Nickel-base superalloys display cuboidal precipitates aligned along the cubic directions, which are the elastic soft directions. At high precipitate volume fraction, the microstructure is often described as a regular array of precipitates organized on a simple cubic macro-lattice. In the present work, we use a stability analysis and 3D phase field simulations to show that such a regular array is in fact unstable whatever the volume fraction of precipitates. The two main instability modes are the longitudinal [100] mode and the transverse [110] mode along the [110] eigenvector. We argue that these instabilities lead to formation of configurational defects closely related to experimentally observed branches and herringbone patterns. The rôles of elastic anisotropy and elastic homogeneity are also discussed.

Two topological parameters derived from pattern formation theory are introduced, and their potential to accurately describe the elasticity-induced coarsening in the microstructure modeling of Ni-based singlecrystal superalloys at macroscale in 2D is investigated. For that purpose, and given the primordial role of the spatial arrangement of the precipitates on microstructure evolution, two-dimensional phasefield calculations of ideal microstructures undergoing slight topological defects have been carried out. The unstable and stable responses of the system respectively against Eckhaus and zigzag instabilites is discussed and quantitatively described by means of the developed topological parameters ψ x and ψ y .

Two topological parameters derived from pattern formation theory are introduced, and their potential to accurately describe the elasticity-induced coarsening in the microstructure modeling of Ni-based singlecrystal superalloys at macroscale in 2D is investigated. For that purpose, and given the primordial role of the spatial arrangement of the precipitates on microstructure evolution, two-dimensional phasefield calculations of ideal microstructures undergoing slight topological defects have been carried out. The unstable and stable responses of the system respectively against Eckhaus and zigzag instabilites is discussed and quantitatively described by means of the developed topological parameters ψ x and ψ y .