臺灣博碩士論文加值系統

本文中建立半連續模型(semi-continuum model)來處理具有面心立方晶體結構的金屬奈米薄膜，考慮厚度在奈米等級，而在膜的平面方向尺寸則遠大於原子間距；在厚度方向考慮材料的不連續性，而在平面方向則以傳統連續體理論處理，將原子間的交互作用，分別以兩個彈簧(常數分別為 、 )來代表最近跟次近原子間的作用。由原子間的作用力，可以推得整個薄膜的應變能，再進而推得其彈性常數(例如楊性模量、蒲松氏常數等)與膜厚度之間的關係，這一個半連續模型將用來探討膜厚度對彈性常數的影響。

A three-dimensional lattice model is constructed to theoretically study the size effects on the elastic properties of nanofilms with the face-center-cubic crystal structure. Unlike the classical continuum theory, this lattice model directly takes the discrete nature in the thickness direction into account. Only the interactions between the nearest and second nearest atoms are considered in this model and represented as harmonic springs. The constitutive relation of the nanofilm is then derived by using the energy approach and the analytical expressions of the elastic moduli of nanofilms, including in-plane, out-plane Young’s modulus and Poisson’s ratio, are obtained. Further, these expressions along different crystal orientations of nanofilms are also formulated. It is shown that the nanofilm in in-plane surface may be stiffer or softer than its bulk counterpart; however the nanofilm in out-plane surface is always softer.

中文摘要 І
英文摘要 II
目錄 III
圖目錄 Ⅵ
符號說明 Ⅸ
第一章 緒論...........................................1
1-1 前言............................................1
1-2 文獻回顧........................................2
1-3 研究動機與目的......................................6
1-4 本文架構............................................7
第二章 半連續模型之基本理論............................9
2-1 奈米薄膜........................................9
2-2 半連續模型......................................9
2-2-1 面心立方晶格模型................................9
2-2-2 原子間的作用力.................................10
2-2-3 半連續模型.....................................10
2-3 應變能密度.....................................17
2-3-1 應變能.........................................17
2-3-2 剛性矩陣.......................................19
2-3-3 簡單拉伸.......................................24
第三章 分析與討論.....................................33
3-1 參數分析.......................................33
3-2 彈簧常數.......................................35
3-2-1 利用塊材值反推....................................35
3-2-2 由勢能函數推得....................................35
3-3 奈米薄膜之彈性係數............................37
3-4 奈米線.........................................38
第四章 晶格方向效應...................................50
4-1 的奈米薄膜....................................50
4-1-1 參數分析..........................................53
4-1-2 奈米薄膜之彈性係數...............................53
4-2 奈米薄膜......................................54
4-2-1 參數分析..........................................53
4-2-2 奈米薄膜之彈性係數...............................53
4-3 能量分析.......................................57
第五章 結論與未來展望.................................74
5-1 結論...........................................74
5-2 未來展望.......................................75


參考文獻................................................77

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