Responsive image
博碩士論文 etd-0723112-131954 詳細資訊
Title page for etd-0723112-131954
論文名稱
Title
以分子靜力學探討奈米多層非晶鋯銅/結晶鋯傾斜界面之機械行為
The investigation of mechanical properties of ZrCu/Zr/ZrCu amorphous-crystalline nanolaminates with inclined interface by molecular statics simulation
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
98
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2012-07-04
繳交日期
Date of Submission
2012-07-23
關鍵字
Keywords
分子靜力學、柏松比、密度泛函理論、Cu-Zr BMGs、TFMGs、擬合、體積模數、剪力模數、楊氏係數
DFT, Cu-Zr BMGs, TFMGs, Molecular Static, Poisson ratio, Young's modulus, fitting, Bulk modulus, Shear modulus
統計
Statistics
本論文已被瀏覽 5682 次,被下載 285
The thesis/dissertation has been browsed 5682 times, has been downloaded 285 times.
中文摘要
本研究藉由密度泛函理論計算(Density Functional Theory)計算銅鋯(Cu-Zr) 合金之空間群對稱性結構:FCC-Cu1Zr3、FCC-Cu2Zr2、FCC-Cu3Zr1、HCP-CuZr、B1及B2為參考結構與能量,再利用Big-Bang(BB)及Basin-Hopping(BH)計算法結合Force-matching(FM)方法擬合出Cu-Zr勢能參數。並以此參數計算Cu46Zr54、Cu50Zr50 及Cu64Zr36比例組成BMG材料之體積模數(Bulk Modulus)、剪力模數(Shear Modulus)、楊氏係數(Young’s Modulus)及柏松比(Poisson Ratio)。之後,再利用分子靜力學模擬壓縮試驗探討傾斜45及水平0角度之CuZr/Zr/CuZr 之多層膜結構變形機制及機械行為,計算壓縮過程中之應力應變曲線。水平0角度因無傾斜面只有內部Zr層所產成之差排,對於傾斜45角度因ZrCu 金屬玻璃薄膜(Thin Film Metallic Glasses, TFMGs)與Zr層界面之能量穩定度,造成滑移速度及最大應力不同主要因素。最後,本研究探討各傾斜角度,在壓縮變形過程中根據不同應變在ZrCu TFMGs所產生的剪切帶、剪力變形區及受力滑移所造成的原子分佈情形。
Abstract
In this study, the mechanical properties of Cu-Zr binary bulk metallic glasses (BMG) were investigated at the nano-scale. The stable amorphous structures and corresponding energies of BMG structures are performed by density functional theory (DFT) calculation as reference data. This study will combine the Force-Matching (FM) method and Basin-Hopping (BH) method to develop a new method for fitting the Cu-Zr Tight-binding (TB) potential parameters. Moreover, the Bulk modulus, Shear modulus, Young's modulus and Poisson ratio of Cu46Zr54, Cu50Zr50 and Cu64Zr36 structures are calculated with the fitting TB parameters. In addition, the compression process of BMG materials is simulated by the Molecular Statics. The stress and strain are obtained to investigate the deformation mechanism of CuZr/Zr/CuZr nanolaminates at 0 and 45 inclined degree.
Finally, we investigate the angle in the deformation process under different strain in the shear band, shear transformation zones (STZs) and force caused by the slip of the atomic distribution of TFMGs layer.
