MR23C-1514
Transport Properties at Different Scales Using Digital Rocks
In this paper we explore how rock heterogeneity translates into scale-dependent permeability and formation factor, as well as the relation between them. We used a detailed 3-D representation of pore structure of unconsolidated sand obtained from X-ray CT scan. For the samples, loose sand grains were collected from Pomponio Beach and Ano Nuevo costal dune (eolian). These loose sand grains were mixed with epoxy, packed and 3D images were digitized by High-resolution X-ray tomography (CT- scanning). Fluid flow and electrical current were computationally simulated through subsets of the microstructure at different scales. The autocorrelation lengths, a, of the entire sample were calculated in three different directions. The autocorrelation lengths show slight anisotropy in Z-direction in both samples. Since the anisotropy wasn't large so it wasn't considered further in the current analysis. Further, the anisotropy in Z-direction can be attributed to change in the resolution in Z-direction as the artifact of the 3D CT scans. The average autocorrelation, however, was used to calculate the Representative Elementary Volume (REV). Keehm (2003) suggested for single phase fluid flow the REV should be approximately ten times the autocorrelation length, a. Hence for the current analysis a REV of 200 x 200 x 200 pixels for the Pomponio Beach sands (a = 20 pixels) while a REV of 120 x 120 x 120 pixels for Aņo Nuevo costal dune sands (a = 12 pixels) were considered. The size of the subsets randomly selected from the microstructure varied from 200 x 200 x 200 pixels (= 10a x 10a x 10a) to 25 x 25 x 25 pixels (= 1.25a x 1.25a x 1.25a) for Pomponio Beach sands where as the size of the subsets for Aņo Nuevo costal dune sands altered from 175 x 175 x 175 pixels (= 14.5a x 14.5a x 14.5a) to 25 x 25 x 25 pixels (= 2.1a x 2.1a x 2.1a). The number of subsets selected for the analysis increased as the size of subset decreased in order to obtain statistically meaningful results. As can be observed the maximum size of subsets chosen was approximately equal to or greater than the REV of the sample. The size of subsets was significantly reduced from the REV sizes in order to study the effect of scales on the transport properties as well as the relationships between these transport properties. Electrical conductivity and single-phase permeability simulations were carried out for the subsets thus obtained. As the size of subsets decreased, the scatter in the computed permeability and resistivity increased although they still followed the expected trends of effective medium relations in each case. Different effective medium relations used to compare with the simulated data in current paper were: (a) For porosity-permeability relation: Kozeny- Carman relation (Carman, 1961), (b) For porosity-formation factor relation: Archie's equation (Archie, 1942) and (c) For permeability-formation factor: Katz and Thompson (Katz and Thompson, 1987). The clouds of the simulated data of different size subsets as well as their corresponding means tended towards a higher value as the size of subsets was decreased though they still fell on the effective medium trend line. However, the computational time required for calculating the bigger subset sizes was far greater than for smaller subset sizes.
MR23C-1515
Quantum Monte Carlo Study of the Elastic Instability of Stishovite Under Pressure
Stishovite is a octahedrally coordinated polymorph of silica which becomes stable at pressures consistent with Earth's lower mantle (10 GPa). The elastic properties of stishovite are potentially important for explaining seismic structure and it serves as a model system for other six-coordinated silicates. At a pressure near 50 GPa, stishovite transforms to the CaCl2-type structure due to an instability in the elastic shear modulus, c11-c12. The instability was predicted by density functional theory (DFT) calculations and later confirmed by Raman spectroscopy and x-ray diffraction. This well understood instability is used to benchmark the ability of Quantum Monte Carlo (QMC) to predict elastic constants. QMC calculates the softening of the elastic shear modulus over the pressure range of 0 to 50 GPa. Results show the QMC elastic shear modulus softens from 270 to 0 GPa in agreement with previous DFT and experimental results. Although at factor of 1400 more in computational cost over DFT, QMC is capable of predicting elastic properties of minerals under pressure accurately. Computations were performed at NERSC on the Cray-XT4 within the early user program. Financial support is provided by the NSF (EAR-0530282, EAR-0310139) and the DOE (DE-FG02-99ER45795).
