臺灣博碩士論文加值系統

本研究利用分子靜力學探討不同晶面的單晶銅金屬Cu(100)、Cu(110)及雙晶銅金屬Cu(100)/Cu(110)、Cu(110)/Cu(100)於奈米壓痕及奈米刮痕下的機械性質及變形機制。
本研究利用奈米壓痕過程中所得到之力量-位移曲線及影響深度-位移曲線及所統計之平均鍵長變化量來探討材料的變形機制。對於單晶銅系統中，探針的下壓與材料內部差排的移動是控制基板原子影響深度的主要因素。然而在雙晶銅系統中，由於界面的存在阻擋差排的移動，其界面型態將成為控制基板原子影響深度的主要因素。
最後，本研究亦分別對單晶銅金屬及雙晶銅金屬做奈米刮痕分析，藉由統計奈米刮痕過程中不同壓痕深度及不同刮痕長度下平均鍵長變化量來探討材料變形過程中結構的變化，並藉此比較在奈米壓痕及奈米刮痕兩種不同的受力情形之下材料的變形機制。

The mechanical properties and the deformation mechanism of Cu single crystal metal and bi-crystal Cu metals are explored by the molecular statics simulations for the nanoindentation and nanoscratching process.
In the simulation of nanoindentation, the relationship of load, influenced depth and displacement are obtained to investigate the deformation mechanism of Cu metals. The variations of averaged bond length are used to understand condition of atoms deformation. For the nanoindentation on two single crystal surfaces, our results indicate that the influenced depths can be affected by the tip indentation and the motion of dislocations. In the case of the bi-crystal system, because the interfaces between two crystal orientations can provide the resistance to the motions of dislocation, the influenced depths can be affected by the existence of the interface.
Eventually, the variations of averaged bond length are also used to explore the structural deformation under the different nanoindentation depths and nanoscratching distances during the nanoscratching process. Moreover, the deformation mechanism during nanoindentation and nanoscratching process are also discussed in this article.

圖目錄 III
表目錄 IV
符號說明 V
中文摘要 VI
ABSTRACT VII
第一章 序論 1
1.1 研究目的與動機 1
1.2 奈米壓痕及奈米刮痕簡介 4
1.3 文獻回顧 5
1.4 本文架構 8
第二章 分子靜力學理論及方法 9
2.1 最佳化理論 9
2.2 勢能函數 12
2.2.1 銅原子之交互作用勢能 12
2.2.2 銅原子與碳原子之交互作用勢能 13
2.3 週期邊界的處理 15
第三章 數值方法 17
3.1 鄰近原子表列數值方法 17
3.1.1 截斷半徑法(Cut-off method) 17
3.1.2 維理表列法(Verlet List) 18
3.1.3 巢室表列法(Cell Link) 21
3.1.4 維理表列結合巢室表列法 (Verlet list combine Cell Link) 23
3.2 模擬流程圖 25
第四章 結果分析與討論 27
4.1 雙晶銅金屬之機械性質探討 27
4.1.1 壓痕物理模型之建構 27
4.1.2 壓痕深度與影響深度之關係 27
4.1.3 雙晶銅金屬之機械性質分析 30
4.2 雙晶銅金屬之磨耗性質探討 40
4.2.1 奈米刮痕模型之建構 40
4.2.1 奈米刮痕之結構分析 40
第五章 結論 56
參考文獻 57

[1]Misra, A., Kung, H., and Embury, J.D.,"Preface to the viewpoint set on: deformation and stability of nanoscale metallic multilayers"Scripta Materialia,50,707-710(2004)
[2]Gannepalli, A. and Mallapragada, S.K."Molecular dynamics studies of plastic deformation during silicon nanoindentation". in 8th Foresight Conference on Molecular Nanotechnology. 2000. Bethesda, Maryland.
