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 quasiharmonic lattice dynamics. We make detailed comparisons between our calculated elastic moduli and their temperature and pressure dependences with available experimental and theoretical data. The isotropic aggregate sound velocities obtained based on the calculated elastic moduli agree with available ultrasonic and diamond-anvil-cell data. Birch's law, which assumes a linear increase in sound velocity with increasing atomic density, fails for bcc Fe under extreme conditions. First-principles linear-response lattice dynamics is shown to provide a tractable approach to examine the elasticity of transition metals at high pressures and high temperatures.