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31.
S. Karato 《Physics of the Earth and Planetary Interiors》1981,24(1):1-14
The rheology of the lower mantle of the Earth is examined from the viewpoint of solid state physics. Recent developments in high-pressure research suggest that the lower mantle contains a considerable amount of (Mg, Fe)O with Fe/Mg + Fe = 0.2–0.3. The pressure and temperature dependences of diffusion in (Mg, Fe)O are estimated by the theory of diffusion in ionic solids. Of the materials composing the lower mantle, (Mg, Fe)O may be the “softest”, and therefore the rheology of the lower mantle may be that of (Mg, Fe)O, unless the framework effect is important.Temperatures in the lower mantle are inferred from the depths of phase transitions and the melting temperatures of the core materials. A thermal boundary layer at the base of the mantle is suggested. The physical mechanisms of creep are examined based on a grain size-stress relation and non-Newtonian flow is shown to be the dominant flow mechanism in the Earth's mantle.The effective viscosity for the temperature models, with and without the thermal boundary layer, is calculated for constant stress and constant strain rate (with depth). For constant strain rate, which may be appropriate for discussing the mechanics of descending slabs, the increase in effective viscosity with depth is smaller than for the constant-stress case, which may be appropriate for discussing the flow induced by the surface motion of plates.The relatively small depth gradient of viscosity, for constant strain rate, suggests that the lower mantle could also participate in convection. The effective viscosity increases with depth, however, by at least 102 to 103 from the top to the bottom of the lower mantle, for a reasonable range of activation volumes and temperatures. There will be a low-viscosity layer at the base of the mantle, in contrast to the high-viscosity layer at the top of the mantle (plates), if a thermal boundary layer is present. The constant Newtonian viscosity inferred from rebound data may be an apparent feature resulting from the difference in deformation mechanisms between isostatic rebound and large-scale flow. 相似文献
32.
S. Karato 《Physics of the Earth and Planetary Interiors》1981,25(1):38-51
A continuum model of point defects in ionic solids is developed and applied to the estimation of the pressure dependence of diffusion (in alkali halides). Activation enthalpies are expressed using macroscopic physical constants (lattice energy, elastic constants, dielectric constants, etc.) by introducing empirical parameters related to the microscopic nature of defects. Systematic relations are found between these parameters and other physical properties (ionic radius, volume fraction of anions in crystals, etc.). The nature of parameters for anions is shown to be significantly different from that for cations, probably due to the difference in “softness” between anions and cations. Such relations make it possible to estimate activation energy and volume of diffusion from the lattice energy, ionic radius, elastic constants, dielectric constants and their pressure derivatives. The calculated activation volumes agree well with experimental data. The effect of phase transition is also examined by comparing NaCl and CsCl structures. It is suggested that by phase transition from a less dense (NaCl) structure to a denser one (CsCl), the anion diffusion constant may not decrease as much as expected from the associated change in other physical properties. The validity of the models of van Liempt and of Keyes is examined. It is shown that van Liempt's model works well except for the migration process (especially anions), and that Keyes' model does not work so well for all processes. 相似文献
33.
Current models of planetary formation suggest a hierarchy in the size of planetesimals from which planets were formed, causing formation of a hot magma ocean through which metal-silicate separation (core formation) may have occurred. We analyze chemical equilibrium during metal-silicate separation and show that the size of iron as well as the thermodynamic conditions of equilibrium plays a key role in determining the chemistry of the mantle (silicates) and core (iron) after core formation. A fluid dynamical analysis shows that the hydrodynamically stable size of iron droplets is less than 10−2 m for which both chemical and thermal equilibrium should have been established during the separation from the surrounding silicate magma. However, iron may have been separated from silicates as larger bodies when accumulation of iron on rheological boundaries and resultant large scale gravitational instability occurred or when the core of colliding planetesimals directly plunged into the pre-existing core. In these cases, iron to form the core will be chemically in dis-equilibrium with surrounding silicates during separation. The relative role of equilibrium and dis-equilibrium separation has been examined taking into account of the effects of rheological structure of a growing earth that contains a completely molten near surface layer followed by a partially molten deep magma ocean and finally a solid innermost proto-nucleus. We show that the separation of iron through a completely molten magma ocean likely occurred with iron droplets assuming a hydrodynamically stable size ( 10−2 m) at chemical equilibrium, but the sinking iron droplets are likely to have been accumulated on top of the partially molten layer to form a layer (or a lake) of molten iron which sank to deeper portions as a larger droplet. The degree of chemical equilibrium during this process is determined by the size of droplets which is in turn controlled by the size and frequency of accreting planetesimals and the rheological properties of silicate matrix. For a plausible range of parameters, most of the iron that formed the core is likely to have been separated as large droplets or bodies and chemical equilibrium with silicate occurred only at relatively low temperatures and pressures in a shallow magma ocean or in their parental bodies. However, a small portion of iron that separated as small droplets was in chemical equilibrium with silicate at high temperatures and pressures in a deep magma ocean during the later stage of core formation. Therefore the chemistry of the core is mostly controlled by the chemical equilibrium with silicates at relatively low temperatures and pressures, whereas the chemistry of the mantle controlled by the interaction with iron during core formation is likely to have been determined mostly by the chemical equilibrium with a small amount of iron at high temperatures and pressures. 相似文献
34.
