Creep Of Olivine Research Articles

Dynamic recrystallization by subgrain rotation in olivine revealed by electron backscatter diffraction

We document how dynamic recrystallization by subgrain rotation (SGR) develops in natural olivine-rich rocks deformed in extension to up to 50% bulk finite strain (1473 K, confining pressure of 300 MPa, and stresses between 115 and 180 MPa) using electron backscatter diffraction (EBSD) mapping. SGR occurs preferentially in highly deformed grains (well-oriented to deform by dislocation glide) subjected to local stress concentrations due to interactions with hard neighboring grains (poorly-oriented olivine crystals or pyroxenes). Subgrains (misorientation <15°) are mainly delimited by tilt walls composed of combinations of dislocations of the [100](001), [001](100), [100](010) and [001](010) systems, in order of decreasing frequency. The activation and prevalence of these systems agree with a Schmid factor analysis using data for high-T dislocation creep in olivine. The development of closed 3D subgrain cells by SGR recrystallization requires the contribution of at least three different slip systems, implying the activation of hard slip systems and high (local) stresses. The transition from subgrain to grain boundaries (misorientation ≥15°) is characterized by a sharp change in the misorientation axes that accommodate the difference in orientation between the two subgrains or grains. We propose that this change marks the creation and incorporation of new defects (grain boundary dislocations with different Burger vectors and, likely, disclinations or disconnections) at the newly-formed grain boundaries and that this might be favoured by stress concentrations due to increasing misalignment between slip systems across the boundary. Finally, we document the development of strong misorientations within the parent grains, due to the accumulation of low angle grain boundaries, and between them and the recrystallized grains. SGR recrystallization may thus produce strong dispersion of the crystal preferred orientation without the need for grain boundary sliding.

Anisotropic high-temperature creep in hydrous olivine single crystals and its geodynamic implications

We compile the experimental data on deformation of hydrated olivine single crystal to determine the influence of water and pressure. We analyse the data from low pressure (P = 0.1 MPa and 0.1–0.3 GPa) high-resolution experiments as well as the results from higher pressures (2 to 6 GPa) containing larger uncertainties, using a flow law of the form ε̇i=ε̇idry+ε̇iwet with (i:slip system). The data are normalized to a common stress (150 MPa) and temperature (1573 K) and we determine the parameters water content exponent (r) and activation volume (V∗). We found largely different values of r and V∗ for different orientations (slip systems) implying that the influence of water and pressure is highly anisotropic providing largely different values of r and V∗. For the [110]c orientation where the [100](010) slip system is activated, we obtain r[100] = 0.35 ±0.08, and V∗[100] = 11.0 ± 3.0 cm3/mol, while for the [011]c orientation where the [001](010) slip system is activated, r[001] = 1.3 ± 0.30, and V∗[001] = 5.6 ± 3.6 cm3/mol (for a fixed water content). The highly anisotropic effects of water and pressure suggest that creep in olivine is not controlled solely by diffusion but also controlled by the density of jogs (or kinks) on dislocations that is controlled by water and pressure. We find that the easier slip system changes from the a-slip (slip along the [100] direction) at low water content and low pressure to the c-slip (slip along the [001] direction) at high water content and high pressure, suggesting that the c-slip is softer than the a-slip in most of the asthenosphere, whereas the opposite is true in most of the lithosphere. Implications of these results are discussed using a model of deformation of a polycrystalline aggregate made of anisotropic crystals. It is suggested that in the asthenosphere where most of plastic deformation occurs, short-term time-dependent small strain deformation associated with post-seismic and post-glacial deformation is dominated by the c-slip and strongly dependent on the water content, whereas the long-term large strain deformation associated with mantle convection is dominated by the a-slip that is only weakly dependent on water content.

