近年來鈦酸鍶在塑性變形上被證實有特殊韌性到脆性，再由脆性至韌性之轉換溫度 (ductile-to-brittle-to-ductile transition)。此轉換溫度被 Sigle 等人依照溫度區分為三個區域，分別為113 K to 1053 K (-160oC to 780oC), 1053 K to ~ 1503 K (780oC to ~ 1230oC) and ~ 1503 K to 1873 K (~ 1230oC to 1600oC)。吾人利用掃描式及穿透式電子顯微鏡報導 (001) 面單晶鈦酸鍶在室溫下透過微硬度壓力試驗之微結構。螺旋及刃差排偶 (dislocation dipole) 之特徵觀察是藉由內外對比之弱電子束暗硬場影像去做確認，此差排偶成因來自於刃差排陷入、紐節拖行以及橫滑移擠壓。此差排偶會因部分螺旋差排互相抵消而殘留一連串差排環 (dislocation loop)，在氧化鋁於溫度1200oC 及及介金屬化合物 γ-TiAl 於室溫下之塑變亦有相似結果。吾人分別於兩種100 g 和 1kg 荷重下皆可誘發 {110}<-11 0> 和 {100}<011> 兩組滑移系統，由於多重滑移系統差排間橫滑移、反應成差排增殖特徵，故吾人推斷塑性變形已達第二階段加工硬化 (work hardening)。

而在奈米壓痕試驗中，吾人直接證明鈦酸鍶單晶能夠在極小應力下產生塑性變形，經由計算結果，最小分解剪應力已經超過鈦酸鍶理論值剪應力(16.1 GPa)。依照實驗所得到荷重與位移 (load-displacement curve ) 測量針對不同階段去作微結構觀察，在曲線平台前，鈦酸鍶在塑性變形上呈現一幾乎彈性行為；相對於平台產生後，藉由穿透式電子顯微鏡觀察到滑移帶出現，進一步證實鈦酸鍶在奈米壓痕下塑變機制來自於不連續荷重與位移曲線產生時。除此之外，由於滑移帶相互反應形成了柏格 (Burgers) 向量為 [1-10] (or [110]) 滑移面為 (110) (or (1-10)) 之不可移動差排促使裂縫產生。

單晶 (001) 面鈦酸鍶在室溫下利用壓力試驗得到應變量約為 19+2%。根據應力應變曲線展現出四階段加工硬化，分別為壓力軸旋轉之第零階段、簡易滑移之第一階段、多重滑移及核壁結構之第二階段，最後為試片破裂前由加工軟化及動態回復所取代，對於單晶鈦酸鍶，吾人針對不同加工硬化階段去做微結構分析有類似於金屬情況。第一階段中主要滑移系統為 [011](0-11) 和 [01-1](011) 於應力應變曲線中平台上，且被視為簡易滑移情況，三種主要特徵為 (a) 方行滑移環 (rectangular glide loops) (b) 分解差排 (collinear partials ) (c) 扭結對 (kink pairs)，其塑性變形來自於刃差排分解上之扭結對 (kink pairs) 的移動，亦可從微結構得知螺旋差排移動速度要比刃差排來的快速。而第二階段誘發多重滑移系統包括 [101](-101)、[10-1](101)、[011](0-11) 和 [0-11](011) 導致與金屬塑變相似核壁結構特徵。在最後第三階段隨著加工硬化率減少，從核壁結構中放出而相反向量差排交互反應而消失，此差排間互相反應成另一組平行於壓力軸 [001] 方向且伯格向量為 [-110] 之組合差排，因為這些組合差排相對於壓力軸是不可移動，故會造成試片在持續應力下而破裂。

由壓力及微硬度試驗產生之裂縫，吾人使用穿透式電子顯微鏡去觀察微裂縫成核及成長行為。在 (001) 面單晶鈦酸鍶破裂過程中，顯示裂縫前端伴隨差排產生，裂縫在遭受局部高應力集中之成核階段中，會發展出一位於裂縫前端之後的無差排區域。當裂縫要推進時，會遭受前端放射出之差排的阻擋，而限制裂縫的前進，吾人基於 Hirsch 等人模型假設，放射出的差排會滑移至裂縫前端而形成塑性變形區，且每一個放射出差排能夠減少裂縫前端應力強度促使裂縫不會繼續往前 (護盾效應)。

Recent interests on the plastic deformation of strontium titanate (SrTiO3) are derived from its unusual ductile-to-brittle-to-ductile transition (DBDT). The transition is divided into three regimes (A, B and C) corresponding to the temperature range of 113 K to 1053 K (-160oC to 780oC), 1053 K to ~ 1503 K (780oC to ~ 1230oC) and ~ 1503 K to 1873 K (~ 1230oC to 1600oC), discovered by Sigle and colleagues in the MPI-Stuttgart. We report the dislocation substructures in (001) single crystal SrTiO3 deformed by Vickers indentation at room temperature, studied by scanning and transmission electron microscopy (SEM and TEM). Dislocation dipoles of screw and edge character are observed and confirmed by inside-outside contrast using g-vector by weak-beam dark field imaging. They are formed by edge trapping, jog dragging and cross slip-pinching off. Similar to dipole breaking off in deformed sapphire (α-Al2O3) at 1200oC and γ-TiAl intermetallic at room temperature, the dipoles pinch off at one end, and emit a string of loops at trail. Two sets of slip systems {110}<-11 0> and {100}<011> are activated under both 100 g and 1 kg load. The suggestion is that plastic deformation has reached the stage II work hardening, which is characterized by multiplication of dislocations through cross slip, interactions between dislocations, and operating of multiple slip systems.
