近年來，奈米科技最重要的議題注重於材料在奈米尺寸時會有尺寸效應，與大尺寸材料相比具有獨特的機械性質。尺寸效應不只是適用於奈米晶材料，也可以在奈米尺寸的單晶觀察此現象。根據Hall-Petch 的關係式，材料強度的尺寸效應已被研究。當試片尺寸減少至奈米尺寸，單晶強度將會隨之增加。

在同樣FCC結構中不同種類的金屬元素中，鋁被選擇為本研究的主要材料是由於鋁價格低廉以及擁有出色的物理和化學性質。此外，鋁比起其他材料具有較低的雙晶界面能、較高的比強度以及較高的疊差能。

在本研究中，我們將探究不同尺寸以及改變施力方向之鋁單晶在不同的拉伸測試下之機械性質和塑性變形行為。在本研究中將探究不同尺寸以及改變施力方向的鋁單晶在不同的拉伸測試下之機械性質以及變形行為。沿著[111]施力方向的毫米等級拉伸、微米等級壓縮以及奈米等級拉伸測試試片的降伏強度分別為60 MPa、180 MPa以及0.75 GPa。沿著[110]施力方向的微米等級壓縮測試試片的降伏強度為116 MPa。從結果可得知鋁單晶在不同的試片尺寸以及施力方向下會有尺寸效應以及方向效應造成之強度差異。

Over recent years, the important issue of nano-technology is the size effect of the materials in nano-scaled. And the nano-scaled materials possess the unique mechanical properties compared to the large size materials. The size effect is not only applied for nanocrystalline materials but also for nano-structured single crystals. The size effect of strength in accordance with the Hall-Petch relationship has been studied. The strength of a single crystal will increase with decreasing sample size to the nano-scaled.

Among various metallic elements with a face centered cubic (FCC) structure, aluminum (Al) is selected in this study due to its low cost and many excellent physical and chemical properties. In addition, aluminum possesses lower twin boundary energy, higher specific strength and higher stacking fault energy.

In this study, the mechanical properties and deformation behaviors of single crystal aluminum with different sizes and loading directions have been investigated via different tension and compression tests. The yield stress for the mini-scaled tension, micro-scaled compression and nano-scaled tension testing loading along [111] direction are 60 MPa, 180 MPa and 0.75 GPa, respectively. The yield stress for the micro-scaled compression testing loading along [110] direction is 116 MPa. The size effect and the orientation effect of the single crystal aluminum were revealed and rationalized.

論文審定書..........................................................................................................................................................i
致謝...................................................................................................................................................................ii
List of Tables...................................................................................................................................................viii
List of Figures....................................................................................................................................................ix
中文摘要...........................................................................................................................................................xiv
Abstract............................................................................................................................................................xv
Chapter 1 Introduction........................................................................................................................................1
Chapter 2 Background and Literature Review........................................................................................................3
2-1 The structure of aluminum..............................................................................................................................3
2-1-1 Crystal structure of aluminum......................................................................................................................3
2-1-2 Mechanical properties of aluminum..............................................................................................................3
2-2 Size effects..................................................................................................................................................5
2-2-1 The Hall-Petch relationship..........................................................................................................................6
2-2-2 Size effects related to mechanical characteristics.........................................................................................7
2-2-3 Size effects of single crystal.......................................................................................................................9
2-3 The mechanism of plastic deformation in crystals..........................................................................................12
2-3-1 Dislocation mechanism.............................................................................................................................12
2-3-2 Plastic deformation mechanism.................................................................................................................13
2-4 Electron back scattered diffraction................................................................................................................15
2-4-1 Advantages of EBSD................................................................................................................................15
2-4-2 The basic principles and set-up of typical EBSD system..............................................................................16
2-5 Mini-scaled characterization via mini-tension..................................................................................................19
2-6 Micro-scaled characterization via micro-pillars compression............................................................................20
2-7 Nano-scaled characterization via nano-tension...............................................................................................22
2-8 Nanoindentation technique............................................................................................................................24
Chapter 3 Experimental Procedures....................................................................................................................26
3-1 Sample preparation......................................................................................................................................26
3-1-1 Raw material............................................................................................................................................26
