本研究利用掃瞄式以及穿透式電子顯微鏡，分析 BaTiO3、BaCeO3、CaTiO3 三種鈣鈦礦結構的陶瓷微觀結構；主要工作集中於它們因為經歷相變化所衍生的雙晶域、anti-phase boundary 晶域，與 inversion boundary 晶域。

相變化衍生雙晶域、或其他晶域，統稱為相變化衍生微觀組織。Tetragonal BaTiO3 中的強電性晶域可以用化學腐蝕差異率，在掃瞄式電子顯微鏡下觀察、鑑別。鈣鈦礦的結晶結構隸屬於 orthorhombic 結晶系統的第 62 號空間群，目前的研究沿襲材料科學家通常使用的 Pbnm ，以免與其他如：地球科學、礦物學領域裡所使用的 Pnma與 Pmcn，在結晶面與方向的標示易生混淆。

無論是單晶CaTiO3 礦物或多晶 BaTiO3、BaCeO3 陶瓷，包括相變化衍生和高溫變形產生，其間的所觀察得之差排與缺陷，分別之柏格向量 (b) 與缺陷位移向量 (R)，均使用傳統穿透式電子顯微鏡技巧的對比分析方法，鑑別並決定其大小、方向。雙晶、anti-phase boundary 晶域界面的原子影像，並且使用高解析度技巧觀察，其所獲得之影像復以 FFT 電腦軟體，增進其反差，以利影像解析。結晶結構之是否具有中心對稱性，並以 Friedel 的定律在非中心對稱的結晶結構中的不適用性來決定、確認。雙晶的型式也能用雙晶晶界面所生成的特殊條紋對比，無論是α、δ或 π 等型式來鑑別；同樣的，晶域界位移向量也用對比分析決定其大小、方向；但是 δ　型式 的晶域界位移向量太小，故目前仍無法確定。至於雙晶是屬於反射式或旋轉式，可以沿用 tilting 實驗對於擇區電子繞射圖所產生的變化，將其判定、確認。
在假設相變化為連續、非擴散式、第二階的特質條件，以符合 Landau 理論的限定的要求之下，相變化衍生微結構的雙晶晶面、anti‐phase boundary 晶面與inversion boundary 晶面，及其相關的缺陷位移向量，均能符合在高對稱結晶相與低對稱結晶相之間，在降溫、相變化發生，對稱性隨之降低時，所伴隨而至的點群對稱元素損失，或減少。雖然這個假設與由此推導而得之相變化衍生微結構，只有在高對稱與低對稱的兩個結晶相之間，存在有 group‐subgroup 關係，因而兩者的結構連續性得以維持的條件之下，方能適用；而目前的研究裡只有 c‐→ t‐BaTiO3 存有此類關係，其他兩者： r‐ → o‐BaCeO3 與 t‐→ o‐CaTiO3，此關係均不成立。根據 Christy 的模式與 Guymont 的 non‐disruption 的假設條件，尋求一個共同空間群的中間介穩相，無論是最低或最高點群對稱的結晶相。以 r‐ →o‐BaCeO3 為例的話，分別是 cubic Pm 3m 與 monoclinic C2/c；以經過中間介穩相的多重相變化路徑，雖然高對稱與低對稱的兩個結晶相不存在有 groupsubgroup關係，依舊可以符合Landau 理論的限定，並能合理的依照結構連續的方式來預測、來推演，解釋相變化衍生雙晶的形式 (晶域的結晶面)、種類 (反射或旋轉式)。
在無壓力燒結的t‐BaTiO3 中，包括 90o 與 180o 的晶域，均為反射式雙晶；以對比分析所決定之晶域界位移向量為：ε<110]，ε 是晶格向量的非分數比。強電性晶域的晶界結晶面分別是：前者為 {110)，後者為 {100) 和 {220)。晶域的 c‐軸極化方向，無論是90o 或 180o，除了根據化學腐蝕差異率決定以外，並且用集束電子繞射技巧確認。
