Rates of Olivine Grain Growth During Dynamic Recrystallization and Postdeformation Annealing

We performed deformation and grain growth experiments on natural olivine aggregates with olivine water contents (COH = 600 ± 300 H/106 Si) similar to upper mantle olivine, at 1000–1200°C and 1,400 ± 100 MPa confining pressure. Our experiments differ from published grain growth studies in that most were (1) conducted on natural olivine cores rather than hot‐pressed aggregates and (2) dynamically recrystallized prior to or during grain growth. We combine our results with similar experiments performed at 1200–1300°C and fit the data to a grain growth relationship, yielding a growth exponent (p) of 3.2, activation energy (EG) 620 ± 145 kJ mol−1 (570 ± 145 kJ mol−1 when accounting for the role of temperature on water content), activation volume (VG) ~5 × 10−6 m3 mol−1, and rate constant (k0) 1.8 × 103 mp s−1. Our EG is within uncertainty of that predicted for dislocation creep of wet olivine (E* = 480 ± 40 kJ mol−1). Grain size in strain rate‐stepping samples adjusted to the olivine piezometer within 1.3–7.9% strain. The active grain boundary migration processes during deformation and dynamic recrystallization affect the kinetics of postdeformation grain growth, as grain boundary migration driven by strain energy density (ρGBM) may delay the onset of grain growth driven by interfacial energy (γGBM). We compared our postdeformation grain growth rates with data from previously published hydrostatic annealing experiments on synthetic olivine. At geologic timescales, the growth rates are much slower than predicted by the existing wet olivine grain growth law.

An important aspect of olivine grain growth is its role in balancing grain size reduction processes during dynamic recrystallization. An olivine aggregate deforming in the dislocation creep regime will dynamically recrystallize to a grain size characteristic of the flow stress (Karato et al., 1980;van der Wal et al., 1993). These newly recrystallized grains can enhance deformation by grain size-sensitive creep (e.g., diffusion creep) at a lower stress, which can lead to weakening and strain localization (Poirier, 1980). Some researchers argue, however, that persistent strain localization resulting from dynamic recrystallization is improbable because of a dynamic balance between grain size reduction and grain growth (e.g., De Bresser et al., 2001). This idea is supported by the paleowattmeter of Evans (2007, 2009), who proposed that grain size evolution is controlled by the rate of mechanical work (σ_ ε) during deformation and that a stabilized grain size distribution is established when grain growth and grain size reduction rates are balanced. The paleowattmeter accurately predicts recrystallized grain sizes in experimentally deformed quartz (Kidder et al., 2016;Stipp & Tullis, 2003), calcite (Barnhoorn et al., 2004;Rutter, 1995;Schmid et al., 1980), and olivine (Karato et al., 1980;van der Wal et al., 1993). If grain growth keeps pace with grain size reduction, strain localization may be less prominent and may be temporary or episodic if the grains are refined and grow in cycles (Drury et al., 1991;Handy, 1989). If grain growth is slow, however, the maintenance of small grain size could enable prolonged localization (Platt & Behr, 2011). Thus, quantifying the rate of olivine grain growth during and after deformation is essential to our understanding of the persistence of strain localization in the upper mantle and the fossilization potential of ancient plate boundaries.
Existing olivine grain growth laws are quantified based on static annealing experiments on synthetic aggregates under a limited range of conditions (e.g., Faul & Scott, 2006;Karato, 1989;Nichols & Mackwell, 1991;Ohuchi & Nakamura, 2007). Faster growth rates are reported for water-saturated olivine annealed at 1200-1300°C and 300 MPa confining pressure (Karato, 1989). Significantly slower growth is predicted for dry forsterite sol-gel at 1200°C and 1,200 MPa confining pressure (Ohuchi & Nakamura, 2007). Few experimental grain growth studies have been conducted on dynamically recrystallized olivine aggregates (e.g., doctoral dissertation of van der Wal, 1993), so the potential influence of stored strain energy on subsequent annealing is not well understood. In this study, we compare syndeformation and postdeformation grain growth of natural olivine aggregates with moderate olivine water content (C OH = 600 ± 300 H/10 6 Si) with static grain growth of water-saturated synthetic olivine (Karato, 1989) to investigate how microstructurally stored strain energy influences grain growth of dynamically recrystallized olivine. We quantify the growth rate of the recrystallized grains, qualitatively assess grain boundary migration processes, and discuss the implications for grain size evolution in upper mantle shear zones.

