  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.
