Density-Functional Theory for Random Alloys: Total Energy within the Coherent-Potential Approximation

A density-functional-based theory is developed for calculation of the total energy and pressure of random substitutional alloys within the Korringa-Kohn-Rostoker coherent-potential approximation. The theory is used to calculate the concentration variation of the equilibrium lattice spacing of $\alpha$-phase ${\mathrm{Cu}}_c{\mathrm{Zn}}_{1-c}$ alloys. We find, in agreement with experiment, that the variation is almost linear and that it deviates from Vegard's rule.