定量相場模擬在合金單向固化問題上之研究

Quantitative phase field modeling of directional solidification of a binary alloy

施智仁(Chih-Jen Shih)

指導教授 ： 藍崇文

國立臺灣大學/工學院/化學工程學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.01739

摘要

當任何合金物質往單一方向進行由液相變成固相的程序，我們稱之為單向固化。在單向固化的過程之中，如果因拉速過快使組成過冷克服溫度梯度和表面張力所提供的穩定因子，界面附近會產生局部過飽和而使之崩潰，並依程度的多寡生長出淺細胞、深細胞，到樹枝狀的界面。冶金學家可以利用固化界面型態的控制，來達到其所希望的合金機械強度；物理學家也發現這些界面所表現出來的波長結構與控制變因（例如拉速和溫度梯度）有許多非線性的關係，基於這些理由，合金單向固化問題在過去幾十年來一直是相當熱門的課題。
在本論文中，我們使用相場模式（Phase field model）來模擬此問題。此模式雖然在處理許多複雜界面型態的問題時，表現出相當強的能力，然而在模擬合金固化時，因為溶質包覆（Solute trapping）的發生，使得定量計算非常困難，為了要解決這個問題，我們除了使用Karma所提出的模式來處理低濃度的問題外，更提出了另一個簡單的界面修正法來處理高濃度問題，這些物理模式的修正讓我們完成首次定量的合金凝固模擬，對相場模式的開發有著重大的意義。
基於以上的模式，我們成功觀察到許多不曾模擬出來的界面形態，並和許多古典理論呈現了良好的一致性，其中也發現許多實驗上所無法確切觀察的長時間尺度的現象。由此可知，藉由模式和計算方法的改進，和實驗一對一的定量相場模擬已經不再是一個遙不可及的夢想，而基於我們以上的努力，本篇論文對日後合金凝固理論的發展，開闢了一條新的道路。

關鍵字

相場模擬 ； 合金 ； 凝固

並列摘要

Directional solidification is a process describing that an alloy solution undergoes phase transformation from melt to solid toward a specific direction. During this process, if the solidification speed is high enough to overcome the stabilizing effects of the thermal gradient and interfacial tension, the planar interface becomes unstable and wrinkled. As observed in the experiments, once the instability starts, shallow cellular structures grow initially followed by deep cells and then dendrites with the increasing speed. By controlling the interfacial morphology during freezing of an alloy, one can design its mechanical properties for many industrial applications. Also, in terms of theoretical aspects, the structural wavelength shows some nonlinear dependence with the control parameters. So far, the directional solidification of an alloy is a popular topic both in physics and material science in past few decades.
The purpose of the research presented in this thesis is to simulate alloy solidification by using the phase field model. The phase field model has emerged as a powerful tool to simulate microstructure evolution in solidification. However, limited by computation and inherent numerical nature, the phase field model has encountered many difficulties to perform quantitative simulation; one of them is the effect of solute trapping due to the diffusive interface. To mend this discrepancy, the anti-trapping current proposed by Karma is added to the standard WBM model to model solidifications of lower concentration. For ones with higher concentration, we introduce a simple interface model to restore the local equilibrium, and the solute trapping is totally eliminated. By using these modifications, the phase field modeling of alloy solidification is simulated quantitatively for the first time.
Based on the models presented here, we observe many interesting morphological evolutions, which have never been simulated. In addition, they also fit nicely to the classical theories. A long-time scale structural transition, which is extremely difficult to observe in real experiments, is also been performed. Consequently, a one-to-one comparison with experiments is quite promising in the future. Our work contributed in this thesis indeed opens a window for the research of alloy solidification.

並列關鍵字

alloy ； solidification ； Phase-field

參考文獻

[3] M.R. Mehrabi, Thesis of Ph.D, Massachusetts Institute of Technology, p. 95, 1994

[7] J.A. Warren and J.S. Langer, Phys. Rev. E 47, 2072, 1993

[8] W. Losert, B.Q. Shi, and H.Z. Cummins, Proc. Natl. Acad. Sci. USA 95, 431, 1998

[9] W. Losert, B.Q. Shi, and H.Z. Cummins, Proc. Natl. Acad. Sci. USA 95, 439, 1998

[10] D.J. Wollkind and L.A. Segel, Philos. Trans. Roy. Soc. London 268, 351, 1970