William B. Durham

Mantle phase changes and deep-earthquake faulting in subducting lithosphere

Inclined zones of earthquakes are the primary expression of lithosphere subduction. A distinct deep population of subduction-zone earthquakes occurs at depths of 350 to 690 kilometers. At those depths ordinary brittle fracture and frictional sliding, the faulting processes of shallow earthquakes, are not expected. A fresh understanding of these deep earthquakes comes from developments in several areas of experimental and theoretical geophysics, including the discovery and characterization of transformational faulting, a shear instability connected with localized phase transformations under nonhydrostatic stress. These developments support the hypothesis that deep earthquakes represent transformational faulting in a wedge of olivine-rich peridotite that is likely to persist metastably in coldest plate interiors to depths as great as 690 km. Predictions based on this deep structure of mantle phase changes are consistent with the global depth distribution of deep earthquakes, the maximum depths of earthquakes in individual subductions zones, and key source characteristics of deep events.

The deformation-DIA: A new apparatus for high temperature triaxial deformation to pressures up to 15 GPa

A new deformation apparatus has been developed, based on the widely used cubic-anvil apparatus known as the DIA. Two differential rams, introduced in the upper and lower guide blocks, allow independent control of the differential strain and stress field under high confining pressure. Testing experiments with synchrotron x rays have demonstrated that this deformation DIA (D-DIA) is capable of generating up to 30% axial strain on a 1–2 mm long sample under confining pressures up to 15 GPa at simultaneous high temperatures. Various compressional strain rates from 10−3 to about 5×10−6 s−1 have been achieved. Extensional experiments have also been carried out successfully. Strains are measured by x-ray imaging of the sample which has a length measurement precision of ∼0.1 μm; pressures are monitored using standard materials with well established equations of state. X-ray transparent anvils made of sintered polycrystalline cubic boron nitride have been successfully tested, with a two-dimensional x-ray charge co...

Peculiarities of Methane Clathrate Hydrate Formation and Solid-State Deformation, Including Possible Superheating of Water Ice

Slow, constant-volume heating of water ice plus methane gas mixtures forms methane clathrate hydrate by a progressive reaction that occurs at the nascent ice/liquid water interface. As this reaction proceeds, the rate of melting of metastable water ice may be suppressed to allow short-lived superheating of ice to at least 276 kelvin. Plastic flow properties measured on clathrate test specimens are significantly different from those of water ice; under nonhydrostatic stress, methane clathrate undergoes extensive strain hardening and a process of solid-state disproportionation or exsolution at conditions well within its conventional hydrostatic stability field.

New technique for decorating dislocations in olivine.

Oxidation of iron-rich olivine induced in the laboratory causes preferential precipitation on lattice dislocations. This simple dislocation decoration technique greatly reduces the cost and time involved in surveying the dislocation structures of deformed olivine crystals and opens the way to a more thorough understanding of the deformation of this important geologic material.

Effects of dispersed particulates on the rheology of water ice at planetary conditions

