  Cobalt-based alloys with {\gamma}/{\gamma}' microstructures have the
potential to become the next generation of superalloys, but alloy compositions
and processing steps must be optimized to improve coarsening, creep, and
rafting behavior. While these behaviors are different than in nickel-based
superalloys, alloy development can be accelerated by understanding the
thermodynamic factors influencing microstructure evolution. In this work, we
develop a phase field model informed by first-principles density functional
theory and experimental data to predict the equilibrium shapes of Co-Al-W
{\gamma}' precipitates. Three-dimensional simulations of single and multiple
precipitates are performed to understand the effect of elastic and interfacial
energy on coarsened and rafted microstructures; the elastic energy is dependent
on the elastic stiffnesses, misfit strain, precipitate size, applied stress,
and precipitate spatial distribution. We observe characteristic microstructures
dependent on the type of applied stress that have the same {\gamma}' morphology
and orientation seen in experiments, indicating that the elastic stresses
arising from coherent {\gamma}/{\gamma}' interfaces are important for
morphological evolution during creep. The results also indicate that the narrow
{\gamma} channels between {\gamma}' precipitates are energetically favored, and
provide an explanation for the experimentally observed directional coarsening
that occurs without any applied stress.
