舒貽忠Shu, Yi-Chung臺灣大學:應用力學研究所沈明憲Shen, Ming-HsienMing-HsienShen2010-06-022018-06-292010-06-022018-06-292008U0001-3007200815314100http://ntur.lib.ntu.edu.tw//handle/246246/184782鐵電材料具有優越介電性、鐵電性、壓電性及焦電性，近年來應用於記憶體元件、電感元件、壓電致動器與光調元件等等。而這些性質源自於材料內部秩序性的微結構排列與演化所導致的宏觀反應。因此，瞭解微觀結構的演化，是必要的工作。本文中發展出一套能夠描述鐵電材料微晶域演化的新式相場模型並且進行數值模擬分析。傳統相場法中，因為以極化向量做為次序參數，而材料內能之數學表達式則藉由特殊藍道多項式展開次序參數得之，其結果相當繁瑣，並需要大量可調參數。而新式相場法利用這組新的場變數，系統的能量基態結構便可以用解析的數學式描寫，且其數學形式可適用於所有的晶體對稱性。態的鐵電材料微結構乃決定於系統總能量之最低點，使得整體微結構需滿足應變與極化的諧和條件，而鐵電材料晶域便是於這樣的規範下排列而成。在本文研究針對鈦酸鋇之正方晶與菱形晶兩種晶體結構進行模擬，其結果發現晶域間始終滿足諧和條件，也與實驗結果符合。最後，我們施加電場，以觀察鐵電材料的壓電性與遲滯性現象。Ferroelectric materials exhibit spontaneous polarization and distortion under the transformation temperature, giving rise to very characteristic microstructures. The arrangement and evolution of microstructures can induce significant nonlinear behaviors, so they are widely used as smart materials. As ferroelectric microstructures are the key to achieving the exceptional properties, it is essential to investigate the mechanism that governs their formation and evolution.n this thesis, we study the prescribed issue by developing a non-conventional phase-field model. It is based on energy arguments where competing energetics are used to describe the coarsening, refinement, selection, and alignment of ferroelectric domains. In addition to the conventional use of polarization as order parameters, we adopt a new set of field variables motivated by multirank laminates to characterize energy-minimizing domain configurations. As a result, the energy-well structure can be expressed explicitly in a unified fashion, and the number of input parameters in the present framework is reduced.his model is applied to domain simulation in both the tetragonal and rhombohedral ferroelectrics. Several electromechanical self-accommodation patterns are obtained in the simulations and found in good agreement with experimental observations. Besides, rearrangements of domains under applied electric field along polar/non-polar directions are investigated. Preliminary result of hysteretic behavior is also presented. Finally, parameter study is also conducted to verify the model.目錄1章 導論 1-1 背景與研究動機 1-2 鐵電材料介紹 1-3 相場法介紹 3-4 本文架構 52 章 理論架構 6-1 數學模型 6-1-1 鐵電兄弟晶 6-1-2 鐵電晶體能量 9-2 熱力學驅動力與演化方程式 12-3限制型態數學模型 15-4 傅立葉轉換解力學平衡問題 17-5 傅立葉轉換解電場問題 223 章 數值計算 25-1 無因次化 25-2 時間積分計算 27-3 各項自由能之離散型式 31-4 計算流程 344 章 數值計算 39-1 鈦酸鋇(BaTiO3)材料 39-2 模擬正方晶微結搆 39-2-1 限制型態數學模型 42-2-2 完全型態數學模型 48-2-3 微小項探討 54-3 模擬菱形晶微結搆 56-3-1 限制型態數學模型 58-3-2 完全型態數學模型 63-3-3 模擬結果與實際觀察比較 67-4 材料自主性調適(self-accommodation)探討 68-5 晶壁探討 71-5-1 斷面分析 71-5-2介面能係數對微結構影響之探討 73-6 異向能係數對微結構影響之探討 76-7 極化-電場曲線圖 80-7-1 外加[100]方向電場探討 80-7-2外加[1 ̅10] 方向電場探討 86-7-3遲滯特性探討 895 章 結論與未來展望 91-1 結論 91-2 未來展望 92考文獻 94考文獻 98錄A 以格林函數計算應力與自發性應變的關係 98錄B 快速傅立葉轉換應用於有限域與無限域褶積問題 101application/pdf43452196 bytesapplication/pdfen-US鐵電材料相場法模型微結構成形多階層狀結構Ferroelectric single crystalPhase-field modelsPattern formationMultirank laminationthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/184782/1/ntu-97-R95543055-1.pdf