Creep strength of ringwoodite measured at pressure–temperature conditions of the lower part of the mantle transition zone using a deformation–DIA apparatus

Earth and Planetary Science Letters 454 (2016) 10–19

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Creep strength of ringwoodite measured at pressure–temperature conditions of the lower part of the mantle transition zone using a deformation–DIA apparatus Takaaki Kawazoe a,b,∗ , Yu Nishihara b , Tomohiro Ohuchi b , Nobuyoshi Miyajima a , Genta Maruyama b,c , Yuji Higo d , Ken-ichi Funakoshi d,e , Tetsuo Irifune b,f a

Bayerisches Geoinstitut, University of Bayreuth, 30 Universitätsstraße, Bayreuth 95440, Germany Geodynamics Research Center, Ehime University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan c Earthquake Research Institute, University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan d Japan Synchrotron Research Institute, 1-1-1 Kouto, Sayo-cho, Hyogo 679-5198, Japan e Research Center for Neutron Science and Technology, 162-1 Shirakata, Tokai-mura, Ibaraki 319-1106, Japan f Earth-Life Science Institute, Tokyo Institute of Technology, 2-12-1-IE-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan b

a r t i c l e

i n f o

Article history: Received 26 February 2016 Received in revised form 25 July 2016 Accepted 8 August 2016 Available online xxxx Editor: J. Brodholt Keywords: ringwoodite mantle transition zone dislocation creep creep strength viscosity deformation–DIA apparatus

a b s t r a c t Creep strength of ringwoodite is important for understanding complicated patterns of the mantle convection in and around the mantle transition zone. To determine the creep strength of ringwoodite, we expanded pressure–temperature conditions of in situ stress–strain measurements in a deformation– DIA apparatus combined with synchrotron X-ray to those of the lower part of the mantle transition zone. The expansion of the pressure–temperature conditions was made by shrinking anvil truncation to 2.0 mm and the development of a cell assembly for in situ deformation experiments up to 1700 K. Utilizing the developed technique, creep–strength measurements on polycrystalline ringwoodite were performed at 16.9–18.0 GPa and 1300–1700 K during axial deformation with strain rates of 1.48–3.59 × 10−5 s−1 to strains of 13.2–24.9%. Based on mechanical and microstructural observations, we infer that ringwoodite deformed by exponential dislocation creep through the Peierls mechanism at 1300–1400 K and powerlaw dislocation creep at 1500–1700 K. The creep strength of ringwoodite is apparently lower than that of bridgmanite, wadsleyite and olivine. The present result implies the possibility that the lower mantle transition zone is a low-viscosity layer. Further creep–strength data of these minerals are necessary to be determined above 13.5 GPa and high temperatures to determine viscosity structure in and around the lower mantle transition zone at strain rates relevant to the mantle convection. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Viscosity of ringwoodite is important in understanding complicated patterns of mantle convection in and around the lower part (∼520–660 km depth) of the mantle transition zone (MTZ). This is because ringwoodite is volumetrically dominant at the lower MTZ (e.g. Irifune and Ringwood, 1987) and is believed to control viscosity of the region. Viscosity contrast between the lower MTZ and the lower mantle plays a key role in controlling stagnation process of subducting slabs according to simulation studies on the mantle convection (e.g. Torii and Yoshioka, 2007). Moreover, the phase transformation from metastable olivine to ringwoodite may

*

Corresponding author at: Bayerisches Geoinstitut, University of Bayreuth, 30 Universitätsstraße, Bayreuth 95440, Germany. E-mail address: [email protected] (T. Kawazoe). http://dx.doi.org/10.1016/j.epsl.2016.08.011 0012-821X/© 2016 Elsevier B.V. All rights reserved.

weaken the subducting slabs because of change in their viscosities (Karato et al., 2001). Furthermore, viscosity contrast between ringwoodite-rich peridotite and former oceanic crust may cause chemical heterogeneity by separation of the former oceanic crust at the 660-km boundary (Karato, 1997). Consequently, the viscosity of ringwoodite is critical for understanding the mantle dynamics in and around the MTZ. The viscosity of the lower MTZ has been controversial among geophysical models. Some models suggested presence of a lowviscosity layer at the MTZ (e.g. Mitrovica and Forte, 2004; Soldati et al., 2009) while such low-viscosity layer was not reported in other models (e.g. Peltier, 1998). Another way to determine the viscosity of the lower MTZ is to derive flow laws of ringwoodite by measuring its creep strength, i.e. stress magnitude at steady-state deformation. The 520-km seismic discontinuity is attributed to the phase transformation from wadsleyite to ringwood-

