Superplasticity in hydrous melt-bearing dunite: Implications for shear localization in Earth’s upper mantle

Earth and Planetary Science Letters 335–336 (2012) 59–71

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Superplasticity in hydrous melt-bearing dunite: Implications for shear localization in Earth’s upper mantle Tomohiro Ohuchi a,n, Yu Nishihara a,b, Takaaki Kawazoe a, Dirk Spengler a,b,c, Rei Shiraishi d, Akio Suzuki d, Takumi Kikegawa e, Eiji Ohtani d a

Geodynamics Research Center, Ehime University, Matsuyama 790-8577, Japan Senior Research Fellow Center, Ehime University, Matsuyama 790-8577, Japan c Institute of Earth and Environmental Sciences, Potsdam University, Potsdam 14476, Germany d Department of Earth and Planetary Materials Science, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan e Photon Factory, High Energy Accelerator Research Organization, Tsukuba 305-0801, Japan b

a r t i c l e i n f o

abstract

Article history: Received 15 June 2011 Received in revised form 1 April 2012 Accepted 23 April 2012 Editor: T. L. Stixrude Available online 14 June 2012

Deformation experiments on hydrous melt-bearing dunite (olivine þ 4 vol% orthopyroxene þ4 vol% clinopyroxene with less than 2.5 vol% of the melt phase) were conducted at pressures of 1.3–5.7 GPa and temperatures of 1270–1490 K in order to explore the effect of intergranular fluids on the plastic flow of olivine in Earth’s upper mantle. The strain rate was proportional to steady-state creep strength to the 2.1 power, and the creep strength markedly increased with increase in grain size. Developments of the crystallographic preferred orientation of olivine and flattening of olivine grains were hardly observed even after 33–55% shortening of the samples. These observations show that grain boundary sliding (GBS) dominated the deformation of olivine (i.e., superplasticity). The creep strength of hydrous melt-bearing dunite was 2–5 times lower than that of melt-free dunite. The dependence of creep rate on melt fraction is known to be expressed empirically as e_ ðfÞ ¼ e_ ð0Þ expðafÞ, where a is a constant and f is the melt fraction. The experimentally obtained value of a was in the range of 150–230, corresponding to 5–7 times the reported values for the olivine–basalt system at 0.3 GPa (i.e., creep strength of dunite was efficiently reduced by the hydrous melt). Superplasticity is the dominant creep mechanism of olivine in fluid-bearing fine-grained peridotites under low-temperature and high-stress conditions (i.e., peridotite shear zones in the upper mantle). Superplasticity induced by geological fluids would play an important role in the shear localization (and thus initiation of subduction) in the upper mantle. & 2012 Elsevier B.V. All rights reserved.

Keywords: olivine hydrous melt grain boundary sliding superplasticity shear localization subduction

1. Introduction The rheological properties of olivine, the major constituent mineral in Earth’s upper mantle, control the dynamics of the upper mantle. Many experimental studies have been performed on the plastic flow behaviors of olivine at high temperatures (i.e., temperatures at the upper mantle) and low pressures (o0.5 GPa) (e.g., Durham and Goetze, 1977). Previous studies showed that the plastic flow of olivine at high temperatures (T41500 K) is controlled by two creep mechanisms, power-law dislocation creep and diffusion creep (e.g., Karato et al., 1986). Some authors argued that other creep mechanisms such as dislocation-accommodated grain boundary sliding and diffusion-accommodated grain boundary sliding also play an important role in the upper mantle (e.g., Hirth and Kohlstedt, 1995a). Both of them (dislocation- and

diffusion-accommodated grain boundary sliding) are often termed as ‘‘superplasticity’’. It has been reported that superplasticity may dominate the plastic flow of minerals in some parts of the Earth (glaciers: Goldsby and Kohlstedt, 2001; shear zones in the lower crust: e.g., Behrmann and Mainprice, 1987; shear zones in the upper mantle: Hiraga et al., 2010a, b; lower mantle: Karato et al., 1995). Although superplasticity is classically defined phenomenologically as the ability of a material to be deformed under tension to large strains (b100%), the term ‘‘superplasticity’’ has been used as the meaning of the mechanism of deformation which appears to be the same as dislocation- and diffusion-accommodated grain boundary sliding in the Earth science community (e.g., Goldsby and Kohlstedt, 2001). We use the term ‘‘superplasticity’’ as the meaning of the deformation mechanisms. Plastic flow of minerals at high temperatures is usually described as shown below:

n

Corresponding author. Tel.: þ81 89 927 8151; fax: þ 81 89 927 8167. E-mail addresses: [email protected], [email protected] (T. Ohuchi). 0012-821X/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.epsl.2012.04.032

e_ ¼ A

  En þ PV n r f H2 O exp  RT G

sn p

ð1Þ

60

T. Ohuchi et al. / Earth and Planetary Science Letters 335–336 (2012) 59–71

where e_ is the strain rate; A a pre-exponential constant; f H2 O the water fugacity; s the differential stress ( ¼ s1  s3); n the stress exponent; G the grain size; p the grain size exponent; En the activation energy; Vn the activation volume; P the pressure; T the temperature; and R the gas constant (e.g., Mei and Kohlstedt, 2000a). Eq. (1) shows that activation volume (Vn) is an important parameter controlling the creep strength of minerals at high pressures. The effects of pressure on the plastic flow of minerals become significant when pressure exceeds a few percent of the bulk modulus of a given material (e.g., Karato and Jung, 2003). Recently, new types of deformation apparatuses such as the rotational Drickamer apparatus (RDA: Yamazaki and Karato, 2001) and deformation-DIA apparatus (D-DIA: Wang et al., 2003) have been developed, and many experimental studies on the Vn of ‘‘dry’’ olivine have been conducted (e.g., Li et al., 2006; Durham et al., 2009; Kawazoe et al., 2009). It has been recognized that a significant amount of water is distributed in the asthenospheric upper mantle (e.g., 8107 490 ppm H/Si: Hirth and Kohlstedt, 1996), showing that the dynamics of the asthenospheric upper mantle needs to be discussed based on the rheology of hydrous olivine rather than on anhydrous olivine. Despite the importance of hydrous olivine in upper mantle rheology, the effects of pressure on the creep of hydrous olivine have not been fully investigated. The creep strength of olivine is drastically decreased by the effect of water (i.e., dissolved water in olivine) (e.g., Chopra and Paterson, 1984). Mei and Kohlstedt (2000a) conducted deformation experiments on olivine at 0.1–0.45 GPa and 1473–1573 K under watersaturated conditions and obtained values of Vn for the diffusion creep of hydrous olivine as 0 and 20 cm3/mol in the case of r¼ 0.7 and 1, respectively (because of narrow pressure ranges, they were unable to determine r and Vn uniquely). Similarly, Mei and Kohlstedt (2000b) obtained the values of Vn for the power-law dislocation creep of hydrous olivine as 4, 20, and 38 cm3/mol in the case of r ¼0.75, 1, and 1.25, respectively. Karato and Jung (2003) determined the value of Vn for the power-law dislocation creep of hydrous olivine as 24 cm3/mol from the experimental data obtained at 0.3–2 GPa. Not only dissolved water but also intergranular melt/fluid phases decrease the creep strength of olivine. In the olivine-basalt system, power-law dislocation creep and diffusion creep are enhanced by the presence of a melt phase (Mei et al., 2002). Moreover, it has been reported that grain boundary sliding (GBS) dominates the deformation of olivine in the olivine–basalt system with a high volume fraction of melt ( 44 vol%) (Hirth and Kohlstedt, 1995a). Similar observations have been reported in aqueous fluid-bearing peridotites (McDonnell et al., 2000). It is known that the dihedral angle between olivine and fluid decreases with pressure (Mibe et al., 1999; Yoshino et al., 2007), which shows a reduction in the solid–solid grain boundary area with increase in pressure. Thus, a significant weakening of olivine aggregates by addition of fluids is expected at high pressures. However, the effects of intergranular fluids on the creep strength of olivine aggregates have not been evaluated at high pressures (pressure range in previous studies: 0.3–0.6 GPa). In order to explore the rheological properties of fluid-bearing dunite (i.e., olivine aggregate) under the conditions of Earth’s upper mantle, we have developed experimental techniques for deformation experiments under wet conditions using a D-DIA apparatus (Ohuchi et al., 2010a). In this study, we used palladium–silver capsules for deformation experiments and succeeded in conducting measurements of in-situ strain and stress values of olivine in hydrous melt-bearing dunite at high pressures (1.3–5.7 GPa) and high temperatures (T¼ 1270–1490 K). Here we show that superplasticity is an important creep mechanism for the deformation of fluid-bearing peridotites in the upper mantle. The superplasticity

of olivine, which is caused by the addition of fluids to peridotite shear zones, promotes shear localization in the upper mantle resulting in the initiation of subduction.

