Volume 125, Issue 9 e2020JB019888
Research Article
Free Access

Rheological Weakening of Olivine + Orthopyroxene Aggregates Due to Phase Mixing: Effects of Orthopyroxene Volume Fraction

Miki Tasaka

Corresponding Author

Miki Tasaka

Department of Earth Science, University of Minnesota, Twin Cities, Minneapolis, MN, USA

Now at Department of Geoscience, Shizuoka University, Shizuoka, Japan

Correspondence to:

M. Tasaka,

[email protected];

[email protected]

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Mark E. Zimmerman

Mark E. Zimmerman

Department of Earth Science, University of Minnesota, Twin Cities, Minneapolis, MN, USA

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David L. Kohlstedt

David L. Kohlstedt

Department of Earth Science, University of Minnesota, Twin Cities, Minneapolis, MN, USA

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First published: 10 August 2020
Citations: 16

Abstract

To understand the effects of secondary minerals on changes in the mechanical properties of upper mantle rocks due to phase mixing, we conducted high-strain torsion experiments on aggregates of iron-rich olivine + orthopyroxene (opx) with opx volume fractions of fopx = 0.15, 0.26, and 0.35. For samples with larger amounts of opx, fopx = 0.26 and 0.35, the value of the stress exponent decreases with increasing strain from n ≈ 3 for γ  5 to n ≈ 2 for 5  γ  25, indicating that the deformation mechanism changes as strain increases. In contrast, for samples with fopx = 0.15, the stress exponent is constant at n ≈ 3.3 for 1  γ  25, suggesting that no change in deformation mechanism occurs with increasing strain for samples with smaller amounts of opx. The microstructures of samples with larger amounts of opx provide insight into the change in deformation mechanism derived from the mechanical data. Elongated grains align subparallel to the shear direction for samples of all three compositions deformed to lower strains. However, strain weakening with grain size reduction and the formation of a thoroughly mixed, fine-grained texture only develops in samples with fopx = 0.26 and 0.35 deformed to higher strains of γ  16. These mechanical and associated microstructural properties imply that rheological weakening due to phase mixing only occurs in the samples with larger fopx, which is an important constraint for understanding strain localization in the upper mantle of Earth.

Key Points

  • High-strain torsion experiments on samples of iron-rich olivine + orthopyroxene have been conducted
  • Only higher orthopyroxene volume fraction samples undergo rheological weakening due to phase mixing
  • The mechanical and associated microstructural properties are important for understanding strain localization in upper mantle shear zones

1 Introduction

Strain weakening associated with localization of deformation in shear zones is essential for understanding the strength and dynamics of the Earth's lithosphere (Bercovici et al., 2000; Bercovici et al., 2015; Tackley, 2000). In naturally occurring shear zones, grain size reduction by dynamic recrystallization coupled with thorough mixing of the constituent phases resulting in fine-grained polycrystalline aggregates is frequently observed (Ambrose et al., 2018; Drury et al., 2011; Linckens et al., 2011; Michibayashi & Mainprice, 2004; Tasaka et al., 2014; Toy et al., 2010; Warren & Hirth, 2006). Once a thoroughly mixed, fine-grained texture has formed, secondary phases efficiently pin the grain boundaries of the primary phase thus inhibiting grain growth, so called Zener pinning (Evans et al., 2001; Smith, 1948). As a result, the grain size stays small permitting strain to localize in the fine-grained layer with deformation occurring by a grain-size sensitive creep mechanism (e.g., Linckens et al., 2011; Tasaka et al., 2014; Warren & Hirth, 2006).

Previous deformation experiments using two-phase aggregates demonstrated that strain weakening is associated with grain size reduction resulting from phase mixing in olivine-pyroxene systems (Farla et al., 2013; Hirauchi et al., 2016; Precigout & Stunitz, 2016; Tasaka, Zimmerman, & Kohlstedt, 2017; Tasaka, Zimmerman, Kohlstedt, Stunitz, & Heilbronner, 2017), olivine-ferropericlase systems (Wiesman et al., 2018), and calcite-halite systems (Cross & Skemer, 2017). Especially for peridotites, several mixing mechanisms have been proposed including dynamic recrystallization, geometrical mixing due to grain boundary sliding, formation of cavities leading to nucleation of new grains under hydrous conditions, formation of new hydrous phases due to reaction of minerals, severing of new grains formed at triple junctions coupled with their transport along grain boundaries, severe shear thinning of individual phases, and stress-driven diffusion processes (Bercovici & Skemer, 2017; Cross & Skemer, 2017; Farla et al., 2013; Hirauchi et al., 2016; Linckens et al., 2014; Precigout & Stunitz, 2016; Tasaka, Zimmerman, Kohlstedt, Stunitz, & Heilbronner, 2017).

To provide new constraints on the physical and chemical processes involved in two-phase mixing, we have extended our previous high-strain torsion experiments on samples of olivine plus 26% orthopyroxene (Tasaka, Zimmerman, & Kohlstedt, 2017; Tasaka, Zimmerman, Kohlstedt, Stunitz, & Heilbronner, 2017) to include both larger and smaller amounts of orthopyroxene. In this paper, we describe the results of experiments on samples with orthopyroxene fractions of fopx = 0.15 and 0.35. Samples with a larger amount of orthopyroxene, such as the samples with fopx = 0.26, undergo a change in deformation mechanism at high strains, while samples with a smaller amount of orthopyroxene, such as the samples with fopx = 0 (Hansen et al., 2012), do not experience this change. The results obtained on the sets of samples are used to provide further insight into rheological weakening due to phase mixing.

2 Methods

2.1 Sample Synthesis and Deformation Experiments

Since sample preparation and experimental methods are described in Tasaka, Zimmerman, and Kohlstedt (2017) and Tasaka, Zimmerman, Kohlstedt, Stunitz, and Heilbronner (2017), we summarize only the essential points here. Aggregates of iron-rich olivine, Fo50, and orthopyroxene, En55, with orthopyroxene volume fractions of 0.15, 0.26, and 0.35 were synthesized for our experiments. Since iron-rich olivine is significantly weaker than natural olivine (~Fo90) (Tasaka et al., 2015, 2016; Zhao et al., 2009, 2018), the chance of slipping on the interfaces between a sample and the pistons is greatly reduced during a high-strain torsion experiment. Furthermore, the lower strength allows us to conduct deformation experiments over a wider range of strain rates and to higher strains than is possible with more magnesium-rich samples (Fo90 and En90). Microstructural changes including crystallographic-preferred orientation (CPO) development during deformation are indistinguishable between Fo50 and Fo90 (Hansen et al., 2014). In addition, the mechanical behavior of iron-bearing olivine can be extrapolated from Fo50 to Fo90 using a flow law that expresses the strain rate as a function of iron content of olivine (Tasaka et al., 2015; Zhao et al., 2009, 2018).