Evidence of phase nucleation during olivine diffusion creep: A new perspective for mantle strain localisation

For the past decades, grain size reduction leading to diffusion creep in olivine is believed to be a very important process for strain localisation in the lithospheric mantle. However, the mechanisms of grain size reduction in this regime are still poorly understood (e.g., Platt, 2015). Here we show new experimental results that document grain size reduction and material weakening during wet olivine diffusion creep. While occurring for both, mono-phase and two-phase aggregates, grain size reduction is coeval with strain localisation and local phase mixing in olivine–pyroxene aggregates. Based on evidence of fluid inclusions and cracks filled with a fine-grained phase mixture, we conclude that grain size reduces as a result of fluid-assisted nucleation that takes place in the presence of an aqueous fluid during diffusion creep. Cavitation induced by grain boundary sliding (creep cavitation) can be inferred, and may play a critical role for olivine grain size reduction. Amongst their implications for rock rheology in general, our findings highlight a key process for strain localisation in the ductile uppermost mantle.

Deformation in the mantle wedge associated with Laramide flat‐slab subduction

AbstractLaramide crustal deformation in the Rocky Mountains of the west‐central United States is often considered to relate to a narrow segment of shallow subduction of the Farallon slab, but there is no consensus as to how deformation along the slab‐mantle lithosphere interface was accommodated. Here we investigate deformation in mantle rocks associated with hydration and shear above the flat‐slab at its contact with the base of the North American plate. The rocks we focus on are deformed, hydrated, ultramafic inclusions hosted within diatremes of the Navajo Volcanic Field in the central Colorado Plateau that erupted during the waning stages of the Laramide orogeny. We document a range of deformation textures, including granular peridotites, porphyroclastic peridotites, mylonites, and cataclasites, which we interpret to reflect different proximities to a slab‐mantle‐interface shear zone. Mineral assemblages and chemistries constrain deformation to hydrous conditions in the temperature range ∼550–750°C. Despite the presence of hydrous phyllosilicates in modal percentages of up to 30%, deformation was dominated by dislocation creep in olivine. The mylonites exhibit an uncommon lattice preferred orientation (LPO) in olivine, known as B‐type LPO in which the a‐axes are aligned perpendicular to the flow direction. The low temperature, hydrated setting in which these fabrics formed is consistent with laboratory experiments that indicate B‐type LPOs form under conditions of high stress and high water contents; furthermore, the mantle wedge context of these LPOs is consistent with observations of trench‐parallel anisotropy in the mantle wedge above many modern subduction zones. Differential stress magnitudes in the mylonitic rocks estimated using paleopiezometry range from 290 to 444 MPa, and calculated effective viscosities using a wet olivine flow law are on the order of 1019−1023 Pa s. The high stress magnitudes, high effective viscosities, and high strains recorded in these rocks are consistent with models that invoke significant basal shear tractions as contributing to Laramide uplift and contraction in the continental interior.

New constraints on upper mantle creep mechanism inferred from silicon grain-boundary diffusion rates

The creep in the Earth's interior is dominated either by diffusion creep which causes Newtonian mantle flow, or by dislocation creep which results in non-Newtonian mantle flow. Although previous deformation studies on olivine claimed a transition from dislocation creep to diffusion creep with depth in the upper mantle, they might misunderstand the creep rates due to experimental difficulties. Since creep in olivine is controlled by silicon diffusion, we measured the silicon grain-boundary diffusion coefficient in well-sintered iron-free olivine aggregates as a function of temperature, pressure, and water content, showing activation energy, activation volume, and water content exponent of 220±30 kJ/mol, 4.0±0.7 cm3/mol, and 0.26±0.07, respectively. Our results based on Si diffusion in forsterite predict that diffusion creep dominates at low pressures and low temperatures, whereas dislocation creep dominates under high pressure and high temperature conditions. Water has negligible effects on both diffusion and dislocation creep. There is a transition from diffusion creep in the shallow upper mantle to dislocation creep in deeper regions. This explains the seismic anisotropy increases at the Gutenberg discontinuity beneath oceans and at the mid-lithosphere discontinuity beneath continents.