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ite. Pressure–temperature ( P –T ) conditions there were estimated to be ∼17.5 GPa (Dziewonski and Anderson, 1981) and ∼1760 K (Akaogi et al., 1989) in the normal mantle. Therefore, the creep strength of ringwoodite is necessary to be measured at such high P –T conditions to determine the viscosity of the lower MTZ. The creep strength of ringwoodite was measured by in situ stress–strain measurements at 21–23 GPa and 1800 K by using a rotational Drickamer apparatus (RDA) with synchrotron X-ray (Hustoft et al., 2013; Miyagi et al., 2014). The creep strength of ringwoodite was 1.6–3.2 GPa at strain rates of 5.8–18 × 10−5 s−1 . However, uncertainty in temperature was reported as ±200 K in their studies. Such large uncertainty in temperature leads difficulty in deriving the flow laws of ringwoodite by considering temperature dependence of Si self-diffusion coefficients in ringwoodite (Shimojuku et al., 2009). Moreover, there were variations in stress and strain rate across the sample in the RDA experiment because the sample was deformed in the torsional geometry. The creep strength of ringwoodite was also measured to 10 GPa at room temperature by the in situ stress–strain measurements using a deformation–DIA (D–DIA) apparatus with synchrotron X-ray (Nishiyama et al., 2005). However, P –T conditions of the study were far below those of the lower MTZ. The in situ stress–strain measurements in the D–DIA apparatus were succeeded at 17 GPa at 600 K (Nishiyama et al., 2007) although temperature condition was limited because of technical difficulty in heating. Ringwoodite was deformed at P –T conditions up to 20 GPa and 1700 K using the D–DIA apparatus (e.g. Kawazoe et al., 2010c) although stress magnitude was not measured because they used anvils with no Xray transparency. Recently, we expanded the P –T conditions of the in situ stress–strain measurements in the D–DIA apparatus to 14.5 GPa and 1700 K by improving a multianvil 6–6 (MA6–6) assembly (Kawazoe et al., 2011). Nevertheless, the pressure condition of the study was below that of the lower MTZ. Therefore, the P –T conditions of the in situ stress–strain measurements in the D–DIA apparatus has been necessary to be expanded to ∼17.5 GPa and ∼1700 K to determine the creep strength of ringwoodite in the lower MTZ. In the present study, we expanded the P –T conditions of the in situ stress–strain measurements in the D–DIA apparatus up to 18 GPa and 1700 K. First, pressure generation tests were performed to reach ∼18 GPa at a relatively small press load (0.50 MN) because breakage of the X-ray transparent anvils at higher press loads limited the accessible P –T conditions. Second, we developed a cell assembly suitable for both temperature generation to 1700 K at 17–18 GPa and the in situ stress–strain measurements with synchrotron X-rays. Third, the in situ stress–strain measurements on polycrystalline (Mg0.9 , Fe0.1 )2 SiO4 ringwoodite were demonstrated at 17–18 GPa and 1300–1700 K during axial deformation at a synchrotron facility. Moreover, we characterized deformation microstructure and water content of recovered samples. In this paper, we report the creep strength of ringwoodite under the P –T conditions of the lower MTZ and discuss deformation mechanisms of ringwoodite and change in the creep strength by the phase transformations relevant to ringwoodite. 2. Materials and methods 2.1. Pressure generation experiment Pressure generation experiments were conducted to optimize dimensions of a truncated edge length (TEL) of second-stage anvils, a cubic pressure medium and preformed gaskets to reach ∼18 GPa at 0.50 MN. The pressure generation experiments were performed using a cubic anvil apparatus MADONNA-II, which is identical to the apparatus used for the in situ stress–strain measurements at the synchrotron facility. The multianvil 6–6 (MA6–6) assembly

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(Kawazoe et al., 2010b; Nishiyama et al., 2008) was adopted with first-stage anvils made of tungsten carbide with a TEL of 27.0 mm. For this purpose, we used six second-stage anvils made of tungsten carbide with ultra-fine grains (Fujilloy TF05, Fuji Die Co. Ltd.) with a TEL of 2.0 mm. The pressure mediums were made of semi-sintered (Mg, Co)O (Mino Ceramic Co. Ltd.). Edge lengths of the pressure mediums were 2.8–4.0 mm (Table S1). The gaskets were made of pyrophyllite and were fired at 973 K for 30 min for its plastic hardening. Thickness of the gaskets was chosen to fill initial gaps between the second-stage anvils (Table S1). Width of the gaskets was 0.5 mm. In the runs with no gaskets, Teflon spacers were used for initial positioning of the second-stage anvils and to prevent material of the pressure medium from falling during compression. The sample pressure was evaluated at room temperature by measuring changes in electrical resistance in ZnTe (9.6 and 12.0 GPa; Kusaba et al., 1993) and GaAs (19.3 GPa; Yagi and Akimoto, 1976). A sample powder was packed into the central part of a hole in the pressure medium. The powder was sandwiched with a pair of copper wire electrodes, whose outer ends contacted with top faces of the top and bottom second-stage anvils. 2.2. Deformation experiment The deformation experiments were conducted using the multianvil apparatus SPEED-Mk.II (Katsura et al., 2004) combined with a D–DIA guide block system (Wang et al., 2003) at the BL04B1 beamline of the synchrotron facility SPring-8, Japan. We adopted the MA6–6 assembly modified for the in situ stress–strain measurements (Kawazoe et al., 2011). Two second-stage anvils made of cubic BN (BNS800, Sumitomo Electric Inc.) were used on the downstream side because of their low X-ray absorption. The other second-stage anvils were made of tungsten carbide with ultra-fine grains (Fujilloy TF05). Diffracted monochromatic X-rays were detected at 2θ angle of up to ∼10◦ through a conical X-ray path on the first-stage anvils and sliding blocks on the downstream side. Deformation rate was controlled with feedback system controlling displacements of the top and bottom anvils. Starting material for the deformation experiments was an olivine aggregate. The aggregate was sintered from a mixture of a San Carlos olivine ((Mg0.9 , Fe0.1 )2 SiO4 ) powder and 8 wt% pyroxene powder (Kilosa, Tanzania) in a Ni capsule at 4 GPa and 1373 K for 1.5 h using a Kawai-type multianvil apparatus. The pyroxene powder was added to control activities of oxide components in the samples. The olivine aggregate contained water (or hydrogen) of 440 wt ppm H2 O (7100 H/106 Si). The cell assembly used for the deformation experiment was composed of the semi-sintered (Mg, Co)O pressure medium, dense Al2 O3 pistons, an MgO electrical insulator, a LaCrO3 furnace, Mo and Cu electrodes and crushable Al2 O3 backup rods (Fig. S1). The pressure medium with an edge length of 3.2 mm was used with the fired pyrophyllite gaskets with a thickness of 0.85 mm. The starting olivine aggregate was packed in a Mo foil capsule whose wall thickness was 5–10 μm. The capsule prevented reaction between the sample and the surrounding materials and kept oxygen fugacity in the sample under the Mo–MoO2 buffer. The capsule foils between the sample and the pistons were 10-μm thick and served as strain markers for the strain measurement. The sample temperature was measured with a W97 Re3 –W75 Re25 thermocouple. Materials of the furnace and the gaskets along the X-ray path were replaced with graphite and boron-epoxy, respectively, for the in situ stress–strain measurements. The samples were compressed to a press load of 0.50 MN for 150 min at room temperature. Temperature was then increased to 1500 K (runs M1267, M1299, M1303 and M1305) or 1700 K (run M1219) at 0.50 MN and kept for 26–42 min for synthesis of

