Creep behavior of Fe-bearing olivine under hydrous conditions

Abstract

To understand the effect of iron content on the creep behavior of olivine, (Mg_xFe_{(1 − x)})₂SiO₄, under hydrous conditions, we have conducted tri-axial compressive creep experiments on samples of polycrystalline olivine with Mg contents of x = 0.53, 0.77, 0.90, and 1. Samples were deformed at stresses of 25 to 320 MPa, temperatures of 1050° to 1200°C, a confining pressure of 300 MPa, and a water fugacity of 300 MPa using a gas-medium high-pressure apparatus. Under hydrous conditions, our results yield the following expression for strain rate as a function of iron content for 0.53 ≤ x ≤ 0.90 in the dislocation creep regime: . In this equation, the strain rate of San Carlos olivine, , is a function of T, σ, and . As previously shown for anhydrous conditions, an increase in iron content directly increases creep rate. In addition, an increase in iron content increases hydrogen solubility and therefore indirectly increases creep rate. This flow law allows us to extrapolate our results to a wide range of mantle conditions, not only for Earth's mantle but also for the mantle of Mars.

Key Points

• Deformation experiments on polycrystalline olivine under hydrous conditions
• The first experiments using various iron contents of polycrystalline wet olivine
• Viscosity of the iron-rich mantle of Mars can be estimated using the flow law

1 Introduction

Since olivine, (Mg_xFe_{(1 − x)})₂SiO₄, is the most abundant mineral not only in the upper mantle of Earth but also of Mars, knowledge of its rheological properties is important for understanding the viscosity of the asthenosphere [e.g., Hirth and Kohlstedt, 2003; Karato and Wu, 2003], the strength of the lithosphere [Kohlstedt et al., 1995], and thereby the tectonic evolution of terrestrial planets. Several studies have investigated the flow properties of olivine as a function of temperature [Hirth and Kohlstedt, 1995a, 1995b], confining pressure [Borch and Green, 1989; Durham et al., 2009; Raterron et al., 2011], oxygen fugacity [Bai et al., 1991], melt fraction [Hirth and Kohlstedt, 1995a, 1995b], water content [Chopra and Paterson, 1981, 1984; Karato et al., 1986; Mei and Kohlstedt, 2000a, 2000b; Karato and Jung, 2003], and iron content [Zhao et al., 2009]. The Martian mantle is thought to be more iron rich than Earth's mantle with an olivine of composition x ≈ 0.75 [Morgan and Anders, 1979; Bertka and Fei, 1997] and to contain some water [Agee et al., 2013]. However, at present, no data exist on the rheological properties of more iron-rich olivine (magnesium content of x < 0.90) under hydrous conditions.

Many important geophysical and geochemical properties of the upper mantle, such as viscosity, water content, and electrical conductivity, depend on the types and concentrations of point defects in the constituent silicate minerals. For olivine, metal vacancies and Fe³⁺ on metal sites are the majority point defects, with their concentrations balanced to maintain charge neutrality [e.g., Nakamura and Schmalzried, 1983, 1984; Tsai and Dieckmann, 2002; Dohmen and Chakraborty, 2007]. The concentration of Fe³⁺ increases with increasing iron content in olivine; therefore, these geophysical and geochemical properties are also related to its iron content. For example, the viscosity of olivine decreases with increasing iron content under anhydrous conditions [Zhao et al., 2009], and water solubility increases with increasing iron content [Zhao et al., 2004; Withers et al., 2011].

In this study, we examine the creep behavior of polycrystalline olivine under hydrous conditions as a function of iron content by conducting tri-axial, compressive creep experiments using samples with Mg contents of x = 0.53, 0.77, 0.90, and 1. The results of our experiments can be applied to a wide range of conditions not only in the mantle of Earth but also that of Mars.

2 Methods

2.1 Sample Preparation

Polycrystalline samples of olivine were prepared with four different iron contents expressed here as Mg (forsterite) contents of x = 0.53, 0.77, 0.90, and 1. The methods used to prepare the olivine powders needed to fabricate these samples are well described in previous studies [Zhao et al., 2009; Koizumi et al., 2010; Hansen et al., 2012a, 2012b, 2012c].

Olivine powders were uniaxially cold pressed into cylindrical Ni cans (inner diameter of ~10 mm) with a pressure of 100 MPa. To make a hydrous sample, 0.05 ml of deionized water was added to the cold-pressed aggregates. In addition, two pieces of oriented single crystal (San Carlos olivine, composition of x = 0.90) were embedded into each aggregate to record the intracrystalline water content of olivine both before and after deformation. The Ni cans were capped with Ni discs and sealed by laser welding, which proved to be an effective method for keeping water inside the capsule. The temperature of the Ni capsule during the welding process was below 100°C. Ni capsules were chosen to fix the oxygen fugacity near the Ni–NiO buffer during both the hot press and the deformation experiment. This oxygen fugacity condition is within the olivine stability field for our experimental conditions [Nitsan, 1974]. Samples with Mg contents of x = 0.53, 0.77, 0.90, and 1 were then isostatically hot pressed in a gas-medium high-pressure apparatus at a temperature of T = 1200°C and a pressure of P = 300 MPa for 3 h. An exception was made for experiments PI-1853 and PI-1856 (x = 0.90), which were hot pressed at T = 1250°C, P = 300 MPa for 30 h and 8 h, respectively, in order to obtain larger average grain sizes. After each hot press, an ~1 mm thick slice of the polycrystalline sample containing an olivine single crystal was removed for analysis of the starting microstructure of the aggregate and water content within the olivine crystal. We analyzed the chemical composition of the samples with a JEOL-JXA-8900 electron probe micro analyzer to determine the iron content of olivine. The chemical compositions of olivine are summarized in Table A1. Small amounts of enstatite (<<1%) were detected in the samples, which buffered the silica activity.

The centers of the hot-pressed samples were removed using a diamond coring drill (diameter 3.3 mm) to make hollow-cylinder samples with typical dimensions of 9 mm outer diameter, 3.5 mm inner diameter, and 20 mm height. A cylinder of talc wrapped with nickel foil (thickness 0.025 mm) was inserted into the axial hole. The Ni foil prevents reaction between the sample and talc during the experiment while allowing diffusion of hydrogen from the talc to the sample. The entire assembly was enclosed in a Ni capsule, which was capped with Ni discs and sealed by laser welding.

