Shielding and Density of States in Alloys

A relationship between the shielding of the ion-core potentials and the electron density of states $\rho (E,c)$ in disordered alloys of concentration $c$ is shown. When one type of atom in a binary disordered alloy is replaced by another type of atom, there will be, in general, a rearrangement of the shielding charge around this site. The change in the total shielding charge contributed by electron states of energy $E$ is proportional to the change in $\rho (E,c)$ with concentration. A general expression is derived for the change in coherent potential with composition. This change is related to the additional scattering introduced when one type of atom is replaced by another. Based on these relations a discussion is given of the size of clusters necessary to calculate $\rho (E,c)$. The shielding length determines the size of the clusters except in the region where the $\rho (E,c)$ spectrum is dominated by fluctuations in composition. Since in a calculation of the shielding length, shielding charge, and the scattering it produces, it is necessary to treat the potential self-consistently, these relationships suggest that the same is true for a correct calculation of $\rho (E,c)$. One cannot treat the potential as an independent parameter but should treat it self-consistently to calculate $\rho (E,c)$ correctly.