Proton Transport Mechanism in Oxides

The self-diffusion coefficient for protons can be written as follows [67,68] 

N is the fraction of vacant jump destinations v is the vibration frequency A,S m is the jump entropy 

The Physical Chemistry of Materials Energy and Environmental Applications 

Thereafter, combining Equations 5.81 through 5.83 the flux of hydrogen can be written with the help of the ambipolar diffusion equation [45,69] 

As we have commented previously for metals, the diffusion in concentration gradients is described with the chemical diffusion coefficient or the interdiffusion coefficient. Here, it is possible to consider that the interdiffusion and the intrinsic diffusion coefficients are equivalent, since we have the movement of only one species, that is, hydrogen. Subsequently, applying the Einstein relation 

---