由於量子元件的迅速發展，對於量子導線的研究上近年來受到許多學者的關著，而金奈米線乃其中之一，當金奈米線直徑小於兩奈米以下時，結構受表面張力之影響，而自組裝成多層殼奈米線，因此若未來要應用於量子元件上，其材料的各種性質是勢必深入了解與探討，藉以做為量子導線未來發展與改良的重要依據。
而本計文系以分子動力學模擬研究直徑兩奈米以下之多殼螺旋金奈米線與直徑3nm以上具有巨觀FCC排列之金奈米線的機械性質，研究辦法系利用拉伸及壓縮試驗以計算出奈米線之應力應變行為，如此便可經由變形過程中得到各種不同物理量包括降服應力、最大應力、楊式模數及斷裂力量等。除此之外，更研究不同長徑比、不同溫度及不同應變率下對奈米線之機械性質及材料變形的影響，以深入了解其材料性質。對於結構及受外力變形等特徵的描述，除了形態結構的展示外，更利用徑向分佈函數(RDF)及角度關係函數(ACF)來解釋結構的特徵角度及相變態過程。對於本文所模擬的勢能函數則採用tight-binding勢能作為金原子與金原子間之交互作用關係。

In recent year, the quantum device has been rapid developed. The quantum conductor has been of great interest for most authors, and one of that is gold nanowire. As the diameter of the gold nanowire is smaller than 2nm, the structure arrangement is affected by surface tensor, and therefore the FCC structure will self assemble to a helical structure. However, the nanowire would be used in quantum devices, therefore, the material property must be understood and investigated. The properties of nanowire would be a significant on development of quantum device in the future.
In this study, the molecular dynamics is employed to investigate the mechanical properties of the helical multi-shall gold nanowires and nanowries of the bulk FCC. The stress and strain relationship is obtained form the tensile and compressed tests. In addition, the yielding stress, maximum stress, Young’s modulus, and breaking force can be determined from the tensile test and compressed test. Moreover, the different length/diameter ratio, temperature, and strain rate effects on mechanical properties and deformation behaviors are also investigated. The structure transform from crystalline to non-crystalline is also observed by the variation of radial distribution function (RDF) and angular correlation function (ACF). In this study, the tight-binding many body potential is employed to model the interaction between gold atoms.

第1章 緒論 1
1.1 奈米線簡介 2
1.2 研究動機與目的 5
1.3 奈米線之機械性質與結構特性研究文獻回顧 8
1.4 本文架構 10
第2章 分子動力學理論方法 11
2.1 勢能函數 12
2.2 運動方程 14
2.3 原子級應力計算方法 15
2.4 徑向分佈函數 (RADIAL DISTRIBUTION FUNCTION, RDF) 19
2.5 角度關聯函數 (ANGULAR CORRELATION FUNCTION, ACF) 21
第3章 分子動力學數值方法 22
3.1 鄰近原子表列法 23
3.1.1 Verlet List表列法 23
3.1.2 Cell Link表列法 24
3.1.3 Verlet List表列法結合Cell Link表列法 25
3.2 無因次化 27
3.3 分子動力學於拉伸試驗之流程圖 29
第4章 結果分析與討論 30
4.1 物理模型之建構 31
4.2 邊界影響 33
4.3 結構特徵 35
4.4 機械性質分析 37
4.4.1 拉伸試驗 37
4.4.2 壓縮試驗 43
4.4.3 不同長徑比對於壓縮試驗之影響 46
4.5 不同應變率之影響 52
4.5.1 HMS 7-1 52
4.5.2 HMS 11-4 55
4.5.3 HMS 14-7-1 57
4.5.4 最大應力與楊式係數 59
4.6 不同溫度之影響 62
第5章 結論與建議 67
5.1 結論 68
5.2 建議與未來展望 71

1. Z. Tang , N. A. Kotov, and M. Giersig, “Spontaneous Organization of single CdTe Nanoparticles into Luminescent Nanowires”, Science Vol. 297, 237(2002).
