it needs to climb by minimum of one climb step, hence the maximum 𝑙𝑔𝑙𝑐 ⁄ratio in this case would the 𝑏[100]𝑏[001]= 4.76 5.99 ⁄⁄ ≈0.80. This implies that a significant part of the strain would be accommodated by dislocation climb alone. This observation becomes even more pertinent because dynamic recrystallization and grain growth are very active in wet specimens and the former is known to randomize the CPO. So, in order to produce a perceptible CPO, the ratio 𝑙𝑔𝑙𝑐 ⁄ should be considerably higher than 1. This can happen only if dislocation segments are actually able to slice through the SiO4 tetrahedra. Another relevant observation in this regard is the deformation studies on olivine single crystal by Durham and Goetze [1977] where they have reported only 20-30% strain by dislocation climb. Figure 4-11: FTIR spectra for hydrous samples show peaks at 3477, 3448, 3629 and 3676 cm-1. These peaks could be arising from hydrogen associated with vacant Silicon sites. [129] As breaking of Si-O covalent bonds is energetically unfavourable, the only reasonable way to achieve this glide may be to replace some of the Si-O bonds by weak hydrogen bonds. Although most of the water in hydrous olivine is known to be associated with divalent metal vacancies, it has been argued that some OHis accommodated by charge balancing through the creation of vacancies at Si sites [Braithwaite et al., 2003; Brodholt and Refson, 2000]. Theoretical modelling on forsterite has shown that the hydrogarnet defect, 4𝐻𝑆𝑖 𝑋 should produce IR peaks around 3425, 3448, and 3478cm-1 [Braithwaite et al., 2003]. Whereas IR peaks at 3674 and 3624 cm-1 could also be band doublets related to Si vacancies [Libowitzky and Beran, 1995]. Broad peaks at 3448 and 3478cm-1 present in the hydrous specimens studied here might result from hydrogarnet substitution and peaks at 3676 and 3629 cm-1 are also present in these specimens (Fig. 4-11). If these peaks indeed result from OH bonds associated with silicon vacancy sites and thus a small of water is dissolved at the silicon site, then such sites could act as preferred locations for dislocation nucleation in (100)[001] slip system. Also, in such a scenario glide on the (100) plane would become the preferred glide plane because it is in fact the densest close packed plane of the olivine oxygen anion sub-lattice. This explanation is also in line with the observation that with increasing water content, glide on (010) plane becomes increasing difficult as evident from the positive slope of the transition boundary between C-type and B-type fabric (Fig. 4-3). [130] 4.4 Viscoplastic self consistent modelling of fabric development in olivine Viscoplastic self consistent modelling is a useful tool for modelling fabric development in mineral phases and has been used particularly to model olivine fabrics [Tommasi et al., 2000]. Input parameters in the model are relative slip system CRSS values for the mineral phase concerned, their elastic constants and stress exponent “n”. Based upon these input parameters, the modelling programme can predict the CPO development in various deformation geometries. Other useful information obtainable from this modelling tool is the nature of interaction between different slip systems and their relative contribution to the total strain in the sample. Furthermore, the fabric data obtained from these models can be employed for predicting seismic anisotropy resulting from activity of the chosen slip systems. The crucial aspect of this kind of modelling is the choice of relative CRSS values. The information about CRSS values can be estimated from the observation of CPO and the nature of dislocations in naturally or experimentally obtained specimens by using various tools such as EBSD and TEM. To perform this kind of modelling initial guesses are made for the relative CRSS values for different slip systems and then these choices can be improved further based upon the predicted activity of different slip systems by the program. Similarity of the visual appearance and strength of the predicted pole figure with the experimentally determined pole figures provides one way to constrain the correct choices for the relative CRSS value. This kind of modelling also provides information on geometrical constraints in the activity of the probable slip systems. In certain cases an easy slip system may be prevented from making significant contribution to the overall strain because of geometrical constraints imposed by the choice of active slip systems. For example, activity of (001)[100] slip system is suppressed in the presence of (010)[001] slip system [Tommasi et al., 2000]. However, it must be borne in mind that this kind of modelling does not take into account the effect of deformation processes other than dislocation glide. Dynamic recrystallization and other diffusive processes may stabilize the activity of some slip systems at levels which are either higher or lower than those predicted by the programme. [131] 4.4.1 Modelling the pole fabric for dry specimen DD455 Specimen DD455 was deformed under dry condition at 8.5 GPa, 1300°C at slow strain rate of 2.5x10-5 s-1. Active slip systems as observed under TEM are (010)[100], (010)[001] and (100)[001]. Pole figure for the specimens shows the presence of A-type and B-type fabric. A minor component of C-type could also be seen. Figure 4-12: Dry samples deformed at 8.5 GPa and 1300°C. Sample deformed at slower strain rate shows dominant slip system to be (𝟎𝟏𝟎)[𝟏𝟎𝟎] and (𝟎𝟏𝟎)[𝟎𝟎𝟏]. Table 4-3: Choice of relative CRSS values used for various models in order to synthetically generate the pole figure for specimen DD455 Models (010)[100] (010)[001] (100)[001] (001)[100] Model 1 1 1 1 1 Model 2 1 1 1 5 Model 3 1 1 5 1 Model 4 1 3 1 4 Model 5 1 3 1.5 5 Model 6 1 3 1 3 In order to synthetically generate a pole figure similar to what is observed in the specimen DD455 (Fig 4-12); a number of models were chosen. Starting by assigning all the slip systems an equal value of CRSS, the relative CRSS values are then iterated until a fair similarity is achieved between the observed pole figure in the specimen and the synthetic pole figure. The first model, which assumes all the slip systems