  We have calculated the equation of state and elastic properties of
face-centered cubic Fe and Fe-rich FeMg alloy at ultrahigh pressures from first
principles using the Exact Muffin-Tin Orbitals method. The results show that
adding Mg into Fe influences strongly the equation of state, and cause a large
degree of softening of the elastic constants, even at concentrations as small
as 1-2 at. %. Moreover, the elastic anisotropy increases, and the effect is
higher at higher pressures.