2. T. T. Albrecht, J. Schotter, G. A. Kastle, N.Emley,”Ultrahigh – Density Nanowire Arrays Grown in self-Assembled Diblock Copolymer Templates”,Science Vol.290, 2126(2000).
3. A. Sugawara, T. Coyle, G..G.. Hembree, and M.R.Scheinfein,”Self-organized Fe nanowire arrays prepared by shadow deposition on NaCl(110) templates”,Appl. Phys. Lett. 70, 1043-1045(2001).
4. 陳貴賢,吳季珍,”一維奈米材料的研究”物理雙月刊,12, p609 (2001)
5. Y. Li et al., “Ordered semiconductor ZnO nanowire arrays and their photoluminescence properties”, Appl. Phys. Lett., 76(15), 2011 (2000).
6. K. Hiruma et al., “Growth and optical properties of nanometer-scale GaAs and InAs whiskers” J. Appl. Phts., 77(2) , 447 (1995).
7. G. S. Cheng et al ., J. Mater. Res., 15, 347 (2000).
8. W. B. Choi et al., Fully sealed, high-brightness carbon-nanotube field-emission displayAppl. Phys. Lett. 75, 3129 (1999).
9. T. Rueckes et al., “Carbon Nanotube-Based Nonvolatile Random Access Memory for Molecular Computing” Science, 289, 94 (2000).
10. C. L. Cheung et al., “Growth and fabrication with single-walled carbon nanotube probe microscopy tips” Appl. Phys. Lett. 76, 3136 (2000).
11. J. Kong et al., “Nanotube Molecular Wires as Chemical Sensors” Science, 287, 622 (2000).
12. J. Kong, M. G. Chapline, H. Dai., “Functionalized Carbon Nanotubes for Molecular Hydrogen Sensors”, Adv. Mater. 13, 1384 (2001).
13. X. Duan et al., “Indium phosphide nanowires as building blocks for nanoscale electronic and optoelectronic devices” Nature, 409,66 (2001).
14. M. H. Huang et al., “Room – temperature ultraviolet nanowire nanolasers ” Science Vol. 292, 1897-1899 (2001).
15. Y.Cui et al., “Nanowire Nanosensors for Highly Sensitive and Selective Detection of Biological and Chemical Species” Science, 293 , 1289 (2001).
16. 川合知二 “圖解奈米技術” 工業技術研究院
17. C. C. Chen et al., “Simple Solution-Phase Synthesis of Soluble CdS and CdSe Nanorods” Chem Mater 12, 1516 (2000).
18. L. Manna et al., J. Am. Chem. Soc., “Synthesis of Soluble and Processable Rod-, Arrow-, Teardrop-, and Tetrapod-Shaped CdSe Nanocrystals” 122, 12700 (2000).
19. M. Gudiksen et al., “Diameter-Selective Synthesis of Semiconductor Nanowires” J. Am. Chem. Soc., 122, 8801 (2000).
20. S. T. Lee et al., J. Mater. Res., 14(12), 4503, (1999).
21. L. C. Chen et al., “Catalyst-free and controllable growth of SiCxNy nanorods”J. Phys. Chem. Solids, 62,1567 (2001).
22. M. He et al., Growth of large-scale GaN nanowires and tubes by direct reaction of Ga with NH3”, Appl. Phys. Lett., 77(23), 3731 (2000).
23. J. D. Holmes et al., “Control of Thickness and Orientation of Solution-Grown Silicon Nanowires” Science, 287, 1471 (2000).
24. Y. Li, et al., “Solvothermal Elemental Direct Reaction to CdE (E = S, Se, Te) Semiconductor Nanorod” Inorg. Chem., 38, 1382 (1999)
25. S. Michotte, S. M. Tempfli, L. Piraux, ”Current – voltage characteristics of Pb and Sn granular superconducting nanowires” ,Applied Physics Letters Vol.82. 4119-4121 (2003)
26. J. D. Holmes, K. P. Johston, R. C. Doty, B. A. Korgel, “Control of thickness and orientation of solution grown silicon nanowires”, Science Vol.287. 1471-1473 (2000).