The porosity of the Fe-bearing olivine samples after hot pressing was ~2%, similar to that reported in previous studies [Hirth and Kohlstedt, 1995a, 1995b; Mei and Kohlstedt, 2000a, 2000b]. The porosity of our Fe-free forsterite sample (PI-1819) was ~4%, as determined by image analysis. The higher porosity of the hot-pressed forsterite sample is most likely due to the lower homologous temperature, T/T_m, of the hot press. Therefore, we also fabricated vacuum-sintered polycrystalline forsterite, which yielded porosities of ~0.1% [Koizumi et al., 2010]. Forsterite powders were shaped into the form of a cylinder using a zirconia die. Cylindrical compacts were vacuum sealed in plastic bags and then dropped into a fluid-medium pressure vessel for cold isostatic pressing at P = 150 MPa for 20 min. Sintering was carried out under a vacuum of ~10⁻² Pa at T = 1360°C in an alumina tube furnace for 5 h. The sintered samples had a right-cylindrical shape with a diameter of ~6 mm and a height of ~12 mm. The forsterite samples were wrapped in nickel foil and then inserted into a hollow cylinder of talc. Typically, the talc cylinder had 9.8 mm outer diameter, 6 mm inner diameter, and 12 mm height. The entire assembly was enclosed in a Ni capsule and sealed by laser welding. To analyze the water content of olivine, a piece of an oriented single crystal of San Carlos olivine (x = 0.90) wrapped with Ni foil was embedded in the talc. The samples were isostatically hot pressed in a gas-medium apparatus at T = 1200°C and P = 300 MPa for 1 h to obtain dense, hydrous, polycrystalline olivine. After hot pressing, a 0.5 mm thick slice of each sample containing an oriented single crystal was obtained for analysis of the starting microstructure of the aggregate and water content of the olivine crystal. To prepare samples for deformation, the dehydrated talc and Ni were removed from the hot-pressed sample. Then, the sample with new Ni foil, talc, and an oriented olivine single crystal was enclosed within a Ni capsule, which was subsequently sealed by laser welding.

2.2 Deformation Experiments and Sample Assembly

Samples were sandwiched between alumina discs, alumina pistons, and zirconia pistons, and inserted into a 0.25 mm thick Fe tube. These sample assemblies were then loaded into a gas-medium high-pressure apparatus [Paterson, 1990]. Tri-axial compression experiments were conducted at P = 300 MPa, T = 1050° to 1200°C, and differential stresses from 25 to 320 MPa, resulting in strain rates of 8.0 × 10⁻⁷ to 1.9 × 10⁻³ s⁻¹ for polycrystalline olivine samples with Mg contents of 0.53 ≤ x ≤ 1 (Table 1). Stress was controlled to ±1 MPa, and temperature was maintained to within ±2°C over the length of the sample. The confining pressure was controlled at 300 ± 1 MPa. Each sample was annealed for 20 min at the deformation temperature and pressure prior to deformation to allow it to become saturated with water. Based on the diffusivity of hydrogen in olivine single crystals determined at our experimental conditions [Kohlstedt and Mackwell, 1998], 20 min annealing time is sufficient to allow hydrogen to saturate the olivine crystal.

Table 1. Experimental Results From Stress-Stepping Tests Under Hydrous Conditions

Exp. #	Mg Content	Stress	Strain Rate	Temperature	na	d	Standard Deviation of dc
	x	MPa	10^−4 × s^−1	°C		µm
1838	0.53	53	0.008	1050	3.3	27.6	14.30
		82	0.01
		129	0.05
		192	0.35
		262	1.20
		123	0.05
		187	0.23
		281	1.34
1824	0.53	25	0.05	1100	2.7	29.6	15.00
		47	0.30
		82	2.47
		149	11.50
		86	0.67
		47	0.10
		155	2.94
		270	18.52
1809	0.53	43	0.49	1200	3.2	28.3	14.95
		69	2.49
		112	10.17
		41	0.44
		67	1.65
1773	0.77	74	0.03	1100	2.4	14.7	7.92
		112	0.11
		170	0.21
		254	0.57
1768	0.77	28	0.01	1150	2.4	5.5	4.53
		50	0.03
		85	0.18
		146	0.34
		239	3.84
		81	0.02
		138	0.18
1806	0.77	49	0.02	1150	3.8	14.1	11.81
		68	0.04
		163	1.50
		241	6.16
		162	0.50
		71	0.02
		28	0.04	1200	3.1	14.1	11.81
		52	0.19
		90	1.53
		52	0.10
1765	0.77	89	0.31	1200	3.1	16.9	10.01
		149	0.72
		246	4.03
		51	0.03
		84	0.07
1799	0.77	31	0.04	1200	2.7	13.4	11.65
		55	0.10
		94	0.69
		161	3.24
		272	12.53
		48	0.16
		84	0.49
1802	0.90	27	0.07	1200	2.4	5.1	3.05
		49	0.29
		87	2.09
		46	0.20
		84	0.43
1815	0.90	27	0.04	1200	2.1	4.0	2.39
		51	0.11
		92	0.64
		161	2.21
		92	0.16
1817	0.90	29	0.07	1200	2.0	4.3	2.25
		53	0.12
		92	0.28
		165	1.28
		312	6.66
		88	0.21
		48	0.08
1853	0.90	173	0.12	1200	3.2	24.7	12.02
		300	0.79
		238	0.17
		169	0.05
		294	0.32
		308	0.34
1856	0.90	174	0.07	1200	4.0	7.9	3.80
		227	0.17
		301	0.51
		320	0.67
		214	0.17
		299	0.90
1819	1.00	82	1.11	1200	3.2	5.7	2.52
		148	4.54
		220	18.44
		45	0.09
1858b	1.00	31	0.06	1200	2.4	6.0	2.88
		66	0.33
		123	2.10
		150	3.51
		63	0.25
		122	1.09
		149	1.42

• ^a n from linear fitting for log stress versus log strain rate space.
• ^b Solid-cylinder sample.
• ^c Standard deviation = [S(d_i - d)² / (N − 1)]^0.5, where N is the number of analyzed grains.

Loading of the sample was initiated by moving the actuator at constant displacement rate until the deformation assembly was contacted. The load was then increased to the desired value and held constant for each deformation step of at least 1% axial strain. After several load steps to higher loads, the actuator was returned to the initial load to check the reproducibility of the load and the measured displacement rate. At the end of experiment, the actuator was backed away from the sample assembly to verify that the zero-load reading on the load cell had not changed. The differential stress was determined from the applied compressional force, taking into account changes in the load bearing area with the assumption that compression was uniform and sample volume was preserved. Displacement rates were converted to strain rates by taking into account the change in sample length at every second during the tests. The strain was determined from the piston displacement with the same assumptions used to calculate the stress. We corrected the measured load for the load supported by the iron jacket and nickel capsule based on published flow laws for iron and nickel [Frost and Ashby, 1982]. In addition, we corrected for the strength of talc based on the observation that the strength of dehydrated talc is approximately equal to the strength of Ni [Mei and Kohlstedt, 2000a, 2000b].

Most samples in this study were thin-walled cylinders with a central cylinder of talc wrapped in Ni foil. Hydrogen from the dehydrated talc diffuses into and through the sample, thus maintaining water-saturated conditions in the sample during the experiment. In contrast, in the assembly composed of an inner forsterite sample cylinder with an outer talc cylinder, hydrogen diffuses both into the sample and out of the deformation assembly. Consequently, in most of our experiments, thin-walled samples with talc inserts were used, although previous deformation experiments of polycrystalline olivine under hydrous conditions used samples with talc on the outside [e.g., Mei and Kohlstedt, 2000a, 2000b]. The mechanical data from the two different sample assemblies are compared in Appendix B. The results of deformation experiments using thin-walled cylinders with talc inside and solid-cylinder samples with talc outside are essentially identical, although having the talc inside allowed us to conduct longer experiments.

