1,721,049 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
Ab initio thermodynamics and phase diagram of solid magnesium: A comparison of the LDA and GGA
No full textThe finite temperature density functional theory and quasiharmonic lattice dynamics have been used to compute numerous thermodynamic properties of hexagonal close packed magnesium using both the local density approximation (LDA) and the generalized gradient approximation (GGA) for the exchange-correlation potential. Generally, it is found that there exist only minor differences between the LDA and GGA computed properties, with both giving good agreement with experiment. The hcp-bcc phase boundary has also been computed and is found to be in agreement with experimental observation. Again, only slight differences are found between the LDA and GGA. (c) 2006 American Institute of Physics
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 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
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
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)
Ab initio calculations on the free energy and high P-T elasticity of face-centred-cubic iron
No full textAb initio finite temperature molecular dynamics simulations have been used to calculate the free energy and elasticity of face-centred cubic (fcc) iron at a state point representative of the Earth's inner core. Whilst the free energy of this phase is found to be higher than that of hexagonal-close-packed (hcp) iron, the difference is only 14 meV/atom. It is possible that this difference might be overcome by the presence of light elements, as previous calculations at zero Kelvin have shown that the addition of elements such as silicon stabilise fec-Fe with respect to hcp-Fe by at least 40 meV/atom. The calculated elastic constants at core pressures and temperatures of pure fec-Fe, and of alloys of Fe with sulphur and nickel (Fe3S and Fe3Ni) derived from the fee structure, lead to average shear wave velocities that are considerably higher than those inferred from seismology; however, these mineralogical and seismological results could be reconciled by the presence of partial melt in the inner core. The calculated P-wave anisotropy of fec-Fe is comparable with the seismological values, but only if there is a high degree of crystal alignment, although the necessity for alignment can be reduced if a layered model for the inner core is invoked. The results presented in this paper therefore suggest that fcc-Fe cannot be ruled out as a candidate for the dominant phase of the Earth's inner core. (c) 2008 Elsevier B.V. All rights reserved
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
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