27. Y. Kondo, Kunio Takayangi, “Synthesis and characterization of helical multi-shell gold nanowires”, Science Vol.289. 606-608 (2000).
28. Kunio Takayangi , Y. Kondo, H. Ohnishi, “Suspended gold nanowires:ballistic transport of electrons”, JSAP International No.3 3-8(2001)
29. Y. Kondo, Kunio Takayangi, ”Gold nanobridge stabilized by surface structure”, Physical Review Letters Vol. 79. 3455-3458 (1997).
30. V. Rodrigues, D. Ugate, “Real time imaging of atomistic process in one-atom-thick metal junctions”, Physical Review B, Vol.63, 073405-1 (2001).
31. M. Barbic, J. J. Mock, D.R. Smith, S. Schultz, “Single crystal silver nanowires prepare by the metal amplification method ”, Journal of Applied Physics Vol.91, 9341-9345 (2002).
32. S. Michotte, S. M. Tempfli, L. Piraux, “Current-voltage characteristics of Pb and Sn granular superconducting nanowires”, Applied Physics Letters, Vol.82, 4119-4121 (2003).
33. Y. Oshima, H. Koizumi, K. Mouri, H. Hirayama, K. Takayanagi, “Evidence of a single-wall platinum nanotube”, Physical Review B, Vol.65, 121401 (2002).
34. R. SORDAN, m. Burghard, K. Kern, “Removable tamplate route to metallic nanowires and nanogaps”, Applied Physics Letters Vol.79, 2073-2075 (2001).
35. D. M. Gillingham, I. Linington, C. Muller, J. A. C. Bland,”quantization of the conduction in Cu nanowires” Journal of Applied Physics Vol.93, 7388-7389 (2003).
36. V. Rodrigues, T. Fuhrer, D. Ugarte, “Signature of atomic structure in the quantum conductance of gold nanowires”, Physical Review Letters Vol.85, 4124-4127 (2000).
37. L. G. C. Rego, A. R. Rocha, V. Rodrigues, D. Ugarte, “Role of structural evolution in the quantum conductance behavior of gold nanowires during streching”, Physical Review B 67, 045412-1 (2003).
38. V. Rodrigues, J. Bettini, A. R. Rocha, L. G. C. Rego, D. Ugarte, “Quantum conductance in silver nanowries:Correlation between atomic structure and transport properties”, Physical Review B, Vol.65, 153402 (2002).
39. G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, F. R. Aussenegg, “Optical properties of Ag and Au nanowire gratings”, Journal of Applied Physics Vol.90, 3825-3830 (2001).
40. R. Komanduri, N. Candrasekaran, L. M. Raff, “Molecular dynamic simulations of uniaxial tension at nanoscale of semiconductor materials for micro electro mechanical systems (MEMS) applications”, Materials Science and Engineering A340. 58-67(2003).
41. J. Schiotz, K. W. Jacobsen, “A maximum in the strength of nanocrystalline copper”, Science Vol.301. 1357-1359 (2003).
42. W. J. Chang, T. H. Fang, “Influence of temperature on tensile and fatigue behavior of nanoscale copper using molecular dynamics simulation”, Journal of Physics and Chemistry of Solids 64 1279-1283 (2003).
43. R. Komanduri, N. Chandrasekaran, L. M. Raff, “Molecular dynamics simulation of uniaxial tension of some single crystal cubic metals at nanolevel”, International Journal of Mechanical Sciences 43 2237-2260 (2001).
44. H. Ikeda, Y. Qi, T. Cagin, K. Samwer, W. Johnson, W. Godard, “Molecular dynamics simulation on plastic deformation of metallic nanowires”, Caltech ASCI Technical Report 018 (2000).
45. P. S. Branicio, J. P. Rino, “Large deformation and amorphization of Ni nanowires under uniaxial strain: a molecular dynamics study”, Physical Review B Vol.62, 16950-16954.(2000).