2.3 Microstructural Analysis

Both undeformed and deformed samples were polished to analyze their microstructures. Sections were cut parallel to the direction of compression for deformed samples. These sections were first polished with diamond lapping film from 30 to 0.5 µm and then with colloidal silica (0.04 µm) for 30 min. Sections were examined under a scanning electron microscope (SEM) equipped with a field emission gun (JEOL 6500F).

Crystallographic orientations of olivine grains were analyzed by electron backscattered diffraction (EBSD) to examine the microstructures and development of lattice-preferred orientations (LPOs). The highly polished sections were prepared with a thin carbon coat (50 Å) and analyzed using a SEM-EBSD system with HKL Channel5 software. EBSD was performed with a tilt angle of 70°, an acceleration voltage of 20 kV, and probe current of ~20 nA. Olivine crystallographic orientation maps were prepared with a grid spacing of 0.5 to 3 µm between analysis points depending on the sample grain size.

The size of each grain was measured using band contrast images, such as those presented in Figure 1, that were obtained from olivine crystallographic orientation maps from EBSD analysis. Outlines of more than 188 grains of olivine were traced to obtain the area (S) of each grain with the help of Scion Image software. The size of each grain was calculated from the conventional derivation of , which assumes each grain to be a perfect sphere. The grain size (d) of the sample is the average of the measured values. To compare our results to average grain sizes determined using the line intercept method, our sample grain-size measurements should be multiplied by 4/π to correct for sectioning bias [Greenman, 1951].

Figure 1

Band contrast images from samples deformed at T = 1200°C using olivine crystallographic orientation maps from EBSD analysis for samples with (a) x = 0.53 (PI-1809), (b) x = 0.77 (PI-1806), (c) x = 0.90 (PI-1815), and (d) x = 1 (PI-1858). Sections were cut parallel to the compression direction.

2.4 Fourier Transform Infrared Analysis

The water content in undeformed and deformed samples was determined using a Nicolet Series II Magna Fourier transform infrared (FTIR) spectroscopy. Doubly polished sections were prepared from the embedded single-crystal San Carlos olivine (~0.5 mm thick) and from the polycrystalline samples (~0.2 mm thick). An unpolarized beam of 50 µm diameter was used for the IR measurements with a KBr beam splitter and liquid nitrogen cooled detector. FTIR spectra were obtained at room temperature from crack- and pore-free areas of the sample. At least five spectra were collected for each section with 256 scans per spectrum at a resolution of 2 cm⁻¹, which is the minimum peak interval that can be distinguished. The infrared beam was parallel to the [010] direction for the single-crystal analysis. FTIR spectra were obtained for wave numbers from 2500 to 4000 cm⁻¹. After the background noise was removed, the FTIR spectra were normalized by the thickness of the specimen. A baseline for each spectrum was determined using a spline fit to the data between 2500 to 3100 and 3650 to 4000 and then subtracted from the normalized FTIR spectra. Water contents for the baseline-corrected FTIR spectra were calculated using the Paterson calibration [Paterson, 1982]

(1)

where C_OH is the water content of olivine, γ is an orientation factor, γ = 1/3 for polycrystalline samples and 1/2 for single crystals, and k(v) is the absorption coefficient for a given wave number v. The density factor of X₁ is chemistry dependent and X₁ = 4.52 × 10⁴, 4.45 × 10⁴, 4.40 × 10⁴, and 4.37 × 10⁴ H/10⁶Si for samples with x = 0.53, 0.77, 0.90, and 1, respectively. The equation to calculate X₁ is given in Bolfan-Casanova et al. [2000]. Multiply the results reported here by 3.5 to compare with water contents calculated using the calibration of Bell et al. [2003].

3 Analytical Procedure for Mechanical Data

Following the approach used in previous studies [e.g., Mei and Kohlstedt, 2000a, 2000b; Zhao et al., 2009], our mechanical data are fit to a flow law of the form

(2)

where is the strain rate, A is a material-dependent creep parameter, σ is the stress, n is the stress exponent, d is the grain size, p is the grain-size exponent, m is the iron content exponent, Q is the activation energy, R is the gas constant, T is the temperature, is the water fugacity, and r is the water fugacity exponent. Note that in the present study, we did not determine the dependence of strain rate on water fugacity, consistent with studies of point-defect thermodynamics for olivine [Nakamura and Schmalzried, 1983; Tsai and Dieckmann, 2002]; we used the dependence determined for sample with x = 0.9. In addition, the activation energy for creep can be expanded in a series as

(3)

where α_i is the coefficient of the ith term in the series expansion and α = α₁. The value of α is associated with the Gibbs free energy of defect formation as a function of iron content of olivine [Schmalzried, 1995, p. 38; Zhao et al., 2004, 2009].

The dependence of strain rate on stress and grain size is analyzed by considering the influence of two mechanisms operating in parallel, either diffusion (diff) and dislocation (disl) creep

(4a)

or diffusion and dislocation-accommodated grain boundary sliding (GBS)

(4b)

In equation 4a-4b,

(5a)

(5b)

and

(5c)

where , , and include iron content, water fugacity, and temperature dependencies from equation 2; that is, . From previous deformation experiments on polycrystalline olivine with x = 0.90, the stress exponent and grain-size exponent have values of (n_diff, p_diff) = (1, 3 or 2) and (n_disl, p_disl) = (3.5, 0) for samples deformed under both anhydrous and hydrous conditions [Chopra and Paterson, 1981, 1984; Karato et al., 1986; Mei and Kohlstedt, 2000b; Hirth and Kohlstedt, 2003] and (n_GBS, p_GBS) = (2.9, 0.7) for samples deformed under anhydrous conditions [Hansen et al., 2011]. Further, previous experiments under anhydrous conditions on polycrystalline samples with x = 0.50 yielded (n_GBS, p_GBS) = (4.1, 0.7) [Hansen et al., 2012a, 2012b, 2012c].

When two mechanisms operate in parallel [equation 4a-4b], the strain rates have to be normalized to fix either stress or grain size to demonstrate the dependence of strain rate on grain size or stress, respectively. For example, when diffusion and dislocation creep operate in parallel [equation 4a], the normalized strain rate with a fixed grain size of 10 µm ( ) is

(6a)

where , σ, and d are observed values in an experiment. Similarly, the normalized strain rate with a fixed stress of 100 MPa ( ) is

(6b)

4 Results

4.1 Microstructures of Olivine

Band contrast images of deformed samples with x = 0.53, 0.77, 0.90, and 1 are shown in Figure 1. Within measurement error, the grain size did not change significantly during any of the deformation experiments. Histograms of logarithmic grain-size distribution for samples of all four compositions deformed at T = 1200°C are shown in Figure 2, with theoretical log normal distributions calculated for the average grain size and the standard deviation included for comparison. Since the grain-size distributions from all the samples are approximately lognormal, the average grain size is representative of the grain size during the deformation experiment and is used in the following analyses. The average grain size increases with increasing iron content for 0.53 ≤ x ≤ 0.90 (Table 1).