當燒結的熱力學驅動力 (Δp) 因為殘餘孔隙的存在而得以同時加乘、放大時，高溫塑性變形便由於受力於此驅動力 (Δp) 而產生，微結構所觀察到的、遍佈於試樣的差排及Frank‐Read 差排源，明顯的可茲佐證。BaTiO3 的滑移系統，因所施加壓力超過其臨界剪力值而啟動，差排滑移、運動，引起塑性變形、降服的結果。這些變形直接導致粉體生胚的整體收縮，陶瓷體的燒結、緻密化，然而塑性變形是否為陶瓷體緻密化時，其動力學的主要提供機制，還是需要燒結動力學的研究來確認。
差排在移動過程中分解為扇貝形狀的部份差排，分析差排柏格向量的結果，顯示差排分解反應為下列三種：
[010] + [001]→ [011]
[001] + [10 1 ] → [100]
[001] + [110]→ [111]
在o‐BaCeO3 中，相變化雙晶和 anti‐phase boundary 晶域同時都觀察得到；前者的雙晶域晶面在 {110) 和 {112)，而後者位移向量為：R = 1/2<111>。位移向量並且以高解析原子影像確認；但是，晶域的位移向量分別為：R = ε<110] 和ε<021]，卻無法如此來確認，因為其位移向量太小，而且是晶格向量非分數比。這些位移向量和部份的差排柏格向量，並且以高角度的集束電子繞射方法來確認。
利用高壓多重砧，在高壓之下熱壓燒結的o‐CaTiO3 陶瓷，很容易的觀察到雙晶域和差排。不過，在高壓引發塑性變形、並且在o‐相相區內熱壓之下，這些雙晶域均為變形雙晶。雖然 {112) 和 {110) 都同時出現，因為其晶域的位移向量均為：R = ε<110]，與相變化雙晶 {112) 裡的 R = ε〈021] 截然不同；所以，{112) 雙晶的位移向量可以視為一種診斷式的特徵，用來判斷o‐CaTiO3 裡的雙晶屬於形變產生或者由於相變化衍生。在高壓多重砧熱壓的試片，其所產生的塑性變形主要來自：滑移與變形雙晶。柏格向量 b = [ 1 10] 的差排與其方向為 u = [001] 可以決定塑性變形係經由滑移系統 [ 1 10]o (110) o 而產生；滑移沿著orthorhombic [110]o方向，等於是 cubic [100]c，也就是：<100>c {001}o，這類的滑移系統也曾經在其他鈣鈦礦結構，例如：t‐BaTiO3 中發現、報導過。
在 CaTiO3 礦物裡所觀察到的 anti‐phase boundary 晶域，其位移向量為：R= 1/2<111>。這個晶域與相變化所衍生的 {112) 和 {110) 都同時出現的事實，並且可以用為推論自然界的 CaTiO3 相變化順序，其可能為： (c) → t (I4/mcm) → o(Pbnm)。當 I4/mcm 在I-中心 (1/2,1/2,1/2) 的晶格點，折損於相變化而結晶結構轉變為 Pbnm 時，以位移向量為：R = 1/2<111> 的anti‐phase boundary 晶域，因而衍生而保存於低對稱性的 orthorhombic 相之中。這個結果可以佐證，且支持前人使用中子與X 光繞射研究，所獲得的結論，是故空間群為 Cmcm 的第二orthorhombic 相相信應為誤判。

Phase-transformation-induced microstructures, including twin domains, anti-phase domains and inversion domains have been analyzed using the scanning and transmission electron microscopy for BaTiO3, BaCeO3 and CaTiO3 of the perovskite structure.

