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Fundamental Structure-Dielectric Property Relationships in Fluorite-Related Ceramics

Permanent Link: http://ufdc.ufl.edu/UFE0041610/00001

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Title: Fundamental Structure-Dielectric Property Relationships in Fluorite-Related Ceramics
Physical Description: 1 online resource (267 p.)
Language: english
Creator: Cai, Lu
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: Materials Science and Engineering -- Dissertations, Academic -- UF
Genre: Materials Science and Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Compounds with anion-deficient fluorite-related crystal structure (A2B2O7), such as weberite and pyrochlore, have gained attention because their ability to accommodate various cations as well as a large variety of distortions, allowing their properties to be tailored. A comprehensive investigation of the structure-property relationships in a series of fluorite-related compounds Ln2(Ln0.5Nb0.5)2O7 (or Ln3NbO7, Ln = rare earth element) and Ln2(Ln 0.5Nb0.5)2O7 (where the ionic radius of Ln is smaller than that of Ln) is the topic of the dissertation. At room temperature, La3NbO7 and Nd3NbO7 are orthorhombic weberite-type with space group Pmcn (No. 62). The crystal structure of Gd3NbO7 is also orthorhombic weberite-type but with a different space group Cm2m (No. 38). It was found that La3NbO7, Nd3NbO7, and Gd3NbO7 have a phase transition. Of particular interest is Gd3NbO7, which exhibits a centrosymmetric to non-centrosymmetric transition on cooling based on second harmonic generation measurement. X-ray measurements were undertaken using synchrotron source. After crystal structure refined using the Rietveld method, the phase transition is mainly due to off-center shifts of Nb5+ and one third of Gd3+ ions within their corresponding polyhedra. There is net dipole along 010, which suggests an incipient ferroelectric. As for Nd3NbO7 and La3NbO7, below the phase transition temperature there are antiparallel shifts of Nb5+ and Ln3+, which indicates an antipolar nature. As for dielectric properties, weberite-type Ln3NbO7 and Ln2Ln NbO7 exhibit dielectric relaxation but there is no relaxation in defect-fluorite Ln3NbO7 (Ln3+ = Dy3+, Er3+, Yb3+, and Y3+). Infrared spectroscopy was used to correlate phase transition with dielectric properties. The infrared spectrum of Gd3NbO7 revealed that a peak at about 450 cm-1 appears at 340 K and becomes stronger with decreasing temperature, consistent with the phase transition. However, the dielectric contribution from the mode is small, less than 2% of the total permittivity. As for structure-dielectric property relationship, it was found that the temperature where the maximum permittivity occurs and the permittivity increase increases with increasing off-center shifts of Ln3+ within LnO8 polyhedra for weberite-type Ln3NbO7. As for Ln2Ln NbO7, the temperature at which the dielectric loss is maximum increase with the ionic radius ratio of cations.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Lu Cai.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Nino, Juan C.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041610:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041610/00001

Material Information

Title: Fundamental Structure-Dielectric Property Relationships in Fluorite-Related Ceramics
Physical Description: 1 online resource (267 p.)
Language: english
Creator: Cai, Lu
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: Materials Science and Engineering -- Dissertations, Academic -- UF
Genre: Materials Science and Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Compounds with anion-deficient fluorite-related crystal structure (A2B2O7), such as weberite and pyrochlore, have gained attention because their ability to accommodate various cations as well as a large variety of distortions, allowing their properties to be tailored. A comprehensive investigation of the structure-property relationships in a series of fluorite-related compounds Ln2(Ln0.5Nb0.5)2O7 (or Ln3NbO7, Ln = rare earth element) and Ln2(Ln 0.5Nb0.5)2O7 (where the ionic radius of Ln is smaller than that of Ln) is the topic of the dissertation. At room temperature, La3NbO7 and Nd3NbO7 are orthorhombic weberite-type with space group Pmcn (No. 62). The crystal structure of Gd3NbO7 is also orthorhombic weberite-type but with a different space group Cm2m (No. 38). It was found that La3NbO7, Nd3NbO7, and Gd3NbO7 have a phase transition. Of particular interest is Gd3NbO7, which exhibits a centrosymmetric to non-centrosymmetric transition on cooling based on second harmonic generation measurement. X-ray measurements were undertaken using synchrotron source. After crystal structure refined using the Rietveld method, the phase transition is mainly due to off-center shifts of Nb5+ and one third of Gd3+ ions within their corresponding polyhedra. There is net dipole along 010, which suggests an incipient ferroelectric. As for Nd3NbO7 and La3NbO7, below the phase transition temperature there are antiparallel shifts of Nb5+ and Ln3+, which indicates an antipolar nature. As for dielectric properties, weberite-type Ln3NbO7 and Ln2Ln NbO7 exhibit dielectric relaxation but there is no relaxation in defect-fluorite Ln3NbO7 (Ln3+ = Dy3+, Er3+, Yb3+, and Y3+). Infrared spectroscopy was used to correlate phase transition with dielectric properties. The infrared spectrum of Gd3NbO7 revealed that a peak at about 450 cm-1 appears at 340 K and becomes stronger with decreasing temperature, consistent with the phase transition. However, the dielectric contribution from the mode is small, less than 2% of the total permittivity. As for structure-dielectric property relationship, it was found that the temperature where the maximum permittivity occurs and the permittivity increase increases with increasing off-center shifts of Ln3+ within LnO8 polyhedra for weberite-type Ln3NbO7. As for Ln2Ln NbO7, the temperature at which the dielectric loss is maximum increase with the ionic radius ratio of cations.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Lu Cai.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Nino, Juan C.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041610:00001


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1 FUNDAMENTAL STRUCTUREDIELECTRIC PROPERTY RELATIONSHIPS IN FLUORITE RELATED CERAMICS By LU CAI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010 2010 Lu Cai

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2 With my deepest love t o my entire family

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3 ACKNOWLEDGMENTS First of all, I would like to acknowledge my advisor, Dr. Juan C. Nino, for his support and guidance. His knowledge, care, optimism, diligence and aspirations inspired me to work hard and expand my potential. I would like to express deepest gratitude to my other committee members (Dr. David P. Norton Dr. Simon R. Phillpot and Dr. Jacob L. Jones and Dr. Arthur F. Hebard) for their time and guidance. I would like to acknowledge all the collaborative work which greatly improved my research. Collaborations are listed without a particular order: Dr. Stanislav Kamba and his students Dmitry Nuzhnyy and Veronica Goian from the Institute of Physics of the Academy of Science of the Czech Republic for their great support and help on the infrared spectroscopy measu rement and c omplex dielectric spectra from the time domain THz spectrometer Brian H. Toby and all other scientists at 11 BM Advanced Photon Source, Argonne National Lab for their help with the high resolution XRD collection. Daniel Arenas and Dr. David Tanner from the Physics Department at University of Florida for their help with infrared measurements. Sava Denev and Dr Gopalan at Penn State for second harmonic generation measurement. Clarina R. Dela Cruz, Ovidiu Garlea, and Ashfia Huq at HB 2A of High Flux Isotope Reactor at Oak Ridge National Laboratory for their help on neutron diffraction data collection. I would like to thank the previous and current group members: Alex Arias, Mohammed Elshennawy, Marta Giachino, Donald Moore, Shobit Omar Satyaj it Phadke,

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4 Wei Qiu, Kevin Tierney, Laurel Wucherer, Peng Xu, Samantha Yates, etc. for providing me excellent research environment and being helpful. L ast but not least, I am deeply indebted to my parents and my husband and their continuous support. Their love has encouraged me to go through the hard times. I cannot imagine myself having any of my progress without my familys strong support behind me.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................. 3 LIST OF TABLES ............................................................................................................ 8 LIST OF FIGURES ........................................................................................................ 10 LIST OF ABBREVIATIONS ........................................................................................... 17 1. INTRODUCTION ....................................................................................................... 20 1.1 Statement of Problem and Motivation ................................................................. 20 1.2 Scientific Approach ............................................................................................. 22 1.3 Organization of Dissertation ................................................................................ 24 1.4 Contributions to the Field .................................................................................... 26 2. BACKGROUND ......................................................................................................... 28 2.1 The Weberite S tructure ....................................................................................... 28 2.1.1 Description of the Weberite Structure ........................................................ 31 2.1.2 Relationship to Fluorite and Pyrochlore ..................................................... 36 2.1.3 Weberitelike Structures ............................................................................ 46 2.1.4 Stability Field ............................................................................................. 49 2.2 Weberitetype Ln3NbO7 ....................................................................................... 53 2.3 Interesting Properties and Potential Applications ................................................ 55 2.3.1 Ferroelectric Pr o perties ............................................................................. 56 2.3.2 Dielectric Properties .................................................................................. 57 2.4 Polarization Mechanisms .................................................................................... 58 2.5 Definitions of Ferroelectric and Antiferroelectric .................................................. 63 2.6 Phase Transitions ............................................................................................... 64 2.7 Second Harmonic Generation ............................................................................. 66 2.8 Normal Mode Determinat ion ............................................................................... 66 3. EXPERIMENTAL PROCEDURES AND PROCESSING ........................................... 73 3.1 Sample Preparation ............................................................................................ 73 3.1.1 Powder Preparation ................................................................................... 73 3.1.2 Pellet Formation ........................................................................................ 74 3.2 Characterization .................................................................................................. 75 3.2.1 Structural Characterization ........................................................................ 75 3.2.2 Particle size measurement ........................................................................ 76 3.2.3 Heat Capacity Measurement ..................................................................... 77 3.2.4 Scanning Electron Microscopy .................................................................. 77 3.2.5 Second Harmonic Generation Measurement ............................................. 79 3.2.6 Dielectric Characterization ......................................................................... 79 4. PRELIMINARY CRYSTALLOGRAPHY OF THE Ln3NbO7 (Ln = La3+, Nd3+, Gd3+, Dy3+, Er3+, Y3+, and Yb3+) and Ln2LnNbO7 (Ln = La3+ and Nd3+; Ln3+ = Dy3+, Er3+, and Yb3+) .................................................................................................................. 81

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6 4.1 Introduction ......................................................................................................... 81 4.2 Crystal Structure of Ln3NbO7 (Ln = Dy3+, Er3+, Y3+, and Yb3+) ............................ 84 4.3 Crystal Structure of Ln3NbO7 ( Ln = La3+, Nd3+, and Gd3+) ................................... 87 4.4 Crystal Structure of Ln2(Ln0.5Nb0.5)2O7 ............................................................... 91 4.5 Conclusion .......................................................................................................... 96 5. DIELECTRIC PROPERTIES OF Ln3NbO7 and Ln2(Ln0.5Nb0.5)2O7 ........................... 98 5.1 Introduction ......................................................................................................... 98 5.2 Dielectric Properties of Defect Fluorite Ln3NbO7 ................................................. 99 5.3 Dielectric Properties of Weberitetype Ln3NbO7 (Ln = La3+, Nd3+, and Gd3+) .... 103 5.3.1 La3NbO7 and Nd3NbO7 ............................................................................ 103 5.3.2 Gd3NbO7 .................................................................................................. 105 5.4 Dielectric Properties of Ln2(Ln0.5Nb0.5)2O7 ........................................................ 110 5.5 Conclusion ........................................................................................................ 117 6. PHASE TRANSITION IN WEBERITETYPE Gd3NbO7 ........................................... 119 6.1 Introduction ....................................................................................................... 119 6.2 SHG and Heat Capacity Measurements ........................................................... 120 6.3 Infrared Spectroscopy ....................................................................................... 122 6.4 High Resolution XRD ........................................................................................ 124 6.5 Conclusion ........................................................................................................ 136 7. PHASE TRANSIT ION IN La3NbO7 and Nd3NbO7 ................................................... 137 7.1 Introduction ....................................................................................................... 137 7.2 Heat Capacity and SHG Measurements ........................................................... 138 7.3 Crystal Structure and Phase Transition of Nd3NbO7 and La3NbO7 ................... 140 7.3.1 Nd3NbO7 .................................................................................................. 140 7.3.2 La3NbO7 .................................................................................................. 158 7.4 Conclusion ........................................................................................................ 165 8. INFRARED SPECTROSCOPY OF Gd3NbO7 ......................................................... 167 8.1 Introduction ....................................................................................................... 167 8.2 Normal Mode Determination ............................................................................. 168 8.3 Infrared Spectra ................................................................................................ 170 8.4 Conclusion ........................................................................................................ 178 9. STRUCTUREDIELECTRIC PROPERT Y RELATIONSHIPS IN FLUORITERELATED Ln3NbO7 AND Ln2LnNbO7 ................................................................... 180 9.1 Introduction ....................................................................................................... 180 9.2 Summary of the Crystal Structure of Investigated Compounds ......................... 180 9.3 Weberitetype Ln3NbO7 ..................................................................................... 184 9.4 Ln2LnNbO7 ....................................................................................................... 191 9.5 Conclusion ........................................................................................................ 200 10. SUMMARY AND FUTURE WORK ........................................................................ 203 10.1 SUMMARY ...................................................................................................... 203 10.1.1 Phase Formation and Crystal Structure of Ln3NbO7 and Ln2LnNbO7 ... 203

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7 10.1.2 Phase Transition in Weberitetype Ln3NbO7 .......................................... 204 10.1.3 Dielectric Properties .............................................................................. 206 10.1.4 IR ........................................................................................................... 207 10.1.5 Structure Dielectric Property Relationship ............................................. 207 10.2 Future Work .................................................................................................... 208 10.2.1 Crystallography ...................................................................................... 208 10.2.2 Thin films of Ln3NbO7 (Ln3+ = La3+, Nd3+, and Gd3+) .............................. 209 10.2.3 Dielectric Properties .............................................................................. 209 APPENDIX A. DIELECTRIC RELAXATION IN THE CaO TiO2Nb2O5 PYROCHLORE AND SYNTHESIS OF PYROCHLORE FILMS BY PULSED LASER DEPOSTION Deposition (PLD) .................................................................................................... 211 B. SUPPLEMENT INFORMATION FOR INFRARED SPECTROSCOPY ................... 217 C. THE TOLERANCE FACTORS OF PYROCHLORE ................................................ 222 D. R AMAN OF Ln3NbO7 .............................................................................................. 238 E. Sm3NbO7 ................................................................................................................ 243 LIST OF REFERENCES ............................................................................................. 246 BIOGRAPHICAL SKETCH .......................................................................................... 267

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8 LIST OF TABLES Table page 2 1. Weberite structure d ata (origin at A cations) with space group of Imma .40 ............ 30 2 2. Pyrochlore ( A2B2X6X ) structure data presented in space group of Imcm (origin at B ).40 .................................................................................................................. 39 2 3. XRD reflections for fluorite, pyrochlore and weberite.40 ......................................... 40 2 4. Examples of bond valence sum for anions and cations by Brese and OKeeffe ... 45 2 5. List of A2B2F7 weberites. ....................................................................................... 67 2 6. List of weberite oxides with the RA/RB and relative ionicity of A O bond. .............. 70 2 7. An example of normal mode determination (the fluorite CeO2) ............................. 72 4 22 and the apparent lattice parameter of Dy3NbO7. ................................................... 85 5 1. Summary of ionic radius (rLn) of rare earth ions. ................................................. 103 6 1. Crystal data and refinement parameters. ............................................................ 129 6 2. Lattice parameters and atomic positions at 345 K and 400 K (space group Cmcm) ................................................................................................................ 129 6 3. Lattice parameters and atomic positions at 100 K and 295 K (space group Cm2m) ................................................................................................................ 130 6 4. The net dipole calculation. .................................................................................. 135 7 1. List of reflections which are forbidden by Cmcm but allowed in Pmcn ............... 141 7 2. Crystal data and refinement parameters. ............................................................ 141 7 3. Atomic positions of Nd3NbO7 at 100 K, and 295 K, from high resolution XRD. .. 144 7 4. Crystal data for the low temperature phase and refinement parameters for neutron diffraction ............................................................................................... 147 7 5. Crystal data for the high temperature phase and refinement parameters for neutron diffraction. .............................................................................................. 147 7 6. Atomic positions and isotropic atomic displacement of Nd3NbO7 at 5 K, 295 K, 310 K, and 390 K from neutron diffraction. ......................................................... 148

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9 7 7. Lattice parameters and atomic positions of Nd3NbO7 at 450 K, 470 K, and 500 K from neutron diffraction. .................................................................................. 151 7 8. Crystal data for the high temperature phase and refinement parameters for neutron diffraction. .............................................................................................. 160 7 9. Crystal data for the high temperature phase and refinement parameters for neutron diffraction. .............................................................................................. 160 7 10. Lattice parameters and atomic positions of La3NbO7 at 20 K, 100 K, 295 K, and 390 K from neutron diffraction. ..................................................................... 161 7 11. Lattice parameters and atomic positions of La3NbO7 at 380K and 470 K from neutron diffraction. .............................................................................................. 162 8 1. Normal mode determination for the low temperature phase of Gd3NbO7 with space group Cm2m. ........................................................................................... 169 8 2. Normal mode determination for the high temperature phase of Gd3NbO7 with space group Cmcm. ............................................................................................ 169 8 3. List of fitting parameters for 33 oscillators at 10 K. .............................................. 171 8 4. List of fitting parameters for 19 oscillators at 600 K. ............................................ 172 8 5. Fitting parameters for 24 oscillators at 300 K ...................................................... 173 9 1. Summary of the lattice parameters, for mula volume, and atomic packing factor (APF) of Ln3NbO7 and Ln2LnNbO7.86,120,159 ........................................................ 183 9 2. A summary of T( m), Tm and their corresponding energy at 1 MHz, and the m/(lgf1lgf2), f1 is 1 MHz, f2 is 10 kHz) of dielectric relaxation. ........................................ 199 B 1. Normal mode determination for RT La3NbO7 and Nd3NbO7 phase with space group Pmcn ....................................................................................................... 218 B 2. Fitting Parameters for the reflectivity of Nd3NbO7 ............................................... 220 B 3. Fitting Parameters for the reflectivity of Sm3NbO7 .............................................. 221 C 1. Comparison of the x value from literature with calculated after Nikiforov176 ....... 229

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10 LIST OF FIGURES Figure ..................................................................................................................... page 1 1 Ion polarizability and ionic radius of rare earth elements. .................................... 21 1 2 Dielectric relaxation in the pyrochlore compounds Bi1.5Zn0.92Nb1.5O6.92 and Ca1.47Ti1.47Nb1.04O7. .............................................................................................. 22 2 1 Ballstick and polyhedral view of A1X8 and e dgeshared A1X8 polyhedral chains in [100]. .................................................................................................... 29 2 2 Ballstick and polyhedral view of A2X8. ................................................................ 30 2 3 A B 1 octahedron in the center and a B 2 octahedron connecting to 4 B 1 octahedra. ............................................................................................................. 31 2 4 Anion coordination of weberite ........................................................................... 31 2 5 B octahedral network and A cations in the nearly [100] direction ......................... 32 2 6 Kagom net presentation and polyhedral representation of A cations on A3B layers. ................................................................................................................... 33 2 7 Kagom net presentation of and polyhedral representation of B cations on AB3 layers. ................................................................................................................... 34 2 8 Stacking vectors (black arrows) between three sequence of HTB layers .............. 34 2 9 The layer of A 1 X8 lines and B 1 X6 lines, viewing in approximately [010].. .......... 35 2 10. The A 2 and B 2 layers, viewing i n approximately [010] ..................................... 35 2 11. Closed packed cationic layers in fluorite, pyrochlore and weberite ..................... 37 2 12. Axial transformation between fluorite pyrochlore, and weberite ......................... 38 2 13. One A3B and AB3 slab of weberite. ..................................................................... 42 2 14. One A3B and AB3 slab of pyrochlore ................................................................... 43 2 15. Relationship between 2O 2M and 3T weberites (origin at A2 site) ................. 48 2 16. Summary of RA vs. RB for weberites (including oxide and fluorine) and pyrochlore oxides. ................................................................................................. 50

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11 2 17. Relative ionicity vs. the ratio of RA/RB for weberite oxides, weberite fluorides and pyrochlore oxides. .......................................................................................... 51 2 18. Stability field for the weberite oxides. ................................................................. 52 2 19. Weberite AVIII 2BVI 2O7, Na2NiInF7 and Ln3B O7. .................................................... 54 2 20. Closed packed cation layers. .............................................................................. 54 2 23. Real and imaginary parts of permittivity as a function of frequency, showing the contribution from the four mechanisms ........................................................... 61 2 24. A schematic representation of ferroelectric, antipolar, and antiferroelectric, and their resp onses under an external field. ......................................................... 64 2 25. T he reciprocal susceptibility near a first o rder ferroelectric transition and a secondorder transition. ........................................................................................ 65 3 1 Flow chart of ceramic powder and pellet synthesis process for Ln3NbO7. ............ 75 3 2 XRD of La3NbO7 during the solid state processing. .............................................. 76 3 3 Particle size distribution of Gd3NbO7. .................................................................... 77 3 4 SEM picture s of Yb3NbO7 ..................................................................................... 78 3 5 SEM picture s of Gd3NbO7 ...................................................................................... 78 3 6 SEM picture s of Nd2YbNbO7 fracture surface. ...................................................... 79 3 7 Sample pellets and experimental set up. .............................................................. 80 4 1 The pyrochlore stability field based on the ratio of ionic radius of A over that of B. .......................................................................................................................... 83 4 2 The pyrochlore and the weberite stability fields based on the ionic ratio of A over B and the relative A O bond ionicity. ............................................................. 83 4 3 XRD of Dy3NbO7 at different calcination temperatures. ........................................ 84 4 4 XRD patterns of Y3NbO7, Yb3NbO7, and Er3NbO7. ............................................... 85 4 5 Nelson Riley function for the lattice parameter calculations of Dy3NbO7, Y3NbO7, Er3NbO7, and Yb3NbO7. ......................................................................... 86 4 6 Lattice parameters (with error) of defect fluorite Ln3NbO7 as a function of Ln3+ ionic radius. The solid line is the linear fitting. ...................................................... 86 4 7 Comparison of experimental XRD of La3NbO7 with theoretical XRD. ................... 88

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12 4 8 Experimental and theoretical XRD of Nd3NbO7 ..................................................... 89 4 9 Experimental and theoretical XRD of Gd3NbO7. ................................................... 90 4 10. XRD patterns of La2(Yb0.5Nb0.5)2O7 ..................................................................... 92 4 11. XRD patterns of La2(Dy0.5Nb0.5)2O7 and La2(Er0.5Nb0.5)2O7. ................................ 95 4 12. XRD patterns of Sm2YbNbO7 and Nd2ErNbO7. ................................................... 96 5 1 Dielectric properties of Dy3NbO7 at 1 kHz, 3 kHz, 8 kHz, 10 kHz, 30 kHz, 80 kHz, 100 kHz, 300 kHz, 800 kHz, and 1 MHz. ...................................................... 99 5 2 Dielectric properties of Yb3NbO7 from 1 kHz to 1 MHz. ....................................... 100 5 3 Dielectric properties of Y3NbO7 from 1 kHz to 1 MHz. ......................................... 100 5 4 Dielectric properties of Er3NbO7 from 1 kHz to 1 MHz. ....................................... 101 5 5 TCC of defect fluorite Ln3NbO7 from 218 K to 350 K. ......................................... 102 5 6 Dielectric properties of La3NbO7 from the temperature 20 K to 473 K at 1 kHz, 3 kHz, 8 kHz, 10 kHz, 30 kHz, 80 kHz, 100 kHz, 300 kHz, 800 kHz, and 1 MHz. ............................................................................................................................ 104 5 7 Dielectric properties of Nd3NbO7 between 1 kHz and 1 MHz from the temperature 20 K to 523 K. ................................................................................. 105 5 8 Dielectric properties of Gd3NbO7 between 1 kHz and 1 MHz from the temperature 20 K to 473 K. ................................................................................. 106 5 9 Arrhenius plot of temperature at which the maximum peak of imaginary part of permittivity occurs in Gd3NbO7. .......................................................................... 107 5 10. Summary of real part of permittivity for all Ln3NbO7 compounds. ..................... 108 5 11. The formula volume vs. the ionic radius of Ln3+ for Ln3NbO7 at room temperature. The red line is the linear fitting and the grey lines show 95% confidence limit of the fitting. .............................................................................. 109 5 12. Summary of TCC for all Ln3NbO7 compounds. The TCC from 218 K to 350 K (circles in the figure ) were calculated for La3NbO7, Nd3NbO7, and Gd3NbO7 but their permittivity does not change linearly with temperature. The TCC (open squares) above the dielectric relaxation temperature. The c apacitance at RT was also used. .................................................................................................... 110 5 13. Dielectric properties of La2(Yb0.5Nb0.5)2O7 at 10 kHz, 100 kHz, 300 kHz, 500 kHz, 800 kHz and 1 MHz .................................................................................... 111

