Predicting local chemical order of NbTaTiHf medium-entropy alloys by cluster expansion method

Although local chemical order (LCO) in high- and medium-entropy alloys plays a crucial role in determining their physical properties, the direct experimental characterization remains challenging due to compositional complexity. In this work, we investigate the LCO behavior of equimolar NbTaTiHf medium-entropy alloys using an efficient computational framework combining density functional theory (DFT), cluster expansion (CE), and Monte Carlo (MC) simulations. Our results show that a CE model trained on 600 DFT-calculated configurations achieves a robust predictive accuracy, enabling reliable prediction of configurational energies in large-scale 3456-atom systems. MC simulations are performed over a temperature range from 400 to 1800 K to identify final equilibrium configurations. Temperature-dependent Warren-Cowley parameters reveal a transition from an ordered state to a random solid solution, accompanied with an alternating ordering mechanism between adjacent coordination shells. Strong chemical preferences are identified for Ti-Hf atomic pairs, indicating sub-nanometer-scale and nanometer-scale LCO. In addition, Ta atoms show a strong tendency to form homoatomic pairs and segregate at the nanoscale, as confirmed by local compositional fluctuation analysis. These findings shed light on the atomic understanding of the LCO in multicomponent solid solutions and design implications of LCO.