本文利用密度泛函理論來模擬計算硼氮奈米管之力學特性與電子特性，接著吸附一氧化碳分子於硼氮奈米管表面，並模擬計算單壁硼氮奈米管 (Boron nitride nanotube, BNNT) 在軸向應變時對吸附一氧化碳的影響，接著利用分子動力學探討(8,8)硼氮奈米管的機械性質與動態行為。本文研究分成三部份：
第一部分，首先，利用密度泛函理論(Density Functionl Theory, DFT)模擬計算硼氮奈米管受軸向應變時的力學特性，並探討在不同應變率下HOMO-LUMO Gap的變化情形，並對於硼與氮鍵結之鍵長、鍵角、鍵級(Bond order)以及徑向挫曲(Radial Buckling)隨應變率的變化做統計，接著討論電子密度態(Density of state)隨應變率的變化趨勢。
第二部份，吸附一個一氧化碳分子於硼氮奈米管表面，並利用密度泛函理論探討在軸向應變時一氧化碳分子的吸附情形，模擬過程中記錄一氧化碳的電荷值以及吸附能隨著應變率所產生的變化，並且探討吸附區域的結構變化以及電荷分佈。
第三部份，利用密度泛函理論與Forec matching method 找出硼氮奈米管的特索夫(Tersoff)勢能參數，接著進行(8,8)硼氮奈米管在溫度300k下受軸向拉伸應變的模擬，並進行(8,8)硼氮奈米管的機械性質與動態行為分析。

In this study, we used the Density functional theory (DFT) to obtain the relationship between mechanical property and electronic property of Boron nitride nanotubes (BNNTs) under the uni-axial strain. Moreover, we also investigated one CO molecule adsorbed on the BNNTs under the uni-axial strain. We also use the molecular dynamics to introduce the mechanical property and dynamic behavior of (8,8)BNNT under the uni-axial strain. There were three parts in this study:
The first part:
The effect of uni-axial strain on the electronic properties of (5,5) and (8,0)boron nitride nanotubes were obtained by DFT calculation. We used the HOMO-LUMO Gap、bond angle、bond length and radial buckling to analyze the electronic properties and mechanical properties. The stress-strain profiles indicated that different BNNTs types displayed very similar mechanical properties, but there were variations in HOMO-LUMO gaps at different strains, indicating that the electronic properties of BNNTs not only depend on uni-axial strain, but on BNNT type. In addition, the variations in nanotube geometries, partial density of states (PDOS) and charges of boron and nitride atoms were also discussed for (8,0) and (5,5) BNNTs at different strains.
The second part:
The DFT was used to investigate electronic properties of CO molecule adsorbed on BNNT under the uni-axial strain. The stress-strain profiles indicated that the CO molecule adsorption on BNNT leaded only to a local mechanical deformation. The strength of BNNT could not be affected when the CO molecule adsorbed on that. Moreover, we obtained that the charge of CO will slightly transfer to the adsorbed atom of BNNT when strain increased. Hence, the adsorption energy increased slightly under the uni-axial strain.
The third part:
The molecular dynamics simulations were performed to investigate deformation behaviors of (8,8)BN nanotubes under axial tensile strains at 300k. Variations with the tensile strain in the axial stress, bond lengths, bond angles, radial buckling, and slip vectors were all examined. The axial, radial, and tangential components of the slip vector were also employed to monitor, respectively, the local elongation, necking, and twisting deformation near the failure of the nanotube. The components of the slip vector grew rapidly and abruptly after the failure strain, especially for the axial component. This implies that the local elongation dominates the failure of the loaded BN nanotube and finally results in a chain-like tensile failure mode.

