Cluster expansion approach for relative stability among different atomic structures in alloys: an approach from a dilute limit

We demonstrate the ability of our cluster expansion approach (CEA) for cohesive energies of alloys, which allows one to Study the chemical trends of the relative stability of different atomic structures of alloys. as an example, X dependence of the atomic structures of Al-rich AIX (X = Sc-Zn) alloys, including ordered structures (Ll(2)(Al3Sc), DO22 (Al3V)), a Mackay icosahedron (a local structure in the Al80Mn20 quasicrystal), and precipitate shapes in decomposition phases (Al1-c,Cu-c, Al1-cZnc; c < 0.05). All the terms in the CEA for Al-rich AIX alloy can be determined uniquely and successively from low-order to high-order by using the total energies of isolated Al and X atoms, pure Al and X metals, and X impurities in Al metal. The total energies of impurity systems are calculated accurately by using the all-electron full-potential Korringa-Kohn-Rostoker (FPKKR) Green's function method, combined with the density-functional theory in the generalized-gradient approximation (GGA), we show: (1) the binding energies of X (X = Cu, Zn) impurities in Al are reproduced very well by the CEA including two- and three-bodv interaction energies of X impurities; (2) the chemical trends of Structural stability among ordered Structures (Ll(2), DO22, DO23) of Al3X (X = Sc, Ti, V), being determined by use of the screened-FPKKR and GGA band-structure calculations. are reproduced by the CEA including only two-body (X-X) interaction energies in Al.