In nanoindentation experiments, it is generally believed that the shear stress at the onset of plasticity can approach the theoretical shear strength of an ideal. Here we report direct evidence that plasticity in a single crystal SrTiO3 can begin at very small forces, remarkably. However, the shear stresses associated with these very small forces is excess the theoretical shear strength of SrTiO3 (16.1 GPa). Our observations entail correlating quantitative load–displacement measurements with individual stage microstructure during nanoindentation experiments in a transmission electron microscope. We also report direct evidence that with the prevalent notion that the first obvious displacement excursion in a nanoindentation test is indicative of the onset of plastic deformation. The SrTiO3 deforms elastically before the pop-in depth, but exhibits a plastic-elastic behavior after that. TEM observations reveal that the slip band is the predominant deformation mechanism in SrTiO3 during indentation. The cracks usually initiate at the intersection of slip bands to produce the sessile dislocations with Burger vectors [1-10] (or [110]) along the (110) (or (1-10)) crack plane. In addition, theoretical analysis confirms that the pop-in event is associated with the onset plasticity of SrTiO3.
The plastic deformation of (001) single crystal SrTiO3 is investigated using compression along [001] at room temperature. A total plastic strain of ~19+2% is consistently obtained. The stress-strain curve exhibiting four work-hardening stages are describable using the stage 0 of axis rotation, the stage I “easy glide”, the stage II multiple slip and the wall-and-cell structure, and the stage III work softening and dynamic recovery before sample fracture takes place. It is revealed by analyzing the microstructure for each work-hardening stage that the plastic deformation of single crystal SrTiO3 closely resembles that of metals. The primary slip systems of [011](0-11) and [01-1](011) predominate in stage I where plastic deformation occurs by the migration of kink pairs in collinear partial dislocations. The activation of multiple slips including [101](-101) and [10-1](101), and [011](0-11) and [0-11](011) in stage II produces the cell-and-wall structure which is also characteristic of plastically deformed metals. In stage III with decreasing work-hardening rate, the bow-out dislocation interaction from opposite walls results in annihilation. The reaction between dislocations from adjacent walls produces the resultant dislocations with b = [-110] parallel to the load axis [001]. These dislocations are sessile, which eventually leads to sample fracture.