2. Experimental procedure 2.1. Starting materials The starting material for dunite was prepared from a mixture of powdered San Carlos olivine (Fo90)þ 8 wt% pyroxenes (clinopyroxene: 4 vol%; orthopyroxene: 4 vol%: Bancroft, Canada). Pyroxenes were added to generate partial melt and to inhibit the grain growth of olivine. The fine-grained mixed powder was placed into a nickel capsule and was sintered at 4.0 GPa and 1373 K for 1.5 h using a Kawai-type multi-anvil high-pressure apparatus (Orange 3000) at Ehime University. The entire cell assembly for the synthesis of dunite was not dried before the sintering experiment in order to provide moisture to the powders. The synthesized dunite (OT-821) consists of 92 vol% of olivine and 8 vol% of pyroxenes (clinopyroxene: 4 vol%; orthopyroxene: 4 vol%). In order to remove water dissolved in the OT-821 sample, a part of the OT-821 sample (OT-821 F) was fired at 0.1 MPa and 1170 K under reducing conditions (log10 f O2  16 bar) for 6 h. The OT-821F sample was used for the deformation of melt-free dunite (TO-13). The dunite sample was core-drilled with a diameter of 1.2 mm and a length of 1.5 mm. 2.2. Deformation experiments We conducted deformation experiments on dunite at pressures of 1.3–5.7 GPa, temperatures of 1270–1490 K, and strain rates of 0.7–8.2  10  5 s  1 using a deformation-DIA apparatus (D-CAP) at the AR-NE7A beam line of the Photon Factory (High Energy Accelerator Research Organization, Tsukuba, Japan). Details of the deformation-DIA apparatus and the beam line are described in Shiraishi et al. (2011). Two of the four sliding blocks on the down-stream side have a conical X-ray path (maximum 2y angle  101). The MA-6-6 system, which consists of six secondstage anvils with truncated edge lengths (TEL) of 5 mm, an anvil guide, and cell assembly, was adopted for the experiments (e.g., Ohuchi et al., 2010a). Two X-ray transparent anvils, which were made from cubic boron nitride (cBN), were used for the secondstage anvils on the lower-stream side. The anvil guide was made of engineering plastic (columns along X-ray path) and stainless steel (other parts) (Kawazoe et al., 2011). A sketch of the cell assembly used for the deformation experiments is shown in Fig. S1. The design of the cell assembly was based on Ohuchi et al. (2010a). A semi-sintered cobalt-doped magnesia ((Mg, Co)O) cube with an edge length of 7 mm was used as the pressure medium. A graphite heater was located at the inner bore of a tubular LaCrO3 thermal insulator. Copper and molybdenum electrodes, hard alumina pistons, and machinable alumina rods were placed along the direction of the axial differential stress (s1  s3). Two X-ray transparent rods, which were made from a mixture of amorphous boron and epoxy, were placed along the X-ray path in the pressure medium. A cored sample of dunite (OT-821F for the TO-13 run; OT-821 for other runs) was placed into a palladium–silver (Pd75%–Ag25%) capsule and then sandwiched between two tungsten or single crystal diamond pistons (Table 1). Alumina pistons were used for the TO-13 run. Two platinum strain-markers, with a thickness of 20 mm, were placed between the sample and the pistons. About 15 wt% of distilled water was added to the palladium–silver capsule using a microsyringe (distilled water was not added to the TO-13 sample), and then the capsule was sealed with a

Table 1 Experimental conditions and results. Run no.

Step no.

P

T

(GPa)a

(K)b

1490 1490 1490 1490 1370 1370 1370 1370 1320 1270 1420 1370 1370 1370 1370 1370 1370

0.33 0.39 0.40

0.55

0.40 0.32

0.52

Strain rate

s(0 2 1)

s(1 0 1)

s(1 3 0)

s(1 3 1)

s(1 1 2)

Mean grain size

(s  1)

(MPa)c

(MPa)c

(MPa)c

(MPa)c

(MPa)c

(mm)

1.6 (7 0.2)  10  5 4.3 (7 0.7)  10  5 1.3 (7 0.2)  10  5 3.8 (7 0.6)  10  5 1.3 (7 0.2)  10  5 2.7 (7 0.4)  10  5 5.8 (7 0.9)  10  5 3.0 (7 0.5)  10  5 3.3 (7 0.5)  10  5 4.0 (7 0.6)  10  5 4.0 (7 0.6)  10  5 5.7 (7 0.9)  10  5 0.7 (7 0.1)  10  5 2.0 (7 0.3)  10  5 6.5 (7 1.0)  10  5 1.7 (7 0.3)  10  5 8.2 (7 1.2)  10  5

155 (7 64) 279 (7 64) 125 (7 57) 194 (7 57) 125 (7 34) 193 (7 34) 255 (7 34) 107 (7 42) 178 (7 42) 436 (7 42) 338 (7 43) 598 (7 43) 430 (7 28) 653 (7 28) 734 (7 28) 91 (7 34) 178 (7 34)

– – – – 128 205 264 103 165 337 345 505 392 537 697 106 219

151 (7 46) 232 (7 46) 143 (7 36) 207 (7 36) 119 (7 30) 175 (7 30) 216 (7 30) 72 (7 26) 132 (7 26) 347 (7 26) 293 (7 44) 590 (7 43) 349 (7 25) 620 (7 25) 703 (7 25) 56 (7 27) 152 (7 27)

124 (7 42) 221 (7 42) 151 (7 51) 278 (7 51) 104 (7 27) 181 (7 27) 236 (7 27) 87 (7 36) 154 (7 36) 391 (7 36) 314 (7 37) 618 (7 37) 329 (7 27) 562 (7 27) 646 (7 27) 67 (7 21) 139 (7 21)

123 (7 45) 179 (7 45) 151 (7 51) 255 (7 51) 119 (7 32) 151 (7 32) 216 (7 32) 95 (7 33) 150 (7 33) 321 (7 33) 225 (7 39) 452 (7 39) 319 (7 22) 523 (7 22) 606 (7 22) 60 (7 22) 128 (7 22)

5.8

An annealing experiment using a D-DIA apparatus without the deformation process TO-07 4.6 1270 0 Annealing experiments using OT-821j 4.0 OT821Fk – 2.0 OT-733l OT-786l 2.0 a

a Kawai-type multi-anvil apparatus 1370 – 1373 1373

(7 47) (7 47) (7 47) (7 40) (7 40) (7 40) (7 65) (7 64) (7 40) (7 40) (7 40) (7 42) (7 42)

Flatnessd

Vmelt þ pore

Water content COH

Water fugacity f H2 O g

(vol. %)e

(ppm H/Si)f

(MPa)

1.8

1.3

515 (7 66)

4.8

1.8

2.4

2257 (7 97)

3.9

1.7

2.4

227 (7 11)

4.0

1.9

1.6

573 (7 29)

3.7

1.8

1.8

254 (7 22)

2.2

1.8

0

402 (7 37)

3.9

1.8

1.7

3266 (7115)

