定量相場模式在三維合金垂直固化之研究

Abstract

在自然界及工程研究中，合金單向凝固非常重要的課題，固化的條件控制會大大的影響材料的性質，例如機械強度、硬度等等，所以如果能夠深入的了解固化程序地機制、原理，可以加強我們掌控材料的性質及應用，這也是為什麼科學家對於這方面有這麼大的興趣主要的原因。 而本篇研究是利用相場模式(Phase field model)及適應性網格來模擬垂直固化，主要探討兩個方向。第一觀察垂直固化的薄膜厚度對於二維的結果影響，我們發現當薄膜厚度很小時，晶體的形狀和二維得到的結果類似，而當增加厚度增加到一定大小時，二維的形狀會漸漸轉變成三維的立方堆積的形狀，並且對於界面的穩定度也會有所改變。 第二我們探討三維垂直固化的問題，討論晶體的性質(如非均向性)，對於晶體的形狀及排列方式所造成的影響，我們發現在不同的非均向性時，晶體排列的方式會有所不同，另外我們更延伸了之前文獻所做出來的結果，使得模擬能更接近實驗所觀察到的結果。

In the nature and the engineering research, directional solidification is a very important topic, the solidification condition control can tremendously influence the characteristics of a material, for example, mechanical strength, degree of hardness and so on. Therefore if we can thoroughly understand the mechanism of solidification, we will be allowed to strengthen us to hold control over the characteristics of the material its application. This is also why scientists have such big interest in this area. In this thesis we use Phase field model and the adaptive mesh refinement(AMR) to simulate directional solidification, and two main topic are discussed. The first is phase field modeling of thin-film directional solidification of a binary alloy－from 2D to 3D transition. The two-dimensional shape can gradually transform to 3D shape. Second, we discuss the problems encountered in three-dimensional directional solidification. The property of crystal, e.g. anisotropic strength, has the influence on the crystal shape and the arrangement, and we discovered that for different anisotropic strength, the arrangement of crystal can act differently. Moreover, we have extended the results made in literature, and enabled the simulation to approach the result experiments have observed.