本文的主旨是研究磁流體薄膜在外加垂直磁場下所形成二維晶格結構之有序性隨時間的變化。磁流體薄膜在外加垂直磁場下會聚集成磁柱，磁柱彼此間因為磁力的作用而形成一特殊的六角對稱二維晶格結構。
依外加垂直磁場的不同可分為交流磁場和直流磁場；交流磁場調變不同的頻率，直流磁場調變磁場最終的強度來進行實驗；同時利用方向相關函數、FFT圖和二維晶格圖來分析二維晶格有序性的變化。並且利用影像處理的技巧來判別不同時間磁柱的位置，進而探討在不同情況下磁柱運動的位移和平均速率。

Magnetic fluid aggregates magnetic columns when a perpendicular magnetic field is applied. The arrangement of magnetic columns forms hexagonal structures in equilibrium state. We study the ordering classification of colummnar lattices with time elapsed.
The perpendicular magnetic field can be categorized as AC and DC fields. To couduct experiments, AC filed changes frequency, and DC field changes the final intensity of magnetice field. We use the bond-orientation correlation function, FFT, and Delaunay triangulation plots of the images to analyze the data which is obtained from experiments. Through digital image processing techniques, we can also determine positions, displacements,and average speed of magnetic columns to undersand the two-dimensional ordering processes, while applying megnetic fields.

第一章導論 1
第二章原理介紹 4
2-1 磁柱形成之二維晶格 4
2-2方向相關函數（orientational correlation function）G6(r) 6
2-3 快速傅利葉轉換（Fast Fourier Transformation）9
2-4 拓樸缺陷（Topological Defects） 11
第三章 實驗方法 14
3-1 實驗樣品製備 14
3-2 實驗儀器架設 16
3-3 數位影像及實驗分析步驟 19
3-3.1數位影像介紹 19
3-3.2實驗影像分析步驟 22
3-3.3磁柱位置之追蹤 25
第四章 實驗結果與討論 27
4-1 交流磁場下二維晶格之有序變化 27
4-2 直流磁場下二維晶格之有序變化 36
4-3 二維晶格有序結構之形成 39
第五章 結論 49
參考文獻 51

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