MR11A-01 INVITED
Quantum Monte Carlo Computations for Minerals at High Pressures
We have performed Quantum Monte Carlo (QMC) computations for silica, FeO, and c-BN as functions of compression. QMC uses no approximate density functional, and the many-body, correlated, Schrödinger equation is effectively solved stochastically. In spite of the great success of DFT there are still some fundamental problems that need improvement. First is the need for increased accuracy for some rather ordinary materials such as silica. Although the local density approximation (LDA) gives excellent results for individual silica phases, such as the CaCl2 transition, it is not so good for comparing energetics of very different structures, such as quartz versus stishovite. Our QMC results will be used to improve density functionals, and show the way towards more accurate computations for Earth materials. Thermal contributions are included using density functional perturbation theory with the code ABINIT. We have computed the shear elastic constant c11-c12 in stishovite, which is associated with the phase transition to the CaCl2 structure, with QMC. We are developing a first-principles high-pressure standard using cubic BN. For this we are performing the first all-electron QMC computations for solids with atoms heavier than He. We are also performing QMC computations on FeO to understand better the importance and nature of magnetism in FeO under pressure. This work is supported by NSF grants EAR-0530282, EAR- 0310139, and by DOE contract DE-FG02-99ER45795 to John Wilkins. Computations were performed on blueice at NCAR under a BTS grant, and on tungsten and abe at NCSA, and at the Carnegie Institution of Washington.
MR11A-02 INVITED
Comparison of Groundstate Quantum Monte Carlo, Finite Temperature Path Integral Monte Carlo with Density Functional Theory and GW Calculations and Application to Helium at High Pressure
In this talk, four different computational methods will be compared, their advantages and disadvantages discussed, and their application to solid and fluid helium described. Helium was chosen because it is a major component of giant gas planets, was studied recently with shock wave experiments [1], and is comparatively simple to treat computationally that allowed us to apply all these different techniques. First we studied the insulator-to-metal transition in solid helium at high pressure. Density functional theory (DFT) was used to optimize the c/a ratio in the h.c.p. solid. Applying groundstate quantum Monte Carlo (QMC) [3], one finds that DFT predicts band gaps that are 4 eV too small. This inaccuracy means that DFT underestimates the metallization density by 20% and the metallization pressure by 40%. The band gaps computed with QMC are in very good agreement with GW calculations. However, GW cannot be used to correct the total energies and the equation of state (EOS). QMC yields the energy directly, and the correlation energy that is missing in DFT can be determined. To study fluids, DFT can also be combined with molecular dynamics for the nuclei by treating the electrons either in the instantaneous groundstate or by including thermal electronic excitations. At temperature above 20000K, electronic excitations affect the EOS significantly and make the material more compressible in shock wave experiments [1,2]. Despite the band gap problem in DFT, one would expect this method describe electronic excitations qualitatively. But it has not yet been demonstrated whether it is quantitatively accurate to determine correction to the EOS due to thermally excited electrons. By comparing with path integral Monte Carlo (PIMC) [4], we demonstrate DFT-MD EOS is surprising accurate but the method eventually becomes impractical because too many electronic orbital must be considered. PIMC, on the other hand, becomes more efficient at high temperature. In [4], we show that PIMC and DFT-MD can be combined to obtain one coherent EOS over several orders of magnitude in temperature. Finally, we compare our computed EOS with recent shock wave experiments [1]. We find good agreement between first-principles simulations and those experiments where the sample has been precompressed statically before the shock is launched. For the experiments without precompression, one finds that our first- principles EOS predicts a lower compressibility than was measured. This work was supported by NSF and NASA. A part of the computational resources were provided by NERSC. [1] J. Eggert et al., Phys. Rev. Lett. 100 (2008) 124503 [2] B. Militzer, Phys. Rev. Lett. 97 (2006) 175501. [3] S. Khairrallah and B. Militzer, Phys. Rev. Lett. 101 (2008) 106407. [4] B. Militzer, cond-mat/08050317.
MR11A-03 INVITED
Prediction of post-post-perovskite transitions
In the Earth, the post-perovskite structure is the final form of MgSiO3. However, in the solar giants and exoplanets in which pressure is much higher than the Earth, we can expect further phase transitions beyond the post-perovskite phase, i.e., post-post-perovskite transitions. Here we propose by first principles two candidates of crystalline post-post-perovskite phases of NaMgF3, which is a low-pressure analog of MgSiO3: U2S3-type and P63/mmc phases. Then we demonstrate that Al2O3 should undergo a transition to the U2S3-type phase at ~3.7 Mbar. This transformation should be important for the analysis of shock data in this pressure range, since alumina is used as window material. Our calculated compression curves agree with shock data excellently, suggesting the presence of two phase transitions (corundum-to-Rh2O3(II)-type and Rh2O3(II)-type-to-CaIrO3-type) in shock data. Our prediction also suggests that the multi-Mbar crystal chemistry of planet-forming minerals might be related to that of the rare-earth sulfides. Computations were performed at the Minnesota Supercomputing Institute. Research was supported by NSF grants EAR-0135533, EAR-0230319, and ITR-0428774 (VLab).
