Flow behavior and microstructures of hydrous olivine aggregates at upper mantle pressures and temperatures

Abstract

Deformation experiments on olivine aggregates were performed under hydrous conditions using a deformation-DIA apparatus combined with synchrotron in situ X-ray observations at pressures of 1.5–9.8 GPa, temperatures of 1223–1800 K, and strain rates ranging from 0.8 × 10−5 to 7.5 × 10−5 s−1. The pressure and strain rate dependencies of the plasticity of hydrous olivine may be described by an activation volume of 17 ± 6 cm3 mol−1 and a stress exponent of 3.2 ± 0.6 at temperatures of 1323–1423 K. A comparison between previous data sets and our results at a normalized temperature and a strain rate showed that the creep strength of hydrous olivine deformed at 1323–1423 K is much weaker than that for the dislocation creep of water-saturated olivine and is similar to that for diffusional creep and dislocation-accommodated grain boundary sliding, while dislocation microstructures showing the [001] slip or the [001](100) slip system were developed. At temperatures of 1633–1800 K, a much stronger pressure effect on creep strength was observed for olivine with an activation volume of 27 ± 7 cm3 mol−1 assuming a stress exponent of 3.5, water fugacity exponent of 1.2, and activation energy of 520 kJ mol−1 (i.e., power-law dislocation creep of hydrous olivine). Because of the weak pressure dependence of the rheology of hydrous olivine at lower temperatures, water weakening of olivine could be effective in the deeper and colder part of Earth’s upper mantle.

Introduction

The creep behavior of hydrous and anhydrous olivine is important for the evaluation of the dynamics of Earth’s upper mantle, because the water content in a typical MORB source is estimated to be between 800 and 1500 H/106Si on the Paterson scale (Hirschmann 2006; Hirth and Kohlstedt 1996). The plastic flow of olivine is known to be described in terms of a flow law of the form:

$$\dot{\varepsilon } = A\frac{{\sigma^{n} }}{{G^{p} }}f^{r}_{{{\text{H}}_{2} {\text{O}}}} \exp \left( { - \frac{{E^{*} + PV^{*} }}{RT}} \right),$$
(1)

where \(\dot{\varepsilon }\) is the strain rate, A is a material-dependent parameter, σ is the differential stress, n is the stress exponent, G is the grain size, p is the grain size exponent, \(f_{{{\text{H}}_{2} {\text{O}}}}\) is the water fugacity, r is the water fugacity exponent, E * is the activation energy, P is the pressure, V * is the activation volume, R is the gas constant, and T is the temperature. Although a monotonic dependence of logarithmic creep strength on pressure is expected under anhydrous conditions (i.e., \(f_{{{\text{H}}_{2} {\text{O}}}}\) = 0), the effects of pressure on creep stress are more complicated under hydrous conditions. This is because the water fugacity increases with increasing pressure (at a constant water content), but the term \(\exp [ - (E^{*} + PV^{*} )/RT]\) decreases with increasing pressure (e.g., Karato and Jung 2003).

Under hydrous conditions, hydrous defects are anticipated to replace iron and/or metal vacancies as majority point defects (Karato 1989a). Previous studies about deformation and electrical conductivity data on olivine have proposed the charge-neutrality condition \([{\text{H}}_{\text{Me}}^{\prime } ] = [{\text{Fe}}_{\text{Me}}^{ \cdot } ]\) or \([({\text{OH}})^{\prime}_{\text{I}} ] = [{\text{Fe}}_{\text{Me}}^{ \cdot } ]\) for iron-bearing olivine (Karato 1989a; Mei and Kohlstedt 2000a; Wang et al. 2006). Mei and Kohlstedt (2000a, b) discussed that the concentration of silicon interstitials and, thus, the rates of diffusion creep and/or dislocation climb increase systematically with increasing water fugacity as a consequence of the charge-neutrality condition. In contrast to the earlier studies, Faul et al. (2016) showed that incorporation of hydrogen to extrinsic defects formed by impurities (e.g., titanium) also plays an important role for water weakening of olivine. The flow behavior of hydrous olivine at pressures lower than 0.5 GPa has been well investigated for power-law dislocation creep (Mei and Kohlstedt 2000b; Tasaka et al. 2015), diffusion creep (Mei and Kohlstedt 2000a), and diffusion-accommodated grain boundary sliding (diffGBS) (McDonnell et al. 1999, 2000). Although water solubility in olivine is proportional to 0.9th power of water fugacity at pressures of <0.5 GPa, water solubility in olivine is controlled by both pressure and water fugacity at higher pressures (Kohlstedt et al. 1996). The relationship between dissolved water content in olivine and water fugacity at upper mantle pressure is expressed in the following equation:

$$C_{\text{OH}} = Bf_{{{\text{H}}_{2} {\text{O}}}} \exp \left( { - \frac{{\Delta H^{{1{\text{bar}}}} + \Delta V^{\text{solid}} P}}{RT}} \right),$$
(2)

where B is a constant, ΔH 1bar is the reaction enthalpy at 1 bar, and ΔV solid is the volume change of the solids (Keppler and Bolfan-Casanova 2006; Kohlstedt et al. 1996). Equations (1) and (2) suggest that water weakening of olivine is significant at upper mantle pressures.

The pressure effects on hydrous olivine rheology have been previously investigated using Griggs rigs and deformation-DIA apparatuses at upper mantle pressures, and many deformation mechanisms such as power-law dislocation creep (Bollinger et al. 2014; Karato and Jung 2003), low-temperature plasticity (i.e., the Peierls mechanism) (Katayama and Karato 2008), diffGBS (Ohuchi et al. 2012b), and dislocation-accommodated grain boundary sliding (disGBS) (Ohuchi et al. 2015) have been identified at upper mantle pressures. Crystallographic preferred orientation of hydrous olivine has also been investigated at a wide range of pressures (Couvy et al. 2004; Demouchy et al. 2012; Jung and Karato 2001a; Jung et al. 2006; Kaminski 2002; Katayama et al. 2004; Ohuchi and Irifune 2013, 2014; Ohuchi et al. 2012a), and it has been shown that olivine fabric changes as a function of dissolved water content in olivine.

However, the pressure effect on the creep strength of hydrous olivine (i.e., V *) has been a controversial issue for many years. The water weakening of olivine has been investigated by earlier studies in the dislocation-creep regime (Chopra and Paterson 1984; Jung and Karato 2001b; Karato et al. 1986; Mei and Kohlstedt 2000b). Hirth and Kohlstedt (2003) estimated the V * for hydrous olivine as 22 ± 11 cm3 mol−1 from the fit to the global data set reported by earlier studies. Using the mechanical data of hydrous olivine obtained at 0.3–2 GPa, Karato and Jung (2003) estimated the value of V * of the power-law dislocation creep as 24 cm3 mol−1. This value is consistent with the estimation by Hirth and Kohlstedt (2003). However, it is unclear whether steady-state creep strength was used for the evaluation of olivine V * in Karato and Jung (2003) because the olivine dislocation density piezometer was applied to estimate stresses (i.e., no stress–strain curves were obtained). Girard et al. (2013) conducted deformation experiments on single crystal olivine at pressures ranging from 4 to 7 GPa and reported the V * as 17.3 cm3 mol−1 (in the case of r = 1.2) for the [100](010) slip system. Recently, Bollinger et al. (2014) examined the pressure effect on hydrous olivine aggregate rheology at pressures up to 8.1 GPa under the assumption that strain rate is independent of water fugacity. They reported the apparent activation energy (hereafter, \(V_{\text{app}}^{*}\)) of the power-law dislocation creep of hydrous olivine as ~13 cm3 mol−1 based on the global dataset for hydrous olivine (dissolved water content C OH >200 H/106Si). Bollinger et al. (2015) also reported similar \(V_{\text{app}}^{*}\) (~12 cm3 mol−1) for hydrous forsterite. To compare the \(V_{\text{app}}^{*}\) with V *, we need to consider the pressure effect on water solubility in olivine. Substituting Eq. (2) into Eq. (1), we obtain the following relationship at a constant C OH:

$$V_{\text{app}}^{*} = V^{*} - r\Delta V^{\text{solid}} .$$
(3)

Using the reported values for r (=1.2: Karato and Jung 2003) and ΔV solid (~10 cm3 mol−1: Kohlstedt et al. 1996), the difference between V * and \(V_{\text{app}}^{*}\) is obtained to be ~12 cm3 mol−1 and thus the V * in the experiments by Bollinger et al. (2014) corresponds to ~25 cm3 mol−1. Therefore, we consider that Bollinger et al. (2014) is consistent with Hirth and Kohlstedt (2003) and Karato and Jung (2003). Korenaga and Karato (2008) re-analyzed published experimental data on the rheological data of hydrous olivine aggregates using a Markov chain Monte Carlo method, and they reported the V * of the dislocation creep of hydrous olivine as 4 ± 3 cm3 mol−1. This value is much lower than the other reported values.

