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We investigated the accuracy of the Mie-Grüneisen approximation, which treats the Grüneisen parameter (γ) as a one-parameter function of volume, for use in describing the thermal equation of state of a silicate liquid. For this study, we focused on a single composition: the diopside-anorthite eutectic, an Fe-free basalt analog that has been extensively studied by shock wave experiments. We tuned an empirical force-field to a small set of ab initio N - V - T molecular dynamics simulations to ensure that it reproduces pressure, heat capacity, and γ at high and low pressures. We then used empirical force-field molecular dynamics simulations in a larger system and for longer run times to ensure accurate extraction of γ at numerous N - V - E state points. To first order, the results show the expected volume-dependence for silicate liquids, with γ increasing as volume decreases. However, there are also significant and systematic variations of γ with internal energy (E) at constant volume. We propose a simple model form that captures the volume and E dependence of γ with only one more free parameter than a typical Mie-Grüneisen formulation. We demonstrate the utility of this new model for well-constrained fitting to sparse shock wave experiment data below 200 GPa, obtaining a marked improvement in the ability to simultaneously fit the pre-heated liquid Hugoniot and points substantially offset from this Hugoniot. [ABSTRACT FROM AUTHOR]

We present first principles predictions of the absolute entropy of a silicate liquid (CaSiO 3) over a wide pressure-temperature range encompassing the Earth's mantle (2000–6000 K, 0–270 GPa). The results are derived from molecular dynamics simulations based on density functional theory and the two-phase thermodynamic (2PT) method, which divides the vibrational density of states into solid-like and gas-like parts, and which we describe in detail. The heat capacity derived from the absolute entropy agrees well with experimental measurements at low pressure. We find that the vibrational contribution accounts for more than 75% of the total entropy over the range of our study. We find that the two-body approximation to the excess entropy (relative to the ideal gas), which is computed with knowledge only of the radial distribution function, is excellent over most of the range considered, except at the lowest pressures and temperatures. We also compute the entropy of CaSiO 3 perovskite and use the entropy of liquid and solid phases to determine their absolute free energies and the melting curve. The melting curve agrees well with experiment and independent theoretical determinations based on Clausius-Clapeyron integration and the ZW method, showing a melting temperature of 5600 K at the Earth's core-mantle boundary. We find a nearly universal scaling of the self-diffusion coefficients with the excess entropy D ∗ = 0.9 exp 1.2 S ex , where D* is the self-diffusion coefficient suitably non-dimensionalized using macroscopic thermodynamic properties, and S ex is the excess entropy in units of the Boltzmann constant per atom. We use our results to estimate the temperature distribution in an isentropic, molten silicate Earth, finding 4.4 kJ/kg/K to be the lowest entropy that is completely molten, and producing a temperature at the core-mantle boundary of 6000 K. [ABSTRACT FROM AUTHOR]

Abstract Ab initio molecular dynamics simulations predict that CaSiO3 perovskite melts at 5600 K at 136 GPa, and 6400 K at 300 GPa, significantly higher than MgSiO3 perovskite. The entropy of melting (1.8 kB per atom) is much larger than that of many silicates at ambient pressure and of simple liquids and varies little with pressure. The volume of melting decreases rapidly with increasing pressure, to 3 % at 136 GPa, producing a melting slope that diminishes rapidly with pressure. We determine the melting temperature via the ZW method, combining the Z method, for which we clarify the theoretical basis, with a waiting time analysis. The ZW method results are internally confirmed by integrating the Clausius‐Clapeyron equation, which also yields our results for the entropy and volume of melting. We find the eutectic composition on the MgSiO3‐CaSiO3 join to be xCa = 0.26 at 136 GPa and that metasilicate melt is denser than coexisting silicates.

