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

Abstract

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 IntroductionIron is one of the most abundant elements in the Earth, and is fundamental to our world. The study of iron at high pressures and high temperatures is of great geophysical interest, since both the Earth's liquid outer core and solid inner core are composed mostly of this element. Although the crystal structure of iron at the extremely high temperature (4000 to 8000 K) and high pressure (330 to 360 GPa) conditions found in the inner core is still under intensive debate, 1-10 the hexagonal-close-packed phase (ε-Fe) is commonly believed to have a wide stability field extending from deep mantle to core conditions, and serves as a starting point for understanding the nature of the inner core. 11 Significant experimental and theoretical efforts have been recently devoted to investigate various properties of hcp iron at high pressures and high temperatures. New high-pressure diamond-anvil-cell techniques have been developed or significantly improved, which makes it possible to reach higher pressures and provide more valuable information on material properties in these extreme states. First-principles based theoretical techniques have been improved in reliability and accuracy, and have been widely used to predicate the high pressure-temperature behavior and provide fundamental understandings to the experiment.Despite intensive investigations, numerous fundamental problems remain unresolved, and many of the current results are mutually inconsistent. 11 The melting line at very high pressures has been one of the most difficult and controversial problems. 12-19Other major problems include possible subsolidus phase transitions 2,4,5,11,20 and the magnetic structure of the dense hexagonal iron. In section II we detail the theoretical methods to perform the first-principles calculations and obtain the thermal properties and elastic moduli. We present the results and related discussions about the thermal equation of state in section III, and about the thermoelasticity in section IV. We conclude with a brief summary in Section V. II. Theoretical methodsThe Helmholtz free energy F for many metals has three major contributionswith V as the volume, T as the temperature, and δ as the strain. E static is the zerotemperature energy of a static lattice, F el is the thermal free energy arising from electronic excitations, and F ph is the lattice vibrational energy contribution. We obtain both E static and F el from first-principles calculations directly, assuming that the eigenvalues for given lattice and nuclear pos...

Sound velocity of hcp-Fe at high pressure: experimental constraints, extrapolations and comparison with seismic models

“…In particular, our results argue for combined effects of high temperature and inner core impurities (such as nickel and light elements) that slightly reduce V P of pure hcp-Fe at constant density. This can be potentially satisfied by assuming that both alloying and high temperature only very moderately lower V P , which, however, is not supported by recent results (Badro et al, 2007;Antonangeli et al, 2010;Sha and Cohen 2010;Mao et al 2012;Martorell et al, 2013). Alternatively, and most likely, effects of impurities (combined effect of nickel and light elements) and high temperature counterbalance, the first increasing velocity at constant density (e.g.…”

“…This is because anharmonic and/or pre-melting effects at high temperature (e.g. Laio et al, 2000;Vočadlo et al, 2009;Sha and Cohen, 2010;Martorell et al, 2013), as well as the possible presence of fluid inclusion in the core (Vočadlo, 2007), or frequency-dependent viscoelastic relaxations (Jackson et al, 2000), are all expected to more strongly influence V S than V P .…”

“…The most reasonable explanation for this difference is the anharmonic effects at high temperature, which are predicted to decrease velocities even at constant density (albeit a larger reduction is anticipated for V S than for V P ) (e.g. Laio et al, 2000;Vočadlo et al, 2009;Sha and Cohen, 2010). Anharmonic effects are expected to increase with increasing temperature, but to decrease with increasing compression, and a quantitative assessment of eventual temperature-induced softening of V P calls for further experimental work at simultaneous high static pressure and high temperature.…”

X-ray diffraction study of the pressure-induced bcc-to-hcp phase transition in the highly magnetostrictive Fe0.81Ga0.19alloy

“…As a result, significant efforts have been devoted to studying and optimizing the physical and chemical properties of these materials. [1][2][3][4] The behavior of iron at high pressures and high temperatures is also a key problem in the geophysical sciences [5][6][7][8][9][10][11][12][13] because iron is the primary component of the Earth's liquid outer core and solid inner core. Galfenol, a new class of iron-based, magnetic Fe 1−x Ga x alloy that exhibits giant magnetostriction, has attracted considerable attention because of its potential for use in mechanical devices.…”

Exploring Thermal and Mechanical Properties of Selected Transition Elements under Extreme Conditions: Experiments at High Pressures and High Temperatures

“…Mie-Grüneisen EoS is one of the widely used solutions to incorporate the high pressure behavior in the CALPHAD to calculate the integral in Anderson, 1995;Stixrude and LithgowBertelloni, 2005;Sha and Cohen, 2010). In the SGTE database (Scientific Group Thermodynamic Europe) reappearance of solid phases above melting temperature is avoided by decreasing the heat capacity of the solid and ultimately it converges to a fixed value.…”