First-principles thermal equation of state and thermoelasticity of hcp Fe at high pressures

We investigate the equation of state and elastic properties of hcp iron at high pressures and high temperatures using first principles linear response linear-muffin-tin-orbital method in the generalized-gradient approximation. We calculate the Helmholtz free energy as a function of volume, temperature, and volume-conserving strains, including the electronic excitation contributions from band structures and lattice vibrational contributions from quasi-harmonic lattice dynamics. We perform detailed investigations on the behavior of elastic moduli and equation of state properties as functions of temperature and pressure, including the pressure-volume equation of state, bulk modulus, the thermal expansion coefficient, the Gruneisen ratio, and the shock Hugoniot. Detailed comparison has been made with available experimental measurements and theoretical predictions.Comment: 33 pages, 12 figure

Structure and Dynamics of Liquid Iron under Earth's Core Conditions

First-principles molecular dynamics simulations based on density-functional theory and the projector augmented wave (PAW) technique have been used to study the structural and dynamical properties of liquid iron under Earth's core conditions. As evidence for the accuracy of the techniques, we present PAW results for a range of solid-state properties of low- and high-pressure iron, and compare them with experimental values and the results of other first-principles calculations. In the liquid-state simulations, we address particular effort to the study of finite-size effects, Brillouin-zone sampling and other sources of technical error. Results for the radial distribution function, the diffusion coefficient and the shear viscosity are presented for a wide range of thermodynamic states relevant to the Earth's core. Throughout this range, liquid iron is a close-packed simple liquid with a diffusion coefficient and viscosity similar to those of typical simple liquids under ambient conditions.Comment: 13 pages, 8 figure

Direct Observation of Martensitic Phase-Transformation Dynamics in Iron by 4D Single-Pulse Electron Microscopy

The in situ martensitic phase transformation of iron, a complex solid-state transition involving collective atomic displacement and interface movement, is studied in real time by means of four-dimensional (4D) electron microscopy. The iron nanofilm specimen is heated at a maximum rate of ∼10^(11) K/s by a single heating pulse, and the evolution of the phase transformation from body-centered cubic to face-centered cubic crystal structure is followed by means of single-pulse, selected-area diffraction and real-space imaging. Two distinct components are revealed in the evolution of the crystal structure. The first, on the nanosecond time scale, is a direct martensitic transformation, which proceeds in regions heated into the temperature range of stability of the fcc phase, 1185−1667 K. The second, on the microsecond time scale, represents an indirect process for the hottest central zone of laser heating, where the temperature is initially above 1667 K and cooling is the rate-determining step. The mechanism of the direct transformation involves two steps, that of (barrier-crossing) nucleation on the reported nanosecond time scale, followed by a rapid grain growth typically in ∼100 ps for 10 nm crystallites

First-principles study of the ferroelastic phase transition in CaCl_2

First-principles density-functional calculations within the local-density approximation and the pseudopotential approach are used to study and characterize the ferroelastic phase transition in calcium chloride (CaCl_2). In accord with experiment, the energy map of CaCl_2 has the typical features of a pseudoproper ferroelastic with an optical instability as ultimate origin of the phase transition. This unstable optic mode is close to a pure rigid unit mode of the framework of chlorine atoms and has a negative Gruneisen parameter. The ab-initio ground state agrees fairly well with the experimental low temperature structure extrapolated at 0K. The calculated energy map around the ground state is interpreted as an extrapolated Landau free-energy and is successfully used to explain some of the observed thermal properties. Higher-order anharmonic couplings between the strain and the unstable optic mode, proposed in previous literature as important terms to explain the soft-phonon temperature behavior, are shown to be irrelevant for this purpose. The LAPW method is shown to reproduce the plane-wave results in CaCl_2 within the precision of the calculations, and is used to analyze the relative stability of different phases in CaCl_2 and the chemically similar compound SrCl_2.Comment: 9 pages, 6 figures, uses RevTeX

Transformation Pathways of Silica under High Pressure

Concurrent molecular dynamics simulations and ab initio calculations show that densification of silica under pressure follows a ubiquitous two-stage mechanism. First, anions form a close-packed sub-lattice, governed by the strong repulsion between them. Next, cations redistribute onto the interstices. In cristobalite silica, the first stage is manifest by the formation of a metastable phase, which was observed experimentally a decade ago, but never indexed due to ambiguous diffraction patterns. Our simulations conclusively reveal its structure and its role in the densification of silica.Comment: 14 pages, 4 figure

Melting of tantalum at high pressure determined by angle dispersive x-ray diffraction in a double-sided laser-heated diamond-anvil cell

The high pressure and high temperature phase diagram of Ta has been studied in a laser-heated diamond-anvil cell (DAC) using x-ray diffraction measurements up to 52 GPa and 3800 K. The melting was observed at nine different pressures, being the melting temperature in good agreement with previous laser-heated DAC experiments, but in contradiction with several theoretical calculations and previous piston-cylinder apparatus experiments. A small slope for the melting curve of Ta is estimated (dTm/dP = 24 K/GPa at 1 bar) and a possible explanation for this behaviour is given. Finally, a P-V-T equation of states is obtained, being the temperature dependence of the thermal expansion coefficient and the bulk modulus estimated.Comment: 31 pages, 8 figures, to appear in J.Phys.:Cond.Matte

Fe–FeO and Fe–Fe₃C melting relations at Earth's core–mantle boundary conditions: Implications for a volatile-rich or oxygen-rich core

International audienceEutectic melting temperatures in the Fe–FeO and Fe–Fe3C systems have been determined up to 150 GPa. Melting criteria include observation of a diffuse scattering signal by in situ X-Ray diffraction, and textural characterisation of recovered samples. In addition, compositions of eutectic liquids have been established by combining in situ Rietveld analyses with ex situ chemical analyses. Gathering these new results together with previous reports on Fe–S and Fe–Si systems allow us to discuss the specific effect of each light element (Si, S, O, C) on the melting properties of the outer core. Crystallization temperatures of Si-rich core compositional models are too high to be compatible with the absence of extensive mantle melting at the core–mantle boundary (CMB) and significant amounts of volatile elements such as S and/or C (>5 at%, corresponding to >2 wt%), or a large amount of O (>15 at% corresponding to ∼5 wt%) are required to reduce the crystallisation temperature of the core material below that of a peridotitic lower mantle

Structure and density of Fe-C liquid alloys under high pressure

International audienceThe density and structure of liquid Fe-C alloys have been measured up to 58 GPa and 3,200 K by in situ X-ray diffraction using a Paris-Edinburgh press and laser-heated diamond anvil cell. Study of the pressure evolution of the local structure inferred by X-ray diffraction measurements is important to understand the compression mechanism of the liquid. Obtained data show that the degree of compression is greater for the first coordination sphere than the second and third coordination spheres. The extrapolation of the measured density suggests that carbon cannot be the only light element alloyed to iron in the Earth's core, as 8-16 at % C (1.8-3.7 wt % C) would be necessary to explain the density deficit of the outer core relative to pure Fe. This concentration is too high to account for outer core velocity. The presence of other light elements (e.g., O, Si, S, and H) is thus required