Shear-Induced Porosity Bands in Three Dimensions
When a compacting porous layer, consisting of a fluid and a ductile solid matrix, is sheared, melt spontaneously segregates into high and low porosity bands if the viscosity of the matrix decreases with porosity. The resulting high porosity bands have been suggested to form high-permeability conduits beneath mid-ocean ridges that can help to channel fluid toward the ridge axis and the band structure has been suggested as a mechanism for decreasing viscosity in the asthenosphere. To date, theoretical and numerical investigations of shear-induced porosity bands have been carried out in two space dimensions. In this contribution, linear theory and numerical modeling of shear-induced melt bands is carried out in three dimensions but assuming two dimensional background shear. We show that when the viscosity of the matrix is porosity dependent but strain-rate independent, two dimensional bands are formed at essentially the same angle to the shear plane as those seen in two dimensional studies. When the viscosity of the matrix is strain-rate dependent, however, bands form and have significant variation in the third space dimension. The bands are also seen to occur at low angles to the shear-plane, similar to what is seen in laboratory experiments. An implication of this work is that shear bands beneath mid-ocean ridges are likely to have a significantly three-dimensional character even if the background flow in these regions is close to two dimensional which would lead to greater along strike variation in melt flow.
Waves and channels for melt migration in an upwelling mantle
The distribution and segregation of partial melts in the mantle have been a subject of extensive geochemical and geophysical studies. To better our understanding of this important problem, we conduct linear stability analysis and high-order accurate numerical simulations of reactive dissolution along a solubility gradient in a viscously deformable, chemically reactive, and vertically upwelling porous column. Linear stability analyses reveal three distinct regimes of reactive dissolution: (1) an unstable fingering regime where small perturbations in porosity grows monotonically; (2) an unstable wave regime where small perturbations in porosity undergo oscillatory growth; and (3) a stable regime where infinitesimal perturbations in porosity decay exponentially. The stability fields depend on three dimensionless parameters: relative upwelling rate, dimensionless solubility gradient, and a fertility ratio. The fingering instability arises from a positive feedback between dissolution and melt percolation. The oscillatory instability results from strong nonlinear feedbacks among compaction, dissolution, and upwelling. Similar to the fingering instability, dissolution and melt flow are destabilizing and compaction is stabilizing. However, in the wave regime, strong nonlinear interaction between compaction and dissolution also gives rise to decompaction which is destabilizing. Numerical simulations show that regions of compaction and decompaction alternate along the vertical direction, resulting in a phase-shift between regions of maximum dissolution rate and regions of maximum compaction and decompaction rates along the vertical direction. This behavior contrasts sharply with the fingering regime where decompaction is absent in the upwelling column and regions of maximum dissolution rate coincide with regions of maximum compaction rate. A parameter study suggests that the wave regime may play an important role for melt migration beneath the mid-ocean ridges. In this case, the horizontal and vertical dimensions of the compaction-dissolution waves are comparable to compaction length. These porosity waves propagate vertically with a phase speed that is an order of magnitude faster than the upwelling rate but is slower than the melt percolation rate. This is different from the solitary wave induced by purely mechanical compaction. High resolution numerical simulations reveal strong interactions between compaction-dissolution waves and high-porosity melt channels. High-porosity melt channels nucleate along the nodal lines of the porosity waves in the upper part of the simulation domain. The upper part of the melt channel is opx-free dunite, whereas the lower part is harzburgite. A wide opx-free dunite channel may contain two or more high-porosity melt channels. A primary high-porosity melt channel developed in the deep mantle may excite secondary and tertiary melt channels in the shallow part of the melting column. The spatial relations among the compaction-dissolution waves, high-porosity melt channels, and their associated lithologies documented in this study may shed new light on a number of field, petrological, geochemical, and geophysical observations related to melt migration in the mantle.