Iron-rich olivine and orthopyroxene powders with fopx = 0.15, 0.26, and 0.35 were fabricated from mixtures of Fe2O3, SiO2, and San Carlos olivine powders using a one-atmosphere, horizontal, alumina-tube furnace with a flowing mixture of CO and CO2 gas to maintain the oxygen fugacity within the olivine stability field. To form samples for torsion experiments, the powders were hot pressed using a gas-medium apparatus (Paterson, 1990) at a temperature of T = 1200°C and a confining pressure of P = 300 MPa for 8 hr. The polymorph of the pyroxene phase was determined with Raman spectroscopy.

To minimize the radial variation in stress within a sample during a torsion experiment, the resulting cylinders were cored to produce thin-walled cylindrical samples, and a nickel cylinder was inserted (Hansen et al., 2012; Paterson & Olgaard, 2000). Each sample was deformed at a constant twist rate with T = 1200°C and P = 300 MPa in a gas-medium torsion apparatus (Paterson & Olgaard, 2000). The olivine aggregates with fopx = 0 were previously deformed at comparable P-T conditions (Hansen et al., 2012). Once the flow stress approached a steady-state value, the twist rate was stepwise increased and decreased to determine the dependence of strain rate on stress. The rate-stepping tests were repeated at shear-strain increments of Δγ ≈ 3. In experiments to very large strains (γ > 16), there is an oscillation in the torque-twist data with a wavelength of ~2π rad, due to some off-axis rotation of the sample assembly. To subtract this background noise from the raw data (i.e., torsion internal torque, Nm-torsion twist, and rad), we imposed a best fit cosine curve with 2π wavelength following the procedure developed for previous high-strain torsion experiments (Lars Hansen, personal communication, 25/5/2015).

2.2 Microstructural Analysis

In preparation for microstructural analyses, undeformed and deformed samples were polished using diamond lapping film with grit sizes from 30 to 0.5 μm and subsequently polished using a colloidal silica slurry with a particle size of 40 nm. For deformed samples, tangential sections, which are parallel to the shear direction and perpendicular to the shear plane, were prepared. To highlight the grain and phase boundaries, the polished samples were thermally etched at T = 1150°C for 30 min at room pressure in a flowing CO/CO2 gas mixture to maintain the oxygen fugacity within the olivine stability field. Minimal microstructural changes occurred during thermal etching as confirmed by comparing the electron backscattered diffraction (EBSD) analyses of samples before and after etching. Thermally etched, polished sections were observed using a field-emission scanning electron microscope. Secondary electron microprobe images, such as those in Figure 1, were obtained for both undeformed and deformed samples. The outlines of olivine and orthopyroxene grains were manually traced from high-resolution images, and equivalent-area diameters, dEA, were calculated using the relationship dEA = 2(S/π)0.5, where S is the grain area. From the equivalent-area diameter, average grain sizes (i.e., arithmetic means) of olivine (dol) and orthopyroxene (dopx) were calculated with a scaling factor of 4/π (Underwood, 1970). The values of fopx were determined from the area fraction of olivine (ΣSol) and orthopyroxene (ΣSopx) measured in undeformed samples. Grain size distributions for samples with fopx = 0.26 are shown in our previous study (Tasaka, Zimmerman, Kohlstedt, Stunitz, & Heilbronner, 2017) using at least 1,300 grains for olivine and for orthopyroxene. For samples with fopx = 0.15 and 0.35, the distributions are similar to those of samples with fopx = 0.26 both in 2-D measurements with a scaling factor and in 3-D grain size distributions determined with STRIPSTAR program (Heilbronner & Barrett, 2014). At least 820 grains were analyzed to calculate average grain sizes for all of the samples.

Details are in the caption following the image
Secondary electron images of tangential sections of undeformed and deformed samples. (a–c) fopx = 0.35; (d–f) fopx = 0.26; (g–i) fopx = 0.15. (j–l) Band contrast images from EBSD analyses of undeformed and deformed samples with fopx = 0 (Hansen et al., 2012, 2014). In pyroxene-bearing samples (a to i), the light gray mineral is olivine, and the dark gray mineral is pyroxene. In pyroxene-free samples (j–l), differences in gray scale indicate crystallographic-orientation differences of olivine grains. All samples were sheared top to the right. A strain ellipse displaying the angle of the long axis relative to the shear plane is included in the lower left corner of each image.

The relative frequency of phase boundaries, fPB, was used to characterize the phase distribution of our samples as random, clustered, or ordered (anticlustered) (Heilbronner & Barrett, 2014). The total lengths of olivine-olivine grain boundaries, orthopyroxene-orthopyroxene grain boundaries, and olivine-orthopyroxene phase boundaries were measured on SEM maps of grain-grain interfaces. From these data, the fractional length of olivine-orthopyroxene phase boundaries and the volume fraction of orthopyroxene were calculated.

To examine the development of the CPO in olivine grains, EBSD data obtained with a JEOL-6500F SEM on polished sections were analyzed with the HKL Channel 5 software package. EBSD analyses were carried out at a 70° tilt angle, 20 kV acceleration voltage, and 20 nA probe current. For each sample, areas of ~400 × 400 μm with grid spacing of 1 μm for undeformed samples and 0.7 μm for deformed samples were analyzed. Grains with less than 4 pixels were excluded from the data to minimize analysis error. On the SEM-EBSD system, only olivine grains were indexed. Orthopyroxene grains could not be indexed because the available pyroxene index file is based on iron-free orthopyroxene, while our samples contain an iron-rich orthopyroxene. The index rate for raw EBSD data was ~50%.

3 Results

The mechanical data for thin-walled cylinders of our two-phase samples with fopx = 0.15 and 0.35 that were deformed in torsion are summarized in supporting information Tables S1 and S2. The corresponding microstructural data are summarized in Table S3. Microstructural and mechanical data for the sample with fopx = 0 and 0.26 were described previously (Hansen et al., 2012; Tasaka, Zimmerman, & Kohlstedt, 2017; Tasaka, Zimmerman, Kohlstedt, Stunitz, & Heilbronner, 2017). Here, descriptions of the mechanical data and the microstructural development focus on the differences among samples with different amounts of iron-rich orthopyroxene.

