Volume 117, Issue B1
Chemistry and Physics of Minerals and Rocks/Volcanology
Free Access

Deformation of olivine under mantle conditions: An in situ high-pressure, high-temperature study using monochromatic synchrotron radiation

Nadège Hilairet

Nadège Hilairet

Center for Advanced Radiation Sources, University of Chicago, Chicago, Illinois, USA

Now at UMET, UMR 8207 CNRS–Université Lille 1, Villeneuve d'Ascq, France

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Yanbin Wang

Yanbin Wang

Center for Advanced Radiation Sources, University of Chicago, Chicago, Illinois, USA

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Takeshi Sanehira

Takeshi Sanehira

Center for Advanced Radiation Sources, University of Chicago, Chicago, Illinois, USA

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Sébastien Merkel

Sébastien Merkel

UMET, UMR 8207 CNRS–Université Lille 1, Villeneuve d'Ascq, France

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Shenghua Mei

Shenghua Mei

Department of Geology and Geophysics, University of Minnesota, Twin Cities, Minneapolis, Minnesota, USA

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First published: 11 January 2012
Citations: 31


[1] Polycrystalline samples of San Carlos olivine were deformed at high-pressure (2.8–7.8 GPa), high-temperature (1153 to 1670 K), and strain rates between 7.10−6 and 3.10−5 s−1, using the D-DIA apparatus. Stress and strain were measured in situ using monochromatic X-rays diffraction and imaging, respectively. Based on the evolution of lattice strains with total bulk strain and texture development, we identified three deformation regimes, one at confining pressures below 3–4 GPa, one above 4 GPa, both below 1600 K, and one involving growth of diffracting domains associated with mechanical softening above ∼1600 K. The softening is interpreted as enhanced grain boundary migration and recovery. Below 1600 K, elasto-plastic self-consistent analysis suggests that below 3–4 GPa, deformation in olivine occurs with large contribution from the so-called “a-slip” system [100](010). Above ∼4 GPa, the contribution of the a-slip decreases relative to that of the “c-slip” [001](010). This conclusion is further supported by texture refinements. Thus for polycrystalline olivine, the evolution in slip systems found by previous studies may be progressive, starting from as low as 3–4 GPa and up to 8 GPa. During such a gradual change, activation volumes measured on polycrystalline olivine cannot be linked to a particular slip system straightforwardly. The quest for “the” activation volume of olivine at high pressure should cease at the expense of detailed work on the flow mechanisms implied. Such evolution in slip systems should also affect the interpretation of seismic anisotropy data in terms of upper mantle flow between 120 and 300 km depth.

Key Points

  • Lattice strains, textures and EPSC modeling define 3 experimental P-T domains
  • V* has no physical meaning if dominating slip systems change gradually with P
  • Such a gradual change would affect interpretations of seismic anisotropy data

1. Introduction

[2] Rheological properties of olivine, a major constituent of the upper mantle, are critical input parameters in modeling geodynamic processes in the upper mantle, including convective flows, evolution of subduction zones, deep seismicity patterns, and post-seismic mantle relaxation [e.g.,van Keken et al., 2002; Freed and Burgmann, 2004; Gerya and Stöckhert, 2002; Kneller et al., 2007]. Interpretation of the upper mantle seismic anisotropy in terms of mantle flow [e.g., Kneller et al., 2005] also relies on our knowledge of crystallographic and shape preferred orientations of polycrystalline olivine which, in turn, are controlled by the deformation mechanisms depending on the physical and chemical conditions of deformation.

[3] The flow behavior of olivine and its rock counterpart dunite are reasonably well documented at high temperatures (HT) and low pressures (<2 GPa) [e.g., Carter and Ave'Lallemant, 1970; Demouchy et al., 2009; Durham and Goetze, 1977; Durham et al., 1977; Faul et al., 2011; Hirth and Kohlstedt, 2003; Karato et al., 1986; Mei and Kohlstedt, 2000a, 2000b]. Recent advances in high-pressure deformation devices [Wang et al., 2003; Yamazaki and Karato, 2001] have expanded experimental capabilities to cover the entire pressure and temperature stability field of this important mantle constituent, up to the transformation into its high-pressure polymorphs. However, most parameters for the flow laws of olivine remain poorly constrained at high pressure (HP; > 2GPa) and high temperatures. The largest discrepancy is centered on the activation volume whose current experimentally determined values vary from 0 to 25 cm3 mol−1 [e.g., Durham et al., 2009; Li et al., 2006; Kawazoe et al., 2009]. No clear connection has been made to the deformation mechanisms at work in previous studies on polycrystalline olivine at HP-HT, contrary to low-pressure studies. Also, recent calculations and experimental data suggest a pressure-induced change in major slip systems during deformation [Durinck et al., 2005; Jung et al., 2006]. For single crystals, this change is found to take place between 6 and 9 GPa at ∼1673 K [Raterron et al., 2009], but its physical conditions are still not tightly constrained. Experimentally, it remains difficult to control and maintain water content in high pressure experiments with in situ x-ray measurements [e.g.,Durham et al., 2009]. Thus, our knowledge on effects of water and pressure on olivine flow mechanisms is far from comprehensive and does not allow for an accurate evaluation of mantle viscosities.

[4] Here we present results from HP-HT deformation experiments of sintered San Carlos olivine polycrystalline samples under controlled strain rates (from 7.10−6 to 3.10−5 s−1). Samples were deformed using a deformation-DIA (D-DIA) at high pressures (3.3 to 7.8 GPa) and high temperatures (1173 to 1676 K) with final strains up to ∼−20% (negative sign indicates shortening). The data were acquired at GSECARS, sector 13 at the Advanced Photon Source (APS), with monochromatic synchrotron x-ray diffraction and radiography, for in situ lattice strain (a function of stress) and macroscopic strain measurements, respectively. While previous studies used white synchrotron x-rays and therefore could not record the full diffraction rings, the monochromatic x-rays used here provide precise information on the stress and texture of olivine polycrystals under deformation. We obtained lattice strains from four to six lattice planes of the deforming samples based on complete 2D x-ray diffraction patterns. Changes in flow behavior have been observed, one as a function of pressure (below and above 4 GPa) and one as a function of temperature (below and above ∼1600 K), delineating three deformation regimes. The complex behavior we observed over the pressure and temperature range questions previous conclusions on activation volume determination: without a clear picture of dominant deformation mechanisms, fitting the stress–strain data with a unique phenomenological power law can yield inadequate results.

2. Experiments

2.1. Samples Synthesis

[5] The sintered polycrystalline samples were prepared at University of Minnesota, MN. Cylinders of polycrystalline olivine, 9.0 mm in diameter and 14.0 mm in length, were hot pressed from mixtures of oven-dried powder of San Carlos olivine plus 5% by weight of enstatite. The enstatite was used to limit grain growth during hot pressing and to buffer the silica activity in the olivine. The starting particle size of the powder was ∼5μm. Power was first cold pressed at ∼200 MPa and then hot pressed at 300 MPa and 1473 K for 4 h. The resultant average grain size was 5 to 10 μm. Sample cylinders, 1.2 mm in diameter and 1.2 mm in height, were then cored from the hot-pressed “rock” for deformation experiments.