Starting Materials
Experiments were conducted on samples cored as is from a single block of Balsam Gap dunite, a natural olivine aggregate with a weak preexisting crystallographic preferred orientation (CPO). The average grain size is~400 μm; however, larger grains (2-5 mm) are observed in some samples. The dunite is composed of 99 vol% olivine (Fo 92 ) and~1 vol% chromium spinel, with homogeneous chemical composition. The olivine exhibits an annealed texture with minor undulose extinction and straight to gently curved grain boundaries that commonly form~120°triple junctions ( Figure 1a).
Olivine hydroxyl concentrations were measured in grains from the starting material (C OH~3 50 H/10 6 Si) and a deformed sample (C OH~9 00 H/10 6 Si) using Fourier transform infrared (FTIR) spectroscopy at The University of Texas at Austin. Note that 1 ppm wt. H 2 0 = 16.35 H/10 6 Si, which is precise for Fo 90 (see Table 1 of Demouchy & Bolfan-Casanova, 2016, for the method of conversion). We applied the calibration of Paterson (1982) using the parameters of Kohlstedt et al. (1996) (see supporting information S1 and Figure S1 for details). After linear baseline correction, spectra were integrated between 3,000 to 3,780 cm −1 . The FTIR spectra in the starting material have sharp peaks at 3,572 and 3,525 cm −1 that are associated with structural water in olivine (Berry et al., 2005;Kohlstedt et al., 1996). However, the spectra are broad in the deformed sample (w2018); broad spectra could result partly from disordered OH groups located in subgrain boundaries and nano-inclusions Keppler & Rauch, 2000). We observe peaks around 3,355 cm −1 in the deformed sample, which have been related to Fe 3+ defects in olivine (e.g., Bai & Kohlstedt, 1992;Padrón-Navarta & Hermann, 2017); the formation of these bands is consistent with our protocol of using Ni jackets to buffer oxygen fugacity at Ni-NiO (e.g., Bai & Kohlstedt, 1992). For comparison, we also used the approach outlined by Demouchy et al. (2012) to only integrate the absorbance in the well-defined OH bands in olivine (starting material: 3,400-3,620 cm −1 ; deformed sample: 3,088-3,650 cm −1 ); the resulting hydroxyl concentrations are 30 and 120 H/10 6 Si, respectively. However, for consistency with previous studies from which the flow laws were calibrated, we apply the water contents determined from the spectra with only the linear baseline correction (i.e., without spline fitting to remove broadband absorbance between 3,000 to 3,780 cm −1 ). This is consistent with our observation that our samples were weak enough to follow the wet olivine flow law (Hirth & Kohlstedt, 2003) for water contents from approximately 300 to 900 H/10 6 Si (see section 3.3). In addition, the OH associated with subgrain boundaries and other defects could contribute to the observed water weakening in olivine, so including this component in the water content estimate facilitates comparison to olivine flow laws. Because of the large uncertainties in our measurements, we use C OH = 600 ± 300 H/10 6 Si to bracket the range of measured olivine water content. Chlorite, talc, and serpentine have been reported in dunites from Balsam Gap (e.g., Hunter, 1941). Although these hydrous phases were not observed in the samples selected for the experiments, dehydration of a very small amount of alteration phases along microcracks or grain boundaries may have elevated the water content during our high-temperature deformation experiments. For example, serpentine contains~14 wt% H 2 O; dehydration of just 0.014 vol% serpentine would produce~20 ppm wt. H 2 O (equivalent to about 320 H/10 6 Si in olivine), and such a small volume fraction would be hard to detect. We determined weight loss (approximately 0.4 wt%) upon drying cores of the dunite starting material in a controlled atmosphere furnace at 1000°C for 10 h (CO:CO 2 = 1:5). Thus, there is enough additional water in the starting material (present along grain boundaries, fluid inclusions, and trace alteration phases) to explain the modest increase in water content for the deformed samples.

Sample Assembly
The sample assembly is shown in Figure 1b. Olivine cylinders (5 mm diameter) were cut to a length of~13 mm, and the ends were ground parallel. Each core was mechanically sealed in an inner Ni and outer Pt jacket, with Ni and Pt end discs, and surrounded by an additional thin Ni sleeve that extended~3 mm beyond the alumina deformation pistons. Temperature was measured with a type-S (Pt-Pt10%Rh) thermocouple seated outside the Ni sleeve at the sample center. A molten salt cell composed of a eutectic mixture of NaCl-KCl was used as the confining medium inside the graphite furnace; solid NaCl was used outside the furnace.

Experimental Procedures
Three types of deformation experiments were conducted to investigate the rate of grain size evolution during and after deformation (Table 1): (1) constant strain rate (1.5 × 10 −4 or 1.5 × 10 −5 s −1 ); (2) strain rate stepping, by decreasing the strain rate from either 1.5 × 10 −4 or 1.5 × 10 −5 s −1 to 1.5 × 10 −6 s −1 ; and (3) postdeformation stress relaxation, accomplished by stopping the advancement of the deformation piston. Samples were deformed in axial compression in a Griggs-type apparatus at 1000-1200 ± 5°C and 1,400 ± 100 MPa confining pressure. Temperature and pressure were incrementally raised to experimental conditions over~8 h and maintained for an additional hour before advancing the deformation piston. Total engineering strain magnitudes up to 38% were obtained at constant displacement rates equivalent to axial strain rates of 1.5 × 10 −4 to 1.5 × 10 −6 s −1 . Upon achieving~30% strain, either samples were quenched or grain growth intervals were initiated through either postdeformation stress relaxation or continued deformation at a slower strain rate (1.5 × 10 −6 s −1 ) for various time increments. The goal of these experiments was to investigate the evolution of grain size upon a change in strain rate; thus, in some cases (i.e., after a short amount of time after the change to a slower strain rate) a new steady state flow stress was not achieved.
To facilitate comparison to previous work on grain growth during static annealing, a hydrostatic grain growth experiment was performed on hot-pressed powders of Balsam Gap dunite and San Carlos olivine that were ground separately in an agate mortar and sieved to a particle size of 10-20 μm. The powders were positioned at the axial position of the thermocouple, separated by Pt discs, bounded by two Balsam Gap dunite cylinders (above and below), and annealed for~25 h at 1100°C. The initial grain size (7-8 μm) of these hydrostatic experiments was constrained by conducting an experiment in which the sample was held at 1000°C for 10 min.
Experiments were terminated by lowering the temperature (~2.2°C s −1 ) to 300°C to preserve the microstructures, then maintaining the differential stress between 100-200 MPa as the remaining temperature and confining pressure were slowly (4-6 h) lowered to room conditions to suppress decompression cracking. After quenching, samples were cut longitudinally and impregnated with epoxy, and one half was used for thin sectioning.

