Effects of valence and spin of Fe in MgSiO\u3csub\u3e3\u3c/sub\u3e melts: Structural insights from first-principles molecular dynamics simulations

Iron (Fe) is present in terrestrial melts and at all depths inside the Earth. How Fe in its varying oxidation and spin states influences the properties of silicate melts is of critical importance to the understanding of the chemical evolution of our planet. Here, we report the results of first-principles molecular dynamics simulations of molten Fe-bearing MgSiO over a wide pressure range covering the entire mantle. Our results suggest that the structural properties of the host melt, such as the average bond length and coordination in Mg–O and Si–O do not differ much when compared with the pure melt. More importantly, they show that the local Fe–O structure is more sensitive to the spin state (high-spin, HS and low-spin, LS) of iron than to its valence state (Fe and Fe ). For iso-valence configurations, the average Fe–O bond length and coordination number differ by more than 10% and ∼30%, respectively, between the HS and LS states. In comparison, the corresponding differences between Fe and Fe for iso-spin configurations are within 5 and 15%, respectively. Ferrous iron shows lower average oxygen coordination numbers of ∼3.8 for HS and ∼3.3 for LS compared to the corresponding numbers of ∼4.1 and ∼3.7 for ferric iron at 0 GPa and 3000 K. As pressure increases, the coordination gap between the ferrous and ferric iron closes for HS but persists for LS. Our analysis of the proportions of non-bridging and bridging oxygens and the rates of bond breaking/formation events suggests an equivalent role of the ferrous and ferric iron in terms of their network forming ability. The predicted structural behavior of iron in its different oxidation states is generally consistent with the experimental inferences for MgO–FeO–SiO melts. Unlike other ferrosilicate compositions for which the experimental data suggest that Fe increases and Fe decreases the viscosity of the melt, the ferrous and ferric iron, due to their structural equivalence, are likely to have a similar influence on the dynamical behavior of deep mantle iron-bearing MgSiO melts. 3 2 3 2+ 3+ 2+ 3+ 3+ 2

Origin of lateral variation of seismic wave velocities and density in the deep mantle

Strong constraints can be placed on the origin of heterogeneity of seismic wave velocities and density if the observed ratios of various parameters are compared with mineral physics predictions. They include the shear to compressional wave velocity heterogeneity ratio, R ≡ δ log V / δ log V , the bulk sound to shear wave velocity heterogeneity ratio, R ≡ δ log V / δ log V , and the density to velocity heterogeneity ratio, R ≡ δ log ρ / δ log V . Using mineral physics considerations, we calculate these ratios in the lower mantle corresponding to the thermal and chemical origin of velocity and density heterogeneity. Both anharmonic and anelastic effects are considered for thermal origin. Anharmonic effects are estimated from the theoretical calculations as well as from laboratory measurements which show a marked increase in R with pressure from ∼1.5 to ∼2.1 in the lower mantle. Such a trend is marginally consistent with seismological observations showing an increase in R with depth (from ∼1.7 to ∼3.2 in the lower mantle). However, anharmonic effect alone cannot explain inferred low R (2.7) and corresponding negative values of R (and R ) in the deep lower mantle which cannot be accounted for by thermal or simple chemical heterogeneity such as the heterogeneity in the Fe/(Fe+Mg) and/or Mg/(Mg+Si) ratios. Possible causes of anomalies in this region are discussed, including the role of anisotropy and a combined effect of heterogeneity in Fe and Ca content. Copyright 2001 by the American Geophysical Union. s/p s p φ/s φ s ρ/s,p s,p s/p s/p ρ/s s/p s/p φ/s ρ/

Diffusional fractionation of helium isotopes in silicate melts

Estimating Helium (He) concentration and isotope composition of the mantle requires quantifying He loss during magma degassing. The knowledge of diffusional He isotope fractionation in silicate melts may be essential to constrain the He loss. Isotopic mass dependence of He diffusion can be empirically expressed as D3He/D4He = (4/3)^β, where D is the diffusivity of a He isotope. However, no studies have reported any β values for He in silicate melts due to technical challenges in both experiments and computations. Here, molecular dynamics simulations based on deep neural network potentials trained by ab initio data show that β for He in albite melt decreases from 0.355 ± 0.012 at 3000 K to 0.322 ± 0.019 at 1700 K. β in model basalt melt takes a smaller value from 0.322 ± 0.025 to 0.274 ± 0.027 over the same temperature range. Based on our results, we suggest using D3He/D4He values of 1.097 ± 0.006 and 1.082 ± 0.008 in natural rhyolite and basalt melt, respectively, to interpret measured He concentration and isotope composition of natural samples

