Quasielastic neutron scattering (QENS) has been applied to study the sodium mobility on nanosecond time scales in the perovskite fluoride cryolite, Na3AlF6, at high temperatures. Up to T = 1153 K the diffusion of Na ions is well described by a diffusion process of jumps between six and eight-fold coordinated sites. Above this temperature, where a step-like increase in the electrical conductivity occurs, the jump length increases, which indicates additional jumps over larger distances. The electrical conductivity derived from the self-diffusion coefficient via the Nernst-Einstein relation and the corresponding activation energy are in excellent agreement with the previous conductivity measurements. We conclude that the jump diffusion of sodium ions is the dominant mechanism for the electrical conductivity in cryolite at high temperatures up to T = 1153 K. (C) 2009 Elsevier B.V. All rights reserved.