[3]Shinn, M., Hultman, L., and Barnett, S.A.,"GROWTH, STRUCTURE, AND MICROHARDNESS OF EPITAXIAL TIN/NBN SUPERLATTICES"Journal of Materials Research,7,901-911(1992)
[4]Hoagland, R.G., Mitchell, T.E., Hirth, J.P., and Kung, H.,"On the strengthening effects of interfaces in multilayer fcc metallic composites"Philosophical Magazine a-Physics of Condensed Matter Structure Defects and Mechanical Properties,82,643-664(2002)
[5]Barshilia, H.C. and Rajam, K.S.,"Characterization of Cu/Ni multilayer coatings by nanoindentation and atomic force microscopy"Surface & Coatings Technology,155,195-202(2002)
[6]Tan, X.H. and Shen, Y.L.,"Modeling analysis of the indentation-derived yield properties of metallic multilayered composites"Composites Science and Technology,65,1639-1646(2005)
[7]Li, Q.Z."Effect of dislocation source length on yield strength of nanostructured metallic multilayer thin films". 2008: Elsevier Science Sa.
[8]Wen, S.P., Zong, R., Zeng, F., Gao, Y., and Pan, F.,"Investigation of the wear behaviors of Ag/Cu multilayers by nanoscratch "Wear,265, 1808- 1813(2008)
[9]Schiotz, J. and Jacobsen, K.W.,"A maximum in the strength of nanocrystalline copper"Science,301,1357-1359(2003)
[10]Fan, Z.F., Smith, P., Rauch, F., and Harris, G.F.,"Nanoindentation as a means for distinguishing clinical type of osteogenesis imperfecta"Composites Part B-Engineering,38,411-415(2007)
[11]Vinogradov, O.,"A new method of molecular statics in polycrystals applications"Computational Materials Science,39,611-615(2007)
[12]Volinsky, A.A., Vella, J.B., and Gerberich, W.W.,"Fracture toughness, adhesion and mechanical properties of low-K dielectric thin films measured by nanoindentation"Thin Solid Films,429,201-210(2003)
[13]Ichimura, H. and Ando, I.,"Mechanical properties of arc-evaporated CrN coatings: Part I - nanoindentation hardness and elastic modulus"Surface & Coatings Technology,145,88-93(2001)
[14]Sundararajan, S. and Bhushan, B.,"Development of AFM-based techniques to measure mechanical properties of nanoscale structures"Sensors and Actuators a-Physical,101,338-351(2002)
[15]Schiotz, J., Di Tolla, F.D., and Jacobsen, K.W.,"Softening of nanocrystalline metals at very small grain sizes"Nature,391,561-563
(1998)
[16]Denis Saraev and Miller, R.E.,"Atomatic-scale simulations of nanoindentation-induced plasticity in copper crystals with nanomete-sized nickel coatings"Acta mater.,54,33-45(2006)
[17]Kang, B.C., Kim, H.Y., Kwon, O.Y., and Hong, S.H.,"Bilayer thickness effects on nanoindentation behavior of Ag/Ni multilayers"Scripta Materialia,57,703-706(2007)
[18]Soer, W.A., De Hosson, J.T.M., Minor, A.M., Morris, J.W., and Stach, E.A.,"Effects of solute Mg on grain boundary and dislocation dynamics during nanoindentation of Al-Mg thin films"Acta Materialia,52,5783-5790(2004)
[19]Lilleodden, E.T., Zimmerman, J.A., Foiles, S.M., and Nix, W.D.,"Atomistic simulations of elastic deformation and dislocation nucleation during nanoindentation"Journal of the Mechanics and Physics of Solids,51,901-920(2003)
[20]Landman, U., Luedtke, W.D., Burnham, N.A., and Colton, R.J.,"ATOMISTIC MECHANISMS AND DYNAMICS OF ADHESION, NANOINDENTATION, AND FRACTURE"Science,248,454-461(1990)
[21]Miesbauer, O., Gotzinger, M., and Peukert, W.,"Molecular dynamics simulations of the contact between two NaCl nano-crystals: adhesion, jump to contact and indentation"Nanotechnology,14,371-376(2003)
[22]Yong, C.W., Smith, W., and Kendall, K.,"Molecular dynamics simulations of (001) MgO surface contacts: effects of tip structures and surface matching"Nanotechnology,14,829-839(2003)
[23]Gannepalli, A. and Mallapragada, S.K.,"Molecular dynamics studies of plastic deformation during silicon nanoindentation "Nanotechnology, 12,
250-257(2001)
[24]Cheong, W.C.D. and Zhang, L.C."A stress criterion for the beta-Sn transformation in silicon under indentation and uniaxial compression". 2003.
