Computer modeling of natural silicate melts: What can we learn from ab initio simulations (original) (raw)
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Properties of planetary silicate melts by molecular dynamics simulation
Chemical Geology, 2018
Because magmatic liquids play a fundamental role in the evolution of the terrestrial planets, a precise knowledge of their physical properties is requisite to better understand the formation and the dynamics of planetary interiors. In using an improved force field for silicates (Dufils et al., 2017), we report the results of a series of molecular dynamics simulations (MD) aiming to evaluate the equation of state (EOS), the viscosity, the electrical conductivity, and the elemental self-diffusion coefficients of various planetary melts representative of the Earth, Mars, the Moon and Mercury. The agreement between MD calculations and experimental data (when they exist) is remarkable, a finding which suggests that the MD simulations can be used on trust to extend the existing laboratory data on planetary melts (as it is proposed here for some lunar, martian and mercurian basalts) or to predict the thermo-physical properties of more exotic compositions (magma oceans, lava planets). Moreover, the MD simulations show that the evolution of the viscosity and of the electrical conductivity with the pressure depends in a complex manner on temperature and composition and that is difficult to extract general trends from these behaviors. Another advantage of the MD simulations is that the transport coefficients (viscosity, conductivity, and diffusivities) being evaluated along the same numerical experiment, one is able to test the validity of the Eyring and the Stokes-Einstein equations relating viscosity and diffusivity, as also as the Nernst-Einstein equation expressing the conductivity as function of the ionic diffusivities. It is shown that the Stokes-Einstein equation is suitable to describe planetary melts of low viscosity (≤ 1 Pa.s), whereas the Eyring relation leads to a better estimation at high viscosities (> 100 Pa.s). Concerning the electrical conductivity, the Nernst-Einstein relation fails to reproduce the conductivity values obtained by MD simulation, a result which can be explained by the crucial role played by ion-ion correlations in silicate melts.
Properties of magmatic liquids by molecular dynamics simulation: The example of a MORB melt
Chemical Geology, 2016
A new atom-atom interaction potential is introduced for describing by classical molecular dynamics (MD) simulation the physical properties of natural silicate melts. The equation of state, the microscopic structure, the viscosity, the electrical conductivity, and the selfdiffusion coefficients of ions in a mid-oceanic ridge basalt (MORB) melt are evaluated by MD over a large range of temperature and pressure (1673-3273 K and 0-60 GPa). A detailed comparison with experimental data shows that the model reproduces the thermodynamic, structural and transport properties of a MORB with an unprecedented accuracy. In particular, it is shown that the MORB melt crystallizes at lower mantle conditions into a perovskite phase whose the equation of state (EOS) is compatible with those proposed in the experimental literature. Moreover, in accordance with experimental findings, the simulation predicts not only that the MORB viscosity exhibits a (slight) minimum with the pressure, but also that the viscosity at high temperature remains very low (<100 mPa.s for T > 2273 K) even at high pressure (up to 40 GPa). However the evolution of the electrical conductivity with temperature and pressure is not always the symmetrical of that of the viscosity. In fact, the relationship between viscosity and electrical conductivity shows a crossover at around 2073 K.
Carbon dioxide in silicate melts at upper mantle conditions: Insights from atomistic simulations
Chemical Geology, 2015
The detail of the incorporation of carbon dioxide in silicate melts at upper mantle conditions is still badly known. To give some theoretical guidance, we have performed first-principle molecular dynamics simulations (FPMD) to quantify the speciation and the incorporation of carbon dioxide in two CO 2-rich silicate melts (~20 wt% CO 2 at 2073 K and 12 GPa), a basaltic and a kimberlitic composition chosen in the CaO-MgO-Al 2 O 3-SiO 2 system. In the basaltic composition, carbon dioxide is incorporated under the form of a minority population of CO 2 molecules and a prevailing population of carbonate ions (CO 3 2-). In contrast, the amount of CO 2 molecules is found to be very small in the kimberlitic melt. Moreover, a new (transient) species has been identified, the pyrocarbonate ion C 2 O 5 2issued from the reaction between CO 2 and CO 3 2-. With regard to the structure of the CO 2-bearing melts, it is shown that the carbonate ions modify the silicate network by transforming some of the oxygen atoms into bridging carbonates, non-bridging carbonates, and free carbonates, with a distribution depending on the melt composition. In the basaltic melt a majority of carbonate ions are non-bridging or free, whereas in the kimberlitic melt, most of the carbonate ions are under the form of free carbonates linked to alkaline earth cations. Surprisingly, the addition of CO 2 only has a weak influence on the diffusion coefficients of the elements of the melt. The consequence is that the strong enhancement of the electrical conductivity reported recently for carbonated basalts (Sifré et al., 2014, Nature 509, 81), can be reproduced by simulation only if one assumes that the ionic charges assigned to the elements of the melt depend, in a non-trivial way, on the CO 2 content. Finally, a comparison of the FPMD calculations with classical molecular dynamics simulations using an empirical force field of the literature (Guillot and Sator, 2011, GCA 75, 1829) shows that the latter one needs some improvement.