目次 Table of Contents
圖次 III
表次 VI
中文摘要 VII
ABSTRACT VIII
第一章 序論 1
1.1研究目的與動機 1
1.2文獻回顧 6
1.3論文架構 10
第二章 理論基礎及方法 11
2.1密度泛函理論(Density Functional Theory) 11
2.1.1 Thomas-Fermi 理論 11
2.1.2 Hohenberg-Kohn 理論 12
2.1.4 Kohn-Sham方程式 12
2.1.5交換相關函數(Exchange-Correlation Functions) 13
2.2最佳化理論 14
2.2.1 LBFGS法 15
2.2.2火炎演算法 17
2.2.3共軛梯度法 18
2.3最佳化結構 19
2.3.1 Big-Bang (BB) method 19
2.3.2 Basin-Hopping (BH) method 20
2.4勢能函數 22
2.4.1原子間作用勢能 22
2.4.2擬合勢能參數 24
2.5原子級應力分析 25
2.6變形分析 29
2.7週期邊界的處理 29
第三章 數值方法 31
3.1鄰近原子表列數值方法 31
3.1.1截斷半徑法 31
3.1.2維理表列法(Verlet List) 32
3.1.3巢室表列法(Cell Link) 34
3.1.4維理表列結合巢室表列法 (Verlet List Combine Cell Link) 35
3.2 模擬流程圖 36
第四章 結果與討論 37
4.1 擬合勢能參數及機械性質分析 37
4.1.1 擬合原子間之勢能參數 37
4.1.2 Cu-Zr比例機械性質分析 43
4.2 模擬壓縮試驗 47
4.2.1 壓縮試驗之物理模型建構 47
4.2.2 壓縮試驗條件環境設定 51
4.3 壓縮試驗結果分析 53
第五章 結論與建議 75
參考文獻 76
參考文獻 References
[1] A. C. Lund and C. A. Schuh, "Topological and chemical arrangement of binary alloys during severe deformation", J. Appl. Phys., 95, 4815-4822 (2004)
[2] W. L. Johnson, "Bulk Glass-Forming Metallic Alloys: Science and Technology", MRS Bull., 24, 42-56 (1999)
[3] A. Inoue, B. Shen, H. Koshiba, H. Kato, and A. R. Yavari, "Cobalt-based bulk glassy alloy with ultrahigh strength and soft magnetic properties", Nature Mater., 2, 661-663 (2003)
[4] N. H. Pryds, "Bulk amorphous Mg-based alloys", Mater. Sci. Eng. A, 375-377,186-193 (2004)
[5] A. Inoue, "Stabilization of Metallic Supercooled Liquid and Bulk Amorphous Alloys", Acta Mater., 48, 279-306 (2000)
[6] T. Mukai, T. G. Nieh, Y. Kawamura, A. Inoue, and K. Higashi, "Influence of Strain Rate on Compressive Mechanical Behavior of Pd40Ni40P20 Bulk Metallic Glass", Intermetallics, 10, 1071-1077 (2002)
[7] W. J. Wright, R. B. Schwarz, and W. D. Nix, "Localized heating during serrated plastic flow in bulk metallic glasses", Mater. Sci. Eng. A, 319-321, 229-232 (2000)
[8] D. M. Xing, T. H. Zhang, W. H. Li, and B. C. Wei, "The Characterization of Plastic Flow in Three Different Bulk Metallic Glass Systems", J. Alloys Compd., 433, 318-323 (2007)
[9] W. Klement, R.H. Willens, and P. Duwez, "Non-crystalline Structure in Solidified Gold–Silicon Alloys", Nature 187, 869(1960)
[10] A. Inoue, H. Yamaguchi, T. Zhang, and T. Masumoto, "Al-La-Cu Amorphous Alloys with a Wide Supercooled Liquid Region", Mater. Trans., JIM, 31, 104 (1990)
[11] H. M. Chen, Y. C. Chang, T. H. Hung, X. H. Du, J. C. Huang, J. S. C. Jang, and P. K. Liaw, "Compression Behavior of Mg-Cu-Gd Bulk Metallic Glasses with Various Specimen Height to Diameter Ratios", Mater. Trans., 48, 1802-1805 (2007)
[12] C. P. Chou and F. Spaepen, "Some mechanical properties of phase separated Pd 0.74Au0.08Si0.38 Metallic Glasses", Acta Metall., 23, 609-613(1975)
[13] G. Y. Yuan and A. Inoue, "The effect of Ni substitution on the glass-forming ability and mechanical properties of Mg–Cu–Gd metallic glass alloys", J. Alloys Compd., 387, 134-138 (2005)
[14] Z. G. Li, X. Hui, C. M. Zhang, and G. L. Chen, "Formation of Mg–Cu–Zn–Y bulk metallic glasses with compressive strength over gigapascal", J. Alloys Compd., 454, 168-173 (2008)
[15] G. Y. Yuan, K. Amiya, and A. Inoue, "Structural relaxation, glass-forming ability and mechanical properties of Mg–Cu–Ni–Gd alloys", J. Non-Cryst. Solids, 351, 729-735 (2005)
