使用來自Cabot公司的工業用奈米級粉末熱壓燒結試片，試片在對於結晶相及包含疊差(stacking fault)和差排(dislocation)的微結構方面，藉由X光的繞射、掃描式及穿透式的電子顯微鏡做一系列的分析。
這個研究包含三個主要努力目標：(a)疊差(stacking fault)的分析，(b)六方相到正方相的轉換矩陣，和(c)差排分析。然而，這本論文描述鈦酸鋇相轉換的部分是利用數學上的公式來表示，熱壓燒結所導致的塑性變形可藉由微結構的分析來表示。利用微結構分析的根據去證實六方相鈦酸鋇高溫塑性變形的模型。
由X光的繞射和穿透式的電子顯微鏡得知，熱壓燒結試片包含主要的六方相鈦酸鋇(6H-多類型(polytype))及一部分的正方相鈦酸鋇。熱壓燒結試片中發現到處都有延伸的平面疊差(Extended planar stacking faults, EPSF’s)，且具有合適的疊差向量RF(I) = (1/2)c + p(I)和RF(II) = (n/6)c + p’(II)，且p(I) = 1/3

Hot-pressed BaTiO3 ceramics are prepared from commercial nano-size powder supplied by Cabot. Samples have been thoroughly analysed for the crystalline phases, microstructure, including stacking faults and dislocations, by X-ray diffractometry, scanning electron microscopy, and transmission electron microscopy.
This research consists of three major endeavours: (a) the analysis of stacking faults, (b) the hexagonal

Abstract….………………………………………………………………………. iii

Content………………………….......…...……………………………………… vii

List of Tables……………………....……………………………………………. xv

List of Figures……………………………….………………………………….. xix

Chapter 1 Introduction........................................................................................ 1

1.1. Objectives of research........................................................................... 6

Chapter 2 Review of relevant literature............................................................ 8

2.1. The structure of perovskites…………………....…………………….. 8
2.2. Crystal structure of BaTiO3……………………....…………………... 11
2.2.1. Phase transformations in BaTiO3…............................................ 15
2.3. Structure of hexagonal-BaTiO3………………....……………………. 19
2.4. Equilibrium phase diagram of the BaO-TiO2 system…....………….... 30
2.4.1. Polytitanate phases...................................................................... 31
2.5. Twining in BaTiO3…………………...................…………………….. 35
2.6. Colour………………………………………......…………………….. 47
2.7. Diffraction from small volumes…………………...........................…. 48
2.7.1. Diffraction from wedge-shaped specimen.................................. 49
2.7.2. Diffraction from planar defects................................................... 49
2.7.3. Diffraction from wedge-shaped specimen and planar defects.... 50
2.8. Planar defects……………………………………................................ 53
2.8.1. α-boundaries................................................................................ 53
2.8.1.1. α-boundaries with = ±2π/3............................................... 54
2.8.2. Determination of type of α-boundaries....................................... 55
2.8.3. π-boundaries: antiphase domain boundaries............................... 56
2.8.4. δ-boundaries................................................................................ 60
2.9. Polytypes of hexagonal-BaTiO3............................................................ 63

Chapter 3 Experimental Procedures.................................................................. 67

3.1. Initial powders…………………………………..........................…… 67
3.2. Preparation of samples ………………………………….....…. 70
3.2.1. Hot-pressing equipment.............................................................. 70
3.2.2. Hot-pressing procedures............................................................. 72
3.3. Characterisation of sintered samples………...............................……. 73
3.3.1. X-ray diffractometry................................................................... 73
3.3.2. Scanning electron microscopy.................................................... 74
3.3.3. Transmission electron microscopy.............................................. 75
3.3.3.1. Thin foil preparation........................................................ 77
3.3.3.2. Bright-field and dark-field image techniques.................. 78
3.3.3.3. Two-beam dynamical diffraction..................................... 79
3.3.3.4. Howie-Whelan equations including a lattice translation 82
3.3.3.5. Effective extinction distance and effective excitation error..............................................................................................
83
3.3.3.6. Image characteristics for a perfect lattice........................ 84
3.3.3.7. Defect lattice contrast...................................................... 87
3.3.3.8. Weak-beam dark-field imaging........................................ 89
3.4. Planar lattice faults............................................................................... 92
3.4.1. Amplitude contrast imaging........................................................ 92
3.4.2. Kinematical theory of stacking-fault contrast............................. 92
3.4.3. Dynamical theory of stacking-fault contrast............................... 94
3.4.4. Analysis of stacking fault............................................................ 95
3.5. Analysis of dislocation substructures.................................................... 98
3.5.1. Determine of the Burgers vector................................................. 100

Chapter 4 Experimental results.......................................................................... 102