Low steady-state stresses in the cold lithospheric mantle inferred from dislocation dynamics models of dislocation creep in olivine

Transmission electron microscopy observations on olivine crystals deformed at moderate (≤1273 K) temperature evidenced dislocations interactions explaining the hardening observed in the experiments, but also recovery mechanisms by the absorption or emission of point defects. Thus we investigate the possibility that, at geological strain-rates, these recovery processes allow steady-state deformation by dislocation creep at low to moderate temperatures in the lithospheric mantle. We test this hypothesis using a 2.5-D dislocation dynamics (DD) model, which combines dislocation glide and recovery by climb. This model shows that diffusion-controlled recovery processes allow for steady-state deformation by dislocation creep in the lithospheric mantle at stresses <500 MPa. For stresses of 50–200 MPa, steady-state strain-rates of 10−15 s−1 may be attained at temperatures as low as 900 K. Fitting of the DD model produces a flow law, which represents a lower bound for the lithospheric mantle strength, since the models describe the deformation of an olivine single crystal in an easy slip orientation. Comparison of strain-rates and Moho temperatures inferred for different geodynamic environments and the predictions of this model-based flow law implies, nevertheless, that, except in incipient rifts, most of the observed deformation may be produced by stress levels ≤200 MPa, consistent with those inferred to be produced by convection. This convergence suggests that the present models, which explicitly calculate the time-dependent dislocation dynamics, may provide a correct first order estimate of the mechanical behaviour of the lithospheric mantle, which cannot be derived directly from any existing data.

Experimental constraints on the strength of the lithospheric mantle

To provide a better understanding of rheological properties of mantle rocks under lithospheric conditions, we carried out a series of experiments on the creep behavior of polycrystalline olivine at high pressures (∼4–9 GPa), relatively low temperatures (673 ≤ T ≤ 1273 K), and anhydrous conditions, using a deformation‐DIA. Differential stress and sample displacement were monitored in situ using synchrotron X‐ray diffraction and radiography, respectively. Experimental results were fit to the low‐temperature plasticity flow law, . On the basis of this analysis, the low‐temperature plasticity of olivine deformed under anhydrous conditions is well constrained by our data with a Peierls stress of σP = 5.9 ± 0.2 GPa, a zero‐stress activation energy of Ek(0) = 320 ± 50 kJ mol−1, and AP = 1.4 × 10−7 s−1 MPa−2. Compared with published results for high‐temperature creep of olivine, a transition from low‐temperature plasticity to high‐temperature creep occurs at ∼1300 K for a strain rate of ∼10−5 s−1. For a geological strain rate of 10−14 s−1, extrapolation of our low‐temperature flow law to 873 K, the cutoff temperature for earthquakes in the mantle, yields a strength of ∼600 MPa. The low‐temperature, high‐stress flow law for olivine in this study provides a solid basis for modeling tectonic processes occurring within Earth's lithosphere.

Numerical modelling of spontaneous slab breakoff and subsequent topographic response

We conducted a set of numerical experiments to study the evolution of a subduction–collision system subject to spontaneous slab breakoff. The study takes into account complex rheological behaviour including plasticity, viscous creep and Peierls creep. By varying the oceanic slab age and initial plate convergence rate, four different end-members were observed. In this parameter space, breakoff depth can range from 40 to 400 km. Each of those breakoff modes displays complex rheological behaviour during breakoff. Peierls creep in olivine turns out to be a key mechanism for slab breakoff, generally causing slabs to break earlier and at shallower depths. Models involving different depths of breakoff are subject to different topographic evolution, but always display a sharp breakoff signal. Post breakoff uplift rates in foreland and hinterland basins range between 0.1 km/My for deep detachment and 0.8 km/My for shallow detachment. Our systematic study indicates an approximately linear relationship between the depth of breakoff and the rate of uplift. Continental crust subduction was observed in breakoff experiments involving oceanic lithosphere older than 30 My. Different exhumation processes such as slab retreat and eduction occur according to the depth of breakoff. These models are likely to undergo large rebound following breakoff and plate decoupling if the subducted oceanic slab is old enough.