5.42E þ 3 5.74E þ 3 1.96E þ 5 1.49E þ 5 8.93E þ 2 1.05E þ3 9.87E þ 2 4.10E þ3 5.09E þ3 4.89E þ 3 5.82E þ 3 4.58E þ 3 1.09E þ4 1.19E þ 4 1.18E þ 4 1.63E þ 5 1.15E þ 5

2.7

1.7

0.9

6752 (7132)

6.30E þ5

13.4

1.7

4071 (7248)

1.56E þ 5

511 (7 30)

–

– –

– –

Addition of waterh

Piston material

Yes

Tungsten

Yes

Tungsten

Yes

Diamond

Yes

Diamond

Yes

Diamond

No

Alumina

Yes

Diamond

Yes

Diamond

i

– 33.9 63.5

– 1.8 1.7

Average values of pressure at a stage of steady-state deformation. Error is within 0.2 GPa in the case of deformation experiments (0.4 GPa in the case of annealing experiments using a Kawai-type multi-anvil apparatus). Temperature at the center of the sample. Values of the axial differential stress (s1  s3). d Average values of ratio of lengths of major and minor axes of the best-fit ellipsoids. e Volume fraction of melt phase and pores. f Water content in olivine in the recovered samples. g Calculated from the water contents in the recovered samples. h Addition of water to the palladium–silver capsule. i An experiment without the deformation process (i.e., the operation of deformation rams). The cell assembly designed for deformation experiments was used for the experiment. Annealing duration: 0.5 h. j Starting material for the deformation experiments (TO-04, 05, 07, 10, 11, 12, 16). k A fired sample of OT-821. The OT-821 sample was fired at 0.1 MPa and 1170 K under reduced conditions (log f O2  16 bar) for 6 h. OT-821F was the starting material for the TO-13 run. l Sintering experiments on olivine aggregates (annealing duration: 1 h). Data of mean grain size are from Ohuchi et al. (2011). b

T. Ohuchi et al. / Earth and Planetary Science Letters 335–336 (2012) 59–71

Deformation experiments TO-04 1 2.8 2 2.9 TO-05 1 5.3 2 5.0 TO-10 1 1.6 2 1.7 3 1.7 TO-11 1 2.2 2 2.3 3 2.2 TO-12 1 3.6 2 3.2 TO-13 1 3.6 2 3.7 3 3.7 TO-16 1 4.3 2 3.9

Total strain

c

61

T. Ohuchi et al. / Earth and Planetary Science Letters 335–336 (2012) 59–71

Axial differential stress and generated pressure were measured by using the radial diffraction of monochromatic X-rays ˚ (energy 50 keV, wavelength 0.245 A). Two-dimensional X-ray diffraction patterns were taken for 8–12 min using an imaging plate (IP). Digitalized diffraction patterns having a resolution of 100 mm were acquired from IPs using a Fuji BAS2000 IP reader. The two-dimensional digitalized diffraction pattern was integrated to a one-dimensional profile (angle step of 22.51), and the peak positions were semi-automatically determined at a certain azimuth angle using software (IPAnalyzer and PDIndexer: Seto et al., 2010). The stress magnitude was calculated based on the following equation (Singh et al., 1998):

palladium–silver lid. The palladium–silver capsule was surrounded by a hexagonal boron nitride (hBN) sleeve. Pressure was first raised to the desired value at a rate of 0.5 MN/h (in press load) by operating the main ram of the deformation-DIA apparatus (hereafter, compression process). Shortening of the samples (5–10%) was observed during compression at room temperature. Temperature was increased at a rate of 25 K/min. Temperature was monitored by a W97Re3–W75Re25 thermocouple placed along one of the diagonal directions of the cubic (Mg, Co)O pressure media. The temperature gradient between the central part and the edge of the sample was less than 50 K at r1673 K (Ohuchi et al., 2010a). The difference in temperature between the hot junction of the thermocouple and the central part of the sample was in the range of 80–100 K at 1493–1673 K (Ohuchi et al., 2011). Temperatures at the center of the samples were estimated from the temperatures monitored by a thermocouple. After the temperature reached the desired value, the sample was annealed for 0.5–1 h (hereafter, annealing process). Then the upper and lower anvils were advanced at a constant rate by operating the deformation rams (hereafter, deformation process). Strain (i.e., e ¼ ln(l/l0), where l0 is the initial length of the sample just before the operation of the deformation rams, and l, the length of the sample during deformation) of the samples was measured by the distance between two platinum strain-markers which was monitored by using insitu monochromatic X-ray radiography (Fig. 1). The uncertainty in the strain rate, which resulted from the shape of the strainmarkers, was within 7%.

h i s 0 dhkl ¼ dhkl 1 þ ð13 cos2 cÞ 6M

ð2Þ

500

Ol (130)

Graphite (002)

Ol (002)

1000

Ol (021) Ol (101) Ol (120, 111)

Intensity (count)

ψ = 90° λ = 0.2495 Å

MgO (200) Diamond (111)

1500

Ol (122)

where dhkl is the d-spacing measured at an azimuth angle c, d0hkl the d-spacing under hydrostatic pressures; M an appropriate   shear modulus for a given crystal orientation hkl , and s the axial differential stress. The M was calculated from olivine single crystal elasticity data (Isaak, 1992; Abramson et al., 1997). The values of a and d0hkl were calculated by fitting the obtained values of dhkl to Eq. (2). The uncertainty of the stress results from the deviation of the obtained values of dhkl from the best-fit curve of Eq. (2). Pressure was determined from the calculated values of d0hkl using the equation of state of olivine (Liu and Li, 2006). The analyses were carried out for five diffraction peaks of olivine (hkl ¼0 2 1, 1 0 1, 1 3 0, 1 3 1, 1 1 2). Representative X-ray diffraction patterns are shown in Fig. 1.

Ol (131) Ol (112) Ol (200, 041) Pd75Ag25 (111)

62

0 3

4

5 2θ (°)

ε=0

2.540

e

6

7

ε = 0.40

Olivine (131) Strain marker

d-spacing (Å)

2.538

2.536

2.532 0

60

120

180 ψ (°)

240

300

360

anvil gap

WC anvil

2.534

Fig. 1. (a) A representative two-dimensional X-ray diffraction pattern during sample deformation at 1.7 GPa and 1370 K (TO-10). (b) A one-dimensional diffraction pattern ˚ Diffraction patterns of olivine (Ol), graphite, diamond, MgO, and palladium–silver were observed. obtained from (a) at an azimuth angle of 901 and wavelength of 0.2495 A. (c) Relationship between the observed d-spacing values of the olivine (131) peak and the azimuth angle (c) obtained from (a). (d, e) X-ray radiographs acquired before (d: e ¼0) and during the deformation (e: e ¼ 0.40) (TO-10). Positions of platinum strain markers are shown by arrows in (d) and (e). Double arrows represent the anvil gap.

T. Ohuchi et al. / Earth and Planetary Science Letters 335–336 (2012) 59–71

2.3. Microstructural observations and water content The recovered samples were cut with a low-speed saw. Secondary electron (SE) and backscattered electron (BSE) images of the polished surfaces of the deformed samples were acquired at magnifications varying between  50 and  3000 by using a JEOL JSM-7000F field-emission scanning electron microscope (FESEM). Grain boundary maps (i.e., outline of grain boundaries) were obtained from forescattered electron (FSE) images of the etched sample, and then diameters of the circles having the same area as individual grains were measured as grain size by using image-processing software (Ohuchi, 2006). Lengths of major and minor axes of the best-fit ellipsoids having the same area as individual grains were measured to evaluate the flatness (i.e., ratio of lengths of major and minor axes of the bestfit ellipsoid) of grains. The crystallographic orientation of olivine grains was evaluated by the indexation of the electron backscattered diffraction (EBSD) patterns using an FE-SEM (JEOL JSM-7000F) equipped with an EBSD camera at Ehime University. EBSD patterns were generated via the interaction of a vertical incident electron beam with a polished sample inclined at 701 with respect to the horizontal. The EBSD pattern of each forsterite grain was obtained at 20 kV acceleration voltage and 7.5 nA probe current. The unpolarized infrared absorption spectra of the polycrystalline sample were obtained from the doubly polished sections of the samples (161–255 mm thick). The measurements were carried out in air by putting the sections on a BaF2 plate and using a PerkinElmer Spectrum One Fourier-transform infrared spectrometer (FTIR). An aperture size of 50  50 mm2 was used for all of the measurements. The water content in the olivine in the samples was determined by integrating the infrared absorption spectra from 3500 to 3700 cm  1 on the basis of the extinction coefficient calibration of Paterson (1982) (Fig. S2). We calculated the water fugacity from the water content in olivine based on Eq. (11) in Keppler and Bolfan-Casanova (2006) and constants reported by Zhao et al. (2004) (see ‘‘Supplementary data’’ for the details of microstructural observations and water content).