Based on the analysis of Reynard et al. (2008), we assumed that the iron-rich ortho-enstatite is stable at our experimental conditions (Figure S1).

3.1 Microstructural Results

Secondary electron microprobe image micrographs of undeformed and deformed samples with fopx = 0.15, 0.26, and 0.35 are presented in Figure 1. Band contrast images from EBSD analysis of pyroxene-free olivine aggregates, fopx = 0, are included for comparison (Hansen et al., 2012; 2014). For all of the orthopyroxene-bearing samples deformed to lower strains of γ  5, dynamically recrystallized olivine and orthopyroxene grains with alternating olivine-rich and orthopyroxene-rich layers are oriented at a low angle (~13°) relative to the shear plane. For samples with fopx = 0.15 deformed to higher strains of γ  26, elongated olivine grains still remain, while most of the orthopyroxene grains are located on olivine grain boundaries. In contrast, in samples with fopx = 0.26 and 0.35 deformed to higher strains, olivine and orthopyroxene grains are small and thoroughly mixed. The inclination angle, θ, calculated from the strain ellipse using the relationship γ = 2/tan (2θ) is included in Figure 1 for each deformed sample.

3.2 Mechanical Results

The stress versus strain curves are similar for samples with fopx = 0.15, 0.26, and 0.35, as illustrated in Figure 2. For each, stress increases with increasing strain reaching a peak stress at γ ≈ 0.2 and then decreases to a nearly steady-state flow stress at γ = 1 to 2. At higher strains, the stress is nearly independent of strain. The peak stress in the sample with fopx = 0.26 is smaller than the peak stress in the sample with fopx = 0.15 and 0.35, whereas the flow stress of ~75 MPa is roughly the same in all samples.

Details are in the caption following the image
(a) Shear stress versus shear strain for samples with fopx = 0.15, 0.26, and 0.35. (b) Once the flow stress reached an approximately constant value, the twist rate was increased or decreased stepwise to determine the value of the stress exponent n in Equation 1. The rate stepping tests were conducted at intervals of γ ≈ 3 to obtain the value of n with increasing strain. The background strain rate is ≈2 × 10−4 s−1.

Equivalent strain rate as a function of equivalent stress determined at the peak stress is plotted in Figure 3 and summarized in Table S1 for samples with fopx = 0.15 and 0.35. The grain size at this point for each composition is taken to be the same as in the corresponding undeformed sample. For comparison, previously determined stress-strain rate values for samples with fopx = 0 are included for the appropriate grain size using the flow law from Hansen et al. (2012) for dislocation-accommodated grain boundary sliding (disGBS) with subgrain boundaries. At a given stress, the strain rate of olivine aggregates with fopx = 0 is a factor of 7.5, 6.2, and 9.0 faster than that of orthopyroxene-bearing samples with fopx = 0.15, 0.26, and 0.35, respectively.

Details are in the caption following the image
Equivalent strain rate as a function of equivalent peak stress at γ ≈ 0.2 for samples with (a) fopx = 0.15, (b) fopx = 0.26, and (c) fopx = 0.35. For comparison, the flow law for samples with fopx = 0 (Hansen et al., 2012) is added as a solid line.
The higher strain portions of our mechanical data are analyzed with a flow law of the form (e.g., Poirier, 1985, pp. 103–109)
urn:x-wiley:21699313:media:jgrb54371:jgrb54371-math-0001(1)
where A is a material-dependent creep parameter, n is the stress exponent, and p is the grain size exponent. The mechanical data on flow stress are summarized in Table S2.

Flow law parameters for samples with fopx = 0.15 determined at 2 < γ < 27 are A1 = 1010.1 ± 0.3 MPan μmp s−1 and n = 3.3 ± 0.3. Since stress-strain rate data for samples with different grain sizes are limited, a grain size exponent of p = 0.73 was used based on results for samples with fopx = 0 (Hansen et al., 2012). Similarly, for the samples with fopx = 0.35 at γ ≈ 4, A1 = 10–10.4 ± 1.8 MPan μmp s−1 and n = 3.2 ± 0.8. At γ ≳ 15, A1 = 10–7.1 ± 3.2 MPan μmp s−1 and n = 2.0 ± 1.5. Here, the value of p was taken from Tasaka, Zimmerman, and Kohlstedt (2017) for the sample with fopx = 0.26, p = 1.1 at lower strains and p = 3.3 at higher strains. The flow law parameters are summarized in Table S4.

The values determined for n are plotted as a function of shear strain in Figure 4 for samples with fopx = 0.15 and 0.35. The values of n for the samples with fopx = 0 (Hansen et al., 2012) and fopx = 0.26 (Tasaka, Zimmerman, & Kohlstedt, 2017) are included for comparison. For samples with fopx = 0.26 and 0.35, n decreases with increasing shear strain, from n ≈ 3 for γ  5 to n ≈ 2 for 5  γ  25. In contrast, for samples with fopx = 0.15, the stress exponent is constant at n ≈ 3.3 for 1  γ  25. Furthermore, for samples with fopx = 0, n = 4.1 ± 0.1 independent of strain (Hansen et al., 2012). In previous deformation experiments on iron-rich olivine and olivine-orthopyroxene aggregates under disGBS creep with subgrain boundaries, regardless of the fopx in the samples, values of the stress exponent varied from n = 3.5 to 4.0 (Hansen et al., 2012; Tasaka, Zimmerman, & Kohlstedt, 2017; Tasaka, Zimmerman, Kohlstedt, Stunitz, & Heilbronner, 2017; Zhao et al., 2009).

Details are in the caption following the image
Stress exponent as a function of shear strain for samples with fopx = 0.15 and fopx = 0.35 from the present study and samples with fopx = 0.26 from Tasaka, Zimmerman, and Kohlstedt (2017). Data for samples with fopx = 0 from Hansen et al. (2012) are included for comparison. The height of the transparent, colored boxes indicate the range of uncertainty for samples of each value of fopx. For the samples with fopx = 0, n = 4.1 ± 0.1. For the samples with fopx = 0.15, n = 3.3 ± 0.3. For the samples with fopx = 0.26, n = 2.7 ± 0.3 at low strain (γ < 8) and n = 2.0 ± 0.2 at high strain (γ > 8). For the samples with fopx = 0.35, n = 2.9 ± 0.4 at low strain (γ < 5) and n = 2.2 ± 0.1 at high strain (γ > 5). Typical error bar for individual data points is shown in the upper right-hand corner of the figure.

