Fabrication, application, and phase formation rules in high-entropy alloys

Abstract High entropy alloys (HEAs) have become the focus of research and industrial attention as a new class of advanced engineering materials due to their exceptional properties and performance. Generally, HEAs exhibit superior performance compared to traditional alloys, especially when they form FCC or BCC single-phase solid solutions. However, achieving such systems is beyond simple mixing of elements and is not always straightforward. It strongly depends on element selection, deliberate design of compositions, processing strategies, and thermodynamic control. Given the vast compositional space of HEAs, the use of predictive tools is Inevitable. Phase formation rules, as an empirical approach, have become effective and valuable tools for accelerating the screening of single-phase FCC or BCC alloys and minimizing trial-and-error efforts due to their low cost, time-saving nature, and simplicity. In this regard, the present review elaborated quantitatively and conceptually the thermodynamic parameters such as Gibbs free energy of mixing (ΔG mix ), configurational entropy (ΔS mix ), enthalpy of mixing (ΔH mix ), and the prediction parameter for solid solution formation (Ω), along with Hume-Rothery criteria, including atomic size difference (δ), valence electron concentration (VEC), and electronegativity difference (Δχ). In addition, the processing and manufacturing routes, economic aspects, and applications of HEAs are discussed. This review provides a comprehensive overview of HEA with a practical framework from element selection, design, and fabrication techniques to the relationship between phase, properties, and performance. The present work bridges the gap between HEAs design, manufacturing processes, practical implementation, and application. Additionally, an overview of cost and manufacturing considerations has highlighted future research directions in targeted design, scalable production, and the industrial application of HEAs.