8,542 research outputs found
Thermodynamic stability of Fe/O solid solution at inner-core conditions
No full textWe present a new technique which allows the fully ab initio calculation of the chemical potential of a substitutional impurity in a high-temperature crystal, including harmonic and anharmonic lattice vibrations. The technique uses the combination of thermodynamic integration and reference models developed recently for the ab initio calculation of the free energy of liquids and anharmonic solids. We apply the technique to the case of the substitutional oxygen impurity in h.c.p. iron under Earth's core conditions, which earlier static ab initio calculations indicated to be thermodynamically very unstable. Our results show that entropic effects arising from the large Vibrational amplitude of the oxygen impurity give a major reduction of the oxygen chemical potential, so that oxygen dissolved in h.c.p. iron may be stabilised at concentrations up a few mol % under core conditions
The melting curve of iron at the pressures of the Earth's core from ab initio calculations
No full textThe solid inner core of the Earth and the liquid outer core consist mainly of iron(1) so that knowledge of the high-pressure thermodynamic properties of iron is important for understanding the Earth's deep interior. An accurate knowledge of the melting properties of iron is particularly important, as the temperature distribution in the core is relatively uncertain(2-4) and a reliable estimate of the melting temperature of iron at the pressure of the inner-core boundary would put a much-needed constraint on core temperatures. Here we used ab initio methods to compute the free energies of both solid and liquid iron, and we argue that the resulting theoretical melting curve competes in accuracy with those obtained from high-pressure experiments. Our results give a melting temperature of iron of similar to 6,700 +/- 600 K at the pressure of the inner-core boundary, consistent with some of the experimental measurements. Our entirely ab initio methods should also be applicable to many other materials and problems
Temperature and composition of the Earth's core
No full textThe Earth's core is a ball of swirling hot metal at the centre of our planet, with a radius roughly one half of the Earth's radius. It is formed by two parts: a solid inner core, with a radius of 1221 km, surrounded by a shell of liquid which extends up to 3480 km from the centre. It is widely believe that the Earth's core is mainly formed by iron, or iron with up to 5-10% of nickel. It is also known that the core must contain a significant fraction of light impurities, in the region of 2-3% in the solid and 6-7% in the liquid. The nature of these light impurities is unknown. The temperature of the core is also inaccessible to direct probing. Here we present a theoretical study on the temperature and the composition of the Earth's core. The investigation is based on the application of the implementation of quantum mechanics known as density functional theory. We shall show that these techniques are very accurate at predicting the properties of iron, and therefore can be usefully used to study the properties of the core. We show that by combining these techniques with direct observations it is possible to predict the temperature of the core, in particular the temperature at the boundary between the solid and the liquid core (the ICB), and put constraints on its composition. The result of this study is that the temperature of the ICB is probably in the region of 5400-5700 K and that the outer core contains a significant fraction (8-13%) of oxygen. As the Earth cools down the solid core grows and expels oxygen in the liquid. Since oxygen is lighter than iron it rises in the liquid, and its gravitational energy is available to drive the convective motions in the liquid core that are responsible for the generation of the Earth's magnetic field
The structure of iron under the conditions of the Earth's inner core
No full textThe inferred density of the solid inner core indicates that it is predominantly made of iron. In order to indicates that it is predominantly made of iron. In order to interpret the observed seismic anisotropy and understand the high pressure and temperature behaviour of the core, it is essential to establish the crystal structure of iron under core conditions. On the basis of extrapolated experimental data, a number of candidate structures for the high PIT iron phase have been proposed, namely, body-centred cubic (bcc), body-centred tetragonal (bct), hexagonal close-packed (hcp), double-hexagonal close-packed (dhcp) and an orthorhombically distorted hcp polymorph (Matsui, 1993; Stixrude and Cohen, 1995; Boehler, 1993; Saxena et al., 1996; Andrault et al., 1997). Here we present the results of the first fully ab initio free energy calculations for all of these polymorphs of iron at core pressures and temperatures. Our results show that hcp-Fe is the most stable polymorph of iron under the conditions of the Earth's inner core
Composition and temperature of the Earth's core constrained by combining ab initio calculations and seismic data
No full textIt is shown how ab initio techniques based on density functional theory can be used to calculate the chemical potentials of the leading candidate impurity elements (S, 0 and Si) in the Earth's solid inner core and liquid outer core. The condition that these chemical potentials be equal in the solid and liquid phases provides values for the ratios of the impurity mol fractions in the inner and outer core. By combining the estimated ratios with ab initio values for the impurity molar volumes in the two phases, and demanding that the resulting density discontinuity across the inner-core boundary agree with free-oscillation data, we obtain estimates for the concentrations of S, O and Si in the core. The results show that O partitions much more strongly than S and Si from solid to liquid, and indicate that the presence of O in the core is essential to account for seismic measurements. We suggest that if compositional convection drives the Earth's magnetic field, then the presence of O may be essential for this compositional convection. (C) 2002 Elsevier Science B.V. All rights reserved
