在本研究中利用單軸向壓縮試驗、維克氏微硬度試驗、及奈米壓印試驗觀察γ相LiAlO2 (γ-LAO)鋁酸鋰單晶的變形行為。另外在變形微結構觀察則使用了光學顯微鏡(OM)、穿透式電子顯微鏡(TEM)、掃描式電子顯微鏡(SEM)和背向散射電子繞射(EBSD)等儀器。
在高温單軸壓縮試驗下，發現鋁酸鋰單晶(LAO)在773-1173K温度下沿著[100]方向壓縮時，會經由雙晶化來變形。利用表面的變形痕跡和EBSD的分析得到雙晶系統為: K1: (1-12), K2: (-112), η1: [-111], η2: [1-11], s = 0.305，且在雙晶化的過程中，由TEM觀察並未發現差排。雙晶發生所需的應力隨著温度的上升而下降，然而低於673K應力高達550MPa時，在試片完全破裂之前除部份破裂現象無發現雙晶化現象。另一方面，沿著[001]方向壓縮時，在應力值達660MPa下除了部份破裂之外亦未觀察到雙晶。
由室溫奈米壓印試驗得到鋁酸鋰單晶(100)和(001)面的硬度值分別為10 GPa和12.5 GPa，而楊氏係數為145 GPa 和168 GPa。經過壓印的(100)面，使用FIB獲得印痕下的(010)和(001)橫截面，利用TEM繞射鑑定得知在變形區γ-LAO相變化為β-LAO。γ-LAO和β-LAO的晶向關係為aγ//cβ, bγ//aβ, and cγ//bβ 接近為平行關係。經由繞射資訊得知，γ-LAO和β-LAO的晶癖面為(10-1)γ//(01-1)β和(101)γ//(011)β平面。另一方面，經由TEM觀察發現在(001)面壓印下的(010)橫截面具有大量的差排。
室溫維克氏微硬度試驗下，在鋁酸鋰單晶(100)和(001)面上利用壓印方向的轉換得到不同的硬度值。在(001)平面上，壓印的對角線沿著[100]和[010]時，硬度值為10.5GPa，而對角線沿著[110]和[1-10]時，硬度值降為9GPa。而在(100)平面上，壓印的對角線沿著[010]和[001]時，硬度值為8.5GPa，而對角線沿著[011]和[0-11]時，硬度值降為6.5GPa。在OM的觀察下發現徑向破裂(radial crack)和橫向破裂(lateral crack)，且在不同壓印平面和方向時破裂的發展形式則各不相同。利用破裂的痕跡，推測在(100)平面上經沿著對角線[011]和[0-11]壓印時，得到破裂面為(001)平面，而沿著對角線[010] and [001]時，破裂面為(001)、(011)和(01 -1)平面。然而在(001)平面上，沿著對角線[110]和[-110]壓印時，得到破裂面為(110)、(-110)、(010)和(100)平面，而沿著對角線[100]和[010]時，破裂面為(010)和(100)平面。

The deformation behavior of γ phase LiAlO2 (γ-LAO) single crystal under various loading conditions has been investigated in the present study. The loading conditions used in this study included uniaxial compression, Vickers microhardness, and nanoindentation. In addition, the deformation microstructure was characterized by using various techniques, including optical microscopy (OM), transmission electron microscopy (TEM), scanning electron microscopy (SEM), and electron backscattered diffraction (EBSD).
In the high temperature compression test, it was found that the LiAlO2 single crystal deformed via a twinning process while compressed along [100] direction at temperatures from 773 K to 1173 K. The twinning elements for the observed deformation twin are summarized as K1: (1-12), K2: (-112), η1: [-111], η2: [1-11], and s = 0.305. No dislocation slips were observed associated with the twinning. The necessary stress for the initiation of twinning increased with decreasing temperature. At 673K, twinning was not found even after loading to a stress of 550 MPa. When the crystal was compressed along [001] direction, no twin but cracks was observed after loaded to 660 MPa.
By using the nanoindentation test with Berkovich indenter at room temperature, the hardness of the (100) surface is determined to be ~10 GPa, and that of (001) surface is ~12.5 GPa. The values of elastic modulus are determined as 145 GPa and 168 GPa for (100) and (001) surface, respectively. The deformed microstructure induced by the nanoindentation was characterized by examining the cross-section from the volume underneath the indent with transmission electron microscope. The phase transformation from γ-LAO to β-LAO was found in the deformed volume after indentation on the (100) surface. The crystallographic orientation relationship between γ-LAO and β-LAO exhibits a nearly parallel relation of aγ//cβ, bγ//aβ, and cγ//bβ. Two sets of habit plane between these two phases are found as (10-1)γ // (01-1)β and (101)γ // (011)β. After indentation on the (001) surface, a deformed structure consisting of dislocation lines was observed.
