鐵電微結構於新式與傳統相場模擬之分析比較

The Comparison between Novel and Conventional Phase Field Simulation of Ferroelectric Microstructure

吳銘胤(Ming-Yin Wu)

指導教授 ： 舒貽忠

國立臺灣大學/工學院/應用力學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.01183

摘要

近年來研究材料微結構演化過程以及晶域分布之最普遍且成功方法即為相場法(Phase Field Method)。相場法又分為傳統相場法與新式相場法，其主要的不同點在於場變數的選擇以及異相性能的表示方法。以鐵電材料為例，傳統相場法以自發性極化本身當場變數且其必須以高階多項式展開來建構其異相性能密度。然而，新式相場法採用自發性極化的體積分率當場變數且其異相性能的建構上相當簡潔明瞭。儘管使用新式相場法有相當多的優點，但新式相場法尚無法處理多相問題(Multi-Phase Problem)，諸如鐵酸鉍(BiFeO3)經由磊晶薄膜成長，可同時擁有正方晶相與菱方晶相之多相結構，所以我們選擇傳統相場模型來模擬這個現象。模擬結果發現現有的異相性能密度因為在能量較高的正方晶相是鞍點結構，所以無法模擬混和相結構。為了解決這個問題，我們自己建構出一全新之異相性能並且其在菱方晶相與正方晶相的點皆為相對低點，而結果也成功模擬出兩相共存的結構。

關鍵字

多鐵材料 ； 鐵酸鉍 ； 微結構 ； 相場法 ； 多相結構

並列摘要

The phase field approach has been employed extensively to study the evolution of microstructure and patterns of domains. There are two phase field models in current literature: conventional and unconventional methods. The main difference between these two approaches is the different choice of field variables and the representation of anisotropic energy. Taking the example of ferroelectrics, the conventional phase field method choose the spontaneous polarization as the field variable and it needs an expansion of polynomials at high orders to construct the anisotropic energy density. Instead, the unconventional phase field method adopts the volume fraction of spontaneous polarization as field variable and the construction of anisotropic energy density is simple and concise. In spite of many advantages of using the unconventional phase field approach, this method is not able to handle the multi-phase problem yet, such as the coexistence of rhombohedral of tetragonal phases in the strained epitaxial bismuth ferrite films (BiFeO3). As a result, we choose the conventional phase field model to simulate this phenomenon. The result shows that the existing anisotropic energy density in the conventional phase field models is not able to simulate the problem of phase coexistence due to the saddle structure in the high energy phase. To resolve it, we develop a new anisotropic energy density taking into account the relative minimum structure of both R- and T-phase. The result satisfactorily demonstrates the coexistence of these two phases.

並列關鍵字

Multiferroics ； Bismuth ferrite ； Microstructure ； Phase Field Method ； Multi-Phase Structure

參考文獻

[50] 張智星.(2000). Matlab程式設計與應用.青蔚科技股份有限公司

[46] 沈明憲. A Novel Phase Field Simulation of Ferroelectric domain.台灣大學應用力學所碩士班論文, 2008.

[43] 顏睿亨. Application of Multirank Lamination Theory to the Modeling of Ferroelectric and Martensitic Materials.台灣大學應用力學所博士班論文, 2008.

[44] 陳宏志. The Application of Parallel Computation and Fast Algorithm to The Study of Martensitic.台灣大學應用力學所碩士班論文, 2007.

[45] 徐建輝.A Novel Phase Field Simulation of Martensitic Microstructures. 台灣大學應用力學所碩士班論文, 2007.