Fig. 1

Initial condition for the phase-field model, resembling a smooth pit at the (001) surface of a solid film. a Γ(x,0) profiles from Eq. (7) obtained for different R values. b Definition of φ in the 3D domain adopted for numerical simulations. It is obtained from Eq. (4) with d(r) the signed distance from Γ(x,y) with R = 0.5. On the left, the solid phase where φ > 0.5 is shown. On the right, a color map showing φ in the 3D domain is reported