At least what order of magnitude does it have?
I need any experimental, calculated from simulations or theoretically estimated values of diffusion (better surface diffusion) coefficients of ions in w-AlN crystal, in any dependencies (better on temperature). I would be glad for article references.
Yes, I've meant self-diffusion in hexagonal wurtzite-type crystal.
Activation energy of AlN is "860 meV in the 500–650 K" according to "Characterization of bulk AlN with low oxygen content" paper.
I think it translates to roughly 2.3 millihertz vacancy hop frequency at room temperature (using simple harmonic oscillator model and assuming conductivity in pure AlN is result of vacancies mobility). Assuming 0.6nm single hop length, it gives diffusion coefficient 8*10^-18 mm2/s
Of course, here is a lot of assumptions, so this number is rather upper limit. Actual self-diffusivity may turn out to be some ~10 orders of magnitudes lower - especially if conductivity of AlN have nothing to do with vacancies and instead driven by some residual impurity.
Thanks for your reply, I've expected estimation based on Frenkel theory, so did you take hop frequency as v=v0*exp(-E/kT) with h*v0=kT for atoms oscillation?
And what factor coefficient for D~a^2*v did you choose?
Just for clarifying.
Regards.
m(Al+N)*v0*v0/4=kT. I do not think h*v0 (if h-Plank constant) give correct units.
I did not estimate a, because do not know rigidity of the bond. Instead assumed constant speed across half-hop long box. Very primitive..
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