The discrepancy of the V * for anhydrous olivine among previous studies has also been serious. The reported values of V * for anhydrous olivine range from 13 to 23 cm3 mol−1 (Karato and Jung 2003; Kawazoe et al. 2009; Ross et al. 1979; Wang 2002). The dispersion of the reported value may be due to two reasons: (1) misinterpretation of the dominant deformation mechanism (e.g., confusion between power-law dislocation creep and disGBS) and (2) an insufficient pressure range for the experimental evaluation of V *. In fact, Durham et al. (2009) reported the V * as 9.5 ± 7.0 cm3 mol−1 for anhydrous olivine and they discussed that such a low V * value may result from a significant contribution of disGBS to the sample deformation in their experiments. The range of reported V * values expands if results on nominally anhydrous olivine are taken into account (0 ± 5 cm3 mol−1: Li et al. 2006; Karato and Rubie 1997: 14 ± 1 cm3 mol−1; 27 cm3 mol−1: Green and Borch 1987; Borch and Green 1989). The large scatter of V * for nominally anhydrous olivine implies that the creep strength of olivine is very sensitive to water fugacity and, thus, the V * for hydrous olivine needs to be carefully evaluated.

Even though hydrous olivine rheology has been investigated by many previous studies, the range of water content examined by previous studies has been mostly limited to less than 3000 H/106Si. In the deep upper mantle, water content in regionally water-rich regions has been estimated to be 3000–10,000 H/106Si (Lizarralde et al. 1995; van der Meijde et al. 2003; Yoshino et al. 2006). To constrain the dominant deformation mechanisms in the actual deep upper mantle, therefore, we further investigate the flow behavior of olivine aggregates containing quite high concentration of water up to ~6300 H/106Si at a wide range of upper mantle pressures and temperatures. Two temperature ranges (i.e., 1223–1423 and 1633–1800 K) were chosen for the experimentals because grain-size-sensitive creep and power-law dislocation creep are presumed to dominate the deformation of olivine at the lower and higher temperature ranges, respectively (Kawazoe et al. 2009; Ohuchi et al. 2015). Experiments were not conducted at the intermediate temperatures (i.e., 1423–1633 K) due to a possibility of contribution of both creep mechanisms to the mechanical data (Nishihara et al. 2014).

Experimental procedure

Starting samples and sample preparation

The starting material for sintered olivine aggregates was prepared from powdered San Carlos olivine (Fo90: MgO 54.1 wt.%, SiO2 40.9 wt.%, FeO 5.0 wt.%). The fine-grained powder was placed into a nickel capsule with an inner diameter of 8 mm and a length of 11 mm and was hot-pressed at 4.0 GPa and 1373 K for 1.5 h using a Kawai-type multi-anvil high-pressure apparatus at Ehime University. The entire cell assembly for the synthesis of olivine aggregates was not dried before the sintering experiment to provide moisture to the powders. The water content in the hot-pressed olivine aggregate was ~4070 H/106Si and the average grain size of olivine was 63 µm (Ohuchi et al. 2015). Therefore, these values correspond to the initial water content and grain size of the olivine samples used for the deformation experiments. Furthermore, the initial water content in the olivine aggregate was ~1300 H/106Si and the initial grain size was 34 µm in the M975 run. The sintered olivine aggregates were core-drilled with a diameter of 0.5 or 1.2 mm and a length of 0.6, 1.2 or 1.5 mm.

Encapsulation: palladium-silver capsules for the olivine + aqueous fluid system at 1223–1423 K

Palladium-silver (Pd75%–Ag25%) capsules and lids were used for many of the experiments in the 6.5-4 and 7-5 type cell assemblies (Fig. 1) to keep water-saturated conditions during the experiment (Table 1). Palladium-silver capsules were fabricated from palladium-silver tubes with an outer diameter of 1.4 mm and a wall thickness of 0.1 mm. After one end of a palladium-silver tube was welded shut and flattened, a core-drilled olivine aggregate with diameter of 1.2 mm (length of 1.2 or 1.5 mm for the 6.5-4 and 7-5 type cell assemblies, respectively) and two pistons made of tungsten or single-crystal diamond (diameter of 1.2 mm and thickness of 0.5 mm) were placed into the capsule. The cored olivine aggregate and two pistons were separated by two platinum strain markers, with a thickness of 20 µm. About 5 wt.% of distilled water (compared with the weight of olivine sample) was also added to the inside of the palladium-silver capsule using a microsyringe. Finally, the second end of the capsule was capped with a palladium-silver lid with an outer diameter of 1.5 mm, a wall thickness of 0.05 mm, and a length of 0.8 mm (Fig. 1). The combination of the capsule and the lid forms a watertight seal against the palladium-silver container rim upon cold pressurization. Effect of the difference in piston material (diamond or tungsten) on the rheological property of olivine has not been observed in our earlier study (Ohuchi et al. 2012b).

Fig. 1
figure1

ac Three types of cell assemblies viewed in cross section (a 7-5 type; b 6.5-4 type; c 4-2.5 type) from the direction parallel to the X-ray path (dashed circles). TC W/Re thermocouple. d A schematic diagram of a sample-capsule assembly for the experiments in the olivine + aqueous fluid system using the 6.5-4 type cell assembly. See text for the details

Table 1 Experimental conditions and results

Encapsulation: other metal capsules for the as-is olivine system at 1633–1800 K

Because the melting temperature of palladium-silver alloy is around 1550 K at high pressures, experiments under water-saturated conditions are quite difficult at temperatures above 1550 K. Instead of the palladium-silver capsule and lid, a nickel capsule with a diameter of 0.5 mm and a length of 0.6 mm (for the 4-2.5 type cell assembly) and molybdenum capsules with a diameter of 1.2 mm and a length of 1.2 mm (for the 6.5-4 type cell assembly) were adopted for the runs conducted at temperatures of 1633–1800 K (M975, M1844, and M1846 runs: Table 1). Absorption of moisture to a sample or water leak from the inside of the capsule could occur because both ends of the nickel and molybdenum capsules were not welded. Use of nickel or molybdenum for the capsule material is known to lead to the Ni-NiO or Mo–MoO2 oxygen buffers in the system (Nishihara et al. 2006). Keefner et al. (2011) reported a power-law dependence of the creep rate of olivine on oxygen fugacity with an exponent of 0.2, suggesting that the use of a nickel capsule in the M975 run leads to ~1.7 times overestimate in the creep strength of olivine compared with the M1844 and M1846 runs. A core-drilled olivine aggregate (4-2.5 type: a diameter of 0.5 mm and a length of 0.6; 6.5-4 type: a diameter of 1.2 mm and a length of 1.2 mm) and two hard alumina pistons were placed into a nickel or molybdenum capsule. To prevent a chemical reaction between the olivine sample and alumina pistons at high temperatures, the cored olivine aggregate and two pistons were separated by two platinum strain markers, with a thickness of 10 or 20 µm.

