本論文以分子動力學(Molecular Dynamics，MD)研究不同置入型析出物的特性對多晶奈米銅線機械性質的影響，其中析出物為鋁化鎳(NiAl)的金屬間化合物，探討析出物的位置、百分比與析出物和基地的鍵結強度對奈米銅線機械性質的影響，並且，比較不同晶粒尺寸含析出物對奈米銅線機械性質的效應。
從模擬結果得知，未含析出物之多晶奈米銅線，其變形機制是先由差排滑動結合晶界滑移所主導。因此，位於晶界上之析出物可有效阻礙並延緩晶界的滑移，因而使晶粒的塑變量增大，大幅提升延伸率。此外，相同晶粒尺寸的試片，差排通過含高百分比析出物之試片，所需之時間相對較長。並且，析出物與晶界之界面鍵結較強者，由於晶界不易發生滑移，使整體強度提升；但是，位於晶粒的析出物與基地較強者，反而有負面效果。另外，不同晶粒尺寸晶界上含析出物時，平均晶粒尺寸AGS(Average Grain Size)12.7nm之奈米線的塑性變形機制會發生改變，由原本的晶界滑移改為差排滑移為主，因此其強度高於晶粒尺寸較小者，而展現Hall-Petch Relation的逆向效應。

In this thesis, molecular dynamics (MD) is used to study the influence of different precipitate characteristics on the mechanical properties of polycrystalline copper nanowires. The precipitate is an intermetallic compound of nickel aluminide (NiAl), and the position and percentage of the precipitate are discussed. The effect of the bond strength of the precipitates and bases on the mechanical properties of copper nanowires, and compare the effects of precipitates with different grain sizes on the mechanical properties of copper nanowires.
From the simulation results, it is known that the deformation mechanism of polycrystalline copper nanowires without precipitates is firstly dominated by dislocation sliding and grain boundary sliding. Therefore, the precipitates located on the grain boundary can effectively hinder and delay the slip of the grain boundary, thereby increasing the plastic value of the crystal grains and greatly increasing the elongation. In addition, for the test piece with the same grain size, dislocation passes through the test piece with a high percentage of precipitates, and the required time is relatively high. In addition, if the interface bond between the precipitate and the grain boundary is stronger, the overall strength is increased because the grain boundary is not easy to slip; however, the precipitate located in the crystal grain and the base is stronger, but it has a negative effect. In addition, when there are precipitates on the grain boundaries of different grain sizes, the plastic deformation mechanism of the average grain size AGS (Average Grain Size) 12.7nm nanowire will change, from the original grain boundary slip to dislocation slip. Mainly, so its strength is higher than that of smaller grain size, and exhibits the reverse effect of Hall-Petch Relation.

1. C. M. Lieber, “Nanoscale science and technology: building a big future from small things,” MRS Bull., Vol.28, pp.486-491(2003).
2. D. Huo, Y. Liang, and K. Cheng, "An investigation of nanoindentation tests on the single crystal copper thin film via an AFM and MD simulation," Journal of Mechanical Engineering Science, Vol. 221, pp. 259-266 (2007).
3. A. Shik, H. E. Ruda, and I. G. Currie, “Electromechanical and electro-optical properties of nanowires,” Journal of Applied Physics, Vol.98, pp.094306(2005).
4. B. Wu, A. Heidelberg, and J. J. Boland, “Mechanical properties of ultrahigh-strength gold nanowires,” Nature Materials, Vol.4, pp.525-529(2005).
5. A. Heidelberg, L. T. Ngo, B. Wu, M. A. Phillips, S. Sharma, T. I. Kamins, J. E. Sader, and J. J. Boland, “A generalized description of the elastic properties of nanowires,” Nano Letters, Vol.6, pp.1101-1106(2006).
6. J. Dian, K. Gall, M. L. Dunn and J. A. Zimmerman, "Atomistic simulations of the yielding of gold nanowires," Acta Materialia, Vol.54, pp.643-653(2006).