MR23C-1516
Electronic properties in the bismuthinite-aikinite series
We perform first-principles calculations using the density-functional theory to investigate the electronic properties of several phases along the bismuthinite (Bi2S3)-aikinite (PbCuBiS3) join. The structures of these compounds can be described in terms of stacking of parallel [Bi4S6]n ribbons. The PbCu <e;> Bi substitution preserves the one-dimensional character of the structure. The electronic band structure exhibits a pronounced quasi-one-dimensional character with the electron localized along the ribbons. The different bands are well separated into several groups corresponding to s, p and s-p hybridized orbitals present in the system. The pressure narrows the electronic gap and slightly increases the connectivity of the structure.
MR23C-1517
Thermodynamics properties and phase transitions in enstatites
Thermodynamics properties of low- and high-clinoenstatite Mg2SiO6 were obtained by means of first principles quasi-harmonic calculations. Structural parameters, equations of state, and pressure dependence of bulk moduli are in excellent agreement with available experimental data. The LDA and GGA determined phase boundaries bracket the experimental one. They have essentially the same Clapeyron which is in excellent agreement with measurements. This is the usual trend displayed by these functionals.
MR23C-1518
An efficient method for computing high PT elascticity by first principles
First principles quasiharmonic (QHA) free energy computations play a very important role in mineral physics because they can predict accurately the structure and thermodynamic properties of materials at pressure and temperature conditions that are still challenging for experiments. They also enable calculations of thermoelastic properties by obtaining the second derivatives of the free energies with respect to Lagrangian strains. However, these are demanding computations requiring 100 to 1000 medium size jobs. Here we introduce and test an approximate method that requires only calculations of static elastic constants, phonon VDOS, and mode Gruneisen parameters for unstrained configurations. This approach is computationally efficient and decreases the computational time by more than one order of magnitude. The human workload is also reduced substantially. We test this approach by computing high PT elasticity of MgO and forsterite. We show one can obtain very good agreement with full first principles results and experimental data. Research supported by NSF/EAR, NSF/ITR (VLab), and MSI (U of MN)
MR23C-1519
Thermodynamically consistent model for the elasticity of ferropericlase across the iron spin transition
First principles quasiharmonic computations of thermoelastic properties of single component phases at high pressure and temperature are quite accurate in the absence of anharmonic fluctuations or strong electronic correlations. The presence of more than one component increases considerably the degree of difficulty of these calculations particularly if the second component has strongly correlated electrons undergoing a spin transition under pressure. Ferropericlase is an outstanding example of primary importance for our understanding of the lower mantle. Here we describe in detail all the ingredients and controlled approximations that went into the computation of the high PT elastic properties of ferropericlase at lower mantle conditions.