Cell assemblies for deformation experiments

To evaluate the pressure effect on the plasticity of hydrous olivine at a wide range of pressure (i.e., 1.5–9.8 GPa), the MA-6-6 system with three different truncated edge lengths (TEL = 2.5, 4 or 5 mm) for the second-stage anvils were adopted for the experiments. Also, three different types of cell assemblies were used in the experiments: the 4-2.5 type for TEL 2.5 mm anvils (Kawazoe et al. 2011), the 6.5-4 type for TEL4 mm anvils (Ohuchi et al. 2015) and the 7-5 type for TEL5 mm anvils (Ohuchi et al. 2012b). The upper limits of the pressure generation range are ~15, ~7, and ~5 GPa for the 4-2.5, 6.5-4, and 7-5 types, respectively (in the case of in situ experiments). The larger cell assembly was chosen for each experimental condition to obtain a larger sample volume and to keep the pressure fluctuation smaller during the sample deformation. Two cubic boron nitride anvils and two sliding blocks with a conical X-ray path (maximum 2θ angle ~10º) were used on the down-stream side of the X-ray path. A semi-sintered cube of cobalt-doped magnesia ((Mg, Co)O) with an edge length of 4, 6.5 or 7 mm was used as the pressure medium for cells of the 4-2.5, 6.5-4, and 7-5 types, respectively. A graphite heater was located at the inner bore of a tubular LaCrO3 thermal insulator in the 6.5-4 and 7-5 type cell assemblies. Instead of a graphite heater, a LaCrO3 heater was adopted to the 4-2.5 type cell assembly. A mixture of amorphous boron and epoxy was placed along the X-ray path in the pressure medium and a LaCrO3 thermal insulator (or a LaCrO3 heater).

Deformation experiments

Deformation experiments on hydrous olivine aggregates were conducted in the uniaxial compression geometry at pressures of 1.5–9.8 GPa and at temperatures of 1223–1800 K and strain rates of 0.8–7.5 × 10−5 s−1 using two deformation-DIA apparatuses at the AR-NE7A beamline of the Photon Factory (Shiraishi et al. 2011) (TO-series in Table 1) and at the BL04B1 beamline at SPring-8 in Japan (M-series in Table 1). The procedures for the in situ deformation experiments are based on Ohuchi et al. (2015). The olivine sample was cold-compressed at a rate of 0.3 MN h−1 up to 0.5 MN (in press load). Temperature was monitored by a W97Re3–W75Re25 thermocouple placed along one of the diagonal directions of the cubic pressure media. Temperature was increased to the desired value and kept for 0.5 h to reduce elastic strain and defects accumulated in olivine crystals during the cold-compression process. After the 0.5-h annealing process, the olivine sample was deformed in the uniaxial compression geometry at a constant rate by advancing the upper and lower first-stage anvils. Two experiments (TO-26 and M1845) were terminated just after the 0.5-h annealing process without the deformation process to evaluate the microstructures just before the deformation process. The temperature gradient between the central part and the edge of the sample was less than 50 K (Ohuchi et al. 2010).

The strain ε (=−ln (l/l 0), where l 0 is the initial length of the sample just before deformation and l is the length of the sample during deformation) of a sample, was measured by the distance between two platinum strain-markers that were monitored by in situ monochromatic X-ray radiography (Fig. 2). The uncertainty in the strain rate, which resulted from the shape of the strain-markers, was within 10%. Two-dimensional X-ray diffraction patterns were taken using an imaging plate or a 2048 × 2048 pixel MAR-CCD camera with 5–12 min of exposure time. The two-dimensional digitalized diffraction pattern was integrated to a one-dimensional profile (angle step of 10°), and the peak positions were semi-automatically determined at a certain azimuth angle using software (IPAnalyzer and PDIndexer) (Seto 2012). Five diffraction peaks of olivine (hkl = 021, 101, 130, 131, and 112) in a two-dimensional X-ray diffraction pattern of monochromatic X-rays (energy 51 keV) were used for the determination of generated pressure and the magnitude of differential stress (Fig. 3). Pressure was determined from the averaged value of d-spacing using the equation of state of olivine (Liu et al. 2005). The stress magnitude was calculated for each hkl-line based on the following equation (Singh et al. 1998):

$$d_{hkl} = d_{hkl}^{0} \left[ {1 + \frac{\sigma }{6M}(1 - 3\cos^{2} \varPsi )} \right],$$
(4)

where d hkl is the d-spacing measured at an azimuth angle ψ; \(d_{hkl}^{0}\) is the d-spacing under hydrostatic pressures; M is an appropriate shear modulus for a given crystal orientation [hkl]; and σ is the axial differential stress. The M was calculated from olivine single-crystal elasticity measurements (Abramson et al. 1997; Isaak 1992). The values of σ and \(d_{hkl}^{0}\) were calculated by fitting the azimuth-angle dependence of d hkl to Eq. (4). The uncertainty of the stress resulting from the accuracy of the measurements (Bollinger et al. 2014) was evaluated from the least-square fit of Eq. (4) (each error bar corresponds to the 1-sigma: Fig. 3c). Flow-law parameters were evaluated for each hkl-line.

Fig. 2
figure2

X-ray radiographs acquired before (a strain ε = 0%) and during the deformation (bf ε = 5–31%) in the M1844 run. Positions of platinum strain markers are shown by arrows. Double arrows represent the anvil gap

Fig. 3
figure3

a A representative two-dimensional X-ray diffraction pattern during sample deformation at 3.32 GPa and 1423 K (TO-17, wavelength = 0.2480 Å). b A one-dimensional diffraction pattern obtained from a at an azimuth angle of 90°. Diffraction patterns of olivine (Ol), graphite, magnesia (MgO) and palladium-silver were observed. c Relationship between the observed d-spacing values of the olivine (021) peak and the azimuth angle (ψ) obtained from a. Error bars corresponding to the 1-sigma of the best-fit curve

Microstructural observations and analysis: scanning electron microscope

The capsule assembly was recovered from the cell assembly, and cut with a low-speed saw. The sectioned plane was parallel to the axial compression direction in the case of the as-is olivine system though that was perpendicular in the case of the olivine + aqueous fluid system because cutting the diamond pistons was quite difficult. The sectioned samples were then impregnated with epoxy under a vacuum and polished using alumina powder followed by colloidal silica suspension. Microstructures of the recovered samples were examined from polished sections using a JEOL JSM-7000F field-emission scanning electron microscope (FE-SEM) equipped with an electron backscattered diffraction (EBSD) camera. The visibility of grain boundaries was enhanced by an etchant (dilute hydrofluoric acid; 23% reagent grade) to evaluate the mean grain size. The mean grain size and grain size distribution were determined from the average diameter of the circles having the same area as individual grains (~200 grains were analyzed in most of the samples).

We evaluated the crystallographic orientation of olivine grains from the EBSD pattern of each grain obtained at 20 kV acceleration voltage and 4 nA probe current. The EBSD patterns were indexed using the CHANNEL5 software from HKL Technology. The measurements were performed on a grain-by-grain basis and in operator-controlled indexing mode to obtain an accurate solution for the evaluation of crystallographic preferred orientation (CPO). About 500 grains were manually analyzed for each crystallographic orientation dataset. To evaluate the dependency of the fabric strength of olivine on axial strain quantitatively, the J-index (i.e., fabric strength) and pfJ (i.e., sharpness of a pole figure) (Bunge 1982; Mainprice and Silver 1993) were calculated from the CPO data. The automatic indexing mode was adopted for the acquisition of crystallographic orientation maps.

Micrometer-scale dislocation microstructures in the deformed samples were examined from backscattered electron (BSE) images taken by an FE-SEM using the internal-oxidation dislocation decoration technique (Kohlstedt et al. 1976b). The relationship between applied stress σ and free dislocation density ρ is described empirically as follows when deformation is controlled by dislocation creep:

$$\rho_{\text{calc}} = \beta \cdot \sigma^{c} ,$$
(5)

where β (=109.21 MPac m−2) and c (=1.39) are constants in the BSE images (Kohlstedt et al. 1976a; Ohuchi et al. 2011). We used the olivine dislocation density piezometer (Eq. 5) to estimate the dislocation density from the stress applied to the sample (ρ calc) under the assumption that the dominant deformation mechanism is dislocation creep. To calculate the dislocation density from the olivine dislocation density piezometer (ρ calc), an averaged value of steady-state creep strength was substituted into Eq. (5).