Shear wave anisotropy beneath Nicaragua and Costa Rica: Implications for flow in the mantle wedge

We present new shear wave splitting data from local events in Costa Rica and Nicaragua recorded by the temporary (July 2004 to March 2006) 48‐station TUCAN broadband seismic array. Observed fast polarization directions in the fore arc, arc, and back arc range from arc‐parallel to arc‐normal over very short distances (&lt;5 km when plotted at raypath midpoints) making the direct interpretation of individual splitting measurements in terms of flow tenuous, even when considering variations in the relationship between lattice‐preferred orientation and deformation (e.g., B‐type dislocation creep in olivine). Therefore, we tomographically invert the splitting measurements to find a three‐dimensional model of crystallographic orientation in the wedge. We assume the elastic constants of olivine and orthopyroxene with hexagonal symmetry and use a damped, iterative least squares approach to account for the nonlinear behavior of splitting when considering three‐dimensional ray propagation and distributions of anisotropy. The best fitting model contains roughly horizontal, arc‐parallel olivine [100] axes in the mantle wedge down to at least 125 km beneath the back arc and arc, which we interpret to indicate along‐arc flow in the mantle wedge. Pb and Nd isotopic ratios in arc lavas provide additional evidence for arc‐parallel flow and also constrain the direction (northwest, from Costa Rica to Nicaragua) and minimum flow rate (63–190 mm/a). With only slightly oblique subduction at 85 mm/a of the relatively planar Cocos Plate, the most likely mechanism for driving along‐arc transport is toroidal flow around the edge of the slab in southern Costa Rica, generated by greater slab rollback in Nicaragua. Two important implications of this arc‐parallel flow are the progressive depletion of the mantle source for arc lavas from Costa Rica to Nicaragua and the possible need for significant decoupling between the wedge and downgoing plate.

Rheology of the deep upper mantle and its implications for the preservation of the continental roots: A review

The longevity of deep continental roots depends critically on the rheological properties of upper mantle minerals under deep upper mantle conditions. Geodynamic studies suggest that the rheological contrast between the deep continental and oceanic upper mantle is a key factor that controls the longevity of the continental roots. Current understanding of rheological properties of deep upper mantle is reviewed to examine how a large enough rheological contrast between the continental and oceanic upper mantle develops that leads to the longevity of the deep continental roots. Based on the microstructures of naturally deformed deep continental rocks as well as on the observations of seismic anisotropy, it is concluded that power-law dislocation creep dominates in most of the deep upper mantle. Deformation by power-law creep is sensitive to water content and therefore the removal of water by partial melting to form depleted continental roots is a likely mechanism to establish a large rheological contrast. The results of experimental studies on the influence of temperature, pressure and water content on plastic flow by power-law dislocation creep are reviewed. The degree of rheological contrast depends critically on the dependence of effective viscosity on water content under “wet” (water-rich) conditions but it is also sensitive to the effective viscosity under “dry” (water-free) conditions that depends critically on the influence of pressure on deformation. Based on the analysis of thermodynamics of defects and high-temperature creep, it is shown that a robust estimate of the influence of water and pressure can be made only by the combination of low-pressure (< 0.5 GPa) and high-pressure (> 5 GPa) studies. A wide range of flow laws has been reported, leading to nearly 10 orders of magnitude differences in estimated viscosities under the deep upper mantle conditions. However, based on the examination of several criteria, it is concluded that relatively robust experimental data are now available for power-law dislocation creep in olivine both under “dry” (water-free) and “wet” (water-saturated) conditions. These data show that the influence of water is large (a change in viscosity up to ∼ 4 orders of magnitude for a constant stress) at the depth of ∼ 200–400 km. I conclude that the conditions for survival of a deep root for a few billions of years can be satisfied when “dry” olivine rheology with a relatively large activation volume (> (10–15) × 10 − 6 m 3/mol)) is used and the substantial water removal occurs to these depths. High degree of water removal requires a large degree of melting in the deep upper mantle that could have occurred in the Archean where geotherm was likely hotter than the current one by ∼ 200 K presumably with the help of water.