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13 5 14. Arrhenius plot of temperature at which the maximum of imaginary parts of permittivity occurs for La2(Yb0.5Nb0.5)2O7 ........................................................... 112 5 15. Dielectric properties of La2(Dy0.5Nb0.5)2O7 at 10 kHz, 100 kHz, 300 kHz, 800 kHz and 1 MHz ................................................................................................... 113 5 16. Arrhenius plot of temperature at which the maximum of imaginary parts of permittivity occurs for La2(Dy0.5Nb0.5)2O7 ............................................................ 113 5 19. Dielectric properties of Nd2(Yb0.5Nb0.5)2O7 between 10 kHz and 1 MHz ........... 116 5 20. Arrhenius plot of Tm for Nd2(Yb0.5Nb0.5)2O7 ....................................................... 117 6 1 Dielectric constant and SHG of Gd3NbO7. .......................................................... 121 6 2 Heat capacity of Gd3NbO7 ................................................................................... 122 6 3 Infrared Spectroscopy of Gd3NbO7. ..................................................................... 123 6 4 High resolution XRD of Gd3NbO7, = 0.414201 ............................................. 125 6 5 Lattice parameters of Gd3NbO7 at different temperatures ................................... 126 6 6 High resolution XRD showing details about the (201) reflection. ........................ 127 6 7 Observed and calculated high resolution powder X ray diffraction. ..................... 128 6 8 Approximately [010] and [100] view of NbO6 octahedron at the high and low temperature phases. ........................................................................................ 131 6 9 [100] view of Gd3NbO7 ........................................................................................ 132 6 10. [100] view of spacing filling Nb and Gd1 chains parallel to the [001] direction .. 132 6 11. [100] view of spacing filling Nb and Gd1. ........................................................ 133 6 12. Approximately [010] and [100] view of Gd1O8 polyhedron at high and low temperature phases. ........................................................................................ 135 7 1 Heat capacity of La3NbO7 and Nd3NbO7. ............................................................ 139 7 2 The real part of permittivity of La3NbO7 and Nd3NbO7. The arrows point to the temperature where the maximum permittivity occurs. ......................................... 139 7 3 SHG of La3NbO7 and Gd3NbO7. .......................................................................... 140 7 4 Details of the forbidden peaks by Cmcm ............................................................. 142 7 5 High resolution XRD of Nd3NbO7 at room temperature ( ) ............. 143

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14 7 6 Neutron diffraction patterns ( ) of Nd3NbO7. ..................................... 145 7 7 Neutron diffraction of Nd3NbO7 at 500 K ( ). .................................... 146 7 8 Detailed fitting from 2 48.5o to 54.5o between 500 K and 295 K ........................ 146 7 9 Lattice parameters (with errors) of Nd3NbO7 at different temperatures. .............. 149 7 10. Unit cell volume (with errors) of Nd3NbO7 at different temperatures. ................ 150 7 11. The Nb5+ ions align along [001] and the polyhedral view of the NbO6 octahedra along [001]. ........................................................................................ 152 7 12. Approximately [001] and [301] view of NbO6 octahedra. ................................... 153 7 13. Off center displacements of Nb5+ inside NbO6 and Nd13+ inside Nd1O8 at different temperatures. ........................................................................................ 154 7 14. Nd1O8 polyhedra.. ............................................................................................. 155 7 15. The [001] view of the Nd13+ and Nb5+ ions ........................................................ 156 7 16. [100] view of space filling Nb and Nd1 chains parallel to the [001] direction. .... 157 7 17. Neutron diffraction patterns of La3NbO7 at different temperatures ( ).. ...................................................................................................................... 159 7 18. Neutron diffraction of La3NbO7 at 290 K ( ). ................................... 159 7 19. Lattice parameters (with errors) of La3NbO7 at different temperatures. ............. 162 7 20. Unit cell volume of La3NbO7 at different temperatures. ..................................... 163 7 21. Offcenter displacements of Nb5+ inside NbO6 and La13+ inside La1O8 at different temperatures. ........................................................................................ 164 7 22. Phase transition temperature for Ln3B O7. ......................................................... 164 8 1 IR reflectivity of Gd3NbO7 at 10 K. ..................................................................... 172 8 2 IR reflectivity of Gd3NbO7 at 600 K. .................................................................... 174 8 3 The real part of permittivity obtained from the timedomain THz spectrometer (dots) combined with the result of the IR reflectivity spectra. .............................. 174 8 4 The imaginary part of permittivity obtained from the timedomain THz spectrometer (dots) combined with the result of the IR reflectivity spectra. ........ 175 8 5 Calculations of the real and imaginary parts of the permittivity at 10 K. .............. 176

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15 8 6 Calculations of the real and imaginary parts of the permittivity at 600 K. ............ 177 8 7 Dielectric permittivity of Gd3NbO7 from 1 kHz to 1 MHz by LCR meter and static permittivity. ................................................................................................ 178 9 1 XRD of Ln2YbNbO7 (Ln3+ = La3+, Nd3+, Sm3+, and Gd3+) showing the peak splitting between (202) and (220), and between (404) and (440). ...................... 181 9 2 The XRD pattern of Gd2YbNbO7. ........................................................................ 181 9 3 The formula volume and APFof Ln3NbO7 and Ln2LnNbO7 as a function of the (average) ionic radius of rare earth element. ...................................................... 182 9 4 Dielectric properties of Gd3NbO7 at 1 kHz, 3 kHz, 8 kHz, 10 kHz, 30 kHz, 80 kHz, 100 kHz, 300 kHz, 800 kHz, 1 MHz, 9 GHz, and 630 GHz ......................... 1 86 9 5 Dielectric response of Gd3NbO7 as a function of frequency at 293 K and 380 K. ............................................................................................................................ 187 9 6 A summary of the real part of permittivity for weberitetype Ln3NbO7 at 1 MHz. The arrows show the difference ( r) between the maximum permittivity and the minimum permittivity. .................................................................................... 188 9 7 Offcenter displacement of 8 cooridinated Ln3+ for Ln3NbO7 at different temperatures. ..................................................................................................... 189 9 8 T( m) and normalized dielectric difference from the maximum to the minimum vs. off center displacement of Ln3+ inside Ln1O8 polyhedra. (measured in 3) is the polarizability of Ln3+. .................................................................................. 189 9 9 Off center displacement of Nb5+ for Ln3NbO7 at different temperatures. ............. 190 9 10. Comparison of off center shifts of the Nb5+ and Ln13+ ions in La3NbO7 and Nd3NbO7. ............................................................................................................ 191 9 11. A summary of the real part of the permittivity for all investigated Ln2LnNbO7 compounds at the frequency of 1 MHz and the temperature of 20 K and room t emperature. The average polarizability of Ln3+ is also included. ....................... 192 9 12. The real part of permittivity of Gd2YbNbO7 and defect fluorite Ln3NbO7 at 1 MHz. ................................................................................................................... 193 9 13. Summary of the real part of the permittivity for defect fluorite Ln3NbO7 and Gd2Y bNbO7 compounds at the frequency of 1 MHz and the temperature of 20 K and room temperature. The average polarizability of Ln3+ is also included. ... 194 9 14. Summary of the real part of permittivity for Ln2YbNbO7 compounds. The arrows point to the temperature where the maximum permittivity occurs. .......... 195

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16 9 15. The imaginary part of permittivity for Ln2YbNbO7 at 1 MHz. ........................... 195 9 16. A summary of the real part of permittivity for La2LnNbO7 compounds. ........... 196 9 17 The imaginary part of permittivity La2LnNbO7 at 1 MHz. ................................. 197 9 18. The temperature (Tm) where the peak of the 1 MHz imaginary occurs vs. the ratio of the ionic radius of A cations over that of B cations for Ln2LnNbO7 ........ 197 9 19. A summary of the temperature coefficient of permittivity for all Ln2LnNbO7. .... 198 9 20. Neutron diffraction of Nd2YbNbO7 at 10 K an 100 K ( = 1.5378 ). ................. 200 9 21. Average ion polarizability vs. average ionic radius of Ln3+ in Ln3NbO7 and Ln2LnNbO7.. ....................................................................................................... 201 101 A typical hysteresis loop for an antiferroelectric material. ................................. 210

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17 LIST OF ABBREVIATIONS ANL Argonne National Lab APF a tomic packing factor APS Advance Photon Source CN coordination number DI d eionized EDS e nergy dispersive spectroscopy HFIR High Flux Isotope Reactor HT h igh temperature IR i nfrared spectroscopy LT l ow temperature MAIC M ajor A nalytical I nstrumentation C enter ORNL Oak Ridge National Lab SEM scanning electron microscopy SHG second harmonic generation TC C t emperature coefficient of capacitance T( m) t he temperature where the maximum of the real part of the permittivity occurs Tm t he temperature where the peak of the imaginary part of the permittivity occurs SA stacking angle SV stacking vector RT r oom temperature

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18 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy FUNDAMENTAL STRUCTUREDIELELCTRIC PROPERTY RELATIONSHIPS IN FLUORITE RELATED CERAMICS By Lu Cai May 2010 Chair: Juan C. Nino Major: Materials Science and Engineering Compounds with aniondeficient fluorite related crystal structure ( A2B2O7), such as weberite and pyrochlore, have gained attention because their ability to accommodate various cations as well as a larg e variety of distortions, allowing their properties to be tailored. A comprehensive investigation of the structureproperty relationships in a series of fluoriterelated compounds Ln2(Ln0.5Nb0.5)2O7 (or Ln3NbO7, Ln = rare earth element) and Ln2(Ln0.5Nb0.5)2O7 ( where the ionic radius of Ln is smaller than that of Ln) is the topic of the dissertation. At room temperature, La3NbO7 and Nd3NbO7 are orthorhombic weberitetype with space group Pmcn (No. 62). The crystal structure of Gd3NbO7 is also orthorhombic weberitetype but with a different space group Cm2m ( No. 38). It was found that La3NbO7, Nd3NbO7, and Gd3NbO7 have a phase transition. Of particular interest is Gd3NbO7, which exhibits a centrosymmetric to noncentrosymmetric transition on cooling based on second harmonic generation (SHG ) measurement. X ray measurements were undertaken using synchrotron source. After crystal structure refined using the Rietveld method, the phase transition is mainly due to off center shifts of Nb5+ and one third of Gd3+ ions within their corresponding polyhedra. There is net

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19 dipole along [010], which suggests an incipient ferroelectric. As for Nd3NbO7 and La3NbO7, below the phase transition temperature there are antiparallel shifts of Nb5+ and Ln3+, which indicates an antipolar nature. As for dielect ric properties, weberitetype Ln3NbO7 and Ln2LnNbO7 exhibit dielectric relaxation but there is no relaxation in defect fluorite Ln3NbO7 (Ln3+ = Dy3+, Er3+, Yb3+, and Y3+). Infrared spectroscopy (IR) was used to correlate phase transition with dielectric properties. The infrared spectrum of Gd3NbO7 revealed that a peak at about 450 cm1 appears at 340 K and becomes stronger with decreasing temperature, consis tent with th e phase transition. However, the dielectric contribution from the mode is small, less than 2% of the total permittivity. As for structure dielectric property relationship, it was found that the T( m) and r) increases with increasing off center shifts of Ln3+ within LnO8 polyhedra for weberitetype Ln3NbO7. As for Ln2LnNbO7, the temperature (Tm) at which the dielectric loss is maximum increase with the ionic radius ratio of cations.

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20 CHAPTER 1 INTRODUCTION 1.1 Statement of Problem and Motivation The fluorite structure ( A O2) is considered to be one of the most flexible for i ts ability to construct superstructures or derivative s.1 Anion deficient fluoriterelated structures (A2B2O7) such as pyrochlore and weberite, maintain the closedpacked cation layers as in the fluorite structure. The deficiency of anions enables accommodation of various cations on both A site and B site Therefore, compounds with fluorite related structure exhibit various interesting properties, including conductivity ( e.g. Bi2Ru2O7 25), dielectric properties ( e.g. B i1.5Zn0.92Nb1.5O6.92 610), ferroelectric properties ( e.g. Cd2Nb2O7 and Ca2Sb2O7 11 14), magnetic properties ( e .g. Ln2(Ln0.5Re0.5)2O7 and Ln2(Ln0.5Os0.5)2O7 1521, where Ln = rare earth element ) as well as photocatalytic activity ( La3NbO7 and Ca2Sb2O7 2225) C ompounds with aniondeficient fluoriterelated structure ( A2B2O7) exhibit interest ing dielectric properties with intermediate dielectric constants especially in niobates, tantalates and titanates ( r ~ 30 100).14 A lot of these materials have been studied for potential electronic applications such as capacitors, filters and resonators. However, due to the large structural flexibility, the huge number of compounds available and diverse nature of the properties, there is a limited comprehension of the fundamental structuredielectric property relationships inside fluoriterelated ceramics To address this issue, a series of Ln3NbO7 and Ln2LnNbO7 compounds have been chosen to achieve a fundamental understanding of structuredielectric property relationships. The series of compounds are ideal for studying the correlation between ionic pol arizability and dielectric permittivity because there is an approximately linear

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21 relationship between the dielectric polarizability and ionic radius of Ln3+ ( Figure 1 1 ). The variation in crystal structure within the fluorite family also provides a stage to investigate structuredielectric property relationships within fluoriterelated ceramics. Figure 1 1 Ion polarizability 26 and ionic radius 27 of rare earth elements. In addition, an interesting phenomenon is that dielectric relaxation is commonly observed in Bi pyrochlores ( Figure 1 2 (A)) At first, it was proposed that dielectric relaxation is related to the lonepair cations Recently d ielectric relaxation was also observed in a nonBi pyroc hlore, Ca1.47Ti1.47Nb1.04O7 ( Figure 1 2 (B)) .28 T h erefore, the origin of the dielectric relaxation is definitely not due to the lonepair since Ca1.47Ti1.47Nb1.04O7 does not have the lone pair but apparently lies in the structural disorder. This study also intends to find the correlation between structure and dielectric relaxation within fluoriterelated structures. 1.17 1.14 1.11 1.08 1.05 1.02 0.993.5 4.0 4.5 5.0 5.5 6.0 6.5 Ion dielectric polarizability (A3) La Nd Gd Dy Er Ybweberite-type defect fluoriteYo Ionic radius ()

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22 0 50 100 150 200 60 75 90 105 120 135 0 4 8 12 Temperature (K) Increasing Frequencyr' r" 100 200 300 400 500 50 60 70 80 90 100 0 2 4 6 8 r' r"Increasing FrequencyTemperature (K) (A) (B) Figure 1 2 Dielectric relaxation in the pyrochlore compounds (A) Bi 1.5 Zn 0.92 Nb 1.5 O 6.92 6 (B) Ca1.47Ti1.47Nb1.04O7.28 1.2 Scientific Approach Crystallographic investigations on Ln3NbO7 can be found dating as far back as 1964.29 Since then, t here have been considerable discrepancies between various studies on the crystal structure of Ln3NbO7 reported in literature S ome investigators referred to Sm3NbO7 and Gd3NbO7 as having an orthorhombic structure ( probably a weberitetype structure) while others determined them to b e pyrochlores.3035 Rossell36 first determined the crystal structure of a series of Ln3NbO7 compounds Though the main features of the structures have been captured, the space groups proposed for La3NbO7 ( Cmcm) and Gd3NbO7 ( C2221) have been questioned by later investigation s. Kahnharari et al .37 studied single crystal La3NbO7 and proposed the space group ( Pnma ) based on x ray diffraction. Astafyev38 measured the second harmonic generation (SHG) and suggest ed a polar space group for Gd3NbO7 rather other C2221. Therefore, the first step of this research is to clarify the crystal structure The second step of this work is to characterize dielectric properties at different temperatures and frequencies. For all defect fluorite samples, the dielectric permittivity

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23 increase s slightly with increasing temperature. By contrast, weberitetype Ln3NbO7 exhibit s dielectric relaxation above room temperature (RT) Effor ts were placed to look for the structural ori gin of dielectric relaxation. The focus on dielectric properties include calculation and analysis of the permittivity (real and imaginary), the temperature coefficient of capacitance ( TC C ) the temperature (T( m)) where the maximum permittivity occurs, th e temperature (Tm) where the peak of the imaginary part of the permittivity happens Contrast between t he dielectric properties/relaxation and structural features such as ionic radius, polarizability, structural openness, phase transition, polyhedra distortion, etc. was performed to identify structureproperty correlations. It was found out that the off center shifts of cations within their polyhedra impact the dielectric properties. A series of new Ln2(Ln0.5Nb0.5)2O7 compounds (where the ionic radius of Ln is smaller than Ln) were introduced to expand the study. The Ln2LnNbO7 compounds have higher permittivity with more polarizable Ln3+. The Ln2LnNbO7 (except Gd2YbNbO7) also exhibits dielectric relaxation but bel ow 100 K. Tm increases with increasing the ratio of ionic radius and TC C increases with decreasing the average ionic radius of Ln3+. Based on heat capacity measurement s, there is a phase transition in Ln3NbO7. Of particular i nterest is that only Gd3NbO7 shows SHG signal. The signal disappears above the phase transition temperature, indicating a noncentrosymmetric to centrosymmetric transition. For all three weberitetype Ln3NbO7 compounds, it is proven the origin of the dielectric relaxation is the phase transition because T( m) is close to the phase transition temperature indicated by the heat capacity data. The next research area focused on the characterization of the crystal structures below and above

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2 4 the phase transition temperature by synchrotron x ray diffraction at Advanced Photon S ource (APS) of Argonne National Laboratory (ANL) and neut ron diffraction at High Flux Isotope Reactor (HFIR) of Oak Ridge National Laboratory (ORNL) The final step wa s to co rrelate the crystal structure, phase transition, and dielectric properties by infrared (IR) spectroscopy and to predict the dielectric properties in the terahertz (THz ) frequency range. These results not only contribute to the comprehension of structuredi electric property relationships, but also lead towards the possibility to control the dielectric relaxation and develop a paradigm for compositional design of fluoriterelated ceramics with optimized dielectric properties. 1.3 Organization of Dissertation Chapter 2 provides a brief introduction and background information on the weberite structure and the weberitetype Ln3NbO7 structure. The correlations between these two structures are discussed. Chapter 2 also introduces t he dielectric polarization mechanism s, the concept of the phase transition, the definitions of ferroelectric, antipolar, and antiferroelectric, the basic concept of second harmonic generation (SHG), and the normal mode determination in Raman and IR Chapter 3 presents the experimental procedures and characterization techniques mainly used in this study Chapter 4 reports the crystallographic study by XRD at room temperature. Chapter 5 present s the dielectric properties for all compounds studied in the investigation. The dielectric properties from 1 kHz to 1 MHz were measured as a function of temperature. Chapter 6 reports the phase transition of weberitetype Gd3NbO7. Heat capacity measurement, second harmonic generation measurement, the infrared (IR)

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25 spectroscopy and dielectric properties measurement are all evidence supporting phase transition. Synchrotron x ray diffractometer was used to study the crystal structure of Gd3NbO7 below and above the phase transition temperature. In Chapter 7, d ifferent techniques including heat capacity measurement, synchrotron x ray and neutron diffraction were performed on Nd3NbO7 and La3NbO7. All results confirmed a phase transition in these compounds. Crystallographic refinement s of all phases below and above phase transition point are also presented. Chapter 8 includes the analysis of infrared (IR) spectroscopy studies in Gd3NbO7. The nuclear site group analysis is used to calculate the possible modes in IR. Oscillator model is utilized to fit the spectrum and calculate the real and imaginary permittivity. Chapter 9 covers correlations between dielectric properties and crystal structure. In weberitetype Ln3NbO7, T( m r ion polarizability of Ln3+) increases with increasing the off center shift of the 8 coordinated Ln13+ ions within their corresponding polyhedra. As for Ln2LnNbO7, the TC C increases with decreasing the average ionic radius of Ln3+ (2/3rLn +1/3rLn). The Tm increases with increasing the ratio of the ionic radius of A (Ln3+) over B (Ln3+ and Nb5+). Finally Chapter 10 presents a summary of the dissertation and discusses the future work in the relevant research areas. At the end of the thesis, there are five appendices including the study on CaO TiO2Nb2O5 film (Appendix A ) tolerance factor for pyrochlore (Appendix B ), Raman spectroscopy (Appendix C ) IR of La3NbO7 Nd3NbO7 and Sm3NbO7 (Appendix D ) and the structure and dielectric properties of Sm3NbO7 (Appendix E)

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26 1.4 Contributions to the Field This work investigates the structureproperty relationships in fluoriterelated Ln3NbO7 and Ln2(Ln0.5Nb0.5)2O7 ceramics. The main contributions of this work to the field of materials science and engineering are summarized below: 1. A series of Ln3NbO7 (Ln3+ = La3+, Nd3+, and Gd3+) compounds were studied to solve the contradict ions regarding their crystal structure. Neutron powder diffraction and s ynchrotron XRD data was collect ed to solve the space group issue and present the correct structure. 2. The La2LnNbO7 (Ln3+ = Yb3+, Er3+ and Dy3+) and Ln2YbNbO7 (Ln3+ = Nd3+, Sm3+, and Gd3+) were synthesized for the first time. B ased on Subramanians14 stability field and Isupovs39 prediction, it was inferred that the crystal structure was likely to be cubic pyrochlore. However, t he structural characterization indicates they (except Gd2YbNbO7) actually have an orthorhombic lattice. Gd2YbNbO7 has a tetragonal lattice The structure is probably intermediate between orthorhombic weberitetype and cubic defect fluorite. 3. The dielectric properties of defect fluorite Ln3NbO7 (Ln3+ = Dy3+, Y3+, Er3+, and Yb3+) were studied first time. The real part of the permittivity increases with increasing temperature. The TC C incr eases with decreasing the ionic radius of Ln3+. 4. The weberitetype Ln3NbO7 (Ln3+ = La3+, Nd3+, and Gd3+) exhibits dielectric relaxation above room temperature (RT) It was proven that the origin of the dielectric relaxation is a phase transition. The phase transition was found out to be chiefly mediated by the off center shifts of both the Nb5+ and 8coordinated Ln13+ ions. 5. A ntipolar displacements were found in the low temperature phase of Nd3NbO7 and La3NbO7, indicating the potential of antiferroelec tric. 6. In the LT phase of Gd3NbO7, there is a net dipole parallel to [010]. It indicates that Gd3NbO7 is an incipient ferroelectric. 7. It was found that t he T( m r center shift of the 8coordinated Ln3+ in weberite type Ln3NbO7. 8. The La2LnNbO7 (Ln3+ = Yb3+, Er3+, and Dy3+) and Ln2YbNbO7 (Ln3+ = Nd3+ and Sm3+) also exhibit dielectric relaxation but below 100 K. There is no phase transition found in these compounds. The Tm increases with increasing the ratio of the ionic radius of A (Ln3+) over B (Ln3+ and Nb5+). The TC C at RT increases with decreasing the average ionic radius of Ln3+. Only Gd2YbNbO7 has positive TC C (~225 M K1). Nd2YbNbO7 and Sm2YbNbO7 have the most st able

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27 permittivity as a function of temperature with TC C ~ 40 MK1. It is possible that a small amount of Gd2YbNbO7 secondary phase inside Sm2YbNbO7 and Nd2YbNbO7 can compensate TC C to zero, which may have potential applications.