Figure 2

Logarithmic grain-size distribution histograms for samples deformed at T = 1200°C with compositions (a) x = 0.53 (PI-1809), (b) x = 0.77 (PI-1799), (c) x = 0.90 (PI-1815), and (d) x = 1 (PI-1858). Theoretical lognormal distributions calculated for the average grain size and the standard deviation are included as solid lines. The inverted triangles indicate the average grain size of each distribution. The images used to determine the grain-size distributions are shown in Figure 1. The experimental number (PI-), average grain size (d), and number of measured grains (N) are included.

In the crystallographic orientation maps in Figures 3a and 3b of olivine from samples with x = 0.53 that were hot pressed and deformed at T = 1200°C, differences in crystallographic orientation are shown by color differences in the orientation map. The density of subgrain boundaries in deformed samples is one-order magnitude larger than in the undeformed samples. The LPOs of both undeformed and deformed olivine samples determined from the orientation maps in Figures 3a and 3b are relatively weak, as shown in Figures 3c and 3d.

Figure 3

Olivine crystallographic orientation maps and pole figures obtained from samples with x = 0.53 (PI-1809). (a) Undeformed sample with a grid spacing of 3 µm in the EBSD map. (b) Deformed sample with a grid spacing 3 µm. Orientation differences are indicated by the color differences. The black lines are grain boundaries (>10° misorientation angle), and the red lines are subgrain boundaries (2 ≤ misorientation angle ≤ 10°). (c) Equal area pole figure, lower hemisphere projections for olivine [100], [010], and [001] axes from an undeformed sample and (d) a deformed sample (PI-1809). Contours are multiples of uniform distribution. Foliation is horizontal and lineation is E-W. The values of J, M, and pfJ are the fabric intensities calculated after Mainprice et al. [2000] and Skemer et al. [2005]. The olivine pole figures are made by one point per grain using the maps in Figures 3a and 3b.

4.2 Mechanical Results

Since a large number of parameters—A, n, p, Q₀, and α—still appear in the flow law [equations 2 and 3], a three-step fitting process was employed. (Note: Water fugacity is not varied in our experiments except for a small change due to a change in temperature.) First, the dependences of strain rate on stress and grain size (n and p) were determined for samples of each iron content at a fixed temperature. Second, the creep parameter, A, in the flow law for olivine with x = 0.90 determined by Hirth and Kohlstedt [2003] was adjusted so that their flow law fits our creep data for the samples with x = 0.90. Third, the dependence of strain rate on iron content was determined using the values of n and p from this flow law. The mechanical data from our deformation experiments are summarized in Table 1.

4.2.1 Step 1: Dependence of Strain Rate on Stress and Grain Size (n and p)

Strain rate as a function of stress for samples with x = 0.90 at T = 1200°C is plotted for the five experiments in Figure 4a. The slope of the plot is n = 1.9 ± 0.2 and 3.6 ± 0.5 for the samples with d ≤ 5.1 µm and d ≥ 7.9μm, respectively. Further, samples with d ≤ 5.1 µm are weaker than those with d ≥ 7.9 µm at any given strain rate.

Figure 4

(a) Strain rate versus stress, (b) strain rate versus stress at fixed grain size, and (c) strain rate versus grain size at fixed stress for samples with x = 0.90 deformed under hydrous conditions at T = 1200°C. In Figure 4a, raw data without any normalization were used. In later figures, we did not correct the data; we simply normalized it to some common values of quantities such as grain size and/or stress. Different symbols indicate different experiments. In Figure 4b, strain rate was normalized to a grain size of d = 10 µm using p_diff = 3 and p_disl = 0 based on the results from fitting our data to equation 4a-4b. In Figure 4c, strain rate was normalized to a stress of σ = 250 MPa using n_diff = 1 and n_disl = 3.7 based on the results from fitting our data to equation 4a-4b. The gray solid lines and dashed line are the best fit values for equations 4a and 7, respectively. The data from previous studies were added for comparison using the stress and grain-size exponents determined in each study [Chopra and Paterson, 1981; Mei and Kohlstedt, 2000b].

For x = 0.90, a nonlinear least squares fitting process was used to obtain values for A_diff, A_{}, n_{}, and p_{} from the experimental data for , σ, and d at T = 1200°C, where {} = disl or GBS [see equations 4a and 4b]. We fixed the values of n_diff = 1 and p_diff = 3 for diffusion creep based on results from previous experiments [Mei and Kohlstedt, 2000a, 2000b; Hirth and Kohlstedt, 2003]. The resulting values for the remaining flow parameters are log A_diff = −4.5 ± 0.1 with A_diff in units of MPa⁻¹ µm³ s⁻¹, log A_{} = −13.6 ± 3.5 with A_{} in units of MPa⁻ⁿ µm^p s⁻¹, n_{} = 3.7 ± 1.3, and p_{} = 0.0 ± 0.6. A value of p_{} = 0 indicates that the observed deformation process is not dependent on grain size and takes place by dislocation creep, combined here with diffusion creep; that is, ; no dislocation-accommodated grain boundary sliding regime (i.e., regime with p > 0 and n > 1) was identified. Strain rate is plotted versus stress with grain size fixed and versus grain size with stress fixed in Figures 4b and 4c, respectively. The flow law accurately reproduces the experimental data in Figures 4b and 4c. The data from previous studies are added for comparison using the stress and grain-size exponents determined in each study [Åheim dunite in Chopra and Paterson, 1981; Mei and Kohlstedt, 2000b].

To test the robustness of the flow law parameters that we determined (Figures 4b and 4c), we also performed least squares fits to individual data sets. Strain rate as a function of stress for samples with x = 0.90 at T = 1200°C is plotted for the five experiments in Figures 5a−5e. For samples with d ≤ 5.1 µm (Figures 5a–5c), a nonlinear least squares fit to equation 4a, which includes both diffusion and dislocation creep, yielded values for , , and n_disl with n_diff = 1 fixed. For the samples with d ≥ 7.9μm (Figures 5d and 5e), a linear least squares fit to equation 5c, which includes only dislocation creep, yielded best values for and n_disl; for these samples with larger grain sizes, no significant contribution of diffusion creep was detected in the data. Although some values of n_disl have relative large errors due to the limited size of our data set, the values for n_disl lie between 2.5 and 4.3, consistent with the value for n_disl obtained in Figure 4b.

Figure 5

(a–e) Strain rate versus stress and (f) normalized strain rate versus grain size for samples with x = 0.90 deformed under hydrous conditions at T = 1200°C. (a) PI-1815, d = 4.0 µm, (b) PI-1817, d = 4.3 µm, (c) PI-1802, d = 5.1 µm, (d) PI-1856, d = 7.9 µm, and (e) PI-1853, d = 24.7 µm. The values determined for n_disl are noted. In Figure 5f, values of strain rate from Figure 5a through Figure 5e were normalized to σ = 100 MPa using the values for A_diff, A_disl, and n_disl from Figures 5a to 5e. The lines are the best fit curves.