First-principles computation of diffusional Mg isotope fractionation in silicate melts

© 2020 Elsevier Ltd Diffusional isotope fractionation occurs in geochemical processes (such as magma mixing, bubble growth, and crystal growth), even at magmatic temperatures. Isotopic mass dependence of diffusion is commonly expressed as [Formula presented], where Di and Dj are diffusion coefficients of two isotopes whose masses are mi and mj. How the dimensionless empirical parameter β depends on temperature, pressure, and composition remains poorly constrained. Here, we conducted a series of first-principles molecular dynamics simulations to evaluate the β factor of Mg isotopes in MgSiO3 and Mg2SiO4 melts using pseudo-isotope method. In particular, we considered interactions between Mg isotopes by simultaneously putting pseudo-mass and normal-mass Mg atoms in a simulation supercell. The calculated β for Mg isotopes decreases linearly with decreasing temperature at zero pressure, from 0.158±0.004 at 4000 K to 0.121±0.017 at 2200 K for MgSiO3 melt and from 0.150±0.004 at 4000 K to 0.101±0.012 at 2200 K for Mg2SiO4 melt. Moreover, our simulations of compressed Mg2SiO4 melt along the 3000 K isotherm show that the β value decreases linearly from 0.130±0.006 at 0 GPa to 0.060±0.011 at 17 GPa. Based on our diffusivity results, the empirically established positive correlation between β and solvent-normalized diffusivity (Di/DSi) seems to be applicable only at constant temperatures or in narrow temperature ranges. Analysis of atomistic mechanisms suggests that the calculated β values are inversely correlated with force constants of Mg at a given temperature or pressure. Good agreement between our first principles results with available experimental data suggests that interactions between isotopes of major elements must be considered in calculating β for major elements in silicate melts. Also, we discuss diffusion-controlled crystal growth by considering our calculated β values

Carbon-bearing silicate melt at deep mantle conditions

Knowledge about the incorporation and role of carbon in silicate magmas is crucial for our understanding of the deep mantle processes. CO bearing silicate melting and its relevance in the upper mantle regime have been extensively explored. Here we report first-principles molecular dynamics simulations of MgSiO melt containing carbon in three distinct oxidation states - CO , CO, and C at conditions relevant for the whole mantle. Our results show that at low pressures up to 15 GPa, the carbon dioxide speciation is dominated by molecular form and carbonate ions. At higher pressures, the dominant species are silicon-polyhedral bound carbonates, tetrahedral coordination, and polymerized di-carbonates. Our results also indicate that CO component remains soluble in the melt at high pressures and the solution is nearly ideal. However, the elemental carbon and CO components show clustering of carbon atoms in the melt at high pressures, hinting towards possible exsolution of carbon from silicate melt at reduced oxygen contents. Although carbon lowers the melt density, the effect is modest at high pressures. Hence, it is likely that silicate melt above and below the mantle transition zone, and atop the core-mantle boundary could efficiently sequester significant amounts of carbon without being gravitationally unstable. 2 3 2

A magma ocean origin to divergent redox evolutions of rocky planetary bodies and early atmospheres

Magma oceans were once ubiquitous in the early solar system, setting up the initial conditions for different evolutionary paths of planetary bodies. In particular, the redox conditions of magma oceans may have profound influence on the redox state of subsequently formed mantles and the overlying atmospheres. The relevant redox buffering reactions, however, remain poorly constrained. Using first-principles simulations combined with thermodynamic modeling, we show that magma oceans of Earth, Mars, and the Moon are likely characterized with a vertical gradient in oxygen fugacity with deeper magma oceans invoking more oxidizing surface conditions. This redox zonation may be the major cause for the Earth’s upper mantle being more oxidized than Mars’ and the Moon’s. These contrasting redox profiles also suggest that Earth’s early atmosphere was dominated by CO and H O, in contrast to those enriched in H O and H for Mars, and H and CO for the Moon. 2 2 2 2

First-principles calculations of the lattice thermal conductivity of the lower mantle