We have analyzed the microstructure of <001> SrTiO3 single crystal deformed using compression at room temperature using transmission electron microscopy. A representative stress-strain (σ-ε) curve is established, similar to that for metals it consists of three hardening stages before failure occurs at a strain ε = 19+2%. Dislocation analysis suggests that the primary slip systems in [011](0-11) and [0-11](011) are activated in the σ-ε curve stress plateau region usually addressed as easy glide. Three characteristic features are identified from samples deformed to stage I hardening by easy glide: (a) rectangular glide loops, (b) collinear partials, and (c) kink pairs. Dislocations have predominantly pure edge character. Kink pairs are observed only on the edge segments suggesting that screw dislocations have higher mobility. In easy glide, the migration and annihilation of kink pairs occurring on both the trailing and leading partials lends support to a previous report by Castillo-Rodriguez and Sigle (2011) that dislocation glide is controlled by the long-segment limit of a kink-pair model. Pure edge dislocations are dissociated into collinear partials with b = 1/2[011] (or 1/2[0-11]) by glide in (0-11) (or(011)), and kink pairs are formed on both leading and trailing partials. The suggestion is that in the low-stress regime hardening by dislocation pile-up in stage I is compensated for by kink pair nucleation and migration. The overall hardening rate thus remains unchanged at approximately zero, resembling easy glide in the deformation of metals, over an increasing strain of ε ? 4% before reaching stage II hardening.
Microcrack nucleation and propagation behavior in the crack tip was investigated by using transmission electron microscopy (TEM) through compressive test and Vickers indenter. Observation results showed that fracture process was completed in this <001> SrTiO3 single crystal material by connecting dislocations. The crack were nucleated and developed in the dislocation free zone (DFZ) or super thinned area ahead of crack tip under local high stress concentration. The cracks were linked with each other by mutual dislocation emission which expedites the propagation of crack tips effectively. We suggested a dislocation based the Hirsch et al. model of plastic-zone evolution in which dislocations emitted from the crack tip glide away to form a crack-tip plastic zone. Each emitted dislocation reduces the crack tip stress intensity via elastic interactions (the ‘‘shielding” effect).

摘要 i
Abstract iii
List of Table viii
List of Figures x
Chapter 1 Introduction 1
1.1. Objectives of research 5
Chapter 2 Review of relevant literature 7
2.1. The structure of perovskite 7
2.1.2 Crystal structure of SrTiO3 8
2.2. Phase transformations in SrTiO3 10
2.3. Mechanical Behavior of Materials 12
2.3.1. Stress–Strain Curves 12
2.3.2. Work-hardening behavior 15
2.3.3. Work Hardening of sigle crytal 16
2.4. Dislocations mobility and nucleation 18
2.4.1. The critical resolved shear stress 18
2.4.2. Generation, multiplication and annihilation of dislocations 19
2.4.3. Dislocations dissociation 24
2.4.4. Peierls-Nabarro (PN) stress 24
2.4.5. Kink Migration 27
2.5. Dislocations in Metal Single Crystals 31
2.5.1. Long-range Internal Stresses 35
2.6. Dislocations in Ceramic Materials 38
2.6.1. Ductility for Ceramic Materials 38
2.6.2. Brittleness for Ceramic Materials 39
2.7 Ductile-to-brittle-to-ductile transition (DBDT) in SrTiO3 40
2.8. Physics of fracture 44
2.8.1. The crack-dislocation interaction 44
2.8.2 Ductile versus brittle in the crack tip 49
2.8.3 Stable crack growth 52
Chapter 3 Experimental procedures 55
3.1. Initial single crystal 55