3. Results 3.1. Microstructures Typical microstructures of the deformed samples are shown in Figs. 2 and S3. Pores in the samples are frequently filled with a glassy phase (i.e., melt), showing that partial melting occurred during the experiments (TO-04, 05, 10, 11, 12, and 16). Pores and melt phase were not observed in the TO-13 sample. Both smoothly curved and faceted mineral–melt interfaces are observed. Spatial distribution of pores and melt phase in deformed samples is heterogeneous, resulting from inhomogeneous grain size distribution of olivine, developments of faceted mineral–melt interfaces (e.g., Faul et al., 1994), and the influence of differential stress on melt topology (Daines and Kohlstedt, 1997). Pores without the glassy phase were also observed (volume fraction of pores were less than 10 vol% of the melt phase). Volume fraction of the melt phase and pores in the deformed samples ranges from 1.3 to 2.4 vol% (Table 1). Chemical compositions of olivine, orthopyroxene, clinopyroxene and melt are summarized in Table S1. The total values of the chemical composition of the melt phase obtained by microprobe analysis were significantly low (  73 wt%), showing that the melt phase contains a large amount of water ( 27 wt%) (i.e., hydrous melt). The deformed samples consist of olivine grains with grain sizes of 1–5 mm (Fig. 2). Curved to lobate grain boundaries are observed in

63

the deformed samples (Fig. S3). Flatness (i.e., ratio of lengths of major and minor axes calculated from the best-fit ellipsoid of each grain) of olivine grains in deformed samples (F ¼1.7–1.9) is similar to that in the hot-pressed (i.e., not deformed) samples (F ¼1.7–1.8) (Table 1), showing that flattening of olivine grains is not significant even after 33–55% shortening of samples. The development of shape-preferred orientation of olivine was hardly observed in the deformed samples (Figs. 2 and S3). The mean grain size of olivine in the samples is summarized in Table 1. The mean grain size of olivine in the deformed samples (2.2–5.8 mm) is smaller than that in the starting material (13.4 mm). Grain size reduction was also observed in an experiment without the deformation process (2.7 mm at 4.6 GPa and 1270 K in the TO-07 run), suggesting that dynamic recrystallization of olivine grains occurred during compression of the cell assembly at room temperature (i.e., compression process). In fact, significantly high stress values on the samples were detected during the shortening of samples caused by the compression process at room temperature (s1–s3 ¼0.96–4.07 GPa: Table S2). A representative dislocation microstructure of the deformed samples is shown in Fig. 2d. Many dislocations and the formation of subboundaries are observed in olivine grains. Considering that the stress values during the compression process are much higher than those during the deformation process (Tables 1 and S2), many of the dislocation microstructures would be formed during the compression process and the subsequent annealing process. Subgrain boundaries (i.e., grain boundaries having low misorientation angles) are observed in some of olivine grains (Fig. 2f). Subgrain size in deformed olivine is typically 0.5–3 mm (Fig. 2d and f). Development (or absence) of crystallographic preferred orientation (CPO) during sample deformation is one of the most important evidences to constrain the deformation mechanism (Karato et al., 1995; Karato, 2008). The CPO patterns of olivine in the undeformed and deformed samples are shown in Fig. 3. The olivine CPO patterns observed in the samples are similar to each other. The ½0 1 0 axes of olivine are preferentially sub-parallel to the direction of the axial differential stress. The ½1 0 0 and ½0 0 1 axes concentrate in the direction normal to the axial differential stress. Increase in the concentration of the ½1 0 0, ½0 1 0, and ½0 0 1 axes is hardly observed even after the deformation process with the 40–52% of strain. These observations show that the CPO patterns were formed during the compression and the subsequent annealing processes, and no further developments of the CPO (i.e., no increase in fabric strength) occurred during the deformation process, namely diffusion creep or superplasticity is suggested to be the dominant deformation mechanism of olivine in melt-bearing dunite (e.g., Behrmann and Mainprice, 1987).

3.2. Water content The average content of water dissolved in the recovered samples obtained by infrared spectroscopy is summarized in Table 1. The infrared beam was strongly absorbed in the wavenumbers ranging from 3500 to 3700 cm  1 in the samples (Fig. S2). The average water contents in the starting materials and the deformed samples were obtained to be 227–3266 ppm H/Si. Even though distilled water was added to the starting materials, the water content in some of the deformed samples (227–573 ppm H/ Si: TO-04, 10, 11, and 12) is much lower than the reported water content in olivine at 1373 K and 2.5–6.5 GPa under water-saturated conditions (2200–8060 ppm H/Si: Kohlstedt et al., 1996). This discrepancy would result from conditions of low activity of water, which can be caused by the presence of melt phase and/or

64

T. Ohuchi et al. / Earth and Planetary Science Letters 335–336 (2012) 59–71

Tungsten piston

Pd70Ag30 capsule

Ol

P Melt

Sample Opx

Cpx 200 μm

5 μm

3 μm

1 μm

Opx

Ol

Cpx

10 μm

: 2-10º : > 10º

Fig. 2. (a) A representative secondary electron image of a deformed sample assembly (TO-05). Large arrows in (a) represent direction of the axial differential stress (s1  s3). Backscattered electron (BSE) images showing typical deformation microstructures in (b) a melt-bearing dunite (TO-10) and (c) a melt-free dunite (TO-13). Ol, olivine; Opx, orthopyroxene; Cpx, clinopyroxene; P, pore. (d) A BSE image showing a typical dislocation microstructure in a deformed sample (TO-10). Bright lines in (d) show grain boundaries or dislocations (a heavy white line at the lower left of (d) shows a crack). Dislocation-free recrystallized grains are observed in (d). (e) A forescattered electron image and (f) an orientation map of olivine in a deformed sample (TO-11). (e) and (f) were obtained at the same place in the sample. Dark patches in (e) are pores and melt phase. White points in (f) represent secondary phases or misindexed points. Red and black lines in (f) represent low-angle grain boundaries having 2–101 misorientation angles and grain boundaries having 4101 misorientation angles, respectively. Wild spikes were removed and orientation data were extrapolated in (f). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

dissolution of carbon from diamond pistons to melt phase (e.g., Litasov et al., 2009). Water content in olivine in melt-bearing dunite is plotted against pressure in Fig. S4. Water contents in olivine deformed (or annealed) at higher pressures ( Z3.9 GPa: 2257–6752 ppm H/Si) are more than 4 times higher than those at lower pressures ( r 3.2 GPa: 227–573 H/Si), showing that water contents in olivine discontinuously increase at pressures 3.2–3.9 GPa. The threshold pressure for the discontinuous increase of water content in olivine coincides with the miscibility boundary between silicate melt and aqueous fluid in the peridotite–H2O system (Mibe et al., 2007). Mibe et al. (2007) reported that two fluid phases (i.e., silicate melt and aqueous fluid) coexist at pressures r3.6–3.8 GPa (at 1270–1490 K), though the two phases become indistinguishable from each other (i.e., supercritical fluid phase) at higher pressures. A possible explanation for the cause of the

discontinuous increase of water content in olivine around 3.6– 3.8 GPa is the change in the partition coefficient of water between olivine and the melt/fluid phase caused by the presence/absence of the supercritical fluid phase. 3.3. Mechanical data and flow laws All the stress–strain curves obtained at P¼1.3–5.7 GPa and T¼1270–1490 K are shown in Figs. 4 and 5. The five diffraction peaks (hkl ¼0 2 1, 1 0 1, 1 3 0, 1 3 1, 1 1 2) produced five different creep curves, and the difference in stress values among the diffraction peaks were within 200 MPa. High stress values during the compression process (0.96–4.07 GPa: Table S2) were drastically reduced during the annealing process. The stress value at the beginning of deformation was less than 100 MPa and increased with strain during the deformation process. In most