3-1-2 Mechanical polishing and electropolishing process.......................................................................................27
3-2 Mini-tension tests........................................................................................................................................27
3-2-1 Preparation for mini-tension sample............................................................................................................27
3-2-2 Mini-tension tests using minitester system..................................................................................................28
3-3 Micro-compression tests..............................................................................................................................28
3-3-1 Preparation for micro-compression sample..................................................................................................28
3-3-2 Micro-compression tests using nanoindentation system...............................................................................29
3-4 Nano-tension tests.......................................................................................................................................29
3-4-1 Preparation for nano-tension sample...........................................................................................................29
3-4-2 Nano-tension tests using nanoindentation system........................................................................................30
3-5 Property measurements and analyses...........................................................................................................31
3-5-1 X-ray diffraction........................................................................................................................................31
3-5-2 Scanning electron microscopy...................................................................................................................32
3-5-3 Electron back scattered diffraction.............................................................................................................32
3-5-4 Transmission electron microscopy.............................................................................................................33
Chapter 4 Results and Discussions....................................................................................................................34
4-1 X-ray diffraction analysis..............................................................................................................................34
4-2 EBSD analysis............................................................................................................................................35
4-3 Mini-scaled tension tests..............................................................................................................................36
4-4 Micro-scaled compression tests....................................................................................................................39
4-4-1 Micro-compression results.........................................................................................................................39
4-4-2 Deformation mechanisms..........................................................................................................................43
4-4-3 Size effects of Al micropillars....................................................................................................................44
4-4-4 Orientation effects of Al micropillars...........................................................................................................46
4-5 Nano-scaled tension tests............................................................................................................................48
4-6 Summary....................................................................................................................................................50
Chapter 5 Conclusions.......................................................................................................................................53
References........................................................................................................................................................56
Tables...............................................................................................................................................................61
Figures..............................................................................................................................................................70

[1] K. Kumar, H. Van Swygenhoven, S. Suresh, Acta Materialia, 51 (2003) 5743-5774.
[2] M.D. Uchic, D.M. Dimiduk, J.N. Florando, W.D. Nix, Science, 305 (2004) 986-989.
[3] J.R. Greer, W.C. Oliver, W.D. Nix, Acta Materialia, 53 (2005) 1821-1830.
[4] C.A. Volkert, E.T. Lilleodden, Philosophical Magazine, 86 (2006) 5567-5579.
[5] D. Kiener, W. Grosinger, G. Dehm, R. Pippan, Acta Materialia, 56 (2008) 580-592.
[6] W.D. Nix, J.R. Greer, G. Feng, E.T. Lilleodden, Thin Solid Films, 515 (2007) 3152-3157.
[7] T.A. Parthasarathy, S.I. Rao, D.M. Dimiduk, M.D. Uchic, D.R. Trinkle, Scripta Materialia, 56 (2007) 313-316.
[8] H. Huang, H. Pei, Y. Chang, C. Lee, J. Huang, Thin Solid Films, 529 (2013) 177-180.
[9] Q. Yu, L. Qi, K. Chen, R.K. Mishra, J. Li, A.M. Minor, Nano letters, 12 (2012) 887-892.
[10] X. Chen, J.J. Vlassak, Journal of Materials Research, 16 (2001) 2974-2982.
[11] M. Zhao, W.S. Slaughter, M. Li, S.X. Mao, Acta Materialia, 51 (2003) 4461-4469.
[12] H. Zhang, B.E. Schuster, Q. Wei, K.T. Ramesh, Scripta Materialia, 54 (2006) 181-186.
[13] S.Y. Kuan, Department of Materials and Optoelectronic Science, National Sun Yet-Sen University, 2013.
[14] W. Witt, Z Naturforsch Pt A, A 22 (1967) 92-&.
[15] G.W.P. W. D. Moffatt, J. Wulff, John Wiley and Son, 1 (1964) 51.
[16] W.D. Callister, John Wiley and Son, (2000).
[17] W.B. Pearson, A handbook of lattice spacings and structures of metals and alloys, 1967.
[18] A. Cottrell, Metallurgizdat, Moscow, (1961) p. 288.
[19] B.F. Figgins, G.O. Jones, D.P. Riley, Philosophical Magazine, 1 (1956) 747-758.
[20] M. Straumanis, J Appl Phys, 20 (1949) 726-734.
[21] T.T. Hu, Department of Materials and Optoelectronic Science, National Sun Yet-Sen University, 2012.