The anisotropy of hardness and cracking behavior of γ-LAO were studied by using Vickers indentation test at room temperature. The hardness of the (001) plane is about 10.5 GPa, when the diagonal directions of the indent are along [100] and [010], however, it decreases to about 9 GPa when the diagonal directions are along [110] and [1-10]. The hardness of the (100) plane is about 8.5 GPa when the diagonal directions of the indent are along [010] and [001], but it decreases to 6.5 GPa as the diagonal directions change to [011] and [0-11]. Both radial cracks and lateral cracks were found, which depended on the indenting plane and the orientation of indent. Based on the observation, the crack planes were determined. For indentation loading on the (100) surface, the crack planes are the (001) plane when the indent diagonal directions are along [011] and [0-11] directions, while (001), (011), and (01-1) planes are the potential cracking planes when the diagonal directions are along the [010] and [001] directions. For indentation loading on the (001) surface with diagonal directions along [110] and [-110], the favorable cracking planes are (110), (-110), (010) and (100), and when the diagonal directions of the indent change to [100] and [010] directions, the potential cracking planes are (010) and (100) planes.

中文摘要....................................................................................................................................iv
Abstract ....................................................................................................................................vi
Contents .................................................................................................................................viii
List of Table ..............................................................................................................................xi
List of Figure captions .............................................................................................................xii
Chapter 1 Introduction .............................................................................................................1
Chapter 2 Literature review .....................................................................................................4
2-1 Introduction of basal material LiAlO2 ................................................................................ 4
2-1-1 Crystal structure of LiAlO2 ............................................................................................. 4
2-1-2 Phase transformation of LiAlO2 ..................................................................................... 5
2-2 Basic properties of LiAlO2 ................................................................................................. 6
2-2-1 Mechanical properties of LiAlO2 .................................................................................... 6
2-2-2 Surface properties ......................................................................................................... 6
2-2-3 Thermal properties ........................................................................................................ 7
2-3 Microstructure of LiAlO2 .................................................................................................. 8
2-3-1 Defect structure revealed from etching pits on the surface of γ-LAO single crystal...... 8
2-3-2 Microstructure revealed by transmission electron microscopy .................................... 9
2-4 Deformation mechanism of crystalline materials ........................................................... 10
2-4-1 Deformation twinning ................................................................................................... 11
2-4-2 Dislocation slip ............................................................................................................ 12
2-4-3 Stress induced phase transformation .......................................................................... 14
2-5 Twinning elements determined by using EBSD .............................................................. 15
2-6 Characteristics of the load-displacement curve generated by nanoindentation………. 18
2-7 Indentation induced cracks in brittle materials ............................................................... 19
2-7-1 Elastic stress fields caused by indentation .................................................................. 19
2-7-2 Cracking sequence during the indentation process .................................................... 21
Chapter 3 Experimental procedures .................................................................. ..................25
3-1 Materials preparation ...................................................................................................... 25
3-2 Uniaxial compression test ............................................................................................... 25
3-3 Vickers microhardness test ............................................................................................. 26
3-4 Nano-indentation test ..................................................................................................... 26
3-5 Microstructure analysis .................................................................................................. 27
3-5-1 Optical microscopy (OM) ............................................................................................. 27
3-5-2 Scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) .... 27
3-5-3 Transmission electron microscopy (TEM) .................................................................... 28
3-5-4 3D profilometer ........................................................................................................... 28
Chapter 4 Deformation of γ-LiAlO2 under uniaxial compression ......................................... 29
4-1 Mechanical properties of γ-LiAlO2 ................................................................................. 29