T. Ohuchi et al. / Earth and Planetary Science Letters 335–336 (2012) 59–71

[100]

[010]

[001]

0.5 1.0 1.6 TO-07: P = 4.6, T = 1270 K, ε = 0, N = 495

0.5 1.0 1.7 TO-10: P = 1.6-1.7, T = 1370 K, ε = 0.40, N = 481

0.3 1.0 1.8 TO-16: P = 3.9-4.3, T = 1370 K, ε = 0.52, N = 458 Fig. 3. Pole figures showing the crystallographic preferred orientation (CPO) of olivine in (a) an undeformed sample (TO-07) and (b, c) deformed samples (b: TO-10; c: TO-16) (equal-area lower hemisphere projections of [1 0 0], [0 1 0], and [0 0 1] directions with a half scatter width of 301). The color coding refers to the density of data points, and the contours correspond to the multiples of uniform distribution. Direction of the axial differential stress (s1  s3) is shown by arrows. The N represents the number of analyzed grains. Pressure, temperature, and strain (e) are also shown.

cases, steady-state creep strength was achieved at a strain of e  0.1 (usually 0.05). The steady-state creep strength is summarized in Table 1. The steady-state creep strength increased with increase in strain rate and with decrease in temperature. Because the volume fraction of the fluid phase (i.e., melt and pores) is similar in each of the deformed melt-bearing samples (1.3– 2.4 vol%: Table 1), flow-law parameters in Eq. (1) can be obtained from the experimental data without including the correction for the effect of the fraction of the fluid phase on the olivine rheology (e.g., Mei et al., 2002). We assumed that the volume fraction of the fluid phase was constant during the deformation process. Three flow-law parameters (n, En, and r) were obtained from selected data sets (see Sections 3.3.1 and 3.3.2) in order to minimize the errors of parameters (i.e., a global fit to all experimental data was not used for the calculation of the parameters), because differences in experimental conditions among runs affect values of the parameters.

65

dataset of the TO-10 run (Table 2). Note that the obtained value of n (and also other parameters) varies depending on the diffraction peak used for the measurements of stress. Other datasets (TO-04, 05, and 16) support the validity of the obtained value of n (Figs. 6a and S5). Similarly, the values of En were obtained to be 250–448 kJ/mol from the dataset of the TO-11 run (note that the effect of PVn on the ‘‘apparent’’ activation energy was subtracted and then En was obtained: see Table 2). The dataset of TO-12 also shows a quite similar temperature dependency on stress, showing the validity of the obtained value of En. Figs. 6a, c, and S5 suggest that the dominant creep mechanism of olivine in melt-bearing dunite was unique and the same in all experiments. The average value of the activation energy (En ¼329 kJ/mol) is closer to the activation energy for diffusion creep of ‘‘wet’’ olivine (295 kJ/mol: Mei and Kohlstedt, 2000a) than that for power-law dislocation creep (470 kJ/mol: Mei and Kohlstedt, 2000b), suggesting that the creep mechanism is mainly controlled by the diffusion process. Steady-state creep strength is plotted against water fugacity in Fig. 6d. The waterfugacity sensitivity of stress was evaluated at two pressure ranges (1.7–2.2 GPa: data from TO-10, 11; 3.6–3.9 GPa: data from TO-12, 16). The slopes of ln s2ln f H2 O indicate that most of the values of r are close to 1. Our results are consistent with the case of r¼1 which is theoretically expected for the diffusion processes (r¼0.7 or 1: e.g., Mei and Kohlstedt, 2000a). In order to evaluate the grain-size dependency of stress, the steady-state creep strength is plotted against the mean grain size in Fig. 6e. All the data in Fig. 6e are normalized to the conditions of 3 GPa, 1370 K, strain rate of 10  5 s  1, and water content of 500 ppm H/Si. Fig. 6e shows that the creep mechanism is the grain-size-sensitive (GSS) creep. Taking into account the obtained values of n and En, the dominant creep mechanism of olivine is expected to be diffusion-accommodated GBS. The slopes of ln s–ln G indicate that most of the values of p are close to 3, suggesting that the rate-limiting process for the creep of olivine is grain boundary diffusion (e.g., Langdon, 2006). Our results are consistent with reported values of p ( ¼3) in the forsterite– enstatite–aqueous fluid system (McDonnell et al., 2000). Pressure is plotted against the steady-state creep strength in Fig. 6f. The creep strength increases with pressure and is strongly affected by water content. Creep strength of the melt-bearing samples is factors of 2–4 lower than the creep strength of olivine calculated from the flow law for the power-law dislocation creep of hydrous olivine (Karato and Jung, 2003) in the case of the same water content. All of the data of melt-bearing samples (TO-04, 05, 10, 11, 12, and 16) are well fitted by Eq. (1) with r¼1 and p¼3 (Fig. 6g), and then we obtained a constant activation volume as Vn ¼21.8–24.0 cm3/mol (Table 2). Dependency of creep strength (the activation volume effects are corrected) on water fugacity is shown in Fig. 6 h. The obtained values of r are similar to the theoretical values of r (¼1). In summary, the olivine flow law in hydrous melt-bearing dunite is expressed as the following formula (stress, water fugacity, and pressure in MPa):

e_ ¼ 1014:8 7 0:3

s2:1 7 0:4 G3

1

f H2 O

! 3297 44 kJ=molþ P  23:0 7 4:5  106 m3 =mol exp  RT ð3Þ n

3.3.1. Melt-bearing dunite The strain rate is plotted against the steady-state creep strength in Fig. 6a (see Section 3.3.2 about Fig. 6b), and the steady-state creep strength is plotted against inverse temperature in Fig. 6c. The logarithmic values of stress linearly increase with increasing strain rate at a constant temperature and with increasing inverse temperature at a constant strain rate. Using the linear least-square fitting method, we obtained the values of n as 1.7–2.5 from the

n

In Eq. (3), averaged values of A, n, E , and V are used, because values of those parameters are different among the diffraction peaks used for the measurement of stress values (Table 2). 3.3.2. Melt-free dunite Dependency of the steady-state creep strength of melt-free dunite (TO-13) is shown in Fig. 6b. Kinked log e_  log s lines are observed in Fig. 6b, suggesting a transition of the deformation

66

T. Ohuchi et al. / Earth and Planetary Science Letters 335–336 (2012) 59–71

0.5

Pressure (GPa)

Differential stress (GPa)

0.5 4.3E-5 s-1 0.4

3.8E-5 s-1 0.4

1.6E-5 s-1

0.3

0.3

0.2

0.2

0.1

0.1

0

0

-0.1 3.5

-0.1 6.0

3.0

5.5

2.5 2.0

TO-04 1490 K 0

0.1

0.2

0.3

Differential stress (GPa)

0.4

Pressure (GPa)

9.5E-5 s-1

TO-05 1490 K

5.0 4.5

0

0.1

0.2

0.3

2.7E-5 s-1 1.3E-5 s-1

0.3

1370 K 3.0E-5 s-1

0.4

1320 K 3.3E-5 s-1

0.3 0.2 0.2 0.1

1270 K 4.0E-5 s-1

0.1

0 2.0

0 2.5

2.0

1.5

1.0

TO-10 1370 K 0

0.1

0.2

0.9

0.6

0.4

1.5 0

TO-11 0.1

0.2

0.3

0.4

0.5

0.6

0.3

1370 K 5.7E-5 s-1

0.8 0.7

0.3

8.2E-5 s-1

1.7E-5 s-1

1420 K 4.0E-5 s-1

0.2

0.5 0.1

0.4

: (021) : (101) : (130) : (131) : (112)