[16] C. Fan, P. K. Liaw, T. W. Wilson, H. Choo, Y. F. Gao, C. T. Liu, T. Proffen, and J. W. Richardson, "Pair distribution function study and mechanical behavior of as-cast and structurally relaxed Zr-based bulk metallic glasses", Appl. Phys. Lett., 89, 231920 (2006)
[17] G. He, W. Loser, J. Eckert, and L. Schultz, "Phase transformation and mechanical properties of Zr-base bulk glass-forming alloys", Mater. Sci. Eng. A, 352, 179-185 (2003)
[18] S. W. Lee, M. Y. Huh, E. Fleury, and J. C. Lee, "Crystallization-induced plasticity of Cu–Zr containing bulk amorphous alloys", Acta Mater., 54, 349-355 (2006)
[19] 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)
[20] 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)
[21] 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)
[22] 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)
[23] Li, Q.Z., "Effect of dislocation source length on yield strength of nanostructured metallic multilayer thin films", Materials Science and Engineering: A, 493, 288-291(2008)
[24] 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)
[25] Anil Gannepalli and Surya K Mallapragada, "Molecular dynamics studies of plastic deformation during silicon nanoindentation", Nanotechnology, 12, 250-257(2001)
[26] Schiotz, J. and Jacobsen, K.W., "A maximum in the strength of nanocrystalline copper", Science, 301, 1357-1359 (2003)
[27] B. C. Snyder, J. Wadsworth, and O. D. Sherby, "Superplastic behavior in ferrous laminated composites", Acta Metall., 32, 919-932 (1984)
[28] Inoue A, Zhang W, Tsurui T, Yavari AR, Greer AL , "Unusual room-temperature compressive plasticity in nanocrystal-toughened bulk copper-zirconium glass", Philos Mag Lett, 85, 221-237 (2005)
[29] Xu D, Lohwongwatana B, Duan G, Johnson WL, Garland C, "Bulk metallic glass formation in binary Cu-rich alloy series – Cu100-xZrx (x=34, 36, 38.2, 40 at.%) and mechanical properties of bulk Cu64Zr36 glass", Acta Mater, 52, 2621–2624 (2004)
[30] Zhang Y, Wang WH, Greer AL, "Making metallic glasses plastic by control of residual stress", Nat. Mater., 5, 857-860 (2006)
[31] T. G. Nieh, T. W. Barbee, and J. Wadsworth, "Tensile properties of a free-standing Cu/Zr nanolaminate (or compositionally-modulated thin film) ", Scripta Mater., 41, 929-935 (1999)
[32] A. Donohue, F. Spaepen, R. G. Hoagland, and A. Misra, "Suppression of the shear band instability during plastic flow of nanometer-scale confined metallic glasses", Appl. Phys. Lett., 91, 241905 (2007)
[33] C. C. Hays, C. P. Kim, and W. L. Johnson, "Microstructure Controlled Shear Band Pattern Formation and Enhanced Plasticity of Bulk Metallic Glasses Containing in situ Formed Ductile Phase Dendrite Dispersions", Phys. Rev. Lett., 84, 2901-2904 (2000)
[34] G. He, J. Eckert, W. Loser, and L. Schultz, "Novel Ti-base nanostructure–dendrite composite with enhanced plasticity", Nature Mater., 2, 33-37 (2002)
[35] D. H. Hofmann, D. C., J. Y. Suh, A. Wiest, M. L. Lind, M. D. Demetriou, and W. L. Johnson, "Development of tough, low-density titanium-based bulk metallic glass matrix composites with tensile ductility", Proc. Natl. Acad. Sci. U.S.A, 105, 20136-20140 (2008)
