Fan Jun, Greenwood Michael, Haataja Mikko, Provatas Nikolas
Department of Materials Science and Engineering and Brockhouse Institute for Materials Research, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4L7.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Sep;74(3 Pt 1):031602. doi: 10.1103/PhysRevE.74.031602. Epub 2006 Sep 12.
Time-dependent simulations of two-dimensional isothermal Ni-Cu dendrites are simulated using a phase-field model solved with a finite-difference adaptive mesh refinement technique. Dendrite tip velocity selection is examined and found to exhibit a transition between two markedly different regimes as undercooling is increased. At low undercooling, the dendrite tip growth rate is consistent with the kinetics of the classical Stefan problem, where the interface is assume to be in local equilibrium. At high undercooling, the growth velocity selected approaches a linear dependence on melt undercooling, consistent with the continuous growth kinetics of Aziz and with a one-dimensional steady-state phase-field asymptotic analysis of Ahmad [Phys. Rev. E 58, 3436 (1998)]. Our simulations are also consistent with other previously observed behaviors of dendritic growth as undercooling is increased. These include the transition of dendritic morphology to absolute stability and nonequilibrium solute partitioning. Our results show that phase-field models of solidification, which inherently contain a nonzero interface width, can be used to study the dynamics of complex solidification phenomena involving both equilibrium and nonequilibrium interface growth kinetics.
使用有限差分自适应网格细化技术求解的相场模型，对二维等温镍 - 铜枝晶进行了时间相关模拟。研究了枝晶尖端速度选择，发现随着过冷度增加，其在两种明显不同的状态之间呈现转变。在低过冷度下，枝晶尖端生长速率与经典斯蒂芬问题的动力学一致，其中界面被假定处于局部平衡。在高过冷度下，所选的生长速度接近与熔体过冷度的线性关系，这与阿齐兹的连续生长动力学以及艾哈迈德的一维稳态相场渐近分析一致[《物理评论E》58, 3436 (1998)]。我们的模拟也与随着过冷度增加而先前观察到的其他枝晶生长行为一致。这些行为包括枝晶形态向绝对稳定性的转变以及非平衡溶质分配。我们的结果表明，本质上包含非零界面宽度的凝固相场模型，可用于研究涉及平衡和非平衡界面生长动力学的复杂凝固现象的动力学。