0.3 1320 K 3.6E-5 s-1

0.2

0

0.1

Pressure (GPa)

0.4

0.5

5.8E-5 s-1

Differential stress (GPa)

1.3E-5 s-1

-0.1

0 4.0

4.5

TO-16 1370 K

3.5 4.0 3.0 TO-12 2.5 0

0.1

0.2

0.3

0.4

Strain

3.5

0

0.1

0.2

0.3

0.4

0.5

Strain

Fig. 4. Stress–strain records for melt-bearing dunite samples: (a) TO-04, (b) TO-05, (c) TO-10, (d) TO-11, (e) TO-12, (f) TO-16. The stress values were obtained from the five diffraction peaks of olivine (cross: 0 2 1, circle: 1 0 1, diamond: 1 3 0, square: 1 3 1, triangle: 1 1 2). The hatched areas represent the steady-state in each deformation step. The change of pressure during the sample deformation is also shown.

mechanism of olivine induced by stress. The values of n  2 under low-stress conditions (s o500 MPa) and  9 under high-stress conditions ( Z500 MPa) are inferred from the slopes of log e_ log s lines. The former value n (  2) is consistent with the experimental results on melt-bearing dunite (Fig. 6a). The latter value of n ( 9) is not consistent with models for power-law creep (e.g., Frost and Ashby, 1982), suggesting that the deformation of olivine was controlled by the Peierls mechanism under highstress conditions (Evans and Goetze, 1979).

In order to evaluate the effect of melt on the creep strength of dunite, steady-state creep strength of melt-free dunite is compared with that of melt-bearing dunite in Fig. 6f. Data are normalized to the conditions of 1370 K, strain rate of 10  5 s  1, and grain size of 4 mm under the assumption that the deformation mechanism of olivine in melt-free dunite is diffusion-accommodated GBS (note that this assumption is based on the value of n ( 2) shown in Fig. 6b). The normalized creep strength of melt-free dunite (in the range of 900–1200 MPa) is  5 times of that of melt-bearing dunite at

T. Ohuchi et al. / Earth and Planetary Science Letters 335–336 (2012) 59–71

0.9 -1

0.7E-5 s

0.8

Differential stress (GPa)

0.7 0.6 0.5 0.4 0.3 0.2 2.0E-5 s-1

0.1

6.5E-5 s-1

0

Pressure (GPa)

4.0

phase would promote diffusion-accommodated GBS. It has been reported that diffusion of cations along the interconnected aqueous fluid phase (and wet grain boundaries) in fluid-bearing dunite is 4–5 orders of magnitude higher than the grain boundary diffusivity in ‘‘dry’’ dunite (Ohuchi et al., 2010b). Considering that the dihedral angle between olivine and fluid is less than 601 (i.e., threshold angle of the interconnection) under the present study’s experimental conditions (aqueous fluid: 40–501 at 3–5 GPa and 1273 K reported by Mibe et al., 1999; hydrous melt: 18–461 at 1–5 GPa and 1473 K reported by Yoshino et al., 2007), enhanced diffusion along the interconnected fluid/melt phase would contribute to the diffusion-accommodated GBS of olivine. Cooper and Kohlstedt (1986) theoretically showed that the effect of melt fraction on the creep strength of dunite in the Coble creep regime is expressed by the following equation:   e_ olmelt Dd 4 ¼ 1 ð4Þ d e_ ol where d is a characteristic grain boundary diffusion distance and Dd is the portion of this characteristic diffusion distance removed due to the presence of melt at triple junctions. The ratio Dd/d is a function of the olivine–melt dihedral angle (y) and melt fraction (f) as shown below (Cooper et al., 1989):

3.5

TO-13 (Melt-free dunite) 1370 K

3.0

2.5

67

0

0.1

0.2

0.3

Strain Fig. 5. Stress–strain records for a melt-free dunite sample (TO-13). The stress values were obtained from the five diffraction peaks of olivine. The symbols represent the same meanings as in Fig. 4. The hatched areas represent the steadystate in each deformation step. The change of pressure during sample deformation is also shown.

3 GPa. The contrast of creep strength between melt-free and meltbearing dunites would be decreased to  2 times if deformation of olivine in melt-free dunite was controlled by the Peierls mechanism or power-law dislocation creep under high-stress conditions.

4. Discussion 4.1. Comparison to other experiments and deformation mechanisms McDonnell et al. (2000) conducted deformation experiments on the forsterite–enstatite–aqueous fluid system (porosity¼ 0.9–3.4 vol%) at 0.6 GPa and 1170–1270 K, and they reported the flow law parameters of forsterite as n ¼1.7, Hn ( ¼En þPVn)¼ 160–450 kJ/mol, and p¼3. These reported values are consistent with our results. McDonnell et al. (2000) discussed that the dominant creep mechanism of forsterite was a GBS-dominated deformation mechanism. Deformation of olivine by dislocationaccommodated GBS is observed in the olivine–melt system (with a fraction of melt 44 vol%: Hirth and Kohlstedt, 1995a). Superplasticity has been reported in the melt-free systems. Hiraga et al. (2010a) performed deformation experiments on the forsterite þ10 vol% periclase (or forsteriteþ 25 vol% enstatiteþ5 vol% diopside) at P ¼0.1 MPa and T ¼1623–1723 K, and concluded that the dominant creep mechanism was GBS based on the flow law parameters and microstructures. Presence of a fluid phase in rocks would promote GBS of grains because of rotation (and sliding) of grains promoted by the reduction in the solid–solid grain boundary area. Enhanced diffusion via interconnected fluid

Dd d

¼ 2:67

pffiffiffi !1=2      1 þcos y p y 1=2 y 2 pffiffiffi sin y 303  f sin 303  90 2 2 9 3

ð5Þ Hirth and Kohlstedt (1995b) experimentally showed that the creep strength of partially molten dunite can be predicted by Eqs. (4) and (5). In the case of small melt fraction ( o15 vol%), the relationship between the creep strength of dunite and melt fraction is approximately expressed as follows: (Kelemen et al., 1997; Mei et al., 2002):

e_ olmelt ¼ expðafÞ e_ ol

ð6Þ

where a is a constant. Combining Eqs. (4) and (6), a is expressed as a function of y and f:   4 Dd ð7Þ a ¼  ln 1 d f The values of a have been reported as 26 (in the case of diffusion creep) and 31 (dislocation creep) in the olivine–basalt system under wet conditions (at 0.3 GPa: Mei et al., 2002). Based on Eqs. (1), (6), and our experimental data obtained at 3.2–3.9 GPa (TO-12, 13, and 16), we evaluated the value of a for olivine in hydrous-melt-bearing dunite (Fig. S6). The value of a was obtained to be in the range of 150–230. The obtained value is 5–7 times higher than that reported by Mei et al. (2002), showing that the creep strength of dunite is efficiently reduced by the hydrous melt. Substituting the values of olivine–fluid dihedral angles under the present study’s experimental conditions (18–501: Mibe et al., 1999, Yoshino et al., 2007) into Eq. (7), theoretical value of a is obtained to be 32–41 in the case of f ¼0.02. This lower estimation of a in the theoretical calculation (i.e., 4–7 times smaller than the experimentally obtained value) would result from the limitation of the model shown in Eqs. (4) and (5), because GBS is not considered in the model. Another explanation for the cause of lower estimation of a is the effect of spatial distribution of melt. In the theoretical model expressed as Eqs. (4)–(7), homogeneous melt distribution is assumed. Heterogeneous melt distribution (Figs. 2 and S3) may contribute to weakening of melt-bearing dunite. Langdon (1994) theoretically showed that the stress exponent, n, for dislocation-accommodated GBS is equal to 2 and 3 in the case of G o l (subgrain size) and G 4 l, respectively. Recently,

68

T. Ohuchi et al. / Earth and Planetary Science Letters 335–336 (2012) 59–71

6.5 -4.1

-4.5 -4.7

TO-10 1.6-1.7 GPa 1370 K

-4.9

n=2

Ln (σ1 - σ3) (MPa)

