Cluster Expansions for Thermodynamics and Kinetics of Multicomponent Alloys

Abstract

Cluster expansions have proven a very useful tool to model thermodynamics and kinetics of substitutional alloys in metallic, ionic, and even covalently bonded systems. Cluster expansions are usually obtained with the structure inversion method in which the energies, or other relevant property, of a set of structures are used to obtain expansion coefficients. The expansion coefficients are multipliers of correlation functions which pertain to clusters of sites on the parent lattice. There are significant practical issues associated with obtaining a cluster expansion, such as selecting which structures and especially which correlation functions are required for an adequate description of the energy. While these issues are significant for binary alloys, they become much more daunting when dealing with multicomponent alloys. Moreover, oftentimes interest is not limited to the energetics of the thermodynamic equilibrium state, but the evolution of quenched alloys with time is just as important. The treatment of diffusion within the context of cluster expansions is then another challenge. The article describes a formal method for utilizing cluster expansions for transition states as occur during vacancy mediated diffusion in substitutional alloys. The methods are illustrated with some applications to the prediction of initial coherent precipitates in Al-Cu and Al-Mg-Si alloys.

Kinetically driven ordering in phase separating alloys

“…Vacancies are treated as an additional species C and are assumed to have the same effective interactions with both atomic species, so their concentration is not dependent on (local) composition or order. If we assign the most abundant species to A, it follows that only effective cluster interactions (ECIs) associated with species B and C are necessary to fully describe the configurational energy because of the sum rules [53,54]. Then we elaborate the A-B-C CE to describe the configurational energy E conf as…”

“…To retain the fixed lattice gas approximation, with there being one and only one atomic species per site, we employ the formalism of Ref. [54]. Two new atomic species D and E are introduced that map the jumping atom at the transition state onto the lattice sites, as shown in the boxed area of Fig.…”

“…To geometrically distinguish different correlation functions, the whole "pseudoatomic pair" β is included when selecting the correlation functions, as discussed in Ref. [54]. We apply the above-described formalism for KRA barriers again first to a 2D square lattice and then to the fcc lattice.…”

“…Purely kinetic factors have not been reported for metallic alloys. With the increasing awareness that vacancy formation and substitutional diffusion in concentrated alloys is strongly dependent on the local environment [24,25,[49][50][51][52][53][54], it is of interest to examine the impact of this local environment dependence of the kinetics.…”

“…Equation 3shows that lowering the height of KRA barrier about 0.1 eV can speed up the vacancy-atom swapping by 50 times at room temperature. In several substitutional alloys, such as Al-Li [50,57] and Al-Cu [54] ab initio calculations have shown that KRA barriers are very sensitive to local configuration. In Al-Cu alloys, KRA barriers might vary by as much as a factor of 3 [54].…”