An Accurate Two-Body Interaction Model for Describing the Structure–Energy Relationship of Binary Alloys

Extraordinary properties of alloys rely on their atomistic level structures; however, a systematic study of their rich and complex structures often remains missing due to the lack of efficient and accurate tools. Herein, a simple two-body interaction model is developed to quantitatively describe the structure–energy relationship for 57 body-centered cubic (bcc) and face-centered cubic (fcc) binary transition metal alloys. The interaction parameters are extracted by the energy differences of a few configurations of an alloy (AB) with A (or B) as the bulk element and two substitutive B (or A) atoms as the kth nearest neighbors (kNN) in fcc/bcc supercells, whose configuration energies are computed using first-principles density functional theory (DFT) calculations. This simple model with two metal atoms at kNN (named the 2M-kNN model) then can be used to both qualitatively and quantitatively predict and explain the relative stability of configurations of an alloy. The parameters of the 2M-kNN model have clear physical meaning and the corresponding energy prediction has similar or higher accuracy for the binary alloys than the machine learning potential and cluster expansion methods. In combination with Monte Carlo simulations, the 2M-kNN model can afford short-range order patterns for the alloys at various temperatures. The structure–energy relationship is further wrapped in a self-defined order parameter that can convert the structural information on a configuration to its energy. An energy extrapolation mechanism is later designed to accurately predict the total energy of any configuration of any sized supercell, with the DFT-level accuracy, only using its order parameter and the DFT energy of a small configuration of the same atom ratio. This 2M-kNN model, in principle, may be extended to treat the structure–energy relationship of alloys of multiple components.