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Title Page

ABSTRACT

국문초록

Contents

Chapter 1. General introduction 18

1.1. Orthophosphates 18

1.1.1. Structure of orthophosphates 19

1.1.2. Current issues in orthophosphates 24

1.2. Phase transformations 27

1.2.1. Classification of phase transformation 27

1.2.2. Solid-solid phase transformations 29

1.2.3. Time-temperature-transformation (TTT) diagram 36

1.3. Powder diffraction techniques for structural analysis 39

1.3.1. Powder vs. single-crystal diffraction 40

1.3.2. Ab initio structure determination 41

1.4. Objectives 47

Chapter 2. Phase transition, spinodal decomposition and reentrant phase formation in LiSrPO₄ 49

2.1. Introduction 49

2.2. Experimental 50

2.2.1. Synthesis 50

2.2.2. Structural analysis 50

2.2.3. Thermal analysis 51

2.2.4. Microstructural study 51

2.3. Results 51

2.3.1. Crystal structure of new polymorph 51

2.3.2. Thermo-diffractometric study 58

2.3.3. Thermal expansion measurements 59

2.3.4. Phase analysis 63

2.3.5. Thermal analysis 66

2.3.6. Morphology 69

2.4. Discussion 72

2.4.1. Phase transition 72

2.4.2. Reentrant phase formation and coherent behavior 74

2.5. Conclusions 77

Chapter 3. Crystal structure of LiBaPO₄: Polymorphism and phase transition 78

3.1. Introduction 78

3.2. Experimental 78

3.2.1. Synthesis 78

3.2.2. Structural analysis 79

3.2.3. Thermal analysis 79

3.3. Results and Discussion 80

3.3.1. Structure description 80

3.3.2. Phase transition 90

3.4. Conclusions 93

Chapter 4. Comparative study on the phase transformations and nonlinear-optical property in LiMPO₄(M＝Ca, Sr, Ba) 94

4.1. Introduction 94

4.2. Experimental 96

4.2.1. Synthesis and structural analysis 96

4.2.2. Phase transformation analysis 96

4.2.3. Optical spectroscopy 97

4.3. Results and Discussion 97

4.3.1. Structure refinements 97

4.3.2. Comparison of phase transformation behaviors 101

4.3.3. Raman spectroscopy 107

4.3.4. Second-harmonic generation (SHG) 109

4.4. Conclusions 112

Chapter 5. Synthesis, crystal structure, and ionic conductivity of a new layered metal phosphate, Li₂Sr₂Al(PO₄)₃ 113

5.1. Introduction 113

5.2. Experimental 114

5.2.1. Synthesis 114

5.2.2. Single-crystal X-ray diffraction 114

5.2.3. Ionic conductivity measurements 115

5.3. Results and discussion 116

5.3.1. Structure determination 116

5.3.2. Structure description 123

5.3.3. Powder synthesis and ionic conductivity 126

5.4. Conclusions 131

REFERENCES 132

List of Tables

Table 1-1. Crystallographic data for various ABPO₄ 26

Table 1-2. Advantages and limitations of single-crystal and powder X-ray diffraction techniques. 44

Table 2-1. Crystallographic data of the monoclinic phase for LiSrPO₄ refined from... 54

Table 2-2. Atomic coordinates and equivalent isotropic displacement parameters for... 55

Table 2-3. Selected geometric parameters (Å, ˚) in monoclinic LiSrPO₄. 55

Table 2-4. Crystallographic data of hexagonal phase for LiSrPO₄ refined from... 65

Table 3-1. Crystallographic data of the monoclinic phase for LiBaPO₄ refined from... 81

Table 3-2. Atomic coordinates and equivalent isotropic displacement parameters for... 82

Table 3-3. Selected geometric parameters (Å, ˚) in monoclinic LiBaPO₄. 82

Table 3-4. Crystallographic data of the trigonal phase for LiBaPO₄ refined from... 87

Table 3-5. Atomic coordinates and equivalent isotropic displacement parameters for... 88

Table 3-6. Selected geometric parameters (Å, ˚) in trigonal LiBaPO₄. 88

Table 4-1. Crystallographic data of LiCaPO₄ refined from conventional X-ray diffraction. 98

Table 4-2. Atomic coordinates and equivalent isotropic displacement parameters for... 99

Table 4-3. Selected geometric parameters (Å, ˚) in trigonal LiCaPO₄. 100

Table 4-4. Theoretical lattice volume/PO₄ formula unit. 107

Table 4-5. The calculated distortions of the LiO₄ and PO₄ polyhedra. 110

Table 5-1. Crystallographic data of Li₂Sr₂Al(PO₄)₃ refined from single-crystal X-ray... 117

Table 5-2. Atomic coordinates (×10⁴) and equivalent isotropic displacement parameters... 118

Table 5-3. Anisotropic displacement parameters (Ų×10³) for Li₂Sr₂Al(PO₄)₃. The... 119

Table 5-4. Selected interatomic distances (Å) for Li₂Sr₂Al(PO₄)₃. 120

Table 5-5. Selected interatomic angles (˚) for Li₂Sr₂Al(PO₄)₃. 121

Table 5-6. Parameters used inEIS fitting procedure at various temperatures. 128

List of Figures

Figure 1-1. Schematic of the crystal structure of high-tridymite along the c direction.... 20