目錄……………………………………………………………………………I
圖目錄………………………………………………………………………III
表目錄………………………………………………………………………VI
中文摘要……………………………………………………………………VII
英文摘要…………………………………………………………………VIII
第一章 緒論 1
1.1 研究動機 1
1.2 硼氮奈米管簡介 2
1.3 硼氮奈米管文獻回顧 8
1.4 本文架構 13
第二章 模擬方法及理論介紹 14
2.1 密度泛函理論 14
2.1.1 電子密度(Electric Density) 14
2.1.2 Thomas-Fermi model (TF model) 15
2.1.3 Hohenberg-Kohn model (HK model) 15
2.1.4 Kohn-Sham equation 16
2.1.5 Psuedopotential 19
2.2 分子動力學理論 19
2.2.1 勢能函數 19
2.2.2 運動方程式 21
2.2.3 積分法則 22
2.2.4 時間步階選取 23
2.2.5 溫度修正 24
2.3 數值統計方法 27
2.3.1 鄰近表列數值方法 27
2.3.2 原子級應力數值計算 29
2.3.3 Force Matching Method 32
2.3.4 Radial Buckling (徑向挫曲) 34
2.3.5 吸附能之計算方法 35
第三章 結果與討論 36
3.1 以密度泛函理論探討單壁硼氮奈米管之機械性質與電學特性 36
3.1.1 物理模型之建構 36
3.1.2 機械性質分析與HOMO-LUMO Gap之變化 41
3.1.3 單壁硼氮奈米管電性分析 48
3.2 以密度泛函理論探討一氧化碳吸附於單壁硼氮奈米管之研究 56
3.2.1 一氧化碳吸附於硼氮奈米管表面之模型 56
3.2.2 吸附點局部構造分析 59
3.2.3 吸附能與電荷變化 63
3.3 以分子動力學探討(8,8)硼氮奈米管之機械性質與動態行為分析 69
3.3.1 物理模型之建構 69
3.3.2 勢能參數修正 71
3.3.3 機械性質與動態行為分析 74
結論 83
參考文獻 86

[1] S. Iijima, "Helical microtubules of graphitic carbon", Nature, vol. 354, p. 56-58, 1991.
[2] X. Q. Wang, B. L. Wang, J. J. Zhao and G. H. Wang, "Structural transitions and electronic properties of the ultrathin SiC nanotubes under uniaxial compression", Chemical Physics Letters, vol. 461, p. 280-284, 2008.
[3] H. Xu, R. Q. Zhang, X. H. Zhang, A. L. Rosa and T. Frauenheim, "Structural and electronic properties of ZnO nanotubes from density functional calculations", Nanotechnology, vol. 18, p. 485713, 2007.
[4] N. G. Chopra, R. J. Luyken, K. Cherrey, V. H. Crespi, M. L. Cohen, S. G. Louie, , "Boron-nitride nanotubes", Science, vol. 269, p. 966-967, 1995.
[5] D. Golberg, Y. Bando, Y. Huang, T. Terao, M. Mitome, C. C. Tang, , "Boron nitride nanotubes and nanosheets", Acs Nano, vol. 4, p. 2979-2993, 2010.
[6] Z. G. Wang, X. T. Zu, F. Gao and W. J. Weber, "Atomistic simulation of brittle to ductile transition in GaN nanotubes", Applied Physics Letters, vol. 89, p. 243123, 2006.
[7] D. J. Zhang and R. Q. Zhang, "Theoretical prediction on aluminum nitride nanotubes", Chemical Physics Letters, vol. 371, p. 426-432, 2003.
[8] D. Golberg, P. Costa, O. Lourie, M. Mitome, X. D. Bai, K. Kurashima, , "Direct force measurements and kinking under elastic deformation of individual multiwalled boron nitride nanotubes", Nano Letters, vol. 7, p. 2146-2151, 2007.
[9] X. Blase, A. Rubio, S. G. Louie and M. L. Cohen, "Stability and band-gap constancy of boron-nitride nanotubes", Europhysics Letters, vol. 28, p. 335-340, 1994.
[10] M. Yang, L. D. Wang, G. D. Chen, B. An, Y. J. Wang and G. Q. Liu, "First-principles study on field emission of C-doped capped single-walled BNNT", Acta Physica Sinica, vol. 58, p. 7151-7155, 2009.
[11] C. W. Chang, A. M. Fennimore, A. Afanasiev, D. Okawa, T. Ikuno, H. Garcia, , "Isotope effect on the thermal conductivity of boron nitride nanotubes", Physical Review Letters, vol. 97, p. 085901, 2006.
[12] Y. Chen, J. Zou, S. J. Campbell and G. Le Caer, "Boron nitride nanotubes: Pronounced resistance to Oxidation", Applied Physics Letters, vol. 84, p. 2430-2432, 2004.
[13] G. Mpourmpakis and G. E. Froudakis, "Why boron nitride nanotubes are preferable to Carbon nanotubes for Hydrogen storage? An ab initio theoretical study", Catalysis Today, vol. p. 341-345, 2007.