. Log10 ε (s-1)

-4.3

3 GPa, 1370 K, 1E-5 s-1 r = 1, 500 ppm H/Si

6.0

TO-16 3.9-4.3 GPa 1370 K

5.5

p=3

5.0 : (021) : (101) : (130) : (131) : (112)

4.5

1

2.0

2.2

2.4

4.0 1.2

2.6

1.4

1.6

Log10 (σ1 - σ3) (MPa) 00

6

30

-4.1 TO-13 (melt-free dunite) 3.6-3.7 GPa

00

00

10

10

-4.9 n=2

H/ Si )

-4.7

4

3

n

2

1370 K, 1E-5 s-1, 4 μm 227-3266 ppm H/Si

Di

slo

ca

tio

-5.1

Melt-free (TO-13)

pp m

n=9

H/S

GB

Dif

(2 00

-4.5

0 S (2

cr ee p

1370 K

i)

pm

0p

5

Pressure (GPa)

. Log10 ε (s-1)

-4.3

1.8

Ln G (μm) 00

1.8

30

-5.1 1.6

1

-5.3 2.4

2.5

2.6

2.7

2.8

2.9

0

3.0

200

400

600

800

1000

1200

σ1 - σ3 (MPa)

Log10 (σ1 - σ3) (MPa) 12

Log10 (σ1 - σ3) (MPa)

2.6

Ln σ·fH2Or/n (MPa(1+r/n))

TO-12 3.2-3.6 GPa 4.0-5.7E-5 s-1

2.8

2.4 2.2 TO-11 2.2-2.3 GPa 3.0-4.0E-5 s-1

2.0

1370K, 1E-5 s-1

11

4 μm, p = 3 r=1

10

9 V* = 21.8-24.0 cm3/mol 8

7

1.8 6.9

7.1

7.3

7.5

7.7

1

7.9

2

3

10000/T (K-1)

4

5

6

Pressure (GPa) Ln σ·exp(-PV*/nRT) (MPa)

6.0

Ln (σ1 - σ3) (MPa)

5.5 TO-12,16 3.6-3.9 GPa

5.0 4.5 4.0

TO-10,11 1.7-2.2 GPa r=1 0.7

3.5

-1

1E-5 s , 1370 K

3.5

2.5

r=1

1.5 1370 K 1E-5 s-1

0.5

4 μm, p = 3 23.0 cm3/mol

3.7-4.0 μm -0.5

3.0 6

7

8

9

10

11

12

Ln fH2O (MPa)

13

6

7

8

9

10

11

12

13

Ln fH2O (MPa)

Fig. 6. (a) Strain rate dependences of steady-state creep strength (hereafter, strength) of melt-bearing dunite (TO-10 and 16: see also Fig. S5). (b) Strain rate dependence of strength of melt-free dunite (TO-13). (c) Strength of melt-bearing dunite plotted against inverse temperatures (TO-11 and 12). (d) Water fugacity sensitivity of the strength of melt-bearing dunite at 1.7–2.2 GPa (from TO-10 and 11) and at 3.6–3.9 GPa (from TO-12 and 16) (data are normalized to a strain rate of 10  5 s  1 and a temperature of 1370 K). (e) Grain size dependence of the strength of melt-bearing dunite (data are normalized to the conditions of 3 GPa, 1370 K, water content of 500 ppm H/Si, and a strain rate of 1  10  5 s  1). (f) Pressure versus strength relationship for melt-bearing dunite (solid symbols) and melt-free dunite (open symbols). Data are normalized to the conditions of 1370 K, a strain rate of 10  5 s  1, and grain size of 4 mm in (f). Solid and dashed curves in (f) represent the strength calculated from Eq. (3) (DifGBS) and the flow law for power-law dislocation creep of olivine reported by Karato and Jung (2003), respectively (calculated for the cases of COH ¼ 200, 1000, and 3000 ppm H/Si). (g, h) r=n Dependency of the strength of melt-bearing dunite on (g) pressure and (h) water fugacity in the case of r¼ 1. The strength is corrected (g) for water fugacity effects (i.e., f H2 O ) and (h) for the activation volume effects (i.e., exp( PVn/nRT)). Data in (g) and (h) are normalized to the conditions of 1370 K, a strain rate of 10  5 s  1 and grain size of 4 mm. The black dashed line in (h) represents the best-fit line in the case of r¼ 1. The symbols represent the same meanings as in Fig. 4. The colored dashed lines in the figures represent the best-fits defined as Eq. (1). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Wang et al. (2010) conducted deformation experiments on finegrained partially molten dunite at 0.2–0.4 GPa and 1473 K, and they reported the GSS creep of olivine characterized by n ¼3.4 and p ¼2.0. Based on the theory by Langdon (1994), they concluded

that the dominant creep mechanism was dislocation-accommodated GBS. In our experiments, the subgrain size (0.5–3 mm) is smaller than the mean grain size (3.7–5.8 mm) in melt-bearing dunite samples. Thus, our experimental conditions correspond to

T. Ohuchi et al. / Earth and Planetary Science Letters 335–336 (2012) 59–71

4

Table 2 Parameters for the flow laws of olivine in hydrous melt-bearing dunite.

Average (0 2 1) (1 0 1) (1 3 0) (1 3 1) (1 1 2) a b c

c

1 1 1 1 1 1

p

3 3 3 3 3 3

b

n

log10 A n (mp s  1 MPa  n  r)

E (kJ/mol)

V ( cm3/mol)

 14.8 70.3  15.0 70.3  14.8 70.3  14.7 70.3  14.6 70.3  14.7 70.3

329 744 326 753 250 727 448 753 287 741 336 744

23.0 7 4.5 21.8 7 3.4 22.8 7 5.0 23.6 7 5.0 24.0 7 4.8 23.0 7 4.3

2.1 70.4 2.0 70.3 2.0 70.4 2.4 70.5 1.7 70.4 2.5 70.2

Peierls mechanism 3

n

Log10 (s1 - s3) (MPa)

Diffraction peak r

a

Based on Mei and Kohlstedt (2000a) and our experimental results. Based on McDonnell et al. (2000) and our experimental results. Averaged values of the parameters obtained from the five diffraction peaks.

2

DifGBS Dislocation creep

1 Shear zone

0

(Diffusion creep) -1 -2

970 K -3

-2

-1

0

1

2

4 Peierls mechanism 3 Log10 (s1 - s3) (MPa)

the case of the theoretical value of n¼ 3 for dislocation-accommodated GBS. Therefore, dislocation-accommodated GBS cannot account for the obtained value of n ( ¼2.1) in this study. The averaged value of activation energy (En ¼329 kJ/mol), which is similar to the activation energy for diffusion creep of hydrous olivine (295 kJ/mol: Mei and Kohlstedt, 2000a), suggests that the dominant creep mechanism of olivine was diffusion-accommodated GBS in our experiments. Developments of olivine CPO and flattening of olivine grains were hardly observed even after 33–55% shortening of samples in our experiments (Fig. 3 and Table 1), suggesting a strong contribution of GBS and diffusion to deformation of samples.

