Microstructural design via spinodal-mediated phase transformation pathways in high-entropy alloys (HEAs) using phase-field modelling

Understanding the phase transformation pathways (PTPs) and microstructural evolution in multi-phase HEAs will aid alloy and process designs to tailor the microstructures for specific engineering applications. In this work, we study microstructural evolution in two-phase HEAs where a disordered parent phase separates into a mixture of two phases: an ordered phase ($β'$) + a disordered phase ($β$) upon cooling following two different PTPs: (i) congruent ordering followed by spinodal decomposition in the ordered phase and then disordering of one of the ordered phases, i.e., $β\rightarrow β' \rightarrow β_1' + β_2' \rightarrow β+ β_2'$ and (ii) spinodal decomposition in the disordered phase followed by ordering of one of the disordered phases, i.e., $β\rightarrow β_1 + β_2 \rightarrow β_1+β'$. We systematically investigate the effects of equilibrium volume fractions of individual phases, free energy landscapes (in particular, the location of the critical point of the miscibility gap relative to the compositions of the final two equilibrium phases), and elastic modulus mismatch between the two equilibrium phases on the microstructural evolution of these HEAs. We focus on the following morphological characteristics: bi-continuous microstructures vs. precipitates + matrix microstructures, ordered matrix + disordered precipitates vs. disordered matrix + ordered precipitates, and the discreteness of the precipitate phase. This parametric study may aid in multi-phase HEA design for desired microstructures.