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polycrystalline ringwoodite and subsequent annealing. For runs at 1300 and 1400 K, temperature was gradually decreased to the target before deformation. The polycrystalline ringwoodite was then deformed in the axial geometry at 1300–1700 K by advancing the top and bottom anvils at rates of 0.5 or 1.0 μm/min. The press load was kept constant during deformation. 2.3. In situ stress–strain measurements The in situ stress–strain measurements were conducted by two-dimensional X-ray diffraction and X-ray radiography at the BL04B1 beamline of SPring-8 (Funakoshi et al., 2010). White Xrays from a bending magnet were monochromatized to energies of 51.02–52.25 keV (wavelengths of 0.2373–0.2430 Å) using a Si (111) double-crystal monochromater. The monochromatic X-rays were collimated to 100 μm × 100 μm or 150 μm × 150 μm with incident slits. Diffracted X-rays were detected with an imaging plate (IP) for 7 or 10 min. The distance between the sample and the IP was determined as 435.70–446.24 mm from X-ray diffraction patterns of a CeO2 powder. The IP data were digitalized with a resolution of 100 μm using a Fuji BAS2000 reader. The computer software “IPAnalyzer” and “PDIndexer” (Seto et al., 2010) were used for integration of the digitalized data to form 72 one-dimensional profiles with an azimuthal angle step of 5.0◦ along the Debye ring pattern and subsequent peak fitting, respectively. X-ray radiographs of the strain markers were taken using an imaging system composed of a YAG crystal and a CCD camera with exposure times of 10–60 s. The magnitude of axial deviatoric stress was determined from the two-dimensional X-ray diffraction data based on a model of relationship between axial stress and lattice strain (Singh et al., 1998),

 dhkl = d0hkl 1 +

σhkl  6M hkl

1 − 3 cos2 ψ

 

(1)

where dhkl is the d-spacing measured as a function of azimuth angle ψ , d0hkl is the d-spacing corresponding to the hydrostatic pressure, M hkl is the effective shear modulus and σhkl is the axial stress for a given hkl. The analyses were made for three diffraction peaks of ringwoodite (220, 311 and 400). The M hkl values were calculated using elastic constants of (Mg0.91 , Fe0.09 )2 SiO4 ringwoodite (Sinogeikin et al., 2003). The stress magnitude and d0hkl were determined by fitting the observed dhkl to Eq. (1) by the least-squares method. Deviation of dhkl from a regression curve was propagated to uncertainty in stress. The sample pressure was determined using unit-cell volume calculated from the d0hkl and an equation of state of (Mg0.91 , Fe0.09 )2 SiO4 ringwoodite calibrated with Shim’s Au pressure scale (Nishihara et al., 2004). Uncertainty in pressure originated from that of the unit-cell volume of ringwoodite and variation in the pressure values during steady-state deformation in which the stress magnitude remained approximately constant with time. Axial strain of the sample was measured with the in situ X-ray radiographs of the two strain markers placed at both ends of the cylindrical sample. True strain and its strain rate were calculated using the following equations: ε = − ln(h/h0 ) and ε˙ = ε /t, where ε is the true strain, ε˙ is the strain rate, t is the time at ε , and h and h0 are the thicknesses of the sample during and before deformation, respectively. Strain rate was deduced using the data during the steady-state deformation. 2.4. Analyses of recovered samples The deformation microstructure of the samples was observed by scanning electron microscopy (SEM) and transmission electron