Differential etching rate was taken to identify the ferroelectric domains in tetragonal (t-) BaTiO3. Space group Pbnm (No. 62) usually adopted for the orthorhombic crystals by materials scientists is assumed throughout this research to avoid confusion of the plane and direction indices. Traditional contrast analysis was adopted for determining dislocation Burgers vectors (b) and fault vectors (R) in deformed and phase-transformed perovskites, synthetic ceramics (BaTiO3, BaCeO3 and CaTiO3) as well as natural minerals (CaTiO3), polycrystalline (BaTiO3, BaCeO3 and CaTiO3) as well as single crystal (CaTiO3). Atomic images for the structures of twin boundaries and anti-phase boundaries were taken by high resolution technique and image contrast enhancement was performed using fast Fourier transform. Failure of Friedel’s law is adopted for determining if the crystal belongs to non-centrosymmetric point groups. Whether the twins are δ-, α- or π-type (i.e. anti-phase domain boundaries) is analysed from the contrast of extreme fringe patterns. Tilting experiments were performed on selected area diffraction patterns containing un-split row of reflections to ensure that the twin boundaries are the reflection or rotation type.

Transformation twinning in all perovskites studied here follows the prediction by the relation of point group symmetries between the high- and low-symmetry phases, assuming continuous, diffusionless, second-order transitions that obey the restrictions imposed by the Landau theory of phase transition. Although such predictions of transformation-induced twinning are only permitted when crystallographic group-subgroup relationship exists and structural coherence retains between the high- and low-symmetry phases, experimental observations for r (rhombohedral) → o-BaCeO3 and t → o in CaTiO3 that are not related by group-subgroup, c (cubic) → t (tetragonal) in CaTiO3 and and c (cubic) → t (tetragonal) in BaTiO3 that are related by group-subgroup, are all consistent with the predictions from loss of point group symmetry elements and change of unit cell volume. In order that the Landau theory is conformed, however, an intermediate phase of either the lowest common supergroup (cubic Pm m) or highest common subgroup (monoclinic C2/c), with phase transition experiencing multistage pathways suggested by Christy and assumption of non-disruption conditions proposed by Guymont, was identified to bridge between two structures, such as rhombohedral and orthorhombic that are not group-subgroup related.

Both the 90o and 180o ferroelectric twin domains in t-BaTiO3 are the reflection type and have been identified in pressureless-sintered ceramics. Further, fault vectors (R = ε<110]) for such domain boundaries were determined, boundary planes of {110) for the former, {100) and {220) for the latter deduced accordingly. The polar c-direction between adjacent domains was determined by differential etching rate across domain boundaries, convergent beam electron diffraction was also adopted for identification and confirmation of the c-axis for two types of domains in t-BaTiO3.

Plastic deformation resulting from the thermodynamic driving force for sintering (?p) intensified by a multiplication factor φ) was evidenced microstructurally from analysing dislocations in pressureless-sintered BaTiO3 where a Frank-Read source was observed. Slip systems are activated for the effective stress acting on the slip plane along the slip direction has exceeded the critical value of resolved shear stress (τCRSS) and yielding occurs. It has contributed to densification, i.e. the overall system shrinkage of a green powder compact, although if such contribution is at all significant requires studies of sintering kinetics to ascertain.

Dislocation dissociation into the scallop-shaped half partials according to the following reactions is determined from analysing corresponding Burgers vectors.

[010] + [001] → [011]

[001] + [10 ] → [100]

[001] + [110] → [111]

Both transformation twins lying in {110) and {112) and anti-phase domain boundaries with R = 1/2<111> are detected in o-BaCeO3. For orthorhombic (o-) BaCeO3, fault vectors of the latter R = 1/2<111> determined by contrast analysis was confirmed by high-resolution imaging, but on the contrary, fault vectors the former R = ε<110] and ε<021], respectively, could not be determined from such images. Utilizing the technique of large-angle convergent beam electron diffraction, such fault vectors and dislocation Burgers vectors determined by traditional contrast analysis have been confirmed.