Analytical Procedures
Axial force, axial displacement, confining pressure, and temperature were recorded at 1 Hz. Axial force was measured with an external load cell in line with the axial column, and axial displacement was measured with an LVDT (linear variable differential transducer) (Tullis & Tullis, 1986). Load values (σ 1 ) were corrected for the piston friction, which we assume is constant for a given displacement rate (Proctor & Hirth, 2015). We also assume a constant sample volume over the duration of our experiments. Axial stress and axial strain were calculated using methods outlined in the RIG program (https://sites.google.com/ site/rigprogram/file-cabinet), which accounts for rig stiffness and changes in confining pressure.
As illustrated below, the observed relationship between flow stress and recrystallized grain size for samples deformed at constant strain rate was consistently within the uncertainty of the olivine grain size piezometer . Thus, the piezometer was used to estimate the recrystallized grain size at the beginning of the grain growth intervals (d 0 ) in rate-stepping and stress relaxation experiments, using the final stress of the preceding deformation interval (Table 1). Due to the limited amount of recrystallization (5-10%) in each sample, the grain sizes of porphyroclasts were similar to that before deformation (~400 μm).
Recrystallized grains were thus easily distinguished from porphyroclasts by their approximately order of magnitude smaller size (~2-36 μm). The recrystallized grains occurred in patches around porphyroclast grain boundaries, and most were surrounded by other recrystallized grains of similar size. The recrystallized grain size was measured in regions near the axial position of the thermocouple to avoid effects of thermal gradients in the samples; however, the recrystallized grain sizes throughout the samples were similar. Measurements were made in cross-polarized light in thin section (~15 μm thick) with Zeiss Zen Pro software connected to a Zeiss Axio Imager M2m petrographic microscope. To analyze recrystallized grain sizes at the end of each experiment (d f ), we measured the length of a line across the intermediate axis (representing the average of the long and short axes) of each grain, applied a geometric correction factor of 1.75 (following van der Wal, 1993), and recorded the geometric mean of the distribution for each sample (Table 1; see supporting information Figure S2 for histograms). For several samples, grain size measurements were also made using two other complementary methods: (1) for three samples we used the mean linear intercept method on crossed-polarized micrographs, and (2) we used the equivalent circle diameter on electron backscatter diffraction (EBSD) maps. Grain sizes measured using all three methods were the same within error.
EBSD maps used to analyze microstructural characteristics were acquired with a Philips/FEI XL30 environmental scanning electron microscope at The University of Texas at Austin, using a 20 kV accelerating voltage,~16 mm working distance, and~0.5-2.0 μm step size. Data were collected using Oxford AZtec software (version 2.1) and processed with MTEX 5.1.1 (Bachmann et al., 2010). Lower-hemisphere, equalarea pole figures of CPO observed in the starting material were constructed using a de la Vallee Poussin half width of 10°; fabric strength was calculated using the J index (Bunge, 1982) and M index (Skemer et al., 2005). Dislocation density (ρ) maps of geometrically necessary dislocations (GND) required to accommodate the intragranular misorientations were constructed following the procedure for estimating dislocation density (https://mtex-toolbox.github.io/GND.html), which is based on the method of Pantleon (2008).

Stress Versus Axial Strain
Differential stress versus axial strain curves are plotted in Figure 2. The stress magnitudes of our samples are consistent with those for wet olivine determined by Chopra and Paterson (1981), several of which were analyzed by van der Wal et al. (1993) for the olivine piezometer. At a given condition, the stress varied somewhat between experiments, likely as a result of heterogeneous water content from dehydration of minor hydrous phases and/or the presence of large porphyroclasts. The associated variation of the recrystallized grain size for these samples (Figure 3a), which follows the piezometer of van der , enabled investigation of postdeformation grain growth over a range of starting grain sizes. In experiments that achieved flow stresses greater than~600 MPa, significant strain weakening was observed following the maximum stress; weakening in lower stress experiments was less pronounced. Constant strain rate experiments were quenched without a grain growth interval ( Figure 2a). In rate-stepping experiments, the flow stress adjusted to the reduced strain rate (Figure 2b). In the rate-stepping experiment that achieved the highest stress (w2069), the stress dropped significantly after the strain rate was reduced and then gradually increased during continued deformation, eventually achieving a final stress similar to that observed in other rate-stepping experiments at the same temperature. In all stress relaxation experiments, the stress decreased rapidly when advancement of the deformation piston was stopped, and accumulation of additional strain was less than 1% ( Figure 2c).

Stress Versus Grain Size
To illustrate the effect of stress reduction on grain growth of deformed (or deforming) olivine aggregates, the final stress magnitude and final grain size data are plotted for each experiment in Figure 3. Because the relationships between flow stress and grain size in constant strain rate experiments (Figure 3a) are consistently within the uncertainty of the olivine grain size piezometer , we used the piezometer to estimate the starting recrystallized grain size in the rate-stepping and stress relaxation experiments. For the rate-stepping experiments, lines connecting each final stress/grain size to the olivine piezometer indicate the flow stress just prior to the change in strain rate and the calculated grain size at the start of the grain growth interval (Figure 3b). In rate-stepping experiments, the stress drop was relatively modest (consistent with the dislocation creep flow law-see section 3.3), and recrystallized grain sizes remained similar to those predicted by the piezometer. In contrast, grain sizes in samples that underwent stress relaxation, wherein stress drops were significantly larger, no longer followed the piezometer (Figure 3c). The final grain size (11.4 ± 3.7 μm) in the sample with the shortest relaxation interval (w1967; 0.2 h) is smaller than, but within uncertainty of, the initial grain size (12 μm) predicted for its flow stress (213 MPa). Data from stress relaxation experiments conducted on the Anita Bay and Åheim dunites at 1200-1300°C (van der Wal, 1993) are also shown. The grain size evolution observed for van der Wal's samples is similar to that we observe for Balsam Gap dunite.

Strain Rate Versus Stress
Strain rate versus differential stress relationships are plotted using the wet olivine flow law for dislocation creep (Hirth & Kohlstedt, 2003) at water contents of C OH = 600 ± 300 H/10 6 Si ( Figure 4). The final stress and strain rate for constant strain rate experiments are plotted in Figure 4a. The data from rate-stepping experiments give "two-point" stress exponents (n) from 2.6 to 4, consistent with deformation by dislocation creep, although most samples from rate-stepping experiments deformed at somewhat higher stresses than predicted by the flow law ( Figure 4b). The higher stress exponent for sample w2012 (n = 5) reflects the short  duration of deformation after the step (0.2 h) during which steady stress was not achieved before quenching.
The stress in the sample deformed at 1000°C (w2076) is significantly lower than predicted by the flow law, which could be related to higher water content. Nonetheless, the recrystallized grain size data for w2076 agree with the recorded flow stress. For the stress relaxation experiments, the strain rate and stress data (prior to relaxation) agree reasonably well with the dislocation creep flow law for this range of water contents ( Figure 4c).