MR23C-1520
Electrolyte-promoted demineralization of biogenic, vitreous, and crystalline silica: A density functional investigation
The dissolution of amorphous and crystalline varieties of SiO2 is an integral part of the global biogeochemical cycle of silicon. Nanoparticulate biogenic silica produced by marine phytoplankton and terrestrial plants are of particular interest because their enhanced reactivity and abundance make them important sources and sinks of dissolved silicon in natural environments. Recent experimental results on (100) surfaces of quartz show that the dominant dissolution mechanism in simple H2O solutions is by retreat of Q2 groups along step edges. In the presence of electrolytes, rates are accelerated by up to 100X in the presence by a crossover in the dominant dissolution mechanism to nucleation of vacancy islands at Q3 terminated species (Dove et al., PNAS, 2005). While the control of surface coordination in reactivity is clear, the molecular pathway by which electrolytes induce dissolution by a nucleated process remains poorly understood. The results of previous ab initio investigations of Si-O bond hydrolysis by water have demonstrated that the reaction proceeds through the dissociative adsorption of H2O at the silica surface, resulting in the formation of a pentacoordinated Si transition state, followed by the transfer of one of the water bound hydrogen atoms to a bridging oxygen in the SiO2 bonded network, and breakage of the Si-O bond. Assuming a similar reaction path, the specific effects of hydrated group II metal cations (Mg2+, Ca2+, Sr2+, Ba2+) on the energetics of Si-O bond hydrolysis have been investigated with density functional methods (B3LYP) and a relatively large neutral silica cluster (H8Si6O16). Reactant, product, and transition states for Q3 to Q2 hydrolysis in the presence and absence of the afore-mentioned cations have been determined with all electron (6-31G(d)) and effective core potential (SDDALL) Gaussian basis sets. The free energy of activation for Q3 to Q2 Si-O bond hydrolysis was determined to be approximately 5 kJ/mol lower for Ca2+ than Mg2+ at the 6-31G(d) level. Similar calculations for Ca2+, Sr2+ and Ba2+ using the SDDALL basis set yielded similar molecular geometries to the all-electron results, and free energies of activation for Sr2+ and Ba2+ that are ~10 kJ/mol and ~15 kJ/mol lower than for Ca2+ respectively. These results are consistent with experimental results, which show that these cations increase the maximum rate of silica dissolution in the order Mg2+ < Ca2+ < Sr2+ < Ba2+. Further investigation of other possible hydrolysis pathways including cationic species and or surface charge is also in progress.
MR23C-1521
A Computational Study of Ionic Vacancies and Diffusion in MgSiO3 Perovskite and Post- perovskite
We have performed first-principles simulations within density functional theory to investigate the effects of pressure on the formation of defects (ionic vacancies) and ionic diffusion in the perovskite (pv) and post- perovskite (ppv) phases of MgSiO3. Our results show that the predicted formation enthalpies of three Schottky (MgO, SiO2 and MgSiO3) defects are similar between the two phases at high pressures (100 to 150 GPa) with MgO Schottky defect being the most favorable. However, the calculated activation enthalpies and activation volumes of diffusion are shown to differ substantially between them. In particular, the activation enthalpies for Mg and Si diffusion in ppv are smaller than the corresponding values for pv, for example, by factors of 2.2 and 3.4, respectively, at 120 GPa, whereas the O migration enthalpy of ppv is only slightly larger than that of pv. The easy migration paths of the cations in ppv are shown to take place along the <100> direction in which Si-O octahedra share the edges. Visualization of the simulation data reveals that the vacancy defects and migrating ions induce substantial distortions in the atomic and electronic structures around them. It is suggested that diffusion is equally easy for all three species in ppv and is likely to occur through extrinsic processes near the bottom of the lower mantle. Our results are expected to be useful in modeling mantle conductivity and dynamics. Future work will focus on investigation of more complex mechanisms such as coupled diffusion or diffusion in the presence of other vacancies, and interstitial mechanisms. Our preliminary results show that in the presence of an O vacancy, the activation volume of Si diffusion becomes negative.
MR23C-1522
Pressure Correction In First-Principles Calculations: MgO As An Example
First-principles (FP) calculations based on Density functional theory (DFT) has been widely used in the studies of structural, thermoelastic, rheological, as well as electronic properties of Earth-forming materials. The exchange correlation term is, however, implemented based on various approximations and it is believed to be the main reason of discrepancies between experiments and theories. In this work, by using MgO as an example, we examine the difference between the pressures calculated by two commonly used versions of exchange correlation approximation, namely, the local density approximation (LDA) and the generalized gradient approximation (GGA). We have performed extensive first-principles calculations at various temperatures and found that the pressure difference vary systematically with temperature and simulation cell volume. Our findings may be useful to the prediction of mineral properties at thermodynamic conditions compatible to deep planets
MR23C-1523
First-Principles Prediction of Crystal Structures at High Temperatures Using the Quasiharmonic Approximation
We show here how first-principles quasiharmonic approximation (QHA) calculations in its simplest statically constrained form can be used to predict crystal structures at high temperatures. This approximation has been extensively used to investigate thermodynamic properties of Earth forming minerals and has offered excellent results for the major mantle phases at relevant conditions. We carefully compare QHA predictions of crystal structures using the local density approximation with crystallographic data in MgSiO3 perovskite at high pressures and temperatures. Small but systematic deviations in the lattice parameters (at most 0.3%) appear at high temperatures (T>2000 K) and are associated with the development of deviatoric thermal stresses. An iterative scheme is proposed to eliminate these spurious thermal stresses and further improve the quality of the predictions of this popular and successful thermodynamics method.