[22] N. Silvestre, International Journal of Composite Materials, 3 (2013) 28-44.
[23] G.E. Dieter, D. Bacon, Mechanical metallurgy, McGraw-Hill New York, 1986.
[24] R. Smallman, D. Green, Acta Metallurgica, 12 (1964) 145-154.
[25] I. Dillamore, E. Butler, D. Green, Metal Science, 2 (1968) 161-167.
[26] G. Groves, A. Kelly, Philosophical Magazine, 8 (1963) 877-887.
[27] E. Hall, Proceedings of the Physical Society. Section B, 64 (1951) 747.
[28] N. Petch, J. Iron Steel Inst., 174 (1953) 25-28.
[29] H. Gleiter, Progress in Materials Science, 33 (1989) 223-315.
[30] T. Nieh, J. Wang, Intermetallics, 13 (2005) 377-385.
[31] H. Conrad, J. Narayan, Scripta materialia, 42 (2000) 1025-1030.
[32] C. Carlton, P. Ferreira, MRS Proceedings, Cambridge Univ Press, 2006, pp. 0976-EE0901-0904.
[33] R. Scattergood, C. Koch, Scripta metallurgica et materialia, 27 (1992) 1195-1200.
[34] J. Lian, B. Baudelet, A. Nazarov, Materials Science and Engineering: A, 172 (1993) 23-29.
[35] G.A. Malygin, Fiz Tverd Tela+, 37 (1995) 2281-2292.
[36] V. Yamakov, D. Wolf, S.R. Phillpot, A.K. Mukherjee, H. Gleiter, Nature materials, 1 (2002) 45-49.
[37] J. Schiøtz, K.W. Jacobsen, Science, 301 (2003) 1357-1359.
[38] R. Masumura, P. Hazzledine, C. Pande, Acta Materialia, 46 (1998) 4527-4534.
[39] H. Van Swygenhoven, M. Spaczer, A. Caro, Acta Materialia, 47 (1999) 3117-3126.
[40] S. Takeuchi, Scripta materialia, 44 (2001) 1483-1487.
[41] V. Yamakov, D. Wolf, S. Phillpot, A. Mukherjee, H. Gleiter, Philosophical magazine letters, 83 (2003) 385-393.
[42] V. Yamakov, D. Wolf, S. Phillpot, A. Mukherjee, H. Gleiter, nature materials, 3 (2003) 43-47.
[43] K. Lu, M. Sui, Scripta metallurgica et materialia, 28 (1993) 1465-1470.
[44] N. Wang, Z. Wang, K. Aust, U. Erb, Acta Metall Mater, 43 (1995) 519-528.
[45] D. Konstantinidis, E. Aifantis, Nanostructured materials, 10 (1998) 1111-1118.
[46] H. Song, S. Guo, Z. Hu, Nanostructured Materials, 11 (1999) 203-210.
[47] G. Fan, H. Choo, P. Liaw, E. Lavernia, Materials Science and Engineering: A, 409 (2005) 243-248.
[48] P.P. Chattopadhyay, S.K. Pabi, I. Manna, Zeitschrift für Metallkunde, 91 (2000) 1049-1051.
[49] J. Schiotz, T. Vegge, F.D. Di Tolla, K.W. Jacobsen, Phys Rev B, 60 (1999) 11971-11983.
[50] C.T. Liu, L. Heatherly, D.S. Easton, C.A. Carmichael, J.H. Schneibel, C.H. Chen, J.L. Wright, M.H. Yoo, J.A. Horton, A. Inoue, Metall Mater Trans A, 29 (1998) 1811-1820.
[51] W.J. Wright, R.B. Schwarz, W.D. Nix, Mat Sci Eng a-Struct, 319 (2001) 229-232.
[52] U. Helmersson, S. Todorova, S.A. Barnett, J.E. Sundgren, L.C. Markert, J.E. Greene, J Appl Phys, 62 (1987) 481-484.
[53] A. Misra, H. Krug, Advanced Engineering Materials, 3 (2001) 217-222.
[54] F. Khater, A. Seoud, Acta Physica Slovaca, 38 (1988) 38-51.
[55] S. Vepřek, S. Reiprich, L. Shizhi, Applied physics letters, 66 (1995) 2640-2642.
