Electronic theory of phase stability in substitutional alloys: The generalized perturbation method versus the Connolly-Williams method

Cluster expansion of electronic excitations: Application to fcc Ni–Al alloys

The cluster expansion method is applied to electronic excitations and a set of effective cluster densities of states (ECDOS) is defined, analogous to effective cluster interactions (ECIs). The ECDOSs are used to generate alloy thermodynamic properties as well as the equation of state (EOS) of electronic excitations for the fcc Ni-Al systems. When parent clusters have a small size, the convergence of the expansion is not so good but the electronic density of state (DOS) is well reproduced. However, the integrals of the DOS such as the cluster expanded free energy, entropy, and internal energy associated with electronic excitations are well described at the level of the tetrahedron-octahedron cluster approximation, indicating that the ECDOS is applicable to produce electronic ECIs for cluster variation method (CVM) or Monte Carlo calculations. On the other hand, the Gruneisen parameter, calculated with first-principles methods, is no longer a constant and implies that the whole DOS profile should be considered for EOS of electronic excitations, where ECDOS adapts very well for disordered alloys and solid solutions.