2.2. Deformation Experiments

[6] We used a cell assembly suited for 4 mm truncation D-DIA anvils (auxiliary material, Figure S1 in Text S1). As such, the assembly was an open system as compared to sealed metal capsules often used in lower pressure experiments. The amorphous boron epoxy pressure medium we used is known to be a rather hydrous environment [Durham et al., 2009]. Nickel foils were used as strain markers, in order to help control oxygen fugacity, similar to previous studies using the D-DIA [Durham et al., 2009; Li et al., 2006; Raterron et al., 2009] although more work is required for actually buffering fO2in this type of cell assemblies. Temperature was imposed by an AC electrical current circulating through the graphite furnace. Temperature was calculated based on off-line calibrations of thermocouple emf versus electrical power, using a W95Re5-W74Re26 thermocouple, with no correction for pressure effects on the emf. From repeated offline calibration measurements [see alsoDurham et al., 2009] the estimated uncertainty in temperature is below 10%. Table 1 summarizes all the experiments.

Table 1. Experimental Conditions and Observations
Run Number and Shortening Number Pa (GPa) Tb (K) Strain Ratec (10−5 s−1) σd (MPa) Maximum Straine (%) Group Observationsf Interpretationsg
D0912-1 4.19 1373 0.670 (0.015) 1385 −13 1 Continuous rings Small crystallite sizes
D0912-2h 3.79h 1600 3.42 (0.29) 212 −13 3 Spotty, short lifetime Growth, g.b. migration, recovery
D0912-3h 4.27h 1600 1.40 (0.04) 215 −18 3 Spotty, long lifetime, little rotations G.b. migration + important part of recovery
D0912-4 5.71 1153 2.70 (0.14) 3092 −7.5 1 Continuous rings Crushing in small crystallites at the beginning
D0966-1i 2.81i 1576/1458 1.35 (0.01) 543i −12 2 Spotty, short lifetime evolving to broadened spots, large spot rotations (sometimes > 5 degrees) Rotation, strained lattices, recrystallization in small grains with preferred orientation, heterogeneous crystallite sizes ?
D0966-2 2.96 1643/1604 1.22 (0.02) 445 −11 2 Very broadened spots with extremely long lifetime (almost continuous ring), large spot rotations Crystallite rotations
D0966-3 5.09 1671/1626 0.98 (0.02) 897 −12 1 Broadened spots evolving to continuous rings, large spot rotation Crystallite rotations
D1040-1 6.80 1593 1.269 (0.009) 169 −18.5 3 Continuous replaced by spots with short lifetime Growth, g.b migration, recovery
D1040-2 7.85 1375 1.100 (0.005) 2895 −17 1 Steady spots evolving to continuous rings, no or little spot rotation Crystallite size reduction
D1040-3 6.16 1375 1.49 (0.02) 2910 −22 1 Continuous rings Small crystallite sizes
D1062-1 5.01 1506 0.344 (0.002) 76 −15 1 to 3 Started in compressive stress, continuous rings evolve to spots with medium-length lifetime, intensity fluctuations Growth, g.b. migration, recovery
D1062-2 4.17 1573 1.592 (0.007) NA −15 3 Spotty with very short lifetime, no smooth intensity variation background g.b. migration, recovery, homogeneous crystallite size
D1062-3 5.84 1506 1.24 (0.06) 1465 −12 3 to 1 Steady spots replaced by continuous rings with broadening and rotation Crystallite size reduction, with preferred orientation + crystal rotations
  • a At 10% strain or on last data point.
  • b From offline calibration (when spectroradiometry was used: calibration/spectroradiometry).
  • c In brackets: standard deviation from the linear regression on strain over time, given in the same power of 10 as the strain rate.
  • d Taken arbitrarily at 10% strain. Average of t(hkl) from the four most intense reflections 021, 130, 131 and 112, for consistency between cycles and comparison with previous studies. NA means not analyzed.
  • e Maximum strain achieved for this specific shortening cycle, reference length taken at null stress at the beginning of this shortening.
  • f See Figure 3.
  • g Here g.b. : grain boundary.
  • h Confining pressure dropped by 200 MPa in D0912-2 and 800 MPa in D0912-3 over the 10% strain, the pressure is taken at 10% strain.
  • i Neither stress nor confining pressure reached a plateau, although strain rate reached a constant value.

[7] In one of the experiments (D0966), the alumina piston and crushable plug on the lower side of the sample were replaced by a moissanite (SiC) single crystal (Figure S1 in Text S1) for temperature measurement using spectro-radiometry [Sanehira et al., 2008, also manuscript in preparation, 2012]. The advantage of this technique is to allow in situ temperature measurement without using a thermocouple, which introduces undesirable gradient asymmetry in the cell. Due to the high thermal conductivity of the moissanite crystal, however, the temperature at the window end of the sample was probably lower than that on the opposite end. Temperatures calculated from furnace calibration were somewhat higher than the ones measured by spectro-radiometry, but still consistent within the experimental uncertainty (10%).

[8] To deform the sample triaxially, the two differential rams in the D-DIA were advanced (or retracted) toward (away from) each other, shortening (elongating) the sample along the vertical axis. Since the differential rams can be adjusted independently from the main hydraulic ram outside the D-DIA module, differential stress and sample axial strain can be controlled essentially independently from hydrostatic pressure. Samples were shortened and lengthened in multiple deformation cycles (cycles are detailed inTable 1). At the end of each cycle, the differential rams were retracted so that samples would change from a shortened to a lengthened state, thereby allowing definition of a zero differential stress state for each stress–strain curve. The length at this zero differential stress point was then used as the reference l0 for strain calculation in each cycle, with the strain defined as ε = (l − l0)/l0, l being the sample length.

[9] Sample axial strains were measured using x-ray radiography with a large monochromatic beam (2 × 3 mm). Radiographs were acquired typically over 10 s using a YAG scintillator and a charge coupled device (CCD, resolution 1.3μm/pixel). The sample length was defined by the shadows of the two Ni foils at its top and bottom. After each x-ray radiograph, a 2-dimensional (2D) x-ray diffraction (XRD) pattern was collected over 300 to 450 s with an area detector (MAR165 CCD). The incident monochromatic beam (wavelengthλ = 0.2755 Å) was collimated to 200 × 200 μm by WC slits. Detector tilt and rotation relative to the incident beam were calibrated with a CeO2 standard using fit2D [Hammersley et al., 1996]. The detector spatial drift was systematically corrected during the analysis by manual adjustment of the diffraction ring center in Fit2D. The repeated image – diffraction data collection was automated for each deformation cycle.

[10] More than 800 image and 2D diffraction pattern pairs over the four experiments were analyzed in this study. For strain measurements, an IDL code, largely inspired by a MATLAB© code provided by L. Li [Li et al., 2003, 2004], was used. This approach takes advantage of the classical image analysis by analyzing the sum of square differences between regions of interest (strain markers) in consecutive image pairs. This method was tested here mainly to account better for irregular shapes or slight tilting of strain markers. Stress analysis was carried out on 2D diffraction patterns using the software Multifit-Polydefix (available online athttp://merkel.zoneo.net/Multifit/) as well as a series of routines developed in-house.

2.3. Water Content Estimates

[11] Water content was estimated using FTIR spectrometry, at the Geodynamics Research Center, Ehime University, with a Perkin Elmer SK spectrometer equipped with a KBr beam splitter and an IR microscope with all-Cassegrainian optics. The samples were prepared in double-polished sections (200 microns thick). They were put on a BaF2 window with air moisture purged using a N2 flow. Backgrounds and transmitted IR spectra were acquired with a 0.1 x 0.1 mm square aperture between 700 and 4000 cm−1 with a resolution of 1 cm−1. 200 scans were stacked for each spectrum. After background and baseline correction, the absorbance was normalized to 1 cm thickness and integrated. For easy comparison with previous rheological studies on olivine, we used the calibration by Paterson [1982] with an appropriate scaling factor [Kohlstedt et al., 1996].