Both twinning and dislocations were observed in hot-pressed CaTiO3 prepared in a multi-anvil apparatus. Such twins are deformation twins since hot-pressing was conducted in the orthorhombic stable phase field at 1000oC under 8 GPa. Since fault vectors R = ε<110] determined for {112) and {110) twins are different from the transformation-induced twins in o-CaTiO3, R = ε<021] determined for the {112) twinning in natural perovskite may serve as a diagnostic feature for the deformation twins. Plastic deformation in hot-pressured sample was contributed by both slip and twinning. Slip occurred via slip systems with dislocations of b = [110] gliding in (110) is therefore {110}o <1 0>o (equivalent to {100}pc <001>pc, where pc for pseudo-cubic) often found in perovskites deformed at high temperatures. Another set of dislocations with b = [001] in screw orientation was also determined.

APB with R = 1/2<111> detected in natural minerals suggests that the phase transition sequence in CaTiO3 is better described by: (c) → t (I4/mcm) → o (Pbnm) and such APB are generated from loss of the lattice point at I-centre (1/2,1/2,1/2) in the absence of a second orthorhombic Cmcm between t-I4/mcm and o-Pbnm reported before from neutron and X-ray powder diffraction studies.

page
List of symbols and abbreviations vii
中文摘要 x
Abstract xiii
List of figures xvi
List of tables xxx
Chapter 1 Introduction 1
Chapter 2 Objectives of study 5
Chapter 3 Classification of Twins 8
3.1 Twins by merohedry and pseudo-merohedry 12
Chapter 4 Extreme fringe contrast 26
4.1 Discrepancy of reflecting g-vectors across twin interfaces 26
4.2 Growth twins in t-BaTiO3 and EBSD 29
4.3 Ferroelectric twins in t-BaTiO3 31
4.4 Inversion domain boundaries 34
4.5 Characteristics of extreme fringe patterns 35
4.6 Anti-phase domains boundaries 41
Chapter 5 Twin types characterized from obliquity, twin axis and SADP 48
5.1 Tilting experiments 48
Chapter 6 Violation of Friedel's law 54
Chapter 7 How and why are domain structures produced? 58
Chapter 8 Structural phase transitions in crystals 64
Chapter 9 Crystal structures and twins in perovskites 71
9.1 Phase transitions in perosvkites and Glazer's tilting systems 73
9.2 Rationale for present research into CaTiO3 84
9.3 Transformation twinning in orthorhombic perovskites - CaTiO3 92
9.3.1 Phase transition sequence 92
9.3.2 Transformation-induced twinning 100
9.4 Transformation twinning in tetragonal perovskites - BaTiO3 106
9.5 Dislocations in sintered tetragonal BaTiO3 112
9.6 Present research for BaTiO3 117
9.7 Twinning in orthorhombic perovskites - BaCeO3 118
9.8 Present research for BaCeO3 126
Chapter 10 Experimental procedures 128
10.1 Initial powders and green compaction 128
10.2 Pressureless-, vacuum-sintering and hot-pressing in diamond anvil cell 130
10.3 Determination of sintered density 133
10.4 Identification of crystalline phases 133
10.5 Samples and thin foils preparation for electron microscopy 133
Chapter 11 Results 138
11.1 Transformation-induced twinning in pressureless-sintered BaTiO3 138
11.1.1 SEM observations 138
11.1.2 TEM analysis 140
11.1.2.1 Ferroelectric 90o domains 142
11.1.2.2 Ferroelectric 180o domains 145
11.1.2.3 Non-centrosymmetric t-BaTiO3 and polar characteristics of 90o and 180o domains 148
11.1.2.4 Convergent-beam electron diffraction and polar direction 152
11.1.2.5 Reflection or rotation twins 153
11.2 {111} Growth twinning in pressreless-sintered BaTiO3 153
11.3 Dislocation substructure in pressureless-sintered BaTiO3 160
11.3.1 General observations 160
11.3.2 Burgers vectors and true line directions 164