We have investigated the effects of initial grain size and hard particulate impurities on the transient and steady state flow of water ice I at laboratory conditions selected to provide more quantitative constraints on the thermomechanical evolution of the giant icy moons of the outer solar system. Our samples were molded with particulate volume fractions, ϕ, of 0.001 to 0.56 and particle sizes of 1 to 150 μm. Deformation experiments were conducted at constant shortening rates of 4.4 × 10−7 to 4.9 × 10−4 s−1 at pressures of 50 and 100 MPa and temperatures 77 to 223 K. For the pure ice samples, initial grain sizes were 0.2–0.6 mm, 0.75–1.75 mm, and 1.25–2.5 mm. Stress-strain curves of pure ice I under these conditions display a strength maximum σu at plastic strains e ≤ 0.01 after initial yield, followed by strain softening and achievement of steady state levels of stress, σss, at e = 0.1 to 0.2. Finer starting grain size in pure ice generally raises the level of σu. Petrography indicates that the initial transient flow behavior is associated with the nucleation and growth of recrystallized ice grains and the approach to σss evidently corresponds to the development of a steady state grain texture. Effects of particulate concentrations ϕ < 0.1 are slight. At these concentrations, a small but significant reduction in σu with respect to that for pure water ice occurs. Mixed-phase ice with ϕ ≥ 0.1 is significantly stronger than pure ice; the strength of samples with ϕ = 0.56 approaches that of dry confined sand. The magnitude of the strengthening effect is far greater than expected from homogeneous strain-rate enhancement in the ice fraction or from pinning of dislocations (Orowan hardening). This result suggests viscous drag occurs in the ice as it flows around the hard particulates. Mixed-phase ice is also tougher than pure ice, extending the range of bulk plastic deformation versus faulting to lower temperatures and higher strain rates. The high-pressure phase ice II formed in ϕ = 0.56 mixed-phase ice during deformation at high stresses. Bulk planetary compositions of ice + rock (ϕ = 0.4–0.5) are roughly 2 orders of magnitude more viscous than pure ice, promoting the likelihood of thermal instability inside giant icy moons and possibly explaining the retention of crater topography on icy planetary surfaces.

Creep of water ices at planetary conditions: A compilation

Many constitutive laws for the flow of ice have been published since the advent of the Voyager explorations of the outer solar system. Conflicting data have occasionally come from different laboratories, and refinement of experimental techniques has led to the publication of laws that supersede earlier ones. In addition, there are unpublished data from ongoing research that also amend the constitutive laws. Here we compile the most current laboratory-derived flow laws for water ice phases I, II, III, V, and VI, and ice I mixtures with hard particulates. The rheology of interest is mainly that of steady state, and the conditions reviewed are the pressures and temperatures applicable to the surfaces and interiors of icy moons of the outer solar system. Advances in grain-size-dependent creep in ices I and II as well as in phase transformations and metastability under differential stress are also included in this compilation. At laboratory strain rates the several ice polymorphs are rheologically distinct in terms of their stress, temperature, and pressure dependencies but, with the exception of ice III, have fairly similar strengths. Hard particulates strengthen ice I significantly only at high particulate volume fractions. Ice III has the potential for significantly affecting mantle dynamics because it is much weaker than the other polymorphs and its region of stability, which may extend metastably well into what is nominally the ice II field, is located near likely geotherms of large icy moons.

Direct observation of reactive flow in a single fracture

We carried out a laboratory experiment to examine the relationship between local rate of dissolution and local aperture during flow of a slightly acidic aqueous solution through a rough fracture in Carrara marble under a confining pressure of 0.2 MPa. Fracture surfaces were digitized in three dimensions before the fluid flow tests and after the tests. Digital reconstruction of the aperture then allowed numerical simulation of flow patterns, and digital comparison of surfaces before and after dissolution allowed mapping of patterns of dissolution. We observed that both mean aperture and fracture permeability decreased as a result of dissolution. Despite the low confining pressure, the experiments thus simulate dissolution in deeply buried formations, in contrast to the gaping and karst formation that occur under vanishingly low confining pressure in the shallow crust. We observed that the growth of new pathways for flow changed from stable to unstable as length scale increased. At the millimeter scale the fracture aperture evolved in stable fashion from a strongly heterogeneous arrangement of tortuous flow channels to a smoother topography, while at the scale of the full rock (50 mm), the aperture developed a single, broad flow channel. The scale dependence of the dissolution pattern may be the result of changes with scale in extent of reaction (i.e., the Damkohler number) and in the relative importance of diffusion (the Peclet number). Finally, we also see evidence of a negative relationship between local fluid flux and local rate of dissolution in some locations in the fracture.