Ab initio molecular dynamics simulations predict that CaSiO3 perovskite melts at 5600 K at 136 GPa, and 6400 K at 300 GPa, significantly higher than MgSiO3 perovskite. The entropy of melting (1.8 kB per atom) is much larger than that of many silicates at ambient pressure and of simple liquids and varies little with pressure. The volume of melting decreases rapidly with increasing pressure, to 3 % at 136 GPa, producing a melting slope that diminishes rapidly with pressure. We determine the melting temperature via the ZW method, combining the Z method, for which we clarify the theoretical basis, with a waiting time analysis. The ZW method results are internally confirmed by integrating the Clausius‐Clapeyron equation, which also yields our results for the entropy and volume of melting. We find the eutectic composition on the MgSiO3‐CaSiO3 join to be xCa = 0.26 at 136 GPa and that metasilicate melt is denser than coexisting silicates. Plain Language Summary: Silicate melting is a major agent of thermal and chemical evolution of the Earth and other rocky planets. The melting temperature of Calcium silicate perovskite, a mineral that exists in Earth's lower mantle, is unknown over most of the pressure range that occurs in the mantle of Earth and super‐Earth exoplanets. We use advanced quantum mechanical simulations to predict the melting temperature of this material. We find that the melting temperature increases with increasing pressure but at a rate that diminishes continuously. The liquid and crystal have very similar volumes in the deep portions of planetary mantles, supporting the view that crystals may float at great depth. Key Points: Calcium silicate perovskite melts at 5600 K at the core mantle boundaryMetasilicate liquids are denser than coexisting crystalline silicates at the core‐mantle boundaryThe Z method allows precise ab initio melting temperature determination [ABSTRACT FROM AUTHOR]

The anomalous behavior displayed by silicate liquid/glass is a long-standing issue in physics, earth sciences, and glass technology. One such well-known unusual behavior is the contrary pressure dependence of silica-rich liquids on transport coefficients in comparison to other liquids. To investigate the origin of this anomalous behavior of silicate liquids, several analyses are newly developed and applied to molecular dynamics simulations of sodium silicate liquids. The cluster analyses performed on an Si O network and simplex sphere reveals obvious structural changes arising as a function of pressure and composition. At lower pressure and/or low silica content, all simplex oxygen spheres containing the modifier cations are connected together, and multiple Si O networks exist in the liquid structure. In contrast, at high pressure and/or high silica content, all SiO 4 tetrahedra belong to a single cluster, and the cluster of simplex oxygen spheres containing the modifier cations is split into multiple clusters. The collective function, which is found to decrease with increasing pressure, reveals the pressure dependence of the dynamic structure. This change represents a change in the diffusive motion from large-group diffusion to small-group diffusion for the Si O network. The complexity factor enables us to analyze the changes in the network structure. The decrease in the complexity factor of sodium disilicate liquids with increasing pressure represents an increase in the complexity of the Si O network, mediated by the formation of additional connections with other domains via ring-opening reactions. These analyses reveal the pressure- and composition-dependent changes in the dominant network in silicate liquids. When the network of corner-sharing SiO 4 tetrahedra is the dominant species in silicate liquids, the Si O bonds become weaker as a result of the Si O Si angle bending, and the shear viscosity decreases with increasing pressure. In contrast, the transport coefficients show normal pressure dependence when the cation domain is fully connected in silicate liquids. [ABSTRACT FROM AUTHOR]

The mixed alkali effect in silicate glass/liquid causes two anomalies: a decrease in the self-diffusivity of alkali ions and a decrease in shear viscosity. Previous studies using molecular dynamics (MD) simulations proposed that the decrease in diffusivity of alkali ions is the result of pathway blocking. However, the actual statistics of the pathway have never been presented. In this study, we revisited the mixed alkali effect in sodium–potassium silicate glass/liquid using MD simulations. The distinct part of van Hove's function indicates that site exchange between different alkali species is significantly slower than between the same species. By introducing simplex sphere analysis and its cluster statistics with varying compositions, we clarified the pathway disconnection caused by alkali mixing. Moreover, we analyzed the geometry and topology of the corner-shared network of the SiO 4 tetrahedra precisely. Both the geometry and topology change linearly with advancing alkali substitution, whereas the calculated shear viscosities have a minimum in the mixed alkali composition. Consequently, a method to quantitatively analyze the changes in relaxation dynamics is required to clarify the viscosity anomaly in mixed alkali liquids. [ABSTRACT FROM AUTHOR]

Ab intio molecular dynamics simulations show that the electrical conductivity of liquid SiO2 is semimetallic at the conditions of the deep molten mantle of early Earth and super-Earths, raising the possibility of silicate dynamos in these bodies. Whereas the electrical conductivity increases uniformly with increasing temperature, it depends nonmonotonically on compression. At very high pressure, the electrical conductivity decreases on compression, opposite to the behavior of many materials. We show that this behavior is caused by a novel compression mechanism: the development of broken charge ordering, and its influence on the electronic band gap. [ABSTRACT FROM AUTHOR]

