Periclase deforms more slowly than bridgmanite under mantle conditions.

Transport of heat from the interior of the Earth drives convection in the mantle, which involves the deformation of solid rocks over billions of years. The lower mantle of the Earth is mostly composed of iron-bearing bridgmanite MgSiO3 and approximately 25% volume periclase MgO (also with some iron). It is commonly accepted that ferropericlase is weaker than bridgmanite1. Considerable progress has been made in recent years to study assemblages representative of the lower mantle under the relevant pressure and temperature conditions2,3. However, the natural strain rates are 8 to 10 orders of magnitude lower than in the laboratory, and are still inaccessible to us. Once the deformation mechanisms of rocks and their constituent minerals have been identified, it is possible to overcome this limitation thanks to multiscale numerical modelling, and to determine rheological properties for inaccessible strain rates. In this work we use 2.5-dimensional dislocation dynamics to model the low-stress creep of MgO periclase at lower mantle pressures and temperatures. We show that periclase deforms very slowly under these conditions, in particular, much more slowly than bridgmanite deforming by pure climb creep. This is due to slow diffusion of oxygen in periclase under pressure. In the assemblage, this secondary phase hardly participates in the deformation, so that the rheology of the lower mantle is very well described by that of bridgmanite. Our results show that drastic changes in deformation mechanisms can occur as a function of the strain rate.

Ultimate mechanical properties of enstatite.

The ultimate mechanical properties of MgSiO3 orthoenstatite (OEN), as characterized here by the ideal strengths, have been calculated under tensile and shear loadings using first-principles calculations. Both ideal tensile strength (ITS) and shear strength (ISS) are computed by applying homogeneous strain increments along high-symmetry directions ([100], [010], and [001]) and low index shear planes ((100), (010), and (001)) of the orthorhombic lattice. We show that the ultimate mechanical properties of OEN are highly anisotropic during tensile loading, with ITS ranging from 4.5 GPa along [001] to 8.7 GPa along [100], and quite isotropic during the shear loading with ISS ranging from 7.4 to 8.9 GPa. During tensile test along [100] and [001], a modified structure close to OEN has been found. This modified structure is more stable than OEN under stress (or strain). We have characterized its elastic and ultimate properties under tensile loading. With ITS ranging from 7.6 GPa along [010] to 25.6 GPa along [001], this modified structure appears to be very anisotropic with exceptional strength along [001]. Supplementary Information: The online version contains supplementary material available at 10.1007/s00269-022-01206-5.

Stress-induced amorphization triggers deformation in the lithospheric mantle.

The mechanical properties of olivine-rich rocks are key to determining the mechanical coupling between Earth's lithosphere and asthenosphere. In crystalline materials, the motion of crystal defects is fundamental to plastic flow1-4. However, because the main constituent of olivine-rich rocks does not have enough slip systems, additional deformation mechanisms are needed to satisfy strain conditions. Experimental studies have suggested a non-Newtonian, grain-size-sensitive mechanism in olivine involving grain-boundary sliding5,6. However, very few microstructural investigations have been conducted on grain-boundary sliding, and there is no consensus on whether a single or multiple physical mechanisms are at play. Most importantly, there are no theoretical frameworks for incorporating the mechanics of grain boundaries in polycrystalline plasticity models. Here we identify a mechanism for deformation at grain boundaries in olivine-rich rocks. We show that, in forsterite, amorphization takes place at grain boundaries under stress and that the onset of ductility of olivine-rich rocks is due to the activation of grain-boundary mobility in these amorphous layers. This mechanism could trigger plastic processes in the deep Earth, where high-stress conditions are encountered (for example, at the brittle-plastic transition). Our proposed mechanism is especially relevant at the lithosphere-asthenosphere boundary, where olivine reaches the glass transition temperature, triggering a decrease in its viscosity and thus promoting grain-boundary sliding.

In Situ Quantitative Tensile Testing of Antigorite in a Transmission Electron Microscope.