3.3 CPOs

The orientations of the crystallographic axes of olivine are plotted on equal-area pole figures for both undeformed and deformed samples in Figure 5. CPOs of pyroxene-free olivine aggregates, fopx = 0, are included for comparison (Hansen et al., 2012, 2014). The CPOs of the undeformed samples in Figures 5a5d are weak with values for the J index of 1.39 to 1.50 and approximately uniform distributions. In contrast, the CPOs of most of the deformed samples are pronounced with J > 4. For samples with fopx = 0, 0.15, and 0.26 at lower strains of γ ≈ 2 in Figures 5e5g, there are two sets of maxima, one with strong concentrations of [100] parallel to the shear direction and [001] perpendicular to shear plane and the other with weak concentrations of [001] subparallel (~30°) to the shear direction and [100] subperpendicular (~30°) to shear plane. At γ ≈ 4 for samples with fopx = 0, 0.15, 0.26, and 0.35, [100] is strongly concentrated parallel to the shear direction with girdles of [010] and [001] in Figures 5h5k. Very weak concentrations of [001] subparallel (~30°) to the shear direction and [100] subperpendicular (~30°) to shear plane still remain as illustrated in Figures 5h5k. In samples with fopx = 0 and 0.15 at the highest strain, [100] is still strongly concentrated parallel to the shear direction with [010] now perpendicular to shear plane and [001] parallel to the shear plane but perpendicular to the shear direction as evidenced by the value of J ≥ 23 (Figure 5l and 5m). In contrast, in samples with fopx = 0.26 and 0.35 at the highest strains, the fabrics are significantly weaker with J < 5 (Figures 5n and 5o).

Details are in the caption following the image
Olivine crystallographic-preferred orientations. Equal-area pole figures, lower hemispheric projections for olivine [100], [010], and [001] axes for undeformed and deformed samples. The images on the left are for samples with fopx = 0, those in the middle are for samples with fopx = 0.15 and 0.26, and those on the right are for samples with fopx = 0.35. Deformed samples were sheared top to the right. The pole figure densities are weighted by grain area. The values of the J and M indices indicate the fabric intensity (Mainprice et al., 2013; Skemer et al., 2005). Based on the flow laws, the contribution of disGBS without subgrain boundaries to deformation is calculated as 51%, 56%, and 77% for Experiments PT-994, 984, and 1006 on samples with fopx = 0.26. The contribution is 65% and 81% for Experiments PT-1035 and 1036 on samples with fopx = 0.35. Crystallographic-preferred orientation data of undeformed and deformed samples with fopx = 0 are from Hansen et al. (2012).

3.4 Grain Size

As demonstrated in Figure 6, the size of both olivine and orthopyroxene grains decreases with increasing shear strain. At the highest strains, the grain size of orthopyroxene is ≈1 μm in all of the samples. In contrast, the grain size of olivine decreases with increasing orthopyroxene content, such that dol = 3.6, 2.4, and 2.1 μm in samples with fopx = 0.15, 0.26, and 0.35, respectively.

Details are in the caption following the image
Average size of (a) olivine and (b) pyroxene grains versus shear strain for all of our samples plus those with fopx = 0.26 from Tasaka, Zimmerman, and Kohlstedt (2017).
Grain growth is inhibited by the presence of secondary phases or particles on the grain boundaries of the primary phase. As a result, the average grain size is smaller in polyphase materials than in single-phase aggregates under the same thermomechanical conditions. This phenomenon is often called Zener pinning (e.g., Evans et al., 2001; Smith, 1948). Under conditions for which Zener pinning is effective, the ratio of the grain size of the primary phase to the grain size of the secondary phase (dI/dII) is inversely proportional to the volume fraction of the secondary phase (fII):
urn:x-wiley:21699313:media:jgrb54371:jgrb54371-math-0002(2)
where β and z are the Zener parameters.

To investigate the relationship between grain size and fopx, olivine grain size versus orthopyroxene grain size for samples of each of the three compositions is plotted in Figure 7. The Zener relationship (Equation 2) with values of β and z determined in previous grain growth experiments on samples of forsterite + enstatite (Hiraga et al., 2010) is included for each composition for comparison. For each composition, the results from deformed samples are well fit by a straight line, as predicted by Equation 2. However, the results from the undeformed samples do not follow this trend, indicating that the two-phase powders were not well mixed during preparation of the starting (undeformed) samples.

Details are in the caption following the image
Olivine grain size versus pyroxene grain size for samples with fopx = 0.15, 0.26, and 0.35. Solid lines were calculated from the Zener relationship (Equation 2), with z = 0.59 and β = 0.74 from Hiraga et al. (2010).

The size of olivine grains as a function of equivalent stress is plotted in Figure 8. The stress-grain size relationship (i.e., grain size piezometer) for olivine aggregates with fopx = 0 (Hansen et al., 2012) is added for comparison. In the pyroxene-free olivine aggregates, grain size decreases systematically with increasing stress, independent of strain. In contrast, in the orthopyroxene-bearing samples, grain size also decreases due to dynamic recrystallization at lower strain γ  5, whereas the stress-grain size relationship is not clear and seems likely independent of stress by γ  16.

Details are in the caption following the image
(a) Olivine grain size as a function of the equivalent stress for samples with fopx = 0.15, 0.26, and 0.35. Color of the symbol indicates shear strain. The piezometric relationship determined by Hansen et al. (2012) for samples with fopx = 0 is added as solid black line for comparison. The gray solid line is the stress-grain size dependence for olivine-pyroxene samples at γ ≤ 4.2 with a slope equal to −1.2 that of piezometer in Hansen et al. (2012).

4 Discussion

Our research group previously conducted a series of high-strain torsion experiments using olivine aggregates with fopx = 0 (e.g., Hansen et al., 20122014) as well as olivine plus orthopyroxene aggregates with fopx = 0.26 (Tasaka, Zimmerman, & Kohlstedt, 2017; Tasaka, Zimmerman, Kohlstedt, Stunitz, & Heilbronner, 2017). The current study adds results for samples with fopx = 0.15 and 0.35 to this series. In this section, the mechanical behavior and microstructural development of samples with different amounts of orthopyroxene that were deformed to high strains in torsion are compared.