Microstructural observations and analysis: transmission electron microscopy

Dislocation microstructures of three deformed samples (M1307, M1356, and M1844) were also investigated using a JEOL JEM-2010 transmission electron microscope (TEM) at 200 kV accelerating voltage. Dark-field images were taken in two-beam conditions, and then the Burgers vector b for the dislocations was determined based on the invisibility criteria (i.e., g · b=0 for screw dislocations; g · b = 0 and g · (b × u) = 0 for edge dislocations; where g and u are the diffraction vector and a unit vector parallel to the dislocation line, respectively). Thin foils for TEM observations were prepared from thin sections and then ion-milled with an accelerating voltage of 3–5 kV and at a beam angle of 7°–10°. A doubly polished thin foil of a deformed sample (M1844) was prepared using a focused ion beam (FIB) system (FEI Scios) at Ehime University. A gallium ion beam was accelerated to 30 kV during the sputtering of the specimen by FIB. The resultant TEM foil was ~100 nm thick.

Fourier-transform infrared analysis

The measurements of unpolarized infrared absorption spectra of the polycrystalline sample were carried out in dried air by putting the doubly polished thin sections with a thickness of 50–234 µm on a BaF2 plate and using a PerkinElmer Spectrum One Fourier-transform infrared spectrometer (FTIR) with a mid-infrared light source, a KBr beam splitter and a mercury cadmium telluride detector. An aperture size of 50 × 50 µm2 was used for all the measurements. At least five spectra were obtained from each section with 128 integrated scans with 4 cm−1 resolution for wave numbers from 700 to 4000 cm−1. After the background noise was removed, spectra were normalized by the thickness of the sections. A baseline for each spectrum was determined using a least-square fit of a cubic function of the wave numbers between 2800 to 3100 and 3650 to 3800 cm−1 and then subtracted from the normalized spectra. The water content in the olivine was determined by integrating infrared absorption spectra from 3100 to 3630 cm−1 on the basis of the extinction coefficient calibration by Paterson (1982):

$$C_{\text{OH}} = \frac{{B_{i} }}{150\gamma }\int {\frac{k(v)}{3780 - v}{\text{d}}v} ,$$
(6)

where C OH is the water content in olivine, B i is the density factor, γ is an orientation factor, and k(ν) is the absorption coefficient for a given wave number ν. A reported value of B i  = 4.39 × 104 H/106Si (Kohlstedt et al. 1996) and an orientation factor of 1/3 were used in this study. We calculated the water fugacity from the dissolved water content in olivine using a theoretical equation (Keppler and Bolfan-Casanova 2006; Kohlstedt et al. 1996) and its constants (the water fugacity exponent = 1 and the activation volume = 10.6 cm3 mol−1: Kohlstedt et al. 1996; the reaction enthalpy at 1 bar = 50 kJ mol−1: Zhao et al. 2004). Due to the presence of a small amount of quench phases in the recovered sample (M1380) or the loss of samples caused by blow outs that occurred in two deformation experiments (TO-15 and M1846), the water contents were not determined in the three recovered samples. Because water fugacity (i.e., water content) is required for calculating the normalized stress from the actual stress value, we assumed that the water contents in the samples are the same as those in the samples that experienced the most similar pressure–temperature conditions to those in our experiments, namely that the water contents in the TO-15 (at 5.7 GPa and 1373 K), M1380 (at 2.3 GPa and 1323 K), and M1846 (at 5.4 GPa and 1633 K) samples are equal to those in the TO-26 (at 5.8 GPa and 1373 K), M1356 (at 1.8 GPa and 1273 K), and M1844 (4.6 GPa and 1673 K) samples, respectively.

Results

Water contents

The infrared beam was strongly absorbed in the wavenumbers ranging from 3450 to 3620 cm−1 in olivine aggregates deformed at temperatures of 1223–1423 K, though strong absorption peaks are also observed in higher wavenumbers (3630–3680 cm−1) for samples deformed at temperatures of 1633–1800 K (Fig. 4). Infrared absorption in wavenumbers >3630 cm−1 are excluded from the calculation of water contents in olivine because the bands observed at ~3640 and ~3670 cm−1 are usually assigned to serpentine and talc (Beran and Libowitzky 2006). A wide range of water contents in the recovered olivine (1020–6360 H/106Si) was obtained in the olivine + aqueous fluid system, showing a significant change in water content from the initial content (4070 H/106Si) during experiments (Table 1). The water contents in olivine were expected to correspond to the water solubility limits in the deformation runs because pores are distributed at triple junctions of grain boundaries and sometimes quench phases (or a melt phase) from the aqueous fluid were observed (Fig. 5).

Fig. 4
figure4

Unpolarized infrared spectra of the olivine aggregates deformed at 1223–1423 K in the olivine + aqueous fluid system (TO-17, TO-21, M1300, M1307, M1354 and M1356) and at 1633–1800 K in the system of as-is olivine (M975 and M1844). Spectra show sharp hydroxyl bands at wavenumbers between 3450 and 3620 cm−1, which are related to the structurally incorporated hydroxyl in olivine. Strong absorption peaks in higher wavenumbers (3630–3680 cm−1) are considered to be assigned to hydrous minerals. See text for the details

Fig. 5
figure5

Backscattered electron (BSE) images of a an undeformed (M1845: strain 0%) and b a deformed (M1844: strain 31%) sample assemblies. Forescattered electron images of olivine aggregates deformed at c 1423 K (M1307) and d 1673 K (M1844). Polished surfaces shown in c and d were etched by dilute hydrofluoric acid to enhance the visibility of grain boundaries. e A BSE image showing pores distributed at triple junctions of grain boundaries in a sample deformed in the olivine + aqueous fluid system (M1356). Some pores are filled with quenched phases (QP) or a melt phase. Ol olivine. f A BSE image showing dislocations in an olivine grain (M1380). The internal-oxidation dislocation decoration technique was adopted for the sample shown in f. Bright lines show dislocations or a crack. The direction of the axial compression is parallel to the up-and-down direction of the images (b, d) or perpendicular to the plane of images (c, e, f)

The water contents in the recovered M1844 and M1845 samples deformed (or undeformed) at 1673 K (i.e., the as-is olivine system) were 700–1360 H/106Si and are lower than the initial water content (4070 H/106Si). The water content in the recovered M975 sample (1460 H/106Si) is comparable to the initial water content of the sample (1300 H/106Si). Pores were not observed in the as-is olivine system (Table 1; Fig. 5d).

Mechanical data

Stress–strain curves obtained using five diffraction peaks (hkl = 021, 101, 130, 131, and 112) and the pressure change during the deformation are shown in Fig. 6. Variation in stress values with (hkl) reflections, which results from the plastic anisotropy of the crystals (Merkel 2006), is observed. The (101) and (130) peaks tend to show the highest and lowest stress values, respectively. The relationship between the (101) and (130) peaks is completely opposite to our early study conducted under anhydrous conditions (Ohuchi et al. 2015), showing the water effect on the plastic anisotropy of the olivine crystal. In many runs, the creep strength approached a quasi-steady-state creep strength at a strain of ε ~4% but it fluctuated at higher strains (we define steady state as the fluctuation of stress being within ±5% at strains higher than 4%). The magnitude of error bars for stress is relatively greater than that in anhydrous olivine (e.g., Ohuchi et al. 2015), because of spotty 2-D diffraction patterns resulting from fast grain growth of some olivine grains (e.g., large grains with pore fluid inclusions: see next section). Large grains disturb the relationship between azimuth-angle and d-spacing expressed as Eq. (5). A significant stress drop (~0.2−0.3 GPa) was observed during the deformation in the M975 run (Fig. 6i), though softening or hardening was not observed in each deformation step of other runs.