Microstructural Observations 3.4.1. Thin Section Scale
To confirm that no significant grain growth occurred during hot-pressing of this coarse-grained aggregate, we performed a "null" experiment, wherein a dunite core was taken to 1100°C and a confining pressure of 1,400 MPa and held for~10 h. As expected, no significant grain growth occurred; the grain size distribution remained similar to that in samples used in the other experiments (~400 μm). Cross-polarized micrographs of the samples are shown in Figure 5. Deformation resulted in variable degrees of grain flattening perpendicular to the direction of maximum principal compressive stress (σ 1 , vertical) and dynamic recrystallization along porphyroclast grain boundaries. Because of the relatively low strain magnitudes and small recrystallized grain size, none of the samples achieved complete recrystallization. The degree of dynamic recrystallization was generally 5-10%, although some higher temperature experiments (e.g., w2018) exhibit up to~30% recrystallization. Several samples exhibit relatively uniform shortening. Others appear somewhat bent, likely due to the presence of large porphyroclasts, as most of the samples with large porphyroclasts bent to some degree. Deformation of one sample (w2089, with a maximum stress of 872 MPa) resulted in a brittle fracture oriented~30°to σ 1 ; however, brittle behavior occurred subsequent to dynamic recrystallization, enabling evaluation of grain growth during stress relaxation. Although no brittle behavior is observed in sample w2090 (with a maximum stress of 1,076 MPa), the sample exhibits kink bands and only minor recrystallization.

Grain Scale
Representative cross-polarized micrographs are shown in Figure 6, and textures of dynamically recrystallized grains quantified from EBSD data are provided in the supporting information (Table S1). Dynamically recrystallized grains are much smaller than the porphyroclasts. Some recrystallized grains are approximately equant; others are somewhat flattened, with aspect ratios up to 3:1. Grain boundaries in samples quenched after deformation at a constant strain rate are lobate and/or sutured (Figure 6a), but regions with straight to gently curved grain boundaries are also observed in EBSD band contrast maps of the same sample (Figure 6b). The intracrystalline deformation textures of samples from rate-stepping experiments (in all of which the strain rate was decreased to 1.5 × 10 −6 s −1 ) are similar to that observed in samples from constant strain rate experiments (Figures 6c and 6d). Samples from stress relaxation experiments have straight to gently curved grain boundaries and~120°triple junctions, and recrystallized grains exhibit a lesser degree of undulose extinction than that observed in samples from constant strain rate and rate-stepping experiments (Figures 6e and 6f). In addition, larger recrystallized grains in the stress relaxation samples tend to have more than six sides and are convex inward on at least one boundary, adjacent to smaller convex-out grains with fewer grain boundaries, indicating grain boundary migration driven by the reduction of grain boundary curvature (Atkinson, 1988).
The original deformation microstructures are overprinted during changing conditions in stress relaxation and rate-stepping experiments; however, the original recrystallization mechanism may be inferred from analysis of the constant strain rate experiments. Grain size in samples deformed at lower stress (<400 MPa) is similar to subgrain size, suggesting that subgrain rotation played a role in recrystallization ( Figure 6a). However, bulging and sutured grain boundaries indicate that gradients in strain energy density also promoted bulge nucleation. Subgrains are less prominent in samples that deformed at higher stress (>400 MPa), and recrystallization is less abundant. In the highest stress samples (>700 MPa), very little recrystallization is observed, and microstructures are characterized by kink bands and/or indicative of brittle behavior.

Microstructures of Hot-Pressed, Annealed Olivine Aggregates
The hot-pressed annealed Balsam Gap dunite and San Carlos olivine (w2084BG and w2084SC, respectively) have relatively uniform grain sizes and straight to gently curved grain boundaries that form~120°triple junctions (Figure 7). Larger grains tend to be convex inward on at least one boundary, and smaller adjacent grains are convex out, consistent with expectations for grain growth. Because this sample was hot-pressed and annealed at a confining pressure of 1,400 MPa, we infer that only a small amount of porosity remains (<1 vol%); similarly, no porosity was observed in the recrystallized regions of the deformed specimens of coarse-grained cores. The grain boundary morphologies of our hot-pressed annealed sample are similar to those from stress relaxation samples, but they differ somewhat from the microstructures of constant strain rate and rate-stepping samples that still exhibit evidence of deformation, such as sutured grain boundaries and undulose extinction.

Dislocation Density Estimation
Dislocation density (ρ) maps of representative samples are shown in Figure 8. Warmer and cooler colors indicate higher and lower ρ, respectively. The color bars represent the log 10 ρ (m −2 ) of geometrically necessary edge and screw dislocations required to accommodate the intragranular misorientations; the step sizes used to acquire each map are indicated. We used a step size of ≤1 μm for most of the maps; although a few maps were acquired at relatively low resolution (2 μm step size), we were still able to use them to make several key qualitative observations. We acknowledge that significant uncertainties arise from the use of lower-resolution EBSD techniques (e.g., Wallis et al., 2016); however, our qualitative comparisons between samples deformed under different conditions of stress and temperature are consistent with expectations for relative differences in ρ between highly deformed porphyroclasts and recrystallized grains. Based on the maps, ρ in the recrystallized grains ranges from~10 12 to 10 14 m −2 (Figure 8).
The nonannealed, hot-pressed sample (w2079BG) has a relatively high ρ, suggesting that dislocations are generated during hot-pressing of the initial high-porosity material ( Figure 8a); ρ was significantly lower (i.e., likely reduced) during annealing (w2084BG, Figure 8b). Samples that were deformed and then relaxed at 1100°C exhibit a reduction in ρ with increased annealing time (Figures 8c and 8d). In a few samples, the grain morphologies of some (often larger) recrystallized grains near the boundaries of porphyroclasts indicate growth preferentially in the direction of high ρ in the porphyroclasts (Figures 8e and 8f, arrows). In contrast, recrystallized grains that are surrounded by other recrystallized grains with similar ρ are similar in size. In sample w2015, which was deformed at a constant strain rate at 1200°C (Figure 8g), the recrystallized grains have a higher and more homogeneous ρ than have the recrystallized grains in the sample that underwent stress relaxation at 1200°C (w2018, Figure 8h).

