Can we determine the activation energy for ionic conduction from the nuclear- and electron-density distributions?

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In this project, we have investigated the crystal structure, nuclear-density distribution, electronic structure and oxygen permeation rate of two K_2NiF_4-type oxides of Pr_2(Ni_0.75Cu_0.25)_0.95Ga_0.05O_4+δ and Pr_2Ni_0.75Cu_0.25_O4+δ. Nuclear-density distributions of Pr_2(Ni_0.75Cu_0.25)_0.95Ga_0.05O_4+δ and Pr_2Ni_0.75 Cu_0.25_O4+δ at high temperatures have visualized the -(apical oxygen O2)- (interstitial oxygen O3)-(apical oxygen O2)- diffusional pathway of oxide ions, which indicates an interstitialcy diffusion mechanism. It was found that the minimum nuclear density on the O2-O3 pathway ρN(T) is a useful microscopic parameter for the oxygen diffusivity. The ρN(T) is regarded as the oxygen probability density at the bottleneck for diffusion. The oxygen permeation rate ρp (T) increases with an increase of ρN (T). The activation energy for oxygen diffusion estimated by the plots of log(the normalized oxygen permeation rate ρP (T)/δ ) against T^-1 (reciprocal of absolute temperature) is independent of temperature, as well as the formation energy of oxygen atoms at the bottleneck from the plots of log(ρN(T)/ δ ) against T^-1. These results indicate that the amount of interstitial oxygen δ is proportional to the carrier concentration for the oxide-ion diffusion.