Calculation of absolute diffusion rates in oxides

Abstract

Abstract.We have calculated the absolute rate of diffusion for Mg'-and Fe3-ions in MgO using atomistic modelling. Our calculations use a shell model. incorporating tested interatomic potentials, and exploit recent advances in computer codes. The agreement is extremely good where experimental data are available for comparison. For Mg'-in MgO at 1400°C we predict a pre-exponential factor of 32.9 THz using simple Vineyard theory (experiment 18 2 7 THz after correction for the important volume dependence of the activation energy) and an activation energy of 2.26 eV (experiment 2.3 0.2 eV). Close inspection of the energy changes for displacements from the saddle point normal to the jump path shows that within kTof the saddle point energy there are significant departures from the harmonic dependence required for validity of Vineyard theory. Corrections by both analytical methods and numerical integration improve agreement with experiment. predicting23-25 THz overall. For Fe3-much slower diffusion is predicted even though the jump path bifurcates to give two saddle points. We do not predict the rapid Fe'-motion reported in aggregation experiments and conclude that other mechanisms are involved.We have also used the dynamical theory of Rice and Slater which gives similar. but by no means identical. predictions for the diffusion rates.

Diffusion of aluminium in MgO from first principles

“…Again, as calculated before Sangster and Stoneham 1984;Weeks et al 1980), we find that the h100i-trimer is energetically favourable over the h110i-trimer at low pressures, but the h110i-trimer has a lower energy at higher pressures. Their relative energies are given in Table 3.…”

“…We previously found bifurcation for magnesium diffusion (Ammann et al 2010a) at low pressures (disappearing above approximately 5 GPa) and it was also reported for Fe 3? (Sangster and Stoneham 1984). An explanation for the bifurcation could be as follows: Consider the ions as solid spheres such that Al 3?…”

Introducing chemistry in atomistic kinetic Monte Carlo simulations of Fe alloys under irradiation

“…For instance, the three vibrational modes of an atom X in an equilibrium first nearest neighbour position to a vacancy, and the two positive modes at the relaxed saddle point can be obtained by moving the X atom by a small amount (for instance 0.05 Å) along each direction. Note that this approach may need to be modified when soft modes are involved as pointed out by Sangster and coworkers 70. Similar to what has been said for the saddle point energy, one should thus, in principle determine the attempt frequency for each possible local environment of the jumping species, which becomes very quickly an intractable task for alloys.…”