The Effect of Intracrystalline Water on the Mechanical Properties of Olivine at Room Temperature

The effect of small concentrations of intracrystalline water on the strength of olivine is significant at asthenospheric temperatures but is poorly constrained at lower temperatures applicable to the shallow lithosphere. We examined the effect of water on the yield stress of olivine during low‐temperature plasticity using room‐temperature Berkovich nanoindentation. The presence of water in olivine (1,600 ppm H/Si) does not affect hardness or yield stress relative to dry olivine (≤40 ppm H/Si) outside of uncertainty but may slightly reduce Young’s modulus. Differences between water‐bearing and dry crystals in similar orientations were minor compared to differences between dry crystals in different orientations. These observations suggest water content does not affect the strength of olivine at low homologous temperatures. Thus, intracrystalline water does not play a role in olivine deformation at these temperatures, implying that water does not lead to weakening in the coldest portions of the mantle.


Introduction
The rheological behavior of the upper mantle is predominantly controlled by the mechanical response of olivine, its most common constituent mineral.The rate of deformation of olivine by the motion of dislocations can be limited by either dislocation glide or dislocation climb.Climb is the rate-controlling process at high temperatures and low stresses, commonly associated with the asthenosphere and lower lithosphere, while dislocation glide is rate-limiting at the low temperatures and high stresses typical of the shallow lithospheric mantle (c.f., Warren & Hansen, 2023).We refer to glide-controlled deformation as low-temperature plasticity (LTP).Glide velocity is predominantly controlled by the Peierls stress, which is the resistance of the crystal lattice to dislocation glide in the absence of thermal activation (e.g., Karato, 2008, Chapter 9).Therefore, lattice resistance and the microphysical processes by which dislocations overcome it are important to determine over the full range of environmental and compositional variables at play in the upper mantle.
Olivine is a nominally anhydrous mineral in that it contains no stoichiometric water (e.g., Bell & Rossman, 1992).However, small concentrations of water (<0.01 wt% H 2 O) can be hosted in the crystal structure of olivine in the form of H + ions, and these small concentrations can have dramatic effects on the physical properties of olivine, including viscosity (e.g., Kohlstedt, 2006) and electrical conductivity (Wang et al., 2006).As LTP typically occurs at relatively shallow depths where interaction between peridotites and hydrous fluids may be most common, constraining the impact of hydrous point defects on the rheological properties of olivine is important for understanding the deformation processes that occur in such settings.Examples include the plastic deformation of asperities on frictional faults (e.g., Boettcher et al., 2007) and the bending of plates entering subduction zones (e.g., Buffett & Becker, 2012).
To refine analyses of these deformation processes, we must distinguish among models that predict the impact of intracrystalline H + on LTP of olivine.There are several potential mechanisms by which small concentrations of H + may decrease the strength of nominally anhydrous minerals (e.g., Griggs, 1967;Hobbs, 1984;Katayama & Karato, 2008), and the role of water in glide-controlled deformation is still unclear.The presence of H + ions may modify the dynamics of dislocation glide through several aspects of the dislocation motion.Dislocation glide is generally considered to occur by the process of nucleation and migration of kinks, which are local displacements of the dislocation line in its glide plane.As detailed in the supplemental material, flow laws based on the glide of dislocations can be derived to explicitly include the behavior of dislocation kinks.Several of the parameters in these flow laws may be affected by the concentration of H + (e.g., Hobbs, 1984).For instance, increasing the concentration of H + may lead to weakening by increasing the concentration of kinks.Weakening may also occur by decreasing the Peierls stress, the intrinsic resistance of the lattice to dislocation motion, or by decreasing the backstress, the resistance to dislocation motion by elastic interaction with other dislocations.
We group models for the role of water in LTP based on which of the flow-law parameters is primarily influenced by H + (Figure 1).We define models 1 and 2 as cases in which H + does not affect LTP, as suggested by Tielke et al. (2017).In model 1, the influence of water on deformation occurs only at high temperatures through its influence on the bulk diffusivities of the major species and therefore on dislocation climb and recovery (c.f., Kohlstedt, 2006), which reduces the backstress, and therefore, the steady-state flow stress (e.g., Breithaupt et al., 2023).In model 2, H + results in charged point defects that couple to the kink concentration through point-defect equilibria because kinks in ionic solids can be charged (Hobbs, 1984).As highlighted in the supplemental material, increasing the kink concentration has little effect during LTP and primarily reduces the flow stress during hightemperature creep.Other models consider H + to hydrolyze Si-O bonds (e.g., Griggs, 1967Griggs, , 1974)), which reduces the Peierls stress, as demonstrated for quartz by Heggie and Jones (1986).In model 3, as suggested by Griggs (1967Griggs ( , 1974)), H + must continually diffuse along dislocation cores to reduce the Peierls stress in the vicinity of dislocations, which will only be effective above an apparent threshold temperature.In model 4 (Karato, 2008, equation 9.10; Katayama & Karato, 2008), this process is never limited by diffusion, and the weakening associated with a reduction in the Peierls stress occurs at all temperatures.
In this study, we aim to distinguish among these models by examining the yield strength of hydrated olivine compared to dry olivine using room-temperature nanoindentation.This technique, in which a small, hard stylus is pressed into a sample to leave a plastically-deformed impression, is commonly used to probe elasticity and plasticity in metals and industrial ceramics (e.g., Kalidindi & Vachhani, 2014;Oliver & Pharr, 1992, 2004).Recently, indentation methods have seen a rise in popularity in the geosciences due to their comparative ease of use, rapid data acquisition, and reproducibility (e.g., Kranjc et al., 2016;Kumamoto et al., 2017;Thom et al., 2022;Thom & Goldsby, 2019).Furthermore, the self-confining nature of the technique allows LTP in olivine to be investigated at room temperature, generating clear microstructural evidence of dislocation activity (Avadanii et al., 2023;Kumamoto et al., 2017;Wallis et al., 2020).These low-temperature experiments are well suited to distinguishing among different models for the influence of water in LTP.

