标题： 冻结铸造的相场模型 显示英文标题

标题： Phase-Field Model of Freeze Casting

摘要： 定向凝固水基溶液已成为模板化分级多孔材料的一种多功能技术。 然而，模式形成的潜在机制仍未完全理解。 在本研究中，我们提出了一个定量相场模型的详细推导和分析，用于模拟这一非平衡过程。 该相场模型扩展了稀释二元合金凝固的薄界面公式，并引入了反捕获项，以纳入部分解理冰-水界面的高度各向异性的能量和动力学特性。 该界面在<0001>方向的基面上是解理的，在基面内的其他方向则是原子粗糙的。 在基面上，模型再现了可以与实验测量相关联的线性或非线性动力学关系。 在两种情况下，都观察到了凝固前沿的自发对称破缺，导致形成部分解理的冰层状结构，并沿<0001>方向之一横向漂移。 我们证明漂移速度由基面上的动力学控制，并随着扩散固液界面厚度的减小而收敛。 此外，我们研究了动力学各向异性的形式，这里选择的形式使得动力学系数的倒数从<0001>方向的有限值线性变化到基面内其他所有方向的零值。 我们的结果表明，冰层状结构的漂移速度不受该线性关系斜率的影响，且在相对较小的斜率值下，冰层状结构尖端的半径和过冷度趋于收敛。 因此，相场模拟在界面厚度和动力学各向异性形式中假设的计算可处理的选择下仍保持定量。 显示英文摘要

摘要： Directional solidification of water-based solutions has emerged as a versatile technique for templating hierarchical porous materials. However, the underlying mechanisms of pattern formation remain incompletely understood. In this work, we present a detailed derivation and analysis of a quantitative phase-field model for simulating this nonequilibrium process. The phase-field model extends the thin-interface formulation of dilute binary alloy solidification with anti-trapping to incorporate the highly anisotropic energetic and kinetic properties of the partially faceted ice-water interface. This interface is faceted in the basal plane normal to the <0001> directions and atomically rough in other directions within the basal plane. On the basal plane, the model reproduces a linear or nonlinear kinetic relationship that can be linked to experimental measurements. In both cases, spontaneous parity breaking of the solidification front is observed, leading to the formation of partially faceted ice lamellae that drift laterally in one of the <0001> directions. We demonstrate that the drifting velocity is controlled by the kinetics on the basal plane and converges as the thickness of the diffuse solid-liquid interface decreases. Furthermore, we examine the effect of the form of the kinetic anisotropy, which is chosen here such that the inverse of the kinetic coefficient varies linearly from a finite value in the <0001> directions to zero in all other directions within the basal plane. Our results indicate that the drifting velocity of ice lamellae is not affected by the slope of this linear relation, and the radius and undercooling at the tip of an ice lamella converge at relatively small slope values. Consequently, the phase-field simulations remain quantitative with computationally tractable choices of both the interface thickness and the slope assumed in the form of the kinetic anisotropy.