Thermodynamic model for partial melting of peridotite by system energy minimization (Invited)
Partial melting of the mantle is an essential process for both material and thermal evolution of the Earth. Thermodynamic modeling is a general approach to describe the melting and can provide an internally consistent model in terms of phase assemblage, composition, and mass and energy balance. However, there exist a number of problems with the previous thermodynamic models, e.g., in algorism for energy minimization of the system, or concerning definition and thermodynamic properties of silicate liquid end-components. In this study, an energy minimization algorism for melt-present system and thermodynamic formulation for molar Gibbs free energy (G_molar) of silicate liquid with newly calibrated thermodynamic parameters are provided to make straightforward thermodynamic descriptions of melting reaction. The algorism presented in this study is straightforward: it calculates gradient of total Gibbs free energy of the system (G_total) with respect to any tiny mass of dissolution or solidification of liquid and solid end-components under the constraint of closed system at constant P and T. Molar contents of solid and liquid end-components are recalculated along the steepest gradient of G_total at each calculation step. Equilibrium state of the system is found where the gradient becomes zero with respect to any tiny mass perturbation, hence G_total is minimized. G_molar of silicate liquid end-component is formulated appropriately for the minimization. In the formulation, specific heat of each liquid end-component is expressed based on "dCp" that is the difference of molar specific heat between corresponding liquid and solid end-component. Previously reported thermodynamic properties and enthalpies of melting of solid end-components are utilized to calculate G_molar of liquid end-components in this formulation. The energy minimization algorism and formulation have been applied to the system SiO2-Al2O3-FeO-Fe3O4-MgO-CaO with olivine, clinopyroxene, orthopyroxene, spinel and silicate liquid. This specific program describes melting of spinel lherzolite at 1 GPa. The dCp values and compressibilities of liquid end-components have been calibrated utilizing previously reported results of high-pressure melting experiments of mantle peridotite and thermodynamic properties of rock forming minerals. In this treatment, G_molar of pure liquid end-component is calibrated at pressure and temperature correspond to melting temperature of mantle rocks, instead of extrapolation from standard state properties. To test these equations and parameters with the simplest model, ideal solution is employed for the mixing model of silicate liquid in this study. Calculated phase relations show a good agreement with experimentally determined melting phase relations of the mantle peridotite. The thermodynamic model predicts the melting phase relationship between bulk composition, temperature, phase fractions including melt fraction remarkably well compared to the previous models such as pMELTS (Ghiorso et al., 2002). On the other hand, melt compositions are not well reproduced when compared with pMELTS. Calibration misfit has some correlation with compositions of melt and/or minerals, suggesting that composition dependent non-ideality of silicate liquid could be required to derive more accurate melt composition.
Comparison of Deep Upper-Mantle Melting in Varying Tectonic Environments: Insights from Seismic Observations (Invited)
Seismic observations of low velocity zones in the deep upper mantle or directly atop the mantle transition zone are becoming increasingly common. These low velocity zones are most commonly interpreted as partially molten layers with neutral or negative buoyancy relative to the ambient mantle. The information given by the properties of seismic waves used to probe a region provide important constraints and implications for layer thickness and the extent of partial melting. The tectonic setting in which these layers are detected should also be taken into consideration when interpreting the cause of these features. While observations to date are most commonly located above subducting slabs, similar layers oceanward of subduction and beneath ocean islands are also observed and may require different melting mechanisms, such as the combined effects of increased water content with increased temperature. Detailed observations of these layers are crucial for joint interpretation of seismic observations with mineral physics experiments and/or geodynamics models. Similarities and differences between observations of low velocity layers in a variety of tectonic settings will be discussed, along with implications for interpretation.
Storage of water in (Mg,Fe)SiO3-perovskite: Synthesis from natural samples
There is significant ambiguity as to the water storage capacity of (Mg,Fe)SiO3 perovskite under lower mantle conditions depending upon the synthesis method and starting materials. Here we present the results of high-pressure synthesis of perovskite from two natural Bamble enstatite samples (Mg/(Fe+Mg) = 0.75; Al2O3 < 0.1 wt%), which were synthesized in the laser-heated diamond anvil cell at 1500-2000 K and 25-65 GPa. One sample is dry with no detectable OH in FTIR, and the second sample contains ~0.08 wt% H2O. The anhydrous sample transforms to perovskite completely with no evidence of other phases present. The hydrous sample, however, forms predominantly perovskite, with some runs resulting in additional minor stishovite, phase D, ferropericlase or a combination of these. The zero-pressure volume and bulk modulus of the resulting perovskite, are indistinguishable between the two sets of experiments (V0 = 163.8(2) Å3 and K0 = 259(4) GPa), indicating little compositional differences. Infrared spectroscopy of the hydrous sample consistently reveals a disordered hydrogen structure consistent with phase D or OH in residual melt (quenched as glass), largely indistinguishable between experiments producing either just perovskite or a combination of perovskite and minor phases. Distinct OH stretching modes become evident upon cooling below 100 K with peaks at 3576, 3378, 3274, and 3078 cm-1, with no evidence of OH in either stishovite or ferropericlase. Additional multiple O-H-O bending modes are evident at between 1255 and 1630 cm-1. We interpret these results as the formation of a minor fraction of hydrous melt at temperatures at or below 1500 K for all pressure to 65 GPa, with a dry residual perovskite phase.