The effect of water on Si and O diffusion rates in olivine and implications for transport properties and processes in the upper mantle

We performed piston cylinder experiments (1200–1350 °C, 2 GPa) to determine the diffusion rates of Si and O in mantle olivine under water undersaturated (brucite absent, 45 ppm H 2O in olivine) as well as close to water-saturated (brucite present, ∼370 ppm H 2O in olivine) conditions. Diffusion couples consisted of oriented and polished San Carlos olivine cylinders coated with thin (∼few 100 nm) films of the same composition enriched in 29Si and 18O, with a protective coating of ZrO 2 on top. Relationships between water solubility in olivine and water fugacity, combined with thermodynamic equilibrium calculations, indicate fH 2O ∼1 GPa, fO 2 ∼IW buffer for brucite absent and fH 2O ∼9 GPa, fO 2 ∼QFM buffer for brucite present experiments. We find that under hydrous conditions D Si ≈ D O and diffusion anisotropy is weak to non-existent. Fitting the raw data at 2 GPa and fH 2O ∼0.93 GPa yields Arrhenius parameters [ D o and E p in D = D o exp(− E p/ RT)] of: 1.68 (±3.52) × 10 −7 m 2 s −1 and 358 ± 28 kJ mol −1 for Si, and 1.43 (±1.80) × 10 −4 m 2 s −1 and 437 ± 17 kJ mol −1 for O, respectively (1 sigma errors). D (2 GPa, fH 2O = 0.97 GPa, 1200 °C): D (1 atm., dry, 1200 °C) is 1000 for Si and 10 for O, respectively. Equations incorporating explicitly the effect of water are discussed in the text. Analysis of our data suggests that O diffuses by an interstitial mechanism whereas Si diffuses via vacancy complexes. The relation between the water fugacity and the Si diffusion rates seems to obey a power law with a water fugacity exponent of 0.2–1. The amount of H incorporated into olivine at the experimental conditions is orders of magnitude higher than the likely concentration of Si vacancies. Therefore, a small fraction (∼0.01%) of the total incorporated H in olivine suffices to considerably enhance the concentration of Si vacancies, and hence diffusion rates. Activation energies for O diffusion under dry and wet conditions are similar, indicating that the mechanism of this diffusion does not change in the presence of water. This inference is consistent with results of computer simulations. Dislocation creep in olivine under wet conditions appears to be controlled by both, Si as well as O diffusion. Absolute creep rates can be calculated from the diffusion data if it is assumed that climb and glide of dislocations contribute equally to creep. Finally, analysis of the various transport properties indicate that <10 ppm of water in olivine is sufficient to cause a transition from “dry” to “wet” laws for most processes. As these water contents are even lower than the observed water contents in most mantle olivines (i.e. minimum values measured at the surface), we conclude that results of water present but undersaturated kinetic experiments are directly applicable to the mantle. Indeed, “wet” kinetic laws should be used for modeling geodynamic processes in the upper mantle, even if the mantle is thought to be undersaturated with respect to water.