[25]Cheong, W.C.D. and Zhang, L.C.,"Molecular dynamics simulation of phase transformations in silicon monocrystals due to nano-indentation"Nanotechnology,11,173-180(2000)
[26]Mulliah, D., Kenny, S.D., Smith, R., and Sanz-Navarro, C.F.,"Molecular dynamic simulations of nanoscratching of silver(100)"Nanotechnology,15,243-249(2004)
[27]Pei, Q.X., Lu, C., Lee, H.P., and Zhang, Y.W.,"Study of Materials Deformation in Nanometric Cutting by Large-scale Molecular Dynamics Simulations"Nanoscale Research Letters,4,444-451(2009)
[28]Maekawa, K. and Itoh, A.,"FRICTION AND TOOL WEAR IN NANO-SCALE MACHINING - A MOLECULAR-DYNAMICS APPROACH"Wear,188,115-122(1995)
[29]Misra, A., Hirth, J.P., and Hoagland, R.G.,"Length-scale-dependent deformation mechanisms in incoherent metallic multilayered composites"Acta Materialia,53,4817-4824(2005)
[30]Lin, Z.C., Huang, J.C., and Jeng, Y.R."3D nano-scale cutting model for nickel material". in 7th Asia Pacific Conference on Materials Processing (APCMP 2006). 2006. Singapore.
[31]Cai, M.B., Li, X.P., and Rahman, M.,"Study of the mechanism of nanoscale ductile mode cutting of silicon using molecular dynamics simulation"International Journal of Machine Tools & Manufacture,47,75-80(2007)
[32]Shiari, B., Miller, R.E., and Klug, D.D.,"Multiscale simulation of material removal processes at the nanoscale"Journal of the Mechanics and Physics of Solids,55,2384-2405(2007)
[33]Chu, C.Y. and Tan, C.M.,"Deformation analysis of nanocutting using atomistic model"International Journal of Solids and Structures,46,1807-1814(2009)
[34]Zhang, J.J., Sun, T., Yan, Y.D., Liang, Y.C., and Dong, S.,"Molecular dynamics study of groove fabrication process using AFM-based nanometric cutting technique"Applied Physics a-Materials Science & Processing,94,593-600(2009)
[35]Lu, L., Chen, X., Huang, X., and Lu, K.,"Revealing the Maximum Strength in Nanotwinned Copper"Science,323,607-610(2009)
[36]Spearot, D.E., Tschopp, M.A., Jacob, K.I., and McDowell, D.L.,"Tensile strength of < 100 > and < 110 > tilt bicrystal copper interfaces"Acta Materialia,55,705-714(2007)
[37]Wang, L., Zhang, H.W., and Deng, X."Influence of defects on mechanical properties of bicrystal copper grain boundary interfaces". 2008.
