本論文主要研究目的為利用分子動力學，探討鈦奈米線分別在[-12-10]、[0001]方向及鈦奈米板材在[-12-10]方向的拉伸，並以不同應變速率和板材厚度等條件，探討其降伏機理、流動應力及破斷模式。
模擬結果顯示，奈米線與板材在不同應變速率下，其降伏應力與楊氏係數沒有太大變化。鈦奈米線[0001]方向的拉伸在降伏時局部區域會產生HCP晶格扭曲之過渡態，促使HCP晶體由[0001]轉變為[10-10]的拉伸方向，且轉變過程之中會因為晶體扭曲行為，而造成FCC晶體結構的產生。鈦奈米線[-12-10]方向的拉伸，降伏時會啟動HCP之次滑動面系統。鈦奈米線兩個拉伸方向皆會在HCP金字塔平面由表面射入部分差排，造成FCC堆積錯誤的產生，且FCC堆積錯誤隨著拉伸過程逐漸地擴大，並在到達一定量後於堆積錯誤中{111}面上，產生部分差排的滑移，藉由部分差排的不斷滑移，最後造成奈米線的破斷。而鈦奈米板材在[-12-10]方向的拉伸，其降伏機制主要也是以HCP之金字塔平面，由表面產生差排射入，最後奈米板材藉由不斷地從表面射入差排、滑移，致使板材破斷。

The main purpose of this paper is using the molecular dynamics to investigate titanium nanowires in [-12-10] and [0001] direction, and titanium nanoplates in [-12-10] direction of stretch in different strain rates, sheet thickness and other conditions to explore its yield mechanism, the flow stress and the breaking mode.
Simulation results show, when the nanowires and nanoplates of stretch in different strain rates, its yield stress and Young's modulus do not change significantly. When titanium nanowires of stretch yields in [0001] direction, the transition would happened with the HCP crystals from [0001] to [10-10] stretch direction, and it is possible to causes FCC crystals formation in the transition. When titanium nanowires of stretch yields in [-12-10] direction, it will use pyramidal plane system to slip. Titanium nanowires in these two directions would use pyramidal plane system to slip and decomposed into two partial dislocations and cause the FCC stacking fault formation. FCC stacking fault will expand gradually as the stretching process. When it reaches a certain number of FCC stacking fault, the partial dislocations would slip again in FCC stacking fault with FCC {111} planes. With the partial dislocations continues slip in FCC stacking fault, it would finally cause the nanowires breaking. The nanoplates of stretch yields in [-12-10] also use pyramidal plane system to slip. Finally the nanoplates use dislocations slip from nanoplates surface and cause it breaking.

C. M. Liber, "Nanoscale Science and Technology: Building a Big Future from Small Things" , MRS Bull, Vol.28, pp.486-491(2003).
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) .
P.G. Partridge, " The crystallography and deformation modes of hexagonal close-packed metals" Metall. Rev., 12 (118), pp. 169–194 (1967).
J. H. 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).
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth and A. H. Teller, "Equation of Calculations By Fast Computing Machines", Journal of Chemical Physics, Vol.21, No.6, pp.1087-1092(1953).
Loup Verlet, "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review, Vol.159, No.1, pp.98-103(1967)
B. Quentrec and C. Brot, "New Method for Neighbors in Molecular Dynamics Computations", Journal of Computational Physics, Vol.13, pp.430-432(1973).
E. Lilleodden, "Microcompression study of Mg (0001) single crystal", Scripta Mater, 62, pp. 532–535 (2010).
Q. Sun, Q. Guo, X. Yao, L. Xiao, J.R. Greer, J. Sun, "Size effects in strength and plasticity of single-crystalline titanium micropillars with prismatic slip orientation", Scripta Mater, 65, p. 473 (2011).
Junqiang Ren, Qiaoyan Sun, Lin Xiao, , Xiangdong Ding, Jun Sun, " Size-dependent of compression yield strength and deformation mechanism in titanium single-crystal nanopillars orientated [0001] and [112 ̅0]", Materials Science and Engineering: A Volume 615, 6 October 2014, Pages 22–28
J. 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).
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).
Philip M. Morse, "Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels", Phtsical Review, Vol.34, pp.57-64(1929).
Murray S. Daw and M. I. Baskes, "Semiempirical Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals", Physical Review Letters, Vol.50, No.17, pp.1285-1301(1983).
Murray S. Daw and M. I. Baskes, "Eambedded-Atom Method: Derivation and Application to Impurities, Surface, and Other Defects in Metals", Physical Review B, Vol.29, No.12, pp.6443-6453(1984).
V. Rosato, M. Guillope and B. Legrand, "Thermodynamical and Structural Properties of FCC Transition Metals Using A Simple Tight-Binding Model" , Philosophical Magazine A: Physics of Condensed Matter, Structure, Defects and Mechanical Properties, Vol.59, pp.321-336(1989).
C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, (1971).
J. M. Haile, Molecular Dynamics Simulation: Elementrary Methods(A Wiley-Interscience Publication), John Wiley & Sons, Inc, USA, (1992).
R. Calusius, "On a Mechanical Theory Applicable to Heat" , Philosophical Magazine, Vol.40, pp.122-127(1870).
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).
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).
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).
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).
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).
Cynthia 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).
F. Cleri and V. Rosato, “Tight-binding potentials for transition metals and alloys”, Physical Review B, Vol. 48, No. 1, pp. 22-33(1993).