We adopt a phase-field model for peritecitc phase transition to investigate the critical orientation angle of a needle-like Al 4 C 3 structure on the surface of graphite. The critical orientation angle is defined as the maximum angle for which the Al 4 C 3 particle can grow. A crystalline (facetted) anisotropy is exploited to depict the formation of the needle-like morphology. While the classical nucleation theory addresses the critical radius for crystal growth, it is still challenging to determine the critical orientation angle when strong anisotropy is involved. For a single Al 4 C 3 particle, we explore the effect of the basis radius of the graphite and the particle size on the critical orientation angle. For two adjacent Al 4 C 3 particles, we rationalize the critical orientation angle with the apart distance, the radius and the individual orientation of the particle. Depending on the geometric configuration, we observe three typical competing effects which determine the critical orientations differing from a single Al 4 C 3 particle. We anticipate that the simulation results can be applied to interpret some microstructural evolutions with strong anisotropies.