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