Figure 1-2. Schematic of the crystal structure of the ideal olivine (Mg₂SiO₄) along the c... 22

Figure 1-3. Schematic of the crystal structure of glaserite (K₃Na(SO₄)₂) along the c... 23

Figure 1-4. Schematic classification of phase transformation in solid materials. 28

Figure 1-5. Schematic diagram of the concentration profile for (a) nucleation and growth... 30

Figure 1-6. Changes in the thermodynamic characteristics (free energy, enthalpy, and... 30

Figure 1-7. Atomically smooth solid/liquid interfaces with atoms represented by cubes. 33

Figure 1-8. Influence of interface undercooling (△Ti) on the growth rate for atomically...(이미지참조) 33

Figure 1-9. (a) Phase diagram of binary system with a miscibility gap. (b) Free energy... 35

Figure 1-10. The example TTT-diagram for an iron-carbon alloy of eutectoid... 38

Figure 1-11. Information about the compound obtained from a powder XRD... 40

Figure 1-12. Diffraction patterns of (a) a single crystal and (b) a polycrystalline (powder)... 43

Figure 1-13. Sequence diagram of ab initio crystal structure determination based on powder diffraction. 45

Figure 1-14. Electron density maps of (001) and (010) sections for LiMg(PO4)P2O7.(이미지참조) 46

Figure 2-1. XRD patterns of LiSrPO₄ from (a) this work, (b) Lin et al. [45], and (c)... 52

Figure 2-2. Rietveld refinement of the synchrotron X-ray diffraction data for LiSrPO₄.... 53

Figure 2-3. Crystal structure of monoclinic LiSrPO₄ viewed along the (a) α-axis and (b)... 57

Figure 2-4. In situ HT-XRD patterns of LiSrPO₄ (top) and approximately calculated... 60

Figure 2-5. Thermal variations of the unit cell volumes calculated based on (a) XRD... 62

Figure 2-6. Rietveld refinement of the synchrotron X-ray diffraction data for LiSrPO₄... 64

Figure 2-7. TG-DSC data of LiSrPO₄ in an air atmosphere 67

Figure 2-8. 2nd Cycle of TG-DSC for LiSrPO₄(이미지참조) 68

Figure 2-9. BSE images of LiSrPO₄ at various magnifications 70

Figure 2-10. Structural comparison of (a) monoclinic and (b) hexagonal phases of... 73

Figure 2-11. Schematic of a miscibility gap, chemical, and coherent curves. 76

Figure 2-12. Expected TTT-diagram of powder and bulk samples for LiSrPO₄. 76

Figure 3-1. Rietveld refinement of the synchrotron X-ray diffraction data for LiBaPO₄.... 83

Figure 3-2. Crystal structure of monoclinic LiBaPO₄ viewed along the (a) α-axis and (b)... 84

Figure 3-3. Rietveld refinement of the synchrotron X-ray diffraction data for LiBaPO₄... 86

Figure 3-4. Crystal structure of trigonal LiBaPO₄ viewed along the (a) [110], and (b)... 89

Figure 3-5. (a) TG-DSC data of LiBaPO₄ in an air atmosphere. Heating and cooling rates... 91

Figure 3-6. In situ HT-XRD patterns of LiBaPO₄ at various temperature. Markers, m and... 92

Figure 4-1. Physical properties of non-centrosymmetric crystal classes 95

Figure 4-2. Rietveld refinement of LiCaPO₄. The measured data, fitted results, Bragg... 99

Figure 4-3. Crystal structure of LiCaPO₄ along the c-axis. Purple and green tetrahedra, and... 101

Figure 4-4. DSC data of LiMPO₄ (M＝Ca, Sr, Ba) in an air atmosphere. 102

Figure 4-5. XRD data of the changed phases for LiMPO₄ (M＝Ca, Sr, Ba). The markers... 103

Figure 4-6. BSE images of LiCaPO₄ for (a) bulk and (b) powder samples, and (c)... 105

Figure 4-7. BSE images of LiSrPO₄ for (a) pellet and (b) powder samples; and LiBaPO₄... 106

Figure 4-8. Raman spectra of (a) LiCaPO₄, (b) LiSrPO₄, and (c) LiBaPO₄. The right... 108

Figure 4-9. SHG signals of LiMPO₄ (M＝Mg, Ca, Sr, Ba). The results of LiCaPO₄ are... 111

Figure 5-1. Local environments of (a) Li(1)O5, (b) Li(2)O₄, (c) Sr(1)O8, (d) Sr(2)O9, (e)...(이미지참조) 122

Figure 5-2. Schematic view along the [001] direction of Li₂Sr₂Al(PO₄)₃. Li+ ions are...(이미지참조) 124

Figure 5-3. (a) [Al(PO₄)₂] framework in Li₂Sr₂Al(PO₄)₃ and (b) [Na(PO₄)₂] framework... 125

Figure 5-4. Arrangements of (a) LiO₄ and PO₄ tetrahedra in Li₂Sr₂Al(PO₄)₃ and (b) SiO₄... 125

Figure 5-5. Rietveld refinement result of Li₂Sr₂Al(PO₄)₃. The measured data, fitted... 128

Figure 5-6. (a) AC impedance data for Li₂Sr₂Al(PO₄)₃ at different temperatures and (b)... 129

Figure 5-7. Difference bond valence sum (DBVS) maps for Li ion with isovalue at ± 0.2... 130

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