Variability in Flow Stress
The variation in flow stress among experiments in this study enabled investigation of syndeformation and postdeformation grain growth for a range of starting grain sizes. The magnitude of the sample-to-sample stress variation in our samples is similar to (slightly larger than) that observed in deformation experiments on Åheim dunite conducted under dry conditions in a Paterson apparatus (Keefner et al., 2011). Variation in stress magnitude may result from differences in temperature, starting material grain sizes and orientations, or water content.

Variation in Temperature
The temperature of each experiment was precise to within ±5°C at the position of the thermocouple; however, shifting of the thermocouple during deformation cannot be ruled out. Although we measured recrystallized grain size at the axial position of the thermocouple (near the sample center), recrystallized grain sizes appeared similar throughout the sample. This suggests that variation in temperature within the sample was not large (current analyses of these gradients indicate that temperature varies less than 30°C in the axial direction; E. Burdette, personal communication, January 2020).

Variation in Porphyroclast Size/Orientation
The size, distribution, and orientation of large porphyroclasts observed in several samples may affect the strength of the material. For example, among 1200°C experiments, the lowest flow stress (118 MPa) was recorded in a sample (w2015) that lacked large porphyroclasts, whereas the others had large porphyroclasts and were stronger (175-254 MPa). A similar correlation is observed in samples deformed at 1100°C. Although we observed a large porphyroclast and high stress in one sample deformed at 1000°C (w2091, 649 MPa), we are unable to determine if the lower stress in the other 1000°C sample (w2076, 405 MPa) may have been related to the absence of large porphyroclasts because large portions of material were plucked during thin sectioning.

Variation in Water Content
Although minor variations are to be expected in a natural aggregate, and cannot be avoided, the cores for each sample were very similar; thus, we infer that the starting water content of each sample was similar. The water source in our samples likely comes from dehydration of serpentine. Individual cores drilled from the block of as-is dunite may have sampled regions inside the rock with altered microcracks or grain boundaries that were not visible at the surface. The dehydration temperature of serpentine is well below the temperatures of our experiments; dehydration would have been accomplished fairly early along the path to 1100°C and 1,400 MPa confining pressure, likely~10 h before deformation was initiated. Under these thermodynamic conditions, the saturated water content of olivine is~2,800 H/10 6 Si (based on Zhao et al., 2004) with a water fugacity of~4,300 MPa, using Wither's fugacity calculator: http://www. esci.umn.edu/people/researchers/withe012/fugacity.htm (see Pitzer & Sterner, 1994); thus, the experiments were not performed under water-saturated conditions. However, three lines of evidence suggest that whatever the water content, it had equilibrated reasonably well prior to the grain growth interval: Figure 7. EBSD band contrast map of hot-pressed annealed Balsam Gap dunite (w2084BG). Larger grains tend to have more than six sides and are convex inward on at least one boundary, adjacent to convex-out grains with fewer grain boundaries (red arrows). Dark regions are plucked grains.
1. the similarity of stress magnitudes recorded in our samples that underwent stress relaxation at 1100°C following deformation at a strain rate of 1.5 × 10 −5 s −1 (Figure 2c); 2. the consistency of the strain rate versus stress data with the wet olivine flow law for our range of water contents (Figure 4c); and 3. the log-linear relationship in the change of grain size with time (see section 4.2 and Figure 9a).
These observations suggest that variation in water content did not affect the grain growth rates in the stress relaxation experiments we used to derive our grain growth law (see section 4.2). In addition, the uncertainties we report in our grain growth parameters account for the uncertainties due to any variation in water content.

Grain Growth Kinetics of Deformed, Moderately Wet Olivine
The rate of postdeformation grain growth was analyzed using the stress relaxation experiments, assuming a normal grain growth relationship: with grain size (d) in meters, a growth exponent (p), time (t) in seconds, and a growth rate (k) following the relationship: where k 0 is the rate constant (m p s −1 ), H is the activation enthalpy (J mol −1 ), R is the ideal gas constant (J K −1 mol −1 ), and T is absolute temperature (Atkinson, 1988). Six of the stress relaxation experiments were conducted at a temperature of 1100°C; one (w1967) was not used because it had an apparent negative growth rate (i.e., its final grain size was slightly smaller than its starting grain size, although still within error). To estimate the growth rate (k) at 1100°C, we used least squares polynomial fits to evaluate the change of grain size with time for grain growth exponents (p) ranging from 2 to 4. Errors are minimized for p = 3.2, although the errors for p = 3.3 were similar. The change of grain size with time is shown in Figure 9a, with associated residuals in Figure 9b. The goodness of fit for the each of the growth exponent values we evaluated is shown in Figure 10a. For the 1100°C experiments, a value of p = 3.2 results in a growth rate (k) of 2 × 10 −21 m p s −1 .
A grain growth exponent of p = 3 has been attributed to various rate-limiting growth mechanisms, such as impurity drag limited by lattice diffusion, and the effects of secondary phases (e.g., Brook, 1976). Our samples contain~1 vol% chromium spinel, and these grains are rare in regions of dynamically recrystallized olivine; thus, we interpret that second-phase pinning effects are minimized. An electron microprobe analysis of several samples suggests the CaO (<0.06 wt%) and Al 2 O 3 (<0.15 wt%) concentrations are low (see supporting information Figure S3); however, minor amounts of these incompatible components concentrated along grain boundaries may contribute to impurity drag and an exponent of p = 3.2 in our samples.
To calculate the parameters of the temperature-dependent growth rate (k), results from grain growth experiments at a range of temperatures are required. Because we only had one stress relaxation experiment at 1200°C, we incorporated the results of similar experiments performed by van der Wal (1993) on the Anita Bay and Åheim dunites (1200-1300°C, 300 MPa confining pressure) in our analysis (Figure 9c). The water content in samples used in van der Wal's experiments is similar to our samples