Further, the values of strain rate for each experiment were normalized to σ = 100 MPa using the flow law parameters determined in Figures 5a–5e in order to construct the plot of strain rate versus grain size in Figure 5f. Data from deformation experiments on Åheim dunite (d = 900 µm) performed under hydrous conditions [Chopra and Paterson, 1981] are also plotted to allow extrapolation to larger grain sizes. A nonlinear least squares fit to the data from our five experiments plus that from Chopra and Paterson yielded values for , , and p_disl with p_diff = 3, using the equation . The value of the grain-size exponent p_disl = −0.2 ± 0.6 is, within error, consistent with the value obtained in Figure 4c. Overall, both fitting procedures give similar values; that is, n_disl ≈ 3.5 and p_disl ≈ 0 (Figures 4 and 5).

For samples of the other three compositions x = 0.53, 0.77, and 1, strain rate versus stress data at T = 1200°C are plotted in Figure 6. A nonlinear least squares fit to equation 4a was used to obtain values for , , and n_disl with n_diff = 1, p_diff = 3, and p_disl = 0 fixed for samples of x = 1, whereas a linear least squares fit to equation 5c was used to obtain the best values for and n_disl for samples of x = 0.53 and 0.77. We fixed the value p_disl = 0 based on the results for samples of x = 0.90 (Figures 4c and 5f) because the range of grain sizes tested in our samples is too small to well constrain p_disl. The stress exponents were determined as n_disl = 3.2 ± 0.1, 2.7 ± 0.2, and 3.4 ± 1.7 for the sample with x = 0.53, 0.77, and 1, respectively. The flow law fits the experimental data quite well, as shown in Figure 6.

Figure 6

Strain rate versus stress for samples with three different iron contents with fixed grain sizes at T = 1200°C. The best fit values for n_disl are indicated. Data are for samples with (a) x = 0.53, d = 28 µm (PI-1809), (b) x = 0.77, d = 14 µm (diamonds, PI-1799; squares, 1806), and (c) x = 1, d = 6 µm (diamonds, PI-1819; squares, PI-1858). In Figures 6b and 6c, to normalize strain rate to a common grain size, values of p_diff = 3 and p_disl = 0 were used based on Figures 4 and 5. The lines are the best fit curves.

4.2.2 Step 2: Rescaling the Flow Law for x = 0.90

The material parameters A_diff and A_disl in the flow law for olivine with x = 0.90 from Hirth and Kohlstedt [2003] are modified to fit our data. A nonlinear least squares fit to following equation was used to explain the observed , σ, and d data for samples with x = 0.90 at T = 1200°C:

(7)

where is the strain rate observed in our deformation experiments for samples with x = 0.90. The values for the parameters n, p, Q, and r for diffusion and dislocation creep are taken from Hirth and Kohlstedt [2003]. The values determined using equation 7 are A_disl = 10^{2.3 ± 0.1} MPa^-3.5s⁻¹, and A_diff = 10^{6.4 ± 0.1} µm³ MPa⁻¹s⁻¹. Note that at our experimental conditions,  ≈ 300 MPa. The flow law in equation 7 fits the experimental data quite well, as shown in Figure 4b.

4.2.3 Step 3: Effect of Iron Content on Dislocation Creep Rate

For samples with x = 0.53 and 0.77, which have relatively large grain sizes, our data are largely in the dislocation creep regime, whereas for samples with x = 0.90 and 1, which have much smaller grain sizes, some data are located near the boundary between diffusion and dislocation creep (e.g., Figures 4-7). In order to constrain the dependence of creep rate on iron content in the dislocation creep regime, we subtract the contribution from diffusion creep for the low stress data. To determine the strain rate due to dislocation creep for each composition, we subtracted the strain rate determined from the flow law for diffusion creep from the measured strain rate for all data for which at least 70% of the observed strain rate was accounted for by dislocation creep: . Here is the measured strain rate and is calculated from the diffusion creep flow law for each specific composition.

Figure 7

Results for samples with three different iron contents. Strain rate versus stress for (a) T = 1200°C and (b) at T = 1100°C. (c) Strain rate normalized to σ = 100 MPa versus 1/T. The different symbols indicate forsterite content. The lines are the best fit curves to equation 8 using α = −226 kJ/mol, r = 5/4, and m = 1/2.

The flow law for dislocation creep for Fe-bearing samples is obtained by combining equations 2, 3, and 7:

(8)

with x = 0.53, 0.77, and 0.90. The term comes from equation 7, such that . The dependence of creep rate on water fugacity in equation 2 has been determined experimentally for samples with x = 0.90, yielding a value of r ≈ 1.2 [Mei and Kohlstedt, 2000a, 2000b; Hirth and Kohlstedt, 2003; Karato and Jung, 2003]. Based on the point-defect analysis presented in section 5.6 and Appendix C, this result leads to the conclusion that r = 5/4 and m = 1/2. A nonlinear least squares fit yields α = −226 ± 11 kJ/mol. Data showing the dependence of strain rate on stress for samples with x = 0.53, 0.77, and 0.90 at 1200°C and 1100°C are plotted in Figures 7a and 7b, respectively. The strain rate determined from the flow law [equation 8] is included for comparison. Data showing the dependence of strain rate on temperature for samples with x = 0.53, 0.77, and 0.90 at constant stress are shown in Figure 7c. Equation 8 fits the strain rate measured in our experiments well, although there is some deviation for the sample with x = 0.53 at lower temperatures (Figure 7c).

To check the reproducibility of the load and the measured displacement rate, the actuator was returned to the initial load. Most of the experiments have good reproducibility of strain rate within experimental uncertainty, whereas some deviation is seen for the sample with x = 0.53 at lower temperatures (Figure 7b).

4.3 Water Content of Deformed Samples

FTIR spectra from the olivine single crystals embedded in the deformed polycrystalline samples are presented in Figure 8a. The water contents are 210, 270, 310, and 320 H/10⁶Si for single crystals embedded in polycrystalline samples with x = 0.53, 0.77, 0.90, and 1, respectively. All the FTIR spectra of the single crystals analyzed in this study exhibit strong peaks near 3237, 3330, 3357, 3528, and 3566 cm⁻¹.

Figure 8

FTIR spectra obtained from (a) the embedded single crystals of San Carlos olivine (x = 0.90) and (b) the polycrystalline olivine samples with four different iron contents.

The FTIR spectra from all of our deformed polycrystalline samples exhibit a broad background extending from 3100 to 3700 cm⁻¹. Representative FTIR spectra are plotted in Figure 8b. The measured water contents are approximately 6330, 5930, 1270, and 150 H/10⁶Si from samples with x = 0.53, 0.77, 0.90, and 1, respectively. For both single crystal and polycrystalline specimens, no variation in water content was observed from the edge to the center.

5 Discussion

5.1 Comparison With Previous Studies of Deformation

Several studies have been published on deformation of polycrystalline olivine with a Mg content of x = 0.90 under hydrous conditions [Chopra and Paterson, 1981, 1984; Karato et al., 1986; Mei and Kohlstedt, 2000a, 2000b; Hirth and Kohlstedt, 2003; Karato and Jung, 2003]. Here we only compare the results from samples that were buffered by Ni/NiO at T = 1200°C to decrease any uncertainty introduced by the experimental design. The strain rates measured in samples deformed by Mei and Kohlstedt [2000b] are a factor of ~1.1 faster than those determined in this study for σ = 100 MPa, d = 10 µm (Figure 4b). The difference in grain size between Åheim dunite (900 µm) [Chopra and Paterson, 1981] and our polycrystalline samples is ~2 orders of magnitude, whereas the difference in strain rate is only a factor of ~2, further demonstrating that there is little or no dependence of strain rate on grain size; that is, p_disl ≈ 0. Consequently, the mechanical data from our experiments with a Mg content of x = 0.90 under hydrous conditions are consistent with those from previous studies.