4.1 Interpretations of Results

4.1.1 Microstructural Development with Increasing Strain

All of the samples with or without orthopyroxene exhibit similar microstructural development at lower strains of γ  5, as shown in Figures 1b, 1e, and 1h. Elongated, dynamically recrystallized olivine and orthopyroxene grains occur in alternating olivine-rich and orthopyroxene-rich layers orientated at a low angle (~13°) relative to the shear plane. This angle is consistent with the calculated inclination angle determined from the strain ellipse. Therefore, it is likely that the alternating layers are formed from large, > 5 μm grains present in the undeformed sample that elongated and dynamically recrystallized during deformation.

By γ  16, thoroughly mixed, fine-grained textures are pervasive in aggregates with fopx = 0.26 and 0.35, as observed in Figures 1c and 1f. In contrast, elongated olivine grains still remain with fine-grained orthopyroxene located on olivine-olivine grain boundaries in samples with fopx = 0.15, as in Figure 1i. Further, relatively large, elongated grains exist in olivine aggregates with fopx = 0, such as in Figure 1l. The microstructural differences observed in samples with different amounts of orthopyroxene deformed to the highest strain provide insight into the processes of forming fine-grained aggregates as well as into the operative deformation mechanism, as discussed below.

4.1.2 Deformation Mechanism

The evolution of the mechanical behavior with increasing strain differs between samples with no or a small amount of orthopyroxene and samples with higher amounts of orthopyroxene. For the samples with fopx = 0 and 0.15, the value of n, and thus the deformation mechanism, does not change with strain, as demonstrated in Figure 4. In contrast, for samples with fopx = 0.26 and 0.35, the stress exponent decreases from n ≈ 3 at lower strains to n ≈ 2 at higher strains (Figure 4), indicative of a change in deformation mechanism.

Based on the measured dependences of creep rate on stress, n = 4.1, and grain size, p = 0.73, Hansen et al. (2012) concluded that pyroxene-free olivine samples deformed by disGBS with subgrain boundaries over the full range of strain are investigated, 0 < γ  15. Similarly, we argue that the mechanical data reported in Figure 4 indicate that our samples with fopx = 0.15 deformed by disGBS with subgrain boundaries for the range of strains are investigated, 0 < γ  27, with n = 3.3.

For samples with fopx = 0.26, Tasaka, Zimmerman, and Kohlstedt (2017) concluded that at lower strains of 1  γ  3, deformation occurred by disGBS with subgrain boundaries based on values of 3.0 and 1.1 are determined for n and p, similar to those reported for pyroxene-free olivine aggregates. However, at higher strains, samples are deformed by disGBS without subgrain boundaries with n = 1.8 and p = 3.3, values quite different from those determined at lower strain and for pyroxene-free olivine aggregates. We propose that samples with fopx = 0.35 behave similarly to those with fopx = 0.26. The mechanical data reported in Figure 4 for samples with fopx = 0.35 reveal a clear decrease in stress exponent from n = 2.7 ± 0.3 for γ  5 to n = 2.0 ± 0.2 for γ  5. This behavior is nearly identical to that reported by Tasaka, Zimmerman, and Kohlstedt (2017) for samples with fopx = 0.26. Therefore, we conclude that our samples with fopx = 0.35 deformed by disGBS with subgrain boundaries at lower strains and by disGBS without subgrain boundaries at higher strains. This change in deformation mechanism with increasing strain is due primarily to the reduction in grain size to a value below the stress-determined subgrain size.

4.1.3 Zener Relationship

The plot of olivine grain size versus orthopyroxene grain size in Figure 7 indicates that the ratio of grain sizes in deformed samples is determined by the Zener relationship, such that the olivine grain size decreases with increasing fopx at a given orthopyroxene grain size. Based on the derivation of Equation 2 (Hiraga et al., 2010; Tasaka & Hiraga, 2013), Zener pinning effectively inhibits grain growth when all of the triple junctions and/or grain boundaries of the primary phase are pinned by the secondary phase. The microstructures of samples deformed to γ  27 are consistent with the results of this process, with small orthopyroxene grains pinning the grain boundaries of olivine (Figures 1c, 1f, and 1i).

The Zener relationship determined in this study is consistent with the data from the grain growth experiments of Hiraga et al. (2010) for aggregates of iron-free forsterite and enstatite at T = 1360°C, P = 0.1 MPa as illustrated in Figure 7. This correlation suggests that the same Zener relationship applies regardless of the iron content of the olivine or orthopyroxene grains, the pressure, the temperature, or static annealing versus dynamic deformation conditions. The Zener parameters, β and z, are determined by the interfacial energies of the phase and grain boundaries as well as the distribution of the secondary phase. Hiraga et al. (2010) suggested that interfacial energy does not change significantly as a function of temperature or iron content in olivine + orthopyroxene systems. In addition, the distribution of the secondary phase in samples deformed to the highest strains in Figures 1c, 1f, and 1i as well as experimentally deformed and/or annealed samples in previous experiments (Hiraga et al., 2010; Tasaka & Hiraga, 2013) is similar, such that the secondary phase effectively pinned the grain boundaries and triple junctions of the primary phase. Therefore, the same Zener relationship appears to apply over a wide range of thermomechanical conditions in the olivine-orthopyroxene system.

4.1.4 Olivine CPO Development

The development of a CPO as a function of strain in olivine (Figure 5) is consistent with the deformation mechanisms proposed above. Two sets of maxima dominate the CPO of samples deformed to 1  γ  2 (Figures 5e, 5f, and 5g), one characterized by a strong concentration of [100] parallel to the shear direction with [001] perpendicular to shear plane and the other by a weak concentration of [001] ~ 30° to the shear direction with [100] ~ 30° from perpendicular to shear plane. Similar bimodal CPOs were observed in pyroxene-free olivine aggregates at low strains (Hansen et al., 2014; Tielke et al., 2016). Overall, for samples deformed to low strains, orthopyroxene-bearing and pyroxene-free samples have the same olivine fabric, suggesting that both types of samples are deformed by the same deformation mechanism.

