The plastic deformation of iron at pressures of the Earth's inner core

Soon after the discovery of seismic anisotropy in the Earth's inner core, it was suggested that crystal alignment attained during deformation might be responsible. Since then, several other mechanisms have been proposed to account for the observed anisotropy, but the lack of deformation experiments performed at the extreme pressure conditions corresponding to the solid inner core has limited our ability to determine which deformation mechanism applies to this region of the Earth. Here we determine directly the elastic and plastic deformation mechanism of iron at pressures of the Earth's core, from synchrotron X-ray diffraction measurements of iron, under imposed axial stress, in diamond-anvil cells. The epsilon-iron (hexagonally close packed) crystals display strong preferred orientation, with c-axes parallel to the axis of the diamond-anvil cell. Polycrystal plasticity theory predicts an alignment of c-axes parallel to the compression direction as a result of basal slip, if basal slip is either the primary or a secondary slip system. The experiments provide direct observations of deformation mechanisms that occur in the Earth's inner core, and introduce a method for investigating, within the laboratory, the rheology of materials at extreme pressures.     

Fine-scale heterogeneity in the Earth's inner core

The seismological properties of the Earth's inner core have become of particular interest as we understand more about its composition and thermal state. Observations of anisotropy and velocity heterogeneity in the inner core are beginning to reveal how it has grown and whether it convects. The attenuation of seismic waves in the inner core is strong, and studies of seismic body waves have found that this high attenuation is consistent with either scattering or intrinsic attenuation. The outermost portion of the inner core has been inferred to possess layering and to be less anisotropic than at greater depths. Here we present observations of seismic waves scattered in the inner core which follow the expected arrival time of the body-wave reflection from the inner-core boundary. The amplitude of these scattered waves can be explained by stiffness variations of 1.2% with a scale length of 2 kilometres across the outermost 300 km of the inner core. These variations might be caused by variations in composition, by pods of partial melt in a mostly solid matrix or by variations in the orientation or strength of seismic anisotropy.     

轧制织构的计算机模拟

分析了金属轧制变形的模拟过程,提出了新的形变模型(PC模型)。PC模型修正了多晶体内各晶粒变形时的切变边界条件,允许各种切变在变形过程中部分存在,从而使模拟更接近实际晶体变形过程。与多晶铝轧制织构的比较表明,PC模型能更好地表达轧制过程中面心立方金属各晶粒取向,在取向空间内的流动倾向及最终稳定位置。     

Development of anisotropic structure in the Earth's lower mantle by solid-state convection

Seismological observations reveal highly anisotropic patches at the bottom of the Earth's lower mantle, whereas the bulk of the mantle has been observed to be largely isotropic. These patches have been interpreted to correspond to areas where subduction has taken place in the past or to areas where mantle plumes are upwelling, but the underlying cause for the anisotropy is unknown-both shape-preferred orientation of elastically heterogeneous materials and lattice-preferred orientation of a homogeneous material have been proposed. Both of these mechanisms imply that large-strain deformation occurs within the anisotropic regions, but the geodynamic implications of the mechanisms differ. Shape-preferred orientation would imply the presence of large elastic (and hence chemical) heterogeneity whereas lattice-preferred orientation requires deformation at high stresses. Here we show, on the basis of numerical modelling incorporating mineral physics of elasticity and development of lattice-preferred orientation, that slab deformation in the deep lower mantle can account for the presence of strong anisotropy in the circum-Pacific region. In this model-where development of the mineral fabric (the alignment of mineral grains) is caused solely by solid-state deformation of chemically homogeneous mantle material-anisotropy is caused by large-strain deformation at high stresses, due to the collision of subducted slabs with the core-mantle boundary.     

Elasticity of iron at the temperature of the Earth's inner core.

Seismological body-wave and free-oscillation studies of the Earth's solid inner core have revealed that compressional waves traverse the inner core faster along near-polar paths than in the equatorial plane. Studies have also documented local deviations from this first-order pattern of anisotropy on length scales ranging from 1 to 1,000 km (refs 3, 4). These observations, together with reports of the differential rotation of the inner core, have generated considerable interest in the physical state and dynamics of the inner core, and in the structure and elasticity of its main constituent, iron, at appropriate conditions of pressure and temperature. Here we report first-principles calculations of the structure and elasticity of dense hexagonal close-packed (h.c.p.) iron at high temperatures. We find that the axial ratio c/a of h.c.p. iron increases substantially with increasing temperature, reaching a value of nearly 1.7 at a temperature of 5,700 K, where aggregate bulk and shear moduli match those of the inner core. As a consequence of the increasing c/a ratio, we have found that the single-crystal longitudinal anisotropy of h.c.p. iron at high temperature has the opposite sense from that at low temperature. By combining our results with a simple model of polycrystalline texture in the inner core, in which basal planes are partially aligned with the rotation axis, we can account for seismological observations of inner-core anisotropy.     