Fig. 6
figure6figure6

Stress–strain records for olivine aggregates deformed at ah 1223−1423 K in the olivine + aqueous fluid system and ik at 1633−1800 K in the system of as-is olivine. The stress values were obtained from the five diffraction peaks of olivine (cross 021, circle 101, diamond 130, square 131, and triangle 112). The hatched areas indicate the steady state achieved in each deformation step. The change of pressure during the sample deformation is also shown

To determine flow-law parameters for hydrous olivine, creep results are compared in Fig. 7. The flow-law parameters were calculated from the experimental data using a linear least-square fitting method. We determined the strain rate dependence of strength at representative conditions (3.3–3.9 GPa and 1373 K: TO-17) and the averaged value of the stress exponent n for hydrous olivine is 3.2 ± 0.6 in the olivine + aqueous fluid system (Fig. 7a; Table 2). We examined the temperature dependence of strength at 1.5–1.8 GPa (M1356) and then the averaged value of the activation enthalpy was obtained to be H * = 390 ± 130 kJ mol−1 (Fig. 7b; Table 2). The values H * obtained from each hkl-line are so scattered that we do not calculate the E * in this study. The temperature dependence of strength seems to be similar at 3.8–4.0 GPa (Fig. 7b). In Fig. 7c, d, we adopt hypothetical values of E * (=423 kJ mol−1) (Ohuchi et al. 2015) for data normalization to the standard temperature (1373 K). The pressure dependency of strength seems to discontinuously change at ~3 GPa and 1273–1423 K in the olivine + aqueous fluid system, and its dependency is stronger at <3 GPa than that at >3 GPa (Fig. 7c). Not only pressure dependency but also water fugacity dependency of strength is different between the two different pressure ranges (Fig. 7d). The averaged activation volume of V * = 17 ± 6 cm3 mol−1 was obtained at pressures higher than 3 GPa in the case of n = 3.2, r = 1.25 and E * = 423 kJ mol−1 (Table 2). At temperatures of 1633–1800 K (i.e., the as-is olivine runs), the pressure dependence of strength is stronger than that observed at 1273–1423 K (Fig. 7c). The observed temperature effect implies a difference in the dominant deformation mechanism between the two different temperature ranges (see “Discussion”).

Fig. 7
figure7

Evaluation of flow-law parameters for olivine aggregates. a Strain rate dependency of steady-state creep strength (hereafter, strength) of olivine at 1373 K in the olivine + aqueous fluid system (TO-17). The stress exponent n was obtained from this dataset without any data normalization. The averaged best-fit values of n (shown by subscript ave) are also shown. b Temperature dependency of the strength of olivine in the olivine + aqueous fluid system at 1.5–1.8 GPa (M1356) and at 3.8–4.0 GPa (TO-21 and M1300). The averaged value of H * obtained at 1.5–1.8 GPa is also shown. c Pressure dependency of the strength of olivine at 1323–1423 K in the olivine + aqueous fluid system and at 1633–1800 K in the system of as-is olivine. The averaged value of V * obtained at 1323–1423 K is also shown. d Dependency of the strength of olivine on water fugacity at 1323–1423 K in the olivine + aqueous fluid system. In c and d, the strength is corrected for the water fugacity effect (i.e., \(f_{{{\text{H}}_{2} {\text{O}}}}^{r/n}\)) or the activation volume effect (i.e., exp(−PV */nRT)). The strength was obtained from each diffraction peak of olivine (cross 021, circle 101, diamond 130, square 131, and triangle 112). Data in bd are normalized to the conditions of 1373 K (E * = 423 kJ mol−1 for disGBS of olivine was assumed: Ohuchi et al. 2015) and a strain rate of 10−5 s−1 (n = 3.2 was assumed) under the assumption of r = 1.25 and V * = 17.0 cm3 mol−1. The dashed lines represent the best-fits defined as the flow law

Table 2 Apparent flow law parameters for olivine aggregates

Deformation microstructures

The mean grain size of olivine in deformed samples ranges from ~3 to 18.3 µm (Table 1). The mean grain sizes of olivine in the undeformed samples (7.6 µm in TO-26 and 29.0 µm in M1845) are also much smaller than that of the starting sample (63 µm), showing that much of the grain size reduction proceeded during the cold-compression process followed by annealing (i.e., before the deformation process). Equigranular fabric is observed (Fig. 5c, d) in both deformed and undeformed samples. Smoothly curved, linear, or serrated grain boundaries are frequently observed, though small grains at the border of large grains tend to have linear grain boundaries (Fig. 8c). Smoothly curved grain boundaries are dominant at pressures lower than 3 GPa (Figs. 5e, 8a). Some pores are trapped inside relatively large grains (>20 µm) in the olivine + aqueous fluid system (Fig. 8a, 8b), showing fast growth of the grains. Orientation maps show that some subgrain boundaries with misorientation angles between 2° to 10° are observed in deformed samples (Fig. 8). Lognormal distributions of olivine grains are frequently observed in both undeformed and deformed samples (Fig. 9), as reported in previous studies (Hansen et al. 2011; Tasaka and Hiraga 2013). The frequency of relatively small grains (G/G mean ~0.5 in Fig. 9) is commonly high compared with the lognormal curve in most of the samples. Slight bimodality is observed in some of deformed samples (TO-15, TO-17, and M1356) and in an undeformed sample (M1845). These observed signatures in size distributions reflect the grain size reduction via dynamic recrystallization that proceeded during the cold-compression process.

Fig. 8
figure8

ac Forescattered electron images and df orientation maps of olivine aggregates deformed at 1.5–1.8 GPa and 1223–1323 K (a, d M1356), 4.8 GPa and 1423 K (b, e M1307), and 4.6 GPa and 1673 K (c, f M1844). The direction of the axial compression is perpendicular to the plane of images (a, b, d, e) or parallel to the up-and-down direction of the images (c, f). The orientation maps are colored by the relationship between the direction of axial compression and olivine axes (blue compression direction is parallel to [100]; green parallel to [010]; red parallel to [001]). Red and black lines in df represent low-angle grain boundaries having 2°–10° misorientation angles and grain boundaries having the misorientation angles greater than 10°, respectively

Fig. 9
figure9

Normalized grain size distributions (G/G mean where G and G mean are grain size and mean grain size, respectively) of olivine in the recovered samples. Dashed curves represent the best-fit lognormal distributions. Frequency corresponds to the number fraction of the analyzed grains

Variations in crystallographic orientations of olivine in the deformed samples are compared in Fig. 10. The fabric strength of olivine calculated from the CPOs at 1223–1423 K is plotted against strain in Fig. 11. The development of olivine CPO is hardly observed and the J-index is less than 3 at pressures of <3 GPa. At pressures higher than 3 GPa, stronger CPOs (J-index > 3) were developed at strains of ≥7%. The [100] axes are strongly concentrated in the direction of the axial compression at a strain of 7% (pfJ[100] = 1.8) even though the initial crystallographic orientation is almost random. The pfJ[100] is weakened with increase in strain but fabric strength of the other principal axes (i.e., pfJ[010] and pfJ[001]) show no strain dependence. The geometrical patterns of CPOs also do not show any strain dependence.

Fig. 10
figure10

Pole figures showing the CPO of olivine at various conditions (a, b undeformed samples; ch deformed at 1223–1423 K in the olivine + aqueous fluid system; i deformed at 1673 K in the system of as-is olivine). The [100], [010], and [001] directions are shown in equal-area lower hemisphere projections with a half scatter width of 30°. The color coding refers to the density of data points, and the contours correspond to the multiples of uniform distribution. Strain (ε) and J-index are also shown. The N represents the number of analyzed grains. Direction of the axial compression is shown by arrows

Fig. 11
figure11

Fabric strength of each principal axis (pfJ) and J-index of hydrous olivine aggregates as a function of strain at 1223–1423 K. Squares and circles represent pfJ or J-index at pressures lower and higher than 3 GPa, respectively. Open and solid symbols are pfJ and J-index, respectively. Red, green, and blue symbols represent the pfJ[100], pfJ[010], and pfJ[001], respectively. Reported J-index values for hydrous olivine deformed in the diffGBS regime (crosses Ohuchi et al. 2012b) and in the dislocation creep regime (green hatched area Demouchy et al. 2014 and Tasaka et al. 2015) are also shown. All the reported J-index values were evaluated in the uniaxial compression geometry

Dislocations observed in the deformed samples are straight or slightly curved, and they are not tangled with each other (Fig. 5f). In Fig. 12, the free dislocation density in each recovered sample is compared with the dislocation density calculated from Eq. (5) and the applied stress. Two stepping tests (TO-17 and M1356) were not considered in Fig. 12 to exclude the effect of their complex deformation histories on the dislocation density in the runs. The error bar for ρ calc is much larger than that for the measured dislocation density (ρ) because the error in the averaged stress value due to the Singh’s physical model (Bollinger et al. 2014) is considered for the calculation. Figure 12 shows that the ρ is much lower than the ρ calc at 1323–1423 K. In contrast, the ρ is comparable to the ρ calc in the case of 1673–1800 K.