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28 CHAPTER 2 BACKGROUND The core of the first section of this chapter is chiefly based on the journal article (Acta Crystallographica Section B Structural Science, 65 269 290 (2009)) titled Complex Ceramic Structures. I. Weberites, by L. Cai, and J.C. Nino.40 It is reprinted with permission from International Union of Crystallography (IUCr). The present chapter briefly summarizes some of the theoretical background required for understanding the research work covered in the following chapters 2.1 The Weberite Structure The weberite crystal structure (space group: Imma No. 74), with typical stoichiometry A2B2X7 ( A and B are cations X is O or F ), is a type of aniondeficient fluorite superstructure ( A X2). Possible ionic valences in weberite include A2 1+B2+B3+F7, A2 2+B2 5+O7 and A2 1+B2 6+O7. While several other compounds posses the same stoichiometry (pyrochlores, layered perovskites, etc. ), weberites are isomorphic compounds with the mineral, Na2MgAlF7. This mineral was originally found in Ivigtut in southwestern Greenland and was named after Theobald Weber .41 In 1944, Bystrm42 determined the crystal struct ure with space group Imm2 basing his studies on the pyrochlore structure, which is another fluoriterelated superstructure. It was later proven that the correct space group is Imma .4344 The detailed history of the controversy of the space group has been reviewed by Yakubovich et al.1 The atomic positions and site symmetry of the weberite structure are given in Table 2 1 The A ions sit in the 4a and 4d atomic positions with site symmetry 2/ m and establish a coordination number of 8 with the anions. The A ions have two different coordination environments. The A1 cations (in atomic position 4 d ) lie in a highly

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29 distorted cube (or square prism) where there are two different A1 X bond lengths ( Figure 2 1 (A) and (B)). The cubes are edgeshared to form a series of chains in the [100] direction ( Figure 2 1 (C)). The A2 cations (in atomic position 4 a ) are located within bihexagonal pyramids in which anions are spaced at three different distances from the central cations ( Figure 2 2 ) Each pyramid is corner shared with other two pyramids and edgeshared with four A1 X8 cubes. As presented in Table 2 1 there are three Wyckoff positions for anions ( X 1 at 8h, X 2 at 16j, and X 3 at 4e). A1 ions only connect to X 1 and X 2 while A2 link to all three types of anions (two X 1 four X 2 and two X 3 ). (A) (B) (C) Figure 2 1 (A) Ball stick view of A1X 8 (B) Polyhedral view of A1X 8 (C) Edge shared A1X 8 polyhedra form chains in [100] The black lines indicate the unit cell.

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30 (A) (B) Figure 2 2 (A) Ball stick view of A2X 8 (B) Polyhedral view of A2X 8 The shape of the polyhedra is bi hexagonal pyramid. Table 2 1 Weberite structure d ata (origin at A cations) with space group of Imma .40 Atoms Wyckoff position Site symmetry Atomic position x y z A (1) 4 d 2/m 0.25 0.25 0.75 A (2) 4 a 2/m 0 0 0 B (1) 4 c 2/m 0.25 0.25 0.25 B (2) 4 b 2/m 0 0 0.5 X (1) 8 h m 0 y 1 z 1 X (2) 16 j 1 x 2 y 2 z 2 X (3) 4 e mm2 0 0.25 z 3 X (1) is on A3B interstitial site, X (2) is in A2B2 tetrahedron, and X (3) is inside A4B2. The B ions are located in the 4b and 4c Wyckoff positions (site symmetry 2/m) and have a coordination number of 6, i.e. A2 VIIIB2 VIIX7. There are two types of B X6 octahedra: B 1 ( B2+ in the case of A2B2+B3+F7, A = Na+ or Ag+) in 4c Wyckoff positions, and B 2 ( B3+ in the case of A2B2+B3+F7) in 4b Wyckoff positions. Each of the six vertices of B 1 octahedra connects to another B octahedron while only four vertices of a B 2 octahedron link to other B octahedra (see Figure 2 3 ). The arrangements of A and B ions lead to three different cation tetrahedra. Six anions occupy the two A3B ( A3B X X 1 ) and four A2B2 tetrahedral interstices ( A2B2X X 2 ) and none are located inside the two AB3 sites ( AB3[], where [] represents a vacant site) in a formula unit. The remaining anion ( X 3 ) maintains four coordination and lies outside the two edgeshared AB3 tetrahedra, very close to the shared B B edge (see Figure 2 4 ).

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31 X 3 can also be considered to sit inside the octahedron ( A4B2), which shares faces with two adjacent AB3 tetrahedra, and distort towards the B B edge.45 (A) (B) Figure 2 3 (A ) a B 1 octahedron in the center and its connection to another six octahedra. ( B ) a B 2 octahedron connecting to 4 B 1 octahedra 40 ( A ) ( B ) ( C ) Figure 2 4 Anion coordination of weberite (A) X 1 inside A 2 B 2 (B) X 2 inside A 3 B (C) X 3 inside A 4 B 2 40 2.1.1 Description of the Weberite Structure A common way to describe the weberite structure is a network of corner shared B X6 octahedra with the penetration of A cations (see Figure 2 5 ). The B 1 octahedra are corner linked to each other and form B 1 octahedral chains parallel to the A1 chains (in the [100] direction). The B 2 octahedra are isolated from each other and link the B 1 octahedra chains to form a 3 D octahedral network.

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32 Figure 2 5 B octahedral network and A cations in the nearly [100] direction 40 The weberite structure can also be considered as a stacking of repeated layers or slabs. The most common way to examine the structure is to view it as stacked, alternating close packed metal layers A3B and AB3 on (011) parallel planes. In A3B layers, four A 1 and two A 2 ions form a hexagonal ring with B 2 occupying the center. In other words, the A cations form Kagomtype networks [ Kagom in Japanese means a bamboobasket woven pattern. It is formed by int erlaced triangles and each lattice point has 4 equivalent bonds. The "Kagom" crystallographic concept was introduced by Husimi46 after he and his co worker Syzi found a new antiferromagnetic lattice by star to triangle transformation from a honeycomb lattice. Syzi47 published the first Kagom paper in 1951. See Figure 2 6 ]. In AB3 layers, the BX6 octahedron arrangement is nearly identical with the basal plane of the hexagonal tungsten bronze

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33 (HTB) structures and A 2 cations are in the center of the hexagonal rings. The HTB like layers can also be simplified by a Kagom net representation ( Figure 2 7 ). The HTB like layers are displaced with respect to each other by an interlayer stacking vector (SV) which is defined as the projected distance, viewed down the (pseudo) six fold axis, between crystallographically similar atoms in adjacent layers. White48 and Cohelho et al.49 used SV as an alternative description for zirconolite, zirkelite, pyrochlore and polymignyte. Here, SV is used to describe weberite. The stacking vectors in the weberite structure are nearly in the [011], [ 311] and [311] directions. They are typica lly of the order 4 The angle between successive stacking vectors (SA) is approximately 120o. The distance between two neighbouring HTB like layers along the (pseudo) six fold axis is approximately 5.8 Figure 2 8 shows the stacking vectors between three sequences of HTB layers. (A) (B) Figure 2 6 (A) Kagom net presentation of A cations on A 3 B layer s. (B) AX 8 polyhedral representation of A 3 B layer s, which are parallel to (011) plane. 40

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34 (A) (B) Figure 2 7 (A) Kagom net presentation of B cations on AB 3 layer s. (B) BX 6 polyhedral representation of AB 3 layer s, which are parallel to (011) plane. 40 (A) (B) Figure 2 8 (a) S tacking vector s (black arrows) between three sequence of HTB layers (b) Kagom nets of three successive HTB layers (purple arrows are stacking vectors). 40

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35 There is yet another way to consider the weberite repeat ed layers. The first layer is formed by the alternating B 1 octahedra chains and A 1 distorted cube (or square prism) chains, which are in [100] direction for classic orthorhombic weberites. In this layer, the B 1 octahedra are edgeshared with A 1 cubes The second layer is alternating B 2 octahedra and A 2 bi hexagonal pyramids in the [100] direction as in Figure 2 9 and Figure 2 10.36,50 Figure 2 9 The layer of A 1 X 8 lines and B 1 X 6 lines, viewing in approximately [010] 40 direction. Figure 2 10 The A 2 and B 2 layer s, viewing in approximately [010] direction. 40

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36 2.1.2 Relationship to Fluorite and Pyrochlore Weberite and pyrochlore ( A2B2X7) are both fluoriterelated superstructures. The coordination number of A and B is the same in both structures. These two structures have a similar cationic sublattice, which is arranged by stacking cubic close packed cation layers, same as the (111) planes in fluorite. These layers alternate between the compositions A3B and AB3 and are parallel to (111) planes in pyrochlore and (011) planes in weberite ( Figure 2 11 ) AB3 layers in pyrochlore can also be described as HTBlike layers. The length of stacking vectors and the value of SA of the pyrochlore structure are almost the same as weberite. However, the difference between the weberite and the pyrochlore structures is the different stacking of two successive AB3 and A3B layers, which will be discussed later in this section. The crystallographic relationship between the weberite and the pyrochlore structures is further confirmed by the fact that the space group of weber ite ( Imma ) is a subgroup of m 3 Fd the space group of pyrochlore. If the lattice parameter of pyrochlores is 2 a with respect to fluorite a ( a ~ 5), then the lattice parameters of the classic orthorhombic weberites are approximately a 2 a and a The rotat ion of 45o about the b axis of the fluorite or the pyrochlore cation sublattice leads to the weberitelike cation sublattice ( Figure 2 12). The (111) planes of pyrochlore or fluorite are transformed to the (011) of the new lattice. Standard crystallographic transformations follow the guidelines from the international table for crystallography:51 T c b a c b af w) ( ) ( ( 2 1 ) where a b and c are the basis vectors. The subscript w stands for weberite and the subscript f indicates fluorite. The transformation matrix T implies both the change of

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37 orientation and the length of the basis vectors. The transformation relationship between weberite (W), fluorite (F), and pyrochlore (P) can be written as following, 5 0 0 5 0 0 1 0 5 0 0 5 0 P 1 0 1 0 2 0 1 0 1 F W ( 2 2 ) (A) (B) (C) Figure 2 11 (A) cationic network on the (111) of fluorite (B) AB 3 layer (C) A 3 B layer on (011) of weberite; dash line s are unit cell 40

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38 (A) (B) Figure 2 12 (A) Axial transformation of fluorite to pyrochlore (black dashed lines is a fluorite cell; blue solid lines is a pyrochlore cell). (B) Axial transformation of fluorite to weberite (black dashed lines a fluorite cell, red solid lines a weberite cell). The transformation of pyrochlore leads to the space group Imcm which is a different setting of Imma The Imma lattice can be achieved by the 90o rotation of the coordinate system of Imcm. The transformation matrix is 0 0 1 1 0 0 0 1 0 P PImcm Imma ( 2 3 )

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39 The resulting lattice parameters in Imma are 2a, a and a In order to match the weberite lattice parameters, the space group Imcm is preferred when presenting the atomic positions of pyrochlore in the weberitelike orthorhombic lattice ( Table 2 2 ). Table 2 2 Py r ochlore ( A2B2X6X ) structure d ata presented in space group of Imcm (origin at B ) .40 Atoms Wyckoff position Site symmetry Atomic position x y z A 4b 2/m 0 0.5 0 4c 2/m 0.25 0.25 0.25 B 4a 2/m 0 0 0 4d 2/m 0.25 0.75 0.25 X 4e mm2 0.5 x+0.25 0.25 4e mm2 0 x 0.25 16j 1 x 0.125 0.125 x+0.125 X' 4e mm2 0.25 0.375 0 The x (0.3125 0.375) is the oxygen parameter inside A2B2 tetrahedral site. It is easy to recognize weberite and distinguish the three structures from powder diffra ction. As it is well known, in Cu K o, the five fluorite characteristic peaks are (111), (200), (220), (311) and (222). The (111) reflection is at o with the highest intensity. In pyrochlore, owing to the doubling of the lattice parameter with respect to fluorite, the five fluorite peaks become (222), ( 400), (440), (622) and (444). The appearance of several weak reflections especially the (111) peak o is a major difference between the XRD patterns of fluorite and pyrochlore. In orthorhombic weberite, the five fluorite peaks are split, for example, the most intense (111)f or (222)p are split into (022)w and (220)w. There are several more reflections in weberite, which are systematic absences in pyrochlore, for example, (101)w and (020)w (corresponding to (200)p). Details on the XRD reflection for fluorite, pyrochlore, and

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40 weberite are listed in Table 2 3 For space reasons, only reflections up to (222)f are presented. Table 2 3 XRD reflections for fluorite, pyrochlore and weberite.40 XRD reflections hkl (Fluorite) hkl (Pyrochlore) hkl (Weberite) Corresponding Pyrochlore plane 1 1 1 0 1 1 1 1 1 1 0 1 2 0 0 0 2 0 0 2 0 2 2 0 0 0 2 2 0 2 1 2 1 2 2 0 2 0 0 2 0 2 3 1 1 1 1 2 3 1 1 2 1 1 3 1 1 0 3 1 1 3 1 1 1 1 2 2 2 0 2 2 2 2 2 2 2 0 2 2 2 2 0 0 4 0 0 2 0 2 4 0 0 0 4 0 0 4 0 3 3 1 0 1 3 3 1 3 1 3 2 3 3 1 2 3 1 3 3 1 1 0 3 4 0 2 2 2 2 4 2 0 3 0 1 4 0 2 1 4 1 2 4 0 1 2 3 4 2 2 0 4 2 2 4 2 3 2 1 4 2 2 2 4 0 2 4 2 3 3 3 0 3 3 3 3 3 5 1 1 2 1 3 5 1 1 3 1 2 5 1 1 0 5 1 1 5 1 2 2 0 4 4 0 0 0 4 4 0 4 2 4 2 4 4 0 4 0 0 4 0 4 Table 2 3 XRD reflections for fluorite, pyrochlore and weberite (Continued).40

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41 XRD reflections hkl (Fluorite) hkl (Pyrochlore) hkl (Weberite) Corresponding Pyrochlore plane 5 3 1 1 1 4 5 1 3 2 3 3 5 3 1 1 5 2 3 5 1 3 3 2 5 3 1 2 5 1 3 5 1 4 1 1 5 1 3 4 4 2 0 2 4 4 2 4 1 4 3 4 4 2 3 4 1 4 4 2 4 2 0 4 2 4 3 0 3 6 0 0 0 6 0 0 6 0 6 2 0 2 0 4 6 0 2 3 2 3 6 2 0 4 0 2 6 0 2 1 6 1 2 6 0 5 3 3 1 3 4 5 3 3 0 5 3 3 5 3 4 3 1 5 3 3 3 1 1 6 2 2 2 2 4 6 2 2 0 6 2 2 6 2 4 2 2 6 2 2 2 6 0 2 6 2 2 2 2 4 4 4 0 4 4 4 4 4 4 4 0 4 4 4 It is important to recall that in fluorites, each anion is at the center of the cationic tetrahedra ( A4X ). The arrangement of A and B leads to different cation tetrahedra: AB3, A3B and A2B2 in weberites and A4, B4 and A2B2 in pyrochlores. The reason for the formation of different cation tetrahedra is that weberites and pyrochlores are different in their stacking two neighboring AB3 and A3B layers, though generally they follow the pattern of cubic close packed cation layers. The three nearest neighbor metal atoms in these layers form pseudo equilateral triangles. The distribution of A and B cations in AB3 layers will lead to 2 types of tri angles: AB2 and B3. The cations in the following A3B layer lie above the centers of these triangles. If an AB3 layer is a reference, there are

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42 a /2 along [100]w or [101]P displacement in the above A3B layer between weberite and pyrochlore. As a result in the A3B layer, A cations are above the center of AB2 triangles and B cations are above B3 triangles in pyrochlore, while in weberite, 2/3 A ( A 1 ) and all B cations are above the AB2 triangles and the remaining A cations ( A 2 ) are above B3 triangles (s ee Figure 2 13 and Figure 2 14). Therefore, these arrangements lead to two AB3, two A3B and four A2B2 in a formula unit of weberite, and in the case of pyrochlore, one A4, six A2B2, and one B4. In addition, different stacking of two neighboring AB3 and A3B layers can explain why the transformation of the pyrochlore cation sublattice into a weberite like lattice results in a different setting of the space group. (A) (B) Figure 2 13 (A) One A 3 B and AB 3 slab of weberite. (B) A 3 B and AB 3 slab of weberite showing the cationic tetrahedra. Cations connected by dotted lines are on the A3B l ayer and by grey lines are on the AB3 l ayer. The red lines (or dashed line) show cation tetrahedra. 40

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43 ( A ) (B ) Figure 2 14 (A) One A 3 B and AB 3 slab of pyrochlore. (B) A 3 B and AB 3 slab of pyrochlore showing the cationic tetrahedra. Cations connected by dotted lines are on the A3B l ayer and by grey lines are on th e AB3 l ayer. The red lines (or dashed line) show cation tetrahedra. 40 As stated before, in a formula unit, the X3 anion of weberite is located outside the cation tetrahedra and leaves two AB3 tetrahedra with a vacant center. In contrast, all anions in the pyrochlore structure are i nside the cation tetrahedra. Therefore, it can be argued that pyrochlore is more closely related to fluorite than weberite sinc e the former preserves all the anions in cation tetrahedral interstices.1,45 In weberite, it is u nderstandable that the X deficient site is more favorable in B rich tetrahedra ( AB3 than A2B2 and A3B ) because B ions have less coordination number. However, it raises the question: why there are two AB3 tetrahedra with a vacant center and the X3 is not inside the cation tetrahedra? Grey et al.45 argued that in Ca2Ta2O7 weberite, the sum of valence ( CN is the coordination number, v is the oxidation states for each ions ) in CaTa3 tetrahedra is so highly over saturated that CaTa3 cannot acco mmodate X3 An ionic structure will be stable if the sum of valence of the cations equals the charge on the anion that the cations bonded to. Actually, the highly over saturated AB3 tetrahedra occur in all weberite compounds: A2 1+B2+B3+F7, A2 2+B2 5+O7 and A2 1+B2 6+O7.

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44 The nominal sum of valence in the center of AB3 is 1.46 for A2 1+B2+B3+F7, 2.75 for A2 2+B2 5+O7, 3.13 for A2 1+B2 6+O7. Thus, anions should distort largely towards A cations to meet the required valence, which would then result in a shorter A X distance than a B X distance. However, A ions are larger and have more CN than B ions and so the A X bond length should be larger than the B X bond length. The end result is that anions cannot move towards A cations and the required valence cannot be ac hieved. By contrast, the sum of valence in the center of AB3 is under saturated, being 0.875 for A2 1+B2+B3+F7, 1.58 for A2 2+B2 5+O7 and 1.375 for A2 1+B2 6+O7. Anions are required to move towards B cations, which is favored by the bond length argument above. As for A2B2 tetrahedra, the sum of valence is 1.08 for A2 1+B2+B3+F7, 2.17 for A2 2+B2 5+O7, and 2.25 for A2 1+B2 6+O7. In this case, the sum of valence is close to the anion oxidation state. In order to check the stability of the X3 the empirical equation by Brese and O Keeffe52 is used to calculate the valence of the X3 : ) / ) exp(( b r R v Vij ij ij i ( 2 4 ) where Rij is the bondvalence parameter, rij is the bond distance and b is a constant. Three representative compounds were chosen for detailed analysis: Na1+ 2Mg2+Al3+F7, Sr2+ 2Sb5+ 2O7 and Ag1+ 2Te6+ 2O7. There is few, if any reported bond length data for Ag2B2F7. Na2MgAlF7 was chosen since it is the aristotype of the weberite compounds. The rij of Na1+ 2Mg2+Al3+F7 is from Knop et al.53 based on single crystal XRD. Sr2+ 2Sb5+ 2O7 was chosen because it is a stable weberite even under high pressure and neutron diffraction data is available.5455 As for A2 1+B2 6+O7 compounds, only Ag2Te2O7 crystal structure has been reported.56 Table 2 4 lists the detailed valence information including all three anion types as well as cations by the empirical equation above using

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45 the bondvalence parameters52,57 and the bond lengths ( rij) from literature. The valence of X3 is close to its oxidation state in these compounds. Table 2 4 Examples of bond valence sum for anions and cations by Brese and O Keeffe ( rij is the bond distance, vij is the bond valence. ) Na2MgAlF7 X(1) in A 3 B tetrahedra X(2) in A 2 B 2 tetrahedra X(3) outside the AB 3 tetrahedra bonds rij () vij ij bonds rij () vij ij bonds rij () vij ij Al F 1.825 0.469 0.972 Mg F 1.960 0.360 1.022 Mg F 1.951 0.368 0.866 Na2 F 2.211 0.236 Al F 1.793 0.512 Mg F 1.951 0.368 Na1 F 2.423 0.133 Na2 F 2.549 0.095 Na2 F 2.689 0.065 Na1 F 2.423 0.133 Na1 F 2.749 0.055 Na2 F 2.689 0.065 Na(1)1+: ij =0.779; Na(2)1+: ij = 0.981; Mg2+: ij = 2.17; Al3+: ij = 2.89 Sr2Sb2O7 X(1) in A 3 B tetrahedra X(2) in A 2 B 2 tetrahedra X(3) outside the AB 3 tetrahedra bonds r ij () v ij ij bonds r ij () v ij ij bonds r ij () v ij ij Sb2 O 1.922 1.056 2.280 Sb1 O 1.971 0.926 2.151 Sb1 F 2.005 0.843 1.963 Sr2 O 2.363 0.515 Sb2 O 2.202 0.512 Sb1 F 2.005 0.843 Sr1 O 2.502 0.354 Sr1 O 2.833 0.145 Sr2 F 2.850 0.138 Sr1 O 2.502 0.354 Sr2 O 2.599 0.273 Sr2 F 2.850 0.138 Sr(1)2+: ij =1.996; Sr(2)2+: ij = 2.40; Sb(1)5+: ij = 5.39; Sb(2)5+: ij = 5.34 Ag2Te2O7 X(1) in A3B tetrahedra X(2) in A2B2 tetrahedra X(3) outside the AB3 tetrahedra bonds r ij () v ij ij bonds r ij () v ij ij bonds r ij () v ij ij Te2 O 1.825 1.281 1.864 Ag1 O 2.806 0.067 2.041 Ag2 O 2.806 0.067 1.983 Ag2 O 2.388 0.207 Ag2 O 2.549 0.134 Ag2 O 2.806 0.067 Ag1 O 2.465 0.168 Te1 O 1.997 0.806 Te1 O 1.946 0.925 Ag1 O 2.465 0.168 Te2 O 1.905 1.034 Te1 O 1.946 0.925 Ag(1)1+: ij = 0.939; Ag(2)1+: ij = 1.084; Te(1)6+: ij = 5.785; Te(2)6+: ij = 5.983. Another significant difference is the formation of BX6 networks. All of the anions in weberites participate in the formation of BX6 octahedra but only 6/7 of the anions in pyrochlores do so The BX6 octahedral network in both structures is fairly rigid. Therefore, in order to maintain the octahedral network, it is difficult for the weberite to form vacancies at anion sites. By cont rast, the pyrochlore structure tolerates X deficiency or paired A and X deficiencies relatively easily. Examples of such pyrochlore oxides are Bi1.5Zn0.92Nb1.5O6.92 and Tl2B2O6 ( B = Nb Ta and U ), Tl2Os2O7x and

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46 Pb2Os2O7x.6,14,58 In addition, the substi tution of small amounts of oxygen by Fmay prevent the formation of weberites. For example, Ca2Sb2O7 pyrochlore transforms into weberite irreversibly above 973 K but CaNaSb2O6F and Ca1.56Sb2O6.37F0.44 pyrochlores are stable.5960 2.1.3 Weberitelike Structures The weberite structures show a wide variety of different modifications including monoclinic and trigonal variants. Grey et al.45 proposed the use of the nomenclature of the International Mineralogical Association Commission New Minerals and Mineral Names (IMA CNMMN), which was initially approved for zirconolite CaZrTi2O7.61 As discussed above, the basic building unit is a slab formed by one A3B and one AB3 layers. The differences between weberites are the crystal system and the number of slabs ( N ) in a unit cell. A notation which combines N and the first letter crystal system is used to indicate different weberites. For example, the notation of the classic orthorhombic weberite is 2 O because it has two slabs in a unit cell. The reported weberites include 2O 2M 3T, 4M 5M 6M 6T, 7M and 8O (NaCu)Cu2F7 (or NaCu3F7, space group C2/c ) and ( Ca0.5Ln1.5)(Ca0.5Sb1.5)O7 (or CaLn1.5Sb1.5O7, space group I2/m11, Ln3+ = La3+, Pr3+, Nd3+, and Y3+) are special 2M weberites and more like pseudo2O weberites for they maintain the structural feature of 2O rather than 2M Ca2Ta2O7based compounds are important in weberite family since for N > 4, only Ca2Ta2O7based compounds have been reported. Grey and co workers45,6264 have shown that Ca2Ta2O7 compounds can crystallize into 3T, 4M 5M 6T, 6M and 7M by different doping or synthesis methods and later Ebbinghaus et al.65 also synthesized an 8O Ca2Ta2O7 single crystal using the optical floating z one method.