Inner-core shear-wave anisotropy and texture from an observation of PKJKP waves

Since the discovery of the Earth's core a century ago, and the subsequent discovery of a solid inner core (postulated to have formed by the freezing of iron) seismologists have striven to understand this most remote part of the deep Earth. The most direct evidence for a solid inner core would be the observation of shear-mode body waves that traverse it, but these phases are extremely difficult to observe. Two reported observations in short-period data have proved controversial. Arguably more successful have been studies of longer-period data, but such averaging limits the usefulness of the observations to reported sightings. We present two observations of an inner-core shear-wave phase at higher frequencies in stacked data from the Japanese High-Sensitivity Array, Hi-Net. From an analysis of timing, amplitude and waveform of the 'PKJKP' phase we derive constraints on inner-core compressional-wave velocity and shear attenuation at about 0.3 Hz which differ from standard isotropic core models. We can explain waveform features and can partially reconcile the otherwise large differences between core wavespeed and attenuation models that our observations apparently suggest if we invoke shear-wave anisotropy in the inner core. A simple model of an inner core composed of hexagonal close-packed iron with its c axis aligned perpendicular to the rotation axis yields anisotropy that is compatible with both the shear-wave anisotropy that we observe and the well-established 3 per cent compressional-wave anisotropy.     

Thermochemical flows couple the Earth's inner core growth to mantle heterogeneity

Seismic waves sampling the top 100 km of the Earth's inner core reveal that the eastern hemisphere (40 degrees E-180 degrees E) is seismically faster, more isotropic and more attenuating than the western hemisphere. The origin of this hemispherical dichotomy is a challenging problem for our understanding of the Earth as a system of dynamically coupled layers. Previously, laboratory experiments have established that thermal control from the lower mantle can drastically affect fluid flow in the outer core, which in turn can induce textural heterogeneity on the inner core solidification front. The resulting texture should be consistent with other expected manifestations of thermal mantle control on the geodynamo, specifically magnetic flux concentrations in the time-average palaeomagnetic field over the past 5 Myr, and preferred eddy locations in flows imaged below the core-mantle boundary by the analysis of historical geomagnetic secular variation. Here we show that a single model of thermochemical convection and dynamo action can account for all these effects by producing a large-scale, long-term outer core flow that couples the heterogeneity of the inner core with that of the lower mantle. The main feature of this thermochemical 'wind' is a cyclonic circulation below Asia, which concentrates magnetic field on the core-mantle boundary at the observed location and locally agrees with core flow images. This wind also causes anomalously high rates of light element release in the eastern hemisphere of the inner core boundary, suggesting that lateral seismic anomalies at the top of the inner core result from mantle-induced variations in its freezing rate.     

Inner core’s seismic anisotropy is related to its rotation

The inner core has a differential rotation relative to the crust and mantle, the relative linear velocity between the solid inner core and the molten outer core is the biggest at the equator and zero at pole area. As a result, the inner core grows faster at the equator than at the pole area. The gravitational force drives the material flow from the equator to the pole area and makes the inner core remain quasi-orbicular. The corresponding axial symmetric stress field makesc-axes of hexagonal close packed (hcp) iron align with inner core’s rotation axis, resulting in observed seismic anisotropy.     

Anisotropy of Earth's D' layer and stacking faults in the MgSiO3 post-perovskite phase

The post-perovskite phase of (Mg,Fe)SiO3 is believed to be the main mineral phase of the Earth's lowermost mantle (the D' layer). Its properties explain numerous geophysical observations associated with this layer-for example, the D' discontinuity, its topography and seismic anisotropy within the layer. Here we use a novel simulation technique, first-principles metadynamics, to identify a family of low-energy polytypic stacking-fault structures intermediate between the perovskite and post-perovskite phases. Metadynamics trajectories identify plane sliding involving the formation of stacking faults as the most favourable pathway for the phase transition, and as a likely mechanism for plastic deformation of perovskite and post-perovskite. In particular, the predicted slip planes are {010} for perovskite (consistent with experiment) and {110} for post-perovskite (in contrast to the previously expected {010} slip planes). Dominant slip planes define the lattice preferred orientation and elastic anisotropy of the texture. The {110} slip planes in post-perovskite require a much smaller degree of lattice preferred orientation to explain geophysical observations of shear-wave anisotropy in the D' layer.     