MR11A-04
Ab initio study of ionic vacancies, proton incorporation and migration in Mg2SiO4 polymorphs under pressure
First-principles simulations are performed to investigate the effects of pressure (up to 30 GPa) and structural phase transitions on the formation and migration enthalpies of the ionic vacancies and proton incorporation in Mg2SiO4 within the local density and pseudopotential approximations. Large differences are found between the vacancies at nonequivalent sites of the atomic species: Mg1 and O3 site vacancies in forsterite and Mg1 and O1 site vacancies in wadsleyite have the lowest energies. The calculated Schottky defect formation enthalpy is shown to increase with pressure in each phase with its value being the lowest for wadsleyite. Among different pseudo-Schottky defects, the MgO defects are most favorable whereas the SiO2 defects are least favorable at all pressures. To understand the proton defects in Mg2SiO4 polymorphs, proton incorporation at interstitial site and cationic vacancies is explored. The incorporation at silicon vacancy is most favorable and this vacancy remains favorable site until there are three protons. Addition of one more proton prefers magnesium vacancy site. Our results suggest that the interstitial protons and hydrogarnet substitutions are energetically unfavorable. The effects of protons on the transition pressure and equation of state are also studied. The migration barriers for Si4+, Mg2+ and O2- ions and protons calculated using the nudged-elastic-band method are found to agree well with the available experimental data. The Mg2+ ion has the lowest migration enthalpy among the three ions (0.77 eV for forsterite at zero pressure, 0.81 eV for wadsleyite at 6 GPa and 1.21 eV for ringwoodite at 10 GPa). For proton migration, the calculated interstitial-to-interstitial barriers are much smaller than the magnesium-to-interstitial barriers and the interstitial-to-interstitial barrier of ringwoodite (0.36 eV) is much smaller than those (about 1.15 eV) for other two phases. This suggests that protons in silicates may contribute significantly to the deep mantle conductivity.
MR11A-05
First Principles Calculations Of Lattice Thermal Conductivity Of MgO At High Temperature And High Pressure
Thermal conductivity (κ) plays an important role in understanding the heat transport processes in Earth and planetary interiors, yet it is difficult to measure directly especially at the relevant ultra-high pressures and temperatures. We have developed a first-principles algorithm to calculate the lattice conductivity of solid insulators at deep mantle conditions. We present our thermal conductivity calculations of MgO, and examine the behavior as a function of pressure and temperature. In our algorithm, explicit calculations of harmonic and anharmonic lattice dynamics and their pressure dependences are first carried out using first-principles density functional theory. Then lattice-anharmonicity- induced phonon lifetime is calculated based on the single mode excitation approximation. Isotope effect on the phonon lifetime is also estimated within the random mass disorder approximation. Mineral thermal conductivity is finally evaluated based on the simple kinetic transport theory. At 2000K, our calculated thermal conductivity of MgO is 8.9 W/K/m at zero pressure. Our preliminary calculations indicate that the thermal conductivity of MgO decreases with increasing temperature, consistent with available measurements. To account for pressure, we propose two models for the relative thermal conductivity κ(P)/κ(P=0), which both predict a linear increase of relative thermal conductivity with pressure. The models suggest that the pressure effect on the relative thermal conductivity is magnified at higher temperatures. In summary, this first-principles based algorithm allows the direct calculation of thermal conductivity for various mineral systems at the conditions mirroring to the Earth's interior. Furthermore it provides a chance to study the heat transport across the core/mantle boundary and the timing of inner core formation.