Effects of pressure on high-temperature dislocation creep in olivine

Effects of pressure on high-temperature, dislocation creep in olivine ((Mg, Fe) 2 SiO 4 ) aggregates have been determined under both water-poor ('dry') and water-saturated ('wet') conditions. New experimental data were obtained at pressures of 1-2 GPa under 'dry' and 'wet' conditions using a newly developed high-resolution dislocation density measurement technique to estimate the creep strength. These data are compared with previous data at lower and higher pressures to determine the pressure dependence of high-temperature dislocation creep in olivine aggregates. We find that the creep strength under 'dry' conditions increases monotonically with increasing pressure, whereas the creep strength under 'wet' conditions changes with pressure in a non-monotonic fashion: it first decreases rapidly with increasing pressure and then becomes less sensitive to pressure at above 1 GPa. Such behaviour can be described by the following formula: where the subscripts d and w refer to parameters for 'dry' and 'wet' conditions respectively. The present study gives A d = 10 6.1 -0.2 s m1 (MPa) mn , , and r = 0 for 'dry' conditions, and A w m10 2.9 -0.1 s m1 (MPa) mn mr , , and r = 1.20 -0.05 for 'wet' conditions ( n = 3.0 -0.1 for both 'dry' and 'wet' conditions). The large activation volume for 'wet' conditions can be interpreted as due to the additional contribution from the activation volume for dissolution of OH in the olivine structure ( ). The value of r ( ,1.2) is consistent with a model in which creep in olivine is rate controlled by the motion of positively charged jogs through the diffusion of silicon via an interstitial mechanism.

A test of the validity of yield strength envelopes with an elastoviscoplastic finite element model

We have generated an elastoviscoplastic (EVP) rheological model of the lithosphere with an extended Maxwell model containing (in series) a linear elastic component, a creep component based on a flow law for dislocation creep in olivine, and a frictional component simulating Drucker–Prager plasticity based on Byerlee’s rule. Finite element analyses for topographic loading of this oceanic lithosphere were carried out with two separate final loads (100 and 150 MPa) that were reached by four different load growth times (0, 0.1, 1, 10 Myr). Our results for the stress state and deformation of loaded lithosphere at 41.7 Myr into the model run are compared to results generated by the mechanical response of a time-independent elastic–perfectly plastic (EP) lithosphere, using a moment–curvature relationship based on the constant strain-rate yield strength envelope (YSE) and adopting a strain-rate representative of the EVP solution at 41.7 Myr. With identical flexural loading and material parameters, the deflection profiles of the EVP and EP solutions are quite similar, but it is unclear how the EP strain rate could be selected a priori without guidance from the EVP solution. For example, this uncertainty translates to about a 5 per cent error per decade of strain rate in the temperature gradient obtained by matching maximum moment and curvature in our EP models. The stress distributions of the time-dependent EVP model show deviations from the EP model (as defined by the YSE and an elastic core) in crystal plastic (macroscopically continuous dislocation creep) regions, where we observe vertical, lateral and temporal variations in the strain rate. At times much greater than the load growth time, the stress distribution in the lithosphere is independent of the loading rate and depends on the load magnitude only in that portion of the lithosphere that yields to frictional slip. After loading ceases, residual creep zones develop (in the vicinity of the brittle–plastic transition and the elastic–creep transition), driven by high stress in these regions.

Continental growth and volatile exchange during Earth's evolution

We investigate the thermal and degassing history of the Earth with the help of a parameterized mantle convection model including the volatile exchange between mantle and surface reservoirs. The weakening of mantle silicates by dissolved volatiles is described by a functional relationship between creep rate and water fugacity. We use flow law parameters of diffusion creep in olivine under dry and wet conditions. The mantle degassing rate is considered as directly proportional to the seafloor spreading rate, which is also dependent on the mantle heat flow and the continental area. To calculate the spreading rate, we assume three different continental growth models: constant growth, delayed growth, and the one proposed by Reymer and Schubert (1984, Tectonics, 3: 63–77). The rate of regassing also depends on the seafloor spreading rate, as well as on other factors. Both mechanisms (degassing and regassing) are coupled self-consistently with the help of a parameterized convection model under implementation of a temperature and volatile-content dependent mantle viscosity. We calculate time series for the Earth's evolution over 4.6 Gyr for the average mantle temperature, the mantle heat flow, the mantle viscosity, the Rayleigh number, the Urey ratio, the volatile loss, and the seafloor spreading rate. In those numerical simulations with continental growth from the beginning and a high initial average mantle temperature water is outgassed rapidly. In the delayed continental growth model there is a very early outgassing event and the delayed continental growth has no remarkable influence on the thermal and outgassing history. A similar situation is found for the linear continental growth model but not for the Reymer and Schubert (1984) model.

