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 <i>k</i>th nearest neighbors (<i>k</i>NN) 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 <i>k</i>NN (named the 2M-<i>k</i>NN 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-<i>k</i>NN model have clear physical meaning and the corresponding energy prediction has similar or higher accuracy for the <i>binary</i> alloys than the machine learning potential and cluster expansion methods. In combination with Monte Carlo simulations, the 2M-<i>k</i>NN 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-<i>k</i>NN model, in principle, may be extended to treat the structure-energy relationship of alloys of multiple components.