2003/02/18 by Jean-Marc Debierre, Jean‐Marc Debierre, Alain Karma +3 · 1 citation
Earth and Planetary Sciences · Engineering · Materials Science · Physics and Astronomy · #Aluminum Alloy Microstructure Properties #Solidification and crystal growth phenomena #cond-mat.mtrl-sci #nanoparticles nucleation surface interactions
paper · pdf · doi:10.1103/physreve.68.041604
1O pages, 2 tables, 17 figures
arxiv created 2003/02/18 · openalex publication_date 2003/10/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the phase-field approach to model the solidification of faceted materials. Our approach consists of using an approximate gamma plot with rounded cusps that can approach arbitrarily closely the true gamma plot with sharp cusps that correspond to faceted orientations. The phase-field equations are solved in the thin-interface limit with local equilibrium at the solid-liquid interface [A. Karma and W.-J. Rappel, Phys. Rev. E 53, R3017 (1996)]. The convergence of our approach is first demonstrated for equilibrium shapes. The growth of faceted needle crystals in an undercooled melt is then studied as a function of undercooling and the cusp amplitude delta for a gamma plot of the form gamma=gamma0[1+delta(/sin theta/+/cos theta/)]. The phase-field results are consistent with the scaling law Lambda approximately V(-1/2) observed experimentally, where Lambda is the facet length and V is the growth rate. In addition, the variation of V and Lambda with delta is found to be reasonably well predicted by an approximate sharp-interface analytical theory that includes capillary effects and assumes circular and parabolic forms for the front and trailing rough parts of the needle crystal, respectively.