4-2 Trace analysis of deformation markings .......................................................................... 29
4-3 The twinning system in γ-LiAlO2 compressed along [100] direction ............................... 30
4-4 Effect of temperature and applied stress on deformation twinning ................................. 34
4-5 Cracks induced by uniaxial compression along [100] directi........................................... 35
4-6 Summary ........................................................................................................................ 36
Chapter 5 Indentation-induced deformation structures in LiAlO2 .......................................... 37
5-1 Mechanical properties of γ-LAO ...................................................................................... 37
5-1-1 Indentation on (100) and (001) surfaces to various loads ............................................ 37
5-2 Deformed microstructure underneath the indent on (100) surface .................................. 38
5-2-1 Microstructure observed in [010] zone axis .................................................................. 38
5-2-2 Crystallographic orientation relationship between γ-LAO and β-LAO........................... 42
5-2-3 Analysis of thin deformation bands ............................................................................... 44
5-2-4 Microstructure observed in [001] zone axis ................................................................... 46
5-2-5 Deformation mechanism related to the indentation on (100) surface……..................... 47
5-3 Deformed microstructure underneath the indent on (001) surface ................................... 49
5-3-1 Microstructure observed in [010] zone axis ................................................................... 49
5-3-2 Deformation mechanism related to the indentation on (001) surface.....................…… 52
5-4 Summary of the deformation mechanisms in γ-LAO single crystal under compressive stress ..................................................................................................................................... 53
Chapter 6 Orientation dependence of cracking in LiAlO2 induced by Vickers indentation ............................................................................................................................. 56
6-1 Observation of cracking induced by Vickers indentation ................................................. 56
6-1-1 Mechanical properties of γ-LAO determined by using Vickers indentation.................... 56
6-1-2 Fracture features induced by Vickers indentation ........................................................ 57
6-2 Comparison with crack development model .................................................................... 60
6-3 Summary ......................................................................................................................... 64
Chapter 7 Conclusion ............................................................................................................ 65
7-1 Uniaxial compression ...................................................................................................... 65
7-2 Nanoindentation ............................................................................................................. 66
7-3 Vickers indentation ......................................................................................................... 66
Table .................................................................................................................................... 68
Figure .................................................................................................................................. 76
Reference ............................................................................................................................ 134

1. Bagnall, D.M., et al., Optically pumped lasing of ZnO at room temperature. Applied Physics Letters, 1997. 70(17): p. 2230.
2. Chou, M.M.C., et al., Crystal Growth of Nonpolar m-Plane ZnO on a Lattice-Matched (100) γ-LiAlO2 Substrate. CRYSTAL GROWTH &DESIGN, 2009. 9: p. 2073.
3. Hino, T., et al., Characterization of threading dislocations in GaN epitaxial layers. Applied Physics Letters, 2000. 76(23): p. 3421.
4. Rosner, S.J., et al., Correlation of cathodoluminescence inhomogeneity with microstructural defects in epitaxial GaN grown by metalorganic chemical-vapor deposition. Applied Physics Letters, 1997. 70(4): p. 420.
5. Tsukazaki, A., et al., Repeated temperature modulation epitaxy for p-type doping and light-emitting diode based on ZnO. Nature Materials, 2004. 4(1): p. 42-46.
6. Waltereit, P., et al., Nitride semiconductors free of electrostatic fields for efficient white light-emitting diodes. Nature, 2000. 406(24): p. 865-868.
7. Chou, M.M.C., H.C. Huang, and Y.F. Chang, Defects and acoustic properties of LiAlO2. Applied Physics Letters, 2006. 88(16): p. 161906.
8. Kim, J.-E., et al., Mechanical properties of the lithium aluminate matrix for MCFC reinforced with metal oxide materials. Current Applied Physics, 2010. 10(2): p. S73-S76.
9. Lee, J.-J., et al., Characteristics of aluminum-reinforced γ-LiAlO2 matrices for molten carbonate fuel cells. Journal of Power Sources, 2008. 179(2): p. 504-510.
10. Murata, I., et al., Benchmark experiment on LiAlO2. Fusion Engineering and Design, 2000. 51-52: p. 821-827.
11. Raux, N., C. Johnson, and K. Noda, Properties and performance of tritium breeding ceramics. Journal of Nuclear Materials, 1992. 191-194: p. 15-22.
12. Wen, Z., et al., Research on the preparation, electrical and mechanical properties of γ-LiAlO2 ceramics. Journal of Nuclear Materials, 2004. 329-333: p. 1283-1286.
13. Oliver, W.C. and G.M. Pharr, An Improved Technique for Determining Hardness and Elastic-Modulus Using Load and Displacement Sensing Indentation Experiments. Journal of Materials Research, 1992. 7(6): p. 1564-1583.
