Anatoly B. Belonoshko

Stability of the body-centred-cubic phase of iron in the Earth's inner core

Iron is thought to be the main constituent of the Earths core, and considerable efforts have therefore been made to understand its properties at high pressure and temperature. While these efforts have expanded our knowledge of the iron phase diagram, there remain some significant inconsistencies, the most notable being the difference between the ‘low’ and ‘high’ melting curves. Here we report the results of molecular dynamics simulations of iron based on embedded atom models fitted to the results of two implementations of density functional theory. We tested two model approximations and found that both point to the stability of the body-centred-cubic (b.c.c.) iron phase at high temperature and pressure. Our calculated melting curve is in agreement with the ‘high’ melting curve, but our calculated phase boundary between the hexagonal close packed (h.c.p.) and b.c.c. iron phases is in good agreement with the ‘low’ melting curve. We suggest that the h.c.p.–b.c.c. transition was previously misinterpreted as a melting transition, similar to the case of xenon, and that the b.c.c. phase of iron is the stable phase in the Earths inner core.

A molecular dynamics study of the pressure-volume-temperature properties of super-critical fluids: I. H2O

The method of molecular dynamics (MD) is used to simulate the pressure-volume-temperature (PVT) of water in the pressure range of 5 kbar to 1 megabar and in the temperature range of 700 to 4000 K. For the MD simulation, we use the exponential-6 form for the intermolecular potential. The parameters of the potential are calculated from the available experimental PVT data. The MD-simulated data fit the experimental (static) and the shock-wave data well. An equation of state based on the experimental and MD-simulated data is as follows: P = aV+bV2 + cV4.586 where a = 1.40203·1E + 5 − 41.2336T,b = −7.72779·1E + 6 + 6.70124·1E + 3·T,c = 6.52012·1E + 9 − 0.45580·1E + 6·T,T in K and P in bar.

Molecular dynamics of NaCl (B1 and B2) and MgO (B1) melting; two-phase simulation

Abstract Melting of NaCl and MgO has been simulated with a two-phase molecular dynamics method at constant pressure using newly developed interaction potentials. Equations of state for NaCl and MgO simulated by molecular dynamics are in good agreement with available experimental data. Equations of state for MgO and NaCl were obtained by fitting simulated volumetric properties at pressures and temperatures up to 300 kbar and 3000 K (for NaCl) and 2000 kbar and 7000 K (for MgO). The pressure dependence of the melting temperature was predicted up to 1000 and 1400 kbar for NaCl and MgO, respectively. Crystallization and melting were observed without hysteresis. The simulated melting curve of NaCl is fully consistent with experimental measurements. The pressure dependence of the melting temperature of MgO is consistent with experimental data at 1 bar and previous theoretical estimations by Jackson (1977) and Ohtani (1983). The melting temperature of MgO is substantially higher than that determined by Zerr and Boehler (1994) (by 1000 K at 300 kbar) and substantially lower than that predicted by Cohen and Gong (1994) (by 1500 Kat 300 kbar). The melting temperature of MgO at the pressure of the core-mantle boundary is calculated to be 6900 ± 200 K. The procedures for simulation of melting of NaCl and MgO, starting from a calculation of the interatomic potential and ending with analysis of results, are identical.

MOLECULAR DYNAMICS OF MGSIO3 PEROVSKITE AT HIGH PRESSURES : EQUATION OF STATE, STRUCTURE, AND MELTING TRANSITION

Abstract Molecular dynamics (MD) simulations of MgSiO 3 -perovskite and melt with the Matsui (1988) interatomic potential are used to resolve the problem of inconsistency between modeled and experimental melting curves. Equations of state for solid and liquid MgSiO 3 -perovskite are in agreement with experimental data and are useful for calculating densities at experimentally inaccessible temperatures and pressures. Comparison with the Preliminary Earth Model ( Dziewonski and Anderson , 1981) shows that the equation of state of MgSiO 3 -perovskite is consistent with seismic parameter for lower mantle. Two-phase MD simulations at constant pressure were also performed to calculate a melting curve of MgSiO 3 -perovskite in agreement with the recent experiments. Overheating does not exceed 400 K in accord with the theoretical estimate for finite systems. Extrapolation of meltings temperature to the coremantle boundary pressure (134 GPa) with the Simon equation gives temperature of ≈6400 K for MgSiO 3 -perovskite and shows that, according to accepted estimates of temperature at core-mantle boundary, MgSiO 3 -perovskite remains solid.

