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Anomalously high Na+ and low Li+ mobility in intercalated Na2Ti6O13.

We report an anomalous diffusion behavior in intercalated Na2Ti6O13. Using first-principles calculations, the direct migration of inserted Na+ along the tunnel direction is predicted to have a barrier of 0.24-0.44 eV, while the migration of inserted Li+ along the tunnel direction has a barrier of 0.86-1.15 eV. Although Li+ can also diffuse along a zig-zag path in the tunnel, the barrier of 0.86-0.99 eV is still much higher than that for Na+. Our results surprisingly lead to the conclusion that the diffusion of larger Na+ is 4-8 orders of magnitude faster than Li+ in the same host lattice, and explain the experimentally observed exceptional rate capability of Na2Ti6O13 as the Na-ion battery anode. The anomalous diffusion behavior is attributed to the geometric features of Na2Ti6O13. For migration of Li+ it is necessary to weaken Li-O bonds and to overcome the repulsion between Li and host Na ions simultaneously, while for Na+ diffusion the improved Na-O bonding at the transition state partially compensates for the energy penalty from the repulsion of host Na ions.