14. Oliver, W.C. and G.M. Pharr, Measurement of hardness and elastic modulus by instrumented indentation Advances in understanding and refinements to methodology. Journal of Materials Research, 2004. 19(1): p. 3-20.
15. Kroon, A.P.d., G.W. Schafer, and F. Aldinger, Crystallography of potassium aluminate K2O。Al2O3. Journal of Alloys and Compounds, 2001. 314: p. 147-153.
16. Marezio, M., The Crystal Structure and Anomalous Dispersion of γ-LiAlO2. Acta Crystal, 1965. 19: p. 396-400.
17. Jhonskowskit, R., Reactivity and Acidity of Li in LiAlO2 Phases. Inorganic Chemistry, 1993. 32(1): p. 1-9.
18. Thery, et al., Bull. Soc. Chim. Fr, 1961: p. 973.
19. DORHOFER, K., A reindexing of the X-ray powder diffraction pattern of β-LiAlO2. Journal of Application crystal, 1979. 12: p. 240-241.
20. Marezio, M. and J.P. Remeika, J. Chem. Phys, 1966. 44: p. 3143-3144.
21. Marezio, M. and J.P. Remeika, J. Chem. Phys, 1966. 44: p. 3348-3353.
22. Chang, C.H. and J.L. Margrave, High-pressure-high-temperature syntheses. III. Direct syntheses of new high-pressure forms of lithium aluminum oxide and lithium gallium oxide and polymorphism in LiMO2 compounds (M =B,Al,Ga). J. Am. Chem. Soc., 1968. 90: p. 2020-2022.
23. Lehmann, H.A. and H.Z. Hesselbarth, Anorg. Allg. Chem., 1961. 313: p. 117-120.
24. Li, X., et al., A new high-pressure phase of LiAlO2. Journal of Solid State Chemistry, 2004. 177(6): p. 1939-1943.
25. Lei, L., et al., Phase transitions of LiAlO2 at high pressure and high temperature. Journal of Solid State Chemistry, 2008. 181(8): p. 1810-1815.
26. Xu, X., et al., Preparation of γ-LiAlO2 green bodies through the gel-casting process. Ceramics International, 2009. 35(4): p. 1429-1434.
27. Wu, S.Q., Z.F. Hou, and Z.Z. Zhu, First-principles study on the structural, elastic, and electronic properties of γ-LiAlO2. Computational Materials Science, 2009. 46(1): p. 221-224.
28. Sun, Y.J., O. Brandt, and K.H. Ploog, Growth of M-plane GaN films on γ-LiAlO[sub 2](100) with high phase purity. Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, 2003. 21(4): p. 1350.
29. Zou, J., et al., Study on the hydrolytic property and thermal stability of LiAlO2 substrate. Journal of Crystal Growth, 2006. 294(2): p. 339-342.
30. Chou, M.M.C., S.J. Huang, and C.W.C. Hsu, Crystal growth and polishing method of lithium aluminum oxide crystal. Journal of Crystal Growth, 2007. 303(2): p. 585-589.
31. Chou, M.M.C., et al., Defect characterizations of γ-LiAlO2 single crystals. Journal of Crystal Growth, 2006. 291(2): p. 485-490.
32. Xu, K., et al., MOCVD Growth of GaN on LiAlO2 (100) substrates. phys. stat. sol., 1999. 176: p. 589-593.
33. Huang, H., et al., A proper solution to study the etch pits on LiAlO2 single crystal. Journal of Crystal Growth, 2010. 313(1): p. 42-46.
34. Chou, M.M.C., P. Chun Tsao, and H. Chun Huang, Study on Czochralski growth and defects of LiAlO2 single crystals. Journal of Crystal Growth, 2006. 292(2): p. 542-545.
35. Liu, T.-Y., Transmission electron microscopy studies of GaN/γ-LiAlO2 heterostructures. 2004.
36. Vanfleet, R.R., et al., Antiphase ordering and surface phases in lithium aluminate. Journal of Applied Physics, 2008. 104(9): p. 093530.
37. Read-Hill, R.E. and R. Abbaschian, Physical metallurgy principles. PWS-Kent Pub, Boston, 1992.
38. Christian, J.W. and S. Mahajant, Deformation twinning. Progress in Materials Science, 1995. 39: p. 1-157.
39. Chu, F. and D.P. Pope, Deformation twinning in intermetallic compounds-the dilemma of shears vs. shuffles. Materials Science and Engineering, A, 1993. 170: p. 39-47.