[36] D. C. Hofmann, J. Y. Suh, A. Wiest, G. Duan, M. L. Lind, M. D. Demetriou, and W. L. Johnson, "Designing metallic glass matrix composites with high toughness and tensile ductility", Nature, 451, 1085-1089 (2008)
[37] Wei Hua Wang , Z. Bian, Ping Wen, Yong Zhang, M.X. Pan, D.Q. Zhao, "Role of addition in formation and properties of Zr-based bulk metallic glasses", Intermetallics, 10, 1249-1257 (2002)
[38] Vinogradov, O., "A new method of molecular statics in polycrystals Applications", Computational Materials Science, 39, 611-615 (2007)
[39] A. Inoue, T. Zhang, T. Masumoto, "Al-La-Ni amorphous alloys with a wide supercooled liquid region", Mater. Trans. JIM, 30, 965 (1989)
[40] A. Inoue, "Stabilization of metallic supercooled liquid and bulk amorphous alloys", Acta Mater., 48, 279 (2000)
[41] J.C. Huang, J.P. Chu, J.S.C. Jang, "Recent progress in metallic glasses in Taiwan", Intermetallic, 17, 973-987 (2009)
[42] X. H. Du, J. C. Huang, K. C. Hsieh, Y. H. Lai, H. M. Chen, J. S. C. Jang, and P. K. Liaw, "Two-glassy-phase bulk metallic glass with remarkable plasticity", Appl. Phys. Lett., 91, 131901 (2007)
[43] Y. M. Wang, J. Li, A. V. Hamza, and J. T. W. Barbee, "Ductile crystalline–amorphous nanolaminates", Proc. Natl. Acad. Sci. U.S.A, 104, 11155-11160 (2007)
[44] Schiotz, J., Di Tolla, F.D., and Jacobsen, K.W., "Softening ofnanocrystalline metals at very small grain sizes", Nature, 391, 561-563 (1998)
[45] 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)
[46] Ioannis N. Mastorakos, Aikaterini Bellou, David F. Bahr, and Hussein M. Zbib, "Size-dependent strength in nanolaminate metallic systems", J. Mater. Res., 26, 1179-1187 (2011)
[47] I.N. Mastorakos, N. Abdolrahim, and H.M. Zbib, "Deformation mechanisms in composite nano-layered metallic and nanowire structures", Int. J. Mech. Sci., 52, 295 (2010)
[48] 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)
[49] Hohenberg P., K. W., "Inhomogenerous electron gas", Physical Review B, 136, 964 (1964)
[50] W. Kohn, L. J. Sham, "Self-Consustent Equation Including Exchange and Correlation Effects", Phys. Rev, 140, A1133-A1138 (1965)
[51] 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)
[52] 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)
[53] Quapp, W., "A growing string method for the reaction pathway defined by a Newton trajectory", Journal of Chemical Physics, 122, 174106 (2005)
[54] 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)
[55] Fletcher, R., "A New Approach to Variable Metric Algorithms", Computer Journal, 13, 317-322 (1970)
[56] Goldfarb, D., "A Family of Variable Metric Updates Derived by Variational Means", Mathematics of Computation, 24, 23-26 (1970)
[57] Shanno, D.F., "Conditioning of Quasi-Newton Methods for Function Minimization", Mathematics of Computation, 24, 647-656 (1970)
[58] 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)
[59] P. A. T. Olsson, S. Melin and C. Persson, "Atomistic simulations of tensile and bending properties of single-crystal bcc iron nanobeams", Physical Review B. , 76, 224112 (2007).
[60] E. Bitzek, P. Koskinen, F. Gahler, M. Moseler and P. Gumbsch, "Structural Relaxation Made Simple", Phys. Rev. Lett. , 97, 170201 (2006).
