臺灣博碩士論文加值系統

鐵電材料是一種智慧材料，近年來被廣泛用於感測器、致動器與記憶體中。因其特殊的電學、熱學、力學等特性，使其受外加應力或環境改變時，其內部微結構排序亦會隨之改變，因此材料微結構為決定材料性質之重要因素。然而現今之微結構模擬模型仍存在些許不足，例如相場法模型雖能精準計算微結構變化過程，但其需耗費龐大計算效能；而陡變介面法能省去大量計算時間，卻無法計算晶壁能量，影響模型準確度。
為了更了解材料內部微結構變化，且改善模型之準確度，本文將發展一套結合不同理論優點之模型，使用有限元素軟體COMSOL進行模擬，首先驗證以新式相場法所建立之鐵電材料模型之準確性，再將陡變介面法模型推得之平衡微結構作為初始值導入相場模型之中進行模擬，分析其微結構演化過程與數據，再與文獻進行對比，驗證此耦合演算模型之可行性。

A procedure is Ferroelectric materials have been widely used in many applications of sensors, actuators and memory devices in recent decades. These materials have strong electrical, thermal, or mechanical coupling, giving an opportunity for crystals to sense the change of external loading or boundary conditions. The microstructure is the most important factor to determining the crystal properties. However, there are some limitations of typical microstructural modeling. For example, certain patterns of microstructure are assumed for sharp interface models, and the small calculation regions for phase field methods. Thus, the aim of this study is to develop a multiscale analysis scheme combining the merits of sharp interface and phase field models.
Firstly, the microstructure pattern can be obtained by sharp interface model based on compatibility equations. Wherein the pattern is determined with the assumption of flat interfaces. Then, the pattern is set as the initial state of the phase field model, for further energy minimization to eliminate the flat interface assumption. The phase field algorithm is implemented by a commercial software COMSOL Multiphysics. Microstructures of the tetragonal and rhombohedral ferroelectrics crystal are both examined in order to demonstrate the validity of the current work. Interesting laminate structures, such as herringbone patterns and stripe patterns, are generated. Also the effect of depolarization energy, applied load and applied electric field will be examined. The current multiscale model eliminates the assumption of flat interfaces, and at the same time, has better efficiency for engineering purposes.
Keywords: phase-field method, ferroelectric, compatible pattern, interfacial energy

摘 要 i
ABSTRACT ii
誌謝 iii
目錄 iv
表目錄 vi
圖目錄 vii
第一章 緒論與文獻回顧 1
1.1 研究背景與目的 1
1.2 文獻回顧 3
1.2.1 相場法(phase-field method) 3
1.2.2 陡變界面法(sharp interface method) 7
第二章 理論架構 10
2.1 鐵電材料 10
2.1.1 鐵電材料性質及兄弟晶 10
2.1.2 諧和條件 12
2.1.3 場變數μ與平均諧和條件(COA) 13
2.2 相場法架構 16
2.2.1 鐵電材料內部能量 16
2.2.2 熱力學驅動力及演化方程式 19
2.2.3 演化方程式無因次化 20
2.3 陡變界面法(Sharp Interface) 21
2.3.1 層狀結構的諧和條件 21
2.3.2 鐵電材料之層狀結構分類 25

第三章 相場模型驗證 26
3.1 材料係數與環境設定 26
3.1.1 正方晶鐵電材料係數 26
3.1.2 正方晶之晶壁 28
3.1.3 模型環境設定 29
3.2 模擬結果 30
3.2.1 不考慮消極化張量 30
3.2.2 考慮消極化張量 33
第四章 結果與討論 36
4.1 二階層狀結構推算 36
4.2 二階層狀結構初始條件 39
4.2.1 結構(1234) 39
4.2.2 結構(1324) 40
4.2.3 結構(1213) 41
4.2.4 結構(1323) 42
4.3 不考慮消極化張量之平衡結果 43
4.4 考慮消極化張量之平衡結果 49
4.5 結果討論 55
第五章 結論與未來展望 59
參考文獻 61
附錄一 COMSOL參數對照表 64
附錄二 材料係數 66

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