A molecular dynamics study of the pressure-volume-temperature properties of supercritical fluids: II. CO2, CH4, CO, O2, and H2

Abstract The method of molecular dynamics (MD) has been used to simulate the pressure-volume-temperature (PVT) properties of CO2, CH4, CO, O2, and H2. For the MD simulation, the exponential-6 form of the intermolecular potential has been adopted. The parameters of the potential are calculated from the available experimental PVT data. The MD-simulated results fit the experimental (static) PVT data well and are in reasonable agreement with the shock-wave P-V data. Based on both the experimental PVT and the MD-simulated data, equations of the type: P = a/V + b/V2 + c/Vn have been formulated for each of the five fluids in the pressure range of 5 Kbar to 1 Mbar at temperatures from 400 to 4000 K. The calculated fugacity of CO2 has been used to show the consistency of the modeled data with the experimental phase equilibrium data on the reactions involving magnesite.

Elastic Anisotropy of Earth's Inner Core

Earths solid-iron inner core is elastically anisotropic. Sound waves propagate faster along Earths spin axis than in the equatorial plane. This anisotropy has previously been explained by a preferred orientation of the iron alloy hexagonal crystals. However, hexagonal iron becomes increasingly isotropic on increasing temperature at pressures of the inner core and is therefore unlikely to cause the anisotropy. An alternative explanation, supported by diamond anvil cell experiments, is that iron adopts a body-centered cubic form in the inner core. We show, by molecular dynamics simulations, that the body-centered cubic iron phase is extremely anisotropic to sound waves despite its high symmetry. Direct simulations of seismic wave propagation reveal an anisotropy of 12%, a value adequate to explain the anisotropy of the inner core.

A unified equation of state for fluids of C-H-O-N-S-Ar composition and their mixtures up to very high temperatures and pressures

Abstract A unified 3-parameter equation of state (EOS) for fluids of C-H-O-N-S-Ar composition based on molecular dynamical simulated data and on an approximation of intermolecular interaction with α-exponential-6 potential is shown to be valid at high pressure and temperature. The equation is parameterized for H 2 O, CO 2 , CH 4 , CO, O 2 , H 2 , Ar, N 2 , NH 3 , H 2 S, SO 2 , COS, and S 2 in the ranges of temperature ( T ) from 400 K (700 K for H 2 O) to 4000 K and pressure from 5 kbar to 1000 kbar. The equation allows one to calculate any mixture of the fluid species in the system applying one-fluid approximation (i.e., using the α-exponential-6 parameters obtained by using mixing rules for the potentials of the pure species). The equation reproduces most of the available experimental data in the limits of experimental accuracy of volume ( V ) measurements.

Origin of the low rigidity of the Earth's inner core

Earths solid-iron inner core has a low rigidity that manifests itself in the anomalously low velocities of shear waves as compared to shear wave velocities measured in iron alloys. Normally, when estimating the elastic properties of a polycrystal, one calculates an average over different orientations of a single crystal. This approach does not take into account the grain boundaries and defects that are likely to be abundant at high temperatures relevant for the inner core conditions. By using molecular dynamics simulations, we show that, if defects are considered, the calculated shear modulus and shear wave velocity decrease dramatically as compared to those estimates obtained from the averaged single-crystal values. Thus, the low shear wave velocity in the inner core is explained.

Stability of the MgCO3 structures under lower mantle conditions

Abstract The presence of carbon in the Earth makes the search for high-pressure carbon-containing phases essential for our understanding of mineral compositions of the Earths mantle. In a recent study Isshiki et al. (2004) demonstrated that magnesite transforms into a new phase at lower mantle pressures. However, the structure of the emerging phase remained unknown. Here we show, by means of first principles calculations, that MgCO3 magnesite can transform into a pyroxene structure at 113 GPa, which further transforms into a CaTiO3-type structure at about 200 GPa.

Molecular dynamics of stishovite melting

Abstract The melting curve of stishovite is calculated using a newly developed interatomic potential and two-phase molecular dynamics simulation at constant pressure. The melting curve is consistent with experimental data at pressures up to 350 kbar. The interatomic potential is suitable for calculation of thermoelastic properties of silica phases over a wide pressure-temperature range. Stishovite is found to melt at a temperature 5850 ± 150 K at 1.4 Mbar pressure. The coordination number of silicon in the melt gradually changes from 4 to 6 along melting curve with increasing pressure.