  The excellent mechanical properties of the Ni-based superalloy IN718 mainly
result from coherent $\gamma''$ precipitates. Due to a strongly anisotropic
lattice misfit between the matrix and the precipitate phase, the particles
exhibit pronounced plate-shaped morphologies. Using a phase-field model, we
investigate various influencing factors that determine the equilibrium shapes
of $\gamma"$ precipitates, minimizing the sum of the total elastic and
interfacial energy. Upon increasing precipitate phase fractions, the model
predicts increasingly stronger particle-particle interactions, leading to
shapes with significantly increased aspect ratios. Matching the a priori
unknown interfacial energy density to fit experimental $\gamma"$ shapes is
sensitive to the phase content imposed in the underlying model. Considering
vanishing phase content leads to 30% lower estimates of the interfacial energy
density, as compared to estimates based on realistic phase fractions of 12%. We
consider the periodic arrangement of precipitates in different hexagonal and
rectangular superstructures, which result from distinct choices of
point-symmetric and periodic boundary conditions. Further, non-volume
conserving boundary conditions are implemented to compensate for strains due to
an anisotropic lattice mismatch between the $\gamma$ matrix and the $\gamma''$
precipitate. As compared to conventional boundary conditions, this specifically
tailored simulation configuration does not conflict with the systems
periodicity and provides substantially more realistic total elastic energies at
high precipitate volume fractions. The energetically most favorable
superstructure is found to be a hexagonal precipitate arrangement.