Methods
Sample M666, a gem-quality single crystal of San Carlos olivine, was hydrated at a pressure of 3 GPa and temperature of 1473 K using a multi-anvil solid-medium apparatus by Li (2015).Fourier transform infrared  (Evans & Goetze, 1979;Hansen et al., 2019;Keefner et al., 2011) and blue for wet olivine (Katayama & Karato, 2008;Tielke et al., 2017).Experimental data cover strain rates from 4.2 × 10 7 to 4.4 × 10 4 s 1 and are plotted without normalization.Flow laws and models of hydrolytic weakening are shown as solid lines for a strain rate of 10 5 s 1 with the minima and maxima of the shaded regions respectively indicating strain rates of 10 6 s 1 and 10 4 s 1 .Dashed lines are schematic transitions between LTP and dislocation creep.Flow laws for power-law creep of wet and dry olivine are from Hirth and Kohlstedt (2003).The LTP flow law for dry olivine is from Hansen et al. (2021).Models 1, 2, and 3 of hydrolytic weakening in the low-temperature regime are schematic and are described in the text.Model 4 is based on the flow law of Katayama and Karato (2008).(B, C, D) Individual models of hydrolytic weakening are highlighted in blue, with dry LTP and dislocation creep in red.The axes of each panel are the same as in (A).See supplemental information for further details of plotted flow laws and models.spectroscopy (FTIR) indicated water concentrations of 1,600 ppm H/Si (Li, 2015).To prepare for nanoindentation, one surface of M666 with a surface normal close to [010] was polished using diamond suspensions down to 0.25 μm and finished with 0.05 μm colloidal silica.An initial set of nanoindentation experiments was performed on this water-bearing M666, the results of which are hereafter referred to as M666-W.After performing nanoindentation experiments on M666-W, it was placed in a gas-mixing furnace and held at a temperature of 900°C for 8 hr.A mixture of CO and CO 2 was used to maintain the oxygen fugacity at approximately the Ni/NiO buffer and within the stability field of olivine.(At the time dehydration was performed, the furnace temperature was not stable above ∼1,000°C, so we chose to dehydrate at 900°C for greater control over the oxygen fugacity.)A second set of nanoindentation experiments was performed on this dehydrated M666, the results of which are hereafter referred to as M666-D.
FTIR was performed on M666-D to determine the residual water content, measured to be 700 ppm H/Si in the ∼0.4-mm-thick sample (see supplement for methodology).As the value from FTIR is a volume-averaged measurement of water concentration, we used a simple diffusion model to estimate the amount of water that remains in the outer 5 μm of the crystal (see supplement for additional detail).A depth of 5 μm covers the typical region over which olivine deforms during our nanoindentation experiments (∼3 times the maximum indent depth), with most strain occurring at even shallower depths (e.g., Avadanii et al., 2023;Wallis et al., 2020).We assume that diffusion along the [010] axis is the relevant dehydration mechanism given the orientation of M666.After 8 hr at 900°C with a diffusion coefficient of 2.05 × 10 13 m 2 s 1 for the [010] direction in olivine (Ferriss et al., 2018), our model indicates that the outer 5 μm of the crystal has an average water concentration of 30 ppm H/Si.This value is below the 50 ppm H/Si suggested as the minimum water concentration required for wet creep to be active in olivine (Hirth & Kohlstedt, 2003) and is similar to the water concentration assumed for our dry San Carlos olivine samples (Table 1) based on previous analyses of hydrogen in San Carlos olivine (Denis et al., 2018;Ferriss et al., 2018;Mackwell et al., 1985).
All other samples used in this study (Table S1 in Supporting Information S1) were prepared by cutting slices of untreated San Carlos olivine with two parallel sides, then polishing one side using diamond suspensions and colloidal silica, as with M666.Samples were mounted on aluminum stubs with their polished surfaces facing up in preparation for nanoindentation experiments.Crystal orientations were measured using electron backscatter diffraction to ensure that a range of orientations were analyzed (see supplement for more information).
Room-temperature nanoindentation experiments were performed using a MTS Nanoindenter XP and a KLA Nano G200, both equipped with a Berkovich (triangular pyramid) diamond tip.With Berkovich indents, the sharpness of the tip forces the sample to accommodate plastic strain nearly as soon as the indenter tip contacts the sample.In addition, the self-similar shape of the Berkovich tip means that the average magnitude of strain induced by the tip is constant, but the size of the plastic zone increases as the tip is pushed further into the sample over the course of the experiment (e.g., Fischer-Cripps, 2011, p. 7).An example array of 16 indents is shown in Figure 2.  Mackwell et al. (1985) have been multiplied by a factor of 3.5 to match the FTIR calibration of Bell et al. (2003) and secondary ion mass spectrometry values.d Averages where the orientation of the Berkovich tip relative to the surface of M666-D was most similar to the orientation of the Berkovich tip relative to the surface of M666-W.e Averages for crystals with surface planes within 10°o f the surface plane of M666.These crystals are CT-SCO1, OP1-2-S, and OP3-3 (Table S1 in Supporting Information S1).