The determination of the mechanical properties of serpentinites is essential toward the understanding of the mechanics of faulting and subduction. Here we present the first in situ tensile tests on antigorite in a transmission electron microscope. A push-to-pull deformation device is used to perform quantitative tensile tests, during which force and displacement are measured, while the evolving microstructure is imaged with the microscope. The experiments have been performed at room temperature on 2 × 1 × 0.2 µm3 beams prepared by focused ion beam. The specimens are not single crystals despite their small sizes. Orientation mapping indicated that several grains were well oriented for plastic slip. However, no dislocation activity has been observed even though the engineering tensile stress went up to 700 MPa. We show also that antigorite does not exhibit a purely elastic-brittle behavior since, despite the presence of defects, the specimens accumulate permanent deformation and did not fail within the elastic regime. Instead, we observe that strain localizes at grain boundaries. All observations concur to show that under these experimental conditions, grain boundary sliding is the dominant deformation mechanism. This study sheds a new light on the mechanical properties of antigorite and calls for further studies on the structure and properties of grain boundaries in antigorite and more generally in phyllosilicates.

The role of diffusion-driven pure climb creep on the rheology of bridgmanite under lower mantle conditions.

The viscosity of Earth's lower mantle is poorly constrained due to the lack of knowledge on some fundamental variables that affect the deformation behaviour of its main mineral phases. This study focuses on bridgmanite, the main lower mantle constituent, and assesses its rheology by developing an approach based on mineral physics. Following and revising the recent advances in this field, pure climb creep controlled by diffusion is identified as the key mechanism driving deformation in bridgmanite. The strain rates of this phase under lower mantle pressures, temperatures and stresses are thus calculated by constraining diffusion and implementing a creep theoretical model. The viscosity of MgSiO3 bridgmanite resulting from pure climb creep is consequently evaluated and compared with the viscosity profiles available from the literature. We show that the inferred variability of viscosity in these profiles can be fully accounted for with the chosen variables of our calculation, e.g., diffusion coefficients, vacancy concentrations and applied stresses. A refinement of these variables is advocated in order to further constrain viscosity and match the observables.

Prediction of Mechanical Twinning in Magnesium Silicate Post-Perovskite.

The plastic properties of MgSiO3 post-perovskite are considered to be one of the key issues necessary for understanding the seismic anisotropy at the bottom of the mantle in the so-called D" layer. Although plastic slip in MgSiO3 post-perovskite has attracted considerable attention, the twinning mechanism has not been addressed, despite some experimental evidence from low-pressure analogues. On the basis of a numerical mechanical model, we present a twin nucleation model for post-perovskite involving the emission of 1/6 <110> partial dislocations. Relying on first-principles calculations with no adjustable parameters, we show that {110} twin wall formation resulting from the interaction of multiple twin dislocations occurs at a twinning stress comparable in magnitude to the most readily occurring slip system in post-perovskite. Because dislocation activities and twinning are competitive strain-producing mechanisms, twinning should be considered in future models of crystallographic preferred orientations in post-perovskite to better interpret seismic anisotropy in the lowermost lower mantle.

Pure climb creep mechanism drives flow in Earth's lower mantle.

At high pressure prevailing in the lower mantle, lattice friction opposed to dislocation glide becomes very high, as reported in recent experimental and theoretical studies. We examine the consequences of this high resistance to plastic shear exhibited by ringwoodite and bridgmanite on creep mechanisms under mantle conditions. To evaluate the consequences of this effect, we model dislocation creep by dislocation dynamics. The calculation yields to an original dominant creep behavior for lower mantle silicates where strain is produced by dislocation climb, which is very different from what can be activated under high stresses under laboratory conditions. This mechanism, named pure climb creep, is grain-size-insensitive and produces no crystal preferred orientation. In comparison to the previous considered diffusion creep mechanism, it is also a more efficient strain-producing mechanism for grain sizes larger than ca. 0.1 mm. The specificities of pure climb creep well match the seismic anisotropy observed of Earth's lower mantle.