microscopy (TEM) using a field-emission scanning electron microscope (LEO, Gemini 1530) and a transmission electron microscope (FEI, Titan G2 80–200 S/TEM), respectively. For the SEM observation, the samples were sectioned in the plane including the axial deformation axis and were mounted in epoxy resin. Exposed surfaces of the samples were polished with a 0.25-μm diamond powder and were then etched with 35 wt% HNO3 for 6 min. For the TEM observation, sample foils were cut from the samples prepared for the SEM observation using a dual beam focused ion milling machine with Ga ion and electron beams (FEI, Scios). A zero-loss energy filter technique was used for the sample M1305 in weakbeam dark-field (WBDF) imaging. The water content of the samples was determined by Fouriertransform infrared (FT-IR) spectroscopy. Unpolarized IR absorption spectra of the samples were taken with spot diameters of 30–50 μm using an FT-IR spectrometer (Bruker, IFS-120 HR). The samples were polished on both sides and kept in a vacuum oven at 398 K for more than 12 h before measurements. The water contents of the samples were calculated using a calibration by Paterson (1982) using a density factor appropriate for (Mg0.9 , Fe0.1 )2 SiO4 ringwoodite. 3. Results 3.1. Pressure generation experiment Efficiency in the pressure generation with the 2.0-mm truncation anvils varied significantly by changing the dimensions of the pressure mediums and the gaskets (Table S1 and Fig. S2). Adoption of the gaskets improved the efficiency in the pressure generation. The highest efficiency in the pressure generation to 12 GPa was achieved using 3.2-mm and 3.0-mm pressure mediums with the gaskets. A pressure of 19.3 GPa was generated at 0.50 MN using the 3.2-mm pressure medium with the gaskets. With the 2.0-mm truncation a pressure of 19.3 GPa was reached at 0.50 MN, which was 0.30 MN lower than when the anvils with a 2.5-mm truncation were used (Kawazoe et al., 2011). Moreover, the pressure-generation efficiency with the anvils made of TF05 is higher than those with the other tungsten carbide materials according to our previous study (Kawazoe, 2014). This high efficiency in the pressure generation enabled to reach the stability field of ringwoodite with no breakage of the X-ray transparent anvils and, in turn, to perform the in situ stress–strain measurements in the D–DIA apparatus up to 18 GPa and 1700 K. 3.2. Conditions of deformation experiments The in situ stress–strain measurements on ringwoodite were performed during axial deformation at 16.9–18.0 GPa and 1300–1700 K and strain rates of 1.48–3.59 × 10−5 s−1 to strains of 13.2–16.9% (Table 1 and Fig. 1). The in situ X-ray diffraction patterns indicated that the starting olivine transformed to polycrystalline ringwoodite before reaching 1500 K. In the run at 1700 K, X-ray diffraction peaks of wadsleyite were observed after a strain of 14.8% indicating partial back-transformation to wadsleyite. The diffraction peaks of wadsleyite were not observed in the runs at 1300–1500 K. Wadsleyite was observed with ringwoodite in the sample deformed at 1700 K (Fig. 2). An amount of wadsleyite was ∼80–90% at both hotter and colder regions in the vicinities of the furnace and the pistons, respectively. Wadsleyite coexists with ringwoodite at 1520–1675 K at 17.3 GPa in (Mg0.9 , Fe0.1 )2 SiO4 (Frost, 2008). This spatial and volumetric distribution of wadsleyite indicated that difference in temperature across the sample was less than 30 K.

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Table 1 Conditions and results of the deformation experiments.a Run No.

M1219

M1267

M1299

M1303

M1305

Pressureb (GPa) Temperature (K) Strain rateb (10−5 s−1 ) Maximum strain (%) Deformation duration (min) Stressb (MPa) Average 220 311 400 Observed phase

17.3 (0.5) 1700 (3) 3.59 (0.05) 24.9 (0.1) 108

17.9 (0.6) 1500 (3) 3.46 (0.14) 15.5 (0.3) 93

16.9 (0.5) 1500 (1) 1.48 (0.02) 13.2 (0.1) 187

17.8 (0.6) 1400 (6) 2.29 (0.03) 16.9 (0.1) 182

18.0 (0.4) 1300 (1) 1.68 (0.02) 14.5 (0.1) 181

130 (40) 220 (40) 130 (30) 50 (40) Ringwoodite Wadsleyite

400 (20) 500 (30) 440 (20) 260 (20) Ringwoodite

280 (20) 390 (30) 310 (20) 140 (20) Ringwoodite

530 (30) 690 (40) 570 (30) 340 (20) Ringwoodite

560 (20) 680 (30) 620 (20) 370 (20) Ringwoodite

1100 (200) 19000 (4000) 0.6–8

–c – 0.8–11

370 (50) 6100 (800) 0.8–14

290 (30) 4700 (500) 0.8–9

610 (140) 10000 (2000) 0.8–11

Water content (wt ppm H2 O) (H/106 Si) Grain size (μm) a b c

Numbers in parentheses are one standard deviation on the last digit. During steady-state deformation. The water content was not measured because of sample loss.

Fig. 1. The in situ X-ray diffraction patterns and radiograph. (a) The IP image taken at 17.6 GPa, 1700 K and a strain of 5.8%. Abbreviation: Rin, ringwoodite. (b) The integrated diffraction pattern of (a) at the azimuth angle of 90◦ . The diffraction peaks of ringwoodite are observed with those of MgO (insulator and pressure medium), diamond (X-ray window) and Mo (capsule). (c) Variation in the d-spacing of ringwoodite (311) with the azimuth angle at 18.4 GPa, 1500 K and a strain of 5.8% (M1267). (d) The radiograph taken at 17.6 GPa, 1500 K at a strain of 16.9% (M1303). The strain markers are visible through the diamond X-ray window in the LaCrO3 furnace and gaps between the second-stage anvils and are indicated with arrows.

3.3. Mechanical observations In the in situ X-ray diffraction patterns, the diffraction peaks of ringwoodite (220, 311 and 400) were clearly observed together with those of Mo (capsule), MgO (insulator and pressure medium) and diamond transformed from graphite (X-ray window) (Fig. 1). The stress magnitudes were successfully derived at ∼17–18 GPa and 1300–1700 K based on the azimuthal dependence of the diffraction peaks of ringwoodite. In the X-ray radiographs, two strain markers were clearly observed between the sample and the pistons through the X-ray windows in the furnace and gaps between the anvils (Fig. 1). The final axial strain reached 13.2–24.9%,

when the top and bottom anvils advanced by 91–108 μm for 93–187 min. Strain rate was relatively low at the beginning of the deformation process, and then increased to a constant rate of 1.48–3.59 × 10−5 s−1 . The steady-state deformation of ringwoodite was achieved at strain larger than ∼4–11% (Fig. 3). Strain to reach the steady-state deformation increased from ∼4% at 1700 K to ∼11% at 1300 K with decreasing temperature and increasing the creep strength of ringwoodite. The observed d-spacings from different diffraction peaks (220, 311 and 400) gave different stress values. The difference in the stress values was up to a factor of 4.6 at the steadystate deformation. A similar phenomenon was previously reported

