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Register a new userThermodynamics of hexagonal-close-packed iron under Earths core conditions
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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.
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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.
Bulk, shear, and compressional aggregate sound velocities of hydrogen and helium in the close- packed hexagonal structure are calculated over a wide pressure range using two complementary approaches: semi-empirical lattice dynamics based on the many-body intermolecular potentials and density-functional theory in the generalized gradient approximation. The sound velocities are used to calculate pressure dependence of the Debye temperature. The comparison between experiment and first-principle and semi-empirical calculations provide constraints on the density dependence of intermolecular interactions in the zero-temperature limit.
The Earth acts as a gigantic heat engine driven by decay of radiogenic isotopes and slow cooling, which gives rise to plate tectonics, volcanoes, and mountain building. Another key product is the geomagnetic field, generated in the liquid iron core by a dynamo running on heat released by cooling and freezing to grow the solid inner core, and on chemical convection due to light elements expelled from the liquid on freezing. The power supplied to the geodynamo, measured by the heat-flux across the core-mantle boundary (CMB), places constraints on Earths evolution. Estimates of CMB heat-flux depend on properties of iron mixtures under the extreme pressure and temperature conditions in the core, most critically on the thermal and electrical conductivities. These quantities remain poorly known because of inherent difficulties in experimentation and theory. Here we use density functional theory to compute these conductivities in liquid iron mixtures at core conditions from first principles- the first directly computed values that do not rely on estimates based on extrapolations. The mixtures of Fe, O, S, and Si are taken from earlier work and fit the seismologically-determined core density and inner-core boundary density jump. We find both conductivities to be 2-3 times higher than estimates in current use. The changes are so large that core thermal histories and power requirements must be reassessed. New estimates of adiabatic heat-flux give 15-16 TW at the CMB, higher than present estimates of CMB heat-flux based on mantle convection; the top of the core must be thermally stratified and any convection in the upper core driven by chemical convection against the adverse thermal buoyancy or lateral variations in CMB heat flow. Power for the geodynamo is greatly restricted and future models of mantle evolution must incorporate a high CMB heat-flux and explain recent formation of the inner core.
The transport properties of iron under Earths inner core conditions are essential input for the geophysical modelling but are poorly constrained experimentally. Here we show that the thermal and electrical conductivity of iron at those conditions remains high even if the electron-electron-scattering (EES) is properly taken into account. This result is obtained by ab initio simulations taking into account consistently both thermal disorder and electronic correlations. Thermal disorder suppresses the non-Fermi-liquid behavior of the body-centered cubic iron phase, hence, reducing the EES; the total calculated thermal conductivity of this phase is 220 Wm$^{-1}$K$^{-1}$ with the EES reduction not exceeding 20%. The EES and electron-lattice scattering are intertwined resulting in breaking of the Matthiessens rule with increasing EES. In the hexagonal close-packed iron the EES is also not increased by thermal disorder and remains weak. Our main finding thus holds for the both likely iron phases in the inner core.
We employ state-of-the-art ab initio simulations within the dynamical mean-field theory to study three likely phases of iron (hexogonal close-packed, hcp, face centered cubic, fcc, and body centered cubic, bcc) at the Earths core conditions. We demonstrate that the correction to the electronic free energy due to correlations can be significant for the relative stability of the phases. The strongest effect is observed in bcc Fe, which shows a non-Fermi liquid behaviour, and where a Curie-Weiss behaviour of the uniform susceptbility hints at a local magnetic moment still existing at 5800 K and 300 GPa. We predict that all three structures have sufficiently high magnetic susceptibility to stabilize the geodynamo.
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