Theoretical investigation of the high pressure structure, lattice dynamics, phase transition, and thermal equation of state of titanium metal

We report a detailed first-principles calculation to investigate the structures, elastic constants, and phase transition of Ti. The axial ratios of both alpha-Ti and omega-Ti are nearly constant under hydrostatic compression, which confirms the latest experimental results. From the high pressure elastic constants, we find that the alpha-Ti is unstable when the applied pressures are larger than 24.2 GPa, but the omega-Ti is mechanically stable at all range of calculated pressure. The calculated phonon dispersion curves agree well with experiments. Under compression, we captured a large softening around Gamma point of alpha-Ti. When the pressure is raised to 35.9 GPa, the frequencies around the Gamma point along Gamma-M-K and Gamma-A in transverse acoustical branches become imaginary, indicating a structural instability. Within quasiharmonic approximation, we obtained the full phase diagram and accurate thermal equations of state of Ti. The phase transition omega-Ti ->alpha-Ti ->beta-Ti at zero pressure occurs at 146 K and 1143 K, respectively. The predicted triple point is at 9.78 GPa, 931 K, which is close to the experimental data. Our thermal equations of state confirm the available experimental results and are extended to a wider pressure and temperature range. (C) 2010 American Institute of Physics. [doi:10.1063/1.3407560]