[38]Spearot, D.E., Capolungo, L., Qu, J., and Cherkaoui, M.,"On the elastic tensile deformation of < 100 > bicrystal interfaces in copper"Computational Materials Science,42,57-67(2008)
[39]Kim, K.J., Yoon, J.H., Cho, M.H., and Jang, H.,"Molecular dynamics simulation of dislocation behavior during nanoindentation on a bicrystal with a Sigma=5 (210) grain boundary"Materials Letters,60,3367-3372(2006)
[40]Zou, F.L., Gao, K.W., Zhu, Q.F., and Xie, J.X.,"Mesomechanical analysis of the tensile deformation of pure copper bicrystal"Acta Metallurgica Sinica,44,297-301(2008)
[41]Hager, W.W. and Zhang, H.C.,"A new conjugate gradient method with guaranteed descent and an efficient line search"Siam Journal on Optimization,16,170-192(2005)
[42]Zhang, L., Zhou, W.J., and Li, D.H.,"Some descent three-term conjugate gradient methods and their global convergence"Optimization Methods & Software,22,697-711(2007)
[43]Quapp, W.,"A growing string method for the reaction pathway defined by a Newton trajectory"Journal of Chemical Physics,122(2005)
[44]Broyden, C.G.,"The Convergence of a Class of Double-rank Minimization Algorithms"Journal of the Institute of Mathematics and Its Applications,6,76-90(1970)
[45]Fletcher, R.,"A New Approach to Variable Metric Algorithms" Computer Journal 13,317-322(1970)
[46]Goldfarb, D.,"A Family of Variable Metric Updates Derived by Variational Means."Mathematics of Computation 24,23-26(1970)
[47]Shanno, D.F.,"Conditioning of Quasi-Newton Methods for Function Minimization "Mathematics of Computation 24,647-656(1970)
[48]Byrd, R.H., Lu, P.H., Nocedal, J., and Zhu, C.Y.,"A LIMITED MEMORY ALGORITHM FOR BOUND CONSTRAINED OPTIMIZATION"Siam Journal on Scientific Computing,16,1190-1208(1995)
[49]Andrei, N.,"Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization"Optimization Methods & Software,22,561-571(2007)
[50]Liu, D.C. and Nocedal, J.,"ON THE LIMITED MEMORY BFGS METHOD FOR LARGE-SCALE OPTIMIZATION"Mathematical Programming,45,503-528(1989)
[51]Daw, M.S. and Baskes, M.I.,"EMBEDDED-ATOM METHOD - DERIVATION AND APPLICATION TO IMPURITIES, SURFACES, AND OTHER DEFECTS IN METALS"Physical Review B,29,6443-6453(1984)
[52]Foiles,S.M.,Baskes,M.I.,and Daw, M.S.,"EMBEDDED-ATOM-METHOD FUNCTIONS FOR THE FCC METALS CU, AG, AU, NI, PD, PT, AND THEIR ALLOYS"Physical Review B,33,7983-7991(1986)
[53]Sun, S.J., Ju, S.P., Lo, Y.C., and Lin, J.S.,"An investigation into the magnetic properties of Co-Cu nanoparticles at different temperatures"Journal of Applied Physics,97(2005)
[54]Frenkel,D. and Smit, B.,"Understanding Molecular Simulation";Academic Press:San Diego(1996)
[55]Allen, M.P. and Tildesley, D.J.,"Computer Simulation of Liquids";Oxford Science:London(1991)
[56]Rapaport, D.C.,"The Art of Molecular Dynamics Simulation";Cambridge University Press:London(1997)
[57]Haile, J.M.," Molecular Dynamics Simulation";Wiley-Interscience:New York(1992)
[58]Kelchner, C.L., Plimpton, S.J., and Hamilton, J.C.,"Dislocation nucleation and defect structure during surface indentation"Physical Review B,58,11085-11088(1998)
[59]Oliver, W.C. and Pharr, G.M.,"AN IMPROVED TECHNIQUE FOR DETERMINING HARDNESS AND ELASTIC-MODULUS USING LOAD AND DISPLACEMENT SENSING INDENTATION EXPERIMENTS"Journal of Materials Research,7,1564-1583(1992)
[60]Tsuru, T. and Shibutani, Y.,"Anisotropic effects in elastic and incipient plastic deformation under (001), (110), and (111) nanoindentation of Al and Cu"Physical Review B,75(2007)
[61]Liang, H.Y., Woo, C.H., Huang, H.C., Ngan, A.H.W., and Yu, T.X.,"Crystalline plasticity on copper (001), (110), and (111) surfaces during nanoindentation"Cmes-Computer Modeling in Engineering & Sciences,6,105-114(2004)