Geophysical Research Letters
10.1029/2023GL106325 Indents were performed using the continuous stiffness method while keeping the ratio of loading rate to load constant at 0.05 s 1 .The maximum depth of each indent was in the range of 1,250-1,500 nm for indents on dry olivine and 80-1,500 nm for indents on M666-W.A subset of indents on M666-W were performed at different ratios of loading rate to load, from 0.005 s 1 to 0.1 s 1 .Raw data of load on the sample, displacement of the tip into the sample, contact stiffness, and time were recorded for each experiment at a rate of 5 Hz.Data were processed to extract Young's modulus (E), hardness (H), and yield stress (σ y ), following the methods by Oliver and Pharr (2004) and Evans and Goetze (1979) and using an area function based on indents performed in fused silica.As the area function is less precise at small indent depths, we only analyze hardness and yield stress for indents deeper than 200 nm.Further details regarding data processing are described in the supplemental information.

Results
Results are summarized in Table 1 and Figure 3.The elastic behavior of both wet and dry olivine compares very well to previous work (Figure 3B).The moduli for M666-W and M666-D are among the lowest of the tested samples, consistent with their orientation and previous measurements of the elastic properties of olivine (e.g., Abramson et al., 1997;Zha et al., 1996).M666-W exhibits a slightly lower Young's modulus than M666-D, which is expected based on a previous experimental investigation of the effect of water on the elasticity of olivine (Jacobsen et al., 2008).As observed in previous experiments (Kumamoto et al., 2017),  For the tests on M666-W (blue lines), an artifact associated with how data were exported results in the truncation of the unloading curves but does not affect our results.(B) Average Young's modulus at 1,000 nm depth for all samples, plotted at the orientation of the surface normal.M666-D is plotted with a red dashed marker edge.M666-W, which sits at an identical position on the plot, has a slightly lower Young's modulus (Table 1).The background is colored by the uniaxial Young's modulus for dry San Carlos olivine from Abramson et al. (1997).(C) Hardness versus displacement.Results are plotted as envelopes enclosing results at depths greater than 200 nm.Each gray envelope encompasses 7-16 nanoindentation experiments on a single crystal orientation.The blue envelope contains 44 experiments performed on M666-W, and the yellow envelope contains 52 experiments performed on M666-D across 6 different orientations of the indenter tip relative to the sample surface.The red envelope contains a subset of 16 experiments performed on M666-D in the two orientations most similar to the experiments performed on M666-W.(D) Yield stress versus displacement.Envelopes are colored as in (C).measurements of Young's modulus using nanoindentation exhibit a reduced degree of anisotropy relative to other measurement techniques due to the multiaxial forces applied during nanoindentation experiments.
The hardnesses and yield stresses of both wet and dry olivine samples are also consistent with previous measurements.Both quantities vary systematically with orientation (Figures 3C and D).The variability in hardness and yield stress for different crystal orientations at any given indentation depth (∼2-3 GPa at depths greater than 500 nm) is approximately the same as that measured previously using spherical nanoindentation (Kumamoto et al., 2017).Due to the complexity of the stress state beneath the indenter tip, many slip systems can be activated beneath an indent in a crystal of any orientation (e.g., Avadanii et al., 2023;Wallis et al., 2020).The (100)[001] and (110)[001] slip systems are generally the most active at room temperature (e.g., Avadanii et al., 2023;Gaboriaud et al., 1981;Wallis et al., 2020) due to their low critical resolved shear stresses (e.g., Hansen et al., 2019).Thus the observed anisotropy in hardness and yield stress in our results is primarily due to different resolved shear stresses on these slip systems depending on the geometry of deformation under the indenter tip.
