A first-principles study of the diffusion coefficients of alloying elements in dilute α-Ti alloys

Abstract

Using first-principles calculations accompanied by the transition state theory and an 8-frequency model, we present a comprehensive investigation of the diffusion coefficients of substitutional alloying elements X in dilute α-Ti alloys, where X denotes Al, V, Nb, Ta, Mo, Zr, and Sn. The alloying elements Mo and Al exhibit a maximum and a minimum diffusion rate in dilute α-Ti alloys, respectively. It is found that the nearest-neighbor solute-vacancy binding energies and activation energies are roughly inversely proportional to the volume changes induced by solute atoms. There are two exceptions to this trend: Al and Mo. Besides the physical effect (i.e., solute size), two other key factors governing solute diffusion in dilute α-Ti are clarified: the chemical bonding characteristics and vibrational features of X-Ti pairs. It verifies that the ultrafast diffusivity of Mo arises from the interactions with Ti atoms by metallic bonds and its low-frequency contributions to lattice vibration, while the more covalent bonding nature and the high-frequency contributions to the lattice vibration of Al lead to its ultraslow diffusivity. In addition, the correlation effects of diffusion coefficients are non-negligible for the large solutes Ta, Nb, and Zr, in which the direct solute-vacancy migration barriers are much smaller than the solvent-vacancy migration barriers.

The role of molybdenum in suppressing cold dwell fatigue in titanium alloys

“…The Mo substitutional defect and vacancy bind with an energy of 0.22 eV when both defects are in the same basal plane, and 0.23 eV when they are in adjacent basal planes. Our results agree fairly well with those of Xu et al [52], with good agreement for the binding energy when the defects are in the same basal plane, and a difference of about 0.1 eV between the binding energies on adjacent basal planes. The larger difference in the latter case could be due to the smaller supercell size of 4 × 4 × 2 used by Xu et al [52].…”

“…The changes in the bond lengths associated with the Mo-vacancy complex are large, varying between −10% and +7% of the ideal bond length in the basal plane. The supercell size parallel to the c lattice vector used by Xu et al [52] is half that used in this study and that may be insufficient to allow the distortions we see in figure 5. Although the binding energy is positive, it is insufficient to bind a Mo-atom and a vacancy at room temperature for a significant period of time.…”

Diffusion in the Ti-Al-V System

“…10(b) in comparison to the impurity diffusion coefficient calculated from first-principles. [41] The current model predicts faster diffusion of V in a-Ti compared to the calculations by Xu et al [41] The calculated diffusion coefficient is not expected to agree with the current experiment since the first-principles calculations were performed on an impurity-and defect free system whereas the current diffusion couple alloys are confirmed to contain impurities which enhance the diffusion. In addition, the first-principles value for the self-diffusion coefficient for a-Ti is smaller than experimental literature data which indicates that the calculations are underestimating the values.…”

“…This includes the impurity diffusion coefficient of Al and V in a-Ti and the Ti selfdiffusion coefficient. [8,41,42] In the case of diffusion in the Ti-rich b-phase of the Ti-Al-V system, several experimental datasets are available. Huang et al [43] reviewed experimental data for interdiffusion in the Al-Ti system published before the year 2011.…”

“…For the calculation, the V content is given by the solubility limit Fig. 10 Calculated diffusion coefficients (solid lines) in comparison to experimental [10,38,40] and DFT data [41] for Al impurity diffusion in Ti (a) and V impurity diffusion in Ti (b) and its variation as a function of Al is included in Fig. 12.…”