Fig. 12
figure12

Measured dislocation density (ρ) in deformed samples compared with the value calculated from the applied stress and the dislocation density piezometer for olivine (Eq. 5). Circles and squares represent the data from hydrous olivine deformed at 1323–1423 K and at 1633–1800 K, respectively. Two stepping tests (TO-17 and M1356) are excluded from this figure

TEM observations

Typical TEM-scale dislocation microstructures in the deformed samples are shown in Fig. 13. All the examined olivine grains contained straight or slightly curved dislocations, and subgrain boundaries were also observed in some grains. The dislocation density was low enough that most of dislocations were not tangled with each other. In the sample deformed at 1.5–1.8 GPa and 1273–1323 K (M1356), some straight dislocations are invisible when g = 400 but those remain when g = 004 and 404 (Fig. 13a–c), suggesting that the dislocations have the Burgers vector b = [001].

Fig. 13
figure13

Dark-field TEM images of ac a hydrous olivine sample deformed at 1.5–1.8 GPa and 1223–1323 K (M1356), df a hydrous olivine sample deformed at 4.8 GPa and 1423 K (M1307), and gi an as-is olivine sample deformed at 4.6 GPa and 1673 K (M1844). White arrows in a show the dislocations that lose their contrast when the reflection g = 400 is used. In the M1307 sample, a few dislocations (pointed by a white arrow in f) are invisible when g = 008 and \(06\bar{2}\) are used. In the M1844 sample, some minor dislocations do not lose their contrast in the case of g = 222, 800, and 022 (shown by black arrows in i). See text for details

In the M1307 sample deformed at 4.8 GPa and 1423 K, many dislocation lines are parallel to the [010] direction. Contrasts of the long and straight dislocations remain when the reflections of g = 008 and \(06\bar{2}\) are chosen (Fig. 13d, e), though the dislocations lose their contrast when the reflection of g = 040 is used (Fig. 13f: the two-beam condition may not be perfect). Therefore, the Burgers vector and the slip plane of the dislocations are determined as b = [001] and (100), respectively. A few dislocations which are parallel to the \(\langle 011\rangle\) direction are visible in the case of g = 040 and \(06\bar{2}\), and their contrasts disappear when g = 008 is used (Fig. 13d–f). The Burgers vector and the slip plane of the minor dislocations are thus determined as b = [010] and (100), respectively.

In the M1844 sample deformed at 4.6 GPa and 1673 K, many dislocation lines are parallel to either [100] or [011] direction. The [100] and [011] dislocations lose their contrast when reflection of g = 022 is used while their contrast remains in the case of g = 222 and 800 (Fig. 13g–i), showing that the Burgers vector of the dislocations is b = [100] and the slip plane is {011}. However, contrasts of some short dislocations parallel to the \(\left\langle {111} \right\rangle\) directions remain when the reflections of g = 222, 800, and 022 are used (Fig. 13i).

Discussion

Interpretation of water contents in the recovered samples

We observed a significant decrease or increase in water content from the initial content (4070 H/106Si) during each experiment (Table 1). The water loss from olivine observed at pressures lower than 5 GPa could be due to the initial water content exceeding the solubility limit of water in olivine. The solubility limit of water in olivine in the olivine + aqueous fluid system (1020–6360 H/106Si) is systematically lower than the reported values at 2.5–8 GPa and 1373 K under the oxygen fugacity controlled by the Ni-NiO buffer (2200–14,000 H/106Si: Kohlstedt et al. 1996) and at 2.5–7.5 GPa and 1448 K under the oxygen fugacity controlled by the Re–ReO2 buffer (~2000–33,000 H/106Si: Férot and Bolfan-Casanova 2012). The differences in solubility limit could be explained by the effect of oxygen fugacity on water solubility in olivine. It has been reported that olivine annealed under the conditions of low-oxygen fugacity (below the Fe–FeO buffer) contains less than half as much water as crystals from relatively more oxidized experiments at 2 GPa and 1373–1573 K (Grant et al. 2007). We adopted diamond (or tungsten) pistons for the experiments to prevent the chemical reaction between olivine and piston material and, thus, the oxygen fugacity is expected to be sufficiently lower than that of the Ni–NiO and Re–ReO2 buffers. However, no significant effect of varying oxygen fugacity on water solubility in olivine has been reported at higher pressures (8 GPa and 1673 K: Withers and Hirschmann 2008).

In the case of the as-is olivine runs at temperatures of 1633–1800 K, the dissolved water contents in the recovered samples are similar to or significantly lower than the initial water contents (Table 1). The water leak during the experiments could result from imperfectly sealed molybdenum (or nickel) capsules used for the runs. We observed strong absorption of the infrared beam at ~3640 and ~3670 cm−1 in the recovered samples deformed at temperatures of 1633–1800 K (Fig. 4), suggesting that a small amount of serpentine and talc were formed at the quench (note that the olivine samples were undersaturated with water before the quench).

Even though the initial and the final water contents are similar to each other (before: 1300; after 1460 H/106Si), a significant softening was observed in the M975 run. The observed softening could be attributed to CPO development (Hansen et al. 2012) but not to grain size reduction via dynamic recrystallization of olivine because dislocation creep would be the dominant deformation mechanism in the run (see discussion in next section). A significant softening or hardening was not observed in other runs, suggesting that water content in olivine was almost constant during each deformation run.

Deformation mechanisms: from the viewpoint of dislocation density

The total strain achieved under creep conditions is expressed as:

$$\varepsilon = \varepsilon_{\text{disl}} + \varepsilon_{\text{GBS}} + \varepsilon_{\text{diff}} ,$$
(7)

where ε disl is the strain associated with the intragranular dislocation processes within the grains, ε GBS is the strain due to grain boundary sliding (GBS) including the associated accommodation through intragranular slip, and ε diff is the strain due to diffusion creep (Langdon 2006). GBS is accommodated by either a diffusional process (i.e., diffGBS) or the motion of dislocations (i.e., disGBS). If GBS and/or diffusion creep contributes strongly to the deformation, the total strain ε is much larger than ε disl (i.e., ε ≫ ε disl). Considering that strain rate is proportional to dislocation density in the case of dislocation creep (i.e, Orowan’s equation: \(\dot{\varepsilon }_{\text{disl}} \propto \rho\)), the dislocation density piezometer underestimates the applied stress (if dislocation density is known) or the dislocation density (if stress is known) in the case of ε ≫ ε disl. Therefore, comparison of the ρ with ρ calc would be an effective method to evaluate the contribution of dislocation motion to the total strain. The relationship of ρ ≪ ρ calc observed at 1323–1423 K (Fig. 12) suggests that not only motion of dislocations but also other processes (i.e., GBS and diffusion) strongly contributed to the sample deformation. In contrast, the ρ is comparable to the ρ calc at 1673–1800 K, suggesting that motion of dislocations dominantly controlled the deformation.

Deformation mechanisms: from the viewpoint of flow-law parameters

We determined the values of n and V * for hydrous olivine as 3.2 ± 0.6 and 17 ± 5 cm3 mol−1, respectively, at 1323–1423 K (Table 2). These values are quite similar to the reported value for olivine controlled by disGBS (n = 3.0 and V * = 17.6 cm3 mol−1: Ohuchi et al. 2015) (Fig. 14). Taking into account three theoretical values for the water fugacity exponent r for olivine (=0.75, 1 or 1.25) (Karato and Jung 2003; Mei and Kohlstedt 2000b), our datasets for hydrous olivine are best-fit by the flow law with r = 1.25 at 1323–1423 K in the olivine + aqueous fluid system (Fig. 7d). This r value is also consistent with the case of disGBS (r = 1.25: Ohuchi et al. 2015). Taking into account our discussions above, it is suggested that disGBS strongly contributed to the deformation at 1323–1423 K. The discontinuous changes of normalized stress–pressure slopes for each hkl line observed at 2–3 GPa and 1323–1423 K (Fig. 7c, d) suggest a change in V * and/or n at the pressure range (i.e., a pressure-induced transition in the dominant deformation mechanism). The large uncertainty in the obtained activation enthalpy at 1.5–1.8 GPa (i.e., 390 ± 130 kJ mol−1) could result from a pressure-induced transition in the dominant deformation mechanism.

