First-Principles Calculations of Free Energies of Unstable Phases: The Case of fcc W

Ab initio molecular dynamics simulations are used to solve the long-standing problem of calculating the free energies of unstable phases, such as fcc W. We find that fcc W is mechanically unstable with respect to long-wavelength shear at all temperatures considered (T > 2500 K), while the short-wavelength phonon modes are anharmonically stabilized. The calculated fcc-bcc enthalpy and entropy differences at T=3500 K (308 meV and 0.74k(B) per atom, respectively) agree well with the recent values derived from analysis of experimental data.