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Fig. 2. Microscopic images of the samples deformed to strains of 14.5–24.9% at 17–18 GPa. (a) Photograph of the sample M1267 in reflective light. (b and c) Secondary electron images of the samples M1219 deformed at 1700 K (b) and M1303 deformed at 1400 K (c). (d) Back-scattered electron image of the sample M1219. Wadsleyite (dark gray) is observed with ringwoodite (light grey) and stishovite (black). (e and f) WBDF TEM images of the samples M1219 (e) and M1305 deformed at 1300 K (f). White lines are dislocations. Direction of axial deviatoric stress is shown by a pair of arrows.

in the deformation experiments of ringwoodite, where the stress values were calculated using the diffraction peaks 220, 311, 400 and 440 at 3.3–9.7 GPa and room temperature (Nishiyama et al., 2005). The phenomenon is attributed to plastic anisotropy caused by difference in critical resolved shear stresses (CRSS) of dominant slip systems. The relative difference in the CRSS in ringwoodite becomes larger at higher temperature (Ritterbex et al., 2015). The effect of temperature on the CRSS of ringwoodite likely causes the large difference in the calculated stress values in the present study. The creep strength of ringwoodite significantly decreased from 560 to 130 MPa with increasing temperature from 1300 to 1700 K (Fig. 4). In Fig. 4 (b), the creep–strength data at different strain rates are compared after normalization to a common strain rate. Temperature dependence of the creep strength at 1300–1400 K is weaker than that at 1500–1700 K. Preliminary flow-law parameters of ringwoodite will be derived in a later section to discuss its deformation mechanisms after describing the deformation microstructure and the water contents of the samples. 3.4. Deformation microstructure and water content Grain boundaries of ringwoodite were serrated in all samples (Fig. 2). Small grains having grain size of ∼0.6–2 μm occupied regions between larger grains having grain size up to 8–14 μm.

This microtexture indicates that partial dynamic recrystallization occurred. The larger grains were elongated to directions normal to the axial deformation axis. The appropriate deformation mechanism for these samples is suggested to be dislocation creep. The in situ X-ray diffraction patterns also indicated that the ringwoodite aggregates partially recrystallized during deformation (Fig. S3). Debye rings of ringwoodite were spotty before deformation and became smoother with increasing strain. This change in shape of the Debye rings indicated increase in a number of grains having different crystallographic orientations, formation of subgrains and/or lattice distortion during deformation at nearly constant diffraction volume. Therefore, the change in the Debye rings supported the partial dynamic recrystallization in these runs. Dislocation microstructure was observed in selected samples deformed at 1300 and 1700 K, whose creep strengths were 560 and 130 MPa, respectively (Fig. 2). In the sample deformed at 1700 K, many dislocations were curved suggesting that deformation occurred by both dislocation glide and climb in the power-law creep regime. On the other hand, most of dislocations were straight in the sample deformed at 1300 K. Moreover, density of dislocations of this sample was higher than that of the sample deformed at 1700 K. The dislocation microstructure of the sample deformed at 1300 K is similar to that observed in

T. Kawazoe et al. / Earth and Planetary Science Letters 454 (2016) 10–19

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Fig. 3. Representative stress–strain curves of ringwoodite. (a) That at 17.3 GPa, 1700 K and a strain rate of 3.59 × 10−5 s−1 . (b) That at 16.9 GPa, 1500 K and a strain rate of 1.48 × 10−5 s−1 . The stress values calculated from ringwoodite 220, 311 and 400 peaks are shown with diamonds, circles and squares, respectively.

Fig. 4. The creep strength of ringwoodite plotted against absolute temperature (a) and reciprocal of temperature (b). Strain rates of the runs in s−1 are shown next to the symbols in (a). The creep–strength data are normalized to 3 × 10−5 s−1 using the stress exponent n of 2.4 (Table 2) in (b). A line is drawn using parameters listed in Table 2 ( H ∗ = 279 kJ/mol).

(Mg0.6 , Fe0.4 )2 SiO4 ringwoodite deformed at 16 GPa and 1600 K by stress relaxation test (Karato et al., 1998). Such microstructure suggests that the sample was deformed mainly by dislocation glide via the Peierls mechanism in the exponential flow law regime. The water (or hydrogen) contents of the samples ranged from 290 to 1100 wt ppm H2 O (from 4700 to 19000 H/106 Si) (Table 1 and Fig. S4). A broad absorption peak was observed at ∼3200–3700 cm−1 in the spectra of all samples. Such broad peak was also observed in wadsleyite deformed at 14.4–17.6 GPa and 1500–2100 K using an RDA (e.g. Hustoft et al., 2013; Nishihara et al., 2008) and a D–DIA apparatus (Kawazoe et al., 2013). The broad absorption peak may be attributed to distortion of crystal lattice induced by dislocations and/or concentration of water at the grain boundaries. The water contents of the samples were similar to that of the starting material (440 wt ppm H2 O) and thereby indicate that ringwoodite was deformed under relatively hydrous conditions.

switches from exponential creep to power-law creep at 1400–1500 K and strain rates of 1.48–3.46 × 10−5 s−1 . This is consistent with a boundary between these mechanisms of ringwoodite suggested by in situ stress relaxation test (Xu et al., 2003). The rheological data obtained at 1500–1700 K were fitted by the least squares method to the power-law equation:



ε˙ = A σ n exp −

H∗



RT

(2)

where A is a pre-exponential constant, n is the stress exponent, H ∗ is the activation energy (enthalpy), R is the gas constant and T is the absolute temperature. Derived flow-law parameters are listed in Table 2 with those of germanate spinels (Lawlis et al., 2001; Shi et al., 2015) and Arrhenius parameters of the Si self-diffusion in ringwoodite (Shimojuku et al., 2009). The stress exponent n of 2.4 ± 0.7 was consistent with that typical for the power-law creep (n = 3) within the error.