MR23C-1524
Investigation of high-pressure MgCO3 phases
The high-pressure phases of magnesium carbonate are investigated by variable cell first-principles molecular dynamics simulations. At pressures compatible to lower mantle conditions (~120 GPa), the carbon atoms are surrounded by 4 oxygen atoms, which is consistent with the work of Skorodumova et al. (2005). Perovskite phase is observed at pressures greater than 300 GPa, but its stability is still subject to further studies. In addition, the possibility of getting post-perovskite phase is also discussed. The results may be useful to the constructions of interior models of giant planets, which may lead to a better understanding in giant plants physics.
MR23C-1525
Electrical conductivity of FeSi under pressure
Chemical arguments suggest that FeSi can result from the reaction of the Fe-rich perovskite and post-perovskite in the D" layer with the Fe of the liquid core [1]. FeSi could thus accumulate in the lower parts of D", in particular the ultra-low velocity zones (ULVZ). Physical arguments (high density) and seismological arguments (low velocities) plead for its existence in these regions [2]. We compute the temperature-dependent electronic conductivity of FeSi from density-functional perturbation theory. From the phonons and electron-phonon coupling we solve the Boltzmann transport equations to the lowest order to give the electrical and thermal conductivities [3]. We find that the electrical resistivity of FeSi at lower mantle and outer core conditions is on the order of 3.5-4.0 micro Ohm m at 2500-3000K. This is about twice the resistivity of Fe in the same conditions, which is similar to the assumed resistivity of the outer core. If present in significant amounts, then the large values of the conductivity computed here suggest FeSi as the major conducting phase in the D" and ULVZ, and the mineral that would ensure the electromagnetic coupling between the mantle and the core. [1] E. Knittle and R. Jeanloz, Science, 251, 1438 (1991). [2] R. Caracas and R.M. Wentzcovitch, Geophys. Res. Lett. 31, No. 20, 10.1029/2004GL020601 (2004) [3] S.Y. Savrasov and D.Y. Savrasov, Phys. Rev. B, 54, 16487 (1996).
