Electronic origins of ordering in multicomponent metallic alloys: Application to the Cu-Ni-Zn system

We investigate the ordering tendencies of the fcc Cu-Ni-Zn system using a recently developed first-principles, density-functional-based theory of atomic short-range order (ASRO) in disordered substitutional alloys of an arbitrary number of components. We find for the binary alloys a variety of effects which should lead to competition in the ternaries: commensurate ordering (Ni-Zn), long-period ordering (Cu-rich Cu-Zn), and clustering (Cu-Ni), in agreement with experiment. We calculate the ASRO of various disordered ternary alloys (as described by the Warren-Cowley pair-correlation function) and discuss its relationship to the electronic structure of the binary and ternary disordered alloys. We find [100]-type ASRO over an extensive composition range for the ternary alloys, even though all of the ordering tendencies for binaries and ternaries have a Fermi-surface—driven component. We discuss how alloying and disorder broadening lead to these ASRO properties. For ${\mathrm{Cu}}_{50}$ ${\mathrm{Ni}}_{25}$ ${\mathrm{Zn}}_{25}$, the agreement for our calculated ASRO and its indication of two ordered states at low temperature are in good agreement with experiments.