11.4 Anti-phase boundaries in pressureless-sintered BaCeO3 174
11.4.1 Crystalline phases by XRD 174
11.4.2 General microstructure and fault fringe patterns 177
11.4.3 Fault vectors determined by conventional contrast analysis 177
11.4.4 Coexistence of transformation twins and anti-phase boundary domains 178
11.4.5 Fault vectors determined by large-angle convergent-beam electron diffraction 183
11.4.6 Fault vectors determined by high-resolution imaging 184
11.4.7 Boundary between two types of transformation twins 184
11.5 Transformation-induced twinning in pressureless-sintered BaCeO3 191
11.5.1 Twin planes, fault vectors and types of twinning - {112) 191
11.5.2 Twin planes, fault vectors and types of twinning - {110) 196
11.5.3 Reflection twinning with twin plane lying in {112) 202
11.5.4 Coexistence of {112) and {110) twins 203
11.5.5 Tweed structures 211
11.5.6 High-resolution imaging of {112) twin boundary 213
11.6 Deformed microstructures in CaTiO3 - hot-pressed using a multi-anvil apparatus 216
11.6.1 Starting powder and its crystalline phases 217
11.6.2 Hot-pressed deformation sample (A) containing low-angle grain boundaries 217
11.6.3 Hot-pressed sample (B) containing anti-phase domain boundaries 220
11.6.4 Inconsistency in twin plane indices 230
11.6.5 Fault vectors determined for "transformation" twins in sample (A) 234
11.6.5.1 Determination of Burgers vectors and line directions for dislocations 235
11.6.5.2 Determination of Burgers vectors using LACBED technique 239
11.6.6 "Transformation" twins in sample (C) 248
11.6.6.1 Fault vectors and dislocation Burgers vectors 252
11.7 Twinning in natural mineral CaTiO3 252
Chapter 12 Discussion 266
12.1 Transformation twinning and polar direction relating to t-BaTiO3 268
12.1.1 Reflection twinning and inversion domains in t-BaTiO3 268
12.2 Reflection vs rotation and merohedral vs pseodu-merohedral twins in t-BaTiO3 274
12.3 Configuration of polar directions in t-BaTiO3 275
12.4 Dislocations, their origin and dissociation reactions in pressureless-sintered t-BaTiO3 277
12.4.1 Plastic deformation 278
12.4.2 Dissociation and interaction of dislocations 279
12.5 Crystallography of lamellar {111} growth twins in t-BaTiO3 284
12.5.1 Twin laws and transformation matrices 284
12.6 Anti-phase domain boundaries in o-BaCeO3 and its crystallographic origin 288
12.6.1. Analytical techniques and existence of o1-Ibmm phase 289
12.6.2 Oxygen vacanies, cation disordering and APB 292
12.7 Twin domains in o-BaCeO3 and its crystallographic origin 293
12.7.1 Loss of point group symmetry elements - first-order transition 295
12.7.2 Loss of point group symmetry elements - second-order transition 298
12.7.3 Any 111 ??180o rotation twins lying in {132) planes? 300
12.8 Origin of tweed structures 304
12.9 Deformation or transformation twinning in o-CaTiO3 308
12.9.1 Deformation twinning 310
12.9.2 Easy glide systems 310
12.9.3 Twin plane and shear direction 313
12.9.4 Growth of deformation twins 314
12.9.5 Slip and twinning 318
12.10 Phase transition sequence derived from transformation induced APB 319
12.10.1 Mineral history of natural perovskite CaTiO3 319
12.10.2 Group theoretical determination for APB fault vectors 323
12.11 Phase transition in persovkites with non-grouo-subgroup relation 326
12.12 Reflection vs rotation twins in centrosymmetric crystals 333

Chapter 13 Conclusions 334
Chapter 14 Suggestions to future research 337
References 340
List of publications derived from this thesis 363
Appendices 365
Author's biographic sketch 370

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