The strain rates determined under anhydrous conditions [Zhao et al., 2009] are always slower than those obtained under hydrous conditions for Fe-bearing olivine. The difference in strain rate measured in samples deformed under anhydrous and hydrous conditions increases with increasing iron content. At T = 1200°C, P = 300 MPa, σ = 100 MPa, and d = 20 µm, the strain rates for anhydrous samples are a factor of 7 and 45 slower than determined for our hydrous samples with x = 0.90 and x = 0.53, respectively. This observation reflects the fact that water solubility increases with increasing Fe content and, thus, results in a larger water-weakening effect in the more Fe-rich samples.

5.2 Comparisons With Previous Studies on Water Content

Two previous studies investigated the water solubility as a function of iron content in olivine. Zhao et al. [2004] conducted hydrothermal annealing experiments from T = 1000° to 1300° at P = 300 MPa using olivine single crystals with Mg contents of 0.83 ≤ x ≤ 1, and Withers et al. [2011] conducted hydrothermal annealing experiments at T = 1200° and 1500°C at P = 3 and 6 GPa using olivine grains with Mg contents of 0.50 ≤ x ≤ 1 that were grown within polycrystalline samples. Both studies demonstrated that water solubility increases with increasing iron content.

The water content measured in our embedded San Carlos crystals (Figure 8a) is consistent with saturation values for our experimental conditions of 290 H/10⁶Si at T = 1200°C, P = 300MPa, and x = 0.90 [Zhao et al., 2004]. Further, the water content from our polycrystalline samples with x = 0.90 is four times larger than the water content from the associated single crystal (Figure 8). The broad absorption band in the FTIR spectra from our polycrystalline samples indicates that water is trapped fluid inclusions within the grains and/or along grain boundaries. The presence of these water bubbles demonstrates that the activity of water is buffered at approximately unity. Consequently, we concluded that our samples were water saturated during the deformation experiments.

5.3 Flow Law Parameters and Creep Mechanisms

We used a three-step process to determine the parameters of equations 2 and 3. First, A_diff, A_disl, n_disl, and p_disl were determined for samples at fixed T = 1200°C with a Mg content of x = 0.90 (section 4.2.1). Since there is only a limited amount of data at small stresses (<50 MPa), the stress and grain-size exponents for diffusion creep were fixed at n_diff = 1 and p_diff = 3 based on previously published results [e.g., Mei and Kohlstedt, 2000a; Hirth and Kohlstedt, 2003]. These values correspond to those predicted for grain boundary diffusion creep [Coble, 1963]. As demonstrated in Figure 4a, the stress exponent decreases with decreasing grain size. The samples with d ≤ 5.1 µm are softer than the samples with d ≥ 7.9μm, and the slope of the plot is n = 1.9 ± 0.2 and 3.6 ± 0.5 for the sample with d ≤ 5.1 µm and d ≥ 7.9μm, respectively. Similarly, as demonstrated in Figures 5a–5c, the stress exponent decreases with decreasing stress. For example, for PI-1817 in Figure 5b, the four data points at higher stress indicate a value for n = 2.7 ± 0.3, whereas the five data points at lower stress indicate a value for n = 1.2 ± 0.1. Those trends imply that the contribution of diffusion creep is larger at lower stress and smaller grain size as expected.

At higher stresses, the stress exponent and grain-size exponent of samples with x = 0.90 deformed under hydrous conditions are n_disl = 3.7 ± 1.3 and p_disl = 0.0 ± 0.6, as determined from a nonlinear least squares fit of our full data set (Figures 4b and 4c). Fits of our individual data sets yield 2.5 ≤ n_disl ≤ 4.3 and p_disl = −0.2 ± 0.6 (Figure 5). The flow law parameters determined by these different methods agree within error, indicating the robustness of the n_disl and p_disl. Due to the absence of a nonlinear relationship between stress and strain rate in Figures 5d and 5e and Figures 6a and 6b for large grain-size samples (d ≥ 7.9μm), a linear least squares fit to equation 5c was used to determine best values of and n_disl.

The grain-size exponent determined for our samples is p_disl ≈ 0 under hydrous conditions for dislocation creep. In contrast, previous deformation experiments on polycrystalline olivine under anhydrous conditions demonstrated that there is a grain-size dependence with p ≈ 1, indicative of a dislocation-accommodated grain boundary sliding process with n ≈ 3 [Hirth and Kohlstedt, 2003; Wang et al., 2010; Hansen et al., 2011, 2012a, 2012b, 2012c]. Mei and Kohlstedt [2000b] and Hirth and Kohlstedt [2003] also observed an absence of a grain-size dependence under hydrous conditions. They noted that the flow law for coarse-grained and fine-grained samples is similar to that for deformation of the weakest slip system in olivine single crystals [see Mei and Kohlstedt, 2000b, Figure 9; Hirth and Kohlstedt, 2003, Figure 6b] and argued that enhanced dislocation climb under hydrous conditions replaced the need for grain boundary sliding observed under anhydrous conditions.

Second, the material-dependent parameters, A_diff and A_disl, in the flow law from Hirth and Kohlstedt [2003] for olivine with x = 0.90 deformed under hydrous conditions were modified to fit the data from this study (section 4.2.2). Their flow law was largely based on a reanalysis of the data from Mei and Kohlstedt [2000a, 2000b], who used the same starting olivine powders and apparatus as used in our study. Most of their data were obtained near the transition between diffusion and dislocation creep due to the small variation of grain size (grain size ranges from 13 to 19 µm) in their samples. In contrast, the grain sizes range from 4 to 25 µm in our experiments. The coarser grained samples (up to ~25 µm vs. ~19 µm) allowed us to obtain a more robust data set in the dislocation creep regime (Figure 5). Consequently, we adjusted the values of A_diff and A_disl from Hirth and Kohlstedt [2003] to fit our data.

Third, we determined the dependence of creep rate on iron content from the fit of our data to equation 8 (section 4.2.3). The resulting dependence on iron content is expressed by two parameters, α and m. The magnitude of α determined for hydrous conditions (α = −226 ± 11 kJ/mol) is larger than that obtained for anhydrous conditions (α = −45 kJ/mol) [Zhao et al., 2009], reflecting the fact that water content increases with increasing iron content of olivine [Figure 8 in this study and also Zhao et al., 2004; Withers et al., 2011]. Thus, the effect of iron content on creep rate is enhanced under hydrous conditions. The data for the sample with x = 1 are excluded in the determination of α, which is discussed in section 5.6.

