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Researchers attributed the orderly arranged nanoscale phases observed in manymulti-principal element alloys (MPEAs) to spinodal/spinodal-mediated phasetransformation pathways. However, spinodal decomposition is not well understoodin multicomponent systems. Although the theoretical background is available,CALPHAD databases were not used to explore the miscibility gap in MPEAs. Inthis work, we develop a CALPHAD framework utilizing the Hessian of free energyto study the stability of solid solutions in MPEAs. In particular, we utilizethe geometry of higher dimensional Gibbs simplex in conjunction with theHessian to calculate concentration modulations in early stages of spinodaldecomposition. We apply this framework to a diverse set of multi-phase MPEAsthat have been studied in the literature including TiZrNbTa (BCC/BCC),Fe15Co15Ni20Mn20Cu30 (FCC/FCC), Al0.5NbTa0.8Ti1.5V0.2Zr (BCC/B2),AlCo0.4Cr0.6FeNi (BCC/B2) and Al0.5Cr0.9FeNi2.5V0.2 (FCC/L12). We show that theMPEA systems are unstable only to certain concentration modulations which couldbe further explored to design microstructurally engineered alloys.

Exploration of Spinodal Decomposition in Multi-Principal Element Alloys (MPEAs) using CALPHAD Modeling