非線性固化動力學相場模式在晶體生長之研究

Abstract

本研究中，我們使用相場模式(Phase field modeling)來解決晶體固化問題。在thin-interface model的架構底下，我們提出了實際上可適用在多維空間的方法來處理針對界面過冷度或界面長速相依的非線性動力學係數。在一維空間中，利用穩態長速作驗證；而二維空間中與理論界面條件相比都獲得一致性的結果。 非線性動力學主要發生在側邊生長機制，其中勢必伴隨著奇異面發展。因此有關動力學控制平衡形狀的研究，本文也提出高非均向動力學模型並用幾何模式等理論作完整的討論。 最後，結合奇異面生長與非線性動力學得到了會依過冷度不同而改變的晶體型態，其中面與面在高、低過冷的競爭觀念與實驗相符，這也是在相場模式研究中首次發表的結果。

The phase field model has emerged as a powerful tool for the simulation of crystal growth. With the thin-interface approximation, the interface thickness could be greatly relaxed to the length scale of microstructures. So far, the model is used only for linear kinetics. However, nonlinear kinetics, where the kinetic coefficient is a function of temperature or velocity, is often encountered in crystal growth, particularly for faceted growth. In this paper, we propose numerical methods to the thin-interface phase field model for nonlinear kinetics. Also the kinetic-controlled shapes are discussed with geometric model. Besides the benchmarking with the available solutions, an example on a facet growth that develops into different morphologies with different undercoolings is simulated for the first time.