MR23C-1526
Metadynamics study of iron phases at the Earth's inner core conditions
Iron is the main element in the Earth core and the stable phase of iron in the Earth's solid inner core is still highly controversial (Sambridge, 2003). In order to predict the properties of iron at high pressures and temperatures, here, we use a novel simulation technique, first-principles metadynamics (Martonak et al., 2003, see also Oganov et al., 2005 ), to unveil the stepwise mechanism of the pressure-induced (350 GPa) transformations between bcc, fcc and hcp iron at the temperatures of 2000 K and 6000 K respectively. We predicted the bcc \{110\}, fcc \{111\} and hcp \{111\} slip planes at the Earth inner core conditions. We also predicted some metastable iron phases (e.g. R-3M and P-6M2 structures) on the pathway of the phase transition. The c/a ratios of the iron structures are also calculated at the simulated conditions. Implications of these results for seismic anisotropy in the Earth inner core will be discussed (Zhang, 2007). References: [1] Sambridge M., (2003) An Ensemble View of Earth's Inner Core. Science, 299, 529-530; [2] Martonak R., Laio A., and Parrinello M., (2003). Predicting crystal structures: The Parrinello-Rahman method revisited. Phys. Rev. Lett. 90, 075503; [3] Oganov A.R., Martonak R., Laio A., Raiteri P., Parrinello M. (2005). Anisotropy of Earth's D" layer and stacking faults in the MgSiO3 post-perovskite phase. Nature 438, 1142-1144; [4] Zhang F. & Oganov A.R., (2007) Metadynamics study of iron phases at the Earth's inner core conditions. (in prep.) http://olivine.ethz.ch/~feiwu/07AGU.html
MR23C-1527
Space-Time Multiresolution Approach to Atomistic Visualization: Application to Silicate Liquids
Ever-larger amounts of data related to the structural, electronic and mechanical properties of Earth materials (in their solid and liquid phases) are routinely produced by massively parallel computer simulations. The simulated data, which are time-dependent and three-dimensional in the nature, are not illuminating by themselves; gaining insight into them is, however, a non-trivial task. In order to take advantage of maximal information contained in various data related to modeling of materials including those of direct geophysical relevance, we have been developing a scalable and adaptive visualization framework, which aims to fulfill domain-specific needs thereby justifying the effectiveness of visualization for fundamental interdisciplinary science. In this presentation, we will talk about our recently developed interactive atomistic visualization scheme. We integrate the complex analysis and rendering of a given atomic position-time series by using an efficient space-time multiresolution approach. On the fly extracted data, which are rendered in an interactive manner, represent a given system at diverse length- (e.g., nearest or second-nearest neighbors or beyond) and time- (instantaneous, finite intervals, finite-time-span or overall averages) scales. In particular, the coordination environments and cluster structures are visualized to gain insight into the structural behavior whereas a variety of displacement data and covariance matrices are visualized to understand the dynamical behavior. It is shown that the interactive frame rates are achievable for systems consisting of up to a thousand atoms in a normal desktop environment. Such system sizes are typical in the case of today's common first-principles molecular dynamics simulations of complex materials systems including geophysically relevant silicate and oxide phases for which we justify the effectiveness and usefulness of our proposed scheme.
MR23C-1528
First-principles Study of Perovskite, Post-perovskte and Molten MgSiO3
We report our recent work on First-principles molecular dynamics (FPMD) simulations of solid MgSiO3 perovskite and post-perovskite, and molten MgSiO3 at core-mantle boundary (CMB) conditions. The equations of state are determined at pressures up to 200 GPa and temperatures up to 6000K. The post- perovskite phase is found to be favoured over the perovskite at pressures above ~102 GPa at zero temperature. Melting of MgSiO3 has been observed by heating both perovskite and post-perovskite at high temperatures (~6000 K). The results indicate that the two (simulated) liquids considerably have the same physical properties as expected. The electronic structures of solid and molten MgSiO3 are also studied.
MR23C-1529
First-Principles Study of Elasticity and Decomposition of Phase D
We have investigated the compressional behavior and elastic properties of phase D (MgSi2H2O6) for pressures up to 60 GPa using first-principles calculations. The calculated bulk modulus K0 is 156.2 GPa; shear modulus G0 is 122.6GPa; p wave velocity Vp is 9.6 Km/s; shear wave velocity Vs is 5.9 Km/s. Their pressure derivative dK/dP and dG/dP are 4.88 and 2.29; dVp/dP and dVs/dP are 0.083 and 0.041. At 0 GPa, Phase D has an elastic anisotropy of 1.21 and 1.19 percent, for compressional and shear waves, respectively, which decreases to 1.03 and 1.07 percent at 45 GPa, our alculated decomposition pressure of phase D. We find that phase D is most likely decomposes by absorbing MgO to form MgSiO3 perovskite and H2O at 45 GPa; we also find that it is unlikely that phase D produces free SiO2 upon decomposition. The decomposition of phase D causes a 1 percent increase in compressional velocity and the shear wave velocity remains unaffected.