The structural stability of Ti in the hexagonal-closed-packed and body-centered cubic structures was studied by means of the full potential linearized augmented plane wave method. The effect of pressure on the bulk modulus of the crystal structures was investigated. In this study, the plane wave ultrasoft pseudopotential method was used to calculate the elastic constants, bulk modulus and phonon frequency of Ti. Phonon calculations were performed by employing the density functional perturbation theory in real space, using the calculated lattice dynamical force constants. All calculations were based on the density functional theory with the generalized gradient approximation and local density approximation, which well describe the properties of the above-mentioned metal.

The martensitic α → ω transition was investigated in Ti under hydrostatic pressure. The calculations were carried out using the density functional theory (DFT) framework in combination with the Birch-Murnaghan equation of state. The calculated ground-state properties of α and ω phases of Ti, their bulk moduli and pressure derivatives are in agreement with the previous experimental data. The lattice constants of α and ω-phase at 0 K were modeled as a function of pressure from 0 to 74 GPa and 0 to 119 GPa, respectively. It is shown that the lattice constants vary in a nonlinear manner upon compression. The calculated lattice parameters were used to describe the α → ω transition and show that the phase transition can be obtained at 0 GPa and 0 K.

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