In the picture below a proportionality equation is shown:

$$\omega \propto \nu \exp\left(\frac{-\Delta G_m}{RT}\right)\propto \dots$$

While $\Delta G_m$ is the Gibbs free energy, $R$ is the gas constant, and $T$ is the temperature, what are the parameters $\omega$ and $\nu$ exactly?

enter image description here

You can see the context on the picture: Yttria-stabilized-zircona.

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    $\begingroup$ Looks like $\omega$ is ionic conductivity and $\nu$ is a frequency factor, but I'm reluctant to provide this as an answer without more information - can you provide more information from the text/publication photo, above? $\endgroup$ Jul 31, 2015 at 14:01

1 Answer 1


$\Delta G_m$ is the free energy barrier for the motion of atom from one site to another. The equation overall looks like a transition state approach to this activated process, and thus $\nu$ is the frequency at which this motion is attempted, i.e. a $\nu$ is a characteristic lattice frequency. In such models, it is often assumed to equal the Debye frequency.

Finally, $\omega$ is the rate of transition from one site to another, or something proportional to it (because the proportionality symbol is used rather than an equality). $\omega$ can be thus be the ionic conductivity, or a diffusion constant.

You can find the same expression and graph in this chapter of undergrad lecture notes, for confirmation.


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