[61] Andrei, N., "Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization", Optimization Methods & Software, 22, 561-571 (2007)
[62] Liu, D.C. and Nocedal, J., "On the limited memory bfgs method for large-scale optimization", Mathematical Programming, 45, 503-528 (1989)
[63] D. J. Wales and J. P. K. Doye, "Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms", Journal of Physical Chemistry A, 101, 5111-5116 (1997)
[64] K. A. Jackson, M. Horoi, I. Chaudhuri, T. Frauenheim, and A. A. Shvartsburg, "Unraveling the shape transformation in silicon clusters", Physical Review Letters, 93, 013401 (2004)
[65] S. Hamad, C. R. A. Catlow, and S. M. Woodley, "Structure and Stability of Small TiO2 Nanoparticles", J. Phys. Chem. B, 109, 15741-15748 (2005)
[66] 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, 59, 321-336 (1989)
[67] 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)
[68] 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)
[69] M.A. Karolewski, "Tight-binding potentials for sputtering simulations with fcc and bcc metals", Radiation Effects and Defects in Solids, 153, 235-239 (2001)
[70] F. Willaime, C. Massobrio, "Development of an N-body interatomic potential for hcp and bcc zirconium", Physical Review B, 43, 14 (1991)
[71] F. Ercolessi and J. B. Adams, "Interatomic Potentials from 1st-Principles Calculations - the Force-Matching Method", Europhysics Letters, 26, 583-588 (1994)
[72] 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)
[73] 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)
[74] D. Srolovitz, K. Maeda, V. Vitek, and T. Egami, "Structural defects in amorphous solids statistical analysis of a computer model", Philosophical Magazine A., 44, 847-866 (1981)
[75] N. Miyazaki, and Y. Shiozaki, "Calculation of mechanical properties of solids using molecular dynamics method", JSME International journal Series A., 39, 606 (1996)
[76] H. Rafii-Tabar, "Computational model ling of thermo-mechanical and transport properties of carbon nanotubes", Physics Reports, 390, 235-452 (2004)
[77] A. Gannepalli and S. K. Mallapragada, "Molecular dynamics studies of plastic deformation during silicon nanoindentation", Nanotechnology, 12, 250-257 (2001)
[78] A. J. Cao, Y. Q. Cheng, and E. Ma, "Structural processes that initiate shear localization in metallic glass", Acta Materialia, 57, 5146-5155 (2009)
[79] Frenkel,D. and Smit, B., "Understanding Molecular Simulation" ;Academic Press:San Diego(1996)
[80] Allen, M.P. and Tildesley, D.J., "Computer Simulation of Liquids"; Oxford Science:London(1991)
[81] Rapaport, D.C., "The Art of Molecular Dynamics Simulation"; Cambridge University Press:London(1997)
[82] Haile, J.M., "Molecular Dynamics Simulation"; Wiley-Interscience:New York(1992)
[83] J.F. Nye. "Physical properties of crystals"; Oxford University Press, (1957)
[84] Y.Q. Cheng , A.J. Cao, E. Ma, "Correlation between the elastic modulus and the intrinsic plastic behavior of metallic glasses: The roles of atomic configuration and alloy composition", Acta Materialia, 57, 3253-3267 (2009)
[85] Johnson WL, Samwer K., "A Universal Criterion for Plastic Yielding of Metallic Glasses with a (T/Tg)2/3 Temperature Dependence", Phys Rev Lett, 95, 195501 (2005)
[86] Duan G, Blauwe KD, Lind ML, Schramm JP, Johnson WL., "Compositional dependence of thermal, elastic, and mechanical properties in Cu-Zr-Ag bulk metallic glasses", Scripta Mater, 58, 159 (2008)
[87] F. Cleri, V. Rosato, "Tight-binding potentials for transition metals and alloys", Physical Review B, 48, 1 (1993)
[88] C. Kittel, "Introduction to Solid State Physics" (1966)
[89] G. Simmons and H. Wang, "Single Crystal Elastic Constans and Calculated Aggregated Properties" (1971)
[90] Mingwei Chen, "Mechanical Behavior of Metallic Glasses: Microscopic Understanding of Strength and Ductility", Annu. Rev. Mater. Res., 38 ,14.1-14.25 (2008)
[91] Argon AS, "Plastic deformation in metallic glasses", Acta Metall. 27,47-58 (1979)
[92] Ming Che Liu, "Mechanical Properties and Deformation Behaviors in Amorphous/Nanocrystalline Multilayers under Microcompression", Department of Materials and Optoelectronic Science National Sun Yat-sen University Doctorate Dissertation (2011)
電子全文 Fulltext
本電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。
論文使用權限 Thesis access permission:自定論文開放時間 user define
開放時間 Available:
校內 Campus: 已公開 available
校外 Off-campus: 已公開 available


紙本論文 Printed copies
紙本論文的公開資訊在102學年度以後相對較為完整。如果需要查詢101學年度以前的紙本論文公開資訊,請聯繫圖資處紙本論文服務櫃台。如有不便之處敬請見諒。
開放時間 available 已公開 available

QR Code