Direct Diffusion through Interpenetrating Networks: Oxygen in Titanium

How impurity atoms move through a crystal is a fundamental and recurrent question in materials. The previous models of oxygen diffusion in titanium relied on interstitial lattice sites that were recently found to be unstable—leaving no consistent picture of the diffusion pathways. Using first-principles quantum-mechanical methods, we find three oxygen interstitial sites in titanium, and quantify the multiple interpenetrating networks for oxygen diffusion. Surprisingly, all transitions contribute to diffusion.

Figure 1

Wyckoff positions [22] and relative energies for oxygen interstitial sites in $\alpha$ titanium. The interstitial site energy $\Delta E$ is reported relative to the octahedral site energy. The geometry of each site is characterized by the nearest neighbor distance after relaxation, $R_{nn}$, with coordination number $Z$. Titanium atom sites are in white, while oxygen interstitial sites are in orange (octahedral), blue (hexahedral), and black (crowdion).

Figure 2

Oxygen interstitial sites and oxygen diffusion pathways in $\alpha$ titanium. White spheres are titanium atoms, orange spheres are octahedral interstitial sites, smaller blue spheres are hexahedral sites, and the smallest black spheres are crowdion sites. The full transition pathway network is in the upper left, and is a superposition of all the remaining subnetworks. The individual transition networks are $o\leftrightarrow o$, $o\leftrightarrow h$, $o\leftrightarrow c$, and $h\leftrightarrow c$. The bottom three networks are formed from pairing up transition networks $o\leftrightarrow h$, $o\leftrightarrow c$, and $h\leftrightarrow c$.

Figure 3

Analytical results and experimental data of oxygen diffusivity in $\alpha$ titanium. We compare our analytical DFT model (bold line) to experimental data from the literature survey by Liu and Welsch [25] (thin lines), and experiments by Bregolin [26] and Vykhodets [27] (symbols).