40. Hay, R.S. and D.B. Marshall, Deformation twinning in monazite. Acta Materialia, 2003. 51(18): p. 5235-5254.
41. Bilby, B.A. and A.G. Crocker, The Theory of the Crystallography of Deformation Twinning. Series A, Mathematical and Physical Sciences, 1965. 288(1413): p. 240-255.
42. Hosford, W.F., Mechanical Behavior of Materials. 2005.
43. Nabarro, F.R.N., Theory of crystal dislocations. 1967.
44. Gilman, J.J., PLASTIC ANISOTROPY OF LiF AND OTHER ROCKSALT-TYPE CRYSTALS. Acta Metallurgica, 1959. 7: p. 608-613.
45. Mitchell, T.E., Dislocations and Mechanical Properties of MgO–Al2O3 Spinel 137
Single Crystals. Journal of the American Ceramic Society, 1999. 82: p. 3305-3316.
46. Mishra, M. and I. Szlufarska, Possibility of high-pressure transformation during nanoindentation of SiC. Acta Materialia, 2009. 57(20): p. 6156-6165.
47. Shimojo, F., et al., Molecular Dynamics Simulation of Structural Transformation in Silicon Carbide under Pressure. PHYSICAL REVIEW LETTERS, 2000. 84(15): p. 3338-3341.
48. Jang, J.-i., et al., Indentation-induced phase transformations in silicon: influences of load, rate and indenter angle on the transformation behavior. Acta Materialia, 2005. 53(6): p. 1759-1770.
49. LIU, Q., A simple method for determining orientation and misorientation of the cubic crystal specimen. Journal of Applied Crystallography, 1994. 27(0021-8898): p. 755-761.
50. MAHAJAN, S., Twinning Matrices and Their Application in Analyzing Electron Diffraction Patterns from Twinned B.C.C. and F.C.C. Lattices. Metallography, 1971. 4: p. 43-49.
51. Randle, V. and O. Engler, Introduction to texture analysis:macrotexture, microtexture and orientation mapping. 2000.
52. 楊平, 電子背散射衍射技術及其應用. 2007.
53. L., J.K., Contact Mechanics. Cambridge, UK: Cambridge University Press, 1985.
54. Lund, A.C., A.M. Hodge, and C.A. Schuh, Incipient plasticity during nanoindentation at elevated temperatures. Applied Physics Letters, 2004. 85(8): p. 1362.
55. Schuh, C.A. and T.G. Nieh, A nanoindentation study of serrated flow in bulk metallic glasses. Acta Materialia, 2003. 51(1): p. 87-99.
56. Cook, R.F. and G.M. Pharr, Direct Observation and Analysis of Indentation Cracking in Glasses and Ceramics. Journal of the American Ceramic Society, 1990. 73(3): p. 787-817.
57. Yoffe, E.H., Elastic stress fields caused by indenting brittle materials. Philosophical Magazine A, 1982. 46(4): p. 617-628.
58. Chiang, S.S., The response of solids to elastic/plastic indentation. I. Stresses and residual stresses. Journal of Applied Physics, 1982. 53(1): p. 298.
59. Chiang, S.S., The response of solids to elastic/plastic indentation. II. Fracture initiation. Journal of Applied Physics, 1982. 53(1): p. 312.
60. Bridgman, P.W. and I. Šimon, Effects of Very High Pressures on Glass. Journal of Applied Physics, 1953. 24(4): p. 405.
61. NIX, W.D. and H. GAO, Indentation size effects in crystalline materials: A law for strain gradient plasticity. Journal of the Mechanics and Physics of Solids, 1998. 46(3): p. 411-425.
62. Stevenson, M.E., M. Kaji, and R.C. Bradt, Microhardnessanisotropy and the indentationsizeeffect on the basalplane of singlecrystalhematite. Journal of the European Ceramic Society, 2002. 22: p. 1137-1148.
63. Tsai, F.-Y., et al., Deformation twinning in LiAlO2 at elevated temperatures. Materials Science and Engineering: A, 2012. 551: p. 218-221.
64. 陳彥名, 以分子束磊晶法於鋰酸鋁基板成長非極性氧化鋅磊晶之研究. Thesis, 2012.
65. Keryvin, V., et al., On the deformation morphology of bulk metallic glasses underneath a Vickers indentation. Journal of Alloys and Compounds, 2010. 504: p. S41-S44.