Thermodynamic properties of titanium from ab initio calculations

The lattice parameters, lattice stability and phonon dispersion curves of five proposed phases of Ti: α, β, γ, δ andεare investigated within density functional theory (DFT). It is found that the sequence of high pressure phases at zero temperature isα ε γ δ β the δ and β phases becoming degenerate at high pressure. However, the γ phase may be unstable as is reflected by the existence of imaginary values in the phonon spectra. The results of the DFT calculations are employed to estimate the entropy and free energies of the α andεphases. It is found that converged phonon calculations lead to an entropy difference which is much smaller than previous estimates, and a much steeper α ε. phase transition line.