3.5. Flow law and deformation mechanisms 4. Discussion Three distinct deformation mechanisms are commonly identified in silicate minerals, which includes power-law dislocation creep, exponential dislocation creep (via the Peierls mechanism) and diffusion creep (Frost and Ashby, 1982). The flow law of ringwoodite in dislocation creep is expected to change from the exponential one at high stress and low temperature to the power law at low stress and high temperature. The deformation mechanism of ringwoodite may switch to diffusion creep at high temperature and at strain rate of ∼10−5 –10−4 s−1 when its grain size becomes smaller than ∼0.4–1 μm (Karato et al., 1998; Shimojuku et al., 2009). The change in temperature dependence of the creep strength (Fig. 4) indicates that the deformation mechanism of ringwoodite

4.1. Conditions of deformation experiments The P –T conditions of the in situ stress–strain measurements in the D–DIA apparatus were expanded to 18 GPa and 1700 K by the technical development in the present study. Fig. S5 summarizes accessible P –T conditions of the deformation experiments with quantitative stress–strain measurements. In the present study, the pressure condition for such deformation experiments with the D– DIA apparatus was extended from 14.5 GPa (Kawazoe et al., 2011) to 18 GPa at 1700 K. The temperature condition achieved in the present study is significantly higher than that of Nishiyama et al. (2007), in which ε -Fe was deformed at 600 K at 17 GPa.

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Table 2 Arrhenius parameters of power-law dislocation creep and diffusion for ringwoodite and germanate spinels. Composition

Property

P (GPa)

T (K)

(Mg0.9 , Fe0.1 )2 SiO4

Creepb

16.9–18.0

1500–1700

Mg2 GeO4 Ni2 GeO4 (Mg0.9 , Fe0.1 )2 SiO4

Creep Creep Diffusion

a

1.8–2.3 0.3 22

1200–1500 1373–1523 1673–1873

log A a

n

H∗ (kJ/mol)

Reference

-0.2 (3.1)

3 (fixed) 2.4 (0.7) 2.9 (1.0) 2.9 (0.1) – –

345 279 228 416 483 402

This study This study Shi et al. (2015) Lawlis et al. (2001) Shimojuku et al. (2009) Shimojuku et al. (2009)

−0.9 (2.6) −3.4 (0.2) 2.95 (0.15) −5.5 (2.8)c −13.2 (2.6)d

(90) (105) (60) (16) (94)c (88)d

Units of the pre-exponential constants are s−1 MPa−n , m2 s−1 and m3 s−1 in power-law creep, Si volume diffusion coefficient (D Si V ) and Si grain-boundary diffusion

coefficient (D Si GB ) times grain-boundary width (δ ), respectively. b c

Power-law dislocation creep. For D Si V.

d

For δ D Si GB .

The P –T conditions achieved in the present study are comparable to those of the middle part of the MTZ. Ringwoodite and majoritic garnet are expected to be dominant in pyrolite and MORB components in the lower MTZ, respectively (Irifune and Ringwood, 1987). The present study enabled the quantitative rheological study of such high-pressure minerals under the P –T conditions equivalent to the lower MTZ using the D–DIA apparatus. 4.2. Deformation mechanisms and flow law The power-law dislocation creep is suggested to be the deformation mechanism of ringwoodite at 1500–1700 K by the following results: (1) The stress exponent n of 2.4 ± 0.7 (Table 2). (2) The stronger temperature dependence of the creep strength at 1500–1700 K (Fig. 4). (3) Presence of the curved dislocations (Fig. 2). On the other hand, exponential creep via the Peierls mechanism is the appropriate mechanism at 1300–1400 K based on the following observations: (i) The weaker temperature dependence at 1400–1500 K. (ii) Presence of the dense straight dislocations. This change in the deformation mechanism is commonly observed in the literature (e.g. Frost and Ashby, 1982). Activation energy of the power-law creep of ringwoodite was 345 ± 90 and 279 ± 105 kJ/mol for the stress exponent n = 3.0 (fixed) and 2.4, respectively (Table 2). These values are between those of Mg2 GeO4 spinel (228 ± 60 kJ/mol) (Shi et al., 2015) and Ni2 GeO4 spinel (416 ± 16 kJ/mol) (Lawlis et al., 2001) and lower than those of the Si self-diffusion coefficients (483 ± 94 and 402 ± 88 kJ/mol for volume and grain-boundary diffusion, respectively) (Shimojuku et al., 2009). However, uncertainty in the activation energy of the present study is large for quantitative comparison because of limited data points. Further deformation experiments of ringwoodite with the in situ stress–strain measurements are necessary to better constrain its flow-law parameters. 4.3. Comparison of creep strength in ringwoodite The results of the present study are compared with the previous data of the creep strength of ringwoodite in Fig. 5. The creep strength of ringwoodite was determined to be ∼5–6 GPa at room temperature and a pressure of 8.1 GPa using the D–DIA apparatus (Nishiyama et al., 2005). The creep strength of ringwoodite decreased by ca. two orders of magnitude with increasing temperature to 1700 K based on the present results and the stress relaxation test (Xu et al., 2003). This is consistent with temperature dependence of critical resolved shear stress of isostructural MgAl2 O4 spinel at 298–2170 K (Mitchell, 1999). Moreover, yield strength of olivine, the polymorph of ringwoodite, also decreased by ca. two orders of magnitude with increasing temperature from 300 to 1773 K at ambient pressure (Evans and Goetze, 1979).