[14] J. X. Zhao and Y. H. Ding, "The effects of O2 and H2O adsorbates on field-emission properties of an (8,0) boron nitride nanotube: A density functional theory study", Nanotechnology, vol. 20, p. 085704, 2009.
[15] R. J. Baierle, T. M. Schmidt and A. Fazzio, "Adsorption of CO and NO molecules on carbon doped boron nitride nanotubes", Solid State Communications, vol. 142, p. 49-53, 2007.
[16] Y. F. Li, Z. Zhou and J. Zhao, "Transformation from chemisorption to physisorption with tube diameter and gas concentration: Computational studies on NH3 adsorption in BN nanotubes", Journal of Chemical Physics, vol. 127, p. 184705, 2007.
[17] M. Arab, F. Picaud, M. Devel, C. Ramseyer and C. Girardet, "Molecular selectivity due to adsorption properties in nanotubes", Physical Review B, vol. 69, p., 2004.
[18] H. Chen, Y. Chen, C. P. Li, H. Z. Zhang, J. S. Williams, Y. Liu, , "Eu-doped boron nitride nanotubes as a nanometer-sized visible-light source", Advanced Materials, vol. 19, p. 1845, 2007.
[19] A. Rubio, J. L. Corkill and M. L. Cohen, "Theory of graphitic boron-nitride nanotubes", Physical Review B, vol. 49, p. 5081-5084, 1994.
[20] A. Loiseau, F. Willaime, N. Demoncy, G. Hug and H. Pascard, "Boron nitride nanotubes with reduced numbers of layers synthesized by arc discharge", Physical Review Letters, vol. 76, p. 4737-4740, 1996.
[21] G. W. Zhou, Z. Zhang, Z. G. Bai and D. P. Yu, "Catalyst effects on formation of boron nitride nano-tubules synthesized by laser ablation", Solid State Communications, vol. 109, p. 555-559, 1999.
[22] M. Terrones, A. M. Benito, C. MantecaDiego, W. K. Hsu, O. I. Osman, J. P. Hare, , "Pyrolytically grown bxcynz nanomaterials: Nanofibres and nanotubes", Chemical Physics Letters, vol. 257, p. 576-582, 1996.
[23] W. L. Wang, X. D. Bai, K. H. Liu, Z. Xu, D. Golberg, Y. Bando, , "Direct synthesis of B-C-N single-walled nanotubes by bias-assisted hot filament chemical vapor deposition", Journal of the American Chemical Society, vol. 128, p. 6530-6531, 2006.
[24] T. W. Odom, J. H. Hafner and C. M. Lieber. Scanning probe microscopy studies of carbon nanotubes. Carbon nanotubes. Berlin: Springer-Verlag Berlin 2001:173-211.
[25] N. G. Chopra and A. Zettl, "Measurement of the elastic modulus of a multi-wall boron nitride nanotube", Solid State Communications, vol. 105, p. 297-300, 1998.
[26] D. Golberg, X. D. Bai, M. Mitome, C. C. Tang, C. Y. Zhi and Y. Bando, "Structural peculiarities of in situ deformation of a multi-walled BN nanotube inside a high-resolution analytical transmission electron microscope", Acta Materialia, vol. 55, p. 1293-1298, 2007.
[27] J. Song, H. Jiang, J. Wu, Y. Huang and K. C. Hwang, "Stone-wales transformation in boron nitride nanotubes", Scripta Materialia, vol. 57, p. 571-574, 2007.
[28] V. Verma, V. K. Jindal and K. Dharamvir, "Elastic moduli of a boron nitride nanotube", Nanotechnology, vol. 18, p. 435711, 2007.
[29] J. Song, Y. Huang, H. Jiang, K. C. Hwang and M. F. Yu, "Deformation and bifurcation analysis of boron-nitride nanotubes", International Journal of Mechanical Sciences, vol. 48, p. 1197-1207, 2006.
[30] B. Baumeier, P. Kruger and J. Pollmann, "Structural, elastic, and electronic properties of SiC, BN, and BeO nanotubes", Physical Review B, vol. 76, p. 085407, 2007.
[31] Y. H. Kim, K. J. Chang and S. G. Louie, "Electronic structure of radially deformed BN and BC3 nanotubes", Physical Review B, vol. 63, p. 205403, 2001.