7. L. Yuan, D. Shan and B. Guo, "Molecular dynamics simulations of tensile deformation of nano-single crystal aluminum," Journal of Materials Processing Technology, Vol.184, pp.1-5(2007).
8. C. Ji, and H. S. Park, “The coupled effects of geometry and surface orientation on the mechanical properties of metal nanowires,” Nanotechnology, Vol.18, pp. 305704(2007).
9. W. Liang, and M. Zhou, “Response of copper nanowires in dynamic tensile deformation,” Journal of Mechanical Engineering Science, Vol.218, pp.599-606(2004).
10. H. S. Park, and J. A. Zimmerman, “Modeling inelasticity and failure in gold nanowires,” Physical Review B, Vol.72, pp.054106(2005).
11. S. J. A. Koh, and H. P. Lee, “Molecular dynamics simulation of size and strain rate dependent mechanical response of FCC metallic nanowires,” Nanotechnology, Vol.17, pp.3451-67(2006).
12. 彭達仁，"分子動力學模擬奈米銅線單軸受力狀態之微觀行為分析"，國立台灣科技大學博士論文，(2008)。
13. N. Hahn. Eric, and A. Meyers. Marc, “Grain-size dependent mechanical behavior of nanocrystalline metals,” Mater. Sci. Eng. A, Vol.646, pp.101-134(2015).
14. E.O. Hall, “The Deformation and Ageing of Mild Steel: III Discussion of Results,” Proc. Phys. Soc. B64, pp.747-753(1951).
15. N.J. Petch, “The Cleavage Strength of Polycrystals,” Journal of the Iron and Steel Institute, Vol. 174, 1953, pp. 25-28.
16. J. Schiøtz, T. Vegge, F. D. Di Tolla, and K. W. Jacobsen, “Atomic-scale simulations of the mechanical deformation of nanocrystalline metals,” Phys. Rev. B, Vol.60, pp.972-983(1999).
17. J. Schiøtz, “Atomic-scale modeling of plastic deformation of nanocrystalline copper,” Scr. Mater. Vol.51, pp.837-841(2004)
18. K. Zhou, B. Liu, Y. Yao and K. Zhong, “Effects of grain size and shape on mechanical properties of nanocrystalline copper investigated by molecular dynamics,” Mater. Sci. Eng. A, Vol.615, pp.92-97(2014).
19. Ting. Zhang, Kai. Zhou, and Z.Q. Chen, “Strain rate effect on plastic deformation of nanocrystalline copper investigated by molecular dynamics,” Mater. Sci. Eng. A, Vol.648, pp.23-30(2015).
20. J. Schiøtz and W. Jacobsen, “A Maximum in the Strength of Nanocrystalline Copper,” Sci. New Series. Vol.301, No.5638, pp.1357-1359(2003).
21. Guo-Jie J. Gao, Yun-Jiang Wang and Shigenobu. Ogata, “Studying the elastic properties of nanocrystalline copper using a model of randomly packed uniform grains,” Comput. Mater. Sci. Vol.79 pp56-62(2013).
22. A. Moitra, “Atomistic simulations of precipitation hardening mechanisms in Mg-Al alloys,” J. Phys.: Conf. Ser. Vol.1579 012012(2020).
23. V.S. Krasnikov, A.E. Mayer, V.V. Pogorelko, F.T. Latypov and A.A. Ebel, “Interaction of dislocation with GP zones or θ" phase precipitates in aluminum: Atomistic simulations and dislocation dynamics,” Int. J. Plast., Vol.125 pp.169-190(2020).
24. Vasiliy S. Krasnikov, Alexander E. Mayer, Victor V. Pogorelko and Marat R. Gazizov, “Influence of θ’ Phase Cutting on Precipitate Hardening of Al–Cu Alloy during Prolonged Plastic Deformation: Molecular Dynamics and Continuum Modeling,” Appl. Sci. Res., 11, 4906(2021).
