First‐principles study of the pressure‐induced α → ω transition in titanium

Abstract

The pressure-induced transition from the α to the ω-phase of Ti is studied with first-principles totalenergy calculations by a procedure that finds the equilibrium structures of each phase directly as a function of pressure from minima of the Gibbs free energy. Good to excellent agreement with experiment is found for the lattice parameters of the two phases both at zero pressure and as functions of pressure up to 900 kbar. The Gibbs free energies of the two phases at zero temperature and without zero-point energy cross at about 500 kbar and then again at 700 kbar. Below 500 and above 700 kbar the α -phase has the lower free energy. Thus, unlike previous theoretical treatments, but in agreement with experiment, our procedure finds the α -phase more stable than the ω-phase below 500 kbar. The α ω AE transition pressure of 500 kbar is much higher than observed experimentally. Possible reasons for this discrepancy, as well as for the non-observance of the re-entrant α -phase above 700 kbar are presented. The importance of the zero-point energy in determining the ground-state phase and transition pressure is noted.

Thermal Stability of α Phase of Titanium by Using X-Ray Diffraction

“…Therefore, c/a also somehow shows a slight increase in terms of temperature from 1.585 at ambient temperature to 1.590 at 923 K (650°C) (Figure 3(b)). This finding is actually in good agreement with both the theoretical [25] and the experimental reports. [3][4][5]15] IV.…”

Density functional theory study of the α → ω martensitic transformation in titanium induced by hydrostatic pressure

“…The extrapolation of experimental data [30] predicted that a martensitic α → ω transition occurs near −1 GPa at 0 K. Our results are within the hysteresis interval (−5 to +8 GPa) and remain in excellent agreement with the other experimental and theoretical works [9,18,31]. Theoretical investigations [9] were carried out using first-principles total-energy calculations and the EBP for finding the equilibrium structures directly as a function of the pressure from the minima of the particular Gibbs free energies.…”

“…These results are summarized in table 2. Theoretical work Pressure [9] 50 GPa [18] 6 GPa [31] −3 GPa This work 0 GPa Based on the comparison between this paper's calculated pressure-induced transition and the extrapolated data from experiments, it can be suggested that this method can also be used for explaining the structural sequence in Ti under pressure for other phases.…”

“…Except in Nguyan-Manh et al [3], theoretical calculations have shown that the ω phase is more stable than the α phase at 0 K [5][6][7][8][9]. Xia et al showed that the ω phase remains stable up to 116 GPa [10].…”

“…All theoretical works on transformation have been based on finding the minimum energy or Gibbs free energy. To obtain the Gibbs free energy for each structure, researchers have used different methods such as the linear Muffin-Tin orbital and the local-density approximation (LDA) methods within the framework of the DFT [5], the full-potential linearized-augmented-plane wave (FP-LAPW) method and LDA [3,13], the FP-LAPW and generalized-gradient approximation (GGA) [7], first-principles energy calculations [17], the tight-binding total energy (TBE) method with first-principles calculations [18], the epitaxial bain path (EBP) combined with FP-LAPW and GGA [9] and the modified embedded-atom potential method and DFT [19].…”