Polymorphic transformations between olivine, wadsleyite and ringwoodite; mechanisms of intracrystalline nucleation and the role of elastic strain

Abstract Kinetic models and rate equations for polymorphic reconstructive phase transformations in polycrystalline aggregates are usually based on the assumptions that (a) the product phase nucleates on grain boundaries in the reactant phase and (b) growth rates of the product phase remain constant with time at fixed P-T. Recent observations of experimentally-induced transformations between (Mg,Fe)2SiO4 olivine (α) and its high pressure polymorphs, wadsleyite (β) and ringwoodite (γ), demonstrate that both these assumptions can be invalid, thus complicating the extrapolation of experimental kinetic data. Incoherent grain boundary nucleation appears to have dominated in most previous experimental studies of the α-β-γ transformations because of the use of starting materials with small (<10-20 µm) grain sizes. In contrast, when large (0.6 mm) olivine single crystals are reacted, intracrystalline nucleation of both β and γ becomes the dominant mechanism, particularly when the P-T conditions significantly overstep the equilibrium boundary. At pressures of 18-20 GPa intracrystalline nucleation involves (i) the formation of stacking faults in the olivine, (ii) coherent nucleation of γ-lamellae on these faults and (iii) nucleation of β on γ. In other experiments, intracrystalline nucleation is also observed during the β-γ transformation. In this case coherent nucleation of γ appears to occur at the intersections of dislocations with (010) stacking faults in β, which suggests that the nucleation rate is stress dependent. Reaction rims of β/γ form at the margins of the olivine single crystals by grain boundary nucleation. Measurements of growth distance as a function of time indicate that the growth rate of these rims decreases towards zero as transformation progresses. The growth rate slows because of the decrease in the magnitude of the Gibbs free energy (stored elastic strain energy) that develops as a consequence of the large volume change of transformation. On a longer time scale, growth kinetics may be controlled by viscoelastic relaxation.

Topography of natural and artificial fractures in granitic rocks: Implications for studies of rock friction and fluid migration

Abstract The topography of fractures and joints has a strong influence on their frictional strength and fracture permeability. Important aspects of the surfaces are the size, distribution and density of contact spots between the surfaces, which can be calculated using topographic data. For a variety of tensile fracture surfaces in granite, including both natural joints and man-made fractures, spectral and statistical properties are similar, suggesting that man-made fractures in granites can be acceptable substitutes for natural fractures in some experimental situations. The topographic data indicate that fracture surfaces at scales from 0.1 to 200 mm are approximately fractal and statistically self-affine. A log-log plot of power spectral density vs spatial frequency, calculated from the fracture surfaces indicates a spectral slope of −2.3 ± 0.2, yielding a fractal dimension D between 2.25 and 2.45. Shear fracture surfaces are also fractal, but have anisotropic roughness, which develops during the fracture initiation process. The amount of anisotropy that develops on the shear fracture surfaces is small in comparison to that exhibited by natural fault surfaces, which include anisotropy that results from post failure wear and from surface evolution. For fractures like those measured in this study, simple simulations indicate that the aperture, size and number density of wall-to-wall contacts between the surfaces change non-linearly with relative shear displacement of the surfaces. It is possible to make preliminary estimates of how the permeability and frictional properties of fractures and joints depend on the size, distribution and character of the contact spots. Furthermore, given that artificial fractures can be generated numerically with statistical properties similar to those of natural or man-made fractures, it is reasonable for systematic studies of the effects of roughness on friction and fluid flow to use computer designed surfaces to provide a range of variability that is not easily accessible in the laboratory.

X-ray strain analysis at high pressure: Effect of plastic deformation in MgO

3^011& at different critical resolved shear stress ratios for the different slip systems. The prediction of the models is correlated with the results of x-ray diffraction measurements. Uniaxial deformation experiments on polycrystalline and single-crystal MgO samples were conducted in situ using white x-ray diffraction with a multielement detector and multianvil high-pressure apparatus at a pressure up to 6 GPa and a temperature of 500 °C. A deformation DIA was used to generate pressure and control at a constant deformation rate. Elastic strains and plastic strains were monitored using x-ray diffraction spectra and x-ray imaging techniques, respectively. The correlation of the data and models suggests that the plastic models need to be used to describe the stress‐strain observations with the presence of plasticity, while the Reuss and Voigt models are appropriate for the elastic region of deformation, before the onset of plastic deformation. The similarity of elastic strains among different lattice planes suggests that the