Cluster expansion method and its application in computational materials science

Accelerating high-throughput searches for new alloys with active learning of interatomic potentials

“…The reduction of the computational time is achieved by constructing a surrogate model that "interpolates" the quantum-mechanical train-ing data and makes subsequent energy evaluations much faster (by orders of magnitude). This is similar in spirit to the cluster expansion method which has been broadly used in different materials discovery applications 12,[17][18][19] . Cluster expansion is quite successful when the stable structures are derivatives of a particular structure (fcc, bcc, etc.)…”

Accurate representation of formation energies of crystalline alloys with many components

“…Accurate computational prediction of the mixing enthalpy and configuration entropy would be very instrumental in studying HEAs, as it is hard to experimentally explore different compositions of five or more elements due to combinatorial complexity. The state-of-the-art methodology of computationally assessing the stability of multicomponent crystalline alloys is based on cluster expansion [5,6,7,8], allowing to fit formation energies of binary systems over the entire range of compositions, ternary and quaternary systems [9,10,11,12] over, typically, some subrange of the composition range, and quinary systems at specific points of the composition range [13].…”

Beyond the Vegard's law: solid mixing excess volume and thermodynamic potentials prediction, from end-members

“…All the mentioned methods assume that the energy of an alloy can be expressed via cluster expansions. The Cluster Expansion method [8] (see [9] for a review. In the case of applications to natural systems, see [10,11]) allows one to exploit a theoretically robust approach, which makes it possible to explore the properties of solid mixings even at extreme conditions, though at exceedingly demanding computing costs [12,13].…”