We present the results of force-field molecular dynamics simulations of the static and dynamic properties of sodium silicate liquids. We studied the relationship between the structure and properties with varying SiO 2 content and pressure. We found that the silicate liquids have at least three types of characteristic structures before the coordination number of Si changes with increasing pressure; these structures are, ionic, network, and coesitic structured liquids. In the ionic liquid like structure, simple diffusion of large silicate anions is dominant in the liquid and their motion is impeded by compression. In contrast, in the network liquid, a small portion of the network of corner-shared SiO 4 tetrahedra diffuses via bond exchange and flow globally. Bond exchange is activated by pressure in the entangled network liquid because of distortion of the corner-shared SiO 4 tetrahedra network and the tetrahedra themselves. The SiO 2 rich liquids soften as a result from of these distortions. The derivative of bulk moduli of the sodium silicate liquids increases significantly at a certain pressure because of changes in densification mechanism. The changes in those densification mechanisms are coherent with the changes in pressure dependence of transport coefficient. [ABSTRACT FROM AUTHOR]

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’s 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 3 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 2 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. [ABSTRACT FROM AUTHOR]

Abstract: We perform a detailed visualization-based analysis of atomic-position series data for model basalt melt obtained from first-principles (quantum mechanical) molecular dynamics simulations. To gain insight into the short- and mid-range order of the melt structure, we extract and visualize the details of radial distribution function (RDF) and coordination environment. The first peaks of all partial RDFs lie in the distance range of 1.6–4Å and the corresponding mean coordination numbers vary from less than 1 to more than 9. The coordination environments involving cations and anions differ substantially from each other, each consisting of a rich set of coordination states. These states vary both spatially and temporally: The per-atom coordination information extracted on the fly is rendered instantaneously as the spheres and polyhedra as well as along the corresponding trajectories using a color-coding scheme. The information is also visualized as clusters formed by atoms that are coordinated at different time intervals during the entire simulation. The Si–O coordination is comprised of almost all tetrahedra (4-fold) whereas the Al–O coordination includes both tetrahedra (4-fold) and pentahedra (5-fold). The animated visualization suggests that the melt structure can be viewed as a dynamic (partial) network of Al/Si–O coordination polyhedra connected via bridging oxygen in an inhomogeneous distribution of mobile magnesium and calcium atoms. [Copyright &y& Elsevier]

Abstract: Time-varying three-dimensional scattered data representing snapshots of atomic configurations produced by molecular dynamics simulations are not illuminating by themselves; gaining insight into them poses a tremendous challenge. In order to take the advantage of maximal information offered by these simulations, we have proposed an efficient scheme, which integrates various analysis and rendering tasks together in order to support interactive visualization of the data at space–time multiresolution. Additional data produced by various analytical techniques on the fly represent the atomic system under consideration at diverse length- (e.g., nearest neighbor, next-nearest neighbor or beyond) and time- (e.g., instantaneous, finite intervals or overall averages) scales. In particular, the radial distribution functions, coordination environments, clusters and rings are computed and visualized to understand the structural behavior whereas a variety of displacement data and covariance matrices are explored to understand the dynamical behavior. While the spatial distributions of atoms need to be reproduced correctly during rendering, we take the advantage of high flexibility in rendering other attributes because of the lack of their direct physical relevance. A combination of different techniques including animation, color maps, pathlines, different types of glyphs, and graphics hardware accelerated approach is exploited to render the original and extracted data. First-principles molecular dynamics simulation data for liquid systems are used to justify the effectiveness and usefulness of the proposed scheme. [Copyright &y& Elsevier]

