# Nordheim Theory for resistivity of alloy

Is there any information on the actual number of Nordheim theory? A paper I found says, the resistivity of a binary alloy follows, $$\rho=x(1-x)(V_a-V_b)^2$$ ,where $$V_a$$ and $$V_b$$ are "potential", which I don't know exactly. And the paper shows the experimental plot of the resistivity of Cu-Au alloy.

I want to estimate the resistivity of Cu-In alloy, but I could not find the specific number of $$V_a$$ and $$V_b$$ in this Nordheim theory.

I didn't come across the $$(V_b^2-V_a^2)$$ term, but what I usually see is an equivalent which looks like $$g \langle \psi | \Delta U | \psi \rangle$$ where $$g$$ is some sort of density of states, $$\psi$$ is the (bloch) wavefunction for the (fully periodic) average lattice, and $$\Delta U$$ is the difference between the potentials of the two crystal lattices. The term I wrote then gives the scattering (in a perturbative sense) off the difference potential. A more detailed consideration 1 shows that the concentration shows up as $$x(1-x)$$ only when the difference potential is 'random'. If the alloy formed a perfect lattice (e.g. AuCu$$_3$$) then it would not hold.