We present here a new model of core formation which is based on the current understanding of planetary accretion and discuss its implications for the chemistry of the Earth's mantle and core. Formation of the Earth by hierarchical accretion of progressively larger bodies on a time scale much longer than that of solid body differentiation in the nebula indicates that a significant fraction of metal in the core could be inherited from preterrestrially differentiated planetesimals. An analysis of the segregation of this iron to form the core suggests that most of the metal settles to the core without interaction with silicates; only a small fraction of the metal chemically equilibrates at high temperatures and pressures with the silicates. The siderophile element abundances in the mantle are considered to be a consequence of a two-step equilibration with iron, once preterrestrially in the planetesimals at low temperatures and pressures, and later in the Earth at high temperatures and pressures. The highly siderophile elements such as Re, Au and the platinum group elements in the mantle are essentially excluded from silicates from the preterrestrial equilibration. We attribute the abundances of these elements in the mantle to the later equilibration in the Earth at substantially reduced metal-silicate partition coefficients (Dmet/sil), for which there is a considerable experimental evidence now. Mass balance considerations constrain the fraction of core metal involved in such an equilibration at approximately 0.3 – 0.5%. The model accounts for the levels and the near-chondritic ratios of the highly siderophile elements in the mantle. The mantle abundances of the less siderophile elements are largely determined by preterrestrial metal-silicate equilibrium and are not significantly affected by the second equilibration. The extreme depletion of sulfur and the lack of silicate melt-sulfide signature in the noble metal abundances in the mantle are natural consequences of this mode of core formation. Sulfur was added to the magma ocean during the high-T, high-P equilibration in the Earth, not extracted from it by sulfide segregation to the core. Except for Ni and Co, the overall siderophile abundances of the mantle can be well matched in this two-step equilibration model.
The mantle characteristics of Ni and Co are unique to the Earth and hence suggest a terrestrial process as the likely cause. One such process is the flotation and addition of olivine to the primitive upper mantle. In our model of core formation, neither the elemental and isotopic data of Re---Os, nor the low sulfur content of the mantle remains as an objection to the existence of a magma ocean and olivine flotation.
The small fraction of core metal that equilibrates with silicates at high T and P suggests that the light elements O, Si or H are unimportant in the core, leaving S (and possibly C) as prime candidates. Sulfur, as FeS associated with incoming iron metal, is directly sequestered to the core along with the bulk of the iron metal. It appears unlikely that other light elements can be added to the core after its formation. U and Th are excluded from the core but the model allows for entry of some K; however, the extent to which K serves as a heat source in the core remains uncertain.
The model is testable in two ways. One is by investigation of the metal-silicate partitioning at high temperatures and pressures under magma ocean conditions to determine if the (Dmet/sil) values are lowered to the levels required in the model. The other is by experiments to determine if a solvus closure between metal and silicate liquids occurs at high temperatures relevant to a magma ocean. 相似文献
35.
