  The recently developed refractory multi-principle element alloy (MPEA),
AlMo$_{0.5}$NbTa$_{0.5}$TiZr, shows an interesting microstructure with cuboidal
precipitates of a disordered phase (${\beta}$, bcc) coherently embedded in an
ordered phase (${\beta}'$, B2) matrix, unlike the conventional Ni-based
superalloys where the ordered phase (${\gamma}'$, L12) is the precipitate phase
and the disordered phase (${\gamma}$, fcc) is the matrix phase. It becomes
critical to understand the phase transformation pathway (PTP) leading to this
microstructure in order to tailor the microstructure for specific engineering
applications. In this study, we first propose a possible PTP leading to the
microstructure and employ the phase-field method to simulate microstructural
evolution along the PTP. We then explore possible PTPs and materials parameters
that lead to an inverted microstructure with the ordered phase being the
precipitate phase and the disordered phase being the matrix phase, a
microstructure similar to those observed in Ni-based superalloys. We find that
in order to maintain the precipitates as highly discrete particles along these
PTPs, the volume fraction of the precipitate phase needs to be smaller than
that of the matrix phase and the elastic stiffness of the precipitate phase
should be higher than that of the matrix phase.