[12] Unpolarized spectra for the starting material and recovered samples from runs D0912 and D0966 are presented Figure S2 in Text S1. Throughout the areas measured, for each sample the spectra were homogeneous. The starting material did not show any detectable water-related band and is considered dry. D0912 and D0966 samples showed a very broad increase in absorbance from 3025 to 3700 cm−1, interpreted as a result mainly of water at grain boundaries. Hydroxyl content within crystals may have varied during quenching and it is impossible to evaluate if water at grain boundaries was present as such during the runs. In D0912 a band at 3690 cm−1 is observed and interpreted as hydroxyl species; this band is likely present in D0966 but not discernable. Maximum possible hydroxyl content, if integrated from 3025 to 3700 cm−1 would be up to 100 ppm H2O by weight (1327 H/106 Si) in sample D0966 and 300 ppm H2O by weight (3981 H/106 Si) in D0912. Integration of the band at 3690 cm−1 gives about 120 ppm for D0912 if the contribution of the broad increase in absorbance is fully removed. Differences between D0912 and D0966 may be due to the difference in cell composition or to the experimental paths (D0966 began by low pressure cycles where H solubility is lower, in which case we may consider COH fixed). We can only infer that the rheological properties measured here represent rather wet conditions, at least for D0912 [Kohlstedt et al., 1996], and that D0966 is dryer than D0912.

2.4. Grain Size and Microstructures

[13] The samples recovered from D0912 and D0966 were examined using Scanning Electron Microscopy (SEM) using a Hitachi S-4700-II SEM at the Electron Microscope Center (Argonne National Laboratory). D0912 shows large grains (2D-sections larger than 10μm) that underwent partial grain size reduction (below 1 micron) at triple junctions; the newly formed grains are equant with junctions at 120° (Figure S3 in Text S1). D0966 has grain population more uniform in 2D sections that are several microns wide. We undertook Transmission Electron Microscopy (TEM) in order to investigate the deformation microstructures; however the complexity of the P-T-deformation path imposed to the samples made it unrealistic to interpret the microstructures in terms of deformation mechanisms associated with P-T conditions.

3. Data Processing

3.1. Lattice Strains

[14] In the absence of non-hydrostatic stress the inter-planar spacing (d-spacing) for a given set of lattice planes undergoes identical elastic deformation regardless of azimuth angle, resulting in perfectly circular diffraction Debye rings. Under a deviatoric stress field, this elastic deformation is a function of orientation of the diffracting planes relative to the stress geometry, resulting in pseudo-elliptical Debye rings. This departure from ideal powder diffraction rings is a function of the differential stress the polycrystalline sample supports, referred to as “lattice strain,” not to be confused with the macroscopic sample strain.

[15] The diffracting plane azimuth φ is defined as the angle between the maximum compression axis and the diffracting plane normal, with φ = 0 for planes whose normal is parallel to the maximum compression axis. The projection of φ on the detector plate is δ, with cos φ = cos θ cos δ, where θ is the diffraction angle.

[16] Each 2D diffraction pattern was integrated over 5 degrees slices of azimuthal range resulting in 72 2θ-intensity spectra, using Fit2D [Hammersley et al., 1996] (Figure 1). At any azimuth angle φ, simple elastic theory assuming no lattice preferred orientation, no plastic relaxation of stress, and under an axial-symmetric stress field predicts the relation between measured d-spacingd(hkl) and lattice strain Q(hkl) to be [e.g., Singh et al., 1998; Uchida et al., 1996]
where dP(hkl)is the isotropic stress d-spacing, corresponding to the hydrostatic pressure d-spacing, for which the right-hand side ofequation (1) is zero. For each plane hkl, d(hkl) and φ are measured from the 2D diffraction pattern (with cos φ = cos θ cos δ), Q(hkl) and dP(hkl) are extracted by fitting d(hkl) versus φ according to (1).
Details are in the caption following the image
Two-dimensional diffraction pattern of polycrystalline olivine at 7 GPa, 1153 K and ∼10% strain. (top) Two-dimensional diffraction image transformed in Cartesian coordinates showing the typical distortion of the diffraction lines induced by the macroscopic deviatoric stress (notedσ, geometry depicted by red arrows). The main diffraction lines from olivine used in this study are indicated; hBN + gr, sample container and graphite furnace. (bottom) Data for 131 and 112 with fit to equation (1) (line).

3.2. Pressure

[17] Unit cell volumes were refined based on d-spacingdP(hkl) of 4 to 6 crystallographic planes (equation (1)). Confining pressures were calculated following a thermal pressure equation of state [Guyot et al., 1996] by adopting the room T pressure values (referred to as “cold” pressure) from a third-order Birch-Murnaghan equation and a thermal pressure corresponding to the measured volume.

3.3. Stress

[18] Differential stresses t(hkl) were calculated for planes from lattice strains Q(hkl) according to
The “effective moduli” G(hkl) were calculated with the elastic compliances Sij from inversion of the stiffness tensor (Cij) for San Carlos olivine at relevant P and T [Isaak, 1992; Zha et al., 1996]. We used the equations by Uchida et al. [1996]with a Reuss (iso-stress) assumption, believed to be closer to reality than the Voigt (iso-strain) assumption [Chen et al., 2006; Uchida et al., 2004].

[19] In order to evaluate the strength of materials and obtain flow laws, a “macroscopic” sample flow stress has to be extracted from these diffraction measurements of microscopic stresses. This stress is usually obtained by averaging all observed hkl reflections. The stresses t(hkl) calculated from the lattice strains of 021, 130, 131 and 112 (the four reflections used in previous studies, for comparison purpose) at −10% strain (constant strain rates) were averaged and are quoted as flow stresses in Table 1.

[20] This approach is biased by the choice or availability of diffraction lines and has no physical ground; however it is used in many studies because there is still no complete theory for evaluation of macroscopic stress from powder diffraction data. We refer the reader to our comments below on the use of EPSC modeling in the case of olivine and to Burnley and Zhang [2008], Merkel et al. [2009], and Wang and Hilairet [2010].

3.4. Texture

[21] Selected diffraction patterns were analyzed for texture; an extensive analysis of the present diffraction data set may deserve another entire study. No significant textural change was observed as the experimental conditions were varied (except when grain growth occurred), although the texture did weaken upon sample elongation during retraction of the differential-rams after axial shortenings episodes.

[22] We used the software MAUD [e.g., Lutterotti et al., 2007] and followed a procedure similar to that described by Miyagi et al. [2006]. Adopting anisotropic functions for crystallite size and microstrains, and freeing isotropic thermal vibrations made the refinement unstable, with no improvement of the fit and no significant change in the pole figure; therefore the crystallite functions were kept isotropic and thermal vibrations were not refined.

[23] The texture was refined with the E-WIMV algorithm, a modification of WIMV [Matthies and Vinel, 1982]. In the case of axial compression, the stress field can be approximated as axial symmetric and textures can be compactly represented with an inverse pole figure (IPF), which displays the relationship between crystallographic directions of crystallites within the sample to the compression direction. Pole densities are expressed in multiples of random distribution (m.r.d.). For a random polycrystal, all orientations have a density of 1 m.r.d. In a single crystal, the m.r.d. is equal to infinity for one orientation and 0 for the others. For orthorhombic materials such as olivine, only one quadrant of the IPF is needed to fully represent the Orientation Distribution Function (ODF). We used a 15 degree resolution for the ODF; initially no geometry was assumed in order to check that pseudo axial symmetry could be observed on the experimental and reconstructed pole figures [e.g., Miyagi et al., 2006], and a cylindrical geometry was imposed for the final fits.