46. H.Ikeda, Y.qi, T. Cagin, K. Samwer, W.L. Johnsion W. A. Goddard, “Strain rate induced amorphization in metallic nanowires” Physical Review Letters Vol 82. 2900-2903(1999).
47. G. Rubio, N. Agrait, S. Vieira, “Mechanical Properties and Formation Mechanisms of a Wire of Single Gold Atoms”, Phys. Rev. Letters 87, 26101-1(2001)
48. S. Tanimori and S. Shimamura, Technical Proceedings of the 2000 International Conference on Modeling and Simulation of Microsystems, MSM 2000 P.110–113.
49. H. D. Espinosa, B. C. Prorok, M. Fischer, Journal of Mechanics and Physics of solids 51, 47-67(2003).
50. S. Sakai, H. Tanimoto, H. Mizubayashi, “Mechanical behavior of high-density nanocrystalline gold prepared by gas deposition method ”, Acta mater 47, 211-217 (1999).
51. G. R. Bollinger, S. R. Bahn, N. Agrait, K.W. Jacobsen, S. Vieira, Phys. Rev. Letters 87, 26101-1(2001)
52. E. Z. Silva, “Theoretical study of the formation, evolution, and breaking of gold nanowires”, Phys. Rev. B 69, 115411 (2004).
53. Coura, P. Z.; Legoas, S. B.; Moreira, A. S.; Sato, F.; Rodrigues, V.; Dantas, S. O.; Ugarte, D.; Galvao, D. S.;, “On the Structural and Stability Features of Linear Atomic Suspended Chains Formed from Gold Nanowires Stretching”, Nano Letters 4, 1187-1191(2004).
54. O. Gulseren, “Noncrystalline Structures of Ultrathin Unsupported Nanowires”, Physical Review Letters 80, 3775(1998).
55. Bilalbegovic, “Structures and melting in infinite gold nanowires”. Solid State Communications, Volume: 115, Issue: 2, June 1, 2000
56. J. W. Kang, J. J. Seo, H. J. Hwang, “Structures of ultrathin copper nanotubes”, Journal of Physics: Condensed Matter 14, 8997-9005(2002).
57. B. Wang, S. Yin, G.. Wang, A. Buldum, J. Zhao, “Novel structures and properties of gold nanowries” Physical Review Letters, Vol.86, 2046-2049 (2001).
58. B. Wang, G. Wang, J. Zhao, ”Magic structures of helical multishell zirconium nanowires”, Physical Review B, Vol.65, 235406-1 (2002).
59. Baolin Wang, Shuangye Yin, Guanghou Wang and Jijun Zhao, “Structures and electronic properties of ultrathin titanium nanowires”, Journal of Physics: Condensed Matter 13, L403-L408(2001).
60. M. Postman, M. J. Geller, J. P. Huchra, “The cluster-cluster correlation function”, The Astronomical Journal Vol.91, 1267 (1986).
61. H. J. C. Berenden et al, Intermolecular Force, Dordrecht, The Netherlands 1981.
62. J. Irving, J. Kirkwood, 1950, ”The statistical mechanical theorey of transport properties. IV. The equations of hydrodynamics,” Journal of Chemical Physics, Vol. 18, pp. 817-829.
63. M. Baskes, J. Nelson, and A. Wright, 1989, “Semiempirical modified embedded-atom potentials for silicon and germanium,” Phys. Rev. B., Vol. 40, Issue. 9, pp. 6085-6100.
64. M. Baskes, 1992, “Modified embedded-atom potentials for cubic materials and impurities,” Phys. Rev. B, Vol. 46, Issue. 5, pp. 2727-2742.
65. J. Slater, G. Koster, 1954, "Simplified LCAO method for periodic potential problem," Physical Review, Vol. 94, No. 6, pp. 1498-1524.
66. C. Kittle, 1996, Introduction to Solid State Physics, John Wiley & Sons, New York.
67. V. Rosato, M. Guillope, and B. Legrand, 1989, “Thermodynamical and structural properties of f.c.c. transition metals using a simple tight-binding model,” Philosophical Magazine A, Vol. 59, No. 2, pp. 321-336.