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47 A significant difference between 2O and non2O weberites is that the AB3 and A3B layers are parallel to the (011) planes for 2O and parallel to the (001) planes for other weberites except for NaCu3F7 and CaLn1.5Sb1.5O7 ( Ln3+ = La3+, Pr3+, Nd3+, and Y3+). The formula unit (Z) of NaCu3F7 and CaLn1.5Sb1.5O7 is also consistent with 2O weberites, 4 rather than 8, the latter the formula unit for other 2M weberites. As in section 2. 1. 2, the lattice parameters of 2O weberites are approximately a 2 a and a ( a ~ 5, the lattice parameter for fluorite). The lattice parameters of 2M weberites are nearly a a and a The [011], [100] and [011] vectors of 2O become [100], [010] and [001] of 2M The lattice parameter difference between 2M 4M 5M 6M and 7M is mainly on the caxis The lattice parameters for nM ( n = 2, 4, 5 and 7) are approximately a a and (n a and they are nearly a a and 3 a for 6M .45,6264 The 8O weberite is closely related to monoclinic variant rather than 2O in both the orientation of AB3 and A3B layers and the lattice parameters. The lattice parameters are nearly a a and 4 a As for 3T, the [100], [ 0.5, 0.5, 0.5] and [012] vectors in 2O are transformed into the basal vectors. The resulting lattice parameters are approximately a a and 2 a The relationship of 2O 2M and 3T weberites is shown in Figure 2 15. Meanwhile, the lattice parameters of 6T are approximately a a and 4 a just double the length of the basal vector in caxis. For 2O weberites, there are two special types in which the body center symmetry is lost. The first case is when Cu2+ is introduced into Na2B2+B3+F7 at B 1 sites such as Na2CuCrF7 and Na2CuInF7.6667 T he CuF6 octahedra are elongated perpendicular to the B 1 chains which leads to the lowering of symmetry while maintaining the orthorhombic lattice. The space group is reduced to Pmnb a subgroup of Imma .1

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48 (A) (B) Figure 2 15 ( A ) Relationship between 2O 2M and 3T weberites (origin at A2 site); large spheres are A ions and small spheres are B ions; blue solid lines are the multiple unit cells of 2O red dotted lines are the unit cell of 2M and green dashed lines are the unit cell of 3T. ( B ) (001) plane of 3T (green dashed lines) and 2M (red dotted lines, also indicating (011) of 2O ). Another case of losing I centring symmetry happens when the ionic radius of B 2 is larger than that of B 1. In a classic 2O weberite structure, the ionic radius of B 2 is equal or smaller than that of B 1. When a larger B 2 ion appears in a weberite compound, the anions, which are shared by two B 1 octahedra neighbours distort toward B 2 ions. As a result, the A 2 ions cannot hold 8coordination and change to 7 coordination. The B 2 ion keeps octahedral coordination with a seventh anion relatively close to it. As in the case of Na2NiInF7, the distance between the distorted anion and B 2 ( In3+) is only 1.3 times larger than the shortest In F bond length in B 2 octahedra.68 In a 2O weberite structure, the ratio of the two distances is higher, such as 1.97 in Na2MgAlF7 or 1.83 in Ca2Os2O7.58,69 The distortion of anion excludes the I centering of

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49 the structure and results in the space group Pnmb .1 The extreme of the second case is Ln2( B, Ln)O7 (or Ln3B O7, where Ln3+ is a rare earth element, and B is Os5+, Re5+, Ru5+, Re5+, Mo5+, Ir5+, Sb5+, Nb5+ or Ta5+) which is covered in detail in section 2.2. 2.1.4 Stability Field Both pyrochlores and weberites have BX6 octahedral networks. Due to the fact that B 2 octahedra have two unpaired vertices, the BX6 octahedral network in weberite is typically less compact. Therefore, weberite has more potential to permit larger radius of A ions. Figure 2 16 shows RA vs. RB diagram for 159 pyrochlore oxides and 131 weberite compounds ( 83 weberite fluorides and 48 weberite oxides, see Table 2 5 and Table 2 6 which are listed at the end of the chapter ). The 159 pyrochlore oxides are taken from two reviews .14,39 Figure 2 16 indicates that the majority of pyrochlores have RA ranging from 0.97 to 1.13 while most weberites have RA value from 1.10 to 1.30 Weberite Ba2U2O7 has the highest RA 1.42 .27,70 This clearly shows that larger RA prefers the formation of the w eberite.71 The ratio of RA/ RB for the weberite is between 1.5 and 2. The two end members are Cd2Sb2O7 and Ag2Te2O7. However, the range of RA/ RB for weberite greatly overlaps with the stability field for pyrochlore, 1.46 ~ 1.8 for A2 3+B2 4+O7 and 1.4 ~ 2.2 for A2 2+B2 5+O7.14 Therefore, ionic radius ratio is not the only determining factor in the structural stability. the formation of weberites is closely relat ed to the covalent character of the bonds .7275 Weller et al.74 A B to picture the stability field of the weberite, but their study only included a limited number of compounds. Lopatin et al.73,76 successfully A and RA/ RB B and RA/ RB to

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50 determine the different regions of the weberite and the layered perovskite. They chose Allred Rochow77 electronegativities (which were completed by Little and Jones78) because AllredRochow ele ctronegativities are more precise when measuring the degree of covalent character of the bonds. Sych et al.72 introduced RA/ RB versus relative ionicity of A O bond, which is a ratio of the ionicity of A O bond to the sum of ionicity of A O and B O bonds. The ionicity of A O bond is calculated as ] ) ( 25 0 exp[ 12 O A O AI -( 2 5 ) They used the electronegativities for the crystall ine state calculated by Batanov.79 The advantage of relative ionicity is that it contains the information for both A O and B O bonds. Therefore, relative ionicity of A O vs. RA/ RB is used to determine the stability field in this study as shown in Figure 2 17 and Figure 2 18. Here, Allred Rochow77 and Little Jones78 electronegativities are used in calculating the ionicity. 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 0.4 0.5 0.6 0.7 0.8 RVI B( )RVIII A( ) Oxide weberite Fluorine weberite Pyrochlore Pyrochlore high pressure Fi gure 2 16. Summary of RA vs. RB for weberites (including oxide and fluorine) and pyrochlore oxides.

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51 In Figure 2 17, there is no obvious separation between weberites and pyrochlores. The reason for this may be that both A2 2+B2 5+O7 and A2 3+B2 4+O7 pyrochlore compounds are plotted. There are very few, if any, A2 3+B2 4+O7 weberites reported. Most weberites are A2 2+B2 5+O7 or (A, A)2 2+(B, B)2 5+O7 and several A2 1+B2 6+O7 ( Na2Te2O7 and Ag2Te2O7) The inclusion of A2 3+B2 4+O7, particularly high pressure phases, complicates the stability field, therefore, Figure 2 18 only contains A2 2+B2 5+O7, (A, A)2 2+(B,B)2 5+O7 compounds, Na2Te2O7 and Ag2Te2O7. Observing the plotted data in Figure 2 18 there is a clear separation between weberites and pyrochlores. The dashed line is for visual effect -above the line, it is the weberite region. Weberites prefer higher ratio of IA O/(IA O+ IB O) and higher ratio of RA/RB than pyrochlores. 1.4 1.6 1.8 2.0 2.2 2.4 0.45 0.50 0.55 0.60 0.65 0.70 RVIIIA/RVIBIA-O/ (IA-O+IB-O) Figure 2 17 Relative ionicity vs the ratio of R A /R B for w eberite oxides, weberite fluorides and pyrochlore oxides.

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52 1.4 1.6 1.8 2.0 2.2 0.40 0.45 0.50 0.55 0.60 0.65 0.70 IA-O/ (IA-O+IB-O)RVIIIA/RVIB Figure 2 18 Stability field for the w eberite oxides. It is worth mentioning four specific compounds: Cd2Sb2O7 ( RCd 2+ = 0.9 ) in the pyrochlore region, and Ca2Sb2O7, Ca2Os2O7 ( Rca 2+ = 1.12 ) and Pb2Sb2O7 ( RPb 2+ = 1.29 ) in the weberite region.27 A high pressure study has been performed on first three compounds to investigate the transformation of pyrochlore and weberite phase s. Cd2Sb2O7 can form a metastable phase of weberite, which can be fully converted to pyrochlore under high pressure. Ca2Sb2O7 weberite is more stable. The same high pressure condition only results in mixed phases of Ca2Sb2O7 pyrochlore and weberite.54 Pyrochlore Ca2Sb2O7 is metastable with respect to temperature and requires mild reaction condition for synthesis .71 Meanwhile, Ca2Os2O7 weberite is stable and the synthesis of pyrochlore Ca2Os2O7 under pressure leads to calcium deficient Ca1.7Os2O7.58,74 The reported cryst al structure of Pb2Sb2O7 also strongly depends on the synthesis conditions. Low temperature firing or wet chemical synthesis resulted in a

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53 cubic pyrochlore phase. The cubic phase was metastable and readily transformed into weberite or rhombohedrally dist orted pyrochlore.12,71 Alt hough these four compounds can form a metastable phase depending on the processing, they are presented here in the regions of their stable phases in the stability field. It is worth noting that though ionic radii ratio and bond ionicity are two major factors, there may be some additional crystallochemical characteristics or parameters that play a role in determining the prevalence of weberite over pyrochlore or vice versa 2.2 Weberitetype Ln3NbO7 As mentioned above, there are two types of B O6 octahedra: corner linked B 1O6 and self isolated B 2O6 ( Figure 2 5 ). T he chains of B 1O6 octahedra are oriented in an anti phase motif ( Figure 2 19 (A)). In this case, the ionic radius of B 2 is equal or smaller than that of B 1. When a larger B 2 ion appears in a weberite compound, the anions which are shared by two B 1 octahedra neighbors, distort toward the B 2 ions. As a result, the A 2 ions cannot hold 8 coordination and change to 7 coordination. The B 2 ion keeps octahedral coordination with a seventh anion relatively close to it a s in the case of Na2NiInF7 ( Figure 2 19 (B) ) .68 One extreme case of Na2NiInF7 is Ln2( B0.5Ln0.5)2O7 (or Ln3B O7, where B is Os5+, Re5+, Ru5+, Re5+, Mo5+, Ir5+, Sb5+, Nb5+, or Ta5+) .1519,2122,37,80101 In the above case, B 2 ions are the same as A ions. As a result, the B 2 sites and A 2 sites are indistinguishable. T he adjacent B O6 chains are in phase and the Ln3+ ions between the two chains (account for 2/3 of the total Ln3+ ions ) result in 7 coordinatio n ( Figure 2 19 (C)). Due to the fact that this type of structure does not maintain the 3D BO6 octahedral network, it is considered a weberitetype structure rat her than the weberite structure. In literature, it is also reported as a La3NbO7 type structure.

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54 ( A ) ( B ) ( C ) Figure 2 19 (A)Weberite A VIII 2 B VI 2 O 7 (B) Na 2 NiInF 7 (when ionic radius of B 1 is smaller than B 2 ), the dashed line represents the distance between the B 2 cation and the relatively close seventh anion. (C) Ln 3 B O 7 Ln3B O7 compounds maintain similar close packed cation layers as in weberite and fluorite. However, due to the large ionic radius of Ln2, the cationic sublattice in Ln3B O7 is distorted. The f irst layer is composed of Ln3+ ions, half of which are 8coordinated Ln1 ions and half are 7coordinated Ln2 ions ( Figure 2 20) In the second layer, there is an equivalent number of Ln2 and B ions (A) (B) Figure 2 20 Closed packed cation layers (A) Ln layers (B) Ln 2 B 2 In addition, there is another way to describe the structure in a layered configuration. The structure has an arrangement of B O6LnO8 layers (much like

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55 weberites see Figure 2 9 (A) ), but a different cation configuration with VII coordination between the layers ( Figure 2 21). The 7coordinated Ln3+ ions account for 2/3 of the total Ln3+ ions. Figure 2 21 Weberite type Ln 3 B O 7 viewing in approximatly [0 01] direction. The layers which are composed of parallel LnO8 lines and B O6 lines are parallel to (001) plane. Between the layers are Ln with 7 coordination number. 2.3 Interesting Properties and Potential Applications For fluorinebased weberites, the magnetic properties attract most of the attention. The triangular network formed by B2+ and B3+ cations in the HTB like planes generally support three different magnetically ordered systems: 1. the diamagnet ic B3+ ions separate linear chains of paramagnetic B2+ ions, for example, antiferromagnetic Na2NiAlF7, Na2FeAlF7 and Na2NiInF7;68,102 2. both B2+ and B3+ are paramagnetic ions, like ferromagnetic Na2NiFeF7 and antiferromagnetic Na2NiCrF7;44,68,102103

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56 3. diamagnetic B2+ forming linear chains which isolate the paramagnetic B3+ such as antiferromagnetic Na2MgFeF7.104 As for weberite oxide, various properties have been investigated including the photocatalytic properties,2225 the resistivity of Ca2Os2O7 w eberite,58 magnetic properties ,21,88,95 ferroelectric properties ,1112 and dielectric properties .64,86,105 The interest in the properties is first due to the fact that the weberite st ructure is considered more favo rable for the realization of a ferroelect ric state than the pyrochlore structure.11 The Sb based compounds are the most investigated weberites for ferroelectric properties. More than t en years ago, Cava et al.105 found out the temperature coefficients of the capacitance ( TCC) of Ca2Ta2O7 Ca2Nb2O7 system can be close to zero. A series of investigations on Ca2Ta2O7based weberites have followed.45,62 65 This section is focus ed on the ferroelectric properties and dielectric properties of weberite oxides. 2.3.1 Ferroelectric Pr o perties A2Sb2O7 ( A = C a2+, Pb2+ and Sr2+) are perhaps the most studied weberites due to their ferroelectric properties. Second harmonic generation and heat capacity measurements indicated a possible ferroelectric phase transition in Pb2Sb2O7. Dielectric constants showed a thermal hysteresis around the Curie temperature ( Tc) in Pb2Sb2O7.11,106 Single crystal Xray and powder neutron diffraction were performed in detailed crystallographic studies .11,13 Below Tc, there is a slight distortion f rom a centrosymmetric structure and ionic displacements cause spontaneous polarization in this structure. The results indicated a noncentrosymmetric (space group I2cm ) to centrosymmetric (space group Imam another setting of Imma ) phase transition.1113 Tc

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57 depends on the A cation: 510 K for Pb2Sb2O7, 110 K for Ca2Sb2O7, and 90 K for Sr2Sb2O7. The substitution of Ca by Pb in Ca2Sb2O7 causes a shift of Tc towards a higher temperature: 200 K for CaPbSb2O7 weberite. Therefore, the A sublattice seems more likely to be the ferroelectrically active one. It is worth noting that Pb2Sb2O7 can also form rhombohedrally distorted pyrochlore.71 The pyrochlore phase is paraelectric even at room temperature. Actually, Pb2Sb2O7 weberite has a higher Tc than most Pb b ased pyrochlores. These facts may serve as evidence that the weberite structure is more suitable for the appearance of ferroelectric state .11,39 As will discussed in Chapter 6, there is net dipole in weberitetype Gd3NbO7 indicating possible ferroelectric behavior. 2.3.2 Dielectric Properties One of the most interesting dielectric properties of Ca2Ta2O7 is that temperature coefficient of the capacitance ( TC C ) is 0 when mixing with 18 mol% of Ca2Nb2O7, meeting the requirement for the application of microwave dielectrics .105 The (1 x)Ca2Ta2O7 xCa2Nb2O7 system can form solid solution up to x ~ 15mol%. TC C ~ 0 can be easily understood because TC C is negative for Ca2Ta2O7 ( 444 M K1 at room temperature (RT) ) and positive for Ca2Nb2O7 (231 M K1 at RT ). As will be discussed in Chapter 9, the TC C of Ln2LnNbO7 changes from negative to positive, depending on the average ionic radius of Ln3+. It may point to the potential avenue controlling TCC. The dielectric constants of 3T Ca1.6N d0.4Ta1.6Zr0.4O7, 5M Ca2Ta1.8Nb0.2O7 and 7M Ca2Ta1.9Nb0.1O7 are approximately stable (18 ~ 19) from 100 kHz up to 5 GHz and reach maximum (22, 24.5 and 26.1, respectively) at about 8 GHz. The dielectric constant is comparable for some important microwave dielectrics, like BaMg1/3Ta2/3O3 (~

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58 24).107 However, the problem with these systems is that they have low quality factors ( Q ~ 200) for technical applications .64 It is also potential to tailor the dielectric properties by structural distortion. The 8O Ca2Ta2O7, which is synthesized by optical floating zone from melting 3T Ca2Ta2O7 powder, have a relative high dielectric constant (~ 60) at room temperature.65 The high dielectric constant may result from a net dipole created by the off center Ta5+ in the TaO6 octahedra of the Ca3Ta layers. As for Ln3NbO7, Gd3NbO7 has a loose structure and may be a polar substance.38,108 The dielectric properties of Gd3NbO7 at 1 kHz were investigated and a dielectric relaxation was observed.38 As will be discussed in details in the following chapters, La3NbO7 and Nd3NbO7 compounds also exhibit dielectric relaxation. The off center shifts of Ln3+ and Nb5+ within their corresponding polyhedra play an important role in the dielectric relaxation behavior of Ln3NbO7. 2.4 Polarization Mechanisms When an external electric field is applied to insulators and dielectric materials, th e re is short range movement or a limited rearrangement of charge carriers, namely polarization. The polarization (P) is determined by the dipole moments (): Nq N P ( 2 6 ) where N is the number of the dipole mo the charges separating distance. High polarization results in a large dielectric permittivity (r): loc rE P 01 ( 2 7 ) where Eloc is the local electric field. In a solid, Eloc is different from the external field b ecause polarization of the surrounding can affect Eloc.

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59 Another important parameter, the polarizability of an atom or ion is defined by locNEP ( 2 8 ) In a solid with a cubic lattice, El oc can be calculated by ) 2 + ( 3 =r loc E E ( 2 9 ) Then, the permittivity can be calculated using by the Clausius Mossotti equation: ) 3 /( 1 / 1 '0 0 N N r ( 2 10) where 0 is the permittivity of free space. The importance of the Clausius Mossotti equation is that it links the macroscopic r and the microscopic polarization phenomena, i.e There are four main polarization mechanisms (only considering linear dielectrics): space charge polarization, dipolar polarization, ionic polarization, and electronic polarization (see Figure 2 22). Space charge polarization, which can respond up to about 106 Hz, is a spatial distribution of charge centers over the microstructure because charge carriers are obstructed at a potential barrier such as a grain boundary or phase boundary after limited transport. Dipolar polarization is the preferential occupation of equilibrium positions with a probability depending on an external field. In other words, randomly oriented dipoles are rotated and aligned under an external field, giving rise to a net dipole. It can respond to frequencies up to ~108 to 1011 Hz. Ionic polarization involves relative displacement of the cation and anion sublattices. It causes shifts of both the center of negative charge and the center of positive charge, resulting in ionic dip oles. It is active up to ~1013 Hz. Electronic polarization (or atomic polarization) occurs when the electron clouds become displaced by the external field relative to the

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60 nucleus. It can respond to very high frequencies ~1015 Hz. The sum of the contribution s is shown in Figure 2 23. Figure 2 22 Four main polarization mechanisms. Left is unpolarized state and right is polarized state. (Diagram from Moulson and Herbert 109 ).

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61 Both electronic polarization and ionic polarization can be simulated by a spring model in which the displaced charge is bound elastically to an equilibrium position. When the frequency of the applied external field ( a) is close to or at 0 (~1013 Hz for ionic polarization and ~1015 for electronic polarization), the vibrational system is at resonance ( Figure 2 23). 110 Figure 2 23 Real and imaginary parts of permittivity as a function of frequenc y, showing the contribution from the four mechanisms. Space charge and dipolar polarizations are relaxation processes while the rest are reso nance processes. (Diagram from Moulson and Herbert 109 ).

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62 The dipolar polarization mechanism is different from electronic and ionic polarization since the former relates to the occupational probability of several equilibrium sites. The probability (p) of an ion making a jump is dependent on the depth of the energy well ( Hm) and temperature (T in Kelvin): ) exp( kT H K pm ( 2 11) where K is a constant, k is the Boltzmanns constant. Without an external electric field, the energy of both sites are equivalent, resulting in an equal occupational probability. Under the applied field (E), the energy well of one position (named A) is HmdipE and the energy well of the second position (named B) becomes Hm+ dipE, where dip is the dipole moment. Then, the jump probability from A to B differs from the probability from B to A. The contribution of the dipolar mechanism to dielectric permittivity under static field is 0 2 2 '4 ) ( 1 kT N zes dip r ( 2 12) where N is the number of dipoles, s is the dist ance between the two sites. It is important to note that dielectric permittivity from the dipolar mechanism decreases with increasing temperature due to thermal randomization. It is worth noting that due to the ion jumping (or dipole reorientation), dipolar polarization takes a longer time to reach its static value Ps when compared to electronic and ionic polarization. Then dielectric relaxation occurs, which is delayed response to an external field. The average residence time ( ) of an atom or ion at any given site (or the relaxation time), is temperaturedependent: ) exp( 10kT Ea ( 2 13)

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63 where 0 is the attempt jump frequency and Ea is the activation energy. Therefore, the r increases with temperature because of the lowering of When the temperature is high enough, r begins to decrease with increasing temperature due to thermal randomization. The imaginary part of the permittivity ( r) undergoes a peak near the temperature (T( m)) where r reaches the maximum. The tempera ture (Tm) at which the peak occurs is related to the frequency of the applied electric field through the Arrhenius relationship: ) exp(0 m akT E ( 2 14) where v is the frequency of the applied field and v0 is the attempt jump frequency. The above equation will be used in Chapter 5 to calculate v0 and the activation energy for dielectric relaxation. 2.5 Definitions of Ferroelectric and Antiferroelectric Ferroelectricity is the occurrence of spontaneous polariza tion that can be reoriented (or reversed) by a realizable electric field. In ferroelectric, the directions of spontaneous polarization are parallel to each other in a domain. By contrast, anti polar crystals have antiparallel orientation to lower the di poledipole interaction energy.111 They can be considered as being composed of two sublattices polarized spontaneously in antiparallel directions. If a ferroelectric phase can be induced by an external field, the antipolar phases are called antiferroelec tric. The free energy of the antipolar dipole arrangement is comparable to that of ferroelectric.112 Figure 2 24 shows the schematic representation of ferroelectric, antipolar, and antiferroelectric phases below the Curie temperature (Tc) with or without an external field.