3.5. EPSC Modeling

[24] EPSC models [Turner and Tomé, 1994] can be used to link activity of slip systems to the experimentally observed lattice strains [e.g., Merkel et al., 2009]. They have been proposed also as a tool to better evaluate the macroscopic stress [Burnley and Zhang, 2008] in order to overcome the issue in evaluating macroscopic stresses, in diffraction based deformation experiments. In an EPSC simulation, boundary conditions (increments of full strain or stress tensor) are imposed on a set of grains described by their orientation distribution and a starting shape. Each grain is treated as an inclusion in a matrix, whose properties are calculated as an average of all other grains, following the Eshelby inclusion theory [Eshelby, 1957]. The deformation modes (slip systems and their resistance to flow) of the material are prescribed and the stress resulting from boundary conditions is resolved on the available slip systems in each grain. The code determines which modes are activated based on the calculated critically resolved shear stress (CRSS) and increments deformation/stress into each grain accordingly.

[25] For each deformation mode the evolution of the instantaneous CRSS τS on the slip plane(s) is expressed by an empirical Voce hardening law [see Tomé et al., 1984]:
where Γ is the accumulated shear strain in the grain. Here, for the sake of simplicity we assume a linear hardening law by forcing τ1S = 0 for all the deformation modes and simplify (3) into
The initial CRSS τ0S and the hardening slope θ1S are the parameters to be tuned in order to model the lattice strain evolution, together with the choice of slip systems made available.

[26] We used a set of 3000 crystals with random orientations and isotropic shape. The analysis method is the same as described by Merkel et al. [2009], except that the reference state was taken at the pressure and temperature at the beginning of the simulated cycle, instead of ambient conditions, in order to avoid modeling the pressurization and heating before deformation. The elastic constants used were those of San Carlos olivine at corresponding pressure and temperature [Isaak, 1992; Zha et al., 1996], and the starting unit cell dimensions were those measured by diffraction at the beginning of the cycle. The deformation was prescribed such that the final macroscopic strain along the compression axis would be −10% and the strain along the transverse axes would allow the same final pressure increase as observed experimentally at −10% (for the experimental curves chosen, about 0.8 GPa).

4. Results

4.1. Diffraction Observations and Lattice Strains

[27] Figures 2a–2c (subset of the data) and Figures S4a–S4l in Text S1 (full data set) show the evolution of lattice strains Q(hkl) with increasing plastic strain for various P, T, and strain rate conditions (Table 1). Three main patterns of lattice strain (groups 1, 2 and 3) emerge with distinct inflexion orders of the individual Q(hkl)-strain curves during yielding and distinct evolution paths with strain.

Details are in the caption following the image
Lattice strains data groups. The Q(hkl) are fitted from the data with equation (1); each symbol represents a different lattice plane (see legend). The error bars are typically the symbol size for (a) group 1 and (b) group 2 and up to three times the symbol size for (c) group 3. The initial length for the bulk sample strain is defined at null average lattice strain. The full data set is presented Figure S4 in Text S1.

[28] Group 1 data (Figure 2a and Figures S4a–S4f in Text S1) show lattice strains of magnitudes 0.003 to 0.010 at 10% strain, with largest strains on 130 and 021 (about equal), then in decreasing order 131, 112, and finally 101. The group 1 lattice strain pattern was observed in high pressure deformation cycles with relatively low temperature (P from 4.2 to 7.85 GPa, T from 1153 to 1626 K).

[29] In group 2 (Figure 2b and Figures S4j–S4k in Text S1) lattice strains were between 0.001 and 0.002, with 021 having the largest lattice strain, then 130 (with more hardening than the others), then 112 and 131 (about equal), and lastly 101 shows the smallest lattice strain. Group 2 patterns were observed at pressures of 2.8 and 3 GPa and relatively low temperatures.

[30] In group 3 (Figure 2c and Figures S4g–S4i and S4l in Text S1) lattice strains from all diffraction planes are about equal within the uncertainties, with none exceeding 0.001. This was observed from 3.8 to 5.6 GPa, only at high temperatures (>1570 K), and was sometimes accompanied by confining pressure drops of 200 to 800 MPa (cf. Table 1). Unlike in groups 1 and 2, no strain hardening is observed in this group.

[31] The smooth and continuous diffraction rings, as observed in groups 1 and 2, became discontinuous then spotty in group 3, strongly suggesting growth of coherent diffracting domains (grain or sub-grain growth) during deformation. This behavior does not seem to depend on pressure or sample strain history in the range tested.

4.2. Grain Sizes and Deformation Mechanisms

[32] In order to obtain qualitative information on the grain sizes and deformation mechanisms, the intensity of the 130 reflection along the full diffraction ring was integrated over a small 2-theta range (14 or 15 pixels, typically a range of 0.15°). This reflection was chosen because it is not overlapping with, and is far from, any other reflections. The δ-intensity data were plotted against the diffraction file number (roughly a function of time), withδ defined in 3.1 (Figure 3). When the average domain size is sufficiently small, the integration results in a homogeneous distribution independent of azimuth angle. With increasing domain size, Debye rings become spotty; this integrated band would exhibit sporadic fluctuation in intensity as a function of azimuth angle. This appearance and disappearance of diffraction spots are a textbook case of crystallite growth. As some crystals are being consumed by others, or swept across by migrating boundaries, grains change their crystallographic orientations, resulting in the “flickering” of diffraction spots. Detailed interpretations are reported in Table 1.

Details are in the caption following the image
Crystallite sizes. Pixels have been integrated around the 130 maximum intensity along the whole diffraction ring (for δ = 0 to 360 degrees, δ being the projection of the diffracting plane normal angle with the maximum compression axis φ on the detector plate), and the δ-intensity pattern obtained is plotted vertically in gray levels, as a function of the diffraction number (roughly a function of time). A smooth intensity variation alongδ corresponds to preferred orientation with small crystallite sizes. Spottiness along δ means that less individual crystallites are present in the diffracting volume (therefore higher crystallite size) compared to a smooth intensity profile. Recrystallization of smaller crystallites in orientation slightly different from the parent grain therefore shows up as broadening in δ of spots over time, growth of crystallites as an increase in spottiness (not necessarily in spots), and recovery as fluctuations in intensity of a spot over time if it is not rotating [e.g., Liss et al., 2009]. Rotation of crystallites that stay in Bragg conditions can be seen when spots moving slightly in δ from one diffraction to another and define a slope; a steady straight line indicates no rotation of the crystallite. Differential stress calculated from average of t(hkl) (equation (2)) and total strain during axial shortening, and experimental conditions are reported below; “r” indicates a retraction during which no diffraction was acquired.

[33] While group 3 lattice strains patterns (low stresses) are always associated with spotty patterns (indication of large crystallites), groups 1 and 2 patterns (high stresses) show smooth diffraction rings, corresponding to smaller crystallite sizes. In Figure 3(bottom) transitions to and from lattice strain group 3 are most easily observed (runs D0912 and D1062). The samples have the remarkable ability to switch back and forth, by varying temperature alone, between the low-stress, large domain size, with a lack of strain hardening, and the high-stress, small-domain size, strong strain hardening behavior (i.e., from group 1 to 3 lattice strain type and conversely). The transition from group 1 to group 3, and vice versa, occurs progressively when the temperature variations are small between deformation cycles (70 K in D1062), but much faster when the temperature is varied by 200–250 K. This behavior is relatively insensitive to strain rate: flow stresses at strain rates varied by a factor 3 were the same (212 and 215 MPa). Data at strain rates differing by a factor of 10 gave somewhat lower stress (212 and 76 MPa). These values are close, since one standard deviation on theQ(hkl) fitted with equation (1) give typically an error on stress of 25 MPa (up to 50 MPa), and the variability of t(hkl) from one diffraction line to another is typically 100 MPa, up to 200 MPa.