Fig. 14
figure14

Activation volumes for the creep of olivine aggregates reported by previous studies and this study. Values are plotted as a function of published year. Activation volumes for dislocation creep of anhydrous olivine (Karato and Jung 2003; Kawazoe et al. 2009; Korenaga and Karato 2008; Ross et al. 1979; Wang 2002), nominally anhydrous olivine (Borch and Green 1987; Karato and Rubie 1997; Li et al. 2006), and hydrous olivine (Bollinger et al. 2014; Hirth and Kohlstedt 2003; Karato and Jung 2003; Korenaga and Karato 2008) are shown by open, gray-solid, and black-solid circles, respectively. The V * for hydrous olivine estimated in this study is also plotted. Values for disGBS of anhydrous olivine (Ohuchi et al. 2015) and for hydrous olivine (this study) are shown by open and solid squares, respectively. The V * reported by Durham et al. (2009) is shown by a cross (deformation mechanism is presumed to be disGBS)

At temperatures of 1633–1800 K, the observed pressure dependency of normalized stress is much stronger than that at 1323–1423 K (Fig. 7c), suggesting that contribution of disGBS to the deformation is small. Considering that the ρ is comparable to the ρ calc at 1673–1800 K (Fig. 12), dislocation creep would be the dominant deformation mechanism in that temperature range. Under the assumption of power-law dislocation creep of hydrous olivine (n = 3.5, r = 1.2, and E * = 520 kJ mol−1: Hirth and Kohlstedt, 2003), the V * is estimated to be 27 ± 7 cm3 mol−1 from our data obtained at 4.6–9.8 GPa and 1633–1800 K. The estimated value is consistent with the reported values within the error bar (22 ± 11 cm3 mol−1: Hirth and Kohlstedt 2003; 24 ± 3 cm3 mol−1: Karato and Jung 2003; 25 ± 5 cm3 mol−1: Bollinger et al. 2014) (Fig. 14).

Deformation mechanisms: from the viewpoint of microstructures

It has been thought that development of CPO during sample deformation is a good indication of important information that will contribute to constraining the deformation mechanism (Karato et al. 1995). However, recent studies by Hansen et al. (2012) and Miyazaki et al. (2014) showed that strong CPOs can be developed in the regimes of disGBS and diffusional creep, respectively. Even in the case of dislocation creep of hydrous olivine, the reported J-index values range from 1.3 to 2.8 at strains of 8–9% in the uniaxial compression geometry (Demouchy et al. 2014; Tasaka et al. 2015) (Fig. 11). These values are comparable to the reported J-index values for hydrous olivine deformed via diffGBS (J-index = 2.2–2.8 in the uniaxial compression geometry: Ohuchi et al. 2012b). Although it has been reported that fabric strength monotonically increases with the deformation in the simple-shear geometry (Hansen et al. 2012), the development of fabric with strain is known to be more sluggish and complex in the uniaxial compression geometry (Boneh and Skemer 2014). The J-index values of olivine fabric developed at <3 GPa and 1273–1423 K are 2.2–2.6, which is comparable to the reported values shown in Fig. 11. Much higher values of the J-index (=3.6–5.2) are obtained at >3 GPa and 1273–1423 K. However, it is quite difficult to conclude whether the apparent pressure effect on fabric strength of olivine is related to a transition in the dominant deformation mechanism.

Our CPO data show that the [010] axes tend to concentrate in the direction of the axial compression in most of the deformed samples (Fig. 10c–i). Viscoplastic self-consistent simulations showed that concentration of the [010] axes to the direction of the axial compression in the uniaxial compression geometry requires the (010) glide planes (Wenk and Bennett 1991) or the condition in which both [100](0kl) and [001](hk0) slip systems have similar strength (Demouchy et al. 2014). Activation of the [100]{011} slip system, which was observed at 4.6 GPa and 1673 K, is consistent with the development of the [010] maxima to the direction of the axial compression (Fig. 10i). However, the dominant slip system [001](100) cannot account for the orientation of the [010] maxima developed at 1323–1423 K (Fig. 10). Development of the [010] maxima to the axial compression direction is known to be possible during GBS (Miyazaki et al. 2014). Taking into account a significant contribution of disGBS to deformation at 1323–1423 K (see discussion above), the olivine CPOs developed at 1323–1423 K might be formed through the GBS process, rather than dislocation glide.

It is well known that water enhances grain growth of olivine (Karato 1989b) and increases size of recrystallized grains of olivine (Jung and Karato 2001a). Mean grain sizes of olivine in the recovered samples were compared with the reported grain growth law for hydrous olivine (Karato 1989b) in Fig. 15. In Fig. 15, initial grain size G 0 = 1 µm is assumed for the calculation of grain growth curves. Grain sizes at <3 GPa and 1223–1323 K are similar or higher than the calculated grain growth curves, suggesting that grain growth more or less proceeded. However, grain sizes at >3 GPa and 1323–1423 K are up to ~3 times smaller than the values expected from the grain growth law. The discrepancy between the grain growth law and the measured grain size is enormous at 1673–1800 K. Although more than 40 µm of a mean grain size is expected from the grain growth law, the actual sizes are 3–5 µm at 1673–1800 K. The actual grain sizes are much lower than the recrystallized grain size expected from a grain-size piezometer for hydrous olivine (>10 µm at stress of <500 MPa: Jung and Karato 2001a). Figure 15 suggests that grain size reduction via dynamic recrystallization is not effective and cannot account for the origin of the observed small grain sizes. The cause of the unexpected small grain sizes might be attributed to sluggish grain boundary migration via the development of many faceted grain boundaries (Figs. 5, 8) (Dresen et al. 1996) and/or the effect of misorientation on the mobility of low-angle boundaries (Huang and Humphreys 2000). Sluggish grain growth would contribute to maintaining the deformation controlled by grain-size-sensitive creep for many hours.

Fig. 15
figure15

Mean grain sizes of olivine plotted against experimental duration (in minutes). Experimental duration includes both the 30-min annealing process just before the deformation and following the deformation process. Symbols represent the mean grain sizes of olivine in the samples (solid triangles <3 GPa and 1223–1323 K; open circles >3 GPa and 1323 K; solid circles >3 GPa and 1373 K; solid diamond >3 GPa and 1423 K; open square 1673 K; solid square 1800 K). Dotted, dashed, dot-dashed curves represent the grain size evolution calculated from the grain growth law for hydrous olivine at temperatures of 1273–1800 K (the grain size exponent m = 2, the pre-exponential term of growth rate constant k 0 = 1.6 × 10−8 m2 s−1, and the activation energy E * = 160 kJ mol−1: Karato 1989b). The initial grain size G 0 was assumed to be 1 µm for the calculations. The thick solid line represents the recrystallized grain size (~10 µm at differential stress of 500 MPa) estimated from the grain-size piezometer for hydrous olivine (Jung and Karato 2001a), namely grain size cannot be reduced to <10 µm via dynamic recrystallization (DRex) of olivine

Comparison to other experiments

To compare our data with flow laws for hydrous olivine reported for the upper mantle pressures (power-law dislocation creep: Karato and Jung 2003; disGBS: Ohuchi et al. 2015; diffGBS: Ohuchi et al. 2012b), the normalized steady-state creep strength (at temperature 1373 K, strain rate 10−5 s−1, and grain size 5 µm) is plotted against pressure in Fig. 16 (see Table 3 for the flow-law parameters used for the calculations). In Fig. 16, our data are normalized using the flow law for disGBS of olivine (n = 3.0, E * = 423 kJ mol−1, V * = 17.6 cm3 mol−1, p = 1: Ohuchi et al. 2015). Stress–pressure curves, which were calculated under the assumption that both diffGBS and disGBS contribute to the deformation by the following equation, are shown in Fig. 16:

$$\dot{\varepsilon } = \dot{\varepsilon }_{\text{diffGBS}} + \dot{\varepsilon }_{\text{disGBS}} ,$$
(8)

where \(\dot{\varepsilon }_{\text{diffGBS}}\) and \(\dot{\varepsilon }_{\text{disGBS}}\) are the proportions to the total strain rate from diffGBS and disGBS, respectively. As expected from our discussion above, our data set for the olivine + aqueous fluid system (i.e., data obtained at 1323–1423 K) is well fitted by Eq. (8) with water content ≥1000 H/106Si. The kink in the stress–pressure slope observed at ~3 GPa in our experiments is also reproduced by Eq. (8) (Fig. 16). The creep strength of hydrous olivine from our results in the olivine + aqueous fluid system is below the curve for power-law dislocation creep of water-saturated olivine. Therefore, we consider that the power-law dislocation creep cannot account for our data in the olivine + aqueous fluid system and, thus, the dominant deformation mechanism of hydrous olivine is diffGBS or disGBS at 1323–1423 K.