Effects of water-dependent creep rate on the volatile exchange between mantle and surface reservoirs

A parameterized model of mantle convection, including the volatile exchange between mantle and surface reservoirs, is used to study the thermal history of the Earth. The influence of dissolved volatiles on mantle rheology is reformulated. The weakening of mantle materials is described by a functional relationship between creep rate and water fugacity. We use flow law parameters of diffusion creep in olivine under dry and wet conditions. The mantle degassing rate is considered as directly proportional to the seafloor spreading rate, which, in turn, is dependent on the mantle heat flow. To calculate the spreading rate, we assume that the heat flow under the mid-ocean ridges is double the average mantle heat flow. The rate of regassing also depends on the seafloor spreading rate, as well as on other factors such as the efficiency of volatile recycling through island arc volcanism. Both mechanisms (degassing and regassing) are coupled self-consistently with the help of a parameterized convection model under implementation of a different formulation of mantle viscosity. The model is run for 4.6 Gyr. Time series of average mantle temperature, volatile loss, mantle viscosity, mantle heat flow, Rayleigh number and Urey ratio are calculated. The effects of changing initial parameters have been tested and found negligible for the final results. Mantle water is outgassed rapidly within a time scale of less than 200 Myr for all numerical simulations. The present-day values of calculated parameters are in the generally accepted range.

Rheology and volatile exchange in the framework of planetary evolution

The thermal history of an Earth-like planet is studied with the help of a parameterized mantle convection model including the volatile exchange between mantle and surface reservoirs. The weakening of mantle silicates by dissolved volatiles is described by a functional relationship between creep rate and water fugacity. We use flow law parameters of diffusion creep in olivine under dry and wet conditions to investigate the negative feedback between dissolved volatiles and outgassing by vigorous mantle convection. The mantle degassing rate is considered as directly proportional to the seafloor spreading rate which in turn is dependent on the mantle heat flow. The rate of regassing also depends on the seafloor spreading rate as well as on other factors like the efficiency of volatile recycling through island arc volcanism. We calculate time series over 4.6 Gyr for the average mantle temperature, the mantle viscosity, the mantle heat flow, the volatile loss, the Rayleigh number, and the Urey ratio. Mantle water is outgassed rapidly within a time scale of less than 200 Myr for all numerical simulations. The present values of the calculated parameters for the Earth are in the generally accepted range. In the case of Venus we find a less efficient outgassing in accordance with data about occurrence of the radiogenic noble gasses.

A numerical assessment of slab strength during high‐ and low‐angle subduction and implications for Laramide orogenesis

A finite element computer program for one‐dimensional heat flow was modified to apply to two‐dimensional subduction where conductive heat transport parallel to the upper and lower plates was neglected. One‐dimensional finite element columns were cut, displaced, and reassembled to model heat advection. Calculated temperature, depth‐dependent pressure, stress levels associated with dislocation creep in olivine at constant strain rate, and a 1‐GPa deviatoric stress maximum were used to calculate the form of the brittle‐plastic failure envelope for profiles across subducted slabs. The failure envelopes were then used to calculate maximum sustainable compression parallel to the slab. Model results suggest the following: (1) In high‐angle subduction without frictional heating and horizontal heat flow, temperatures along the interplate contact zone remain below about 120°C, which is far below temperatures necessary for olivine plasticity. Without substantial frictional heating or lateral heat flow from the adjacent magmatic arc, the subducted slab will gain rather than lose strength before its upper surface contacts asthenosphere. In addition, viscous coupling due to olivine plasticity and associated ablation of the upper plate will be unimportant. Slab strength reduction due to heating occurs rapidly after the top of the slab comes into contact with asthenosphere. (2) In low‐angle subduction the top of the slab remains in contact with overlying lithosphere and does not contact asthenosphere. Slab strength reduction due to conductive heating from above occurs slowly because the upper plate is cooled by the lower plate and is the source of progressively less heat. Temperatures along the interplate contact zone may be sufficient for olivine plasticity at large distances from the trench, and viscous coupling between plates and associated ablation of the upper plate may be important in this tectonic setting. (3) Low‐angle subduction for distances of over 1500 km during the Laramide orogeny in southwestern North America appears viable. At 50 Ma, slab strength beneath the Black Hills of South Dakota is predicted to have been comparable to, or greater than, strength at the trench.