Fig. 5. Comparison of the creep strength of ringwoodite. Circles and a square indicate those of this study and that determined at 8.1 GPa (Nishiyama et al., 2005) using the D–DIA apparatus, respectively. Triangles represents those determined at 20 GPa by the stress relaxation test (Xu et al., 2003). Diamonds show those obtained at 23 GPa using the RDA (Hustoft et al., 2013; Miyagi et al., 2014). The data at 300–1400 and 1500–1700 K are normalized to a strain rate of 3.0 × 10−5 s−1 using the exponential law (Xu et al., 2003) and the power law with the stress exponent n of 3.0, respectively. A dotted line indicates its strength in diffusion creep estimated for a 0.6-μm grain size at 3.0 × 10−5 s−1 using its diffusion data (Shimojuku et al., 2009).

However, the results of the present study is considerably lower than those (1.6–2.9 GPa) determined at 23 GPa, 1800 K and strain rates of 5.8–8.0 × 10−5 s−1 using the RDA (Hustoft et al., 2013; Miyagi et al., 2014) (Fig. 5). One of their samples contained water of 3500 wt ppm, which is higher than those of the present study (290–1100 wt ppm H2 O). Therefore, the discrepancy between these studies was not caused by water weakening of ringwoodite. One of the causes for the discrepancy may be complexity of the deformation geometry of the RDA experiments, as discussed later. The results of the present study are also compared with creep strength estimated for diffusion creep of ringwoodite in Fig. 5. We estimate its creep strength in diffusion creep using the Si self-diffusion coefficients of ringwoodite containing water of 130–220 wt ppm (Shimojuku et al., 2009). The coefficients for volume diffusion (D V ) and grain-boundary diffusion (D GB ) are expressed as

 D = A exp −

H∗ RT

 (3)

where D is the diffusion coefficient (Table 2). Strain rate in diffusion creep is estimated according to the following equations (e.g. Frost and Ashby, 1982):

ε˙ = 14σ and

D eff Ω d2 R T

(4)

T. Kawazoe et al. / Earth and Planetary Science Letters 454 (2016) 10–19

D eff = D V +

πδ d

D GB

17

(5)

where D eff is the effective diffusion coefficient, d is the grain size, Ω is the molar volume and δ is the width of grain boundary. Si is considered as the rate-controlling species of diffusion creep because Si is the slowest diffusion element among major elements in ringwoodite. The smallest grain size observed in the present study (0.6 μm) is chosen for the estimation. The creep strength estimated for diffusion creep is higher than those of the present study suggesting that dislocation creep is the appropriate deformation mechanism at the experimental conditions of the present study. 4.4. Comparison of creep strength between ringwoodite and bridgmanite Creep strength of bridgmanite is supposed to be representative for that of the lower mantle because of the following reasons: (1) Microstructure of a bridgmanite–ferropericlase aggregate showed that of load-bearing framework (LBF) type after the phase transformation from ringwoodite at 25 GPa and 1700–1900 K (Yamazaki et al., 2014). (2) The creep strength of bridgmanite is comparable to that of the bridgmanite–ferropericlase aggregate having the LBF-type microstructure (Yamazaki and Karato, 2001). The results of the present study are compared with the creep strength of bridgmanite in Fig. 6. The creep strength of bridgmanite was measured in the bridgmanite–ferropericlase aggregates at 24.1–27.5 GPa and strain rates of 3.2–4.3 × 10−5 s−1 using the RDA (Girard et al., 2016) and by the stress relaxation test at 20 GPa up to 1073 K (Chen et al., 2002). Water content of bridgmanite was not reported in these studies. The creep strength of bridgmanite in diffusion creep is estimated at 25 GPa and 3.0 × 10−5 s−1 using its Si self-diffusion coefficients (Yamazaki et al., 2000) and Eqs. (3)–(5). The Si volume diffusion coefficient of Yamazaki et al. (2000) is similar with that of Xu et al. (2011) in which the water content of bridgmanite was ∼3–10 wt ppm. Grain size of bridgmanite is chosen to be 1 μm according to microstructure observation on the bridgmanite–ferropericlase aggregates after the phase transformation from ringwoodite at 25 GPa and 1700–1900 K (Yamazaki et al., 2014). The estimated strength of bridgmanite corresponds to the lower limit of its strength because of its grain growth with time. The creep strength of ringwoodite of the present study is lower by ca. two orders of magnitude than that of bridgmanite in diffusion creep at 1700 K. Moreover, the creep strength of bridgmanite determined by the stress relaxation test is higher than that of ringwoodite of the present study at 1073–1300 K. Furthermore, the creep strength of ringwoodite is also lower by ca. 1–2 orders of magnitude than that of bridgmanite at ∼2000 K by taking the temperature dependence of the creep strength of ringwoodite. Thus, the result of the present study indicates the possibility for abrupt increase in viscosity at the 660-km boundary. 4.5. Comparison of creep strength between ringwoodite and wadsleyite The creep strength of ringwoodite is compared with that of wadsleyite in Fig. 7 because the phase transformation between wadsleyite and ringwoodite may result in abrupt change in viscosity at the 520-km discontinuity. The creep strength of wadsleyite was obtained at 14.4–21.3 GPa and 1500–2200 K at strain rates of 0.9–6.4 × 10−5 s−1 using the RDA (Farla et al., 2015; Hustoft et al., 2013; Kawazoe et al., 2010a; Nishihara et al., 2008) and at 14.5 GPa at a strain rate of 3.88 × 10−5 s−1 using the D–DIA apparatus (Kawazoe et al., 2011). The creep strength of ringwoodite of the present study is apparently lower than those of wadsleyite obtained in both RDA and D–DIA experiments when