3.2. Preparation of samples 55
3.2.1. Vickers hardness 59
3.2.2. Nanoindentation 59
3.2.3. Universal testing machine 60
3.2.4. Compression Test 62
3.3. Characterisation of deformed samples 64
3.3.1. Scanning electron microscopy 64
3.3.2. Transmission electron microscopy 64
3.4 Analysis of dislocation substructure 69
3.4.1. Determination of the Burgers vector 69
3.4.2. Determination of true direction from electron micrographs 69
3.4.3. The characteristics of perfect dislocation images 71
3.4.4. The characteristics of dissociated dislocation images 72
Chapter 4 Experimental Results 73
4.1. Macroscopic identification of Vickers indenter 73
4.1.1. Initial single crystal 73
4.1.2. Fracture toughness of deformed sample 73
4.1.3. Slip Lines and Dislocation Etch Pits 75
4.2. Microstructure analysis of SrTiO3 by Vickers indenter 75
4.2.1. Burgers Vectors analysis of dislocations 79
4.2.2. True directions and character of dislocations 79
4.2.3. Dislocation intersection and screw dipoles 87
4.2.4. Dislocation intersection and screw dipoles 94
4.3. Study the pop-in event during a nanoindentation test in SrTiO3 100
4.3.1. Load and displacement curves 100
4.3.2. Indentation modulus and hardness in plastic regime 101
4.3.3. Slip lines and dislocation etch pits 101
4.4 The microstructure during incipient plasticity of SrTiO3 105
4.4.1. Analysis of dislocation in the initial stage using nanoindentation 105
4.4.2. True directions and character of slip bands 117
4.4.3. Burgers Vectors and true directions analysis of slip band dislocations 120
4.4.4. Burgers Vectors analysis of straight dislocations on sample (iv) 125
4.5. Plastic Deformation of <001> Single Crystal SrTiO3 by Compression 129
4.5.1. Stress-Strain Curve 129
4.5.2. Macroscopic of slip lines 133
4.5.3. Dislocations and Slip Systems 133
4.6. Kink-Pair Mechanism in stage I Hardening 178
4.6.1. Slip Systems 178
4.6.2. Dislocation Source, Dislocations and Their Dissociation 179
4.6.3. Dissociation Plane and Formation of Double Kink Pairs 194
4.6.4. End of the stage I 196
4.7. Microscopic Analysis of Crack tip 205
4.7.1. Analysis dislocations of crack tip by the indentation 205
4.7.2. Analysis dislocations of crack tip by compressive test 210
Chapter 5 Discussion 236
5.1. Deformation in (001) Single Crystal Strontium Titanate by Vickers Indentation 236
5.1.1 Mechanisms of dipole formation 236
5.1.2. Formation of dislocation loops by cross slip 238
5.1.3. Plasticity at room temperature 242
5.2. Deformation in (001) Single Crystal Strontium Titanate by nanoindentation 242
5.2.1. Stress Analysis of Indentation by load and displacment 243
5.2.2. Dislocation nucleation and multiplication at a discontinuous P-h curve 245
5.2.3. Crack nucleation and propagation 248
5.3. Plastic Deformation of (001) Single-Crystal SrTiO3 by Compression at Room Temperature 252
5.3.1. Easy glide and transition to stage I 252
5.3.2. Transition from Stage I to II 254
5.3.3. Cell-and-Wall Structure in Stage II 255
5.3.4. Strain Softening in Stage III Followed by Sample Failure 256
5.4. Kink-Pair Mechanism in <001> SrTiO3 Single Crystal Compression-Deformed 258
5.4.1. Planar Core of Edge Dislocations 258
5.4.2. Double Kink Migration 259
5.4.3 Nucleation of Kink Pairs under Low-Stress and with High Stacking Fault Energy 260
5.5. Crack tip dislocations in SrTiO3 264
5.5.1. Brittle-ductile transitions 265
5.5.2. Dislocation structures and dislocation mobility 265
5.5.3. Dislocation emission at cleavage crack tips 267
5.5.4. Crack tip shielding and propagation clue to dislocations 269
Chapter 6 Conclusions 273
Chapter 7 Suggestions to future work 275
References 278
Appendices 296

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