Integrated Density of States Lloyd's Formula for Disordered Alloys with Short-Range Order via a KKR-based Dynamical Cluster Approximation*

Within Korringa, Kohn and Rostoker (KKR) multiple scattering theory, we have formulated {\footnote{D.A. Biava et al, Phys. Rev. B 72 113105 (2005)}} a static version of the Dynamic Cluster Approximation (DCA) {\footnote{M. Jarrell and H R Krishnamurthy, Phys. Rev. B 63 125102 (2001)}}, which is a cluster (or non-local) generalization of the coherent potential approximation (NLCPA) {\footnote{D.A. Rowlands et al, Phys. Rev. B 67 115109 (2003)}} that includes environmental effects, including short-range order. Within our KKR-DCA/NL-CPA we present an analytic expression for configurationally-averaged integrated density of states $<$$N(E)$$>$, or generalized Lloyd's formula. We show also that this Lloyd's formula is stationary with respect to changes in the DCA/NLCPA effective medium, providing a rigorous electronic density functional theory and total-energy formalism for (partially) disordered alloys with(out) short-range order that is exact for infinite sized clusters and reduces to the single-site CPA for a cluster size of one. We show applications to various alloys with(out) short-range order.