Dislocation theory of steady and transient creep of crystalline solids: Predictions for olivine.

In applications critical to the geological, materials, and engineering sciences, deformation occurs at strain rates too small to be accessible experimentally. Instead, extrapolations of empirical relationships are used, leading to epistemic uncertainties in predictions. To address these problems, we construct a theory of the fundamental processes affecting dislocations: storage and recovery. We then validate our theory for olivine deformation. This model explains the empirical relationships among strain rate, applied stress, and dislocation density in disparate laboratory regimes. It predicts the previously unexplained dependence of dislocation density on applied stress in olivine. The predictions of our model for Earth conditions differ from extrapolated empirical relationships. For example, it predicts rapid, transient deformation in the upper mantle, consistent with recent measurements of postseismic creep.

Strength of Dry and Wet Quartz in the Low-Temperature Plasticity Regime: Insights From Nanoindentation.

At low-temperature and high-stress conditions, quartz deformation is controlled by the kinetics of dislocation glide, that is, low-temperature plasticity (LTP). To investigate the relationship between intracrystalline H2O content and the yield strength of quartz LTP, we have integrated spherical and Berkovich nanoindentation tests at room temperature on natural quartz with electron backscatter diffraction and secondary-ion mass spectrometry measurements of intracrystalline H2O content. Dry (<20 wt ppm H2O) and wet (20-100 wt ppm H2O) crystals exhibit comparable indentation hardness. Quartz yield strength, which is proportional to indentation hardness, seems to be unaffected by the intracrystalline H2O content when deformed under room temperature, high-stress conditions. Pre-indentation intracrystalline microstructure may have provided a high density of dislocation sources, influencing the first increments of low-temperature plastic strains. Our results have implications for fault strength at the frictional-viscous transition and during transient deformation by LTP, such as seismogenic loading and post-seismic creep.

Insight into the microphysics of antigorite deformation from spherical nanoindentation.

The mechanical behaviour of antigorite strongly influences the strength and deformation of the subduction interface. Although there is microstructural evidence elucidating the nature of brittle deformation at low pressures, there is often conflicting evidence regarding the potential for plastic deformation in the ductile regime at higher pressures. Here, we present a series of spherical nanoindentation experiments on aggregates of natural antigorite. These experiments effectively investigate the single-crystal mechanical behaviour because the volume of deformed material is significantly smaller than the grain size. Individual indents reveal elastic loading followed by yield and strain hardening. The magnitude of the yield stress is a function of crystal orientation, with lower values associated with indents parallel to the basal plane. Unloading paths reveal more strain recovery than expected for purely elastic unloading. The magnitude of inelastic strain recovery is highest for indents parallel to the basal plane. We also imposed indents with cyclical loading paths, and observed strain energy dissipation during unloading-loading cycles conducted up to a fixed maximum indentation load and depth. The magnitude of this dissipated strain energy was highest for indents parallel to the basal plane. Subsequent scanning electron microscopy revealed surface impressions accommodated by shear cracks and a general lack of dislocation-induced lattice misorientation. Based on these observations, we suggest that antigorite deformation at high pressures is dominated by sliding on shear cracks. We develop a microphysical model that is able to quantitatively explain Young's modulus and dissipated strain energy data during cyclic loading experiments, based on either frictional or cohesive sliding of an array of cracks contained in the basal plane. This article is part of a discussion meeting issue 'Serpentinite in the earth system'.

Olivine anisotropy suggests Gutenberg discontinuity is not the base of the lithosphere.

Tectonic plates are a key feature of Earth's structure, and their behavior and dynamics are fundamental drivers in a wide range of large-scale processes. The operation of plate tectonics, in general, depends intimately on the manner in which lithospheric plates couple to the convecting interior. Current debate centers on whether the transition from rigid lithosphere to flowing asthenosphere relates to increases in temperature or to changes in composition such as the presence of a small amount of melt or an increase in water content below a specified depth. Thus, the manner in which the rigid lithosphere couples to the flowing asthenosphere is currently unclear. Here we present results from laboratory-based torsion experiments on olivine aggregates with and without melt, yielding an improved database describing the crystallographic alignment of olivine grains. We combine this database with a flow model for oceanic upper mantle to predict the structure of the seismic anisotropy beneath ocean basins. Agreement between our model and seismological observations supports the view that the base of the lithosphere is thermally controlled. This model additionally supports the idea that discontinuities in velocity and anisotropy, often assumed to be the base of the lithosphere, are, instead, intralithospheric features reflecting a compositional boundary established at midocean ridges, not a rheological boundary.

Weighted Burgers Vector analysis of orientation fields from high-angular resolution electron backscatter diffraction.

The Weighted Burgers Vector (WBV) method can extract information about dislocation types and densities present in distorted crystalline materials from electron backscatter diffraction (EBSD) maps, using no assumptions about which slip systems might be present. Furthermore, high-angular resolution EBSD (HR-EBSD) uses a cross-correlation procedure to increase the angular precision of EBSD measurements by an order of magnitude compared to conventional EBSD. However, the WBV technique has not previously been applied to HR-EBSD data and therefore it remains unclear as to which low-angle substructures can be reliably characterised by WBV analysis of conventional EBSD data and which require additional HR-EBSD processing. To establish some practical examples that can be used to guide future data-acquisition strategies, we compare the output of the WBV method when applied to conventional EBSD data and HR-EBSD data collected from the most common minerals in Earth's lower crust (plagioclase feldspar) and upper mantle (olivine). The results demonstrate that HR-EBSD and WBV processing are complementary techniques. The increase in angular precision achieved with HR-EBSD processing allows low-angle (on the order of 0.1°) structures, which are obscured by noise in conventional EBSD data, to be analyzed quantitatively using the WBV method. Combining the WBV and HR-EBSD methods increases the precision of calculated WBV directions, which is essential when using information about active slip systems to infer likely deformation mechanisms from naturally deformed microstructures. This increase in precision is particularly important for low-symmetry crystals, such as plagioclase, that have a wide range of available slip systems that vary in relative activity with changing pressure, temperature and differential stress. Because WBV directions are calculated using no assumptions about which slip systems may be present, combining this technique with HR-EBSD to refine the precision of lattice orientation gradients is ideal for investigating complex natural materials with unknown deformation histories.