Constraints on the composition of the Earth's core from ab initio calculations
No full textKnowledge of the composition of the Earth's core(1-3) is important for understanding its melting point and therefore the temperature at the inner-core boundary and the temperature profile of the core and mantle. In addition, the partitioning of light elements between solid and liquid, as the outer core freezes at the inner-core boundary, is believed to drive compositional convection(4), which in turn generates the Earth's magnetic field. It is generally accepted that the liquid outer core and the solid inner core consist mainly of iron(1). The outer core, however, is also thought to contain a significant fraction of light elements, because its density-as deduced from seismological data and other measurements-is 6-10 per cent less than that estimated for pure liquid iron(1-3). Similar evidence indicates a smaller but still appreciable fraction of light elements in the inner core(5,6). The leading candidates for the light elements present in the core are sulphur, oxygen and silicon(3). Here we obtain a constraint on core composition derived from ab initio calculation of the chemical potentials of light elements dissolved in solid and liquid iron. We present results for the case of sulphur, which provide strong evidence against the proposal that the outer core is close to being a binary iron-sulphur mixture(7)
The melting curve of iron from quantum mechanics calculations
No full textThe high-pressure melting curve of iron is of major importance to the Earth's sciences, as it provides a close estimate of the temperature of the Earth's core. Despite being studied experimentally for more than a decade and, more recently, using theoretical quantum mechanics techniques, there are still large discrepancies between different groups. In this article, we will describe our theoretical approach to the problem and discuss the reason of the discrepancies with other theoretical calculations. (C) 2004 Elsevier Ltd. All rights reserved
Thermodynamics from first principles: temperature and composition of the Earth's core
No full textWe summarize the main ideas used to determine the thermodynamic properties of pure systems and binary alloys from first principles calculations. These are based on the ab initio calculations of free energies. As an application we present the study of iron and iron alloys Under Earth's core conditions. In particular, we report the whole melting curve of iron under these conditions, and we put constraints oil the composition of the core. We found that iron melts at 6350+/-600 K at the pressure corresponding to the boundary between the solid inner core and the liquid outer core (ICB). We show that the core Could not have been formed from a binary mixture of Fe with S, Si or 0 and we propose a ternary or quaternary mixture with 8-10% of S/Si in both liquid and solid and all additional similar to8% of oxygen in the liquid. Based oil this proposed composition we calculate the shift of melting temperature with respect to the melting temperature of pure Fe of similar to-700 K, so that our best estimate for the temperature of the Earth's core at ICB is 5650+/-600 K
Ab initio chemical potentials of solid and liquid solutions and the chemistry of the Earth's core
No full textA general set of methods is presented for calculating chemical potentials in solid and liquid mixtures using ab initio techniques based on density functional theory (DFT). The methods are designed to give an ab initio approach to treating chemical equilibrium between coexisting solid and liquid solutions, and particularly the partitioning ratios of solutes between such solutions. For the liquid phase, the methods are based on the general technique of thermodynamic integration, applied to calculate the change of free energy associated with the continuous interconversion of solvent and solute atoms, the required thermal averages being computed by DFT molecular dynamics simulation. For the solid phase, free energies and hence chemical potentials are obtained using DFT calculation of vibrational frequencies of systems containing substitutional solute atoms, with anharmonic contributions calculated, where needed, by thermodynamic integration. The practical use of the methods is illustrated by applying them to study chemical equilibrium between the outer liquid and inner solid parts of the Earth's core, modeled as solutions of S, Si, and O in Fe. The calculations place strong constraints on the chemical composition of the core, and allow an estimate of the temperature at the inner-core/outer-core boundary. (C) 2002 American Institute of Physics
Iron under Earth’s core conditions: Liquid-state thermodynamics and high-pressure melting curve from ab initio calculations
No full textAb 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 Earth’s core. The 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 ab initio system, with thermal averages computed by 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 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 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 Grüneisen 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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