Modeling defects and plasticity in MgSiO3 post-perovskite: Part 3-Screw and edge [001] dislocations.

In this study, we investigate the complex structure of [001] screw and edge dislocation cores in MgSiO3 post-perovskite at the atomic scale. Both [001] screw and edge dislocations exhibit spontaneous dissociation in (010) into two symmetric partials characterized by the presence of <100> component. In case of edge dislocations, dissociation occurs into ½<101> partials, while for the screw dislocations the <100> component reaches only 15%. Under applied stress, both [001](010) screw and edge dislocations behave similarly. Above the Peierls stress, the two partials glide together while keeping their stacking-fault widths (~11 and ~42 Å for the screw and edge dislocations, respectively) constant. The Peierls stress opposed to the glide of [001](010) screw dislocations is 3 GPa, while that of edge dislocations is 33% lower. Relying on the observed characteristics of the dislocation cores, we estimate the efficiency of [001](010) dislocation glide under the P-T conditions relevant to the lowermost mantle and demonstrate that dislocation creep for this slip system would occur in the so-called athermal regime where lattice friction for the considered slip system vanishes when the temperature rises above the critical T a value of ~2,000 K.

Low viscosity and high attenuation in MgSiO3 post-perovskite inferred from atomic-scale calculations.

This work represents a numerical study of the thermal activation for dislocation glide of the [100](010) slip system in MgSiO3 post-perovskite (Mg-ppv) at 120 GPa. We propose an approach based on a one-dimensional line tension model in conjunction with atomic-scale calculations. In this model, the key parameters, namely, the line tension and the Peierls barrier, are obtained from density functional theory calculations. We find a Peierls stress σp = 2.1 GPa and a line tension Γ = 9.2 eV/Å, which lead to a kink-pair enthalpy (under zero stress) of 2.69 eV. These values confirm that this slip system bears a very low lattice friction because it vanishes for temperatures above approximately 500 K under mantle conditions. In the Earth's mantle, high-pressure Mg-ppv silicate is thus expected to become as ductile as ferropericlase. These results confirm the hypothesis of a weak layer in the D″ layer where Mg-ppv is present. Easy glide along [100](010) suggests strong preferred orientations with (010) planes aligned. Highly mobile [100] dislocations are also likely to respond to stresses related to seismic waves, leading to energy dissipation and strong attenuation.

Low-temperature plasticity of olivine revisited with in situ TEM nanomechanical testing.

The rheology of the lithospheric mantle is fundamental to understanding how mantle convection couples with plate tectonics. However, olivine rheology at lithospheric conditions is still poorly understood because experiments are difficult in this temperature range where rocks and mineral become very brittle. We combine techniques of quantitative in situ tensile testing in a transmission electron microscope and numerical modeling of dislocation dynamics to constrain the low-temperature rheology of olivine. We find that the intrinsic ductility of olivine at low temperature is significantly lower than previously reported values, which were obtained under strain-hardened conditions. Using this method, we can anchor rheological laws determined at higher temperature and can provide a better constraint on intermediate temperatures relevant for the lithosphere. More generally, we demonstrate the possibility of characterizing the mechanical properties of specimens, which can be available in the form of submillimeter-sized particles only.

Modeling defects and plasticity in MgSiO3 post-perovskite: Part 1-generalized stacking faults.

In this work, we examine the transferability of a pairwise potential model (derived for MgSiO3 perovskite) to accurately compute the excess energies of the generalized stacking faults (GSF, also called γ-surfaces) in MgSiO3 post-perovskite. All calculations have been performed at 120 GPa, a pressure relevant to the D″ layer. Taking into account an important aspect of crystal chemistry for complex materials, we consider in detail all possible locations of slip planes in the post-perovskite structure. The γ-surface calculations emphasize the easiness of glide of slip systems with the smallest shear vector [100] and of the [001](010) slip system. Our results are in agreement with previous ab initio calculations. This validates the use the chosen potential model for further full atomistic modeling of dislocations in MgSiO3 post-perovskite.