Diffusion and Viscosity of Anorthite and Silica Liquids from First Principles Molecular Dynamics Simulations
We have carried out first principles molecular dynamics simulations of CaAl2Si2O8 (anorthite) and SiO2 liquids as a function of pressure and temperature within density functional theory. Along the 3000 K isotherm, the self-diffusion coefficients of Al/Si and O vary anomalously - they initially increase with pressure, reach a maximum (5 to 15 GPa), and then decrease upon further compression. The calculated melt viscosity also shows an anomalous behavior with a local minimum around similar pressure. We find that anorthite liquid is much more mobile and shows weaker anomaly than silica liquid because of its high content of nonbridging oxygens (NBO) and oxygen triclusters (O3). The predicted pressure variations can be associated with structural changes consisting of the pressure-induced maximum in the abundance of pentahedral states (fivefold Al/Si-O coordination) and rapid increase in the O3 abundance in both liquids.
Chemical Reaction at the Core-Mantle Boundary from Experimental Study with a Diamond-Anvil Cell (Invited)
Element partitioning between molten iron and mantle minerals was investigated to 146 GPa by a combination of laser-heated diamond-anvil cell and analytical transmission electron microscope. The chemical compositions of co-existing quenched molten iron and (Mg,Fe)SiO3 perovskite/ferropericlase were determined quantitatively with energy-dispersive X-ray spectrometry and electron energy loss spectroscopy. The results demonstrate that the oxygen solubility in liquid iron co-existing with ferropericlase decreases with pressure to 38 GPa and, whereas the pressure effect is small at higher pressures. It was also revealed that the quenched liquid iron in contact with perovskite contained substantial amounts of oxygen and silicon at the core-mantle boundary (CMB) pressure. The chemical equilibrium between perovskite, ferropericlase, and molten iron at the P-T conditions of the CMB was calculated in Mg-Fe-Si-O system from these experimental results. Note that perovskite is a predominant phase instead of post-perovskite above 3500 K at the CMB pressure. We found that molten iron should include oxygen and silicon more than required to account for the core density deficit of below 10% when co-existing with both perovskite and ferropericlase at the CMB. This suggests that the bulk outer core liquid with <10% density deficit is not in direct contact with the mantle. Dissolutions of light elements from the mantle can produce a gravitationally stratified liquid layer at the topmost outer core, which can be responsible for the low-P wave velocity layer observed there. Such layer physically separates the mantle from the bulk outer core liquid, hindering the chemical reaction between them.
Visualizing Earth’s Core-Mantle Interactions using Nanoscale X-ray Tomography
Early-stage, core-mantle differentiation and core formation represent a pivotal geological event which defined the major geochemical signatures. However current hypotheses of the potential mechanism for core-mantle separation and interaction need more experimental input which has been awaiting technological breakthroughs. Nanoscale x-ray computed tomography (nanoXCT) within a laser-heated diamond anvil cell has exciting potential as a powerful 3D petrographic probe for non-destructive, nanoscale (<40nm) resolution of multiple minerals and amorphous phases (including melts) which are synthesized under the high pressure-temperature conditions found deep within the Earth and planetary interiors. Results from high pressure-temperature experiments which illustrate the potential for this technique will be presented. By extending measurements of the texture, shape, porosity, tortuosity, dihedral angle, and other characteristics of molten Fe-rich alloys in relation to silicates and oxides, along with the fracture systems of rocks under deformation by high pressure-temperature conditions, potential mechanisms of core formation can be tested. NanoXCT can also be used to investigate grain shape, intergrowth, orientation, and foliation -- as well as mineral chemistry and crystallography at core-mantle boundary conditions -- to understand whether shape-preferred orientation is a primary source of the observed seismic anisotropy in Earth’s D” layer and to determine the textures and shapes of the melt pockets and channels which would form putative partial melt which may exist in ultralow velocity zones.