Phase field modeling provides an extremely general framework for predicting microstructural evolutions in complex systems. However, its numerical implementation requires a discretization grid with a small enough grid spacing to preserve the diffuse character of the theory. Recently, a new inherently discrete formulation, called S-PFM, in which interfaces are resolved with essentially only one grid point, has been proposed [1]. This discrete formulation significantly improves the numerical performance of this type of approaches.

The S-PFM approach requires the choice of (i) an arbitrary lattice, (ii) an interface width, (iii) a direction n ⃗_0  in which translational invariance is mathematically imposed, (iv) a set of directions {n ⃗_α } for which all interfacial energies are made equal. In this presentation, we will discuss all these choices, and show that a proper choice ensures translational and rotational invariance of the model, while keeping the interface width of the order of the grid spacing distance. Specifically, several lattices will be compared (square and triangular in 2D, simple cubic and face centered cubic in 3D). Simple S-PFM models for precipitation and ideal grain growth [2] will be used as examples. Finally, the performance of these models will be compared to the numerical solution of the corresponding continuous phase field models.

[1] A. Finel, Y. Le Bouar, B. Dabas, B. Appolaire, Y. Yamada, T. Mohri, A Sharp-Interface Phase Field Method, Phys. Rev. Lett. 121  025501 (2018).
[2] A. Dimokrati, Y. Le Bouar, M. Benyoucef, A. Finel, S-PFM model for ideal grain growth, Acta Materialia 201, pp. 147--157 (2020).