  This paper presents an efficient and quantitative phase-field model for
elastically heterogeneous alloys that ensures the two mechanical
compatibilities$\unicode{x2014}$static and kinematic, in conjunction with
chemical equilibrium within the interfacial region. Our model contrasts with
existing phase-field models that either violate static compatibility or
interfacial chemical equilibrium or are computationally costly. For
computational efficiency, the partial rank-one homogenization (PRH) scheme is
employed to enforce both static and kinematic compatibilities at the interface.
Moreover, interfacial chemical equilibrium is ensured by replacing the
composition field with the diffusion potential field as the independent
variable of the model. Its performance is demonstrated by simulating four
single-particle and one multi-particle cases for two binary two-phase alloys:
Ni-Al $\gamma^{\prime}/\gamma$ and UO$_2$/void. Its accuracy is then
investigated against analytical solutions. For the single-particle
$\gamma^{\prime}/\gamma$ alloy, we find that the accuracy of the phase-field
results remains unaffected for both planar and non-planar geometries when the
PRH scheme is employed. Fortuitously, in the UO$_2$/void simulations, despite a
strong elastic heterogeneity$\unicode{x2014}$the ratio of Young's modulus of
the void phase to that of the UO$_2$ phase is $10^{-4}\unicode{x2014}$we find
that the PRH scheme shows significantly better convergence compared to the
Voigt-Taylor scheme (VTS) for both planar and non-planar geometries.
Nevertheless, for the same interface width range as in the $\gamma^{'}/\gamma$
case, the interface migration in these simulations shows dependence on
interface width. Contrary to the $\gamma^{\prime}/\gamma$ simulations, we also
find that the simulated elastic fields show deviations from the analytical
solution in the non-planar UO$_2$/void case using the PRH scheme.
