Ab initio calculations of the thermodynamics and phase diagram of zirconium

The finite-temperature density-functional theory and quasiharmonic lattice dynamics are used to calculate the Gibbs free energy and quasiharmonic phonons of the hexagonal-close-packed (hcp) and omega (omega) crystal structures for Zr. The hcp phonon dispersions agree with experiment; the omega phonon dispersions have not been measured yet. From the free energy, the volume thermal expansion coefficients of alpha-Zr are predicted. The calculated volume thermal expansion coefficients for alpha-Zr are in good agreement with the experiment data at T>100 K. Our calculated results found that at zero-temperature the lowest-energy phase is not the omega but the hcp phase. This conclusion is in accordance with the result of Schnell and Albers, but in disagreement with those of Ahuja and Jona and Marcus. The predicted phase boundary of alpha ->omega is in good agreement with the available experiment; however, other theoretical results are far from the experiment at high temperatures.