Fig. 16
figure16

Pressure dependency of the strength of olivine aggregates under hydrous conditions. All data are normalized to an axial strain rate of 10−5 s−1, a temperature of 1373 K, and a grain size of 5 µm (p = 1 is assumed for disGBS: Ohuchi et al. 2015). Solid triangles and circles represent the strength of hydrous olivine aggregates in the olivine + aqueous fluid system at pressures lower and higher than 3 GPa, respectively. Solid squares represent the strength of as-is olivine. Other symbols represent the data from previous studies. Crosses water-saturated olivine aggregates controlled by dislocation creep (Mei and Kohlstedt 2000b; Karato and Jung 2003). Open diamonds and squares hydrous olivine aggregates controlled by dislocation creep at 1373 K (diamonds) and 1473–1673 K (squares) (Bollinger et al. 2014). Open circle hydrous olivine aggregates controlled by disGBS (Ohuchi et al. 2015). Open triangles hydrous-melt bearing olivine aggregates controlled by diffGBS (Ohuchi et al. 2012b). Star hydrous olivine aggregates controlled by the Peierls mechanism (Katayama and Karato 2008). Half-filled circles water-saturated olivine aggregates controlled by diffusion creep (Mei and Kohlstedt 2000a). Dashed curves represent the strength of olivine aggregate controlled by dislocation creep (thin 1000 and 3000 H/106Si of water in olivine; thick water-saturated). Solid curves represent the strength of olivine aggregate controlled by both disGBS and diffGBS (thin 1000 and 3000 H/106Si of water in olivine; thick water-saturated)

Table 3 Flow law parameters for olivine aggregates used for the calculation of deformation mechanism maps

Our data set of as-is olivine (i.e., data obtained at 1633–1800 K) is best described by the power-law dislocation creep, though our data point at 9.8 GPa (1460 H/106Si) is significantly above the curve for power-law dislocation creep with water content of 1000 H/106Si (Fig. 16). This discrepancy may result from the use of a reported value of V * (=24 cm3 mol−1: Karato and Jung 2003) for the calculation of the stress–pressure curve in Fig. 16, namely our value of 27 ± 7 cm3 mol−1 (Fig. 7c; Table 2) could be better for the calculation. The effect of oxygen fugacity may have also contributed to the discrepancy.

In Fig. 16, our data are compared with previously reported values for hydrous olivine. Because the chosen temperature (1373 K) is around the boundary temperature for the transition from the power-law dislocation creep to the low temperature plasticity (i.e., the Peierls mechanism) (Katayama and Karato 2008), the stress values for the power-law dislocation creep (Karato and Jung 2003) and the Peierls mechanism (Katayama and Karato 2008) are similar to each other at 2 GPa. The stress values reported for disGBS (Ohuchi et al. 2015) and diffGBS (Ohuchi et al. 2012b) are within the range of the curves calculated from Eq. (8). Bollinger et al. (2014) have reported creep strength data for hydrous olivine at 1373–1673 K and they interpreted that the deformation was solely controlled by the power-law dislocation creep. Some of their plots (open squares in Fig. 16) are consistent with the flow law for the power-law dislocation creep, though others (especially open diamonds in Fig. 16) are significantly below the lower limit of the power-law dislocation creep and seem to be explained by disGBS (or diffGBS).

Creep mechanisms of hydrous olivine in the deep upper mantle

Ohuchi et al. (2015) evaluated the creep mechanisms controlling the upper mantle flow based on the reported flow laws of olivine, and they discussed that the contribution of disGBS to the flow of the upper mantle is very limited under hydrous conditions. However, Ohuchi et al. (2015) and other previous studies have not investigated the creep mechanism of water-saturated olivine at pressures >2 GPa. Here, we revisit the dominant deformation mechanism of hydrous olivine under deep upper mantle conditions. Figure 17 shows deformation mechanism maps of water-saturated olivine as a function of stress and grain size. The flow of hydrous mantle is dominantly controlled by dislocation creep or diffusion creep at 7 GPa and 1723 K (i.e., adiabatic temperature). Figure 17b–d suggests that disGBS is one of the most effective deformation mechanisms at higher pressures and/or lower temperatures (e.g., subducting slabs) due to a relatively low value of V * for disGBS (e.g., Ohuchi et al. 2015). Because both disGBS and diffusion creep are grain-size-sensitive creep mechanisms, the evolution of olivine grain size could control the strength of cold slabs. An empirical relationship between stress and recrystallized grain size of olivine (Van der Wal et al. 1993) suggests that dynamic recrystallization of olivine is not expected at typical upper mantle pressures and temperatures (Fig. 17). Alternative grain size reduction processes such as chemical reaction (Vissers et al. 1995) and the olivine-wadsleyite phase transformation (Liu et al. 1998) may contribute to softening of subducting slabs in the deep upper mantle. Also, sluggish grain growth due to faceting of grain boundaries observed in this study (Fig. 15) would assist in maintaining the grain-size-sensitive creep of olivine.

Fig. 17
figure17

Deformation mechanism maps for water-saturated olivine on the axes of differential stress versus grain size (G). Pressures of 7–11 GPa and temperatures of 1423–1773 K are assumed for the calculations (1723–1773 K: typical asthenospheric upper mantle conditions; 1423–1473 K: cold slabs). The boundaries (blue solid lines) were calculated from the flow laws of olivine for dislocation creep, diffusion creep, disGBS, and diffGBS (flow-law parameters are summarized in Table 3). The gray dashed lines represent the contours of strain rates. The purple solid line represents the recrystallized grain size predicted by the empirical piezometric relationship for olivine (Van der Wal et al. 1993). The yellow- and red-hatched areas represent typical conditions of the asthenospheric upper mantle and the experimental conditions, respectively. The range of grain size in the upper mantle is from the dataset of olivine in peridotite xenoliths beneath the continental extension zones and cratons (Mercier 1980). The range of stress in the yellow-hatched area is based on the depth-viscosity profiles in the upper mantle estimated by Ohuchi et al. (2015)

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Acknowledgements

The authors wish to thank Y. Nishihara, K. Funakoshi, T. Kikegawa, and T. Irifune for their technical support for the synchrotron experiments, T. Sakai for preparation of a TEM foil using the FIB system, and K. Fujino for his help with TEM observations. Official review by three anonymous reviewers improved the manuscript. This research was conducted with the approvals of the Photon Factory Program Advisory Committee (Proposal Nos. 2010G136 and 2012G133) and SPring-8 (No. 2013B0082), supported by the Grant-in-Aid for Scientific Research (Nos. 22340161 and 25707040).

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Ohuchi, T., Kawazoe, T., Higo, Y. et al. Flow behavior and microstructures of hydrous olivine aggregates at upper mantle pressures and temperatures. Contrib Mineral Petrol 172, 65 (2017). https://doi.org/10.1007/s00410-017-1375-8

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Keywords

  • Olivine
  • Upper mantle
  • Pressure
  • Water
  • Grain boundary sliding
  • Dislocation creep