4.1. Macroscopic identification of crystalline phases................................... 102
4.1.1. Initial powder............................................................................... 102
4.1.2. Crystalline phases........................................................................ 104
4.1.3. Morphological microstructure of hot-pressed samples................ 112
4.1.4. Microstructure analysis of t-BaTiO3............................................ 114
4.1.5.. Microstructure of partially grown spherulitic h-BaTiO3 grains.. 118
4.1.6. Microstructure of fully grown spherulitic h-BaTiO3 grains........ 119
4.1.7. Twinning in t-BaTiO3 grains........................................................ 127

4.2. α-type staking faults containing no dislocations.................................... 134
4.2.1. Crystalline phases........................................................................ 134
4.2.2. General microstructure................................................................ 134
4.2.2.1. Fringe patterns.................................................................. 134
4.2.2.2. Invisibility criterian........................................................... 141
4.2.3. High-resolution images................................................................ 144

4.3. α-type staking faults with dislocations embedded……................…... 148
4.3.1. General observations - fringe patterns.......................................... 148
4.3.2. Determination of fault vectors for faults F1-F6............................ 156
4.3.2.1. Faults F1, F2, F3, and F4.................................................... 156
4.3.2.2. Fault F1’, F5 and F6........................................................... 159
4.3.3. Determination of dislocation types associated with faults........... 167

4.4. Dissociation of dislocations................................................................... 172
4.4.1. Fringes patterns............................................................................ 172
4.4.2. Burgers vectors analysis of dissociated dislocations.................... 176
4.4.3. True directions and character of dislocations............................... 180
4.4.4. Stacking faults bounded by the Shockley partial dislocations..... 185

4.5. Dissociation of dislocation lying in fault planes - I................................ 188
4.5.1. General observations.................................................................... 188
4.5.2. Dislocations and their analysis..................................................... 189
4.5.2.1. Dislocation Burgers vectors.............................................. 199
4.5.3. Dissociation into partials.............................................................. 206
4.5.4. Fault fringe pattern....................................................................... 208

4.6. Dissociation of dislocations lying in fault planes - II............................. 210
4.6.1. Analysis of stacking faults and dislocations................................. 210
4.6.2. High-resolution imaging.............................................................. 215
4.6.3. Stacking fault vectors.................................................................. 219

4.7. Dissociation of dislocations lying in fault planes - III........................... 223
4.7.1. General observations.................................................................... 223
4.7.2. Fault vectors................................................................................. 227
4.7.3. Dislocations and their analysis..................................................... 228
4.7.4. Dissociation into Shockley partials.............................................. 232
4.7.5. High-resolution atomic images.................................................... 232
4.7.5.1. Fault FA1............................................................................ 232
4.7.5.2. Fault FA2............................................................................ 234
4.7.5.3. Fault FA3............................................................................ 236
4.7.5.4. Fault FA4............................................................................ 236
4.7.5.5. Fault FA5............................................................................ 237
4.7.6. Summary...................................................................................... 243

4.8. The coexistence of tetragonal and hexagonal-BaTiO3......................... 244
4.8.1. Hexagonal-BaTiO3 particle in tetragonal-BaTiO3 matrix............ 244
4.8.1.1. Foil tilting along two standard triangles of the stereographic projection of t-BaTiO3.............................................
248
4.8.1.2. Zone axis patterns of h-BaTiO3 along the corresponding standard triangles............................................................................
248
4.8.1.3. Superlattice reflections..................................................... 252
4.8.1.4. Commensurate superlattice reflections............................. 253
4.8.1.5. Incommensurate superlattice reflections........................... 254
4.8.2. Tetragonal-BaTiO3 particle in hexagonal-BaTiO3 matrix........... 260
4.8.2.1. Superlattice reflections...................................................... 266

Chapter 5 Discussion…………………………………………............................ 274

5.1. Twinning in t-BaTiO3............................................................................. 274
5.1.1. Crystallographic orientation relationships................................... 276
5.1.2. Coincident site lattice................................................................... 277
5.1.3. Transformation matrix of twining in tetragonal-BaTiO3.............. 279

5.2. α-type staking faults containing no dislocations..…………………...... 281
5.2.1. Two general types of fault vectors............................................... 281
5.2.2. Eligible fault vectors for extrinsic faults...................................... 284
5.2.2.1. Fault FA............................................................................. 285
5.2.2.2. Fault FB............................................................................. 286
5.2.2.3. Fault FC.............................................................................. 288
5.2.2.4. Fault FD............................................................................. 288
5.2.2.5. Why faults FC and FD having an identical prismatic component in fault vectors could be oppositely inclined in high-resolution images?.................................................................

293
5.2.3. Why only three of the six fault vectors containing <01 0> are valid?......................................................................................................
293
5.2.4. Fault vector RFE = 1/3<1 1>........................................................
299
5.2.5. Metastable retention and formation of

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