69

DifGBS

2

Dislocation creep

1

: 1 GPa, 800 ppm : 5 GPa, 800 ppm : 5 GPa, 4000 ppm

Shear zone

0

(Diffusion creep) -1

4.2. Creep strength of fluid-bearing peridotite mylonites in the upper mantle: implications for the initiation of subduction

-2

In the present study, we demonstrated that diffusion-accommodated GBS dominates the deformation of olivine in fluidbearing dunite under upper mantle conditions. Previous studies pointed out that other creep mechanisms such as power-law dislocation creep and diffusion creep control the viscosity of Earth’s upper mantle (e.g., Karato et al., 1986). Using the olivine flow laws reported by the present study and previous studies (‘‘wet’’ dislocation creep: Karato and Jung, 2003; ‘‘wet’’ diffusion creep: Hirth and Kohlstedt, 2003; Mei and Kohlstedt, 2000a; the Peierls mechanism: Evans and Goetze, 1979; Kawazoe et al., 2009), we calculated deformation mechanism maps as a function of stress and grain size under mantle wedge conditions (Fig. 7a and b). Based on the discussions in Section S2 (in Supplementary data), we assumed V ndif f ¼ 21 cm3 =mol (i.e., the lower-limit of V ndif f under wet conditions) in Fig. 7. Note that the boundary between diffusion creep and diffusion-accommodated GBS shifts to the low-stress side if V ndif f is larger than 21 cm3/mol. Diffusion creep of olivine in the fluid-bearing dunite system has not been reported in previous experimental studies. McDonnell et al. (1999) showed that the dominant deformation mechanism of forsterite in aqueous fluid-bearing dunite was superplasticity even at low stress levels (9–81 MPa at 0.6 GPa and 1123–1273 K), suggesting that the regime of diffusion creep is limited to a very low stress level (or does not exist) in the fluid-bearing dunite system. In Fig. 7a and b, effects of pressure and water content on the transitions of the creep mechanism are small. The region of diffusion-accommodated GBS is distributed in the area of finegrain ( o0.1 mm) and high-stress (410 MPa) conditions. The diffusion-accommodated GBS field expands with decrease in temperature. Therefore, diffusion-accommodated GBS would be the dominant creep mechanism of olivine in fluid-bearing fine-grained peridotites under the conditions of low-temperature and high-stress (i.e., mylonites in shear zones). In fact, many

35

1270 K -3

-2

-1

0

DifGBS

1

2

Dislocation creep

30

973 K

Log10 h (Pa·s)

1573 K (80 ppm H/Si)

1173

25

1373

20

1573 Initiation of subduction 0.01 MPa

15

800 ppm H/Si 10

-4

-3

-2

-1 0 Log10 G (mm)

1

2

Fig. 7. Deformation mechanism maps for olivine in the hydrous melt-bearing dunite on the axes of differential stress versus grain size (G) at pressures of 1 and 5 GPa and temperatures of (a) 970 K and (b) 1270 K. Water content in olivine (COH) was fixed to 800 or 4000 ppm H/Si for the calculation of the maps. The solid lines represent the boundaries between deformation fields (DifGBS: diffusion-accommodated GBS). Because diffusion creep of olivine has not been reported in fluidbearing dunite, the diffusion creep dominant region is hypothetically shown by dashed lines. The shaded area in (a) and (b) represents the conditions observed in natural peridotite shear zones (e.g., Jin et al., 1998; Warren and Hirth, 2006). (c) Viscosity of olivine plotted against grain size in the case that the dominant deformation mechanism is diffusion-accommodated GBS or power-law dislocation creep. Eq. (3) was used for the calculation of viscosity of olivine controlled by diffusion-accommodated GBS. Calculations for thin solid lines were made under the conditions of 3 GPa, 973–1573 K, differential stress of 0.01 MPa, and water content in olivine COH ¼ 800 ppm H/Si. The dot-dashed line in (c) represents the viscosity of the asthenosphere having water content of COH ¼ 80 ppm H/Si at 3 GPa and 1573 K. The initiation of subduction is possible in the green hatched area (o1020 Pa s). The thick dashed line in (c) represents the boundary between two deformation fields.

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petrological observations have shown that GSS creep processes promote strain localization in fine-grained mylonites in shear zones (e.g., Newman et al., 1999; Warren and Hirth, 2006). Grain size in shear zones is maintained to be small (orders of 1–100 mm) by the combined effects of grain size reduction and second phase pinning (e.g., Warren and Hirth, 2006). Recent grain growth experiments on forsterite–pyroxene bimineralic rocks have shown that the grain growth rate of the dominant phase is drastically reduced by the presence of second-phase particles (e.g., Ohuchi and Nakamura, 2007a,b; Hiraga et al., 2010b), supporting the idea of ‘‘second phase pinning’’ proposed by Warren and Hirth (2006). Shear localization caused by GSS creep is expected to play an important role in the initiation of the subduction of the oceanic lithosphere. Regenauer-Lieb et al. (2001) theoretically showed that a combination of the water weakening effect on olivine and thermal–mechanical feedback can generate a narrow low-viscosity shear zone which is needed for the initiation of subduction. They also showed that the critical value of the viscosity in the shear zone for the initiation of subduction is 1020 Pa s, which is one order of magnitude lower than that of the model asthenosphere (i.e., 1021 Pa s). In their model (Regenauer-Lieb et al., 2001), they assumed the power-law dislocation creep of ‘‘wet’’ olivine reported by Mei and Kohlstedt (2000b) for rheology in the shear zone. In order to evaluate the effect of diffusion-accommodated GBS on the initiation of subduction, we calculated the upper mantle viscosity under mantle wedge conditions (Fig. 7c). In the calculation for Fig. 7c, we used the ‘‘updated’’ olivine flow law for the power-law dislocation creep under wet conditions reported by Karato and Jung (2003). We assumed a reference stress value of s ¼0.01 MPa so as to obtain the viscosity of the asthenosphere (COH ¼80 ppm H/Si: the same as in Regenauer-Lieb et al., 2001) as 1021 Pa s. Based on Regenauer-Lieb et al. (2001), water content in the shear zone was fixed to 800 ppm H/Si. Viscosity of olivine is plotted against grain size in Fig. 7c. In Fig. 7c, we considered two deformation mechanisms (diffusionaccommodated GBS and dislocation creep). High temperature (T41573 K) is required for ‘‘wet’’ olivine to achieve threshold viscosity (i.e., 1020 Pa s) if deformation is controlled by dislocation creep. In contrast, viscosity in the shear zone (G ¼1–100 mm) can be lower than 1020 Pa s at lower temperatures (TZ973 K) in the case of diffusion-accommodated GBS. Therefore, subduction of slabs would be easily initiated if the creep mechanism of olivine is dominated by diffusion-accommodated GBS in the shear zone. Diffusion-accommodated GBS of olivine would be induced by the addition of fluids to the shear zones. In Fig. 7c, diffusion creep of olivine was not considered. If we use the flow law for diffusion creep instead of that for diffusion-accommodated GBS in Fig. 7c, viscosity in the shear zone would be lower than 1020 Pa s at much lower temperatures. The thermal–mechanical feedback due to shear heating, which is assumed in the theoretical model by Regenauer-Lieb et al. (2001), would not be critical for the initiation of subduction if we consider the olivine flow controlled by GSS creep such as diffusion-accommodated GBS. In various theoretical models, it has been proposed that the shear localization is caused not only by shear heating (e.g., Balachandar et al., 1995) but also by other mechanisms such as grain size reduction (e.g., Braun. et al., 1999) and a combination of void generation and microcracking (i.e., ‘‘damage’’ model: Bercovici, 2003). Grain size reduction is an effective mechanism for the shear localization in the case of GBS, and grain size reduction in shear zones is caused by the fluid-rock reaction (e.g., Vissers et al., 1995; Dijkstra et al., 2002). Once grain size is reduced and then the dominant creep mechanism is switched from power-law dislocation creep to diffusion-accommodated GBS (or other GSS creep mechanisms), the shear

localization would be maintained since small grain size is maintained by second phase pinning (e.g., Warren and Hirth, 2006).

Acknowledgments T.O. conceived the idea, conducted the experiments, and wrote the manuscript. All authors contributed to the discussion and development of experimental techniques. We are grateful to Y. Seto for his support with the analysis of X-ray diffraction patterns, and M. Nishi for his assistance on the experiments. Official reviews by two anonymous reviewers improved the manuscript. This study has been conducted under the approval of the Photon Factory Program Advisory Committee (Proposal No. 2010G136). This study was supported by the Global COE program of Ehime University ‘‘Deep Earth Mineralogy’’, the Sasakawa Scientific Research Grant from the Japan Science Society, and the Grantin-Aid for Scientific Research (Nos. 22340161 and 23740393).

Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.epsl.2012.04.032.

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