In samples with fopx = 0.15, by a strain of γ ≈ 4, a strong fabric (J ≈ 11) develops that is consistent with the glide on the (010)[100] and (001)[100] slip systems with a very weak contribution from the (100)[001] slip system (Figure 5i). By γ ≈ 27, a very strong fabric (J ≈ 29) develops indicative of slip on (010)[100] (Figure 5m). A similar pattern of CPO development as a function of shear strain occurs in olivine aggregates with fopx = 0 (Bystricky et al., 2000; Hansen et al., 2014). Hansen et al. (2014) proposed that these samples were deformed by disGBS with subgrain boundaries with the evolution of CPO resulting from a combination of deformation on the (010)[100], (001)[100], and (100)[001] slip systems. Consequently, for samples with fopx = 0 and 0.15, the olivine CPO develops due to dislocation glide and associated lattice rotation. Thus, grains elongate and dynamically recrystallize, forming trails of small grains as observed in Figures 1h and 1i. As a result, the angle that the elongated grains and the trails of recrystallized grains form with the shear direction coincides with the long axis of the finite strain ellipse, common features in samples deformed by dislocation-accommodated creep (Herwegh & Handy, 1998; Zhang & Karato, 1995).

For the samples with fopx = 0.26 and 0.35, both the (010)[100] and the (001)[100] slip systems contribute at γ ≈ 4 (Figures 5j and 5k). At this strain, the CPO of these samples is similar to but somewhat weaker than that of aggregates with fopx = 0 and 0.15 (Figures 5h and 5i). At γ  15, the (010)[100] slip system dominates for samples with larger amounts of orthopyroxene; however, the strength of the CPO pattern is much weaker with J ≈ 4 for samples with fopx = 0.26 and 0.35 (Figures 5n and 5o) than for aggregates with fopx = 0 and 0.15 with J ≈ 20 (Figures 5l and 5m). For samples with fopx = 0.26 and 0.35, the olivine CPO pattern becomes weaker with increasing strain because rigid body rotation of grains, which is easier at finer grain sizes, tends to wipeout the CPO formed by dislocation glide with associated lattice rotation. Similar behavior has been observed in olivine-ferropericlase aggregates in which Zener pinning occurs similar to that observed in our samples (Harison Wiesman, personal communication, 16/1/2020), as well as in the partially molten olivine-basalt aggregates in which rigid grain rotation occurs as olivine grains become elongated in the [001] direction in the presence of melt (Qi et al., 2018).

4.1.5 Strength of Two-Phase, Olivine-Orthopyroxene Aggregates

To assess the influence of phase boundaries on the strength of our two-phase aggregates, we calculated the volume-weighted strength from rheological data of the endmembers, olivine, and orthopyroxene. Since no creep data are available for the iron-rich orthopyroxene composition used in our experiments, En55, the relative strength of olivine and orthopyroxene was evaluated by comparing creep data for aggregates of Fo90 (Hansen et al., 2011) with creep data for En90 (Bystricky et al., 2016). While the results for olivine were analyzed in the framework of disGBS, those for orthopyroxene were modeled as a combination of diffusion and dislocation creep. However, Bystricky et al. (2016) allowed for the possibility that some component of dislocation-accommodated grain-boundary sliding may also occur in their orthopyroxene samples. For samples deformed in the orthopyroxene stability field, grain sizes were reported to lie in the range 3 to 10 μm. Thus, creep results for orthopyroxene were compared to those for olivine samples with grain sizes of 4.6, 5.4, and 6.3 μm. Data were selected from experiments carried out at 1200°C to match the conditions used in our experiments. This comparison indicates that orthopyroxene is a factor of 2–3 stronger than olivine.

To compare the strength of our two-phase (2ϕ) samples with that calculated from the strengths of the endmembers, we applied the uniform strain rate approximation (Bishop & Hill, 1951; Taylor, 1938) for which
urn:x-wiley:21699313:media:jgrb54371:jgrb54371-math-0003(3)
This approximation is anticipated from finite-element analyses of plastic deformation of two-phase materials (Tullis et al., 1991; Karato, 2008, pp. 220–221). It is also supported by an analysis of creep results on two-phase, Fe-free aggregates of forsterite plus enstatite deformed primarily in the diffusion creep regime (Tasaka et al., 2013). To compare the strengths of samples with different orthopyroxene contents with that predicted by Equation 3, stresses from Table S2 normalized to a strain rate of urn:x-wiley:21699313:media:jgrb54371:jgrb54371-math-1003 1 × 10−4 s−1 and d = 3 μm are plotted versus fopx for samples deformed to strains of γ = 1.9 to 4.3 in Figure 9, conditions for which samples were deformed by disGBS with subgrain boundaries. At these conditions, the flow stress for the sample with fopx = 0 is a factor of 1.6, 1.8, and 2.1 smaller than those for samples with fopx = 0.15, 0.26, and 0.35, respectively. Also included in Figure 9 is the volume-weighted strength calculated from Equation 3 using a value of σopxol = 4.2. This value is a factor of ~2 larger than anticipated from creep results described above for Fo90 and En90. Thus, we conclude that the strength of our two-phase samples is reasonably well approximated by a volume-averaged strength of the endmembers, suggesting the role of phase boundaries is similar to that of grain boundaries. This conclusion is in distinct contrast with that reached for samples composed of olivine plus clinopyroxene (Zhao et al., 2019) for which two-phase mixtures were observed to be significantly weaker than the endmembers, a result attributed to enhanced phase-boundary sliding.
Details are in the caption following the image
Equivalent stress versus pyroxene volume fraction for samples deformed to strains of 1.9 ≤ γ ≤ 4.3 in the dislocation-accommodated grain-boundary sliding with subgrain regime. Stresses are normalized to a strain rate of 1 × 10−4 s−1, a grain size of 3 μm, and a temperature of 1200°C using the flow law determined in this study. The stress for pyroxene-free olivine aggregates was determined based on the flow law of Hansen et al. (2012) for Fo50 samples. The solid curve, determined from a nonlinear least squares fit to the rule of mixtures model (Equation 3), corresponds to σοpx/σol = 4.2.

4.1.6 Strain Weakening

The degree of strain weakening in samples with fopx = 0, 0.15, 0.26, and 0.35, as indicated by the slope of the stress-strain curves in Figure 2, is related to microstructural development with increasing strain. During constant twist rate experiments, at a given strain rate, the degree of strain weakening is determined by the strengths of the constitutive minerals, the fraction of each mineral, the grain size of each mineral, and/or geometrical softening (Hansen et al., 2012; Tasaka, Zimmerman, & Kohlstedt, 2017).