Oxygen self-diffusion along high diffusivity paths in forsterite.

Diffusion profiles of 18O tracer in single crystals of forsterite following anneals at 1100° and 1200°C have been determined by a depth profiling technique using secondary ion mass spectrometry. The diffusion penetration profiles showed error function forms with developed tails. The profiles were analyzed in terms of diffusion in the forsterite lattice together with a contribution from dislocation. The present results of lattice diffusion lie in the range of the extrapolation of lines on Arrhenius plots reported previously for intracrystalline diffusion in forsterite. The dislocation diffusion coefficients are about 104 times faster than the lattice diffusion at the same temperature. Diffusion along the dislocations takes place within a pipe with radius of about 0.1 nm surrounding the dislocation line. Based on the above results, O diffusion along high diffusivity paths, such as dislocations and grain boundaries, play an important role on the diffusional creep in olivine under laboratory condition.

Oxygen diffusion in olivine: Effect of oxygen fugacity and implications for creep

Oxygen self‐diffusion experiments on single crystals of San Carlos olivine (∼Fo92) at 1200° ≤ T ≤ 1400°C, oxygen fugacities (ƒO2) along the Ni‐NiO and Fe‐FeO buffers, and silica activity at the olivine‐orthopyroxene buffer yielded results that follow the relationship D = 2.6 × 10−10 ƒO20.21±0.03 exp [−266±11 (kJ mol−1/RT)], where D is the diffusion coefficient in m2 s−1 and ƒO2 is given in pascals. The activation energy compares reasonably well with results for pure forsterite. The positive dependence of ƒO2 implies that the oxygen defect responsible for diffusion is an interstitial rather than a more sterically reasonable oxygen vacancy. Diffusion of oxygen in other close‐packed oxides has also shown a positive dependence on ƒO2. The rate of creep of single‐crystal olivine at fixed orthopyroxene activity also shows a positive ƒO2 dependence. If oxygen interstitials should be shown to be unimportant in oxygen diffusion in oxides, then coupled mechanisms such as countervacancy diffusion must be appealed to in order to explain the positive ƒO2 dependence. Such processes are rate‐limited by the diffusion of metal vacancies which also display a positive ƒO2 dependence in olivine. Compared with data for silicon diffusion in forsterite, our data indicate that oxygen is not the slowest diffusing species in olivine. The activation energy for oxygen diffusion is also low compared to that obtained in a majority of measurements of creep in single‐crystal olivine. Hence if oxygen diffusion contributes to the control of creep in olivine, it must be coupled to another process having a nonzero activation energy. A subinvestigation of the rate of sublimation from polished olivine surfaces, using a high‐resolution thermal balance, showed surface erosion rates at 1300°C of 0.13±0.10 nm/h. Such values are far too slow to noticeably affect our diffusion measurements at temperatures ≤1400°C.

Dependence of creep in olivine on homologous temperature and its implications for flow in the mantle

Creep data for olivine, when normalized by the melting temperature, can be extrapolated directly to the pressure, temperature and chemical environment of the upper mantle by using the appropriate solidus and geotherms. The data presented here, collected over a broad pressure range, predict effective viscosities that are consistent with geophysical and tectonic constraints for a dry upper mantle. These systematics suggest that the effective viscosity of the mantle has risen over the age of the Earth as outgassing has progressively raised the solidus.