[32] X. J. Wu, J. L. Yang, J. G. Hou and Q. S. Zhu, "Deformation-induced site selectivity for hydrogen adsorption on boron nitride nanotubes", Physical Review B, vol. 69, p. 153411, 2004.
[33] R. Z. Ma, Y. Bando, H. W. Zhu, T. Sato, C. L. Xu and D. H. Wu, "Hydrogen uptake in boron nitride nanotubes at room temperature", Journal of the American Chemical Society, vol. 124, p. 7672-7673, 2002.
[34] C. C. Tang, Y. Bando, X. X. Ding, S. R. Qi and D. Golberg, "Catalyzed collapse and enhanced Hydrogen storage of BN nanotubes", Journal of the American Chemical Society, vol. 124, p. 14550-14551, 2002.
[35] Q. Dong, X. M. Li, W. Q. Tian, X. R. Huang and C. C. Sun, "Theoretical studies on the adsorption of small molecules on Pt-doped BN nanotubes", Journal of Molecular Structure-Theochem, vol. 948, p. 83-92, 2010.
[36] Y. Chen, C. L. Hu, J. Q. Li, G. X. Jia and Y. F. Zhang, "Theoretical study of O2 adsorption and reactivity on single-walled Boron Nitride nanotubes", Chemical Physics Letters, vol. 449, p. 149-154, 2007.
[37] H. Chen, H. Z. Zhang, L. Fu, Y. Chen, J. S. Williams, C. Yu, , "Nano au-decorated boron nitride nanotubes: Conductance modification and field-emission enhancement", Applied Physics Letters, vol. 92, p. 243105, 2008.
[38] P. Hohenberg and W. Kohn, "Inhomogeneous electron gas", Physical Review B, vol. 136, p. B864, 1964.
[39] W. Kohn and L. J. Sham, "Self-consistent equations including exchange and correlation effects", Physical Review, vol. 140, p. 1133, 1965.
[40] D. M. Ceperley and B. J. Alder, "Ground-state of the electron-gas by a stochastic method", Physical Review Letters, vol. 45, p. 566-569, 1980.
[41] J. Tersoff, "Empirical interatomic potential for Silicon with improved elastic properties", Physical Review B, vol. 38, p. 9902-9905, 1988.
[42] O. Teleman, B. Jonsson and S. Engstrom, "A molecular-dynamics simulation of a water model with intramolecular degrees of freedom", Molecular Physics, vol. 60, p. 193-203, 1987.
[43] S. Nose, "A unified formulation of the constant temperature molecular-dynamics methods", Journal of Chemical Physics, vol. 81, p. 511-519, 1984.
[44] W. G. Hoover, "Canonical dynamics - equilibrium phase-space distributions", Physical Review A, vol. 31, p. 1695-1697, 1985.
[45] N. Chandra, S. Namilae and C. Shet, "Local elastic properties of carbon nanotubes in the presence of stone-wales defects", Physical Review B, vol. 69, p. 094101, 2004.
[46] N. Tokita, M. Hirabayashi, C. Azuma and T. Dotera, "Voronoi space division of a polymer: Topological effects, free volume, and surface end segregation", Journal of Chemical Physics, vol. 120, p. 496-505, 2004.
[47] D. Srolovitz, K. Maeda, V. Vitek and T. Egami, "Structural defects in amorphous solids statistical-analysis of a computer-model", Philosophical Magazine a-Physics of Condensed Matter Structure Defects and Mechanical Properties, vol. 44, p. 847-866, 1981.
[48] J. F. Lutsko, "Stress and elastic-constants in anisotropic solids - molecular-dynamics techniques", Journal of Applied Physics, vol. 64, p. 1152-1154, 1988.
[49] K. S. Cheung and S. Yip, "Atomic-level stress in an inhomogeneous system", Journal of Applied Physics, vol. 70, p. 5688-5690, 1991.
[50] Y. S. Noriyuki MIYAZAKI, "Calculation of mechanical properties of solids using molecular dynamics method", JSME International Journal Series A, vol. 39, p. 606, 1996.
[51] F. Ercolessi and J. B. Adams, "Interatomic potentials from 1st-principles calculations - the Force-Matching Method", Europhysics Letters, vol. 26, p. 583-588, 1994.
[52] K. Albe, W. Moller and K. H. Heinig, "Computer simulation and boron nitride", Radiation Effects and Defects in Solids, vol. 141, p. 85-97, 1997.