  Diffusion of dopants in rutile is the fundamental process that determines the
performance of many devices in which rutile is used. The diffusion behavior is
known to be highly sample-dependent, but the reasons for this are less well
understood. Here, rutile is studied by using first-principles calculations, in
order to unravel the microscopic origins of the diverse diffusion behaviors for
different doping elements. Anomalous diffusion behavior in the open channel
along [001] direction is found: larger atoms include Sc and Zr have lower
energy barrier for diffusion via interstitial mechanism, apparently
contradicting their known slow diffusion rate. To resolve this, we present an
alternate model for the overall diffusion rate of the large-size dopants in
rutile, showing that parallel to the [001] channel, it is limited by the
formation of the interstitial states, whereas in the direction perpendicular to
[001], it proceeds via a kick-out mechanism. By contrast, Co and Ni, prefer to
stay in the interstitial site of rutile, and have conventional diffusion with a
very small migration barrier in the [001] channel. This leads to highly
anisotropic and fast diffusion. The diffusion mechanisms found in the present
study can explain the diffusion data measured by experiments, and these
findings provide novel understanding for the classic diffusion topic.
