In this paper, we review our results from phase field simulations of tilted dendritic growth dynamics and dendrite to seaweed transition in directional solidification of a dilute alloy. We focus on growth direction selection, stability range and primary spacing selection, and degenerate seaweed-to-tilted dendrite transition in directional solidification of non-axially orientated crystals. For growth direction selection, the DGP law (Phys. Rev. E, 78 (2008) 011605) was modified through take the anisotropic strength and pulling velocity into account. We confirm that the DGP law is only validated in lower pulling velocity. For the stability range and primary spacing selection, we found that the lower limit of primary spacing is irrelative to the misorientation angle but the upper limit is nonlinear with respect to the misorientation angle. Moreover, predicted results confirm that the power law relationship with the orientation correction by Gandin et al. (Metall. Mater. Trans. A. 27A (1996) 2727-2739) should be a universal scaling law for primary spacing selection. For the seaweed-to-dendrite transition, we found that the tip-splitting instability in degenerate seaweed growth dynamics is related to the M-S instability dynamics, and this transition originates from the compromise in competition between two dominant mechanisms, i.e., the macroscopic thermal field and the microscopic interfacial energy anisotropy.