MR11A-06 INVITED
Multimillion to billion atom simulations of nanosystems under extreme conditions
Advanced materials and devices with nanometer grain/feature sizes are being developed to achieve higher strength and toughness in ceramic materials and greater speeds in electronic devices. Below 100 nm, however, continuum description of materials and devices must be supplemented by atomistic descriptions. Current state of the art atomistic simulations involve 10 million – 1 billion atoms. We investigate initiation, growth and healing of wing cracks in confined silica glass by multimillion atom molecular dynamics (MD) simulations. Under dynamic compression, frictional sliding of pre-crack surfaces nucleates nanovoids, which evolve into nanocrack columns at the pre-crack tip. Nanocrack columns merge to form a wing crack, which grows via coalescence with nanovoids in the direction of maximum compression. Lateral confinement arrests the growth and partially heals the wing crack. Growth and arrest of the wing crack occur repeatedly, as observed in dynamic compression experiments on brittle solids under lateral confinement. MD simulation of hypervelocity projectile impact in aluminum nitride and alumina has also been studied. The simulations reveal strong interplay between shock- induced structural phase transformation, plastic deformation and brittle cracks. The shock wave splits into an elastic precursor and a wurtzite-to-rocksalt structural transformation wave. When the elastic wave reflected from the boundary of the sample interacts with the transformation wave front, nanocavities are generated along the penetration path of the projectile and dislocations in adjacent regions. The nanocavities coalesce to form mode I brittle cracks while dislocations generate kink bands that give rise to mode II cracks. These simulations provide a microscopic view of defects associated with simultaneous tensile and shear cracking at the structural phase transformation boundary due to shock impact in high-strength ceramics. Initiation of chemical reactions at shock fronts prior to detonation and dynamic transition in the shock structure of an energetic material (RDX) and reaction of aluminium nanoparticles in oxygen atmosphere followed by explosive burning is also discussed.
MR11A-07
A modeling analysis of internal elastic strains in polycrystalline cobalt deformed under high pressure
Understanding the link between single crystal plasticity and polycrystalline behavior is fundamental for modeling and interpreting mineral properties within the Earth. It is also critical for understanding and interpreting x-ray diffraction data collected on polycrystals. Here, we show how a modification of the elasto-plastic self-consistent (EPSC) model of Turner and Tomé can be used to predict the development of internal elastic strains within grains of a sample of polycrystalline cobalt plastically deformed in the diamond anvil cell up to 42 GPa. The EPSC model is used to simulate the macroscopic flow curves and internal strain development within the sample. Input parameters are single crystal elastic moduli and their pressure dependence, critical resolved shear stresses and hardening behavior of slip and twinning mechanisms. The comparison between experimental and predicted data leads us to conclude that the plastic behavior of hcp-Co deforming at high pressure is dominated by basal and prismatic slip of < a > dislocations, accompanied by either pyramidal slip of < c + a > dislocations, or compressive twinning, or a combination of the two. The model also allows us to compare internal stresses within each grain and average stresses in the polycrystal, and hence to understand key relationships between single crystal and polycrystalline properties. Visco-plastic self-consistent techniques have been used for many years to relate seismic anisotropy, texture in polycrystals, and plastic deformation mechanisms at the grain scale. Here we show how elasto-plastic self- consistent techniques can be used to understand how stresses and strains scale from the grain level to the aggregate. Both methods are being merged with the inclusion of grain reorientation in EPSC and preliminary investigations of the effect of grain re-orientation on the model will also be presented.
MR11A-08
Modelling dislocation cores in perovskites: highlighting the influence on non cubic distortions
It is widely accepted that MgSiO3 Perovskite is one of the most abundant minerals of the Earth's mantle. Therefore, the convective flow and the seismic properties of the Earth's deep mantle should depend strongly on the mechanical and physical properties of this mineral for which deformation experiments remains highly challenging. In this study, we propose a theoretical modeling of dislocation glide systems in several perovskite-structured materials based on ab initio calculations and the Peierls-Nabarro (PN) model. The following cases have been considered: SrTiO3 (cubic) at 0 GPa; CaSiO3 (calculated as cubic) at 0, 30 and 100 GPa; CaTiO3 (orthorhombic) at 0 GPa and MgSiO3 (orthorhombic, more distorted than CaTiO3) at 0, 30 and 100 GPa. SrTiO3 represents an interesting test case. Since this mineral is stable at ambient pressure and widely used in microelectronics, its defects microstructures have been detailed in study. In particular, we present comparison between high-resolution TEM images of dislocation cores and our results which validates the PN model. Peierls-Nabarro modeling shows that <110>{110} is the easiest slip system in CaSiO3 perovskite. Moreover, the dislocation core is widely spread, leading to the first discovery of a silicate which exhibits negligible lattice friction at mantle pressure. Qualitatively, dislocations in CaTiO3 perovskite exhibit the same core profiles as those reported in MgSiO3 perovskite. From the quantitative point of view, it is shown that lattice friction increases when orthorhombic distortions increase from one mineral to the other. The present study provides a further evidence of the importance of non-cubic distortions on dislocation core structures and mobility within the perovskite family. Despite this quantitative difference, perovskite CaTiO3 appears to be a satisfactory structural analogue for MgSiO3 perovskite as far as dislocation glide is concerned.