Modeling defects and plasticity in MgSiO3 post-perovskite: Part 2-screw and edge [100] dislocations.

In this study, we propose a full atomistic study of [100] dislocations in MgSiO3 post-perovskite based on the pairwise potential parameterized by Oganov et al. (Phys Earth Planet Inter 122:277-288, 2000) for MgSiO3 perovskite. We model screw dislocations to identify planes where they glide easier. We show that despite a small tendency to core spreading in {011}, [100] screw dislocations glide very easily (Peierls stress of 1 GPa) in (010) where only Mg-O bonds are to be sheared. Crossing the Si-layers results in a higher lattice friction as shown by the Peierls stress of [100](001): 17.5 GPa. Glide of [100] screw dislocations in {011} appears also to be highly unfavorable. Whatever the planes, (010), (001) or {011}, edge dislocations are characterized by a wider core (of the order of 2b). Contrary to screw character, they bear negligible lattice friction (0.1 GPa) for each slip system. The layered structure of post-perovskite results in a drastic reduction in lattice friction opposed to the easiest slip systems compared to perovskite.

Disclinations provide the missing mechanism for deforming olivine-rich rocks in the mantle.

Mantle flow involves large strains of polymineral aggregates. The strongly anisotropic plastic response of each individual grain in the aggregate results from the interactions between neighbouring grains and the continuity of material displacement across the grain boundaries. Orthorhombic olivine, which is the dominant mineral phase of the Earth's upper mantle, does not exhibit enough slip systems to accommodate a general deformation state by intracrystalline slip without inducing damage. Here we show that a more general description of the deformation process that includes the motion of rotational defects referred to as disclinations can solve the olivine deformation paradox. We use high-resolution electron backscattering diffraction (EBSD) maps of deformed olivine aggregates to resolve the disclinations. The disclinations are found to decorate grain boundaries in olivine samples deformed experimentally and in nature. We present a disclination-based model of a high-angle tilt boundary in olivine, which demonstrates that an applied shear induces grain-boundary migration through disclination motion. This new approach clarifies grain-boundary-mediated plasticity in polycrystalline aggregates. By providing the missing mechanism for describing plastic flow in olivine, this work will permit multiscale modelling of the rheology of the upper mantle, from the atomic scale to the scale of the flow.

Modelling the rheology of MgO under Earth's mantle pressure, temperature and strain rates.

Plate tectonics, which shapes the surface of Earth, is the result of solid-state convection in Earth's mantle over billions of years. Simply driven by buoyancy forces, mantle convection is complicated by the nature of the convecting materials, which are not fluids but polycrystalline rocks. Crystalline materials can flow as the result of the motion of defects--point defects, dislocations, grain boundaries and so on. Reproducing in the laboratory the extreme deformation conditions of the mantle is extremely challenging. In particular, experimental strain rates are at least six orders of magnitude larger than in nature. Here we show that the rheology of MgO at the pressure, temperature and strain rates of the mantle is accessible by multiscale numerical modelling starting from first principles and with no adjustable parameters. Our results demonstrate that extremely low strain rates counteract the influence of pressure. In the mantle, MgO deforms in the athermal regime and this leads to a very weak phase. It is only in the lowermost lower mantle that the pressure effect could dominate and that, under the influence of lattice friction, a viscosity of the order of 10(21)-10(22) pascal seconds can be defined for MgO.

Implications for plastic flow in the deep mantle from modelling dislocations in MgSiO3 minerals.

