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Register a new userIron under Earths core conditions: Liquid-state thermodynamics and high-pressure melting curve
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{em Ab initio} techniques based on density functional theory in the projector-augmented-wave implementation are used to calculate the free energy and a range of other thermodynamic properties of liquid iron at high pressures and temperatures relevant to the Earths core. The {em ab initio} free energy is obtained by using thermodynamic integration to calculate the change of free energy on going from a simple reference system to the {em ab initio} system, with thermal averages computed by {em ab initio} molecular dynamics simulation. The reference system consists of the inverse-power pair-potential model used in previous work. The liquid-state free energy is combined with the free energy of hexagonal close packed Fe calculated earlier using identical {em ab initio} techniques to obtain the melting curve and volume and entropy of melting. Comparisons of the calculated melting properties with experimental measurement and with other recent {em ab initio} predictions are presented. Experiment-theory comparisons are also presented for the pressures at which the solid and liquid Hugoniot curves cross the melting line, and the sound speed and Gr{u}neisen parameter along the Hugoniot. Additional comparisons are made with a commonly used equation of state for high-pressure/high-temperature Fe based on experimental data.
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The free energy and other thermodynamic properties of hexagonal-close-packed iron are calculated by direct {em ab initio} methods over a wide range of pressures and temperatures relevant to the Earths core. The {em ab initio} calculations are based on density-functional theory in the generalised-gradient approximation, and are performed using the projector augmented wave (PAW) approach. Thermal excitation of electrons is fully included. The Helmholtz free energy consists of three parts, associated with the rigid perfect lattice, harmonic lattice vibrations, and anharmonic contributions, and the technical problems of calculating these parts to high precision are investigated. The harmonic part is obtained by computing the phonon frequencies over the entire Brillouin zone, and by summation of the free-energy contributions associated with the phonon modes. The anharmonic part is computed by the technique of thermodynamic integration using carefully designed reference systems. Detailed results are presented for the pressure, specific heat, bulk modulus, expansion coefficient and Gr{u}neisen parameter, and comparisons are made with values obtained from diamond-anvil-cell and shock experiments.
We report on the thermal and electrical conductivities of two liquid silicon-oxygen-iron mixtures (Fe$_{0.82}$Si$_{0.10}$O$_{0.08}$ and Fe$_{0.79}$Si$_{0.08}$O$_{0.13}$), representative of the composition of the Earths outer core at the relevant pressure-temperature conditions, obtained from density functional theory calculations with the Kubo-Greenwood formulation. We find thermal conductivities $k$ =100 (160) W m$^{-1}$ K$^{-1}$, and electrical conductivities $sigma = 1.1 (1.3) times 10^6 Omega^{-1}$ m$^{-1}$ at the top (bottom) of the outer core. These new values are between 2 and 3 times higher than previous estimates, and have profound implications for our understanding of the Earths thermal history and the functioning of the Earths magnetic field, including rapid cooling rate for the whole core or high level of radiogenic elements in the core. We also show results for a number of structural and dynamic properties of the mixtures, including the partial radial distribution functions, mean square displacements, viscosities and speeds of sound.
Melting of orthorhombic boron silicide B6Si has been studied at pressures up to 8 GPa using in situ electrical resistivity measurements and quenching. It has been found that in the 2.6-7.7 GPa range B6Si melts congruently, and the melting curve exhibits negative slope of -31(2) K/GPa that points to a higher density of the melt as compared to the solid phase. At very high temperatures B6Si melt appears to be unstable and undergoes disproportionation into silicon and boron-rich silicides. The onset temperature of disproportionation strongly depends on pressure, and the corresponding low-temperature boundary exhibits negative slope of -92(3) K/GPa which is indicative of significant volume decrease in the course of B6Si melt decomposition.
The electronic state and transport properties of hot dense iron are of the utmost importance to geophysics. Combining the density functional and dynamical mean field theories we study the impact of electron correlations on electrical and thermal resistivity of hexagonal close-packed $epsilon$-Fe at Earths core conditions. $epsilon$-Fe is found to behave as a nearly perfect Fermi liquid. The quadratic dependence of the scattering rate in Fermi liquids leads to a modification of the Wiedemann-Franz law with suppression of the thermal conductivity as compared to the electrical one. This significantly increases the electron-electron thermal resistivity which is found to be of comparable magnitude to the electron-phonon one. The implications of this effect on the dynamics of Earths core is discussed.
We discuss the role of dynamical many-electron effects in the physics of iron and iron-rich solid alloys under applied pressure on the basis of recent ab initio studies employing the dynamical mean-field theory (DMFT). Electronic correlations in iron in the moderate pressure range up to 60 GPa are discussed in the first section. DMFT-based methods predict an enhancement of electronic correlations at the pressure-induced transition from body-centered cubic (bcc) alpha-Fe to hexagonal close-packed (hcp) epsilon-Fe. In particular, the electronic effective mass, scattering rate and electron-electron contribution to the electrical resistivity undergo a step-wise increase at the transition point. One also finds a significant many-body correction to the epsilon-Fe equation of state, thus clarifying the origin of discrepancies between previous DFT studies and experiment. An electronic topological transition is predicted to be induced in epsilon-Fe by many-electron effects; its experimental signatures are analyzed. Next section focuses on the geophysically relevant pressure-temperature regime of the Earths inner core (EIC) corresponding to the extreme pressure of 360 GPa combined with temperatures up to 6000 K. The three iron allotropes (bcc, hcp and face-centered-cubic) previously proposed as possible stable phases at such conditions are found to exhibit qualitatively different many-electron effects as evidenced by a strongly non-Fermi-liquid metallic state of bcc-Fe and an almost perfect Fermi liquid in the case of hcp-Fe. A recent active discussion on the electronic state and transport properties of hcp-Fe at the EIC conditions is reviewed in details. We also discuss the impact of a Ni admixture, which is expected to be present in the core matter. We conclude by outlining some limitation of the present DMFT-based framework and perspective directions for further development.
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