Choudhury Abhik, Plapp Mathis, Nestler Britta
Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 1):051608. doi: 10.1103/PhysRevE.83.051608. Epub 2011 May 26.
We investigate lamellar three-phase patterns that form during the directional solidification of ternary eutectic alloys in thin samples. A distinctive feature of this system is that many different geometric arrangements of the three phases are possible, contrary to the widely studied two-phase patterns in binary eutectics. Here, we first analyze the case of stable lamellar coupled growth of a symmetric model ternary eutectic alloy, using a Jackson-Hunt-type calculation in thin film geometry, for arbitrary configurations, and derive expressions for the front undercooling as a function of velocity and spacing. Next, we carry out phase-field simulations to test our analytic predictions and to study the instabilities of the simplest periodic lamellar arrays. For large spacings, we observe different oscillatory modes that are similar to those found previously for binary eutectics and that can be classified using the symmetry elements of the steady-state pattern. For small spacings, we observe a new instability that leads to a change in the sequence of the phases. Its onset can be well predicted by our analytic calculations. Finally, some preliminary phase-field simulations of three-dimensional growth structures are also presented.
我们研究了薄样品中三元共晶合金定向凝固过程中形成的层状三相模式。该系统的一个显著特点是，与二元共晶中广泛研究的两相模式不同，三相存在许多不同的几何排列方式。在此，我们首先分析对称模型三元共晶合金稳定层状耦合生长的情况，在薄膜几何结构中使用杰克逊 - 亨特型计算方法，针对任意构型，推导前沿过冷度随速度和间距变化的表达式。接下来，我们进行相场模拟以检验我们的解析预测，并研究最简单周期性层状阵列的不稳定性。对于较大间距，我们观察到不同的振荡模式，这些模式与之前在二元共晶中发现的模式相似，并且可以使用稳态模式的对称元素进行分类。对于较小间距，我们观察到一种新的不稳定性，它会导致相序发生变化。其起始点可以通过我们的解析计算得到很好的预测。最后，还给出了一些三维生长结构的初步相场模拟结果。
