Thermal effects on lattice strain in hcp Fe under pressure

We compute the c/a lattice strain versus temperature for nonmagnetic hcp iron at high pressures using both first-principles linear response quasiharmonic calculations based on the full potential linear-muffin-tin-orbital (LMTO) method and the particle-in-cell (PIC) model for the vibrational partition function using a tight-binding total-energy method. The tight-binding model shows excellent agreement with the all-electron LMTO method. When hcp structure is stable, the calculated geometric mean frequency and Helmholtz free energy of hcp Fe from PIC and linear response lattice dynamics agree very well, as does the axial ratio as a function of temperature and pressure. On-site anharmonicity proves to be small up to the melting temperature, and PIC gives a good estimate of its sign and magnitude. At low pressures, hcp Fe becomes dynamically unstable at large c/a ratios, and the PIC model might fail where the structure approaches lattice instability. The PIC approximation describes well the vibrational behavior away from the instability, and thus is a reasonable approach to compute high temperature properties of materials. Our results show significant differences from earlier PIC studies, which gave much larger axial ratio increases with increasing temperature, or reported large differences between PIC and lattice dynamics results.Comment: 9 figure

First-principles thermoelasticity of bcc iron under pressure

We investigate the elastic and isotropic aggregate properties of ferromagnetic bcc iron as a function of temperature and pressure by computing the Helmholtz free energies for the volume-conserving strained structures using the first-principles linear response linear-muffin-tin-orbital method and the generalized-gradient approximation. We include the electronic excitation contributions to the free energy from the band structures, and phonon contributions from quasi-harmonic lattice dynamics. We make detailed comparisons between our calculated elastic moduli and their temperature and pressure dependences with available experimental and theoretical data.Comment: 5 figures, 2 table

Elastic isotropy of hcp-Fe under Earth core conditions

Our first-principles calculations show that both the compressional and shear waves of hcp-Fe become elastically isotropic under the high temperatures of Earth inner core conditions, with the variation in sound velocities along different angles from the c axis within 1%. We computed the thermoelasticity at high pressures and temperatures from quasiharmonic linear response linear-muffin-tin-orbital calculations in the generalized-gradient approximation. The calculated anisotropic shape and magnitude in hcp-Fe at ambient temperature agree well with previous first-principles predictions, and the anisotropic effects show strong temperature dependences. This implies that other mechanisms, rather than the preferential alignment of the hcp-Fe crystal along the Earth rotation axis, account for the seismic P-wave travel time anomalies. Either the inner core is not hcp iron, and/or the seismologically observed anisotropy is caused by inhomogeneity, i.e. multiple phases.Comment: 16 pages, 3 figure

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

Atomic structural and electronic bandstructure calculations for borophene

Density of states (DOS) and electronic bandstructure diagrams with ε ( k ) versus k are found for particular allotropes of borophene with much improved accuracy by ab initio quantum calculations using hybrid functionals of several types. The particular types of hybrid functionals are delineated in detail. Varying levels of k-point discretization are utilized to evaluate accuracy. Structural relaxation has been carefully applied prior to electronic bandstructure simulations. Results indicate whether or not one has regions in k-space which display Dirac type non-gapped behavior or parabolic gapped behavior. This work is required in order to determine what types of electronic uses 2D single atomic layer borophene is appropriate for in modern nanoscopic devices