  Researchers attributed the orderly arranged nanoscale phases observed in many
multi-principal element alloys (MPEAs) to spinodal/spinodal-mediated phase
transformation pathways. However, spinodal decomposition is not well understood
in multicomponent systems. Although the theoretical background is available,
CALPHAD databases were not used to explore the miscibility gap in MPEAs. In
this work, we develop a CALPHAD framework utilizing the Hessian of free energy
to study the stability of solid solutions in MPEAs. In particular, we utilize
the geometry of higher dimensional Gibbs simplex in conjunction with the
Hessian to calculate concentration modulations in early stages of spinodal
decomposition. We apply this framework to a diverse set of multi-phase MPEAs
that 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 the
MPEA systems are unstable only to certain concentration modulations which could
be further explored to design microstructurally engineered alloys.

Materials Science;Mesoscale and Nanoscale Physics