Abstract: We discuss the geophysical implications of recent first principles molecular dynamics simulations of MgSiO3 liquid, in particular the findings that the Grüneisen parameter increases by a factor of three on two-fold compression, and the predicted melting curve. The predicted melting temperature of MgSiO3 perovskite at 136 GPa is 5400±600 K, which if lowered by freezing point depression by 1300 K, yields a mantle solidus temperature of 4100 K, identical to recent estimates of the temperature at the base of the mantle. We argue on this basis that partial melting at the base of the mantle is plausible. While MgSiO3 perovskite is denser than the isochemical liquid, reasonable values of iron partitioning and bulk iron contents, leads to the conclusion that a melt at the base of the multi-component mantle would be denser than its surroundings and therefore buoyantly stable. We predict the bulk sound velocity of this melt to be 10.9 km s−1, less than that of ultra-low velocity zones, and consistent with the explanation of these regions as being due to partial melting. The increase on compression of the Grüneisen parameter in the liquid state yields isentropes that are much hotter than previously thought: a potential temperature of only 2450 K is sufficient to melt the entire mantle, and a magma ocean will begin crystallization at mid-mantle depths, rather than at the base of the mantle. [Copyright &y& Elsevier]

Abstract: Melting experiments on a Fe-rich carbonate-saturated pelite were performed at 850–1300 °C and 2.5–5.0 GPa to define melting relations, melt compositions, and the conditions under which carbonates remain residual. In the selected fertile bulk composition, 30 wt.% potassic granite (2.5 GPa) or phonolite (5.0 GPa) melt is generated at the fluid-absent solidus. The temperature of the latter increases from 900 °C at 2.4 GPa to 1070 °C at 5.0 GPa. Phengite+quartz/coesite control initial silicate melting and melt productivity through the reaction phengite+quartz/coesite+clinopyroxene+calcite=silicate melt+kyanite+garnet, which leaves most of the Fe–Mg–calcite in the residue. Na remains compatible in clinopyroxene (D Na cpx/melt =3.1 to 7.3 at the fluid-absent solidus), resulting in silicate melts with K2O/Na2O wt-ratios of 5.8–8.6. Such highly potassic carbonated silicate melts represent ideal metasomatic agents for the source mantle of group II kimberlites. From 3.7 to 5.0 GPa, Fe–Mg–calcite disappears only through the formation of Ca–carbonatite at 1100 °C. The experiments provide a possible source for Ca–carbonatites in combination with alkaline granitic to phonolitic melts at temperatures unlikely to be achieved during ongoing subduction. Large scale carbonate transfer to the subarc mantle can thus only be achieved when burying rates slow considerably down or subducted crust becomes incorporated into the mantle. Consequently, it is likely that carbonates will not be extensively mobilized in a typical subarc region, thus extending and confirming earlier results from subsolidus studies (Connolly, J.A.D., 2005. Computation of phase equilibria by linear programming: a tool for geodynamic modelling and its application to subduction zone decarbonation. Earth Planet. Sci. Lett. 236, 524–541.), that >70–80% of the subducted carbonate will bypass the volcanic arc region and get buried to larger depths. [Copyright &y& Elsevier]

First-principles molecular dynamics simulations of complex material systems such as geophysically relevant oxide and silicate liquids produce massive amounts of time-varying three-dimensional data for the atomic configurations. Given the high accuracy of these data, it is desirable to extract as much information hidden in the data as possible. In this paper, we elaborate on our recently proposed scheme to support interactive visualization at space–time multiresolution of the atomistic simulation data. Instead of just focusing on direct rendering of the given data, additional data (containing more quantitative and qualitative information) that usually have to be extracted by some other means are extracted and rendered on the fly. This allows us to gain better insight into the global as well as local spatio-temporal behavior of the data in the context of bonding, radial distribution, atomic coordination, clustering, structural stability and distortion, and diffusion. We illustrate such visualization for the simulation data on the liquid phases of MgO and MgSiO3—the two most abundant components of Earth’s mantle. Our analysis shows that the structure and dynamics of both liquids change substantially with compression, with no discernible effects of temperature in most cases. [ABSTRACT FROM AUTHOR]