5.4 Rate-Limiting Creep Mechanism

To evaluate the rate-limiting deformation mechanism, we examine the process of climb-controlled dislocation creep. Hirth and Kohlstedt [2015] have recently presented a model based on dislocation climb to account for the measured value for the stress exponent, n_disl ≈ 3.5 (vs. the predicted value of n_disl = 3) [e.g., Poirier, 1985, pp. 108–109] and the sluggish rate of Si lattice diffusion in olivine under both anhydrous and hydrous conditions [Dohmen et al., 2002; Costa and Chakraborty, 2008; Fei et al., 2012, 2013]. They argued that both of these issues can be understood if Si is the slowest diffusing and thus rate-limiting species and if the flux of Si ions is dominantly along dislocations, so-called pipe diffusion. From Orowan's equation, recall that , where v is dislocation velocity. Following the model of Hirth and Kohlstedt [2015], if the dislocation velocity is determined by the velocity of climb (v_c), then , where is the pipe diffusion coefficient for Si. In addition, we note that the diffusivity of Si equals the product of the diffusivity and the concentration of Si vacancies, , where is the diffusivity of Si vacancies and [V_Si]^tot is the total concentration of Si vacancies, as discussed in more detail in section 5.6. Thus, for climb-controlled, dislocation creep, . Below, we examine the implications of this relationship between strain rate and vacancy concentration in terms of the influence of Fe.

5.5 Influence of Iron on Creep Rate: A Point-Defect Perspective for Anhydrous Conditions

Under anhydrous conditions, the types and concentrations of point defects in olivine have been investigated using several different experimental techniques, including thermogravimetry [Nakamura and Schmalzried, 1983; Tsai and Dieckmann, 2002], electrical conductivity [Constable and Roberts, 1997; Constable and Duba, 2002], and ionic diffusion [Nakamura and Schmalzried, 1984; Dohmen and Chakraborty, 2007]. These studies conclude that and are the majority point defects, such that the charge neutrality is given by for Fe-bearing olivine. (Kröger and Vink [1956] notation is used to express the species, charge, and site of various point defects.) However, this charge-neutrality condition is obviously not valid for the Mg end-member, forsterite with x = 1. Metal vacancies are also expected to be a majority point defect for forsterite with a possible charge-neutrality condition given by [Smyth and Stocker, 1975; Brodholt, 1997; Fei et al., 2012].

If strain rate is proportional to the concentration of Si vacancies (section 5.4), the charge-neutrality conditions combined with point-defect chemistry for Fe-bearing and Fe-free olivine allow us to predict the dependence of strain rate on iron content—that is, the value of m in equation 2, —under anhydrous conditions. Specifically, based on Table C1 with , for Fe-bearing olivine. Creep results for olivine samples of different compositions in the 0 ≤ x ≤ 0.90 are consistent with this prediction [Zhao et al., 2009]. Not surprisingly, for Fe-free olivine, for all charge-neutrality conditions. The dependence of the concentration of Si vacancies on iron content for these charge-neutrality conditions is shown in Figure 9a.

Figure 9

(a) Dependence of Si vacancy concentration on iron content for two charge-neutrality conditions under anhydrous conditions. The number associated with each line is the iron content exponent for the given charge-neutrality condition. (b) Plot of strain rate versus iron content for samples deformed in the dislocation-accommodated grain boundary sliding regime under anhydrous conditions for T = 1200°C, σ = 100 MPa, and d = 20 µm. The data from previous experiments for different forsterite content samples are included [Zhao et al., 2009; Hansen et al., 2011; Tasaka et al., 2013]. The line is the flow law from Zhao et al. [2009] for the charge-neutrality condition . Dashed line is the extrapolation of equation of Zhao et al. [2009] for Mg-rich olivine. (c) The dependence of the concentration of Si vacancies on iron content for two charge-neutrality conditions under hydrous conditions. The lines indicate that different iron content dependency for the given charge-neutrality conditions. (d) Plot of strain rate versus iron content for samples deformed by dislocation under hydrous conditions with T = 1200°C, P = 300 MPa, and σ = 100 MPa is the flow law determined in this study for the charge-neutrality condition . Dashed line is the extrapolation of equation 8 for Mg-rich olivine. The data from previous experiments for different forsterite content samples are included for T = 1200°C, and σ = 100 MPa [Chopra and Paterson, 1981; Mei and Kohlstedt, 2000b; McDonnell et al., 2000].

We compiled the results of previous deformation experiments on samples with various iron contents deformed at T = 1200°C under anhydrous conditions by dislocation-accommodated grain boundary sliding creep [Zhao et al., 2009; Hansen et al., 2011; Tasaka et al., 2013]. Strain rate is plotted versus iron content in Figure 9b for σ = 100 MPa and d = 20 µm, using n_disl and p_disl values derived in these studies. Strain rate as a function of iron content from the flow law from Zhao et al. [2009] is also plotted in Figure 9b. Strain rate decreases with decreasing iron content. The strain rate of the Fe-free sample (x = 1) is roughly equal to the estimated strain rate for an Fe-bearing sample with x = 0.99, indicating a change in charge-neutrality condition near that composition.

5.6 Influence of Iron on Creep Rate: A Point-Defect Perspective for Hydrous Conditions

Under hydrous conditions, the concentrations of water-derived point defects, such as and , become significant; here p^• indicates a proton and the curly brackets {} indicate a defect associate. It is anticipated that one or both of these hydrous defects will replace and/or , respectively, as majority point defects [Karato, 1989; Kohlstedt, 2007]. Based on deformation, diffusion, and electrical conductivity data, the charge-neutrality condition has been proposed for Fe-bearing olivine [Karato, 1989; Mei and Kohlstedt, 2000a; Karato, 2008; Wang et al., 2006] and for forsterite [Fei et al., 2014]. Given these charge-neutrality conditions for hydrous conditions, if the deformation is rate limited by diffusion of Si, the dependence of the strain rate on iron content [i.e., the value of m in equation 2] can be determined from Table C1.

We summarize the results of our deformation experiments in the dislocation creep regime at T = 1200°C with σ = 100 MPa using n_disl = 3.5 in Figure 9d. The data from previous studies on samples with a forsterite content of x = 0.90 deformed by dislocation creep under hydrous conditions [Åheim dunite from Chopra and Paterson, 1981; Mei and Kohlstedt, 2000b] are also included for σ = 100 MPa using n_disl from their studies. The strain rate as a function of iron content of olivine determined from our flow law [equation 8], assuming the charge-neutrality condition for Fe-bearing olivine, is also plotted. With decreasing iron content, the strain rate decreases for x ≤ 0.90. However, the observed strain rate for the sample with x = 1 is larger than the observed strain rate of the sample with x = 0.90 (Figure 9d).

Since are significantly more mobile than vacancies in olivine [Kohlstedt and Mackwell, 1998], the concentration of Si vacancies is best described by the sum of Si vacancies, including those that are associated with one or more ; that is, , where, for example, . As described in Appendix C, the dependence of the strain rate on iron content and water fugacity (i.e., the values of m and r) can be determined for each type of silicon vacancy. Previous diffusion and deformation experiments demonstrated that water fugacity exponent r ≈ 1.2 in Fe-bearing olivine [Mei and Kohlstedt, 2000a; Costa and Chakraborty, 2008; Karato and Jung, 2003]. A water fugacity exponent of r = 5/4 indicates that is the primary type of silicon vacancy in these systems (i.e., ), consistent with the ab initio calculations of Brodholt and Refson [2000].