[56] P.H. Mayrhofer, C. Mitterer, L. Hultman, H. Clemens, Progress in Materials Science, 51 (2006) 1032-1114.
[57] Y. Choi, S. Suresh, Acta materialia, 50 (2002) 1881-1893.
[58] E. Arzt, G. Dehm, P. Gumbsch, O. Kraft, D. Weiss, Progress in Materials science, 46 (2001) 283-307.
[59] L. Lu, Y. Shen, X. Chen, L. Qian, K. Lu, Science, 304 (2004) 422-426.
[60] L. Lu, X. Chen, X. Huang, K. Lu, Science, 323 (2009) 607-610.
[61] A. Sergueeva, C. Song, R. Valiev, A. Mukherjee, Materials Science and Engineering: A, 339 (2003) 159-165.
[62] R. Pippan, F. Wetscher, M. Hafok, A. Vorhauer, I. Sabirov, Advanced Engineering Materials, 8 (2006) 1046-1056.
[63] K. Hemker, W. Sharpe Jr, Annu. Rev. Mater. Res., 37 (2007) 93-126.
[64] C. Motz, T. Schöberl, R. Pippan, Acta Materialia, 53 (2005) 4269-4279.
[65] G. Dehm, Progress in Materials Science, 54 (2009) 664-688.
[66] H. Bei, S. Shim, E.P. George, M.K. Miller, E. Herbert, G.M. Pharr, Scripta Materialia, 57 (2007) 397-400.
[67] C. Volkert, E. Lilleodden, D. Kramer, J. Weissmuller, Applied Physics Letters, 89 (2006) 061920-061920-061923.
[68] J. Biener, A.M. Hodge, J.R. Hayes, C.A. Volkert, L.A. Zepeda-Ruiz, A.V. Hamza, F.F. Abraham, Nano letters, 6 (2006) 2379-2382.
[69] M.D. Uchic, P.A. Shade, D.M. Dimiduk, Annu Rev Mater Res, 39 (2009) 361-386.
[70] O. Kraft, P.A. Gruber, R. Mönig, D. Weygand, Annu Rev Mater Res, 40 (2010) 293-317.
[71] J.R. Greer, W.D. Nix, Phys Rev B, 73 (2006) 245410.
[72] N. Fleck, G. Muller, M. Ashby, J. Hutchinson, Acta Metall Mater, 42 (1994) 475-487.
[73] J. Stölken, A. Evans, Acta Materialia, 46 (1998) 5109-5115.
[74] N. Fleck, J. Hutchinson, Journal of the Mechanics and Physics of Solids, 49 (2001) 2245-2271.
[75] B. Weiss, V. Gröger, G. Khatibi, A. Kotas, P. Zimprich, R. Stickler, B. Zagar, Sensors and Actuators A: Physical, 99 (2002) 172-182.
[76] W.D. Nix, Metallurgical transactions A, 20 (1989) 2217-2245.
[77] M. Atkinson, Journal of materials research, 10 (1995) 2908-2915.
[78] Q. Ma, D.R. Clarke, Journal of Materials Research, 10 (1995) 853-863.
[79] K. McElhaney, J. Vlassak, W. Nix, Journal of Materials Research, 13 (1998) 1300-1306.
[80] M. Haque, M. A Saif, Scripta Materialia, 47 (2002) 863-867.
[81] J.Y. Kim, D.C. Jong, J.R. Greer, Acta Materialia, 58 (2010) 2355-2363.
[82] J.Y. Kim, J.R. Greer, Acta Materialia, 57 (2009) 5245-5253.
[83] J.Y. Kim, D. Jang, J.R. Greer, International Journal of Plasticity, 28 (2012) 46-52.
[84] L. Huang, Q.J. Li, Z.-W. Shan, J. Li, J. Sun, E. Ma, Nature communications, 2 (2011) 547.
[85] A. Schneider, D. Kaufmann, B. Clark, C. Frick, P. Gruber, R. Mönig, O. Kraft, E. Arzt, Physical review letters, 103 (2009) 105501.
[86] C.M. Byer, B. Li, B. Cao, K. Ramesh, Scripta Materialia, 62 (2010) 536-539.
[87] E. Lilleodden, Scripta Materialia, 62 (2010) 532-535.
[88] W.D. Callister, D.G. Rethwisch, Fundamentals of materials science and engineering: an integrated approach, John Wiley & Sons, 2012.