4.3. Texture Analysis

[34] Figures 4a and 4b show the results of azimuthal dependent Rietvelt refinements and the corresponding IPF obtained for patterns at ∼−11% strain, temperatures of ∼1600 K, and confining pressures of 3.0 GPa and 5.1 GPa. The texture index F2 [Bunge, 1982], which measures the sharpness of the texture, is 1.03 at 3.0 GPa and 1.25 at 5.1 GPa, with ODF maxima of 1.66 and 1.77 m.r.d., respectively. At 3.0 GPa (Figure 4a), the IPF maximum defines a girdle extending from the 101 pole up to 130. At 5.1 GPa (Figure 4b), the maximum in the IPF defines a girdle starting at the 101 pole, toward 111, and almost up to 121. For both IPFs, distinct minima are observed in the 100 and 001 directions. This significance of these differences will be discussed later.

Details are in the caption following the image
(left) Textures below and above P ∼ 4 GPa in polycrystalline olivine axially shortened. Experimental data from (a) shortening cycle D0966-2 and (b) shortening cycle D0966-3, and corresponding refinements using the software MAUD [e.g.,Lutterotti et al., 2007]. (right) Corresponding inverse pole figures for the axial compression direction (15 degrees resolution ODF). Note the difference in color scales. The hatched areas correspond to unfitted areas (graphite and hBN from the experimental cell).

[35] Some discrepancies (Figure 4) could not be corrected in the refinement of the diffraction patterns, mostly on the (021) plane, whose intensity was always lower in the fit than in the experimental data.

4.4. Slip Systems From EPSC Modeling

[36] EPSC modeling of olivine lattice strain presents some important limitations, due to the well-known lack of available slip systems in olivine to account for an imposed plastic deformation. In real olivine, this is compensated by plastic processes other than glide which are not taken into account in the code we used. At high temperature especially, significant lattice strain relaxation could be provided by dislocation climb, grain boundary sliding, grain rotation and diffusive processes, even if they are not the main contributors to the bulk strain [Lebensohn et al., 2010]. Strictly, without the inclusion of some of these mechanisms—which is beyond the scope of this publication—for olivine, i) the calculated bulk and grain strain values should not be compared with real strain values, ii) threshold stresses used can only help assessing relative strength of slip systems, and iii) one cannot obtain a quantitative average (macroscopic) stress for flow law determination, in contrast to quartz at low temperatures [Burnley and Zhang, 2008]. Therefore we only attempt to interpret the different lattice strain patterns observed in terms of activation of dislocation glide systems, and do not provide a full EPSC model of the experiments.

[37] We investigated combinations of known slip systems from the literature (Table 2). Following Castelnau et al. [2008, 2010], Tommasi et al. [2000] and Wenk et al. [1991] we also examined the influence of an additional “convenience” group of slip systems 〈1urn:x-wiley:01480227:media:jgrb16958:jgrb16958-math-00050〉 {111} (which have never been identified in olivine), used for numerical stability in their visco-plastic self-consistent (VPSC) models. In contrast to the EPSC approach which models elasticity and uses empirical hardening laws, a VPSC model neglects the elastic effects and assumes a nonlinear viscous response [Lebensohn and Tomé, 1993]. In VPSC models, introduction of the artificial systems mentioned above is known to have a significant influence on calculated stresses [e.g., Castelnau et al., 2008; Lebensohn et al., 2010].

Table 2. EPSC Models and Parametersa
Model Figure Number (001)[100] and/or (100)[001] (010)[100] (010)[001] {0kl}[100] {111}〈1 urn:x-wiley:01480227:media:jgrb16958:jgrb16958-math-00050〉b Comments
A S3 100/1 100/1 100/1 - - Fully elastic
B S3 0.3/0.1 100/1 100/1 - - Cij at 5.7 GPa 1153 K
C S3 0.3/0.1 0.35/0.08 100/1 Cij at 2.24 GPa 1604 K
E 5 and S3 0.4/0.1 0.5/0.1 1.3/1.5 - - Cij at 2.24 GPa 1604 K
E-2 S3 0.2/0.1 0.3/0.1 1.3/1.2 0.3/0.1 - Cij at 2.24 GPa 1604 K
F 5 and S3 0.2/0.1 1/1 1.1/1 - - Cij at 5.7 GPa 1153 K
F-2 S3 0.2/0.1 1/1 1.1/1 0.8/1.0 - Cij at 5.7 GPa 1153 K
H S3 0.2/0.1 1.5/1.0 1.1/0.1 - - Cij at 5.7 GPa 1153 K
H-2 S3 0.2/0.1 1.1/1 0.3/0.1 - - Cij at 5.7 GPa 1153 K
J S3 0.4/0.05 0.9/0.1 1/1 - 1.4/2.5 Cij at 5.7 GPa 1153 K
  • a Slip system properties are presented as τ0 (CRSS, GPa)/θ1 (hardening slope). 100/1 is used to prevent the activation of one or more slip systems in some models.
  • b This deformation mode has never been observed in olivine; see text for discussion.

[38] The most significant results are presented in Figure 5; Figure S5 in Text S1 presents the results for all the models. Table 2 summarizes the slip systems and parameters used. The choice of the initial CRSS was the main factor affecting the following results. Varying the hardening slope had a much smaller influence, mostly on the detail of the shape of the curves.

Details are in the caption following the image
EPSC modeling results and comparison with experimental data: (left) slip system activities from EPSC model (normalized to total activity) as a function of strain and (right) lattice strains Q(hkl) from the EPSC model (solid lines) and experimental data (symbols) as a function of strain. The two most relevant EPSC models are presented. (a) EPSC model E (lines) relevant for experimental data (symbols) at low pressure (group 2), with easy glide on [100](001) and with the so-called “a-slip” [100](010) much easier than “c-slip” [001](010). These properties result in a large activity of [100](001) and a-slip almost immediately after the beginning of deformation, and c-slip intervenes after about 2% strain (Figure 5a, left). Lattice strains from the model are scaled by 0.1 for visual comparison (Figure 5a, right). (b) EPSC model F (lines) relevant for experimental data (symbols) at high pressure (group 1), with easy glide on [100](001) and with “a-slip” [100](010) almost as hard as “c-slip” [001](010). These properties result in large activity of [100](001) almost immediately after the beginning of deformation; after about 1% strain a-slip and c-slip start to be active and at final c-slip has a higher activity compared to a-slip (Figure 5b, left). Lattice strains from the model are scaled by 0.7 for visual comparison (Figure 5b, right). The 002 model is not consistent with experimental data and was removed for clarity; the full results are shown in Figure S5 inText S1.

[39] Model A (Figure S5 in Text S1) corresponds to purely elastic deformation. No deformation mode is activated, and no inflexion of the lattice strain evolution with bulk strain is observed.

[40] Model B corresponds to the activation of one or both of the “easy” slip systems [100](001) and [001](100) (results are identical), with an initial CRSS of 300 MPa. Their activation results in an inflection of the lattice strain for 101 and 112 while other diffraction lines showing a quasi-linear behavior (Figure S5 inText S1). The lower amplitude of 101 is observed in all our experimental lattice strain curves, and cannot be produced by the individual activation of any other slip systems tested.

[41] Model C used the same parameters as model B, plus the so-called a-slip system [100](010) with an initial CRSS of 350 MPa, slightly higher than for the easy slip system. This model shows a lattice strain pattern with relative amplitudes similar to group 2 experimental data (low pressure, <4 GPa), but does not reproduce the hardening on 130 compared to 131.