Fig. 6. Comparison of the creep strength between ringwoodite and bridgmanite. Circles and diamonds indicate the ringwoodite strength of this study and those obtained at 23 GPa using the RDA (Hustoft et al., 2013; Miyagi et al., 2014), respectively. Squares and a triangle represent those of bridgmanite obtained in bridgmanite–ferropericlase aggregates at 24.1–27.5 GPa using the RDA (Girard et al., 2016) and by the stress relaxation test at 20 GPa (Chen et al., 2002). The data at 1300–1400 and 1500–2150 K are normalized to a strain rate of 3.0 × 10−5 s−1 using the exponential law (Xu et al., 2003) and the power law with the stress exponent n of 3.0, respectively. A solid line shows the bridgmanite strength in diffusion creep estimated for a 1-μm grain size at 3.0 × 10−5 s−1 using its diffusion data at 25 GPa (Yamazaki et al., 2000).

Fig. 7. Comparison of the creep strength between ringwoodite and wadsleyite. Filled circles and diamonds indicate those of ringwoodite obtained using the D–DIA apparatus in this study and those from the RDA measurements (Hustoft et al., 2013; Miyagi et al., 2014). Open and half-filled symbols represent those of wadsleyite measured at 14.4–21.3 GPa using the RDA (Farla et al., 2015; Hustoft et al., 2013; Kawazoe et al., 2010a; Nishihara et al., 2008) and at 14.5 GPa using the D–DIA apparatus (Kawazoe et al., 2011), respectively. The data at 1300–1400 and 1500–1700 K are normalized to a strain rate of 3.0 × 10−5 s−1 using the exponential law (Xu et al., 2003) and the power law with the stress exponent n of 3.0, respectively.

compared at a certain temperature. However, quantitative comparison is difficult because of variation in water (hydrogen) content in their samples from 12 to 2100 wt ppm H2 O (from 200 to 33000 H/106 Si). Therefore, effects of water on the creep strengths of both minerals are necessary to be determined for the quantitative discussion. The creep strengths of ringwoodite and wadsleyite measured in the RDA experiments are consistently higher than those measured using the D–DIA apparatus. Moreover, the creep strength of ringwoodite is similar to that of wadsleyite when compared among the RDA measurements. In the RDA experiments, the sample was deformed by both compression and simple shear. This complexity of the deformation geometry of the RDA may cause the discrepancy between the RDA and D–DIA measurements. 4.6. Comparison of creep strength between ringwoodite and olivine Metastable olivine can exist to the lower MTZ in subducting slabs (e.g. Kaneshima et al., 2007) and directly transforms to ringwoodite in the region. The metastable olivine is expected to be dry

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T. Kawazoe et al. / Earth and Planetary Science Letters 454 (2016) 10–19

Fig. 8. Comparison of the creep strength between ringwoodite and olivine. Circles and triangles indicate those of ringwoodite in this study and those obtained at 20 GPa by the stress relaxation test (Xu et al., 2003), respectively. The data at 923–1400 and 1500–1700 K are normalized to a strain rate of 3.0 × 10−5 s−1 using the exponential law (Xu et al., 2003) and the power law with the stress exponent n of 3.0, respectively. Solid and dotted lines represent the strength of dry olivine (Kawazoe et al., 2009) and olivine containing hydrogen of 19000 H/106 Si (Karato and Jung, 2003) estimated at 17 GPa and 3.0 × 10−5 s−1 , respectively.

and cold below ∼1000 K according to transformation kinetics from olivine to wadsleyite/ringwoodite (e.g. Kubo et al., 2009). Change in viscosity associated with the olivine–ringwoodite transformation is important for understanding stagnation of the subducting slabs. The results of the present study and Xu et al. (2003) are compared with creep strength of olivine in Fig. 8. The creep strength of dry olivine is calculated below 1000 K at 17 GPa using its exponential flow law (Kawazoe et al., 2009). For comparison, we also calculated the creep strength of olivine with water content similar to the present samples (19000 H/106 Si) at 17 GPa using the power law of hydrous olivine (Karato and Jung, 2003). The creep strength of ringwoodite is lower than those of olivine suggesting weakening of the subducting slabs after the olivine–ringwoodite transformation in the lower MTZ. The weakening of the subducting slabs should contribute to the stagnation of the slabs in the lower MTZ. However, large uncertainties are expected for the creep strength of olivine estimated at the P –T conditions of the lower MTZ. This is because the used exponential and power laws of olivine were established based on data obtained below 10 GPa (Kawazoe et al., 2009) and 2 GPa (Karato and Jung, 2003), respectively. Therefore, the flow laws of olivine are necessary to be determined to the P –T conditions relevant to the lower MTZ. Acknowledgements This study has been supported by the global COE program “Deep Earth Mineralogy”, the power user program of SPring-8 and grants from the Ministry of Education, Culture, Sports, Science, and Technology of the Japanese Government No. 22740346 and 22340161. The FIB facility at Bayerisches Geoinstitut is supported by DFG grant INST 91/315-1 FUGG. We are grateful to H. Schulze, R. Njul, U. Trenz, K. Marquardt and S. Petitgirard for their supports for the sample polishing, the SEM analysis and the FIB cutting. We appreciate reviews by two anonymous reviewers. Appendix A. Supplementary material Supplementary material related to this article can be found online at http://dx.doi.org/10.1016/j.epsl.2016.08.011. References Akaogi, M., Ito, E., Navrotsky, A., 1989. Olivine-modified spinel–spinel transitions in the system Mg2 SiO4 –Fe2 SiO4 : calorimetric measurements, thermochemical calculation, and geophysical application. J. Geophys. Res. 94, 15671–15685.

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