Journal of Geophysical Research: Solid Earth
(C OH = 600 H/10 6 Si; Behn et al., 2009). The growth rate (k) is an exponential relation; thus, the activation enthalpy and rate constant may be obtained by taking the natural logarithm of both sides of Equation 2 to yield: which gives an activation enthalpy of H = 622 kJ mol −1 and a rate constant of k 0 = 1.8 × 10 3 m 3.2 s −1 . The good agreement between growth rates determined during stress relaxation of dynamically recrystallized olivine (van der Wal, 1993, this study) suggests that confining pressure has only a minor effect on the growth rates at the pressures of these experiments (300 and 1,400 MPa, respectively). To assess the effect of the pressure difference, we evaluated the components of the activation enthalpy (H), which is defined by the following relationship: where E G is the activation energy for grain growth (J mol −1 ), P is the confining pressure (Pa), and V G is the activation volume for growth (m 3 mol −1 ). Recognizing that, at the conditions of van der Wal's experiments, the pressure dependence of H is relatively small, we estimated E G by testing V G values in the range of 1 × 10 −7 to 1 × 10 −5 m 3 mol −1 and found E G = 619-622 kJ mol −1 at P = 300 MPa. We tested four values of E G over this range of V G and compared the predicted grain sizes with those from our stress relaxation experiments. Errors are minimized in the range of V G = 4.6 × 10 −6 to 6.7 × 10 −6 m 3 mol −1 . When we applied these values of E G and V G to both our results and van der Wal's data, the best fit was E G = 620 ± 145 kJ mol −1 , where errors are minimized for V G =~5 × 10 −6 m 3 mol −1 (Figure 10b). We note that our activation energy for grain growth (E G ) is within uncertainty of the activation energy for dislocation creep of wet olivine (E* = 480 ± 40 kJ mol −1 for constant water content; Hirth & Kohlstedt, 2003), acknowledging the relatively large uncertainty in our data. Accounting for the influence of temperature on the water content of olivine (with an activation energy of~50 kJ mol −1 ; Zhao et al., 2004), our estimate of E G would be slightly lower (i.e., 570 ± 145 kJ mol −1 ).

Comparison of Static Annealing and Postdeformation Growth 4.3.1. Comparison to Our Olivine Grain Growth Parameters
Curves for predicted grain size evolution in our stress relaxation and rate-stepping samples, stress relaxation experiments by van der Wal (1993), and our hot-pressed annealed sample are plotted using our parameters and Equation 1 along with final grain sizes in Figure 11a. Although data from the rate-stepping experiments are not included in the derivation of our parameters, they agree reasonably well with the stress relaxation experiments. Grain size in sample w2012 (6.2 ± 1.9 μm), for which the duration of the strain rate step was only 0.2 h, is within the uncertainty of the final grain size (7.6 μm) predicted for its final stress (300 MPa). All of the other samples from rate-stepping experiments at 1100°C record grain sizes (~10-11 μm) that are similar to those observed after stress relaxation experiments. These grain sizes are also similar to that predicted by the piezometer for the final stress observed during the step (~200 MPa), which would limit the grain sizes to these values. Grain size in a 1200°C rate-stepping sample (w2014) is larger than, but also within uncertainty of, the grain size predicted by our grain growth parameters. In the sample that was deformed and then relaxed at 1200°C (w2018), the grain size is also larger than predicted by our parameters.
Our grain growth parameters predict grain sizes that are smaller than, but within uncertainty of, the final grain sizes observed in our hot-pressed annealed sample (w2084) with Balsam Gap dunite and San Carlos olivine (stars, Figure 11a). Although the San Carlos olivine is dry, diffusion of water from the Balsam Gap core (and powder) could result in a similar water content and similar growth rates in both materials. Using a Pt disc (instead of Ni) to separate the hot-pressed aggregates may have impacted the oxygen fugacity, but the growth rates of the hot-pressed San Carlos olivine and Balsam Gap dunite powders were very similar to each other and to that observed in the stress relaxation samples. At a confining pressure of 1,400 MPa, densification was near complete; thus, most grain boundaries were in contact, and growth may not have been significantly inhibited by porosity. This interpretation is supported by the similarity of growth rates at 1100°C of our hot-pressed annealed and stress relaxation samples in which no porosity was observed (and unlikely, since the recrystallized grains form by grain boundary migration and subgrain rotation from single crystal porphyroclasts). In the absence of deformation, we expected an initially low ρ and grain growth driven completely by the reduction of interfacial energy in the hot-pressed annealed sample. Interfacial energy-driven grain boundary migration (γGBM) acts to reduce boundary curvature, resulting in~120°triple junctions (Humphreys & Hatherly, 1995). However, we observed relatively high ρ in the nonannealed sample (Figure 8a), which was higher than that observed after annealing (Figure 8b). Similarly, ρ is reduced with increased annealing time during stress relaxation (Figures 8c and 8d); ρ in the hot-pressed annealed sample (Figure 8b) is lower than that observed in the recrystallized grains of the stress relaxation sample with a relatively short annealing time (Figure 8c) but similar to that observed in the stress relaxation sample with a longer annealing time (Figure 8d). A difference in ρ across a grain boundary induces strain energy-driven grain boundary migration (ρGBM); grains with lower ρ grow as their grain boundaries migrate into grains with higher ρ, which shrink in the process (Beck et al., 1950). If the distribution of dislocations is more homogeneous, however, grain boundaries will migrate randomly with little net change in the grain size distribution (Platt & Behr, 2011). The microstructures of the hot-pressed annealed and stress relaxation samples indicate that γGBM was dominant by the end of the experiment, but an interval of random ρGBM may have delayed the onset of γGBM or reduced its efficiency. Otherwise, it follows that γGBM itself leads to the observed grain growth rates.
In Figure 11b, we compare our grain growth parameters to the grain size data from previously published hydrostatic annealing experiments on hot-pressed olivine aggregates conducted under "wet" conditions at 1200-1300°C and a confining pressure of 300 MPa (Karato, 1989). The grain sizes plotted in Figure 11b have been normalized to account for the fact that Karato used a geometric correction factor of 1.5 (i.e., we removed his original correction factor by dividing by 1.5 and then multiplied his grain sizes by 1.75). Although the grain sizes of a few of Karato's 1200°C samples are reasonably well predicted by our

