diffusion coefficient

[zsoltrak]

Dear users,

I'm calculating the diffusion coefficient of Fe and Ni in chromia with cNEB using the formula D = D0 * exp(-Ea/kT). My question is related the calculation of the activation energy Ea: is it just the energy barrier (Eb) given by the cNEB calculation or does it include the defect formation energy as well (Ea= Eb+E_defect_formation)?

Thank you.

[graeme]

If there are no preexisting (non-thermal) defects in the system then yes, the formation energy will give you the concentration of defects and the barrier will give you the hopping rate. The product of these two will tell you about the diffusivity. This product will contain a Boltzmann factor with the sum of the two energies (formation and hopping).

[zsoltrak]

Thank you for the prompt reply.

I am still somewhat confused about how to proceed with the diffusion coefficient calculation. If I calculate the prefactor as D0 = n/6 * a^2 * v, where v is the ratio of 3N frequencies at the stable position to the 3N-1 frequencies at the transition state (with dymprefactor.pl) do I still need to include the defect formation energy in the expression for the activation energy. In other words, is the diffusion coefficient given by D = D0*exp(-(E_barrier+E_defect_formation)/kT) ? There are articles published in the literature where only the energy barriers calculated with the cNEB method are considered in the diffusivity calculations (e. g. J Phys Chem C 2014, 118 18133-18145). Are they incorrect or am I missing something?

Thanks again,
Zsolt

[graeme]

Here is a good reference (e.g. pp 57-63):