Low Strain Rate Deformation of Directionally Solidified Alloys, and the Earth's Inner Core
The elastic anisotropy of the Earth's inner core (IC) is likely due to a lattice preferred orientation (LPO) of Fe crystals, though there is debate about the stable phase of Fe under inner core conditions. The cause of the LPO is likely due to either solidification or deformation, though it seems increasingly likely that no one explanation may suffice to understand the complex IC structure that seismologists are beginning to reveal. We have begun experiments to understand the high temperature deformation mechanism, recovery, and recrystallization of directionally solidified alloys. We start with directionally solidified, 3 weight percent Sn-Zn castings that have the columnar, dendritic structure that has been proposed for the IC. Zn is hexagonal close- packed (hcp), a probable phase of Fe in the IC. Hcp dendrites assume a platelet morphology. Typical grain sizes in our castings are 5 mm in the short dimension, with .4 mm platelet spacings. We then heat a slice of a casting to a high homologous temperature (greater than .95), at which the interdendritic Sn-rich phase melts, but the primary Zn-rich phase remains solid. While held at this temperature, we subject the slice to torsion at constant strain rate, while measuring the torque to infer the stress. We examine each slice before and after deformation for changes in crystalline orientation, microstructure (morphology and grain size), and chemical variations. So far we have obtained order one strains at low strain rates (2 x 10-6 1/s), which for fine-grained (.1 mm), pure Zn is near the boundary between diffusional flow and recrystallization. Inferring the stress during deformation (as of this writing we know only the maximum normalized stress is less than 10-5 Pa) and observing changes in microstructure and LPO will hopefully yield the deformation mechanism of these coarse-grained, dendritic alloys, as well as the lengthscale (grain size or dendritic spacing) relevant to deformation. As a control, we anneal (no strain) sample slices for similar times. The hope is that this study will help to interpret IC elastic and attenuation anisotropies, and to give insight on the relevant lengthscale and viscosity of the IC, both of which relate to the deformation mechanism.
Hemispheric Dichotomy in Seismic Structures of the Earth's Inner Core
In the past several years, we have made effort to understand the lateral and depth extent of the inner core "east-west" hemispheric dichotomy. In this presentation, we will review some peculiar characteristics of the inner core hemispheric differences that have been recently discovered. These major findings include: 1) along equatorial paths, the east-west hemispheric dichotomy in seismic velocity, with the velocity in the eastern hemisphere (40°E - 180°E) being higher than that in the western hemisphere (180°W - 40°E) by about 1%, extends larger than 400 km of the inner core. Seismic velocity and attenuation structures in the eastern hemisphere appear to be complex: an anomalously small velocity gradient in the top 235 km of the inner core, a gradual velocity transition at depths of 235-375 km, and a PREM-like velocity gradient in the deeper portion of the inner core. The attenuation structure in the eastern hemisphere has an average Q value of 300 in the top 300 km and an average Q value of 600 in the deeper portion of the inner core. Seismic velocity and attenuation structures in the western hemisphere appear to be simple: a constant gradual velocity gradient and an average Q value of 600 in the top 400 km of the inner core; 2) magnitude of the inner core anisotropy is larger in the western hemisphere (about 3% - 4%) than in the eastern hemisphere (about 0.5%), but the presence of anisotropy appears to be shallower in the western hemisphere (about 0 - 100 km) than in the eastern hemisphere (about 200 km); 3) a correlation between high attenuation and high velocity is ubiquitously observed in the seismic data. Along equatorial paths, the eastern hemisphere has high attenuation (a Q value of 300) compared to the western hemisphere (a Q value of 600). The attenuation structure along polar paths in the western hemisphere has even higher attenuation (a Q value of about 200- 250) compared to that along equatorial paths. Such a polar-equatorial difference in attenuation corresponds to a polar-equatorial difference in velocity with the velocity along polar paths being higher than that along equatorial paths by 1.3% - 2.8%; 4) near the east-west border at 20°W - 40°E (beneath Africa), seismic anisotropic structures appear to be complex within the uppermost 80 km of the inner core: a laterally undulating isotropic layer increases from 0 km beneath eastern Africa to 50 km beneath central Africa and the velocity anisotropy in the deeper portion of the inner core varies from 1.6%-2.2%. The above modeling results suggest that the east-west hemispheric dichotomy and the polar-equatorial anisotropy can be explained by different alignment of the anisotropic hcp iron crystals, under the hypothesis that the axis of high velocity corresponds to that of high attenuation.
Tectonic history of Earth's inner core preserved in seismic structure
We present here an evolutionary model of inner core growth and tectonics that couples preferential crystallization in the equatorial region (Yoshida et al.,1996) with the likely presence of density stratification within the inner core, which we let evolve over the whole history of the inner core - from its nucleation to the present time. The dynamic importance of the density stratification increases during the inner core history; we show that the deformation regime of the inner core gradually evolves from a regime where the flow penetrates deep in the inner core to a regime where the deformation is confined to the uppermost inner core, leaving the deeper inner core unaffected by any deformation mechanism. When the effect of density stratification is strong, the flow is concentrated in a shallow shear layer where the resulting strain rates are large enough to induce significant texturation. In contrast, the deep inner core is unaffected by any flow, suggesting that the deep structure of the inner core has been most likely inherited from past texturation mechanisms.