[42] In Model E, [100](001) and [100](010) had close initial CRSS values, like in model C (400 and 500 MPa respectively), and the so-called c-slip [001](010) was allowed, with its initial CRSS set much higher at 1.3 GPa. Model E is the closest to the low pressure data; it was scaled by a factor of 0.1 to facilitate comparison with experimentalQ(hkl) in Figure 5a. The hardening and evolution of all the hkl considered are relatively similar except for the 002 (Figure S5 in Text S1). The c-glide in (010) added in model E is less active than other modes but plays an important role since the hardening on 130 is reproduced, while it was not in model C.

[43] Model E-2 is a variation of model E, with the [100]{0kl} “pencil glide” slip systems activated (initial CRSS of 0.3 GPa, equal to that of [100](010)). The added pencil glide represents a third of the total activity, but does not modify significantly the lattice strains compared to E since geometrically it is a combination of [100](001) and [100](010).

[44] Model F used a low initial CRSS of 200 MPa for the easy slip system [100](001) and higher initial CRSS of 1.0 and 1.1 GPa for [100](010) and [001](010), respectively. This model best resembles the higher pressure experimental data (>4GPa, group 1) with the hkl yielding in a consistent order. However, the modeled hardening on 130 and 112 shows notable discrepancies with experimental data (Figure 5b), and 002 is in disagreement with the experimental data (Figure S5 in Text S1). F-2 is the variation of model F with addition of the [100]{0kl} family and showed no significant difference with F.

[45] Models H and H-2, investigating the use of a lower initial CRSS of [001](010) than that of [100](010), do not reproduce well the experimental lattice strains. A lowerτS for [001](010) than for [100](010) is therefore less consistent with experimental data.

[46] All the subsets of known slips systems investigated in the above models gave calculated amplitudes higher than those measured in the experiments (up to one order of magnitude). Setting very small values for threshold stresses (τ0S) and hardening (θ1S) did not improve this discrepancy. We tried without success using two additional parameters (equation (3)) in order to allow a saturation of CRSS. Importantly, the lattice strain of 002 modeled with known slip systems does not show the significant relaxation observed in experimental data; this suggests a mechanism implying at least relaxation along [001] is lacking in the model. Finally, the models E and F that reproduce experimental lattice strains both imply that [001](100) and/or [100](001) are the lowest CRSS, easiest slip systems.

[47] In model J a convenience family of slip systems 〈1 urn:x-wiley:01480227:media:jgrb16958:jgrb16958-math-00050〉 {111}was added to [100](001), [100](010) and [001](010) to investigate the effect of additional deformation modes on the amplitudes of lattice strains. For the artificial mode the initial CRSS of 1.4 GPa, and its evolution were set high enough so that its activation would influence the lattice strains only after the other slip systems are activated. The calculated lattice strain amplitudes decreased below 0.01, and strain hardening is much smaller than in other models. For high pressure data the lattice strains match quite well (Figure S5 in Text S1); this additional slip system represents about 40% of the total activity once activated, and largely influences the 130 and 002 lattice strains.

[48] The results from model J confirm that amplitude discrepancies between model and experimental data are due to the use of a model that reproduces glide only, while the deformation mechanisms of olivine are much more complex.

5. Discussion

5.1. Evolution of Slip Systems With Pressure

[49] The experimental textures measured at 3 and 5 GPa show significant differences. In both, we observed a pronounced minimum at 001 and 100 (Figure 4). At 3 GPa, the IPF maximum extends between 101 and 130. At 5 GPa, the IPF maximum concentrates in the region between 101 and 111. A simplistic interpretation based on the known slip systems of olivine (e.g., summarized by Durham and Goetze [1977]) (Table 1) would suggest that, with increasing pressure, slip on (010) becomes less important. Full interpretation of the experimental textures would require a full VPSC model, which is famously difficult because of a lack of available slip systems for grain rotation in olivine. We did try some VPSC modeling using combinations of slip systems available in the literature [e.g., Castelnau et al., 2010; Tommasi et al., 2000; Wenk et al., 2004], but the simulated compression textures are different from those observed experimentally. Models E and F from Table 2 provide better results, but cannot reproduce the minimum experimentally observed at 001. At this point, we only suggest that the change in observed compression textures between 3 and 5 GPa indicates a change in plastic deformation mechanism. We attribute part of the relative weakness of the textures to the low total strain (below −20%), similar to lower pressure experiments in axial deformation by Ave'Lallemant and Carter [1970], Nicolas et al. [1973] and Zhang et al. [2000], and part to dislocation climb and other diffusion-controlled mechanisms because of the high-temperature (1600 K) in this experiment.

[50] The attempts to model lattice strain using EPSC suggest that the difference between high- and low-pressure data may be related to the increasing CRSS for a-slip on (010) with pressure. The discrepancies in lattice strain magnitude between the EPSC modeling and experimental data, together with the dramatic effect when an artificial deformation mode was added, confirms the strong influence of plastic relaxation processes other than glide in the observed lattice strains. Thus, changes observed in experimental textures and EPSC modeling of the observed lattice strains give consistent indications for a change in plastic behavior between 3 and 5 GPa. The P-T conditions for this modification as inferred from our results are depicted inFigure 6.

Details are in the caption following the image
P-T fields and deformation regimes. The change in properties of the a-slip on (010) system in olivine with pressure is drawn as follows based on our data: below 3–4 GPa a-slip [100](001) is much easier than c-slip [001](100) (group 2, yellow field), above these pressures a-slip is active and almost as hard as c-slip (group 1, blue field). This evolution of a-slip mobility is sketched on the right side of the P-T graph. A-slip hardens with increasing pressure in an unknown fashion, and is therefore depicted with a dotted line. The boundary at 11 GPa for inhibition of a-slip is based on the work byCouvy et al. [2004] (see section 5.1). In samples with the higher water content estimates, the growth and recovery processes occurred readily above 1570 K, and group 3 (data indicated by arrows, within purple field) is observed instead of group 2. These processes are expected to occur at lower pressures also, hence the extension of group 3 field. Temperature uncertainty is estimated below 10%; 5% are shown. This uncertainty has no incidence on the interpretation since we do not see a temperature dependence of the change in slip systems, in our experimental conditions. The pressure uncertainty is ∼0.5 GPa.

[51] Several experimental studies gave consistent results indicating changes in olivine slip system with increasing pressure. A transition from dominant a-slip on (010) to c-slip on (010) was inferred at about 6 to 9 GPa and 1673 K from experiments on single crystals byRaterron et al. [2009]. A similar transition was also observed in simple shear deformation experiments, from olivine crystallographic preferred orientation (CPO) in dry peridotites it is inferred to occur between 2.5 and 3.1 GPa [Jung et al., 2009] and from CPO in dry olivine polycrystals between 5.5 and 7.6 GPa, below ∼1600 K, by Ohuchi et al. [2011]. Low temperature data by Mei et al. [2010] show the same relative t(hkl) as in our group 2 data. Nishihara et al. [2010] reported that the highest t(hkl) was first on the (021) plane at 3.21 to 4.9 GPa, and then on (130) above 6.4 GPa. This last observation corresponds to the same change in relative magnitudes of Q(hkl) in our results (Figure 2 and Figure S4 in Text S1). Finally Couvy et al. [2004]observed complete inhibition of a-glide at about 11 GPa. Our data are consistent with an increased contribution of c-slip on (010), or decreased contribution of a-slip, but do not indicate an inhibition of a-slip up to at least 7.8 GPa. The hardening of [100](010) with increasing pressure relative to slip on [001](010) was previously proposed from first-principles calculations byDurinck et al. [2005]. The decreased activity for the a-slip begins at 3–4 GPa in our experiments.Ohuchi et al. [2011] results are fairly consistent since they reported a decrease in fabric strength with increasing pressure between 2.1 and 3.0–5.2 GPa. However, we have no evidence of a complete transition at 7.6 GPa as Ohuchi et al. [2011] suggest. This might be explained by their experimental geometries promoting single slip systems while our geometry promotes multislip, or simply by uncertainties in pressure estimates. Combining our observations with previous studies, we conclude that pressure induces a progressive change in deformation mechanisms in polycrystalline olivine which may start from as low as 90–120 km depth in the mantle.