The nanoindentation tests exhibit the indentation size effect in that hardness decreases with increasing indent depth (e.g., Koizumi et al., 2020;Kumamoto et al., 2017;Nix & Gao, 1998;Pharr et al., 2010).The size effect for each orientation can be characterized by a power law, with the exponent ranging from 0.03 to 0.17.Yield stress, calculated from modulus and hardness following the method of Evans and Goetze (1979), has a similar relationship with indent size, with a power-law exponent ranging from 0.02 to 0.22.Previous indentation studies on olivine identified size effects of similar magnitudes (Koizumi et al., 2020;Kumamoto et al., 2017).
When directly compared, measurements of hardness and yield stress for M666-W and M666-D overlap for nearly the entire experimental range of depths (Figures 3C and D).Small differences between the datasets on M666-W and M666-D can be attributed to the azimuthal anisotropy of the Berkovich tip.We tested 6 different tip orientations on M666-D by rotating the triangular pyramidal Berkovich tip about its axis of symmetry and then indenting the same crystal surface.We found that at a depth of 1,000 nm, the modulus varied by 7%, the hardness varied by 4%, and the yield stress varied by 3% (Table S1 in Supporting Information S1).In contrast, the difference between M666-W and M666-D for similar indent orientations (the red fields in Figures 3C and D; "similar indent ori" in Table 1) is 0.6% for hardness and 2% for yield stress.Thus, even the minor anisotropy induced by the orientation of the indenter tip relative to a single crystal surface has a greater effect on hardness and yield stress than that of the water content.

Discussion
In a previous study on the role of water in glide-controlled deformation of olivine, Katayama and Karato (2008) interpreted the weakening effect of water in their experiments as being due to a reduction in the Peierls stress by a factor of ∼3.They suggested this single mechanism could describe the effect of water on both low-and hightemperature rheological behavior due to the influence of the Peierls stress on the formation energy of both kinks and jogs (local displacements of the dislocation perpendicular to the glide plane).This type of weakening corresponds to model 4 (Figure 1).
Our experiments at low temperature demonstrate that the Peierls stress is not lowered by high water concentrations, ruling out model 4. M666-W and M666-D are extremely similar in hardness and yield stress despite the significant difference in water content (Table 1, Figure 3).Dry olivine samples in similar orientations (e.g., CT-SCO1) are also quite close to M666-W in their mechanical properties (Table 1, Table S1 in Supporting Information S1).The difference in yield stress of 0.1-0.2GPa between M666-W and M666-D is within the 95% confidence interval of ±0.6 GPa on the yield stresses and is an order of magnitude less than the effect of anisotropy due to crystal orientation observed in this study.The similarities in mechanical behavior between M666-D and M666-W suggest that any effect of water on dislocation glide is inconsequential at room temperature.By comparison, in the dislocation-creep regime at a temperature of 1,250°C and a constant strain rate of 10 5 s 1 , we would expect the strength of M666-W to be ∼30% of that of dry olivine (see supplemental material for specific flow-law parameters).
Other models presented for hydrolytic weakening in olivine (Figure 1) are still possible.For instance, the Peierls stress could still be reduced at elevated temperatures (model 3).H + may also lead to weakening at high temperatures and not at low temperatures by increasing the kink concentration (model 2) or increasing diffusivities and reducing the backstress (model 1).