The heat capacities of 29 glasses and supercooled liquids in the Na2O-SiO2, Na2O-Al2O3-SiO2, Na2O-(FeO)-Fe2O3-SiO2, and Na2O-TiO2-SiO2 systems were measured in air from 328 to 998 K with a differential scanning calorimeter. The reproducibility of the data determined from multiple heat capacity runs on a single crystal MgO standard is within ± 1% of the accepted values at temperatures ≤ 800 K and within ± 1.5% between 800 and 1000 K. Within the resolution of the data, the heat capacities of sodium silicate and sodium aluminosilicate liquids are temperature independent. Heat capacity data in the supercooled liquid region for the sodium silicates and sodium aluminosilicates were combined and modelled assuming a linear compositional dependence. The derived values for the partial molar heat capacities of Na2O, Al2O3, and SiO2 are 112.35 ± 0.42, 153.16 ± 0.82, and 76.38 ± 0.20 J/gfw · K respectively. The partial molar heat capacities of Fe2O3 and TiO2 could not be determined in the same manner because the heat capacities of the Fe2O3- and TiO2-bearing sodium silicate melts showed varying degrees of negative temperature dependence. The negative temperature dependence to the configurational C P may be related to the occurrence of sub-microscopic domains (relatively polymerized and depolymerized) that break down to a more homogeneous melt structure with increasing temperature. Such an interpretation is consistent with data from in situ Raman, Mössbauer, and X-ray absorption fine structure (XAFS) spectroscopic studies on similar melts. [ABSTRACT FROM AUTHOR]

Accurate knowledge of the diffusion mechanism of network-forming elements (NFs) in silicate liquids is essential for modeling transport properties such as the shear viscosity. Previous studies focusing on alkali diffusion in silicate liquids/glasses have revealed that alkali ions diffuse via thermal hopping event. However, the diffusion mechanism for NFs remains poorly understood. Herein, molecular dynamics simulations and various analysis methods based on chemical species and bond-breaking events are presented. The analysis results reveal the following diffusion mechanism of NF. Oxygen atoms diffuse similar to a site exchange through the non-bridging oxygen (NBO) state. By contrast, Si diffusion is unlike the exchange regime, and occurs gradually through a bond-exchange event, deforming the network. The dominant mechanism is a rare long flight during Si—O bond breaking, and most bond-breaking events do not contribute, similar to local events. The supporting mechanism is network deformation after a bond-exchange event. [ABSTRACT FROM AUTHOR]

We present the results of force field molecular dynamics simulations of calcium aluminosilicate, sodium aluminosilicate, calcium silicate, and sodium silicate liquids under temperature gradient conditions. Non-equilibrium molecular dynamics simulations of these liquids under temperature gradient conditions reproduced the trend reported for Soret coefficients, with network-forming cations having larger coefficients compared with network-modifying ones. We found a linear relationship between the Soret coefficients and the variance of the potential energy distribution of each cation, which corresponds to the activation energy of diffusion. The Soret coefficients of sodium aluminosilicate liquids show a somewhat different behavior compared with that of the other liquids. This behavior could be explained by charge compensation of fourfold-coordinated aluminum species by sodium cations. Further studies of a larger variety of systems will reveal the full details of the relationship between Soret coefficients and microscopic structure/energy distribution, and enable us to estimate the Soret coefficients. [ABSTRACT FROM AUTHOR]

Ab initio molecular dynamics simulations predict that CaSiO 3 perovskite melts at 5600 K at 136 GPa, and 6400 K at 300 GPa, significantly higher than MgSiO 3 perovskite. The entropy of melting (1.8 k B per atom) is much larger than that of many silicates at ambient pressure and of simple liquids and varies little with pressure. The volume of melting decreases rapidly with increasing pressure, to 3 % at 136 GPa, producing a melting slope that diminishes rapidly with pressure. We determine the melting temperature via the ZW method, combining the Z method, for which we clarify the theoretical basis, with a waiting time analysis. The ZW method results are internally confirmed by integrating the Clausius-Clapeyron equation, which also yields our results for the entropy and volume of melting. We find the eutectic composition on the MgSiO 3 -CaSiO 3 join to be x Ca  = 0.26 at 136 GPa and that metasilicate melt is denser than coexisting silicates.

Ab intio molecular dynamics simulations show that the electrical conductivity of liquid SiO 2 is semimetallic at the conditions of the deep molten mantle of early Earth and super-Earths, raising the possibility of silicate dynamos in these bodies. Whereas the electrical conductivity increases uniformly with increasing temperature, it depends nonmonotonically on compression. At very high pressure, the electrical conductivity decreases on compression, opposite to the behavior of many materials. We show that this behavior is caused by a novel compression mechanism: the development of broken charge ordering, and its influence on the electronic band gap., Competing Interests: The authors declare no conflict of interest.