Structure and density of basaltic melts at mantle conditions from first-principles simulations
The origin and stability of deep-mantle melts, and the magmatic processes at different times of Earth’s history are controlled by the physical properties of constituent silicate liquids. Here we report density functional theory-based simulations of model basalt, hydrous model basalt and near-MORB to assess the effects of iron and water on the melt structure and density, respectively. Our results suggest that as pressure increases, all types of coordination between major cations and anions strongly increase, and the water speciation changes from isolated species to extended forms. These structural changes are responsible for rapid initial melt densification on compression thereby making these basaltic melts possibly buoyantly stable at one or more depths. Our finding that the melt-water system is ideal (nearly zero volume of mixing) and miscible (negative enthalpy of mixing) over most of the mantle conditions strengthens the idea of potential water enrichment of deep-mantle melts and early magma ocean.
Iron and silicon isotope fractionation in silicate melts using first-principles molecular dynamics
Geochimica et Cosmochimica Acta, 2022
The direct determination of silicate melts iron and silicon isotopes signature remains a major challenge of high-temperature isotope geochemistry. For this reason, melts are often approximated by silicate glasses. Calculation of precise equilibrium Si and Fe isotopes fractionation factors between minerals and melt would indeed allow us to distinguish equilibrium fractionation from diffusion-driven kinetic fractionation involved in the iron and silicon isotopes signatures of Earth and other planets. In this study, we use for the first time, first-principles molecular dynamics based on density functional theory to determine iron and silicon isotope compositions of different silicate melts, namely: iron-rich basalt, iron-depleted basalt, basanite, trachyte and phonolite. The 57Fe/54Fe reduced partition function ratios (-factors) of the different melts span over a 1.1 ‰ range at 1000 Kelvin (K) while 30Si/28Si 𝛽-factors are much less influenced by the melt composition with a 0.5 ‰ fractionation range at the same temperature. The main parameter controlling iron isotope fractionation in silicate melts having similar iron oxidation state is, after temperature, the average Fe-O bond length. The chemical environment around iron (e.g. Fe-Fe distances) is suggested to contribute to Fe isotope fractionation as well. Silicon isotopes fractionation seems also affected, but to a lesser extent, by its local chemical composition with decreasing Si-Fe distances leading to slightly higher Si 𝛽-factor in the melt. From these melts Fe and Si 𝛽-factors, a new set of equilibrium fractionation factors between a variety of minerals and melts has been calculated. These new Δ57Femin-melt and Δ30Simin-melt sets allow us to discuss whether processes such as fractional crystallization, partial melting and diffusion could be responsible for the documented Fe and Si isotopes variations in igneous rocks. Our results suggest that: 1) fractional crystallization may explain at least part of the Fe and Si isotopic evolution during magmatic differentiation, for values up to 57Fe = 0.65 ‰ and 30Si = -0.1 ‰, respectively, 2) partial melting of the upper mantle can produce the Mid-Ocean Ridge Basalts (MORB) iron isotopes signature. Finally, we calculated that olivine at equilibrium with a basaltic melt could display an iron isotope composition down to -0.1 ‰ for 57Fe. Hence, the lower isotopic compositions (57Fe < -0.1 ‰) observed in natural olivines are most likely due to diffusion-driven kinetic fractionation.
An equation of state for silicate melts. IV. Calibration of a multicomponent mixing model to 40 GPa
American Journal of Science, 2004
Mixing relations for the "high-pressure" parameters of the equation of state of Ghiorso (2004a) are developed and compositional coefficients are optimized to permit calculation of melt density in portions of the system SiO 2 -TiO 2 -Al 2 O 3 -FeO-MgO-CaO-Na 2 O-K 2 O to pressures in excess of 40 GPa and temperatures up to 2500°C. Four data sets are analyzed and fitted to yield an internally consistent model: (1) density estimates made from measurements of the sinking/floating of reference mineral markers in silicate liquids at known temperatures and pressures, (2) density estimates obtained from shock compression studies on molten liquids, (3) liquid densities inferred from the temperature and pressure dependence of the slopes of mineral fusion curves, and (4) estimates of densities of molten silicate liquids obtained by molecular dynamics simulations. Calibration compositions include chemically complex liquids (komatiite, peridotite and MORB bulk compostions) as well as simple liquids with mineral-like stoichiometry. The model recovers density with an average error of ϳ2 percent. The model is limited by not including the effects of volatiles or oxidized iron at elevated pressure.
