# Diffusion equation I can't seem to find anywhere

So I was looking through some old lecture notes from a few years back when I stumbled upon a useful and simple equation that should, according to my former professor describe the diffusion in solid state compounds quite easily. As I forgot however what the single variables mean I tried to find the equation anywhere. I can only find Fick's laws and differential equations with their solution but I haven't found this equation yet.

$$D=\frac{f⋅σ⋅k⋅T}{n⋅(z⋅e)^2}$$

I remember that we used to describe a lot of things with the help of that equation like how diffusion is slower when higher charged ions are used or that warmer temperatures have to be used for reactions. Or how you can use fluxes to lower the concentration and therefore increase the mobility.

Does anyone either know what the other variables describe or can anyone tell me where to find this equation?

I could only guess here, k and T come from Boltzman's part, n should be something related to the number of ions, z and e have the charges and f is probably some specific diffusion constant. So σ may, for example, be something like the specific surface (hence describing why you have to grind your reactants to a fine powder) but I just don't know.

• In the diffusion of charged particles $D=\mu k_BT$ where the mobility $\mu=\sigma/(nZ^2e^2)$ and $\sigma$ is the conductivity (siemen/m$^2$) for $n$ particles with charge $Ze$. $D$ has units $\mathrm{m^2s^{-1}}$. – porphyrin Sep 29 '18 at 21:33