To quantify the degree of strain weakening in samples with fopx = 0, 0.15, 0.26, and 0.35, deformation mechanism maps are introduced in Figure 10. The flow laws for the deformation mechanism map for samples with fopx = 0.15 and 0.35 are shown in Table S4. The flow laws for samples with fopx = 0 and 0.26 are from Hansen et al. (2012) and Tasaka, Zimmerman, and Kohlstedt (2017), respectively. For pyroxene-poor olivine aggregates with fopx = 0 and 0.15 (Figures 10a and 10b), strain weakening associated with geometrical softening, that is, due to the development of a relative strong CPO, occurs as γ increases to ~2. This geometrical softening results in a decrease in stress of ~30% in samples with fopx = 0 (Hansen et al., 2012). For samples with fopx = 0.26 and 0.35 with relatively weak CPOs (Figures 10c and 10d), strain weakening primarily occurs due to a change in the deformation mechanism resulting from grain size reduction during the formation of thoroughly mixed olivine + pyroxene aggregates. Presumably, geometrical softening also occurs, although it is a relatively minor contributor. In this case, the stress decreases by 30% to 70% as strain increases from γ ≈ 0.2 to γ ≈ 26. The degree of strain weakening in samples with fopx = 0.26 and 0.35 is largely determined by the amount of grain size reduction at higher strains. Consequently, for strain weakening due to phase mixing to occur in samples with higher amounts of pyroxene, a change in deformation mechanism is required, as indicated by changes in the values of n and p.

Details are in the caption following the image
Deformation mechanism maps plotted as differential stress as a function of grain size for samples with (a) fopx = 0, (b) fopx = 0.15, (c) fopx = 0.26, and (d) fopx = 0.35. Blue symbols are values of the peak stress using the grain size of undeformed samples; red symbols are values of the flow stress at the end of each deformation experiment using the grain sizes the deformed samples. Gray shaded areas in (a) and (b) define the range of grain size and stress for which no deformation experiments have been conducted. Light blue box in (a) represents the stress-grain size conditions studied by Zhao et al. (2009). Red line in (a) is the grain size piezometer determined by Hansen et al. (2012). Gray arrow indicates the trend of strain weakening. Different symbols indicate different experiments. The thick solid gray lines in (c) and (d) are the deformation mechanism boundary between disGBS with subgrain boundaries and disGBS without subgrain boundaries. The contour lines mark strain rates in units of s−1.

4.2 Geophysical/Geological Applications

4.2.1 How Do Thoroughly Mixed, Fine-Grained Olivine + Orthopyroxene Aggregates Form?

Identification of the processes forming thoroughly mixed, fine-grained olivine + pyroxene aggregates is important for understanding strain weakening in naturally deformed rocks observed in shear zones. In a previous paper (Tasaka, Zimmerman, Kohlstedt, Stunitz, & Heilbronner, 2017), we proposed that such textures form due to differences in the diffusivities of Si, O, and Me (Me = Fe or Mg). Si is the slowest diffusing species both through the lattice and along the grain boundaries in olivine and orthopyroxene (e.g., Dohmen et al., 2002; Farver & Yund, 2000; Gardes et al., 2011; Gardes & Heinrich, 2011; Milke et al., 2007). Furthermore, chemically, only the molar ratio of SiO2 to MeO differ between these two minerals. Therefore, it may be possible to form thoroughly mixed, fine-grained olivine + orthopyroxene aggregates during deformation because diffusion of MeO is faster than diffusion of SiO2 (see Figure 10 in Tasaka, Zimmerman, Kohlstedt, Stunitz, & Heilbronner, 2017).

As a result of above mixing process, new orthopyroxene grains are preferentially nucleated on olivine-olivine grain boundaries that are in deviatoric extension, whereas new olivine grains are preferentially nucleated on orthopyroxene-orthopyroxene grain boundaries that are in deviatoric compression. As fopx increases so does the density of orthopyroxene-orthopyroxene grain boundaries, thus reducing the diffusion distance necessary to form fine-grained aggregates. Thoroughly mixed, fine-grained textures are pervasive in aggregates with fpx = 0.26 and 0.35 (Figures 1c and 1f), whereas elongated olivine grains still remain in samples with fpx = 0.15 (Figure 1i), consistent with our mixing model.

Several other mixing mechanisms have been proposed as described in section 1 with two particularly appropriate for samples deformed under dry conditions (Bercovici & Mulyukova, 2018; Bercovici & Skemer, 2017; Cross & Skemer, 2017). Cross and Skemer (2017), who conducted high-strain torsion experiments on samples formed from mixtures of calcite and anhydrite, suggested a geometric phase-mixing concept. In this model, clusters of grains are stretched out until layers are only a single-grain thick, typically after a shear strain of γ ≈ 100. In contrast, based on the microstructure presented in Figure 1 and in Tasaka, Zimmerman, Kohlstedt, Stunitz, and Heilbronner (2017), the initial stages of phase mixing are already evident by γ ≈ 2.

Bercovici and Skemer (2017) proposed a mechanism for phase mixing in olivine + orthopyroxene aggregates in which tiny olivine grains are extruded along orthopyroxene grain boundaries. The process is initiated as small particles or “teeth” of olivine form at triple junctions between olivine-orthopyroxene-orthopyroxene contacts and then migrate along pyroxene grain boundaries driven by stress gradients associated with deformation (see also Bercovici & Mulyukova, 2018). Indeed, some of the microstructural features in Figure 1 are consistent with this model. However, in this context, it is difficult to explain how the initial stage of the formation of an olivine-orthopyroxene mixing texture develops quickly, by γ ≈ 2, as noted in Figures 2b and 2c of Tasaka, Zimmerman, Kohlstedt, Stunitz, and Heilbronner (2017).

4.2.2 “Steady-State” Grain Size in Pyroxene-Free and Pyroxene-Bearing Olivine Aggregates

The evolution of grain size with increasing strain differs between pyroxene-free and pyroxene-bearing olivine aggregates. For pyroxene-free olivine aggregates, the steady-state, dynamically recrystallized grain size is determined by stress (piezometric relationship) after reaching a critical strain, as illustrated in Figure 8. In contrast, for olivine + orthopyroxene aggregates, grain size decreases with increasing strain to a value substantially smaller than that predicted by the single-phase piezometer. As olivine and orthopyroxene grains begin to mix, as observed in Figure 1, growth of olivine grains is impeded by the presence of orthopyroxene grains that pin olivine grain boundaries and growth of orthopyroxene grain is impeded by the presence of olivine grains along orthopyroxene grain boundaries, that is, Zener pinning occurs as described by Equation 2. Consequently, the “steady-state” grain size in olivine-pyroxene systems is smaller than in pyroxene-free aggregates of olivine.

