Shielding, the bulk chemical potential, and cohesion in alloys

It is shown that the bulk chemical potential in alloys is intimately related to the spatial dependence of the shielding cloud that results when the electronic charge rearranges itself as one atom type is replaced by another at a given site. Such a relationship fixes the relative energy scale between the alloy and its pure constituents, important in determining the stability of alloys. A correct treatment of shielding is thus essential to quantitative calculations of alloy stability. A model calculation of the bulk chemical potential and cohesion of alloys in the tight-binding approximation is presented as a numerical example. In the course of this investigation a general invariant of an integral over the shielding cloud is derived.