where N denotes the total number of mobile atoms in the system, r j (t) is the position vector of the j th ion at time t, t is the time difference, and the angular bracket indicates the average over several points in time. The factor four appeared in the denominator of eq. 2b is because of two-dimensional diffusion, whereas it is six for the three-dimensional case. The diffusion coefficient, D, depends on the temperature (T ) according to the Arrhenius equation,