**6. Summary**

Phase-field method is an excellent technique to study the rafting process in nickel-based superalloys. Incorporating the theory of crystal plasticity in the phase-field method makes it possible to analyze the rafting kinetics with internal physical characteristics (the γ/γ' lattice misfit, elastic constants, and dislocation densities) as well as the mechanical behavior (heterogeneous elasticity and plastic deformation) of superalloys. Raft structures with N-type/P-type or other complex types can be formed during creep deformation under different loading modes. The creep deformation may lead to the collapse of raft structures and the topological inversion of the γ/γ' microstructures.

Introducing damage parameters or variation of lattice misfit in the phase-field models under elasto-plastic framework makes it possible to illustrate the individual processes for the microstructure evolution. The development of multiphase-field models provides the foundation to study the contribution of solute atoms to the rafting behavior and to better design and optimize superalloys for industrial applications. Future efforts are expected to focus on complex situations for industrial applications of single crystal superalloys, which likely include orientation-dependent, temperature-dependent, and composition-dependent mechanical properties. The evolution of the mechanical properties needs to be correlated to the microstructure evolution, such as the rafting. Additionally, the interactions between raft structures and defects, such as dislocations, micro-voids, micro-cracks, etc., need to be incorporated in the models. Further study is needed to expand the capability of the phase-field simulation in the analysis of the effects of voids and cracks of millimeter size.

**Author Contributions:** Conceptualization, Z.Y. (Zhiyuan Yu), X.W. and F.Y.; methodology, Z.Y. (Zhiyuan Yu) and F.Y.; software, Z.Y. (Zhiyuan Yu) and F.Y.; validation, X.W., Z.Y. (Zhufeng Yue) and J.C.M.L.; formal analysis, X.W. and F.Y.; investigation, Z.Y. (Zhiyuan Yu) and F.Y.; resources, F.Y., Z.Y. (Zhufeng Yue) and J.C.M.L.; data curation, X.W. and F.Y.; writing—original draft preparation, Z.Y. (Zhiyuan Yu) and F.Y.; writing—review and editing, Z.Y. (Zhiyuan Yu), X.W., F.Y. and J.C.M.L.; visualization, Z.Y. (Zhiyuan Yu) and F.Y.; supervision, Z.Y. (Zhufeng Yue) and J.C.M.L.; project administration, X.W. and F.Y.; funding acquisition, X.W. and Z.Y. (Zhufeng Yue). All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China (Grant Nos. 51775438 and 51875461).

**Conflicts of Interest:** The authors declare no conflict of interest.
