Lattice dynamics and thermodynamics of bcc iron under pressure: First-principles linear response study

Abstract

We compute the lattice-dynamical and thermal equation of state properties of ferromagnetic bcc iron using the first principles linear response linear-muffin-tin-orbital method in the generalizedgradient approximation. The calculated phonon dispersion and phonon density of states, both at ambient and high pressures, show good agreement with inelastic neutron scattering data. We find the free energy as a function of volume and temperature, including both electronic excitations and phonon contributions, and we have derived various thermodynamic properties at high pressure and temperature. The thermal equation of state at ambient temperature agrees well with diamond-anvil-cell measurements. We have performed detailed investigations on the behavior of various thermal equation of state parameters, such as the bulk modulus K, the thermal expansivity α, the Anderson-Grüneisen parameter δ T , the Grüneisen ratio γ, and the heat capacity C V as function of temperature and pressure. A detailed comparison has been made with available experimental measurements, as well as results from similar theoretical studies on nonmagnetic bcc Tantalum. PACS number(s): 05.70. Ce, 64.30.+t, 71.20.Be 1

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

“…We obtain both E static and F el from first-principles calculations directly, assuming that the eigenvalues for given lattice and nuclear positions are temperature-independent and only the occupation 4 numbers change with temperature through the Fermi-Dirac distribution. 33,38,41 The validity of the static eigenvalue approximations is well justified by the fact that the calculated electronic entropies of nonmagnetic hcp Fe agree well with the values from self-consistent high temperature Linear-Augmented-Plane-Wave (LAPW) method 33 over a wide temperature (6000-9000K) and volume (40-90 bohr 3 /atom) range. The linear response method gives the phonon dispersion spectrum and phonon density of states, which provide both a microscopic basic for and a means of calculating the thermodynamic and elastic properties.…”

“…3, which show typical features of transition metals: thermal expansion and decrease of bulk modulus with increasing temperature. 41,63 We obtain the pressure analytically from the Vinet EoS parameters:…”

Atomic forces at finite magnetic temperatures: Phonons in paramagnetic iron

“…The first approximation (FM) assumes that even at high temperatures, where the magnetic order is destroyed, it is still possible to use the magnetic groundstate, e.g., the ferromagnetically saturated state for bcc iron [9,11,13,20]. The theoretical calculations are carried out at the experimental volume at the considered temperatures [36].…”

“…A prominent example is the paramagnetic regime. Due to the lack of alternatives, current theoretical approaches for, e.g., vibronic contributions of magnetic materials such as bcc iron, rely on calculations performed in the magnetic groundstate (e.g., the ferromagnetically saturated state) [13,20], or take the missing data from experiment [7]. Approaches going beyond these simple approximations employ fixed-spin calculations [6,21] or GGA+U [5], but still employ magnetically fully ordered configurations.…”

The influence of pressure on the phase stability of nanocomposite Fe89Zr7B4 during heating from energy dispersive x-ray diffraction

“…22 In Figure 4, the calculated a-Fe lattice parameters for each pressure are compared to a thermal equations of state presented by Sha and Cohen. 23 The expanded lattice parameters can arise from the presence of B and Zr in the crystal matrix and contact with lower density crystal/matrix interface. At higher pressure, the nanocrystalline lattice parameter approaches the value for bulk a-Fe.…”