Evgeny Wasserman

Composition and temperature of Earth's inner core

We compare a theoretical prediction of the equation of state of iron at high pressures and temperatures to the properties of the Earths inner core. The theoretical result is based on a first principles treatment of the static pressure and the pressure due to thermal excitation of electrons and an approximate ab initio (cell model) treatment of the Vibrational pressure. The density of iron is found to be greater than that of the inner core even for unrealistically high temperatures of 8000 K. The isentropic bulk modulus of iron is found to be consistent with that of the inner core over a wide range of temperatures (4000–8000 K). We conclude on the basis of these comparisons that the inner core contains a substantial fraction of elements lighter than iron. Assuming ideal solutions, we find the temperature and light component mass fraction required to simultaneously match the density and bulk modulus of the inner core. For a temperature of 7000 K, 1 wt % O as FeO, satisfies the inner core observations. The temperature and mass fraction of S required depend on whether S is included as pyrite (2 wt % S, 5500 K) or as Fe0.9S (>8 wt % S, <3500 K). On the basis of this result and empirical mixing rules for Fe-O solutions, we argue that Fe-light element solid solutions at inner core conditions may be significantly nonideal. We derive expressions for the properties of nonideal multicomponent solutions that are valid in the limit of small amounts of impurities. These lead to general results for the properties of the alloy fraction that are required by comparisons of our equation of state of iron with seismological models.

Ewald methods for polarizable surfaces with application to hydroxylation and hydrogen bonding on the (012) and (001) surfaces of α-Fe2O3

We present a clear and rigorous derivation of the Ewald-like method for calculation of the electrostatic energy of the systems infinitely periodic in two dimensions and of finite size in the third dimension (slabs). We have generalized this method originally developed by Rhee et al. (Phys. Rev. B 40 (1989) 36) to account for charge-dipole and dipole-dipole interactions and therefore made it suitable for treatment of polarizable systems. This method has the advantage over exact methods of being significantly faster and therefore appropriate for large-scale molecular dynamics simulations. However, it involves a Taylor expansion which has to be demonstrated to be of sufficient order. The method was extensively benchmarked against the exact methods by Leckner and Parry. We found it necessary to increase the order of the multipole expansion from 4 (as in the original work by Rhee et al.) to 6. In this case the method is adequate for aspect ratios (thickness/shortest side length of the unit cell) ≤ 0.5. Molecular dynamics simulations using the transferable/polarizable model by Rustad et al. were applied to study the surface relaxation of the nonhydroxylated, hydroxylated and solvated surfaces of α-Fe2O3 (hematite). We find that our nonhydroxylated structures and energies are in good agreement with previous LDA calculations on α-alumina by Manassidis et al. (Surf. Sci. 285 (1993) L517). Using the results of molecular dynamics simulations of solvated interfaces, we define end-member hydroxylated-hydrated states for the surfaces which are used in energy minimization calculations. We find that hydration has a small effect on the surface structure, but that hydroxylation has a significant effect. Our calculations, both for gas-phase and solution-phase adsorption, predict a greater amount of hydroxylation for the α-Fe2O3 (012) surface than for the (001) surface. Our simulations also indicate the presence of four-fold coordinated iron ions on the (001) surface.

Compositional effects on the transport and thermodynamic properties of MgOSiO2 mixtures using molecular dynamics

Abstract We have carried out equilibrium molecular dynamics simulations of MgOSiO2 mixtures with compositions continuously ranging from 20 to 80 mol.% MgO using Born-Mayer-type pairwise interaction potentials. Enthalpies of mixing, self-diffusion and mutual diffusion coefficients, shear viscosities, radial distribution functions and infrared absorption spectra were calculated. Self-diffusion coefficients determined at various pressures and temperatures ranging from 3500 to 5000 K increase significantly with greater amounts of MgO. The compositional increase of the mutual diffusion coefficient is less pronounced. The calculated compositional dependence of shear viscosity differs significantly from that expected from Stokes-Einstein or Eyring relationships. Computed radial distribution functions, velocity autocorrelation functions, and infrared absorption spectra allow for the monitoring of changes in melt structure with varying composition.

An extended molecular mechanics (MM3(96)) force field for benzocrown ethers, calixarenes, and spherands

Abstract The X-ray crystal structures of 60 molecules containing aliphatic and conjugated ether functional groups were calculated with an extended version of the molecular mechanics MM3(96) force field. The structures fit well with overall deviations of 0.014 A in bond length, 1.1 ° in bond angle, and 3.2 ° in torsion angle.

The Magnetite (001) Surface: Insights from Molecular Dynamics Calculations

A classical polarizable potential model is used in a molecular dynamics model of the magnetite (001) surface. The model, previously applied to the tetrahedral, or “A” termination of magnetite (001) is here applied to the octahedral or “B” termination, as well as to the hydroxylation of both the “A” and “B” termination. Surface relaxations for the “B” terminated surface are small, and consistent with the observed (√2×√2)R45 cell observed in LEED experiments. Additionally, it is shown that the relaxation of a tetrahedral defect on the “B” terminated surface does not give rise to the same relaxation mechanism as that calculated for the tetrahedral sites on the “A” surface. The lack of a “dimer” forming at the defect site is consistent with recent STM studies. Calculations on charge-ordered magnetite slabs indicate that, within the context of the ionic model used here, the surface energy of the “A” termination of magnetite is lower than that of the “B” termination over a wide range of oxygen ftigacities. Hydr xylation has a negligible effect on the relative energies of the “A” and “B” surfaces, however, the large gain in energy associated with tetrahedral ion relaxation on the “A” surface could explain the lack of two high temperature peaks expected for successive removal of adsorbing waters from the same tetrahedral site.

Elasticity, Thermal Properties, and Molecular Dynamics Using Non-Empirical Tight-Binding

We have further developed and applied a new non-empirical tight-binding total energy model to properties of Si, Xe, and Fe at high pressures. We have studied elasticity of various phases of each of these, demonstrating that the new model is applicable to a wide range of materials, including semiconductors, rare gases, and transition metals. We have used the particle-in-a-cell method to study the thermal equation of state of hep Fe and find excellent agreement with the shock equation of state. A molecular dynamics code has been developed based on this method, and we have studied the properties of Fe liquid at high pressures.