25. J. Dalton, A new system of chemical philosophy. Cambridge University Press, 2010.
26. J. Irving and J. G. Kirkwood, "The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics," The Journal of chemical physics, vol. 18, no. 6, pp. 817-829, 1950.
27. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, "Equation of state calculations by fast computing machines," The journal of chemical physics, vol. 21, no. 6, pp. 1087-1092, 1953.
28. L. Verlet, "Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules," Physical review, vol. 159, no. 1, p. 98, 1967.
29. B. Quentrec and C. Brot, "New method for searching for neighbors in molecular dynamics computations," Journal of Computational Physics, vol. 13, no. 3, pp. 430-432, 1973.
30. J. Diao, K. Gall, and M. L. Dunn, “Yield strength asymmetry in metal nanowires,” Nano Letters, Vol.4, pp.1863-1867(2004).
31. Y. Liu, J. Zhao, and F. Wang, “Influence of length on shock-induced breaking behavior of copper nanowires,” Physical Review B, Vol.80, 115417(2009).
32. J. H. Shim, H. J. Lee Voigt, B. D. Wirth, "Temperature dependent dislocation bypass mechanism for coherent precipitates in Cu-Co alloys," Acta Materialia, Vol.110, pp.276-282(2016).
33. Shehu Adam Ibrahima, Qingyu Wanga, Yue Zhangc, Mohammed doa, Gyang Davou Chungd, and M. Mustafa Azeema, “Molecular dynamics simulation of strengthening dependence on precipitate Cr composition in Fe-15at.% Cr alloy,” Micron, Vol.131 102823(2020).
34. E. Jones, "On The Determination of Molecular Fields. I. From the Variation of the Viscosity of a Gas with Temperature," Proceedings of the Royal Society of Physical Character, Vol.106, no.738, pp.441-462(1924).
35. J. E. Jones, "On The Determination of Molecular Fields. II. From the Equation of State of a Gas," Proceedings of the Royal Society of London. Series A. Containing Papers of a Mathematical and Physical Character, Vol.106, no.738, pp.463-477(1924).
36. P.M. Morse, "Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels," Physical Review, Vol.34, pp.57-64(1929).
37. M.S. Daw and M.I. Baskes, "Embedded-Atom Method: Derivation and Application to Impurities, Surface, and Other Defects in Metals," Physical Review B, Vol.29, no.12, pp.6443-6453(1984).
38. M.S. Daw, "Model of Metallic Cohesion: The Embedded-Atom Method," Physical Review B, Vol.39, no.11, pp.7441-7452(1989).
39. R.A. Johnson, "Analytic Nearest-Neighbor Model for FCC Metals," Physical Review B, Vol.37, no.8, pp.3924-3931(1988).
40. R.A. Johnson, "Alloy Models with The Embedded-Atom Method,” Physical Review B, Vol.39, no.17, pp.12554-12559(1989).
41. R.A. Johnson and D.J. Oh, "Analytic embedded atom method model for bcc metals"
42. Y. Mishin and D. Farkas, "Interatomic Potentials for Monoatomic Metals from Experimental Data and Ab Initio Calculations,” Physical Review B, Vol.59, no.5, pp.3393-3407(1999).
43. M. I. Baskes, "Modified embedded-atom potentials for cubic materials and impurities," Physical review B, vol. 46, no. 5, p.2727 (1992).
44. M. Tuckerman, B. J. Berne, and G. J. Martyna, "Reversible multiple time scale molecular dynamics," The Journal of chemical physics, vol. 97, no. 3, pp. 1990-2001(1992).
45. C. W. Gear, Numerical initial value problems in ordinary differential equations. Prentice Hall PTR (1971).
46. J. Haile, I. Johnston, A. J. Mallinckrodt, and S. McKay, "Molecular dynamics simulation: elementary methods," Computers in Physics, vol. 7, no. 6, pp. 625-625(1993).