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64 Figure 2 24 A schematic representation of ferroelectric, antipolar, and antiferroelectric, and their responses under an external field. T c is the Curie temperature. 113 2.6 Phase Transitions A phase transition can occur when there is an external stress such as a change in temperature or pressure. It is defined as an event which entails a discontinuous (sudden) change of at least one property of a material,114 such as dielectric properties, which will be discussed extensively in this thesis. Commonly, structural changes are involved in the phase transition. A first order transition happens when the first derivatives (entropy S and volume V) of the free enthalpy (G = U + pV TS) experiences discontinuous change, i.e. one of the second derivatives of G experiences a discontinuity but S and V are continuous. The second derivatives are the specific heat at constant pressure divided T < TcT < Tc E Ferroelectric Antipolar Antiferroelectric

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65 by temperature ( Cp/T) and the multiplication of the volume and the compressibility at constant temperature ( Vk). The main difference is that the first order transition involves the latent heat and the secondorder is absent of the latent heat. The recipr ocal of dielectric susceptibility behaves differently near a first order ferroelectric transition and a secondorder one ( Figure 2 25). Also, near a secondorder phase transition, there tends to be a shape anomaly in the heat capacity vs. temperature pl ot. Temperature (K)1/Tc Temperature (K)1/Tc (A) (B) Figure 2 25 For ferroelectric materials (A) the reciprocal susceptibility near a first order ferroelectric transition; (B) the reciprocal susceptibility near a secondorder transition. 113 Solid state phase transitions can be categorized into three types: reconstructive phase transitions, displacive phase transitions, and order disorder transitions. Reconstructive phase transitions are always first order transitions. They involve the broken and reforming chemical bonds and considerable atomic movements. Order disorder transitions are usually secondorder. Order disorder transitions happen when the atoms that are perfectly ordered on crystallographically nonequivalent sites become stati stically distributed on an crystallographically equivalent site. Displacive phase transitions implicate limited atomic shifts and no primary chemical bond broken. The transitions have only straightforward changes in symmetry: e.g. symmetry operations

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66 are gained or lost.114 For example, the transitions in BaTO3 from orthorhombic to tetragonal and to cubic are displacive phase transitions. 2.7 Second Harmonic Generation When an electromagnetic wave propagates in a material, its electric field causes electric p olarization. Materials with a noncentrosymmetric crystal structure can have a nonlinear susceptibility (2): ...2 2 1 0 E E P ( 2 14) where P is the polarization and E is the electric field of the wave. If E is a sinusoidal function, then ... sin sin2 2 0 2 0 1 0 t E t E P ( 2 15) Since sin2( t) = 1 cos(2 t), the polarization has a component at twice of the frequency of E as shown below: ... 2 cos 1 2 1 sin2 0 2 0 1 0t E t E P ( 2 16) This process is called secondharmonic generation (SHG) or frequency doubling, where an input wave generates another wave with twice the optical frequency in the medium.115116 The nonlinearity (2) can only occur in noncentrosymmetric material. In Chapter 6 and 7, the SHG measurements were used to test whether the material is centrosymmetric or not. 2.8 Normal Mode Determination The nuclear site group anal ysis allows the determination of the infrared (IR) and Raman active modes of each symmetry without detailed analysis of the symmetry elements in the unit cell. For crystals, the only information needed is the space group and the Wyckoff position of each atom in the unit cell. The table A, table B, and table E provided by Rosseau et al.117 have sufficient information to determine the selection

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67 rules. Table 2 7 presents a simple example of the mode determination in CeO2. CeO2 has a fluorite structure with space group m 3 Fm with Ce at 4 a site and O at 8c site. The table A provides the site symmetries based on the space group and the Wyckoff position. From the table 32A (32 is the point group number), the site symmetry of Ce and O is Oh and Td. The table B sp ecifies lattice modes for each symmetry and the table E presents the selection rule of each mode. From the table 32B, the representation of the symmetry Oh is F1u and that of Td is F1u + F2g. The table 32E indicates F1u is IR active and acoustic mode and F2g is Raman active. The irreducible representation is calculated by the sum of Raman active modes and IR active modes minus the acoustic modes, in case of CeO2, = 1 F1u (IR) + 1 F2g (R). The normal determination i s more complex for Ln3NbO7 and will prese nt in Chapter 8 and Appendix B Table 2 5 List of A2B2F7 weberites Space group Z Lattice parameters RA () RB () Properties investigated a () b () c () 2O Na2MgCrF7 117 Imma 4 7.39 7.15 10.20 1.18 0.67 2O Na 2 MgGaF 7 117 Imma 4 7.42 7.16 10.16 1.18 0.67 2O Na 2 MgScF 7 117 Imma 4 7.55 7.34 10.43 1.18 0.73 2O Na2MgVF7 117 Imma 4 7.45 7.24 10.30 1.18 0.68 2O Na 2 NiFeF 7 43,102,118 Imma 4 7.2338 (3) 10.3050 (3) 7.4529 (3) 1.18 0.62 Magnetic 2O Na2NiAlF7 101,119 Imma 4 7.31 (2) 7.07 (2) 10.04 (2) 1.18 0.60 Magnetic 2O Na 2 NiCoF 7 118119 Imma 4 7.40 (2) 7.20 (2) 10.24 (2) 1.18 0.62 Magnetic

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68 Table 2 5 List of A2B2F7 weberites (Continued). Space group Z Lattice parameters RA () RB () Properties investigated a () b () c () 2O Na2NiCrF7 120 121 Imma 4 7.183(1) 10.224(1) 7.414(1) 1.18 0.65 Magnetic 2O Na 2 CoGaF 7 122 Imma 4 7.3011(6) 10.5436(9) 7.3845(7) 1.18 0.65 2O Na2CoInF7 122 Imma 4 7.4032(6) 10.3892(8) 7.5302(9) 1.18 0.75 2O Na 2 CoScF 7 122 Imma 4 7.431(1) 10.546(1) 7.544(1) 1.18 0.72 2O Na2MnTIF7 122 Imma 4 7.371(1) 10.369(3) 7.603(1) 1.18 0.67 2O Na2NiGaF7 122123 Imma 4 7.1805 (7) 10.2433 (9) 7.4256 (7) 1.18 0.66 2O Na2NiInF7 122 Imma 4 7.3632 (5) 10.3490 (7) 7.5274 (6) 1.18 0.75 2O Na2NiScF7 122 Imma 4 7.3116 (7) 10.3278 (9) 7.4779 (7) 1.18 0.72 2O Na2MgTIF7 122 Imma 4 7.3756 (8) 10.418 (1) 7.5496 (8) 1.18 0. 70 2O Na 2 ZnFeF 7 122 Imma 4 7.281(1) 10.446(2) 7.459(1) 1.18 0.65 Na2ZnGaF7 122 Imma 4 7.2494 (7) 10.3283 (8) 7.3582 (6) 1.18 0.68 2O Na2ZnInF7 122 Imma 4 7.4077(6) 10.4759(9) 7.5732(6) 1.18 0.77 2O Na2ZnTIF7 122 Imma 4 7.338(1) 10.300(2) 7.539(1) 1.18 0.71 2O Na 2 MgFeF 7 103,117 Imma 4 7.49 7.25 10.26 1.18 0.64 Magnetic 2O Na2MgAlF7 41,52 Imma 4 7.501(1) 9.968(2) 7.285(1) 1.18 0.62 2O Na2ZnAlF7 124 Imma 4 7.092(1) 10.092(1) 7.337(1) 1.18 0.64 2O Ag 2 CuMnF 7 122 Imma 4 7.5006(9) 10.5025(9) 7.6452(8) 1.28 0.66 2O Ag2CoAlF7 125 Imma 4 7.252 10.16 7.601 1.28 0.60 2O Ag 2 CoGaF 7 125 Imma 4 7.313 10.35 7.678 1.28 0.66 2O Ag2CoInF7 125 Imma 4 7.544 10.72 7.851 1.28 0.75 2O Ag 2 CoScF 7 125 Imma 4 7.497 10.64 7.789 1.28 0.72 2O Ag2MnAlF7 125 Imma 4 7.360 10.32 7.601 1.28 0.60 2O Ag 2 MnGaF 7 125 Imma 4 7.465 10.62 7.787 1.28 0.65 2O Ag2MnScF7 125 Imma 4 7.634 10.78 7.802 1.28 0.71 2O Ag2NiGaF7 125 Imma 4 7.255 10.28 7.650 1.28 0.66 2O Ag2NiScF7 125 Imma 4 7.463 10.54 7.771 1.28 0.72 2O Ag2MgAlF7 125 Imma 4 7.197 10.01 7.571 1.28 0.62 2O Ag2MgGaF7 125 Imma 4 7.257 10.21 7.664 1.28 0.67 2O Ag 2 MgInF 7 125 Imma 4 7.495 10.62 7.832 1.28 0.76

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69 Table 2 5 List of A2B2F7 weberites (Continued). Space group Z Lattice parameters RA () RB () Properties investigated a () b () c () 2O Ag2MgScF7 125 Imma 4 7.427 10.52 7.782 1.28 0.73 2O Ag2CuAlF7 125 Imma 4 7.109 10.22 7.684 1.28 0.62 2O Ag 2 CuGaF 7 125 Imma 4 7.200 10.34 7.755 1.28 0.68 2O Ag2ZnAlF7 125 Imma 4 7.237 10.14 7.590 1.28 0.64 2O Ag 2 ZnGaF 7 125 Imma 4 7.303 10.32 7.688 1.28 0.68 2O Ag2ZnInF7 125 Imma 4 7.531 10.71 7.841 1.28 0.77 2O Ag2CoCrF7 122 Imma 4 7.349(1) 10.376(1) 7.683(1) 1.28 0.65 2O Ag 2 CoFeF 7 122 Imma 4 7.3711(8) 10.437(1) 7.7145(8) 1.28 0.62 2O Ag 2 MnFeF 7 122 Imma 4 7.490(1) 10.612(2) 7.731(1) 1.28 0.61 2O Ag2MnInF7 122 Imma 4 7.6747(8) 10.856(1) 7.8641(7) 1.28 0.74 2O Ag 2 MgCrF 7 122 Imma 4 7.2746(6) 10.3128 (9) 7.7060(7) 1.28 0.67 2O Ag 2 MgFeF 7 122 Imma 4 7.3100(7) 10.335(1) 7.6972(9) 1.28 0.64 2O Ag2MgTIF7 122 Imma 4 7.2506(9) 10.362(2) 7.497(1) 1.28 0.70 2O Ag2CuCrF7 122 Imma 4 7.2103(6) 10.454(1) 7.7871(8) 1.28 0.67 2O Ag2CuFeF7 122 Imma 4 7.2435(9) 10.474(2) 7.769(1) 1.28 0.64 2O Ag2CuInF7 122 Imma 4 7.3461(6) 10.7501( 9) 7.9098(6) 1.28 0.77 2O Ag2ZnCrF7 122 Imma 4 7.3165(7) 10.362(1) 7.6877(8) 1.28 0.68 2O Ag2ZnFeF7 122 Imma 4 7.359(1) 10.409(2) 7.706(1) 1.28 0.65 2O Ag2ZnMnF7 122 Imma 4 7.408(1) 10.503(1) 7.6972(9) 1.28 0.66 2O Ag2NiAlF7 126 Imma 4 7.564(6) 7.210(6) 10.139(15 ) 1.28 0.60 Magnetic 2O Ag2NiCrF7 126 Imma 4 7.673(6) 7.305(6) 10.285(9) 1.28 0.65 Magnetic 2O Ag2NiFeF7 126 Imma 4 7.692(6) 7.345(6) 10.345(9) 1.28 0.62 Magnetic 2O Ag2NiInF7 126 Imma 4 7.822(6) 7.499(6) 10.622(9) 1.28 0.75 Magnetic 2O -II Na2CuInF7 66 Pmnb 4 7.318 10.602 7.712 1.18 0.77 Magnetic 2O -II Na 2 CuCrF 7 65,127 Pmnb 4 7.100(1) 10.338(1) 7.518(1) 1.18 0.67 2O -II Na 2 CuScF 7 124 Pmnb 4 7.260(1) 10.534(1) 7.658(1) 1.18 0.74 2O III Na2NiInF7 67 Pmnb 4 7.356 10.334 7.523 1.18 0.75 Magnetic 2O III Na2MgInF7 128 Pnma 4 10.435(1) 7.345(1) 7.533(1) 1.18 0.76 Magnetic

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70 Table 2 5 List of A2B2F7 weberites (Continued). Space group Z Lattice parameters RA () RB () Properties investigated a () b () c () o ) 2M Na2CuGaF7 66 C2/c 8 12.325 (5) 7.318 (1) 12.780 (5) 109.29 (2) 1.18 0.68 Magnetic 2M & 4M Na2CuFeF7 65,129130 C2/c 8 12.46 (1) 7.363 (8) 12.93 (1) 109.36 (7) 1.18 0.64 C2/c 1 6 12.444 (2) 7.343 (1) 24.672 (5) 99.27 (3) 3T Na2MnAlF7 122 6 7.2854(4) 17.844(1) 1.18 0.59 3T Na2MnInF7 122 6 7.6006(3) 18.617(1) 1.18 0.74 3T Na2MnScF7 122 6 7.5442(4) 18.479(1) 1.18 0.71 3T Na 2 MnGaF 7 131 P3121 6 7.421(3) 18.166(6) 1.18 0.65 3T Na 2 MnCrF 7 131 P3121 6 7.401(1) 18.091(2) 1.18 0.64 3T Na2MnVF7 132 P3121 6 7.467 18.216 1.18 0.65 3T Na2MnFeF7 118,133134 P3121 6 7.488(2) 18.257(6) 1.18 0.61 Magnetic 3T Ag2MnInF7 122 6 7.751(1) 18.838(4) 1.28 0.74 4M Na 2 CoAlF 7 134135 C2/c 16 12.378 (4) 7.210 (3) 24.019(9) 99.67 (2) 1.18 0.61 Magnetic 4M Na 2 ZnGaF 7 123 C2/c 16 12.519 7.303 24.353 99.74 1.18 0.68 4M Na 2 ZnFeF 7 123 C2/c 16 12.610 7.359 24.538 99.70 1.18 0.65 4M Na2FeVF7 136 C2/c 16 12.710 (3) 7.429 (1) 24.716 (5) 100.03 (3) 1.18 0.63 4M Na2CoVF7 136 C2/c 16 12.703 (5) 7.39 1 (3) 24.651 (5) 100.02 (3) 1.18 0.65 4M Na2FeCrF7 136 C2/c 16 12.625 (3) 7.391 (1) 24.695 (5) 99.93 (3) 1.18 0.61 4M Na 2 FeFeF 7 1,118119 C2/2 16 12.676 (3) 7.422 (1) 24.710 (5) 99.97 (3) 1.18 0.58 Magnetic 4M Na 2 CoFeF 7 118119,129,134 C2/c 16 12.622 (10) 7.360 (4) 24.516 (20) 99.71 (5) 1.18 0.62 Magnetic 4M Na2CoCrF7 134,136 C2/c 16 12.578 (3) 7.335 (1) 24.415 (5) 99.64 (3) 1.18 0.65 Magnetic 4M Na 2 FeAlF 7 119,123 C2/c 16 12.426 7.278 24.206 99.99 1.18 0.56 Magnetic Table 2 6 List of weberite oxides with the RA/RB and relative ionicity of A O bond. Type Lattice Parameters RA () RB () Properties investigated a () b () c () 2O Cd2Sb2O7 70,137 7.21 7.33 10.14 0.9 0.6

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71 Table 2 6 List of weberite oxides with the RA/RB and relative ionicity of A O bond (Continued). Lattice Parameters RA () RB () Properties investigated a () b () c () 2O Ca2Sb2O7 12,2425,137 7.28 7.44 10.18 1.12 0.6 Ferroelectric & photocatalyti c 7.3060 7.4627 10.2263 7.2900 10.2000 7.4500 2O Sr2Sb2O7 2425,53 54 7.452 7.687 10.381 1.26 0.6 Ferroelectric & photocatalyti c 7.4557(2) 10.3708(3) 7.6860(1) 7.4557 10.3708 7.6860 2O Pb2Sb2O7 12 13 7.484(1) 7.857(1) 10.426(2) 1.29 0.6 Ferroelectric 7.4774 7.8549 10.4250 2O Ca2Os2O7 57,73 7.2104(2) 10.1211(3) 7.3813(2) 1.12 0.575 Electronic 2O Sr2Bi2O7 53 7.70 7.91 10.58 1.26 0.76 2O Ba2U2O7 69 8.1665(15) 11.3081(21) 8.1943(16) 1.42 0.76 2O Na2Te2O7 138 7.233(5) 10.104(7) 7.454(5) 1.18 0.56 2O Ag2Te2O7 55 7.266(2) 10.1430(9) 7.6021 (17) 1.28 0.56 2O CaPbSb2O7 12 7.3577 7.5362 10.3521 1.205 0.6 Ferroelectric 2O DyNaSb2O7 139 7.26(6) 7.41(5) 10.20(6) 1.1035 0.6 2O GdNaSb2O7 139 7.29(1) 7.47(0) 10.20(7) 1.1165 0.6 2O EuNaSb2O7 139 7.30(0) 7.47(2) 10.21(4) 1.123 0.6 2O SmNaSb2O7 139 7.30(8) 7.45(7) 10.22(7) 1.1295 0.6 2O NdNaSb2O7 139 7.32(7) 7.49(2) 10.24(2) 1.1445 0.6 2O PrNaSb2O7 139 7.33(7) 7.50(6) 10.25(5) 1.153 0.6 2O LaNaSb2O7 139 7.37(8) 7.50(1) 10.28(8) 1.17 0.6 2O KLuSb2O7 55,71,140 7.23 10.23 7.39 1.2435 0.6 2O KYbSb2O7 55,71,140 7.24 10.25 7.40 1.2475 0.6 2O KErSb2O7 55,71,140 7.26 10.25 7.41 1.257 0.6 2O KHoSb2O7 55,71,140 7.26 10.25 7.42 1.2625 0.6 2O KYSb2O7 55,71,140 7.26 10.25 7.43 1.2645 0.6 2O KYTa2O7 141 7.78 10.82 7.50 1.2645 0.64 2O KDyTa2O7 141 7.80 10.88 7.70 1.2685 0.64 2O KGdTa2O7 141 7.84 10.86 7.72 1.2815 0.64 2O KSmTa2O7 141 7.86 10.82 7.76 1.2945 0.64 2O NaDyV2O7 141 7.53 10.94 7.44 1.1035 0.54 2O NaGdV2O7 141 7.56 10.88 7.46 1.1165 0.54 2O NaSmV2O7 141 7.58 10.86 7.48 1.1295 0.54 2O NaNdV2O7 141 7.62 10.82 7.50 1.1445 0.54 2O NaSrSbTeO7 74 Not reported 1.22 0.58 2O NaCdSbTeO7 74 Not reported 1.04 0.58 2O NdCaSbTeO7 74 Not reported 1.15 0.58

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72 Table 2 6 List of weberite oxides with the RA/RB and relative ionicity of A O bond (Continued) Table 2 7 An example of normal mode determination (the fluorite CeO2) Wyckoff position (table A) (table B) Site Symmetry F 1u F 2g Ce 4a O h 1 0 O 8c T d 1 1 Acoustic Modes (table E) 1 0 Lattice Modes 1 1 Selectrion Rules (table E) IR Raman Lattice Parameters RA () RB () Properties investigated a () b () c () o) 2O Na 0.5 Cd 1.5 (Fe 0.5 Te 1.5 )O 7 74 7.131 7.317 10.183 1.12 0.56 2O Na 0.5 Ca 1.5 (Fe 0.5 Te 1.5 )O 7 74 Not reported 1.14 0.56 2O Ba 0.5 Ca 1.5 (Fe 0.5 Te 1.5 )O 7 74 7.176 7.464 10.140 1.20 0.57 2M CaLa1.5Sb1.5O7 142 7.5753(3) 10.6870(5) 7.5482(3) 90.346(3) 1.15 0.7 2M CaPr1.5Sb1.5O7 142 7.5188(3) 10.611194) 7.4952(2) 90.315(2) 1.12 0.7 2M CaNd1.5Sb1.5O7 142 7.5019(2) 10.5890(3) 7.4770(2) 90.298(2) 1.11 0.7 2M CaY1.5Sb1.5O7 142 7.3905(1) 10.4563(2) 7.3894(1) 90.049(1) 1.04 0.7 3T Ca1.5Mn0.5Sb2O7 143 7.282(2) 17.604(4) 1.04 0.6 3T Mn2Sb2O7 144 7.191 17.402 0.96 0.6 3T Ca1.92Ta1.92Nd0.08Zr0.08O7 44 7.356(1) 18.116(1) 1.12 0.66 3T Ca2Ta2O7 62,104 7.355 (1) 18.09(1) 1.12 0.64 Dielectric 4M Ca1.92Ta1.92Nd0.08Zr0.08O7 44 12.761(1) 7.358(1) 24.565(1) 100.17 1.12 0.64 5M Ca 1.8 Ta 1.8 Sm 0.24 Ti 0.17 O 7 61 12.763(1) 7.130(1) 30.190(1) 94.09(1) 1.14 0.63 5M Ca2Ta1.8Nb0.2O7 63 12.749(1) 7.347(1) 30.23(1) 94.23(1) 1.12 0.64 Dielectric 6M Ca2Ta2O7 62 7.348(3) 12.727(3) 36.44(5) 95.9(1) 1.12 0.64 6T Ca1.89Ta1.86 Sm0.16 Ti 0.1 O 7 61 7.353(1) 36.264(1) 1.18 0.64 7M Ca2Ta1.9Nb0.1O7 63 12.714(1) 7.370(1) 42.45(1) 95.75(1) 1.12 0.64 Dielectric 8O Ca2Ta2O7 64 7.3690(2) 12.7296(3) 48.263(1) 1.12 0.64 Dielectric & Optical

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73 CHAPTER 3 EXPERIMENTAL PROCEDURES AND PROCESSING 3.1 Sample Preparation 3.1.1 Powder Preparation Polycrystalline specimens were prepared by solid state processing. The starting materials were Dy2O3 (Alfa, 99.99%), Er2O3 (Alfa, 99.99%), Y2O3 (ACROS, 99.9 9 %), Nd2O3 (Alfa, 99.9%), La2O3 (CERAC, 99.99%), Yb2O3 (Alfa, 99.9%), and Nb2O5 (Alfa, 99.9985%). The powders of L n2O3 and Nb2O5 with molar ratio of 3:1 were mixed with 70 ml deionized water and 2 ml ammonium polyacrylate dispersant (Darvan 821 A). The milling media contained 60 g of YSZ spheres with diameter 10 mm and 110 g of YSZ spheres with diameter 3 mm. T h e slurry was ball milled for 24 hours at 85 rpm. The slurry was then poured onto a Teflon sheet, covered with aluminum foil, and subsequently dried in the oven at 393 K for 16 hours followed by grinding with a corundum mortar and pestle and sieving through a 212 m mesh. The powders were then placed in an alumina crucible and calcined in air with 400 K/h heating and cooling rate. The calcination temperature was in the range of 1 573 K 1 773 K. For the defect fluorite compounds, the pure phase was formed when Dy3NbO7 was calcined at 1573 K for 8 h and Er3NbO7, Y3NbO7, and Yb3NbO7 were calcined at 1673 K for 8 h. The pure phase of Gd3NbO7 was formed after calcination at 1673 K for 8 h. A ny impurity phase of Nd3NbO7 cannot be detect ed by when calcined at 1673 K for 8 h. As for La3NbO7, multiple calcinations with intermediate grinding were needed to eliminate the LaNbO4 phase. La3NbO7 had to be calcined at 1773 K for at least 48 h in total.