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Journal of Geophysical Research: Solid Earth parameters, most are overestimated; our parameters predict grain sizes significantly larger than observed for all of his 1300°C samples. As noted by Karato (1989), growth was inhibited by porosity in the samples used in his study. This could explain why the grain sizes in most of his samples are significantly smaller than predicted by our parameters, which are based on grain growth in samples wherein porosity was not observed.

Comparison to the Existing Wet Olivine Grain Growth Law
We compare the grain sizes observed in our study (and van der Wal, 1993) with a grain growth law for wet olivine (Karato, 1989; with p = 2, H = 160 kJ mol −1 , and k 0 = 1.6 × 10 −8 m 2 s −1 ) in Figure 11c. In this case, to facilitate direct comparison to the grain growth law, the grain sizes plotted in Figure 11c are normalized using the geometric correction factor of 1.5 used by Karato (1989) (i.e., we removed our original correction factor by dividing by 1.75 and then multiplied our grain sizes by 1.5). The Karato (1989) grain growth law is consistent with the grain sizes observed in van der Wal's samples that were deformed and then relaxed at 1200°C (blue triangles, Figure 11c). However, it over-estimates the grain sizes in both our hot-pressed Figure 11. Comparison of olivine grain growth using the parameters of (a, b) this study and (c, d) Karato (1989), with growth curves plotted from the grain size at the start of the grain growth interval. The data points in each plot represent (a) final grain sizes from samples in this study (and relaxation experiments by van der Wal, 1993); (b) grain sizes from static annealing samples (Karato, 1989) normalized to our geometric correction factor of 1.75; (c) same data as in (a) but normalized to Karato's geometric correction factor of 1.5; and (d) grain size data from Karato (1989). The circled crosses in (d) indicate the samples Karato (1989) used to derive the grain growth law. Error bars in (a) and (c) represent one standard deviation of the grain size distribution. For data points and growth curves, temperature is indicated by colors in the legend in Figure 11c.
annealed sample and the samples from our stress relaxation experiments conducted at 1100°C, and underestimates the grain sizes from van der Wal's stress relaxation samples at 1300°C. These observations are consistent with the difference between the activation enthalpy we determined and the lower value estimated by Karato (1989).
Curves for predicted grain growth at 1100-1300°C are plotted using the parameters of Karato (1989) in Figure 11d, along with the final grain size data of the wet samples in his study that were annealed at 1200-1300°C and a confining pressure of 300 MPa (crosses, Figure 11d). The data he used to derive the grain growth law are shown as circled crosses; we note that Karato (1989) did not perform annealing experiments at 1100°C. The initial grain size of his samples was~1-4 μm. Because grain growth was inhibited by porosity in his samples, Karato only used samples with densities at least 97% of the theoretical density of olivine (3.33 g cm −3 ) in his derivation. In addition, he performed progressive annealing experiments on two samples (one at 1200°C and one at 1300°C), wherein each sample underwent repeated annealing and quenching (to examine the grain size) over four sequential grain growth intervals; for these samples, only the final grain size data were used in the grain growth law (the two circled crosses plotted at t = 8 h in Figure 11d).
An important difference between the static grain growth experiments of Karato (1989) and the stress relaxation experiments in this study (and van der Wal, 1993) is the effect of deformation and dynamic recrystallization on grain growth. For example, at the stress magnitudes of our samples that were deformed and then relaxed at 1100°C, ρ is very high, temperature-dependent grain boundary mobility is relatively low, and recovery by dislocation climb is sluggish. The distribution of dislocations in the recrystallized grains appears fairly homogeneous (Figures 8c and 8d), which would promote random ρGBM with little change in the grain size distribution (cf. Platt & Behr, 2011). However, we observed annealed microstructures even in samples with relatively short relaxation intervals, suggesting that strain energy was dissipated (via ρGBM) fairly rapidly. The grain boundaries then migrated toward their centers of curvature (γGBM), and larger grains grew at the expense of smaller grains, resulting in the observed grain size adjustment. The delayed onset of γGBM may help to explain the significant difference between our observed growth rates and those of Karato (1989). However, the similarity of the final grain sizes of 1100°C samples with similar recrystallized grain sizes but different annealing times (w1966,~1.4 h; w1964,~14 h) provides evidence that even after strain energy is dissipated, growth by γGBM is slower than predicted by the Karato (1989) grain growth law.

