Unraveling the two-stage precipitation mechanism in a hierarchical-structured fcc/L2₁ high-entropy alloy: Experiments and analytical modeling

Understanding the phase stability and precipitation mechanisms is crucial for engineering multiphase nanostructured alloys with optimal mechanical properties. In this work, we studied the formation and temporal evolution of nanoprecipitates and their effect on mechanical properties of an fcc/L2₁ eutectic high-entropy alloy through a combination of experiments and analytical modeling. Aging the alloy at 1023 K results in the precipitation of coherent L1₂ nanoparticles in the fcc phase and coherent bcc nanoparticles in the L2₁ phase, leading to the formation of an fcc/L1₂ + L2₁/bcc hierarchical structure. Notably, the scanning transmission electron microscopy (STEM) results reveal that the precipitation in both the fcc and L2₁ phases is not through a one-step nucleation, but a two-stage transformation consisting of an initial chemical separation via spinodal decomposition and subsequent structural ordering/disordering. The Gibbs free energy diagrams of the fcc and L2₁ phases were modeled through numerical techniques, and the spinodal decomposition regions of the two systems at different temperatures were calculated. Based on the modeling results, we discussed the phase stability and thermodynamics of spinodal decomposition of the two phases. In addition, the formation of hierarchical structure substantially enhances the strength of the alloy. Modeling of the strengthening mechanisms reveals that the order strengthening of L1₂ nanoparticles plays a major role in enhancing the yield strength of the alloy, whereas the contribution from the bcc nanoparticles can be negligible. Our findings provide insights into the phase stability, precipitation and strengthening mechanisms of hierarchical-structured alloys.