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74 Ln2LnNbO7 was synthesized in the same manner as to Ln3NbO7. Multiple and long time calcinations with intermediate grinding were also necessary to reach the equilibrium phase. 3.1.2 Pellet Formation After the pure phase was formed, 1 wt% 3 wt% of PVA binder (Celvol 103) was added to assist in pellet formation. The binder contained 20vol% PVA and 80vol% deionized water. An additional 3wt% of binder was needed in pellet forming for the powders with def ect fluorite crystal structure. The binder and the powders were mixed with the mortar and pestle and sieved through 212 m mesh. The mixed powders were then dried in oven at 373 K for 5 min to evaporate water. After that, the powders were uniaxially pressed at 1 5 0 MPa into cylindrical pellets with a diameter of 13 mm or 7 mm or 3 mm and a thickness of approximately 1 mm A geometric green density was calculated, and the pellets with a density greater than 50% of the theoretical value were sintered at 1923 K for 4 hours for the defect fluorite pellets and 1873 K for 4 hours for all other pellets following a binder burnout step at 723 K for 2 hours. The heating and the cooling rate was 200 K/h. The sintered pellets were first checked for surface finish. The weight and the dimension of the pellets without surface cracks were measured, and then the geometric density was determined. If the geometric densit y of the pellet w as above 92 % of the theoretical value, Archimedes method, which does not account for the open pores, was used to measure the density of the pellet The process has also been summarized in Figure 3 1

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75 F igure 3 1 Flow chart of ceramic powder and pellet synthesis process for Ln3NbO7. 3.2 Characterization 3.2.1 Structural Characterization Philips AP D 3720 and Inel CPS x ray diffractometer s were used for structural characterization. The XRD was conducted using CuK radiation with the operation conditions 40 kV and 20 mA for APD and 30 kV and 30 mA for CPS. Figure 3 2 shows an example of XRD collected during the solid state processing. Bef ore calcination, XRD was performed on powder mixtures to assure the right starting materials as well as that no impurity was introduced. As in case of La3NbO7 in Figure 3 2 the powder after ball milling showed two phases Nb2O5 and La(OH)3, which is reaso nable since deionized water was used during ball milling process. After every calcination process, XRD was used to check the phase purity after the powders were grounded by mortar and pestle. After the pellets were sintered, XRD was used again to check phase purity and to Ball milling for 24 h Drying for 16 h at 393 K Calcining at 1573 K 1773 K Forming pellets Burning out binder at 723 K for 2 h Grinding and sieving through 212 m mesh Grinding and sieving through 212 m mesh DI water Dispersant Binder 3 Ln2O3+ Nb2O5 Sintering at 1873 K for 4 h

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76 ensure that the phase of the pellets is consistent with the powders and no secondary phase was produced. 0 10 20 30 40 50 60 70 1573 K 8 h 1673 K 8 h 2 (degrees)Intensity (arb. units)Sintered Pellet 1773 K 48 h Before Calcination La3NbO7 Figure 3 2 XRD of La 3 NbO 7 during the solid state processing. In addition to the above, the 11 BM high resolution powder diffractometer118 in the Advanced Photon Source, Argonne National Laboratory and the HB 2A neutron powder diffractometer in High Flux Isotope Reactor at Oak Ridge National Laboratory were used at different temper atures for crystal structure and phase transition characterization. 3.2.2 Particle size measurement The particle size and size distribution of ceramic powders was characterized using laser scattering (Beckman Coulter LS 13320). The powders were suspended in dei onized water and placed in an ultrasonic bath for at least 30 seconds before analysis. Figure 3 3 shows a typical particle size distribution (Gd3NbO7)

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77 0.1 1 10 0 2 4 6 8 Particle Diameter ( m)Number %Gd3NbO7 Figure 3 3 Particle size distribution of Gd 3 NbO 7 3.2.3 Heat Capacity Measurement H eat capacity measurement on pellet s was conducted using d ifferential scanning calorimeter ( DSC, Seiko Instrument, Inc.) following ASTM E 126905.119 The measurement was done in a nitrogen atmosphere using a synthetic sapphire disk as a standard from 170 K to 673 K. 3.2.4 Scanning Electron Microscopy The microstructure of the sintered ceramic pellets was characterized using scanning electron microscopy (SEM, JEOL 6335F). The SEM was operated under the condition of an accelerating voltage of 15 kV, a probe current of 8 A, and a working distance of approximately 15 mm. To prepare SEM samples, the sintered ceramic pellets were first mechanically polished to a near mirror finish using sandpapers with different grit sizes followed by diamond l apping f ilm s. After polishing, the pellets were

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78 sonicated in deionized water for 5 min. Then the pellets were heated at the rate of 400 K/h to 100 K below the sintering temperature for 1 hour to thermally etch the surface. In some cases ceramic pellets were fractured using a pestle to examine fracture surfaces. All samples were then sputter coated with approximately 20 nm carbon film. Figure 3 4 Figure 3 5 and Figure 3 6 show the typical microstructure of Ln3NbO7 and Ln2LnNbO7 samples. Limited closed porosity is observed at the grain boundaries. As mentioned before, the overall porosity in all of the synt hesized pellets is below 8%. (A) (B) Figure 3 4 (A) SEM picture of Yb 3 NbO 7 with 3000 X magnification. (B) SEM picture of Yb 3 NbO 7 with 8000 X magnification. (A) (B) Figure 3 5 (A) SEM picture of Gd 3 NbO 7 with 3000 X magnification. (B) SEM picture of Gd 3 NbO 7 with 8000 X magnification.

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79 (A) (B) Figure 3 6 (A) SEM picture of Nd 2 YbNbO 7 fracture surface with 3000 X magnification. (B) SEM picture of Nd 2 YbNbO 7 cross sectionwith 11000 X magnification. 3.2.5 Second Harmonic Generation Measurement The second harmonic generation ( SHG ) signal was measured by D. Sava and Professor V. Gopalan at Penn State University. The sintered pellets were polished progressively with smaller sizes of alumina powder and finally submicron size colloidal silica. T he laser source wa s an amplified Ti: sapphire laser with 1 kHz repetition rate, 800 nm wavelength and 130 fs pulse width. The signal was collected using photomultiplier tube and lock in amplifier to reduce noise. The laser was incident at 45 degrees to the sample surface. 3.2.6 Dielectric Characteri zation To prepare parallel plate capacitors, Au/Pd or Au electrodes were sputtered on both sides of the polished pellets followed by a painted coat of air dried Ag paste ( Figure 3 7 (A)) D ielectric properties were measured using an Agilent 4284A or 4980A LCR meter over a frequency range of 1 kHz 1 MHz. The measurements were computer controlled with samples inside Delta 9023 ( Figure 3 7 (B)) oven from 113 K to

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80 500 K ( liquid nitrogen cooled) or in a closed cycle cryogenic workstation ( see Figure 3 7 (C), CTI Cryogenics, Model 22) in the temperature range of 20 K to 295 K The measurements were conducted both during the cooling and heating cycle The real parts of permittivity were compensated for porosity as follows: 2 3 1' f m rV ( 3 1 ) where m is measured permittivity and Vf is the volume fraction of pores Vf is determined by the percentage of theoretical density of the pellet using Archimedes method. The equation is reduced from James Maxwells derivation based on 30 composite system.109 (A) (B) (C) Figure 3 7 (A) Different sizes of pellets with electrodes. (B) Delta oven for dielectric measurement from 113 K to 500 K. The digital multimeter above the oven is connected to the thermocouple inside the oven. (C) C ryogenic workstation for dielectric measurement from 20 K to 350 K.

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81 CHAPTER 4 PRELIMINARY CRYSTALLOGRAPHY OF THE Ln3NbO7 (Ln = La3+, Nd3+, Gd3+, Dy3+, Er3+, Y3+, and Yb3+) and Ln2LnNbO7 (Ln = La3+ and Nd3+; Ln3+ = Dy3+, Er3+, and Yb3+) 4.1 Introduction The core of this chapter is chiefly based on three article s: 1. the journal article (Journal of the European Ceramic Society, 27 (13 15) 39713976 (2007)) titled Structure and Dielectric Properties of Ln3NbO7 (Ln = Nd, Gd, Dy, Er, Yb, and Y), by L. Cai and J.C. Nino;86 2. the journal article (Journal of the European Ceramic Society 30 (2 ) 307313 (2010)) titled Phase Formation and Dielectric Properties of Ln2(Ln0.5Nb0.5)2O7 (Ln = rare earth element) by L. Cai and J.C. Nin o;120 3. the proceedings article (Solid State of Inorganic Materials VI (Materi als Research Society Symposium Proceeding), 998E 0988qq0104 (2007)) titled Phase Formation and Dielectric Properties of Ln3NbO7 (Ln = rare earth elements), by L. Cai, J. Guzman, L. Perez, and J.C. Nin o.85 They are reprinted with permission from Elsevi er and MRS E Proceedings. It has been proved that the crystal structure of Ln3NbO7 shifts from orthorhombic weberitety pe structures to a cubic defect fluorite structure with decreasing Ln3+ ionic radius .15,2223,29,36,80,108,121122 The crystal structure of La3NbO7 and Nd3NbO7 is an orthorhombic weberitetype. Additionally, Gd3NbO7 has also been reported as an orthorhombic lattice, however, with another weberitetype structure Meanwhile, others have reported Gd3NbO7 as a pyrochlore.2223,29,123 A cubic defect fluorite structure has been reported for Ln3NbO7, in which the ionic radius of Ln3+ cation is equal to or less than that of Dy3+ (1.027 ).2223,27,29,80,124 Unlike

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82 pyrochlore ( A2B2O7) in which A B cations, and the oxygen vacant sites have ordered arrangements, the defect fluorite structure has both disordered cations as well as disordered oxygen deficiency sites. It is important to note that some investigations indicated that Ln3NbO7 compounds hav e a pyrochloretype structure.29,108,121,125 In fact, there is some evidence showing that these compounds may have local ordering. This evidence includes six pyrochlorecharacteristic Raman active vibrations found in Y3NbO7, 121 along with the appearance of weak reflections, which are not associated with the fluorite structure, in the electron diffraction pattern.80 However, the evidence does not seem to strongly relate these compounds to the pyrochlore structure. The five less intensive Raman active vibrations seem too broad and too vague to be claimed as peaks.121 The Raman spectra of Y3TaO7, an isomorphic compound to Y3NbO7, confirmed a fluorite structure.22 The weak reflections in the electron diffraction patterns of Ho3TaO7, Y3NbO7, Er3TaO7, and Er3NbO7 were not clearly defined, but were determined to not be related to the pyrochlore or the orthorhombic weberitetype phases.80 The crystal structure of a series of Ln2LnNbO7 ( where the ionic radius of Ln3+ is smaller than that of Ln3+) was also investigated. The Ln2(Ln'0.5Nb0.5)2O7 compounds lie in or close to the pyrochlore stability area where 1.46 < rA/ rB < 1.80 f or A2 3+B2 4+O7 by Subramanian et al.14 as shown in Figure 4 1 Meanwhile, these compounds are in the pyrochlore range of the stability field proposed by Cai et al.40 shown in Figure 4 2 which was also covered in Chapter 2. As also suggested by Isupov ,125 Ln2(Ln'0.5Nb0.5)2O7 are expected to crystallize in the pyrochlore structure. Therefore, to test this prediction and

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83 further understand fluoriterelated superstructures, the structure of three compounds La2(Yb0.5Nb0.5)2O7, La2(Er0.5Nb0.5)2O7, and La2(Dy0.5Nb0.5)O7 were studied here. 0.70 0.75 0.80 0.851.0 1.2 1.4 1.6 1.8 La High pressure synthesis 1 atm synthesis Ln 3 NbO7 Ln 2 Ln'NbO 7 rA3+( A ) [VIII coord.]rB4+( A ) [VI coord.]Nd GdDyY Yb Eroo Figure 4 1 The pyrochlore stability field based on the ratio of ionic radius of A over that of B after Subramanian et al.14 T he stability field i s where the rA/rB is between 1.46 and 1.8 for A2B2O7 pyrochlore. The points other than Ln3NbO7 and Ln2LnNbO7 are from Subramanian et al.14 The ionic radius are after Shannon. 27 1.4 1.6 1.8 2.0 2.2 0.40 0.45 0.50 0.55 0.60 0.65 Weberite Pyrochlore Ln2Ln'NbO7 IA-O/ ( IA-O+IB-O)rA(VIII)/rB(VI) Figure 4 2 The pyrochlore and the weberite stability fields based on the ionic ratio of A over B and the relative A O bond ionicity 40

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84 In this chapter, structural characterization of Ln3NbO7 (Ln3+ = La3+, Nd3+, Gd3+, Dy3+, Er3+, Y3+, and Yb3+) and Ln2LnNbO7 was based on XRD at room temperature. 4.2 Crystal Structure of Ln3NbO7 (Ln = Dy3+, Er3+, Y3+, and Yb3+) Pure fluorite phase of Dy3NbO7 powders was formed when calcined at 1573 K ( Figure 4 3 ). The XRD pattern shows no reflections associated with the pyrochlore structure or any other related superstructures. To ensure the equilibrium state, the powders were then calcined at 1673 K and 1773 K with intermediate grinding. All XRD profiles for Dy3NbO7 were found to be consistent with the cubic fluorite structure, and showed no evidence of the pyrochlore phase. 10 20 30 40 50 60 70 1773 K 1673 K Dy3NbO7Intensity (arb. units)2 (degree)1573 K(111) (200) (220) (311) (222) Figure 4 3 XRD of Dy 3 NbO 7 at different calcination temperatures. The XRD patterns of Ln3NbO7 (Ln3+ = Y3+, Er3+, and Yb3+) is also consistent with a cubic fluorite structure and shows no reflections associated with the pyrochlore structure ( Figure 4 4 ) As expected, there are shifts in 2 changes in the lattice parameter s. The lattice parameters are calculated by the Nelson Riley function:

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85 k a aa2 2 0 0cos sin cos ( 4 1 ) where a is the apparent lattice parameter, a0 is the lattice parameter, and k is a constant. The NelsonRiley function is used to correct for the sample displacement error. Table 2 1 lists an example of the cos2 s2 based on a single reflection. Figure 4 5 indicates the apparent lattice parameter a vs. cos22 a0. The lattice parameters have a linear relationship with the ionic radius of Ln3+ as shown in Figure 4 6 10 20 30 40 50 60 70 Y 3 NbO 7 Yb3NbO7Er3NbO7 (111) (200) (220) (311) (222) 2 (degree)I ntensity (arb. units) Figure 4 4 XRD patterns of Y 3 NbO 7 Yb 3 NbO 7 and Er 3 NbO 7 Table 4 1 22 parameter, and the apparent lattice parameter of Dy3NbO7. hkl a () 29.52 111 7.300 5.2367 34.19 200 6.1699 5.2408 49.02 220 3.9310 5.2517 58.17 311 3.0759 5.2559 61.005 222 2.857 5.2570

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86 2 3 4 5 6 7 8 5.16 5.18 5.20 5.22 5.24 5.26 5.28 Yb3NbO7: Er3NbO7: Y3NbO7: y = 5.232(2) 0.0024(2)x Lattice Parameters (A)ocos2 /sin + cos2 / y = 5.2701(6) 0.0046(1)x y = 5.194(5) 0.0051(4)x y = 5.253(4) 0.0044(2)x Dy3NbO7: Figure 4 5 Nelson Riley function for the lattice parameter calculations of Dy 3 NbO 7 Y 3 NbO 7 Er 3 NbO 7 and Yb 3 NbO 7 1.04 1.03 1.02 1.01 1.00 0.99 0.98 5.18 5.20 5.22 5.24 5.26 5.28 Lattice Parameters ( )Ionic radius of Ln3+()Dy3NbO7Er3NbO7Y3NbO7Yb3NbO7 Figure 4 6 Lattice parameters (with error) of defect fluorite Ln3NbO7 as a function of Ln 3+ ionic radius. The solid line is the linear fitting.

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87 4.3 Crystal Structure of Ln3NbO7 (Ln = La3+, Nd3+, and Gd3+) Two space groups have been used to describe the crystal structure of La3NbO7. One space group, used by Rossell36, was Cmcm (No. 63), with the lattice parameters being 11.167 7.517 and 7.624 On the other hand, Kahnharari et al.37 used the space group Pmcn (No. 62) with the lattice parameters being 11.149 7.611 and 7.747 (in Kahnhararis original paper, the sp ace group Pnma which is another setting of Pmcn with the lattice parameters 7.747 11.149 7.611 was used.51 Here, the author transformed the space group to Pmcn to match with the axes for a better comparison). Figure 4 7 shows the comparison bet ween the experimental XRD pattern and simulated XRD profiles after Rossell and Kahnharari. All 53 observed peaks are associated with the La3NbO7 structure and the peaks with relative intensities less than 8% are indicated by diamond symbols. However, the experimental diffraction pattern seems to be in agreement with both simulated profiles, therefore making it impossible to determine which space group is correct. ray) base d on the description of the La3NbO7 structure with space group Pmcn while there are only 85 calculated reflections for that of Cmcm. Based on the simulation from PowderCell, the 67 extra reflections from Pmcn are so weak and close to their neighboring peaks that they are easily buried in the background or overlapped with their neighboring peaks.126 The highest relative intensity o. The (121) reflection is only about 0.7o away from the strongest r eflection (220). Therefore, there is a possibility that the (121) reflection is buried in the tail of the (220) reflection or the background noise. As a result, it is clear that La3NbO7 crystallizes into a weberite type

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88 discussion about the space group and the crystal structure of La3NbO7 will be presented in Chapter 7 based on neutron diffraction. 10 20 30 40 50 60 70 (404) (242) (224) (620) (241) (422) (511) (022) (400) (221) (220) (202) (021) (421) Relative intensity <8%2 (degrees)Intensity (arb. units)La3NbO71773 K 48 h Cmcm Pnma Fi gure 4 7 Comparison of experimental XRD of La 3 NbO 7 with theoretical XRD after Rossell 36 (space group Cmcm ) and Kahnharari 37 (space group Pnma ). The XRD profile of Nd3NbO7 is shown in Figure 4 8 T he experimental pattern of Nd3NbO7 is in reasonably good agreement with the theoretical XRD patter n based on the atomic positions after Rossell (space group Cmcm).36 While all of the experimentally observed peaks are part of the Nd3NbO7 crystal structure, on ly the peaks with relative intensities larger than 8% are indexed in Figure 4 8 The lea st intense peaks are indicated by diamond symbols It is important to note that although there are few, if any, published atomic positions for Nd3NbO7 with the space group Pnma, it was

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89 nonetheless proposed as an acceptable space group of Nd3NbO7.127128 Similar to La3NbO7, it is difficult to figure out the correct space group of Nd3NbO7 Therefore, both synchrotron x ray and neutron powder diffraction wer e performed on Nd3NbO7 and will be discussed in Chapter 7. 10 20 30 40 50 60 70 (404) (242) (224) (620) (241) (422) (511) (022) (400) (221) (220) (202) (021) Nd3NbO7 1673 K for 8 h Theroetical pattern(421) Intensity (arb. units)2 (degrees)Relative intensity <8% Figure 4 8 Experimental and theoretical XRD of Nd 3 NbO 7 36,86 The XRD pattern for Gd3NbO7 is shown in Figure 4 9 At first glance, it matches well with a cubic fluorite p rofile However, the Gd3NbO7 pattern contains more minor peaks with intensities below 1 % of the rela t ive intensity. These minor peaks have been identified in the past as superlattice lines typically associated with the pyrochlore structure by Abe et al.23 H owever, Abes claim was not based on any detailed XRD analysis. B ased on the Gd3NbO7 XRD profile collected here, some of the peaks cannot be attribute d to the pyrochlore structure. These peaks are indexed as the pl anes with

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90 mixed odd and even h k, l values and they violate the reflection conditions for pyrochlore, where h k, l values should be either all odd or all even By contrast, all of the peaks c an be correctly indexed on the basis of the Gd3TaO7 compound ( JCPDS 38 1409, Gd3TaO7 is a similar compound to Gd3NbO7) which according to Yokogawa et al.129 is a weberitetype structure with the space group C2221. 10 20 30 40 50 60 70 (124) (440) (162) (224) Intensity (arb. units)2 (degrees) (220) (040) (013) (302) (242)Gd3NbO71673 K 8 h -Relative intensity <1% Figure 4 9 Experimental and theoretical XRD of Gd 3 NbO 7 80 Although the space group C2221 was initially proposed for Gd3NbO7 by Allpress et al.80, it was later questioned by Astafyev et al.38 due to the fact that Gd3NbO7 exhibited second harmonic generation (SHG) signals at room temperature. Astafyev then proposed the space group Cmm2 without proof. Therefore, in this work, Le Bail structureless whole pattern fitting by PowderCell126 was performed using the space groups C2221 and Cmm2 to see which one was a better fit However, the fitting for both of these space groups gave a good match with the experimental data since every

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91 observed peak can be indexed in these two space groups. At this stage, although it is proven that Gd3NbO7 crystallizes into a weberitetype structure, the correct space group is still in question. Synchrotron x ray diffraction is therefore necessary for further investigation, as will be discussed in Chapter 6. 4.4 Crystal Structure of Ln2(Ln0.5Nb0.5)2O7 The XRD profiles of La2(Yb0.5Nb0.5)2O7 at different calcination temperatures and the stoichiometric mixture of the La2O3, Yb2O3 and Nb2O5 are shown in Figure 4 10 (A). After initial calcination at 1673 K for 8 h, the resulting pattern showed a mixture phase of L a2(Yb0.5Nb0.5)2O7, Yb3NbO7, and La2O3. After the subsequent calcination at 1773 K for 24 h, there was no obvious La2O3 phase and Yb3NbO7 phase is greatly depressed, which relative intensity of the strongest peak decreased from 42% to 7%. After the third calcination at 1773 K for 24 h, it was clearly shown that there are no unreacted La2O3, Yb2O3 Nb2O5 or Yb3NbO7 in the La2(Yb0.5Nb0.5)2O7 pattern. The XRD profile remained the same after additional calcination at 1773 K for 12 h. Therefore, equilibrium was presumed after the third calcination. The pattern is very similar to the cubic fluorite profile. Upon further inspection, some of the intense peaks are in fact split into two peak reflections. When compared with the fluorite, the peak splits occur a position of (111), (220), (113) and (222). The splitting may be due to the formation of two phases. However, the existence of two phases should also cause the splitting of 33o, which is not obvious in the XRD pattern. It could be possible that the (002) peaks are greatly overlapped and hard to be distinguished. However, i n the means the splitting at (002) should be larger than the splitting at (111). Therefore, since

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92 this is not the case, it is concluded that the peak splitting is not due to the formation two phases. 20 30 40 50 60 70 1673 K 8 h 1673 K 8 h 1773 K 24 h 24 h 1673 K 8 h 1773 K 24 h 2 (degrees)Intensity (arb. units) 2La2O3 + Nb2O5 + Yb2O3 (A) 20 30 40 50 60 70 (040) (400) (004) (044) (440) (422) (224) (202) (242) (022)La2( Yb0.5Nb0.5)2O7 2 (degrees)Intensity (Arb. Units)La2( Yb0.5Nb0.5)2O7(220)Relative intersity < 4%27 28 29 56 58 60 2 (degrees) (022) (220) (044) (440) (422) (224) (B) (C) Figure 4 10 (A) XRD patterns La 2 (Yb 0.5 Nb 0.5 ) 2 O 7 at different calcination temperatures and time, and the mixture of La2O3, Nb2O5 and Yb2O3 (B) Indexed XRD profile of La2(Yb0.5Nb0.5)2O7 after calcinations at 1673 K for 8h and 1773 K for 24 h and 24 h (c) details of the peak splitting in La 2 (Yb 0.5 Nb 0.5 ) 2 O 7 120

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93 By contrast, the peak splitting observed is consistent with an orthorhombic distortion of the cubic fluorite structure. If the lattice parameter of the cubic fluorite is a (where a ~ 5), then the lattice parameters of the orthorhombic structure are approximately a 2 a and a The transformation relationship from the cubic to the orthorhombic structure can be written as following: 1 0 1 0 2 0 1 0 1 Cubic ic Orthorhomb ( 4 2 ) Therefore, the (111) plane in the cubic structure corresponds to (220) and (022) planes in the orthorhombic structure in the XRD pattern and the (222)c (the subscript c means cubic) is transformed into (440)o and (044)o (the subscript o means orthorhombic) as in Table 2 3 The (220)c splits into (400)o, (004)o and (242)o while the (113)c converts to (422)o and (224)o. Meanwhile, the pattern contains several weak peaks with intensities below 5% relative intensity. These weak reflections may suggest the formation of a fluorite superstr ucture. The lattice parameters are initially given by the TREOR program in Crysfire and refined in Maud program.130131 The sample displacement is also refined. The DebyeScherrer geometry is used for the pattern collected from the inel CPS diffractometer. The obtained lattice parameters are 7.5623(13) 10.7666(23) 7.6619(13) The lattice parameters are in the range of orthorhombic fluoriterelated compounds such as pyrochlore Cd2Nb2O7 (7 .3295 10.3655 7.3295 ), weberite Ca2Sb2O7 (7.3060 10.2263 7.4627 ) and weberite Ba2U2O7 (8.1665 11.3081 and 8.1943 ).12,70,132 It is worth noting that the peak at o ((002)c) should also split into (202)o and (040)o only 0.059o

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94 between (022) and (220) is 0.260o shown in Figure 4 10 (C)). The step size of the XRD detector is about 0.038o. Therefore, it is safe to assume that the (022) and (040) peaks are overlapped and the splitting cannot be detected. The XRD pattern of La2(Yb0.5Nb0.5)2O7 is similar to the XRD profile of orthorhombic pyrochlore Cd2Nb2O7 (space group Ima2 ), which also have some additional minor peaks compared to the fluorite structure and peak splitting at characteristic fluorite peaks. Therefore, the initial guess of the structure is based on Cd2Nb2O7. The Powdercell program was used to refine the experimental XRD profile.133 All the peaks but one with 2% o were fitted with the proposed structure. For clarify, the peaks with relative intensities larger than 4% are indexed and the other below 4% relative intensities are indicated by diamond symbols in Figure 4 10 (B). The XRD profiles of La2(Dy0.5Nb0.5)2O7 and La2(Er0.5Nb0.5)2O7 are shown in Figure 4 11. The 5 characteristic fluorite peaks are all split into two or more peak reflections. The patterns contain more weak peaks than in the case of La2(Yb0.5Nb0.5)2O7. The minor o, 29.5o and 31o violate the reflection condition for the orthorhombic pyrochlore in which the value of h + k + l should be even. The XRD profiles of La2(Dy0.5Nb0.5)2O7 and La2(Er0.5Nb0.5)2O7 were compared with the XRD of fluorite related structures including orthorhombic weberite, weberitetype La3NbO7 (or Nd3NbO7), weberite type Gd3NbO7, orthorhombic ZrO2, monoclinic ZrO2, Zirkelite and Zirconolite. The XRD patterns were found similar to the weberitetype La3NbO7 and Nd3NbO7. Le Bail f itting was performed to confirm that all peaks can be fitted based on the weberitetype structure using Powdercell program.133 The peaks