Grain Size Evolution Following a Reduction in Flow Stress
The olivine piezometer was calibrated using both wet and dry olivine in the stress range of 30-300 MPa. It is based on data from both constant strain rate and rate-stepping experiments, combined with results from single-crystal experiments reported in 1980 by Karato et al. (van der Wal et al., 1993). The recrystallized grain sizes we observe for constant strain rate experiments agree well with the olivine piezometer, even at the higher stress magnitudes made possible by use of the Griggs rig with a molten salt cell. The consistency of our grain sizes with the piezometer over a range of temperatures provides further evidence that the steady state recrystallized grain size is not temperature dependent. Some models for recrystallized grain size explicitly predict temperature-dependent piezometric relationships when the activation enthalpy for grain growth is different than that for creep (e.g., Austin & Evans, 2009, and references therein). The observation that our activation enthalpy for grain growth during and subsequent to deformation is similar to that for creep provides a possible explanation for the lack of temperature dependence in the piezometer.
The recrystallized grain sizes observed in samples from rate-stepping experiments are also consistent with the piezometer. Van der Wal (1993) investigated grain size evolution after changes in strain rate and found that the grain size adjusted to the new stress within 1.5-3% axial strain. The characteristic strain required for stress-grain size equilibrium has also been reported for other minerals, such as quartz (~3%; Kidder et al., 2016) and salt and calcite (3-6% and 20-35%, respectively; Braun et al., 1999, and references therein).
With the exception of our sample w2012, the additional strain accumulated during the rate-stepping experiments in this study was 1.3-7.9%, which provides further evidence that the strain required for the recrystallized grain size to keep pace with the piezometer is small for modest changes in stress magnitude. We interpret that the grain size adjustment was facilitated by ρGBM in grains with heterogeneously distributed ρ and additional recrystallization (from the remaining original porphyroclasts) at the lower stress. Following the large stress drop in our stress relaxation experiments, less than 1% additional strain accumulated, and grain sizes in these samples are no longer consistent with the piezometer. Additional recrystallization 10.1029/2020JB020415

Journal of Geophysical Research: Solid Earth
would have been very limited; thus, the grain size adjustment can be attributed almost entirely to grain growth.

Implications for the Persistence of Strain Localization
Exhumed upper mantle shear zones often preserve dynamically recrystallized grain sizes <1 mm with inferred temperatures <1000°C (e.g., van der Wal & Vissers, 1996;Vissers et al., 1997;Warren & Hirth, 2006), and significant water content (up to~3,000 H/10 6 Si) has been measured in mantle xenoliths and peridotites (e.g., Demouchy & Bolfan-Casanova, 2016, and references therein). Predicted growth curves using our parameters are shown in Figure 12. The solid curves represent growth from the recrystallized grain sizes predicted by the olivine piezometer based on the stress magnitudes predicted by the wet olivine flow law for C OH = 600 H/10 6 Si, a strain rate of 10 −14 s −1 and a range of temperatures (800-1000°C) at a confining pressure of 3 GPa. The shaded regions represent the uncertainties in our grain growth law. Our results suggest that grain growth of deformed, moderately wet olivine aggregates is much slower than predicted by the existing static grain growth law for wet olivine (Karato, 1989;dashed curves). Also shown in Figure 12 (dashed box) is the range of olivine grain sizes commonly observed in unmixed regions of olivine-rich peridotite xenoliths, including formerly recrystallized and now partially annealed grains (e.g., Ave Lallemant et al., 1980;Baptiste et al., 2012;Bernard & Behr, 2017;Bernard et al., 2019, and references therein;Mercier, 1980;Tommasi et al., 2008;Zaffarana et al., 2014). Although exact durations of annealing, and dynamically recrystallized grain sizes prior to annealing, are not known for each individual case, for most tectonic settings the eruption age postdates the timing of the last tectonic event by at least 1 million years. Our grain growth law is reasonably consistent with the range of observed grain sizes and annealing temperatures for the mantle xenoliths, as well as those reported from exhumed dunites that exhibit evidence of deformation followed by annealing (e.g., Cao et al., 2017).
Although our coarse-grained samples deformed by dislocation creep, and strain localization was not observed, grain size reduction ("damage") by dynamic recrystallization can enhance weakening and strain localization through a switch in deformation mechanism from grain size-insensitive dislocation creep to a grain size-sensitive creep mechanism (Poirier, 1980). Our results suggest that grain growth ("healing") at lower temperatures is sluggish enough to allow the long-term preservation of small grain size, which could promote grain size-sensitive creep and enable persistent strain localization in the lithosphere.

Conclusions
We performed deformation and grain growth experiments on natural olivine aggregates with water contents (C OH = 600 ± 300 H/10 6 Si) similar to those found in upper mantle olivine. Recrystallized grain sizes in samples quenched after deformation at a constant strain rate agree well with the olivine grain size piezometer . In samples that underwent a reduction in strain rate, grain size adjusted to the piezometer within~1.3-7.9% strain, suggesting that the critical strain required for stress-grain size equilibrium is small if the stress reduction is small. We quantified postdeformation grain growth rates from stress relaxation experiments, which, when extrapolated over geologic time, predict significantly slower growth than that reported for undeformed, wet synthetic olivine (Karato, 1989). We interpret that the grain boundary migration processes that are active during deformation and dynamic recrystallization affect the kinetics of postdeformation grain growth. In samples from our stress relaxation experiments, the development of abundant 120°triple junctions suggests that the reduction of interfacial energy became more important than that of strain energy at some point during the relaxation interval, but growth by γGBM may have been delayed by an interval of random ρGBM. In addition to the effects of grain boundary pinning by secondary phases in naturally deformed mantle rocks (Nes et al., 1985), the results of this study imply that because Figure 12. Predicted growth curves using our parameters (solid curves; shaded regions represent the uncertainties in our grain growth law) and the existing wet olivine grain growth law (Karato, 1989; dashed curves). The initial grain size is assumed to follow the olivine piezometer  for the stress predicted by the wet olivine flow law for C OH = 600 H/10 6 Si (Hirth & Kohlstedt, 2003) at a strain rate of 10 −14 s −1 and confining pressure of 3 GPa. The range of olivine grain sizes observed in mantle xenoliths is also shown (dashed box).

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Journal of Geophysical Research: Solid Earth postdeformation grain growth is slow even in moderately wet olivine aggregates, grain size reduction by dynamic recrystallization can play an important role in the persistence of strain localization in the upper mantle.