47. J. D. Honeycutt and H. C. Andersen, "Molecular dynamics study of melting and freezing of small Lennard-Jones clusters," Journal of Physical Chemistry, vol. 91, no. 19, pp. 4950-4963(1987).
48. C.L. Kelchner, S.J. Plimpton and J.C. Hamilton, "Dislocation Nucleation and Defect Structure During Surface Indentation,” Physical Review B, Vol.58, no.17, pp.11085-11088(1998).
49. S. Nosé, "A unified formulation of the constant temperature molecular dynamics methods," The Journal of chemical physics, vol. 81, no. 1, pp. 511-519(1984).
50. W. G. Hoover, "Canonical dynamics: Equilibrium phase-space distributions," Physical review A, vol. 31, no. 3, p. 1695(1985).
51. R. Calusius, "On a Mechanical Theory Applicable to Heat,” Philosophical Magazine, Vol.40, pp.122-127(1870).
52. Z.S. Basinski, M.S. Duesbery and R. Taylor, "Influence of Shear Stress on Screw Dislocations in a Model Sodium Lattice,” Canadian Journal of Physics, Vol.49, pp.2160-2180(1971).
53. D. Srolovitz, K. Maeda, V. Vitek and T. Egami, "Structural Defects in Amorphous Solids Statistical Analysis of a Computer Model,” Philosophical Magazine A, Vol.44, pp.847-866(1981).
54. N. Miyazaki and Y. Shiozaki, "Calculation of Mechanical Properties of Solids Using Molecular Dynamics Method,” JSME International Journal Series A, Vol.39, no.4, pp.606-612(1996).
55. Y.C. Lin, and D.J. Pen, "Atomic Behavior Analysis of Cu Nanowire Under Uniaxial Tension with Maximum Local Stress Method,” Molecular Simulation, Vol.33, pp. 979-988(2007).
56. T. Iwaki, "Molecular Dynamics Study on Stress-Strain in Very Thin Film(Size and location of Region for Defining Stress and Strain)" , JSME International Journal Series A, Vol.39, no.3, pp.346-353(1996).
57. S. Plimpton, "Fast parallel algorithms for short-range molecular dynamics," Journal of computational physics, vol. 117, no. 1, pp. 1-19(1995).
58. A. Stukowski, “Visualization and analysis of atomistic simulation data with OVITO – the Open Visualization Tool,” Mater. Sci. Eng. 18, 015012(2010).
59. Y. Mishin, M. J. Mehl, D. A. Papaconstantopoulos, A. F. Voter and J. D. Kress, “Structural stability and lattice defects in copper: Ab initio, tight-binding and embedded-atom calculations,” Physical Review B, Vol. 63, 224106.
60. L. A. Girifalco and V. G. Weizer, “Application of the Morse Potential Function to Cubic Metals,” Physical Review, Vol. 114, no. 3, pp. 688-690(1958).
61. B. J. Lee, J. H. Shim, M. I. Baskes, “Semiempirical atomic potentials for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, Al, and Pb based on first and second nearest-neighbor modified embedded atom method,” Physical Review B, Vol. 68, 144112(2003).
62. P. Hirel, “Atomsk A tool for manipulating and converting atomic data files,” Comput. Phys. Commun., Vol. 197, pp. 212-219(2015).
63. J. LIAN and D. ZHOU, “Diffuse Necking and Localized Necking under Plane Stress,” Mater. Sci. Eng., Vol. 111, pp. 1-7(1989).
64. T. G. LANGDON, “Grain boundary sliding revisited: Developments in sliding over four decades,” J MATER. SCI, Vol. 41, pp.597-609(2006).
65. A. H. Chokshi, “Grain Boundary Processes in Strengthening, Weakening, and Superplasticity,” Adv. Eng. Mater., Vol. 22, 1900748(2020).