68. F. Cleri, and V. Rosato, 1993, “Tight-binding potentials for transition metals and alloys,” Phys. Rev. B, Vol. 48, Issue. 1, pp. 22-33.
69. 劉東昇，化學量子力學，徐氏基金會出版，台北，1992
70. 江元生，結構化學，五南圖書出版，台北，1998
71. L. Colombo, 1998,"A source code for tight-binding molecular dynamicssimulation," Computational Materials Science, Vol. 12, pp. 278-287.
72. J. Haile, 1997, Molecular Dynamics Simulation: Elementary Methods, John Wiley & Sons, Inc., New York.
73. D. Rapaport, 1997, The Art of Molecular Dynamics Simulation, Cambridge University Press, London.
74. N. Chandra, S. Namilae, and C. Shet, “Local elastic properties of carbon nanotubes in the presence of Stone-Wales defects”, Physical Review B 69, 94101 (2004).
75. N. Tokita, M. Hirabayashi, C. Azuma, T. Dotera, “Voronoi space division of a polymer: Topological effects, free volume, and surface end segregation”, Journal of Chemical Physcs. 120, 496(2004).
76. D. Srolovitz, K. Maeda, V. Vitek, T. Egami, “Structural defects in amorphous solids statistical analysis of a computer model”, Philosophical Magazine A 44, 847-866 (1981).
77. N. Miyazaki, and Y. Shiozaki, JSME International journal Series A 39,606(1996).
78. H. Rafii-Tabar, “Computational modelling of thermo-mechanical and transport properties of carbon nanotubes ”, Physics Reports 390, 235-452 (2004).
79. D. Frenkel “Understaning Molecular Simulation from algorithms to applications”, Academic Press, 1996.
80. S. P. Ju, J. S. Lin, W. J. Lee “A molecular dynamics study of the tensile behaviour of ultrathin gold nanowires ”, Nanotechnology 15, 1221-1225(2004).
81. L. Haiyi, ACTA mechanica sinica vol.34, 208(2002).
82. G. Rubio, “Atomic-Sized Metallic Contacts: Mechanical Properties and Electronic Transport”, Physical Review Letters 76, 2302(1996).
83. G. R. Bollinger, “Helical and rotational symmetries of nanoscale graphitic tubules”, Physical Review B, Vol 47, 5485 (1993).
84. K. M. Liew, X. Q. He and C. H. Wong, “On the study of elastic and plastic properties of multi-walled carbon nanotubes under axial tension using molecular dynamics simulation ”, ACTA Materialia, Vol. 52, P.2521-2527(2004)
85. R. E. Rudd, J. Q. Broughton, “Atomistic Simulation of MEMS Resonators Through the Coupling of Length Scale”, Journal of Modeling and Simulation of Microsystems vol.1, 29-38 1999)
86. William D. Callister, JR., Materials science and Engineering an Introduction 4/e, John Wiley & Sons, New York.
87. EZ da Silva, AJR da Silva and A. Fazzio, “Breaking of gold nanowires”, Computational Materials Science vol.30, 73-76 (2004).
88. E. Z. da Silva, “How Do Gold Nanowires Break?”, Physical Review Letters 87, 256102(2001).
89. C. F. Cornwell, “Elastic properties of single-walled carbon nanotubes in compression ”, Solid State Commun. Vol. 101,pp. 555 .(1997)
90. J. Diao, K. Gall, M. L. Dunn, “Yield strength asymmetry in metal nanowires”, Nano Letters 4, 1863-1867.(2004)
91. E. Hahn , “in Driven fcc-bct Phase Transition of Pseudomorphic Cu Films on Pd(100)”, Physical Review Letters Vol.74 1803 (1995)
92. F. A. Gilabert, Proceedings of XXX summer school “Advance Problems in Mechanics”, St. –Petersburg, Russia. 2002. Accepted.
93. J. Diao, K. Gall and M. L. Dunn, “Surface-stress-induced phase transformation in metal nanowires”, Nature materials Vol., 656 (2003).