Crystallographic preferred orientation of akimotoite and seismic anisotropy of Tonga slab

The mineral akimotoite, ilmenite-structured MgSiO(3), exists at the bottom of the Earth's mantle transition zone and within the uppermost lower mantle, especially under low-temperature conditions. Akimotoite is thought to be a major constituent of the harzburgite layer of subducting slabs, and the most anisotropic mineral in the mantle transition zone. It has been predicted that if akimotoite crystals are preferentially oriented by plastic deformation, a cold subducted slab would be extremely anisotropic. However, there have been no studies of crystallographic preferred orientations and very few reports of plastic deformation experiments for MgSiO(3) ilmenite. Here we present plastic deformation experiments on polycrystalline akimotoite, which were conducted at confining pressures of 20-22 GPa and temperatures of 1,000-1,300 degrees C. We found a change in crystallographic preferred orientation pattern of akimotoite with temperature, where the c-axis maximum parallel to the compression direction develops at high temperature, whereas the c axes are preferentially oriented parallel to the shear direction or perpendicular to the compression direction at lower temperature. The previously reported difference in compressional-wave seismic anisotropy between the northern and southern segments of the Tonga slab at depths of the mantle transition zone can conceivably be attributed to the difference in the crystallographic preferred orientation pattern of akimotoite at varying temperature within the slab.     

立方晶体宏观织构取向分布函数的程序化

取向分布函数(ODF)从宏观整体上反映了多晶体各晶粒取向的统计分布,它突破了传统的极图法、反极图法用一维或二维图形来描述晶体的空间取向分布的局限性,可实现晶体取向分布的三维空间描述.针对具有立方结构的多晶体材料,采用级数展开法模型计算取向分布函数的理论模型,利用程序对ODF值进行了计算,并以Voronoi增量算法为基础生成包含有5000个晶粒的多晶体材料各晶粒的几何数据信息,与计算得到的ODF值一起导入OpenGL进行可视化处理,直观显示了多晶体材料中ODF值在各晶粒内的分布.通过对立方系多晶体材料的ODF测算,对该种材料的织构类型研究与分布规律分析具有重要的指导意义.     

合金凝固过程枝晶生长的界面前沿跟踪法模拟

为预测铝合金铸件凝固时的微观组织演化,本文采用当量法对KGT模型进行扩展,建立了适应多元合金的界面前沿跟踪模型?应用该模型对Al-6Si-4Cu合金凝固过程的微观组织的演化过程进行了模拟?实验结果表明,所建立的模型能够再现凝固过程中自由枝晶生长形态?液相中的溶质分布以及多晶生长时枝晶的竞争生长过程?该模型可以实时地跟踪凝固界面前沿的位置,节省计算时间,提高效率?     

Hemispherical variations in seismic velocity at the top of the Earth's inner core

Knowledge of the seismic velocity structure at the top of the Earth's inner core is important for deciphering the physical processes responsible for inner-core growth. Previous global seismic studies have focused on structures found 100 km or deeper within the inner core, with results for the uppermost 100 km available for only isolated regions. Here we present constraints on seismic velocity variations just beneath the inner-core boundary, determined from the difference in travel time between waves reflected at the inner-core boundary and those transmitted through the inner core. We found that these travel-time residuals-observed on both global seismograph stations and several regional seismic networks-are systematically larger, by about 0.8 s, for waves that sample the 'eastern hemisphere' of the inner core (40 degrees E to 180 degrees E) compared to those that sample the 'western hemisphere' (180 degrees W to 40 degrees E). These residuals show no correlation with the angle at which the waves traverse the inner core; this indicates that seismic anisotropy is not strong in this region and that the isotropic seismic velocity of the eastern hemisphere is about 0.8% higher than that of the western hemisphere.     