Plastic deformation of garnets: systematics and implications for the rheology of the mantle transition zone 总被引：14，自引：0，他引：14
Shun-ichiro Karato Zichao Wang Bofa Liu Kiyoshi Fujino 《Earth and Planetary Science Letters》1995,130(1-4):13-30
Plastic properties of materials with garnet structure have been studied under wide temperature conditions, ranging from room temperature to 95% of the melting temperatures, using uniaxial compression and hot microhardness tests. Garnets studied include single crystals of oxide garnets (Y3Al5O12, Gd3Ga5O12 and Y3Fe5O12) and silicate garnets (various solid solutions, including grossular, almandine, andradite, pyrope, spessartine and uvarovite). Both uniaxial compression and hot hardness tests indicate that there is a general trend in the plasticity of garnets when the data are compared at normalized conditions (T/Tm andσ/μ), and that the resistance to plastic deformation in garnets is significantly higher than most of the other minerals in the Earth's mantle. Based on both stress-dip tests and microstructural observations, it is proposed that the creep strength of garnet is largely controlled by the resistance to dislocation glide rather than by recovery processes. This conclusion is consistent with the high Peierls stress inferred from the hot hardness tests. The high Peierls stress in garnets is, presumably, due to the large unit cell (i.e., long Burgers vectors) and/or the bcc packing, which are common to all garnets. We postulate, therefore, that the present results can be applied to the strength of high-pressure garnet (majorite) and suggest that garnet-rich layers in the Earth, such as subducted oceanic crust in the transition zone or a possibly garnet-rich (bottom part of the) transition zone, will be considerably stronger than surrounding regions. 相似文献
36.
Seismic Anisotropy in the Deep Mantle, Boundary Layers and the Geometry of Mantle Convection 总被引：2，自引：0，他引：2
S. Karato 《Pure and Applied Geophysics》1998,151(2-4):565-587
—An attempt is made to explore the geodynamical significance of seismic anisotropy in the deep mantle on the basis of mineral physics. The mineral physics observations used include the effects of deformation mechanisms on lattice and shape preferred orientation, the effects of pressure on elastic anisotropy and the nature of lattice preferred orientation in deep mantle minerals in dislocation creep regime. Many of these issues are still poorly constrained, but a review of recent results shows that it is possible to interpret deep mantle seismic anisotropy in a unified fashion, based on the solid state processes without invoking partial melting. The key notions are (i) the likely regional variation in the magnitude of anisotropy as deformation mechanisms change from dislocation to diffusion creep (or superplasticity), associated with a change in the stress level and/or grain-size in the convecting mantle with a high Rayleigh number, and (ii) the change in elastic anisotropy with pressure in major mantle minerals, particularly in (Mg, Fe)O. The results provide the following constraints on the style of mantle convection (i) the SH > SV anisotropy in the bottom transition zone and the SV > SH anisotropy in the top lower mantle can be attributed to anisotropy structures (lattice preferred orientation and/or laminated structures) caused by the horizontal flow in this depth range, suggesting the presence of a mid-mantle boundary layer due to (partially) layered convection, (ii) the observed no significant seismic anisotropy in the deep mantle near subduction zones implies that deformation associated with subducting slabs is due mostly to diffusion creep (or superplasticity) and therefore slabs are weak in the deep mantle and hence easily deformed when encountered with resistance forces, and (iii) the SH > SV anisotropy in the cold thick portions of the D" layer is likely to be due to horizontally aligned shape preferred orientation in perovskite plus magnesiowüstite aggregates formed by strong horizontal shear motion in the recent past. 相似文献
37.
Experimental Studies of Shear Deformation of Mantle Materials: Towards Structural Geology of the Mantle 总被引：1，自引：0，他引：1
S. Karato S. Zhang M. E. Zimmerman M. J. Daines D. L. Kohlstedt 《Pure and Applied Geophysics》1998,151(2-4):589-603
—A brief outline is given on experimental studies carried out in the Minnesota Mineral and Rock Physics Laboratory of microstructural evolution and rheology of mantle mineral aggregates or their analogues, using a simple shear deformation geometry. A simple shear deformation geometry allows us to unambiguously identify controlling factors of microstructural evolution and to obtain large strains at high pressures and temperatures, and thus provides a unique opportunity to investigate the "structural geology of the mantle." We have developed a simple shear deformation technique for use at high pressures and temperatures (pressure up to 16 GPa and temperature up to 2000 K) in both gas-medium and solid-medium apparati. This technique has been applied to the following mineral systems (i) olivine aggregates, (ii) olivine basaltic melt, (iii) CaTiO3 perovskite aggregates. The results have provided important data with which to understand the dynamics of the earth’s mantle, including the geometry of mantle convection, mechanisms of melt distribution and migration beneath mid-ocean ridges, and the mechanisms of shear localization. Limitations of laboratory studies and future directions are also discussed. 相似文献
38.