Interestingly, the size of orthopyroxene grains is nearly constant at dopx ≈ 1 μm for γ  5, regardless of the pyroxene volume fraction (Figure 6b). A similar feature was observed in a naturally deformed peridotite ultramylonite at the center of a shear zone in the Oman ophiolite (Tasaka et al., 2014), where the pyroxene grain size was nearly constant at ~5 μm regardless of pyroxene volume fraction with the olivine grain size following the Zener relationship. In other words, the olivine grain size appears to be determined by pyroxene grain size and pyroxene content, urn:x-wiley:21699313:media:jgrb54371:jgrb54371-math-0005, where dpx is approximately constant for a given thermomechanical condition (i.e., P, T, and σ) for 0 < fpx < 0.5. The “steady-state” grain size in olivine-pyroxene systems is determined by a balance between grain size reduction due to dynamic recrystallization and grain growth via Ostwald ripening limited by Zener pinning. Similar microstructures were previously observed in high-strain deformation experiments on olivine-orthopyroxene samples (Farla et al., 2013).

4.2.3 Implications for Natural Shear Zones

Microstructural development with increasing strain is similar for naturally and experimentally deformed rocks, suggesting that the same physical-chemical processes operate in these two cases leading to strain weakening. For example, a recent study of naturally deformed peridotites from the Oman ophiolite (Ambrose et al., 2018) reported microstructural textures similar to those observed in our experiments (Figure 2 in Tasaka, Zimmerman, Kohlstedt, Stunitz, & Heilbronner, 2017); Ambrose et al. (2018) suggested that the distribution of olivine and pyroxene grains in this natural peridotite ultramylonite is consistent with our mixing model for forming thoroughly mixed, fine-grained olivine + pyroxene aggregates. Furthermore, olivine grain size in thoroughly mixed, fine-grained domains in mantle shear zones formed in different tectonic setting and under varied deformation conditions follows a single Zener relation, demonstrating the important control of orthopyroxene content on grain size and consequently on strain localization (Czertowicz et al., 2016; Hansen & Warren, 2015; Tasaka et al., 2014). Therefore, as demonstrated in this and our previous studies (Tasaka, Zimmerman, & Kohlstedt, 2017; Tasaka, Zimmerman, Kohlstedt, Stunitz, & Heilbronner, 2017), the difference in grain size evolution between single-phase and polyphase materials is critical in determining the amount of strain weakening that occurs, an important consideration for understanding strain localization in the upper mantle of Earth.

5 Conclusions

The mechanical behavior and microstructural development of olivine-rich samples with orthopyroxene fractions of fopx = 0, 0.15, 0.26, and 0.35—all deformed to high strain in torsion—are compared. All of the samples, independent of pyroxene content, exhibited similar microstructural development at lower strains of γ  5 characterized by elongated, dynamically recrystallized olivine and pyroxene grains occurring in alternating olivine-rich and pyroxene-rich layers. At γ  16, thoroughly mixed fine-grained textures are pervasive in aggregates with fopx = 0.26 and 0.35, whereas elongated olivine grains still remain with small grains of pyroxene located on olivine-olivine grain boundaries in samples with fopx = 0.15. The microstructural differences observed in samples with different amounts of pyroxene deformed to the highest strain provide insight into the processes involved in the formation of fine-grained aggregates as well as into the operative deformation mechanism.

For the samples with fopx = 0 (Hansen et al., 2012) and fopx = 0.15 (this study), the value of n, and thus the deformation mechanism, does not change with strain. In contrast, for samples with fopx = 0.26 and 0.35, the stress exponent decreases from n ≈ 3 at lower strains to n ≈ 2 at higher strains, indicative of a change in deformation mechanism. This change in deformation mechanism with increasing strain is due primarily to the reduction in grain size to a value below the stress-determined subgrain size.

The evolution of grain size with increasing strain differs between pyroxene-free and pyroxene-bearing olivine aggregates. The steady-state, dynamically recrystallized grain size of pyroxene-free olivine aggregates (fopx = 0) is determined by stress described by a piezometric relationship. In olivine-pyroxene aggregates, grain size also decreases with increasing strain due to dynamic recrystallization. However, due to mixing of the two phases, growth of olivine and pyroxene grains is inhibited as pyroxene grains pin olivine grain boundaries and olivine grains pin pyroxene grain boundaries, characteristic of Zener pinning that occurs due to phase mixing. The size of pyroxene grains is nearly constant at dopx ≈ 1 μm for γ  5 regardless of the pyroxene volume fraction.

The resulting mechanical and associated microstructural properties demonstrate that rheological weakening due to grain size reduction resulting from phase mixing occurs in samples with fopx  0.26. The difference in grain size evolution between single-phase and polyphase materials plays an important role in determining the amount of strain weakening that occurs in ductile shear zone in the upper mantle of Earth.

Acknowledgments

We thank A. Dillman, J. Tielke, M. Pec, C. Qi, and C. Meyers for valuable technical assistance and stimulating discussions. We also thank Y. Kouketsu for assistance in analysis of Raman spectroscopy results, T. Hiraga and M. Morishige for discussions of science, and L. Hansen for providing the original EBSD data in Hansen et al. (2012, 2014). The manuscript was significantly improved by insightful comments from two anonymous reviewers. This research was supported by a JSPS Research Fellowship for Young Scientists 26-4879 and the Japan Society for the Promotion of Science 18K13634 and 16K17832 (M. T.), NSF Grant EAR-1755805 (D. L. K.), NASA Grant NNX11AF58G (M. E. Z), and NSF Grant EAR-1345060 (M. E. Z.). EBSD and SEM analyses were carried out in the Institute of Technology Characterization Facility, University of Minnesota, which receives partial support from NSF through the MRSEC program.

    Data Availability Statement

    Data related to mechanical data of deformation experiments, SEM images, grain size analysis, electron backscatter diffraction, and Raman analysis can be accessed through the Data Repository (https://zenodo.org/record/3742468).