The dynamics of the Earth's interior is largely controlled by mantle convection, which transports radiogenic and primordial heat towards the surface. Slow stirring of the deep mantle is achieved in the solid state through high-temperature creep of rocks, which are dominated by the mineral MgSiO3 perovskite. Transformation of MgSiO3 to a 'post-perovskite' phase may explain the peculiarities of the lowermost mantle, such as the observed seismic anisotropy, but the mechanical properties of these mineralogical phases are largely unknown. Plastic flow of solids involves the motion of a large number of crystal defects, named dislocations. A quantitative description of flow in the Earth's mantle requires information about dislocations in high-pressure minerals and their behaviour under stress. This property is currently out of reach of direct atomistic simulations using either empirical interatomic potentials or ab initio calculations. Here we report an alternative to direct atomistic simulations based on the framework of the Peierls-Nabarro model. Dislocation core models are proposed for MgSiO3 perovskite (at 100 GPa) and post-perovskite (at 120 GPa). We show that in perovskite, plastic deformation is strongly influenced by the orthorhombic distortions of the unit cell. In silicate post-perovskite, large dislocations are relaxed through core dissociation, with implications for the mechanical properties and seismic anisotropy of the lowermost mantle.

Comet 81P/Wild 2 under a microscope.

The Stardust spacecraft collected thousands of particles from comet 81P/Wild 2 and returned them to Earth for laboratory study. The preliminary examination of these samples shows that the nonvolatile portion of the comet is an unequilibrated assortment of materials that have both presolar and solar system origin. The comet contains an abundance of silicate grains that are much larger than predictions of interstellar grain models, and many of these are high-temperature minerals that appear to have formed in the inner regions of the solar nebula. Their presence in a comet proves that the formation of the solar system included mixing on the grandest scales.

Pressure sensitivity of olivine slip systems and seismic anisotropy of Earth's upper mantle.

The mineral olivine dominates the composition of the Earth's upper mantle and hence controls its mechanical behaviour and seismic anisotropy. Experiments at high temperature and moderate pressure, and extensive data on naturally deformed mantle rocks, have led to the conclusion that olivine at upper-mantle conditions deforms essentially by dislocation creep with dominant [100] slip. The resulting crystal preferred orientation has been used extensively to explain the strong seismic anisotropy observed down to 250 km depth. The rapid decrease of anisotropy below this depth has been interpreted as marking the transition from dislocation to diffusion creep in the upper mantle. But new high-pressure experiments suggest that dislocation creep also dominates in the lower part of the upper mantle, but with a different slip direction. Here we show that this high-pressure dislocation creep produces crystal preferred orientations resulting in extremely low seismic anisotropy, consistent with seismological observations below 250 km depth. These results raise new questions about the mechanical state of the lower part of the upper mantle and its coupling with layers both above and below.

Dislocation creep in MgSiO3 perovskite at conditions of the Earth's uppermost lower mantle.

Seismic anisotropy provides an important observational constraint on flow in the Earth's deep interior. The quantitative interpretation of anisotropy, however, requires knowledge of the slip geometry of the constitutive minerals that are responsible for producing rock fabrics. The Earth's lower mantle is mostly composed of (Mg, Fe)SiO3 perovskite, but as MgSiO3 perovskite is not stable at high temperature under ambient pressure, it has not been possible to investigate its mechanical behaviour with conventional laboratory deformation experiments. To overcome this limitation, several attempts were made to infer the mechanical properties of MgSiO3 perovskite on the basis of analogue materials. But perovskites do not constitute an analogue series for plastic deformation, and therefore the direct investigation of MgSiO3 perovskite is necessary. Here we have taken advantage of recent advances in experimental high-pressure rheology to perform deformation experiments on coarse-grained MgSiO3 polycrystals under pressure and temperature conditions of the uppermost lower mantle. We show that X-ray peak broadening measurements developed in metallurgy can be adapted to low-symmetry minerals to identify the elementary deformation mechanisms activated under these conditions. We conclude that, under uppermost lower-mantle conditions, MgSiO3 perovskite deforms by dislocation creep and may therefore contribute to producing seismic anisotropy in rocks at such depths.