PAGE 95

95 with relative intensities larger than 8% are indexed and the other less intense peaks are indicated by diamond symbols in Figure 4 11 20 30 40 50 60 70 La2( Dy0.5Nb0.5)2O7(112) (421) (242) (224) (040) (422) (004) (022) (400) (220) Intensity (arb. units)2 (degrees) (202)Intesities < 8%La2( Er0.5Nb0.5)2O7 Figure 4 11 XRD patterns of La2(Dy0.5Nb0.5)2O7 and La2(Er0.5Nb0.5)2O7.120 The reason why La2(Yb0.5Nb0.5)2O7 is pyrochlorerelated, and La2(Er0.5Nb0.5)2O7 and La2(Dy0.5Nb0.5)2O7 are weberitetype, is probably that La2(Yb0.5Nb0.5)2O7 has a higher rA/rB ratio. The RA/RB ratio of La2(Er0.5Nb0.5)2O7 (rA/rB = 1.50) and La2(Dy0.5Nb0.5)2O7 ( rA/rB = 1.49) is closer to the edge of the pyrochlore stability field (1.46 1.8) than La2(Yb0.5Nb0.5)2O7 ( rA/rB = 1.51); thus the first two compounds are less likely to form a pyrochlore phase The lattice parameters of La2(Dy0.5Nb0.5)2O7 are 10.9220(8) 7.5646(12) and 7.7060(13) The lattice parameters of La2(Er0.5Nb0.5)2O7 are 10.9220(8) 7.5915(12) and 7.7189(5)

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96 10 20 30 40 50 60 70 (510) (440) (400) (220)Nd2YbNbO7 (332) (232) (130) (404) (602) (422) (112) (202) (020) (011) Intensity (arb. units)2 (degrees) Sm2YbNbO7 Figure 4 12 XRD patterns of Sm 2 Yb NbO 7 and Nd 2 ErNbO 7 120 The XRD profiles of Sm2YbNbO7 and Nd2YbNbO7 are shown in Figure 4 12. The XRD patterns can be indexed using an orthorhombic lattice. The lattice parameters of Sm2YbNbO7 are 10. 566(8) 7.443(5) and 7. 528(8) The lattice parameters of Nd2YbNbO7 are 10.624( 4 ) 7.482(4) and 7. 582(3) The summary of lattice paramet ers of all investigated compounds will be presented in Chapter 9. 4.5 Conclusion Structural characterization of Ln3NbO7 (Ln = La3+, Nd3+, Gd3+, Dy3+, Er3+, Y3+, and Yb3+) and La2LnNbO7 was presented here. It was found that if the ionic radius of Ln3+ is equa l to or smaller than Dy3+ (1.027 ), then the crystal structure of Ln3NbO7 is confirmed by XRD analysis to be a defect fluorite structure, with the lattice parameter increasing linearly with increasing ionic radius of Ln3+. Additionally, it can be noted that La3NbO7 and Nd3NbO7 crystallize into a weberitetype structure. However, it is difficult to determine the correct space group ( Pnma or Cmcm3NbO7

PAGE 97

97 was found to have another weberitetype structure, similar to that of Gd3TaO7. Again, the correct space group for the Gd3NbO7 structure is still in question. As for La2LnNbO7, these compounds have an orthorhombic fluoriterelated structure. La2(Yb0.5Nb0.5)2O7 is orthorhombic pyrochlore, and La2(Er0.5Nb0.5)2O7 and La2(Dy0.5Nb0.5)2O7 are weberiteD, synchrotron x ray and neutron powder diffraction were also performed on the weberitetype Ln3NbO7 compounds as will be discussed in Chapter 6 and Chapter 7.

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98 CHAPTER 5 DIELECTRIC PROPERTIES OF Ln3NbO7 and Ln2(Ln0.5Nb0.5)2O7 5.1 Introduction The core of this chapter is chiefly based on three article s: 1. the journal article (Journal of the European Ceramic Society, 27 (13 15) 39713976 (2007)) titled Structure and Dielectric Properties of Ln3NbO7 (Ln = Nd, Gd, Dy, Er, Yb, and Y), by L. Cai and J.C. Nino;86 2. the journal article (Journal of the European Ceramic Society 30 (2 ) 307313 (2010)) titled Phase Formation and Dielectric Properties of Ln2(Ln0.5Nb0.5)2O7 (Ln = rare earth element) by L Cai and J.C. Nin o;120 3. the proceedings article (Solid State of Inorganic Materials VI (Materials Research Society Symposium Proceeding), 998E 0988qq0104 (2007)) titled Phase Formation and Dielectric Properties of Ln3NbO7 (Ln = rare earth elements), by L. Cai, J. Guzman, L. Perez, and J.C. Nin o.85 They are reprinted with permission from Elsevier and MRS E Proceedings. There are a few scattered investigations on the dielectric properties of Ln3NbO7. Chincholkar134 first reported the dielectric properties of x Sm3NbO7 + (1 x) La3NbO7 system (x is from 0 to 1). The reported room temperature dielectric permittivity of pure La3NbO7 was high, 800 at 1 kHz. Since the study was limited to 1 kHz the high permittivity may mainly contribute from space charge polarization mechanism. The results were not convincing as well because of lack of description of experimental procedures. Astafev et al.38 investigated the dielectric properties of Gd3NbO7 at 1 kHz from 200 K to 380 K. The dielectric permittivity increases with increasing temperature until 330 K and decreases above 330K, accompanied by a dielectric loss peak at about 300 K. As for defect fluorite Ln3NbO7, literature review shows there are no

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99 investigations on the dielectric properties of these compounds. To explore the fundamental structure dielectric properties relationships, in the present work, research was conducted on the dielectric properties of Ln3NbO7 (Ln3+ = La3+, Nd3+, Gd3+, Dy3 +, Er3+, Y3+, and Yb3+) and Ln2(Ln0.5Nb0.5)2O7 over a broad range of frequency and temperature. 5.2 Dielectric Properties of Defect Fluorite Ln3NbO7 The sample preparati on was described in Chapter 3. The dielectric properties between 1 kHz and 1 MHz from 113 K to 473 K for Dy3NbO7 are shown in Figure 5 1 The real part of permittivity increases from 3 5 to 39 with increasing temperature, and increases slightly with decreasing frequency The positive temperature coefficient of capacitance shows two slope variations (inflection points) with associated changes in the imaginary part with a peculiar cross over at approximately 350 K. T he imaginary part of permittivity is on the order of 101 at 1 MHz from 11 3 K to 473 K 100 150 200 250 300 350 400 450 500 33 34 35 36 37 38 39 40 41 0.2 0.4 0.6 0.8 1.0 1.2 1.4 r' Increasing Frequency Decreasing Frequency r"Temperature (K) Figure 5 1 Dielectric properties of Dy3NbO7 at 1 kHz, 3 kHz, 8 kHz, 10 kHz, 30 kHz, 80 kHz, 100 kHz, 300 kHz, 800 kHz, and 1 MHz.

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100 100 150 200 250 300 350 400 450 500 27 30 33 36 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Increasing Frequency Decreasing Frequency r" r'Temperature (K) Figure 5 2 Dielectric properties of Yb 3 NbO 7 from 1 kHz to 1 MHz. 100 150 200 250 300 350 400 450 500 25 30 35 40 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Decreasing Frequency Decreasing Frequency r" r'Temperature (K) Figure 5 3 Dielectric properties of Y 3 NbO 7 from 1 kHz to 1 MHz.

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101 100 150 200 250 300 350 400 450 500 26 28 30 32 34 36 0.3 0.6 0.9 1.2 1.5 Decreasing Frequency Decreasing Frequency r' r"Temperature (K) Figure 5 4 Dielectric properties of Er 3 NbO 7 from 1 kHz to 1 MHz. The dielectric properties of Yb3NbO7 ( Figure 5 2 ), Y3NbO7 ( Figure 5 3 ), and Er3NbO7 ( Figure 5 4 ), and show the same trend as Dy3NbO7. The room temperature real part of permittivity is 34.7, 31.4, and 31.2 for Y3NbO7, Er3NbO7, and Yb3NbO7 respectively T he imaginary part is on the order of 101 from 11 3 K to 473 K at 1 MHz The real part of permittivity of these four compounds increases with increasing temperature. The temperature coefficient of capacitance (TC C ) was calculated f rom 218 K to 350 K T C C TCCRT 1 = ( 5 1 ) RT is the 1 (parts per million per K). As shown in Figure 5 5 TCC incre ases with increasing ionic radius of Ln3+. As stated in the introduction of Chapter 4, other study indicated that the

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102 defect fluorite may have local ordering.80 It is reasonable to expect that the local ordering increase with the increasing difference between ionic radius of Nb5+and Ln3+. Therefore, it implies that TCC may increase with the structural disorder. The TCC values are also listed in Table 5 1 1.04 1.03 1.02 1.01 1.00 0.99 0.98 250 300 350 400 Average ionic radius of Ln3+ ( ) Yb3NbO7Er3NbO7Y3NbO7Dy3NbO7TCC ( MK-1) Figure 5 5 TCC of defect fluorite Ln 3 NbO 7 from 218 K to 350 K. When the observed dielectric constant for these compounds is compared with the predicted values using the Clausius Mosotti equation, t he calculated values only account for 50% of the experimentally observed dielectric constant ( Table 5 1 ). It is important to note that the Clausius Mosotti equation is derived under the assumption that ions of one type are symmetrically arranged around ions of another type.135 As such, the equation is used to estimate the dielectric constants contributed by electronic and ionic mechanism with the calculated values agreeing well for the majority of non polar inorganic oxides.26 The large deviation of cal from mea indicates that the assumption may not hold for defect fluorite structures because of unoccupied oxygen

PAGE 103

103 sites and the disorder of the lanthanide and niobium ions It may also suggest that there exist s a weak dipolar contribution contributing to the permittivity in these compounds. Table 5 1 Summary of ionic radius (rLn) of rare earth ions, lattice parameters of Ln3NbO7, polarizablity ( Ln), e xperimental (room temperature) and calculated dielectric constants of Ln3NbO7 (Ln3+ = Y3+, Yb3+, Er3+, and Dy3+) and the temperature coefficient of capacitance (TCC). rLn ( )27 a () Ln (3)26 r (measured) r (calculated) TCC (MK-1) Dy3NbO7 1.027 5.2700(6) 4.07 37.75 20.31 272.24 Y3NbO7 1.019 5.2533(10) 3.81 34.38 18.17 291.94 Er3NbO7 1.004 5.2317(10) 3.81 31.47 19.73 354.05 Yb3NbO7 0.985 5.194(2) 3.58 31.18 19.43 389.58 5.3 Dielectric Properties of Weberitetype Ln3NbO7 (Ln = La3+, Nd3+, and Gd3+) 5.3.1 La3NbO7 and Nd3NbO7 La3NbO7 exhibits a temperaturedependent dielectric relaxation shown in Figure 5 6 The variation of dielectric permittivity of La3NbO7 with frequency between 1 kHz and 1 MHz is negligible from 20 K to 475 K. The room temperature real part of permittivity is approximately 48 at all measured frequencies. The value is reasonable since it is on the same order of the dielectric permittivity for other Ln3NbO7.38,86 The real part of permittivity increases from 32 to 59 with increasing temperature between 20 K and 360 K. The TCC is 2965 MK1 from 218 K to 350 K. Above 370 K, the permittivity decreases with increasing temperature in an approximately linear manner. The TCC is then 733 MK1 from 370 K to 470 K. The imaginary part of permittivity is on the order of 102 between 8 kHz and 1 MHz, smaller than that of all of the defect fluorite Ln3NbO7 (on the order of 101).

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104 0 100 200 300 400 500 20 30 40 50 60 0.0 0.1 0.2 0.3 0.4 0.5 Temperature (K)r' Decreasing Frequency Decreasing Frequency r" Figure 5 6 Dielectric properties of La 3 NbO 7 from the temperature 20 K to 473 K at 1 kHz, 3 kHz, 8 kHz, 10 kHz, 30 kHz, 80 kHz, 100 kHz, 300 kHz, 800 kHz, and 1 MHz. Figure 5 7 shows the dielectric properties for Nd3NbO7 as a function of temperature at different frequencies from1 kHz to 1 MHz. The dielectric behavior of Nd3NbO7 resembles that of La3NbO7. The variation of the real part of permittivity with frequency is negligible. The real part of permittivity is relative stable between 20 K and 100 K. It increases from 35 to 62 with increasin g temperature between 100 K and 450 K. The TCC from 218 K to 350 K is 1718 MK1. Above 465 K, the variation of the real part of permittivity as a function of temperature is small and with a negative slope (~ 0.02), accompanied by a sharp increase in the imaginary part of dielectric permittivity at 1 kHz (~ 0.9 at 523 K). The TCC from 465 K to 523 K is 443 MK1. The dielectric responses of both compounds indicate the dipolar polarization may play a role since the variation of the real part permittivit y as a function of temperature

PAGE 105

105 changes from positive to negative. As will be discussed in detail in Chapter 7, the dielectric relaxation is related to phase transition in both compounds. 0 50 100 150 200 250 300 350 400 450 500 20 30 40 50 60 70 r' r"Temperature (K)0.0 0.4 0.8 1.2 1.6 2.0 Decreasing Frequency Decreasing Frequency Figure 5 7 Dielectric properties of Nd3NbO7 between 1 kHz and 1 MHz from the temperature 20 K to 523 K. 5.3.2 Gd3NbO7 T h e dielectric behavior of Gd3NbO7 as a function of temperature at frequencies from 1 kHz to 1 MHz is shown in Figure 5 8 The real part of permittivity is between 3 3 and 48, and the imaginary part of permittivity is on the order of 104 to 101 at 1 MHz from 2 0 K to 475 K. It is observed that the dielectric response undergoes a frequency and temperature dependent dielectric relaxation. The real part of permittivity of Gd3NbO7 at different frequencies becomes more dispersive with rising temperature, increasing sharply from 2 0 K to 3 30 K where a maximum is reached. The TCC from 218 K to 350 K is 1575 MK1. At higher temperatures the permittivity decreases slightly

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106 with increasing temperature in an almost linearly manner. The TCC is 90 MK1 from 340 K to 470 K. The temperature, at which the peak of the imaginary part occu rs, shifts to higher temperatures with increas ing freque ncy. That being the case, it is unclear why there is no clear shift in the maxima of the real part of the permittivity. 0 100 200 300 400 500 15 20 25 30 35 40 45 50 55 r' r"Temperature (K) Decreasing Frequency Decreasing Frequency 0.0 0.4 0.8 1.2 1.6 Figure 5 8 Dielectric properties of Gd 3 NbO 7 between 1 kHz and 1 MHz from the tem perature 20 K to 473 K. To better understand the phenomena, t he Arrhenius f unction is used to model the relaxation behavior of Gd3NbO7: ] exp[0 m B aT k E ( 5 2 ) where is the measuring frequency, the preexponential is the attempt jump frequency, Ea is the activation energy, and kB is Boltzmann s constant. Tm is determined by fitting the peak of the imaginary part of permittivity for each measuring frequency to a Gaussian function. The nonsymmetric tails of the peaks are cut off during fitting. The resulting Arrhenius plot is present ed in Figure 5 9 From the linear fit, 0

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107 0 = 1.51 1011 Hz, and the activation energy Ea is 0.4 5 eV, which is larger than typical values observed in Nb based pyrochlores, for example 0.32 eV in Ca Ti Nb O pyrochlore and 0.14 eV in Bi ZnNb O pyrochlore.6,28 However, other ionic and dipolar compounds systems have even higher activation energies; for example, 0.53 eV for CaF2 doped NaF and 1.02 eV for (Ba0.8Sr0.2)(Ti1xZrx)O3.136137 Thus, the calculated Ea is acceptable. 2.1 2.4 2.7 3.0 3.3 3.6 103104105106 R2=0.9929 =1.51 1011 exp(-0.45/kT)Frequency (Hz)103/Temp (1/K) Figure 5 9 Arrhenius plot of temperature at which the maximum peak of imaginary part of permittivity occurs in Gd 3 NbO 7 A summary of the permittivity of Ln3NbO7 at room temperature and 1 MHz is shown in Figure 5 10. While it can be expected that the more polarizable Ln3+ ions would result in higher permitt ivity it is clear that the room temperature permittivity does not follow the trend. Gd3NbO7 has higher dielectric permittivity than that of Nd3NbO7, even though the polarizability of Gd3+ is lower than that of Nd3+. Sirotinkin et al.108 revealed an abnormally loose structure in Ln3NbO7 compounds in the middle of the

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108 series (Sm, Eu, and Gd). Ac cording to the lattice parameter s calculated in this work, Gd3NbO7 has the highest ratio of the formula volume to the Ln3+ ionic radius ( Figure 5 11) The formula volume is determined by the unit cell volume divided by the formula number Z (Z is 4 for weberite type and 1 for defect fluorite). The formula volume is generally a linear relationship with respect to the ionic radius of Ln3+ (the red line is the linear fitting). The formula volume of Gd3NbO7 is outside the 95% confidence limit of the linear fi tting (the grey lines), which indicate a more open structure. On the other hand, the formula volume of Nd3NbO7 is on the lower side of the confidence limit. It is predicted that the structural openness causes an easier polarization of the material .38 The openness may be also responsible for lower dielectric relaxation temperature. A detailed discussion about structuredielectric property relationships will be presented in Chapter 9. Figure 5 10 Summ ary of real part of permittivity for all Ln 3 NbO 7 compounds. Ionic radius () 1.16 1.12 1.08 1.04 1.00 0.96 25 30 35 40 45 50 La3NbO7Gd3NbO7Nd3NbO7Dy3NbO7Y3NbO7Er3NbO7Yb3NbO7 'r

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109 Figure 5 1 2 shows the TCC for all investigated Ln3NbO7 compounds. Above the dielectric relaxation temperature, the TCC of Ln3NbO7 (Ln3+ = La3+, Nd3+, and Gd3+) is negative and follows the same trend as defect fluorite Ln3NbO7, increasing ionic radius of Ln3+. From 218 K and 350 K, the TCC of Ln3NbO7 (Ln3+ = La3+, Nd3+, and Gd3+) decreases with decreasing ionic radius of Ln3+. The TCC is large due to rapid change in permittivity the dielectric relaxation temperature. The relative large change of permittivity may contribute from dipole reorientations, which involves activation energy and the jump frequency. Therefore, a simple relationship cannot apply. Figure 5 11 The formula volume vs. the ionic radius of Ln 3+ for Ln 3 NbO 7 at room temperature. The red line is the linear fitting and the grey lines show 95% confidence limit of the fitting. 1.16 1.12 1.08 1.04 1.00 0.96 130 140 150 160 170 Vformula= Vunit cellZ Gd3NbO7La3NbO7Nd3NbO7Dy3NbO7Er3NbO7Y3NbO7Yb3NbO7 Ionic radius ()Formula Volume (3)

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110 Figure 5 12 Summary of TCC for all Ln 3 NbO 7 compounds. The TCC from 218 K to 350 K (circles in the figure) were calculated for La3NbO7, Nd3NbO7, and Gd3NbO7 but their permittivity does not change linearly with temperature. The TCC ( open squares) above the dielectric relaxation temperature. The capacitance at RT was also used. 5.4 Dielectric Properties of Ln2(Ln0.5Nb0.5)2O7 The dielectric behavior of La2(Yb0.5Nb0.5)2O7 as a function of temperature at frequencies from 10 k Hz to 1 MHz is shown in Figure 5 13. The real part of permittivity is between 43.5 and 44.5 from 20 K to 295 K, and the imaginary part of permittivity is on the order of 101 at 1 MHz It is observed that the dielectric behavior undergoes a frequency and temperature dependent dielectric relaxation. T he permittivity increases slightly with increasing temperature from 20 K to 140 K where a maximum is reached (~ 44.5 at 1 MHz). The temperature, where the maximum permittivity occurs, and consequently the temperature (Tm), where the peak of the imaginary part of permittivity Ionic radius () 1.16 1.12 1.08 1.04 1.00 0.96 -1000 -500 0 500 1000 1500 2000 2500 3000 La3NbO7Nd3NbO7Gd3NbO7 Yb3NbO7Er3NbO7Y3NbO7Dy3NbO7TCC ( MK-1)

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111 is located, both increase with increasing frequency. However, the dielectric relaxatio n behavior of La2( Yb0.5Nb0.5)2O7 is different from that observed in weberitetype Gd3NbO7.86 In Gd3NbO7, t here is no clear shift in the maxima of the dielectric permittivity and a larger variation of Tm as a function of frequency 0 50 100 150 200 250 300 40 41 42 43 44 45 r''Increasing frequencyr'Temperature (K) 0.0 0.2 0.4 0.6 0.8 1.0 Figure 5 13 Dielectric properties of La 2 (Yb 0.5 Nb 0.5 ) 2 O 7 at 10 kHz, 100 kHz, 300 kHz, 500 kHz, 800 kHz and 1 MHz To better understand the phenomena, as customarily, the Arrhenius function is used to model the relaxation behavior of La2(Yb0.5Nb0.5)2O7. The resulting Arrhenius plot is presented in Figure 5 140 = 1.21014 Hz, and the activation energy Ea is 0.14 eV. The attempt frequency is low er than cubic pyrochlore CaO TiO2Nb2O5 (4.61014 Hz), but higher than pyrochlore Bi1.5ZnNb1.5O7 (31012 Hz).28,138 It is proposed that lighter A site cations result in a higher attempt frequency in pyrochlore because the attempt frequency is related to the O A O bending phonon modes.28,139 The calculated attempt frequency of La2(Yb0.5Nb0.5)2O7 is also acceptable as the mass of A cations (La3+) is intermediate between Bi1.5ZnNb1.5O7 and cubic pyrochlore CaO -

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112 TiO2Nb2O5. The observed activation energy is smaller than that of weberitetype Gd3NbO7, 0.45 eV and close to B1.5ZnNb1.5O7, 0.136 eV.86,138 Figure 5 14 Arrhenius plot of temperature at which the maximum of imaginary parts of permittivity occurs for La 2 (Yb 0.5 Nb 0.5 ) 2 O 7 The dielectric properties of La2(Dy0.5Nb0.5)2O7 are shown in Figure 5 15 The permittivity slightly increases from 54.9 to 55.2 from 25 K to 86 K, and then decreases to 51 at room temperature and 1 MHz. The imaginary part of per mittivity is on the order of 101 at 1 MHz, the same as the La2(Yb0.5Nb0.5)2O7. This compound also exhibits a dielectric relaxation. The maximum of the permittivity shifts to a higher temperature with increasing frequency. The Arrhenius function is also used to model the relaxation behavior of La2( Dy0.5Nb0.5)2O7. The resulting Arrhenius plot is presented in Figure 5 16. 0 = 1.91013 Hz, and the activation energy Ea is 0. 12 eV. The attempt frequency of La2(Dy0.5Nb0.5)2O7 is between Bi1.5ZnNb1.5O7 (3 1012 Hz) and the CaO TiO2Nb2O5 pyrochlore (4.61014 Hz) .138 The activation energy is close to that of La2(Yb0.5Nb0.5)2O7 and Bi1.5ZnNb1.5O7.6 11 12 13 14 104105106 eV 14 0 EaHz 10 2 114 0 vR2= 0.98 m B aT k E v v exp0 Frequency (Hz)103/T (1/K)