The observation in Figure 9d that Fe-free olivine is weaker than Fe-bearing olivine under hydrous conditions is unexpected, if both materials are deforming by the same mechanism. A comparison of our results on forsterite with those of McDonnell et al. [2000] reveals a clear dependence of creep rate on grain size; that is, p_disl > 0. Together with a stress exponent of n ≈ 3, we conclude that the Fe-free samples are deforming by dislocation-accommodated grain boundary sliding. In contrast, the Fe-bearing samples under hydrous conditions deform by dislocation creep. In previous studies on Fe-bearing olivine, Mei and Kohlstedt [2000b] and Hirth and Kohlstedt [2003] proposed that sample with x = 0.90 deformed not only by dislocation-accommodated grain boundary sliding under anhydrous conditions but by dislocation creep under hydrous conditions because the addition of water significantly enhanced dislocation climb, reducing the importance of grain boundary sliding in the deformation process. Extension of their analysis to the present study suggests that water has a larger effect on dislocation climb in Fe-bearing olivine than in Fe-free olivine, consistent with the significantly larger hydrogen solubility in Fe-bearing olivine than in forsterite [Zhao et al., 2004; Withers et al., 2011].

5.7 Application for Geological Conditions

Deformation experiments using various amounts of iron in olivine under hydrous conditions are an important first step in determining the relevant flow law necessary for modeling dynamical processes occurring in the Martian mantle. The results provide first-order constraints on the viscosity profile in the upper mantle, the strength of lithosphere, and tectonic evolution of the planet. Because the viscosity of olivine-rich rocks depends on iron content, mantle composition directly affects the interior dynamics of a planet. Analyses of Martian meteorites and geophysical observations of the Martian mantle from orbiters suggest that the Martian mantle is composed of more iron-rich olivine (x ≈ 0.75) than Earth's mantle (x ≈ 0.90) and contains some water [Morgan and Anders, 1979; Bertka and Fei, 1997; Agee et al., 2013]. Because olivine is thought to be the dominant mineral in both the upper mantle of Earth and Mars, the Martian mantle will be less viscous than the Earth's mantle due to the higher iron content of olivine. For the thermodynamic conditions of our experiments, the viscosity of the mantle of Mars will be a factor of ~20 lower than viscosity of the mantle of Earth.

Acknowledgments

We would like to thank the Kohlstedt lab members for helpful discussions and technical assistance with the experiments, A. van der Handt for assistance of electron microprobe analyses, and N. Seaton for assistance of EBSD analyses. Forsterite powder was supplied from T. Hiraga through Earthquake Research Institute's cooperative research program. The manuscript was significantly improved by insightful comments from two anonymous reviewers. This study was supported by JSPS research fellowship for young scientists (26-4879) to M.T., by NSF grant (1345060) and NASA grant (NNX11AF58G) to M.E.Z., and by NASA grant (NNX10AM95G and NNX15AL53G) to D.L.K. Parts of this work were carried out in the Characterization Facility in the College of Science and Engineering at the University of Minnesota, a member of the NSF-funded Materials Research Facilities Network (www.mrfn.org) via the MRSEC program. Electron microprobe analyses were carried out at the Electron Microprobe Laboratory, Department of Earth Sciences, University of Minnesota-Twin Cities. Data used in this paper are available by request from the corresponding author.

Appendix A: Chemical Composition of Olivine

The chemical compositions of our olivine samples measured by electron microprobe are summarized in Table A1. Both wavelength dispersive measurements and energy dispersive X-ray mapping indicate that all samples are chemically homogeneous. The Mg₂SiO₄ samples were prepared from high-purity powders; their chemical composition is given in Koizumi et al. [2010]. In contrast, all of our Fe-bearing samples have some impurities or trace elements including Ni and Mn due to impurities present in the San Carlos olivine (Table A1). No metal oxide was detected in any of the samples as a secondary mineral.

Table A1. Microprobe Results of Synthesized Fe-rich Olivine

Forsterite Content: x	0.00	0.53	0.77	0.90
SiO2	29.97	33.78	36.67	38.90
FeO	70.39	41.00	22.09	9.67
MnO	–	0.04	0.10	0.12
MgO	0.06	25.25	40.54	50.80
CaO	0.02	–	–	–
K2O	0.01	–	–	–
NiO	0.06	0.30	0.44	0.39
Total	100.50	100.36	99.85	99.87
Mg#a	0.00	0.53	0.77	0.90

• ^a Mg# = Mg / (Mg + total Fe).

Appendix B: Thin-Wall Cylinders Versus Solid Cylinders

The Fe-bearing samples in this study were thin-wall cylinders, while the Fe-free sample PI-1858 was a solid cylinder. Previous deformation experiments on polycrystalline olivine (x = 0.90) under hydrous conditions used solid cylinders [e.g., Mei and Kohlstedt, 2000a, 2000b]. To compare the creep rates for these two sample geometries, we conducted deformation experiments using samples with a Mg content of x = 0.77 at T = 1200°C, P = 300 MPa under anhydrous conditions with Ni replacing talc as the central core of the thin-wall sample. Deformation experiments using thin-wall and solid-cylinder samples yielded essentially identical results (Table B1).

Table B1. Experimental Results of Stepping the Weight Test Under P = 300 MPa at Anhydrous Conditions

Exp. #	Forsterite Content: x	Stress	Strain Rate	Temperature	d	nc
		MPa	10^−4 × s^−1	°C	µm
1781a	0.77	38	0.01	1200	5.1	1.78
		64	0.01
		92	0.02
		155	0.05
		263	0.26
		310	0.53
		88	0.02
		149	0.05
		60	0.02
1788b	0.77	47	0.02	1200	7.2	2.18
		80	0.02
		128	0.04
		204	0.12
		317	0.75
		340	1.15
		117	0.04
		185	0.11

• ^a Solid-cylinder sample.
• ^b Thin-wall sample.
• ^c n from linear fitting for log stress versus log strain rate space.

Appendix C: Point-Defect Chemistry

Table C1 summarizes the dependence of several point defects on iron content [i.e., m in equation 2] and water fugacity [i.e., r in equation 2] for a number of charge-neutrality conditions. In discussing the concentration of Si vacancies available for diffusion, we calculate the total concentration as , because is significantly more mobile than vacancies in olivine [Kohlstedt and Mackwell, 1998]. As an example, note that the shorthand notation is often used in place of . However, the latter more clearly expresses the importance of H⁺ ions to kinetic properties of nominally anhydrous minerals.

Table C1. Possible Charge Neutrality Conditions and Dependencies of Si Vacancy Concentrations in Olivine Under Anhydrous and Hydrous Conditions

Hydrous Conditions	Charge Neutrality
Fe-rich Ol		m	2	3/2	1	1/2	0
		r	−1	−1/4	1/2	5/4	2
Mg-rich Ol		m	0	0	0	0	0
		r	0	1/2	1	3/2	2
Anhydrous Conditions	Charge neutrality
Fe-rich Ol		m	4/3
		r	0
Mg-rich Ol		m	0
		r	0