An apparatus for measuring nonlinear viscoelasticity of minerals at high temperature.

We describe a high-temperature, uniaxial creep apparatus designed to investigate nonlinear attenuation of materials over a wide range of temperatures (25-1300 °C) using forced oscillations combined with a bias stress. This apparatus is primarily designed for investigation of minerals and rocks with high melting temperatures. An oscillatory compressional stress is used to determine attenuation and Young's modulus at frequencies of 10-1-102 Hz and high stress amplitudes (>0.1 MPa). Large bias stresses are applied in addition to the oscillatory stresses such that attenuation tests are conducted simultaneously with the ongoing creep. The complex compliance of the apparatus was characterized by conducting calibration tests on orientated crystals of sapphire. The real part of the apparatus compliance exhibits a dependence on sample length and frequency, whereas the imaginary part is only dependent on frequency. The complex compliance is not dependent on the oscillation amplitude or the bias stress. We assess the accuracy and precision of this calibration by comparing measurements of the attenuation and Young's modulus of aluminum and acrylic to previously published values. We outline a set of criteria defining the conditions over which this apparatus can precisely determine the attenuation and Young's modulus of a sample based on the sample length and expected values of attenuation and Young's modulus.

Dislocation interactions in olivine control postseismic creep of the upper mantle.

Changes in stress applied to mantle rocks, such as those imposed by earthquakes, commonly induce a period of transient creep, which is often modelled based on stress transfer among slip systems due to grain interactions. However, recent experiments have demonstrated that the accumulation of stresses among dislocations is the dominant cause of strain hardening in olivine at temperatures ≤600 °C, raising the question of whether the same process contributes to transient creep at higher temperatures. Here, we demonstrate that olivine samples deformed at 25 °C or 1150-1250 °C both preserve stress heterogeneities of ~1 GPa that are imparted by dislocations and have correlation lengths of ~1 µm. The similar stress distributions formed at these different temperatures indicate that accumulation of stresses among dislocations also provides a contribution to transient creep at high temperatures. The results motivate a new generation of models that capture these intragranular processes and may refine predictions of evolving mantle viscosity over the earthquake cycle.

Size effects resolve discrepancies in 40 years of work on low-temperature plasticity in olivine.

The strength of olivine at low temperatures and high stresses in Earth's lithospheric mantle exerts a critical control on many geodynamic processes, including lithospheric flexure and the formation of plate boundaries. Unfortunately, laboratory-derived values of the strength of olivine at lithospheric conditions are highly variable and significantly disagree with those inferred from geophysical observations. We demonstrate via nanoindentation that the strength of olivine depends on the length scale of deformation, with experiments on smaller volumes of material exhibiting larger yield stresses. This "size effect" resolves discrepancies among previous measurements of olivine strength using other techniques. It also corroborates the most recent flow law for olivine, which proposes a much weaker lithospheric mantle than previously estimated, thus bringing experimental measurements into closer alignment with geophysical constraints. Further implications include an increased difficulty of activating plasticity in cold, fine-grained shear zones and an impact on the evolution of fault surface roughness due to the size-dependent deformation of nanometer- to micrometer-sized asperities.

Geometrically necessary dislocation densities in olivine obtained using high-angular resolution electron backscatter diffraction.

Dislocations in geological minerals are fundamental to the creep processes that control large-scale geodynamic phenomena. However, techniques to quantify their densities, distributions, and types over critical subgrain to polycrystal length scales are limited. The recent advent of high-angular resolution electron backscatter diffraction (HR-EBSD), based on diffraction pattern cross-correlation, offers a powerful new approach that has been utilised to analyse dislocation densities in the materials sciences. In particular, HR-EBSD yields significantly better angular resolution (<0.01°) than conventional EBSD (~0.5°), allowing very low dislocation densities to be analysed. We develop the application of HR-EBSD to olivine, the dominant mineral in Earth's upper mantle by testing (1) different inversion methods for estimating geometrically necessary dislocation (GND) densities, (2) the sensitivity of the method under a range of data acquisition settings, and (3) the ability of the technique to resolve a variety of olivine dislocation structures. The relatively low crystal symmetry (orthorhombic) and few slip systems in olivine result in well constrained GND density estimates. The GND density noise floor is inversely proportional to map step size, such that datasets can be optimised for analysing either short wavelength, high density structures (e.g. subgrain boundaries) or long wavelength, low amplitude orientation gradients. Comparison to conventional images of decorated dislocations demonstrates that HR-EBSD can characterise the dislocation distribution and reveal additional structure not captured by the decoration technique. HR-EBSD therefore provides a highly effective method for analysing dislocations in olivine and determining their role in accommodating macroscopic deformation.