to have similar CRSS value, clearly fails to recreate the pole figure for the specimen DD455. By suppressing the slip system (001)[100] with a choice of higher CRSS in model 2, because the relevant fabric generated [132] by this slip system shows very weak contribution in the original pole figure for DD455, a closer similarity in the visual appearance of the simulated and measured pole figures is achieved. Model 3 is again very different from the original pole figure. On the other hand, models 4, 5 and 6 which assume (010)[100] and (010)[001] to have very similar CRSS with later being slightly more difficult than the former, produces a much better match in the visual appearance and relative concentration of different crystallographic directions. The last 3 models also assume that (100)[001] and (001)[100] slip systems are at least three times more difficult than the slip systems with (010) glide plane. When the best fit models are examined they all identify the (010)[100] slip system as the easiest slip system at 8.5 GPa and 1300°C under dry conditions. Two of the successful models also identify the (100)[001] slip system as being of comparable strength to (010)[100],however, any model that impose this slip system to be weaker than (010)[100] results in a poor match with the experimental pole figure. This observation is in line with our other observations that there is no appreciable hardening of a-slip with pressure up to 11 GPa. Figure 4-14 shows that activity of various slip systems may vary with changes in strain to maintain the strain homogeneity in the aggregate without the need for grain boundary migration or other secondary strain generating processes. In this sense, models 4 and 5 are very stable and this is additional evidence that relative CRSS choices representing models 4 and 5 are representative of the slip systems active in specimen DD455. [133] Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Figure 4-13: Pole figures for models described in the table 5-3. Models which assume very similar CRSS value for (010)[100] and (010)[001] and at least three times higher CRSS value for other two slip systems can mimic the experimental pole figure. [134] Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Figure 4-14: Normalized activity versus equivalent strain plot for various model. Model 1 to 6 is shown here. Activity of slip systems can change with increasing strain because of geometrical constraints. In this sense, model 4 and 5 appear very stable 4.4.2 Modelling the pole fabric for dry specimen DD456 Specimen DD456 was deformed under wet condition at 8.5 GPa, 1300°C at a relatively fast strain rate of 5x10-5 s-1. Active slip systems as observed under TEM are (010)[001] and (100)[001]. The pole figure for the specimens shows the presence of C-type and B-type fabric. [135] Figure 4-15: Wet samples deformed at 8.5 GPa and 1300°C. The specimens shows two likely active slip systems – (010)[100] and (100)[001] which has also been confirmed by TEM study on this sample. Table 4-4: Choice of relative CRSS values used for various models in order to synthetically generate the pole figure for specimen DD456 Models (010)[100] (010)[001] (100)[001] (001)[100] Model 1 10 1 1 10 Model 2 10 2 1 10 Model 1 Model 2 Figure 4-16: Pole figures for models described in the table 5-4. Models which assume (100)[001] to be the easiest and (010)[100] as slightly higher than the former along with very high value of CRSS for (010)[100] and (001)[100] i.e. for a-slip can reproduce well the pole figure for the specimen DD456. Models (table 4-4) that assume the (010)[001] system to be the easiest with (010)[001] being slightly harder can recreate the pole figure for DD456 (Fig 4-16). These models also require that the other two slip systems involving a-slip i.e. (010)[100] and (001)[100] should be considerably hard to prevent the alignment of olivine [100] axes along the shear direction. [136] Seismic anisotropy in the upper mantle – Implications from this study Crystallographic preferred orientation of major mantle mineral phases e.g. olivine, pyroxene and garnet is believed to be the major cause of seismic anisotropy in the upper mantle. Seismic anisotropy by CPO development is the result of intrinsic seismic anisotropy of these crystals. Compositionally, mantle peridotite consists of up to 60% olivine, of orthopyroxene, clinopyroxene, ∼0%–20% of garnet, and spinel depending on the depth (e.g., Ringwood [1975]. Olivine, being the compositionally dominant and mechanically weakest phase in the peridotite, dictates the overall anisotropy of the aggregate and contribution of pyroxenes results in slight dilution of the overall P-wave and S-wave anisotropy [Blackman et al., 2002; Mainprice et al., 2000; Mainprice et al., 2005]. Whereas, garnet is known to develop only weak LPO in the presence of other weaker phases e.g. olivine and pyroxenes [Mainprice et al., 2004]. The general characteristic of Seismic anisotropy resulting from LPO of olivine, as seen in the natural samples, is that the fastest S-wave polarization direction lies (sub-)parallel to the foliation plane. The maximum shear wave splitting is observed normal to the lineation direction in the foliation plane. P-wave velocity is the fastest along the olivine a-axis. Symmetry of S-wave anisotropy is influenced by both [100] and [001] axis and P-wave anisotropy is mainly dependent upon [100] axis. Overall magnitude of the seismic anisotropy is dependent upon the orientations of all three olivine axis [Ben Ismail and Mainprice, 1998]. Magnitude of Seismic anisotropy increases the fabric strength but does not increase beyond 20% for P-waves and 15% for S-waves [Ben Ismail and Mainprice, 1998]. P-wave propagation direction is also fastest parallel to its [100] axis like in olivine. However, unlike in olivine where the maximum splitting directions occurs at an angle of 15 −20° from the c-axis direction, polarization direction of the fastest s-wave in enstatite lies at ~25° from the b-axis [Blackman et al., 2002]. In case of olivine, the ratio 𝑉𝑆𝐻 𝑉𝑆𝑉 ⁄ varies from fabric to fabric. In general, A-type fabrics are known to produce stronger 𝑉𝑆𝐻 𝑉𝑆𝑉 ⁄ ratio than E-type fabric with ratio being