5.2. Olivine Flow at High Pressure and Below ∼1600 K

[52] Figure 7 compares our stress results with data from previous in situ studies on polycrystalline olivine at pressure above 2 GPa. Stresses were normalized to 10−5 s−1 using the following equation:
where urn:x-wiley:01480227:media:jgrb16958:jgrb16958-math-0007 is strain rate in s−1, σ the stress in MPa, P the pressure in Pa, T the temperature in K, R the gas constant in J K−1 mol−1 (8.31447), Ais a pre-exponential constant in MPa−n s−1, Ea the activation energy in J mol−1 and V* the activation volume in m3 mol−1, and a value of 3.5 for the stress exponent n. Data by Mei et al. [2010] and Kawazoe et al. [2009] relative to low temperature plasticity were normalized according to the equations cited by the authors.
Details are in the caption following the image
Comparison with previous studies. Average stresses are normalized to 10−5 s−1 using the power law equation (5) with n = 3.5 for data from this study, data from L06 [Li et al., 2006] and data relevant to power law in K09 [Kawazoe et al., 2009]. Data for LTP (low temperature plasticity) from K09 and M10 [Mei et al., 2010] is normalized using the exponential type law from these studies. Stresses were averaged in this study from the planes (021), (130), (131), (112); L06: (021), (130), (131), (112); D09 [Durham et al., 2009]: (131), (112); K09: (130) and (112), (131) when available; N08 [Nishihara et al., 2008]: (130). M10: (130), (131), (112). The total strains at which these stresses are taken varies from one study to the others and participate to the discrepancies (see section 5.1.2). Temperature uncertainty is below 10%; 5% are shown. The span in stress calculated from different planes can range from 10 MPa to more than 1000 MPa. The pressure uncertainty is ∼0.5 GPa. (a) Flow stress normalized to 10−5 s−1 against temperature. Labeled lines refer to the power laws or exponential laws calculated for pressures of 4 and 8 GPa. They illustrate the wide discrepancies in the parameters of these laws, due to the large uncertainties in flow stresses. The transition between LTP described by exponential laws and dislocation creep described by power laws is also badly defined. K09 Dry is plotted for V* = 20 cm3 mol−1. (b) Flow stress normalized to 10−5 s−1 against confining pressure: points at the same temperature should align with a positive slope for a positive activation volume (slope shown here for V* = 6 cm3 mol−1, dark line 1473 K and dashed line 1673 K). The temperature (K) is given left of each data point from our study. A trend (arrow) where stress has no pressure or negative pressure dependence appears from our data (at ∼1600 K corresponding to deformation cycles where growth occurred) and previous studies data. This might explain part of the discrepancies in V* from previous studies.

[53] We emphasize that a large part of the discrepancies in stresses at the same P and T can be attributed to differences in data analysis. Stresses from our study are calculated from four diffraction planes identical to Li et al. [2006], but different from Durham et al. [2009] and Kawazoe et al. [2009]. The flow stresses in this study are taken arbitrarily at −10% strain and constant strain rate, with the reference length taken at the beginning of each deformation cycle when the differential stress crosses zero. If this definition of the strain was used with data from Li et al. [2006] and Durham et al. [2009], some of their flow stresses would correspond to much lower strains (a few percent) than ours.

[54] We interpret the difference observed between lattice strains at low and high pressures as a change in slip system activities with increasing pressure. Because of the modifications in slip systems, data from groups 1 and 2 should be considered separately. Since the data in group 2 are too few to draw any conclusions on the influence of P and T, we focus here on the subset at P > 4 GPa.

[55] Most rheological studies aim at fitting data sets using a flow law such as (5). The direct implication of a gradual modification of slip systems with pressure in group 2 is that any V* fitted with equation (5) becomes a mere mathematical parameter; its physical significance becomes extremely difficult to assess. Therefore, our purpose in the following is not to determine a flow law for a specific mechanism or flow regime but rather to show the dramatic influence of assumptions made when fitting such data sets.

[56] For the sake of comparison with previous studies only, we fitted the present data set above 4 GPa to flow laws of power law (equation (5)) and exponential type [e.g., Mei et al., 2010; Nishihara et al., 2010; Kawazoe et al., 2009]. Since we are unable to quantify grain size evolution, we assumed no grain size dependence; at confining pressures below 2 GPa dry olivine may deform in a power law grain-size sensitive regime [Hirth and Kohlstedt, 2003] but this has not been shown for wet olivine. No water content COH was included since i) we do not really control this quantity during this type of experiments and ii) we only have measurements on polycrystalline samples and did not quantify the hydrogen content properly (i.e., on single crystals). The data point at 1173 K could not be reconciled with our other data points at 1373 K when fitting with any power (equation (5)) or exponential-type deformation law. At 1173 K deformation likely occurred with the most important contribution from the so-called “low-temperature” plasticity, controlled by lattice friction, usually described by a law with an exponential dependence on stress [e.g.,Mei et al., 2010; Nishihara et al., 2010; Faul et al., 2011]. Lattice friction may well participate in the control of deformation in our data points at and above 1373 K, and/or to the ones at highest pressures. However, its contribution decreases with temperature (or stress) in proportions that cannot be quantified here. The transition temperatures calculated from the intersection of exponential and power law type flow laws vary from 1300 K [Mei et al., 2010], 1400 K [Katayama and Karato, 2008] to 1600–1700 K [Kawazoe et al., 2009] for strain rates of 10−5 s−1. Our data from 1173 to 1373 K do not help narrow this range. Finally, no exponential law could fit any subsets or all of our data above 1300 K.

[57] The remaining five points in group 1 fitted using equation (5) with n = 3.5 which assumes a dislocation creep regime, give ln(A) = −23.3(2.5) (A in MPa-3.5.s−1), Ea = 133(34) kJ mol−1, and V* = 6.7(1.8) cm3 mol−1, with a R2 of 0.95. The activation energy we obtained is much lower than the 470 to 530 kJ mol−1 measured at low confining pressure (300 MPa) [e.g., Hirth and Kohlstedt, 2003; Karato et al., 1986; Mei and Kohlstedt, 2000a, 2000b]. It is also highly dependent on the choice to use a flow law including a dependence on water COH: using our water contents into such an equation [Hirth and Kohlstedt, 2003] with an exponent r = 1 increases Ea above 200 kJ mol−1.

