A comparative study of dendritic growth by using the extended Cahn-Hilliard model and the conventional phase-field model

An extended Cahn-Hilliard model (ECHM) was compared with the conventional phase-field model (CPFM) for simulating the operating state of a dendrite tip during the two-dimensional solidification of pure undercooled melts over a wide range of interfacial energy anisotropy. ECHM differs from CPFM in terms of how interfacial energy anisotropy is introduced. In ECHM, anisotropy comes solely from the anisotropic nature of the fourth-rank tensor terms included in free energy density, and not from assuming an orientation-dependent gradient energy coefficient ε(θ), which is the case in CPFM. ECHM resulted in dendrites growing with a rounded tip, even when anisotropy (δ) was greater than its critical value (δ_c), but the tip radius at large anisotropy (δ ≥ δ_c) was limited by the interface width. In contrast to CPFM, ECHM did not engender an anomalous increase in the tip radius with bulk undercooling at small anisotropy (δ < δ_c). In the simulation by ECHM, the tip velocity increased continuously with increasing δ beyond δ_c. When compared in terms of the selection parameter σ∗ of the dendrite tip, data obtained from ECHM fitted better to the σ∗ ∝ δ^7/4 relationship over a wider range of δ than those obtained from CPFM. The present comparative study suggests that ECHM hinders the transition of the dendritic growth kinetics from diffusion-limited to interface-kinetic-limited, which occurs in the case of CPFM as the tip velocity increases with an increase in either undercooling or anisotropy.