10.1029/2023GL106325
Our results demonstrate that intracrystalline H + has little to no impact on olivine deformation at low temperatures.For instance, intracrystalline water likely does not affect the frictional strength of faults if frictional strength is controlled by dislocation motion near contacts between plastically deforming asperities (e.g., Aharonov & Scholz, 2019;Boettcher et al., 2007;Tabor, 1981;Thom et al., 2022).Intracrystalline water also likely does not influence the maximum strength of the lithosphere near the brittle-ductile transition, at which LTP acts in tandem with brittle deformation mechanisms (e.g., Warren & Hansen, 2023)

Figure 1 .
Figure 1.Stress as a function of temperature measured in experiments and predicted by models of hydrolytic weakening.(A) Models and data are shown in red for dry olivine(Evans & Goetze, 1979;Hansen et al., 2019;Keefner et al., 2011) and blue for wet olivine(Katayama & Karato, 2008;Tielke et al., 2017).Experimental data cover strain rates from 4.2 × 10 7 to 4.4 × 10 4 s 1 and are plotted without normalization.Flow laws and models of hydrolytic weakening are shown as solid lines for a strain rate of 10 5 s 1 with the minima and maxima of the shaded regions respectively indicating strain rates of 10 6 s 1 and 10 4 s 1 .Dashed lines are schematic transitions between LTP and dislocation creep.Flow laws for power-law creep of wet and dry olivine are fromHirth and Kohlstedt (2003).The LTP flow law for dry olivine is fromHansen et al. (2021).Models 1, 2, and 3 of hydrolytic weakening in the low-temperature regime are schematic and are described in the text.Model 4 is based on the flow law ofKatayama and Karato (2008).(B, C, D) Individual models of hydrolytic weakening are highlighted in blue, with dry LTP and dislocation creep in red.The axes of each panel are the same as in (A).See supplemental information for further details of plotted flow laws and models.

Figure 2 .
Figure 2. A secondary electron image of an array of 16 indents in sample MN1.

Figure 3 .
Figure 3. Results of 311 Berkovich nanoindentation experiments.(A) Load on the sample versus vertical displacement of the indenter tip into the sample surface.Experiments are shown as individual lines, with experiments on M666-W in blue, M666-D in red, and other dry San Carlos olivine in gray.For the tests on M666-W (blue lines), an artifact associated with how data were exported results in the truncation of the unloading curves but does not affect our results.(B) Average Young's modulus at 1,000 nm depth for all samples, plotted at the orientation of the surface normal.M666-D is plotted with a red dashed marker edge.M666-W, which sits at an identical position on the plot, has a slightly lower Young's modulus (Table1).The background is colored by the uniaxial Young's modulus for dry San Carlos olivine fromAbramson et al. (1997).(C) Hardness versus displacement.Results are plotted as envelopes enclosing results at depths greater than 200 nm.Each gray envelope encompasses 7-16 nanoindentation experiments on a single crystal orientation.The blue envelope contains 44 experiments performed on M666-W, and the yellow envelope contains 52 experiments performed on M666-D across 6 different orientations of the indenter tip relative to the sample surface.The red envelope contains a subset of 16 experiments performed on M666-D in the two orientations most similar to the experiments performed on M666-W.(D) Yield stress versus displacement.Envelopes are colored as in (C).

Table 1
Denis et al. (2018), andFerriss et al. (2018)ardness (H), and yield stress (σ y ) are averaged over a narrow depth range (arbitrarily chosen to be 995-1,005 nm) to remove any variation among different samples due to the indentation size effect.N is the number of indentation tests in each group.Data for the average mechanical behavior of San Carlos olivine are a compilation from this study (TableS1in Supporting Information S1) andKumamoto et al. (2017)and exclude experiments on M666.95% confidence intervals are reported for all measurements.aFromLi(2015).bThiswaterconcentration is for the outer 5 μm of M666-D based on diffusion modeling.The water concentration for the whole crystal measured by FTIR is 700 ppm H/Si.cAverage based on measurements of water concentration in San Carlos olivine (9 measurements with a range of 0-64 ppm H/Si) byMackwell et al. (1985),Denis et al. (2018), andFerriss et al. (2018).Values from . analyses, David Kohlstedt for analyzing the FTIR data, Kay Song for performing EBSD analyses, Christopher Thom for useful discussions regarding nanoindentation, and reviewer Jacob Tielke and editor Quentin Williams for their thoughtful comments.Funding for this project was provided by National Science Foundation grants EAR-1255620 and EAR-1625032 to JMW, EAR-1806791 to KMK, and EAR-2022433 to LNH, Natural Environment Research Council grant NE/M000966/1 to LNH, the Netherlands Organisation for Scientific Research, User Support Programme Space Research, grant ALWGO.2018.038 to DW and LNH and grant ENW.GO.001.005 to DW, TB and LNH, UKRI Future Leaders Fellowship grant MR/V021788/1 to DW, and a fellowship from the Royal Commission for the Exhibition of 1851 to TB.This work was partially performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.LLNL-JRNL-853683.