A computer simulation study of natural silicate melts. Part I: Low pressure properties
Geochimica et Cosmochimica Acta, 2007
In implementing into a molecular dynamics simulation code a simple interionic potential developed to describe the nine component system K 2 O-Na 2 O-CaO-MgO-FeO-Fe 2 O 3-Al 2 O 3-TiO 2-SiO 2 (KNCMFATS), it has been possible to reproduce satisfactorily a number of thermodynamic, structural and transport properties of a representative set of natural silicate melts. An important conclusion reached in this study is the good transferability of the potential from felsic to ultramafic compositions although this transferability becomes less accurate with high silica contents (rhyolitic composition and beyond) and with very iron-rich silicates (e.g. fayalite). A key feature of the simulation is to make the link between macroscopic properties of the melt and its microscopic structure and dynamics. We thus obtain a relationship between the molar volume of the melt, the number of network modifiers and the oxygen coordination number. The simulation also allows one to quantify the coordination environment around the cations as function of the melt composition. Furthermore, the electrical conductivity of the high temperature liquid is investigated.
Isotope fractionation by diffusion in silicate melts: Insights from molecular dynamics simulations
Geochimica et Cosmochimica Acta, 2012
Molecular dynamics simulations were performed to determine the isotope effect on diffusion in SiO 2 and MgSiO 3 liquids. The influence of an element's atomic mass on its diffusivity can be expressed in terms of the empirical relation D 1 D 2 ¼ m 2 m 1 b. For Si, b has a value of $0.05 in both SiO 2 and MgSiO 3 liquids, and is independent of pressure. The exponent b for Mg in MgSiO 3 is larger, 0.135 at 1 atm, and decreases with pressure, to 0.084 at 50 GPa. Varying the mass and concentration of an isotope of one element is also found to have a significant influence on the diffusivity of other elements, due to the cooperative motions of the many atoms that are involved in diffusion. Interdiffusion between basaltic and rhyolitic magmas is inferred to be capable of producing isotope fractionations of tenths of per mil in Si, and tens of per mil in Mg. Significant diffusive fractionation of Si and Mg isotopes is also possible during the growth of olivine phenocrysts, if the growth rate is on the order of cm/yr or faster.
Geochemistry, Geophysics, Geosystems, 2002
1] We describe a newly calibrated model for the thermodynamic properties of magmatic silicate liquid. The new model, pMELTS, is based on MELTS [Ghiorso and Sack, 1995] but has a number of improvements aimed at increasing the accuracy of calculations of partial melting of spinel peridotite. The pMELTS algorithm uses models of the thermodynamic properties of minerals and the phase equilibrium algorithms of MELTS, but the model for silicate liquid differs from MELTS in the following ways: (1) The new algorithm is calibrated from an expanded set of mineral-liquid equilibrium constraints from 2439 experiments, 54% more than MELTS. (2) The new calibration includes mineral components not considered during calibration of MELTS and results in 11,394 individual mineral-liquid calibration constraints (110% more than MELTS). Of these, 4924 statements of equilibrium are from experiments conducted at elevated pressure (200% more than MELTS). (3) The pMELTS model employs an improved liquid equation of state based on a third-order Birch-Murnaghan equation, calibrated from high-pressure sink-float and shockwave experiments to 10 GPa. (4) The new model employs a revised set of end-member liquid components. The revised components were chosen to better span liquid composition-space. Thermodynamic properties of these components are optimized as part of the mineral-liquid calibration. Comparison of pMELTS to partial melting relations of spinel peridotite from experiments near 1 GPa indicates significant improvements relative to MELTS, but important outstanding problems remain. The pMELTS model accurately predicts oxide concentrations, including SiO 2 , for liquids from partial melting of MM3 peridotite at 1 GPa from near the solidus up to 2525% melting. Compared to experiments, the greatest discrepancy is for MgO, for which the calculations are between 1 and 4% high. Temperatures required to achieve a given melt fraction match those of the experiments near the solidus but are 2560°C high over much of the spinel lherzolite melting interval at this pressure. Much of this discrepancy can probably be attributed to overstabilization of clinopyroxene in pMELTS under these conditions. Comparison of pMELTS calculations to the crystallization and partial melting experiments of Falloon et al. [1999] shows excellent agreement but also suffers from exaggerated calculated stability of clinopyroxene. Finally, comparison of pMELTS
Nature Communications, 2020
Transport properties like diffusivity and viscosity of melts dictated the evolution of the Earth’s early magma oceans. We report the structure, density, diffusivity, electrical conductivity and viscosity of a model basaltic (Ca11Mg7Al8Si22O74) melt from first-principles molecular dynamics calculations at temperatures of 2200 K (0 to 82 GPa) and 3000 K (40–70 GPa). A key finding is that, although the density and coordination numbers around Si and Al increase with pressure, the Si–O and Al–O bonds become more ionic and weaker. The temporal atomic interactions at high pressure are fluxional and fragile, making the atoms more mobile and reversing the trend in transport properties at pressures near 50 GPa. The reversed melt viscosity under lower mantle conditions allows new constraints on the timescales of the early Earth’s magma oceans and also provides the first tantalizing explanation for the horizontal deflections of superplumes at ~1000 km below the Earth’s surface.