Resistance to mantle flow inferred from the electromagnetic strike of the Australian upper mantle

Seismic anisotropy is thought to result from the strain-induced lattice-preferred orientation of mantle minerals, especially olivine, owing to shear waves propagating faster along the a-axis of olivine crystals than along the other axes. This anisotropy results in birefringence, or 'shear-wave splitting', which has been investigated in numerous studies. Although olivine is also anisotropic with respect to electrical conductivity (with the a-axis being most conductive), few studies of the electrical anisotropy of the upper mantle have been undertaken, and these have been limited to relatively shallow depths in the lithospheric upper mantle. Theoretical models of mantle flow have been used to infer that, for progressive simple shear imparted by the motion of an overriding tectonic plate, the a-axes of olivine crystals should align themselves parallel to the direction of plate motion. Here, however, we show that a significant discrepancy exists between the electromagnetic strike of the mantle below Australia and the direction of present-day absolute plate motion. We infer from this discrepancy that the a-axes of olivine crystals are not aligned with the direction of the present-day plate motion of Australia, indicating resistance to deformation of the mantle by plate motion.     

深基坑桩锚支护结构变形和内力分析方法探讨

利用弹性地基梁法和有限差分法,分别计算桩锚支护体系在深基坑开挖过程中支护结构的变形和内力,并与实测数据对比分析后发现:两种设计分析模型由于选型差异和对实际桩土作用模拟的情况不同,分析结果与实测结果间存在程度不同的差异,其中弹性地基梁法在支护结构水平位移分析中误差较大,在以强度控制为主的设计情况下使用较妥;有限差分法能更真实地反映桩锚支护结构在深基坑开挖过程中土体与支护结构的变形及内力变化,但计算模型复杂。     

Anisotropy of thermal diffusivity in the upper mantle.

Heat transfer in the mantle is a key process controlling the Earth's dynamics. Upper-mantle mineral phases, especially olivine, have been shown to display highly anisotropic thermal diffusivity at ambient conditions, and seismic anisotropy data show that preferred orientations of olivine induced by deformation are coherent at large scales (>50 km) in the upper mantle. Thus heat transport in the upper mantle should be anisotropic. But the thermal anisotropy of mantle minerals at high temperature and its relationship with deformation have not been well constrained. Here we present petrophysical modelling and laboratory measurements of thermal diffusivity in deformed mantle rocks between temperatures of 290 and 1,250 K that demonstrate that deformation may induce a significant anisotropy of thermal diffusivity in the uppermost mantle. We found that heat transport parallel to the flow direction is up to 30 per cent faster than that normal to the flow plane. Such a strain-induced thermal anisotropy implies that the upper-mantle temperature distribution, rheology and, consequently, its dynamics, will depend on deformation history. In oceans, resistive drag flow would result in lower vertical diffusivities in both the lithosphere and asthenosphere and hence in less effective heat transfer from the convective mantle. In continents, olivine orientations frozen in the lithosphere may induce anisotropic heating above mantle plumes, favouring the reactivation of pre-existing structures.     

Global azimuthal seismic anisotropy and the unique plate-motion deformation of Australia

Differences in the thickness of the high-velocity lid underlying continents as imaged by seismic tomography, have fuelled a long debate on the origin of the 'roots' of continents. Some of these differences may be reconciled by observations of radial anisotropy between 250 and 300 km depth, with horizontally polarized shear waves travelling faster than vertically polarized ones. This azimuthally averaged anisotropy could arise from present-day deformation at the base of the plate, as has been found for shallower depths beneath ocean basins. Such deformation would also produce significant azimuthal variation, owing to the preferred alignment of highly anisotropic minerals. Here we report global observations of surface-wave azimuthal anisotropy, which indicate that only the continental portion of the Australian plate displays significant azimuthal anisotropy and strong correlation with present-day plate motion in the depth range 175-300 km. Beneath other continents, azimuthal anisotropy is only weakly correlated with plate motion and its depth location is similar to that found beneath oceans. We infer that the fast-moving Australian plate contains the only continental region with a sufficiently large deformation at its base to be transformed into azimuthal anisotropy. Simple shear leading to anisotropy with a plunging axis of symmetry may explain the smaller azimuthal anisotropy beneath other continents.     

岩石应力敏感曲线机制分析

根据固体力学的有关知识,研究了岩石应力敏感曲线测试过程中的机理问题。岩芯应力敏感曲线测试时因封套的塑性变形,使得加载曲线与卸载曲线产生了较大的差异,也夸大了岩石的应力敏感程度。实际上,应力敏感测试时,岩芯只产生弹性变形,而不产生塑性变形。加载时封套有塑性变形,卸载时封套和岩芯都无塑性变形。卸载曲线的应力敏感程度,包含了封套的弹性变形部分。扣除封套的变形因素,岩石自身的应力敏感程度极其微弱。     

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.