Lateral Variations in the Lowermost Outer Core
Lateral variation in the uppermost solid inner core has been documented in elastic anisotropy, attenuation, and scattering of high frequency body waves. Less well established are lateral variations in structure in the lowermost outer core (F region), on the liquid side of the solidifying boundary of the inner core (ICB). The assumption of lateral homogeneity in the lowermost outer core is consistent with a turbulently convecting, low viscosity, outer core with negligible lateral gradients in chemistry and temperature from its top to bottom. In conflict with this assumption are clues to the existence a dense, high viscosity, chemically distinct region in the lowermost 400 km of Earth's outer core. These include evidence for a thin zone of non-zero rigidity and high viscosity above the inner core, the travel times and decay of compressional waves diffracted around the inner core boundary, and the lateral variation in the difference of the travel times of compressional waves that are reflected by the (ICB) from those that bottom above the (ICB). These observations are reexamined for possible correlations of lateral variations in F region structure with lateral variations for large scale flow near the inner core boundary predicted by numerical geodynamos from lateral variation of heat flow through the core-mantle boundary inferred from seismic tomography.
Large scale imaging of the lower mantle
In our previous studies we developed a method for imaging heterogeneity at and near the core mantle boundary (CMB) with a generalized Radon transform (GRT) of broadband ScS (transverse component) and SKKS (radial component) wavefields and their precursors and coda, and we developed a statistical model for producing images of the D" discontinuity at variable confidence levels. Inverse scattering with ScS enables large-scale imaging of the lowermost mantle, but only a few geographic regions are amenable to topside scanning of the CMB with ScS (e.g., Central and North America, East Asia) due to the data coverage. In contrast to ScS, SKKS provides excellent data coverage of the core mantle boundary region over large areas, including those that are not adequately sampled -- or not at all -- by ScS data. This allows hemisphere scale imaging of the lower mantle using SKKS data. And at regions where both SKKS and ScS data have reasonably good coverage a joint inversion is applied to generate better image. And a multi-scale analysis through 3-D curvelet transform is applied to the images we obtain. About 3,000,000 SKKS radial components are used in our study. Our preliminary results show a discontinuity about 200-300 km above the CMB almost everywhere.
Spin transitions in Fe-bearing MgSiO3 in the Earth's lower mantle
We study the spin transition in Fe-bearing MgSiO3 perovskite and post-perovskite at Earth's lower mantle conditions. We analyze the crystallochemical effects induced by the presence of Fe in the structure and we monitor the compressibility as a function of Fe spin state and Fe content. We have found that at low pressures the high-spin antiferromagnetic structure is the most stable one. At mantle pressures, the high-spin to low- spin transition occurs in perovskite in association with a small structural distortion on the Fe site. This distortion is responsible for the reduction of the coordination volume that favors a smaller volume iron. There is no obvious change in the structural compressibility during the spin transition. Next we derive the seismic properties of (Mg,Fe)SiO3 perovskite and post-perovskite as a function of Fe2+ spin state and Fe distribution and observed that the effects of Fe2+ spin state are rather small on the compressional seismic wave velocities and larger on the shear seismic wave velocities. During the calculation of the elastic moduli of post-perovskite from density functional perturbation theory, we found that the low-spin configurations are dynamically unstable. We analyze these instabilities and we find new stable structures. We determine the elastic tensors for the new structures and discuss in detail their seismic properties as well as the implications of the spin transition on the D" layer.
Spin transition in ferrous iron in MgSiO3 perovskite under pressure
We present a density functional study of the pressure-induced spin transition in ferrous iron in MgSiO3 perovskite. We address the influence of iron concentration and configuration (structural and magnetic), as well as technical issues such as the nature of the exchange correlation (XC) functional (CA-LDA versus PBE-GGA) on the spin transition pressure. Supercells containing up to 160 atoms were adopted to tackle these issues. We show that there are preferred configurations for high-spin and low-spin iron and that the spin transition pressure depends strongly on iron concentration and XC functionals. We also address changes of atomic structure around Fe atoms and electronic structure including the blue shift accompanying the spin transition. Research supported by NSF/EAR 013533, 0230319, and NSF/ITR 0428774 (VLab). Computations were performed at the Minnesota Supercomputing Institute and Indiana University's BigRed system.
Topography of Transition Zone Discontinuities beneath the Hawaii-Emperor Seamount Chain
A generalized Radon transform (GRT) is applied to SS waves reflected at the underside of seismic discontinuities in order to detect, image, and characterize transition zone interfaces under Hawaii and the Hawaii-Emperor sea mount chain. The GRT makes use of scattering theory and extracts structural information from broad band data windows that include precursors to SS (which are the specular reflections at the discontinuities that form the main arrivals) as well as non-specular scattered energy (which is often discarded as noise). More than 150,000 seismograms (from the IRIS Data Management Center) are used to form a 3-D image of the transition zone discontinuities beneath the central Pacific. In addition to clear signals near 410, 520, and 660 km depth, the data also reveal scatter interfaces near 370 km dept and between 800-1000 km depth, which may be regional, laterally intermittent scatter horizons. Our results reveal a conspicuous thinning of the transition zone due to uplift of the 660 discontinuity and downwarping of the 410 discontinuity west of Hawaii. This observation may suggest the presence of a deep-rooted mantle plume (with a lower-mantle origin) underneath Hawaii hotspot. The part with the largest topography difference from the ambient mantle is located several 100 km west of the active volcanoes of Hawaii, which may imply that the presumed plume conduit is tilted, for instance by large scale mantle advection. This observation may put (local) constraints on "mantle wind" and have important implications for our understanding of mass flux across the transition zone and the geological evolution of the Hawaii-Emperor sea mount chain.