The influence of water and stress on the lattice-preferred orientation (LPO) of olivine aggregates was investigated through large strain, shear deformation experiments at high pressures and temperatures (P = 0.5–2.1 GPa, T = 1470–1570 K) under both water-poor and water-rich conditions. The specimens are hot-pressed synthetic olivine aggregates or single crystals of olivine. Water was supplied to the sample by decomposition of a mixture of talc and brucite. Deformation experiments were conducted up to γ (shear strain) 6 using the Griggs apparatus where water fugacity was up to 13 GPa at the pressure of 2 GPa. The water content in olivine saturated with water increases with increasing pressure and the solubility of water in olivine at P = 0.5–2 GPa was 400–1200 ppm H/Si. Several new types of LPO in olivine are found depending on water content and stress. Samples deformed in water-poor conditions show a conventional LPO of olivine where the olivine [100] axis is subparallel to the shear direction, the (010) plane subparallel to the shear plane (type-A). However, we identified three new types (type-B, C, and E) of LPO of olivine depending on the water content and stress. The type-B LPO of olivine which was found at relatively high stress and/or under moderate to high water content conditions is characterized by the olivine [001] axis subparallel to the shear direction, the (010) plane subparallel to the shear plane. The type-C LPO which was found at low stress and under water-rich conditions is characterized by the olivine [001] axis subparallel to the shear direction, the (100) plane subparallel to the shear plane. The type-E LPO which was found under low stress and moderate water content is characterized by the olivine [100] axis subparallel to the shear direction, the (001) plane subparallel to the shear plane. Observations by transmission electron microscopy (TEM) and scanning electron microscopy (SEM) show that the dislocations in water-poor samples (type-A) are curved and both b = [100] and b = [001] dislocations have a similar population. Numerous subgrains are seen in water-poor samples in backscattered electron images. In contrast, water-rich samples (both type-B and type-C) contain mostly b = [001] dislocations and dislocations are straight and sub-grain boundaries are rare compared to those in water-poor samples. These observations suggest that (1) dominant slip systems in olivine change with water fugacity (and stress) and (2) grain boundary migration is enhanced in the presence of water. Seismic anisotropy corresponding to the fabrics under water-rich condition is significantly different from that under water-poor condition. Consequently, the relationship between seismic anisotropy and flow geometry in water-rich regions is expected to be different from that in water-poor regions in which type-A fabric dominates (i.e., the lithosphere). A few cases are discussed including anisotropy in the subduction zone and in the deep upper mantle. 相似文献
39.
40.
Shun-ichiro Karato 《Earth and Planetary Science Letters》2011,301(3-4):413-423
Various methods for inferring the water distribution in Earth's mantle are reviewed including geochemical and geophysical methods. The geochemical approach using the water contents of basalts shows that the water content in the source regions of ocean island basalt is generally larger than that of the source region of mid-ocean ridge basalt, but the location of the source regions of ocean island basalts is poorly constrained. Geophysical approaches have potential of providing constraints on the spatial distribution of water but their usefulness depends critically on the sensitivity of geophysical observations to water content relative to other factors, in addition to the resolution of geophysical observations. Existing experimental data on the influence of water on seismologically observable properties and on electrical conductivity are reviewed. Frequently used seismological observations such as the anomalies in seismic wave velocities and of the topography on the mantle discontinuities are only weakly sensitive to water content but more sensitive to other factors such as the major element chemistry and temperature for a typical range of water contents. In contrast, electrical conductivity is highly sensitive to water content and only modestly sensitive to other factors such as temperature, oxygen fugacity and major element chemistry. Models of electrical conductivity–depth profiles are constructed where the influence of hydrogen and iron partitioning among coexisting minerals and of the depth variation in oxygen fugacity are incorporated. It is shown (i) that the electrical conductivity varies more than two orders of magnitude for a plausible range of water content in the mantle (~ 10 ppm wt to ~ 1 wt.%) and (ii) that if water content is constant with depth, there will be a drop in electrical conductivity at ~ 410-km. Although the resolution is not as high as seismological observations, geophysically inferred electrical conductivity distributions generally show higher conductivity in the mantle transition zone than the upper mantle, suggesting that the water content in the transition zone is higher than that in the upper mantle with some lateral variations. Implications of inferred water distribution are discussed including the possible partial melting near 410-km and its role in global water circulation. 相似文献