[58] The apparent activation volume is better defined, because it is constrained by three points at different pressures and the same temperature. As stated before this V* cannot be related directly to specific slip system properties if the activity of different slip systems varies progressively with pressure. It is similar within uncertainties to the 3 ± 4 cm3 mol−1from single-crystal deformation promoting c-slip at HP-HT byRaterron et al. [2009]. Bejina et al. [1999] using the model by Jaoul [1990] obtained V* of ∼6 cm3 mol−1 for creep of dry olivine assisted by dislocation climb, from Si diffusion measurements between 4 and 9 GPa. On dry samples, Durham et al. [2009] found V*∼9.5 ± 7.0 cm3 mol−1 for a confining pressure range of 2 to 5 GPa and Kawazoe et al. [2009] 15 to 25 cm3 mol−1 for pressures above 4.9 GPa. Li et al. [2006] obtained 0 ± 5 cm3 mol−1on wet samples at pressures of 3.5 to ∼9 GPa. Given the P-T conditions ofLi et al. [2006], and the lattice strains patterns in Durham et al. [2009], these two studies seem to have sampled several deformation regimes, thus resulting in even more debatable apparent V* (Figures 7a and 7b). The experiments by Kawazoe et al. [2009] were dry and had a strong uniaxial stress component which may have promoted a more important lattice friction during deformation. More importantly, in their fits, Li et al. [2006], Durham et al. [2009] and Kawazoe et al. [2009] assumed high activation energies of 470, 500 and 530 kJ mol−1, respectively, all based on the low pressure data (300 MPa). These assumptions may have biased somewhat their activation volumes toward lower values: forcing the activation energy to be 470 kJ mol−1 when fitting our data decreases the activation volume to 0.0 (1.8) cm3 mol−1 with R2 degraded to 0.27.

[59] From the present picture, the flow mechanisms of olivine above ∼3 GPa cannot be described by a single law, even for subsets of data restricted to temperatures above ∼1300 K. More precisely, the activation volume as described by equation (5) and determined in previous rheological studies on polycrystalline olivine is a purely apparent parameter.

5.3. Olivine Flow Mechanisms Above 1600 K (Wet Samples)

[60] The decrease in flow stress between group 3 and group 1 is too large to be reconciled by a temperature-dependent rheology, nor can it be reconciled by a grain-size dependent [e.g.,Hirth and Kohlstedt, 2003] rheology. We interpret this dramatic decrease in flow stresses as the enhancement of diffusion controlled processes above ∼1600 K. At the intragranular length scale, a balance established between strain hardening due to dislocation interactions under stress and the recovery processes helped by climb would account for the absence of strain hardening (Figures S4g–S4i and S4l in Text S1). At the inter-granular scale, increasing temperature is likely to enhance or activate migration and/or sliding of grain boundaries, which would relax strain incompatibilities and decrease the flow stress. The observation of growth, tied to the grain boundary mobility, corroborates this interpretation. The relative amplitudes of the lattice strains for the different hkl depend strongly on plastic relaxation [e.g.,Merkel et al., 2009]. Therefore the closer amplitudes we observed in the group 3 deformation cycles (Figures S4g–S4i and S4l in Text S1) may indicate a plastic relaxation more isotropic in nature than dislocation glide, which would also be consistent with grain boundary migration and growth. This could be helped by increased bulk diffusion processes too; however bulk diffusion would become more and more difficult as grain growth proceeds. Progressive transitions in run D1062 (Figure 3d) may indicate the proximity to a threshold temperature, above which climb and boundary migrations rates are enhanced sufficiently to overcome the defect creation rate. Grain size reduction down to the diffusion creep field [e.g., Zhang et al., 2000] is not a requirement to lower the flow strength of olivine at experimental timescales: enhanced recovery (i.e., climb), and enhanced grain boundary migration at high temperature provide an intrinsic weakening mechanism.

[61] The relationship between equilibrium grain size and stress is a paleo-wattmeter and reduces to an inverse dependence of stress over average grain size (known as a paleo-piezometer) [Austin and Evans, 2007; Ricard and Bercovici, 2009; Twiss, 1977]. This has been evaluated experimentally on dynamically recrystallized olivine grains [e.g., Jung and Karato, 2001; Van der Wal et al., 1993]. The switching back and forth between large crystallite size, low stresses and small crystallite size, high stresses (run D1062, Figure 3(bottom left)), is the first in situ observation at high pressure of this paleo-wattmeter that can exist in a system at equilibrium, where average grain size may be considered as a pseudo-state function. Assuming the empirical relationship of an average recrystallized grain sized proportional to σ −1.18 [Van der Wal et al., 1993] holds under our experimental conditions and is independent of temperature, a stress increase by a factor of 5 to 7 (to ∼1000–1500 MPa) between group 3 and group 1 deformation cycles suggests a factor of 5 to 7 decrease in crystallite size with decreasing temperature across ∼1600 K.

[62] Some cycles (run D0966) were conducted at temperatures between 1576 and 1671 K but did not show diffraction data that belong to group 3. The large crystallites present initially were replaced by strained crystallites, and at first by more heterogeneous sizes than in other runs at similar P-T conditions (Figure 3, bottom right), meaning recovery and growth processes were much slower. This may be related to a lower water content in this run (cf. 2.3): in wet samples grain boundary mobility estimates are an order of magnitude higher than in water-free samples at confining pressure of 1 GPa [Karato, 1989], and wet olivine polycrystals deformed at 2 GPa are more extensively recrystallized than dry ones [Jung and Karato, 2001]. If this assumption is correct, water plays an important role in growth and/or recovery at pressures up to about 7 GPa at least. However, we cannot rule out uncertainties in temperature as an explanation for these discrepancies. Sample history and grain size distribution could play a role but in experimental studies at high pressure we are not able to resolve these yet.

6. Geophysical Implications and Conclusion

[63] From high-pressure deformation experiments of polycrystalline olivine coupled with synchrotron monochromatic radiation, we defined three domains in P-T space having different evolution of lattice strains with total bulk strain and texture development, interpreted as different deformation regimes.

[64] Most importantly, above a confining pressure of ∼4 GPa, the gradual hardening of a-slip on (010) over at least a 3–4 GPa pressure interval, rather than a sharp “switch” from one slip system to another, makes meaningless the quest for a single activation volume value for olivine at high pressure. It adds more complexity in extrapolating low-pressure laboratory flow laws to high pressure mantle conditions, as well as in interpreting seismic anisotropy patterns in terms of upper mantle flow.

[65] Understanding olivine deformation mechanisms remains challenging even with in situ and high-quality data sets. Our results indicate that an accurate description of olivine flow mechanisms requires investigations beyond the fitting of phenomenological flow laws. A careful study of grain size, distributions of grain sizes and microstructures, during the course of high-pressure rheology experiments is now necessary in order to tighten constraints on HP-HT olivine flow laws, understand the partitioning between intracrystalline and inter-crystalline processes, and extrapolate the dominant mechanisms over specific regions of the mantle. The present data demonstrate the potential of x-ray diffraction as an in situ tool to discriminate between these factors in further studies. The difficulties we encountered in EPSC modeling for interpretation of these data may be helped by further implementation of high temperature processes in crystal plasticity models. Although they are not transferable to mantle rheology yet, our in situ observations emphasize the dramatic influence of high-temperature induced recovery and growth on flow stresses in polycrystalline olivine.


[66] We gratefully acknowledge Carlos Tomé for providing the EPSC code and comments. We also acknowledge help from Yu Nishihara for FTIR at the Geodynamics Research Center (GRC), Ehime University, financial support from GRC as a visitor, the Electron Microscopy Center staff at Argonne National Laboratory, and financial support provided by the NSF (EAR-0652574 and EAR-0968456). We thank William Durham, an anonymous reviewer and the associate editor for their constructive comments which improved the manuscript. GeoSoilEnviroCARS is supported by the National Science Foundation, Earth Sciences (EAR-0622171) and Department of Energy, Geosciences (DE-FG02-94ER14466). Use of the Advanced Photon Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract DE-AC02-06CH11357. The electron microscopy was accomplished at the Electron Microscopy Center for Materials Research at Argonne National Laboratory, a U.S. Department of Energy Office of Science Laboratory operated under contract DE-AC02-06CH11357 by UChicago Argonne, LLC.