The temperature variations on top of the core-mantle boundary are governed by the thermal conductivity of the minerals that comprise the overlying mantle. Estimates of the thermal conductivity of the most abundant phase, MgSiO3 perovskite, at core-mantle boundary conditions vary by a factor of ten. We performed ab initio simulations to determine the lattice thermal conductivity of MgSiO3 perovskite, finding a value of 6.8 ± 0.9 W m-1 K-1 at core-mantle boundary conditions (136 GPa and 4000 K), consistent with geophysical constraints for the thermal state at the base of the mantle. Thermal conductivity depends strongly on pressure, explaining the dynamical stability of super-plumes. The dependence on temperature and composition is weak in the deep mantle: our results exhibit saturation as the phonon mean free path approaches the interatomic spacing. Combining our results with seismic tomography, we find large lateral variations in the heat-flux from the core that have important implications for core dynamics

High pressure elasticity of MgSiO\u3csub\u3e3\u3c/sub\u3e perovskite, MgO and SiO\u3csub\u3e2\u3c/sub\u3e

Full elastic constant tensors (c ) of three minerals namely, MgSiO perovskite, MgO and SiO , are obtained as a function of pressure up to 140 GPa using first-principles computer simulations based on the local density and pseudopotential approximations. The zero pressure values and initial pressure dependence of athermal elastic constants derived from stress-strain relations are in excellent agreement with available experimental data. We find that elastic moduli, wave velocities and anisotropy of the minerals are strongly pressure dependent, particularly, in the vicinity of the structural transformations. In the view of the present experimental limitations at realistic conditions of the inner Earth, our results for high pressure elasticity are expected to be of substantial geophysical significance. Comparisons based on compressional and shear wave velocities support the prevailing hypothesis of Mg-rich silicate perovskite dominated composition for the lower mantle. ij 3

First-principles computation of mantle materials in crystalline and amorphous phases

First-principles methods based on density functional theory are used extensively in the investigation of the behavior and properties of mantle materials over broad ranges of pressure, temperature, and composition that are relevant. A review of computational results reported during the last couple of decades shows that essentially all properties including structure, phase transition, equation of state, thermodynamics, elasticity, alloying, conductivity, defects, interfaces, diffusivity, viscosity, and melting have been calculated from first principles. Using MgO, the second most abundant oxide of Earth\u27s mantle, as a primary example and considering many other mantle materials in their crystalline and amorphous phases, we have found that most properties are strongly pressure dependent, sometimes varying non-monotonically and anomalously, with the effects of temperature being systematically suppressed with compression. The overall agreement with the available experimental data is excellent; it is remarkable that the early-calculated results such as shear wave velocities of two key phases, MgO and MgSiO perovskite, were subsequently reproduced by experimentation covering almost the entire mantle pressure regime. As covered in some detail, the defect formation and migration enthalpies of key mantle materials increase with pressure. The predicted trend is that partial MgO Schottky defects are energetically most favorable in Mg-silicates but their formation enthalpies are high. So, the diffusion in the mantle is likely to be in the extrinsic regime. Preliminary results on MgO and forsterite hint that the grain boundaries can accommodate point defects (including impurities) and enhance diffusion rates at all pressures. The structures are highly distorted in the close vicinity of the defects and at the interface with excess space. Recent simulations of MgO-SiO binary and other silicate melts have found that the melt self-diffusion and viscosity vary by several orders of magnitudes with pressure, temperature, and composition. The predicted high compressibility and complex dynamical behavior can be associated with structural changes (involving non-bridging oxygen, oxygen tri-clusters, Si-O pentahedra, etc.) occurring on compression. We envision future prospect for massively parallel/distributed computing of unprecedented magnitude and scope in the study of relevant materials for Earth, super-Earth, and other planets. A renewed computational theme perhaps should be the first-principles simulations of large systems (with long runs) that are necessary to explore realistic (natural) compositions, polycrystalline phases, multi-component melts, crystal/melt interfaces, trace element partitioning, etc. 3

First-principles molecular dynamics simulations of silicate melts: Structural and dynamical properties

The study of silicate melts from first principles is computationally intensive due to the need of relatively large atomic systems and long simulation runs. Recent advances in hardware and software have made it possible to accurately simulate the liquid phase at pressures and temperatures that are geophysically relevant. This paper reports the details of the methodology used in the context of simulations and subsequent analysis of the output data. The simulations are performed using the parallel first-principles molecular dynamics (FPMD) technique within the framework of density functional theory. Various physical properties including the equation of state, thermodynamics, atomic and electronic structures, self-diffusion and viscosity are obtained from simulations. The position time series are visualized to gain insight into underlying physical mechanisms. We review the recent first-principles studies of three liquids along the MgO-SiO join including MgSiO melt to show that the structural and dynamical properties of these liquids are highly sensitive to pressure and temperature. 2