[89] R. Hooke, Lectures de potentia restitutiva, or of spring explaining the power of springing bodies, John Martyn, 1931.
[90] J. Huang, Y. Wu, H. Ye, Acta materialia, 44 (1996) 1211-1221.
[91] T. Blewitt, R. Coltman, J. Redman, J Appl Phys, 28 (1957) 651-660.
[92] J. Venables, Philosophical magazine, 6 (1961) 379-396.
[93] C. Liauo, J. C. Huang, 科儀新知, 19 (1998) 43-51.
[94] Link Opal Operater’s Guide, Oxford Instruments plc, Buckingghamshire, UK, 1997.
[95] V. Randle, Oxford Guide Book Series, 1996, pp. 3.
[96] V. Randle, Microtexture Determination and Its Applications, Institute of Materials, London, 1992.
[97] http://www.ebsd.com/popup/polefigure.htm.
[98] D. Hardwick, Thin Solid Films, 154 (1987) 109-124.
[99] J.R. Davis, Tensile testing, ASM international, 2004.
[100] M.D. Uchic, D.M. Dimiduk, Materials Science and Engineering: A, 400 (2005) 268-278.
[101] K. Ng, A. Ngan, Acta Materialia, 56 (2008) 1712-1720.
[102] D. Dimiduk, M. Uchic, T. Parthasarathy, Acta Materialia, 53 (2005) 4065-4077.
[103] A. Budiman, S. Han, J. Greer, N. Tamura, J. Patel, W. Nix, Acta Materialia, 56 (2008) 602-608.
[104] D. Kiener, C. Motz, T. Schöberl, M. Jenko, G. Dehm, Advanced Engineering Materials, 8 (2006) 1119-1125.
[105] A. Kunz, S. Pathak, J.R. Greer, Acta Materialia, 59 (2011) 4416-4424.
[106] Z. Wang, Q. Li, Z. Shan, J. Li, J. Sun, E. Ma, Applied Physics Letters, 100 (2012) 071906.
[107] H. Shimamura, T. Nakamura, Polymer Degradation and Stability, 94 (2009) 1389-1396.
[108] J. Pethicai, R. Hutchings, W. Oliver, Philosophical Magazine A, 48 (1983) 593-606.
[109] C.A. Schuh, Materials Today, 9 (2006) 32-40.
[110] J. Loubet, J. Georges, O. Marchesini, G. Meille, Journal of tribology, 106 (1984) 43-48.
[111] W. Oliver, C. McHargue, S. Zinkle, Thin Solid Films, 153 (1987) 185-196.
[112] T.H. Sung, 國立中山大學材料與光電科學學系硏究所, Taiwan, 2012.
[113]http://www.ebsd.com/sample-preparation/sample-preparation-for-ebsd/electrolyte-polishing-and-etching.
[114] M.D. Uchic, D.M. Dimiduk, R. Wheeler, P.A. Shade, H.L. Fraser, Scripta materialia, 54 (2006) 759-764.
[115] R. Langford, A. Petford-Long, J Vac Sci Technol A, 19 (2001) 2186-2193.
[116] J. Ye, R. Mishra, A. Minor, Scripta Materialia, 59 (2008) 951-954.
[117] Z. Zhang, H. Zhang, X. Pan, J. Das, J. Eckert, Philosophical Magazine Letters, 85 (2005) 513-521.
[118] B.W. Schmid E, Kristallplastizität: Mit Besonderer Berücksichtigung der Metalle, Berlin, 1936.
[119] J.J. Gilman, Appl Micromech Flow Solids, (1953) 185-190.
[120] M. Tagami, K. Kashihara, T. Okada, F. Inoko, Japan Institute of Metals, Journal, 64 (2000) 535-542.
[121] U. Kocks, Acta Metallurgica, 8 (1960) 345-352.
[122] A.P. Day, HKL Technology A/S, Hobro, Denmark, 2001.
[123] https://www.mts.com/ucm/groups/public/documents/library/dev_003371.pdf.
[124] http://khvic.nsysu.edu.tw/khvic/JL/93_fib.htm.
[125] http://www.msm.cam.ac.uk/mechtest/docs/XP User's Manual.pdf.
[126] A.S. Khan, S. Huang, Continuum theory of plasticity, John Wiley & Sons, 1995.