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113 Figure 5 15 Dielectric properties of La 2 ( Dy 0.5 Nb 0.5 ) 2 O 7 at 10 kHz, 100 kHz, 300 kHz, 800 kHz and 1 MHz 12 13 14 15 16 104105106 Hz v13 010 9 1 eV Ea119 0 R2= 0.998 m B aT k E v v exp0 103/T (1/K)Frequency (Hz) Figure 5 16 Arrhenius plot of temperature at which the maximum of imaginary parts of permittivity occurs for La 2 ( Dy 0.5 Nb 0.5 ) 2 O 7 Figure 5 17 shows the dielectric properties for La2(Er0.5Nb0.5)2O7 as a function of temperature at different frequencies from 1 0 kHz to 1 MHz. The permittivity is between 48 and 50.4 from 20 K to 295 K, and the imaginary part of permittivity is also on the 0 50 100 150 200 250 300 40 45 50 55 60 r' r"Temperature (K) Increasing Frequency 0.0 0.2 0.4 0.6 0.8

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114 order of 101 at 1 MHz This compound also exhibits a frequency and temperature dependent dielectric relaxation. The real part of permittivity of La2(Er0.5Nb0.5)2O7 at different frequencies becomes more dispersive near the relaxation tem perature while above 150 K, the variation of permittivity as a function of frequency is negligible. At the same time, the variation of the real part of permittivity as a function of temperature near the relaxation temperature is smaller than that from roo m temperature to 100 K. There is no clear shift in the maxima of the dielectric permittivity with respect to frequency in La2(Er0.5Nb0.5)2O7, which is similar to weberite type Ln3NbO7.86 0 50 100 150 200 250 300 44 45 46 47 48 49 50 51 52 r'Increasing Frequency Temperature (K)r''0.0 0.1 0.2 0.3 0.4 0.5 0.6 Figure 5 17 Dielectric properties of La 2 ( Er 0.5 Nb 0.5 ) 2 O 7 between 10 kHz an d1 MHz Tm increases with increasing frequency from 10 kHz to 1 MHz. The Arrhenius function is also used to model the relaxation behavior of La2(Er0.5Nb0.5)2O7 as shown in Figure 5 18 The calculated 0 is 1.31012 Hz, and the activation energy Ea is 0. 09 eV. While this compound is neither, a dipolar glass or relaxor ferroelectric [ A well known example for dipolar glass is 1at% Li3+ doped KTaO3 system. In this type of materials, the dipoles freeze with no net polarization in the absence of an external field applied.140 Relaxaor ferroelectric is one kind of ferroelectric materials. Unlike the other ferroelectric,

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115 the maximum of the real part of the permittivity does not correspond to a transition from nonpolar phase to a ferroelectric polar phase. The archetype is PbMg1/3Nb2/3O3.141142] it is important to note that similar activation energies have been observed or calculated for those type of materials and thus the measured activation energy value (0.09 eV) is not unheard of.143145 13 14 15 16 17 18 104105106 Hz v12 010 3 1 eV Ea09 0 R2= 0.997 m B aT k E v v exp0 103/T (1/K)Frequency (Hz) Figure 5 18 Arrhenius plot of temperature at which the maximum of imaginary parts of permittivity occurs for La 2 (Er 0.5 Nb 0.5 ) 2 O 7 The dielectric properties of Nd2(Yb0.5Nb0.5)2O7 are shown in Figure 5 19. The real part of permittivity at 1 MHz is between 36 and 37 at measured temperature range. It slightly increases with temperature from 20 K to about 80 K, and decreases with increasing temperature above 80 K. The imaginary part of permittivity is on the order of 101 at 1 MHz, the same as the above La2(Ln0.5Nb0.5)2O7. This compound also exhibits a dielectric relaxation. The maximum of the permittivity (both the real part and the imaginary part) shifts to a higher temperature with an increase in frequency. It is interesting to note that the imaginary part of permittivity has narrower peaks than the

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116 above La2(Ln0.5Nb0.5)2O7 compounds. The Gaussian function was used to fit the peaks and the Arrhenius function is also used to model the relaxation behavior The resulting Arrhenius plot is presented in Figure 5 200 = 2.481010 Hz, and the activation energy Ea is 0. 04 eV. The activation energy is on the same order of La2(Er0.5Nb0.5)2O7 as discussed above. 0 50 100 150 200 250 300 350 400 30 32 34 36 38 40 0.0 0.1 0.2 0.3 0.4 0.5 r" r'Temperature (K) Increasing frequency Figure 5 19 Dielectric properties of Nd 2 (Yb 0.5 Nb 0.5 ) 2 O 7 between 10 kHz and 1 MHz It is interesting to note that all investigated Ln2(Ln0.5Nb0.5)2O7 compounds exhibit temperature and frequency dependent dielectric relaxation. The temperature where the maximum permittivity occurs is much lower than that of weberitetype Ln3NbO7. It is not clear what causes dielectric relaxation in Ln2Ln'NbO7. It may be due to a phase transition, similar to weberite Ln3NbO7, or cation disorder, similar to pyrochlore ( e.g. Ca1.46Ti1.38Nb1.11O7 28). The understanding of the structural origin that causes the dielectric relaxation may lead to potential avenues towards co ntrolling the dielectric

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117 relaxation observed in fluoriterelated materials. The topic of structuredielectric relaxation relationships will be discussed in more detail in Chapter 9. 20 22 24 26 28 30 32 34 104105106 Hz 10 48 210 0 veV 04 0 EaR2= 0.998 m B aT k E v v exp0 1000/Temp (1/K)Frequency (Hz) Figure 5 20 Arrhenius plot of T m for Nd 2 (Yb 0.5 Nb 0.5 ) 2 O 7 5.5 Conclusion The experimentally determined room temperature dielectric permittivity for rare earth niobates ranges between 29 and 45 at 1 MHz. Gd3NbO7 has a higher room temperature permittivity than Nd3NbO7, probably because the former has a more open structure. The different structures show different dielectric property behavior s as a function of temperature. The dielectric permittivity of Ln3NbO7 ( Ln3+ = Dy3+, Er3+, Yb3+, and Y3+) increases with increasing temperature from 115 K to 475 K. Weberitetype Ln3NbO7 and Ln2(Ln0.5Nb0.5)2O7 exhibit dielectric relaxation. There are three main differences in dielectric behavior between Ln3NbO7 and Ln2(Ln0.5Nb0.5)2O7: The temperature, where maximum of permittivity occurs, in weberite type Ln3NbO7 is a much higher than in Ln2(Ln0.5Nb0.5)2O7;

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118 In Gd3NbO7, there is no clear shift in the maxima of the real part of permittivity On the other hand, the maxima of the real part of permittivity increases with an increase in frequency for Ln2(Ln0.5Nb0.5)2O7; Gd3NbO7 has a larger variation of Tm as a function of frequency The Arrhenius function was used to model the relaxation behavior for Gd3NbO7 and Ln2(Ln0.5Nb0.5)2O7. Gd3NbO7 has the highest calculated ac tivation energy, 0.45 eV. By contrast, Nd2(Yb0.5Nb0.5)2O7 has the lowest activation energy, 0.04 eV. A more detailed discussion about the correlation between structure and dielectric relaxation will be the topic of Chapter 9.

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119 CHAPTER 6 P HASE T RANSITION IN W EBERITETYPE Gd3NbO7 6.1 Introduction The core of this chapter is chiefly based on the journal article (Journal of the American Ceramic Society 93(3) 875880 (2010)) titled Phase Transition in Weberitetype Gd3NbO7, by L. Cai, D. Sava, V. Gopolan, and J.C. Nino.146 It is reprinted with permission from Wiley Blackwell. It was discussed previously in Chapter 4 that the correct space group of Gd3NbO7 ray diffraction. Furthermore, in Chapter 5, it reported that the Gd3NbO7 exhibi ts dielectric relaxation. The current chapter attempts to solve the space group issue and present the possible structural origin of the dielectric relaxation. A review of the literature shows the c rystal structure of Gd3NbO7 was first determined by Rossell .36,80 Rossell assign ed the space group C2221 to Gd3NbO7 at room temperature However, the nonpolar space group C2221 was later questioned by Astafyev et al.38 as Gd3NbO7 exhibits second harmonic generation (SHG) signal at room temperature. The SHG signal disappears above 330 K, consistent with a noncentrosymmetric to centrosymmetric transition. It was suggested then that the transition was between Cmm2 and Cmmm without proof The existence of a transition was further confirmed by heat capacit y measurement by Astafyev et al.38 and Klimenko et al.147 and Raman spectroscopy by Kovyazina et al.121 In addition, as stated in Chapter 5, Gd3NbO7 exhibits a dielectric relaxation and t he relaxation temperature where maximum permittivity occurs is close to the transition temperature.8586

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120 It is important to note that a phase transition is commonly observed in Ln3B O7 family and there has been considerable study especially in crystallographic aspects on Ln3IrO7,91 Ln3MoO7,8182,87,148 Ln3OsO7,149 and Ln3RuO7.150151 Here, high resolution XRD was collected on Gd3NbO7 powder before and after the reported phase transition to solve the space group issue and for the first time determine an unequivocal space group and crystal structure that is consistent with all the experimental data available (dielectric property, infrared spectroscopy, heat capacity, SHG, XRD, etc.) In addition, heat capacity and SHG measurements were also conducted on Gd3NbO7 samples in this study as the experimental procedures were not well stated by Astafyev et al.38 It indicated using the same method with Sirotinkin's.108 However, two methods were used by Sirotinkin et al.108, furnace cooled (calcined from 1473 K to 1673 K) and quenched from 1593 K. It is not clear which experimental method was used for preparing the SHG sample.38 To avoid possible discrepancy, all measurements in this study were conducted on Gd3NbO7 samples within the same batch. 6.2 SHG and H eat C apacity M easurements The SHG of Gd3NbO7 was measured twice, the second time with higher power yielding higher intensity and it is shown in Figure 6 1 B oth measurements confirm ed that the SHG signal disappears at about 340 K Figure 6 1 also shows the real part of permittivity and the reciprocal of dielectric susceptibility at 1 MHz.86 It clearly indicates that t he dielectric relaxation temperature, at which the maximum of the dielectric constant occurs, matches well with the temperature, at which the SHG signal disappears Wh en comparing with typical ferroelectric behavior on first and second order transition, the susceptibility plot resembles that of a 2nd order Before the transition, Gd3NbO7 should have a polar space group. There are only three point

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121 groups corresponding to an orthorhombic lattice: 222, mm2 and mmm ; and the only polar group is mm2 It is thus fairly evident that the transition has to be between mm2 and mmm; further validation comes from the fact that mmm is a supergroup of mm2 32 36 40 44 48 r Temperature (K)1/ 100 200 300 400 500 0.020 0.024 0.028 SHG (arb. units) Figure 6 1 Dielectric constant and SHG of Gd 3 NbO 7 146 The heat capacity of Gd3NbO7 was re measured in this study and the measuring temperature was extended down to 160 K as presented in Figure 6 2 It shows a phase transition between 310 K and 340 K. This result matches previous studies .38,147 The heat capacity was fitted combining the Debye and Einstein models for photonic specific heat: 2 p)) / ( ) / ( ( 3 ) ( C T B T A T E n T D m R TE D ( 6 1 ) DE/T) are Debye and Eins tein functions, respectively.152153 There are in total six fitting parameters, m D, n E, A B Because Debye and Einstein functions are for isochoric molar heat capacities, the terms A and B account for the difference between isochoric and isobaric molar heat capacities. The difference between experimental and fitted data shows the specific heat associated with

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122 phase transition. Near 273 K, heat capacity data becomes noisy, probably due to the solidification of moisture. Approaching the structural phase transition, there is a diverging of the specific heat, resembling a lambda shape. Both of the reciprocal of susceptibility and the lambdashape specific heat suggest a 2nd order nature of the phase transition ( Figure 6 2 ) 200 300 400 500 600 700 150 180 210 240 270 300 Experimental FittingDifference ( J/ ( K mol ) )Temperature (K) Temperature (K)Heat Capacity ( J/ ( K mol ) ) 300 400 500 0 20 40 60 80 Difference Figure 6 2 Heat capacity of Gd 3 NbO 7 146 6.3 Infrared Spectroscopy Two independent experiments were performed to measure the IR of Gd3NbO7 by Daniel Arenas in Professor Tanners lab at University of Florida and Vero nica Goian in Professor Kambas lab at Institute of Physics of the ASCR, Czech Republic Observable vibrational modes match well with each other. A peak at about 450 cm1 disappears above the phase transition temperature ( Figure 6 3 (A)). In Figure 6 3 (B), it can be clearly seen that with increasing temperature there is a decrease in the intensity

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123 of the peak, which disappears above the phase transition temperature (~ 340 K). This is strong evidence supporting the phase transition. Detailed IR analysi s will be presented in Chapter 8. 100 200 300 400 500 600 0.0 0.2 0.4 0.6 0.8 1.0 50 K 300 K 360 K ReflectivityWavenumber ( cm-1) (A) 400 500 600 0.0 0.2 0.4 0.6 0.8 1.0 300 K 320 K 340 K 360 K 600 K ReflectivityWavenumber ( cm-1) 10 K 50 K 100 K 150 K 200 K 250 K (B) Figure 6 3 (A) Infrared Spectroscopy of Gd 3 NbO 7 at 50 K, 300 K, and 360 K. The arrow indicates the mode disappearing above the transition temperature. (B) More detailed view of the mode at 450 cm 1

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124 6.4 High Resolution XRD Synchrotron XRD (11 BM, Advanced Photon Source of Argonne National Laboratory) at 100 K, 295 K, 345 K, and 400 K was collected on Gd3NbO7 as shown in Figure 6 4 (A) The diffraction has high sensitivity that allows weak reflections to be distinguished from the background. The instrumental resolution is smaller than 2104 o at 30 keV The monchromator is Si(111) double crystal. There are 12 degrees.118 The wavelength used was 0.4009 for the pattern at 100 K and 0.4142 for all higher temperatures using the wavelength 0.4142 in Figure 6 4 Diamond symbols indicate low intensity peaks all of which are associated with the structure determined below. It is seen that with increasing temperature from 100 K to 345 K, there is increased peak splitting of the first two stronges t reflections (220) and (022) as shown in Figure 6 4 (B) Using Gaussian peak fitting, at 100 K the splitting is negligible, at 295 K the peaks split by 0.010o, and at 345 K by 0.016o. There is no obvious change in peak splitting between 345 K and 400 K. A similar splitting trend is observed for the (440) and (044) peaks; increasing from 100 K to 345 K and no obvious increase between 345 K and 400 K. This is consistent with anisotropic lattice expansion. By contrast, i t i s also interesting to note that both (022) and (044) peaks shift to the right from 295 K to 345 K, which i ndicates contraction across those planes as a function of temperature. Figure 6 5 (A) show s a summary of lattice parameters at the four different temperatures. While lattice parameters b and c increase with increasing temperature, l attice parameter a exhibit s an anomalous decrease from 100 K to 345 K, which is also indicative of a possible phase transiti on. Th is type of lattice parameter shrinkage also

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125 happens near the phase transition temperature in Gd3RuO7, which also has a weberitetype structure.151 0 5 10 15 20 25 30 (660) (642) (246) (444) (620) (080) (404) (044) (440) (062) (224) (422) (004) (400) (111) (110) (040) (202) (022)400 K 345 K 295 K 2 (Degrees)Intensity (Arb. Units)100 K(220) (A) 7.65 7.70 7.75 7.80 7.85 (044) (440)(022)400 K 345 K 295 K 2 (Degrees)Intensity (Arb. Units)100 K(220) 15.2 15.4 15.6 15.8 (B) Figure 6 4 (A ) High resolution XRD of Gd 3 NbO 7 = 0.414201 ( B ) High resolution XRD showing details about the increasing peak split of (220) and (022), and (044) (440)

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126 It is worth remembering that the weberitetype structure is a superstructure of fluorite, and the lattice parameters of the weberitetype can be viewed as af, 2 af and af ( af is the lattice parameter of fluorite, ~ 5 ). Figure 6 5 (B) shows af calculated from lattice parameters a b c and the unit cell volume at four different temperatures. It clearly shows that although a exhibits anomalous lattice contraction from 100 K to 345 K, the overall effect is still volumetric expansion. 100 150 200 250 300 350 400 7.52 7.53 7.54 7.55 10.60 10.65 Lattice Parameters ( ) Temperature (K)b a c 100 150 200 250 300 350 400 5.30 5.31 5.32 5.33 5.34 34 V 2 b 2 c 2 a Lattice parameters af( )Temperature (K) (A) (B) Figure 6 5 (A) Lattice parameters of Gd 3 NbO 7 at different temperatures (B) Lattice parameters of a f Upon detailed inspection of the XRD patterns, perhaps the strongest evidence of phase transition is revealed in that the (201) reflection appears o at 100 K and 295 K but does not above 345 K ( Figure 6 6 ). The disappear ance of (201) reflection adds an extra reflection condition above 345 K : both h and l are 2 n ( n is an integer) for ( h 0 I ) At all measured temperatures the reflection conditions also have to satisfy h + k = 2 n for (hkl) and l = 2 n for (00 l ). The software Checkcell was used to sear ch the space groups that can be consistent with these observations.154 The initial search resulted in 8 space groups with mm2 point group for the low temperature (LT) phase and 3 space

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127 groups with mmm point group for the high temperature (HT) phase. The similarity of XRD patte r ns suggests that the transition is displacive with only straightforward changes in symmetry : e.g. symmetry operations are gained or lost. Therefore, it is safe to assume that the space groups of the LT phase and the HT phase shoul d have a subgroup and super group relation ship Previously, Astafyev et al.38 proposed that the transition is between Cmm2 and its super group Cmmm. However, (201) reflection is allowed in the Cmmm space group. Among the 8 candidate space groups for th e LT phase and 3 for the HT phase, only space group Cm2m (No.38) and Cmcm (N o .63) have a subgroup and super group relationship. In light of the above information, Cm2m and Cmcm were selected for the LT structure and the HT structure, respectively and utilized as the basis for the pattern refinement described below. 6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 (131) (211) (201) (200)400 K 345 K 295 K 2 (Degrees)Intensity (Arb. Units)100 K(002) Figure 6 6 High resolution XRD showing details about the (201) reflection.

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128 The initial structural model was based on Na2NiInF7 as Ln3M O7 are extreme cases of Na2NiInF7 in the weberite family as discussed in Chapter 2.40 The space group of Na2NiInF7 is Pnma .68 A s pace group transformation between Pnma and Cm2m was applied using Powdercell126 through their common subgroup Pmc21 to get the initial atomic positions of Gd3NbO7 in a C centered unit cell. The powder diffraction patterns were refined with GSAS software.155156 Table 6 1 shows a summary of refinement par ameters. There are a total of 71 refined parameters for low temperature and 54 parameters for high temperature phases including crystal structure (lattice, atomic positions, and isotropic atomic displacement), diffractometer constants (zero shift and polarization), scale factor, background, and profile function. The observed intensities, calculated intensities, and their difference at 100 K are shown in Figure 6 7 Figure 6 7 Observed and calculated high resolution powder X ray diffraction. 0 5 10 15 20 25 30 Rwp = 12.91% and Rp = 9.16% observed calculated difference peak position 2 (degrees)Intensity ( arb. units)

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129 Table 6 1 Crystal data and refinement parameters Temperature 100 K 295 K 345 K 400 K Lattice 7.5393(3) 10.6108(3) 7.5327(3) 7.5324(1) 10.6185(2) 7.5476(1) 7.5294(2) 10.6202(2) 7.5522(1) 7.5321(2) 10.6239(2) 7.5554(2) Z 4 4 4 4 Space group Cm2m Cm2m Cmcm Cmcm ) 0.400919 0.414201 0.414201 0.414201 range (deg) 0.5 ~ 29.999 0.5 ~ 29.999 0.5 ~ 29.999 0.5 ~ 29.999 Total no. reflections 29501 29501 29501 29501 No. peaks 432 404 371 373 No. Parameters refined 71 71 54 54 R wp 12.91% 10.39% 10.28% 11.06% R p 9.16% 7.93% 8.10% 8.69% GOF ( 2 ) 8.100 5.169 4.989 5.808 Table 6 2 and Table 6 3 list atomic positions and isotropic atomic displacement parameters of Gd3NbO7 at 400 K, 345 K, 295 K, and 100 K after Rietveld refinement. It is important to note that due to the limitations of X ray, the atomic displacement of ox ygen ions may not be accurate. Usually, neutron diffraction is more s uitable for refining the atomic position s and displacement parameters of oxygen. However, since Gd absorbs thermal neutrons, neutron diffraction cannot be used on Gd3NbO7. Table 6 2 Lattice parameters and atomic positions at 345 K and 400 K (space group Cmcm) 345 K 400 K Site and Wyckoff x y z U iso (100) x y z U iso (100) Gd1 4b 0 0.5 0 2 05(1) 0 0.5 0 2 61(1) Gd2 8g 0.7337(3) 0.7330(2) 0.25 1 303(5) 0.7341(3) 0.73335(3) 0.25 1 871(6) Nb 4a 0 0 0 0 67(1) 0 0 0 1 15(2) O1 4c 0 0.0648(5) 0.25 1 8(2) 0 0.0648(6) 0.25 2 5(2) O2 4c 0 0.6288(5) 0.25 0 6(1) 0 0.6289(6) 0.25 1 2(1) O3 4 c 0 0.3640(5) 0.25 0 8(1) 0 0.3642(6) 0.25 1 5(1) O4 16h 0.1918(3) 0.8794(3) 0.0317(3) 2 02(9) 0.1922(4) 0.8794(3) 0.0319(4) 2 8(1)

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130 The Gd3NbO7 structure has an arrangement of NbO6Gd1O8 layers and VII coordinated Gd2 between layers It is seen that the Gd2 (Wyckoff position 8g) splits into two Wyckoff positions, 4e (Gd2(1)) and 4d (Gd2(2)) Also, the four oxygen atomic positions in Cmcm split into eight types in Cm2m Table 6 3 Lattice parameters and atomic positions at 100 K and 295 K (space group Cm2m) 100 K 295 K Site and Wyckoff x y z U iso (100) x y z U iso (100) Gd1 4c 0 0.5060(4) 0.2440(1) 2 91(1) 0 0.4943(5) 0.2546(2) 2 91(1) Gd2(1) 4e 0.7734(2) 0.2327(4) 0.5 4 55(2) 0.7681(2) 0.2275(5) 0.5 3 48(2) Gd2(2) 4d 0.2661(1) 0.2678(4) 0 0 242(5) 0.2664(1) 0.2618(5) 0 0. 733(6) Nb 4c 0 0.9996(4) 0.7353(3) 1 48(2) 0 0.9993(5) 0.7551(2) 1 20(1) O1(1) 2a 0 0.952(1) 0 0 03(24) 0 0.932(2) 0 3 0(3) O1(2) 2b 0 0.070(1) 0.5 3 7(4) 0 0.060(2) 0.5 3 3(3) O2(1) 2a 0 0.623(1) 0 0 17(22) 0 0.616(1) 0 1 2(2) O2(2) 2b 0 0.348(3) 0.5 2 9(4) 0 0.340(1) 0.5 1 7(3) O3(1) 2a 0 0.377(1) 0 2 4(3) 0 0.379(1) 0 0 4(2) O3(2) 2b 0 0.634(2) 0.5 3 8(4) 0 0.6387(9) 0.5 0 4(2) O4(1) 8f 0.2144(8) 0.8754(8) 0.7304(8) 1 1(1) 0.203(1) 0.878(1) 0.7285(9) 1 8(1) O4(2) 8f 0.669(1) 0.6168(8) 0.2132(9) 3 2(2) 0.680(1) 0.6184(9) 0.2103(9) 2 4(1) At 345 K and 400 K, Nb5+ ions occupy Wyckoff position 4a with site symmetry 2/ m in the center of NbO6 polyhedra (distorted octahedra). Each Nb5+ ion is bonded to two O1 and four O4 with O1 being corner shared by neighboring NbO6 polyhedra. The bond angle of O1Nb O1 is 180o. The NbO6 polyhedra align in a zigzag manner along [001] and the Nb5+ ions are separated along [001] with constant distance ( c/2, c being the lattice parameter). When cooling down to the transition temperature, Nb5+ ions shift slightly away from the 2fold axis parallel to the [100] direction but still in the mirror plane which is perpendicular to [100].( Figure 6 8 ) Therefore, there is no Nb5+ displacement projected on the a axis. The shift of the Nb5+ ions from t he 2/ m site projected on the c axis ( c) is opposite with their two nearest Nb5+ neighbors along [001] ( Figure 6 9 and Figure 6 10). The distances between two neighboring Nb5+ ions

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131 become alternatively c/ 2 + 2 c or c/ 2 2 c. By contrast, the shift of the Nb5+ from the 2/ m site projected on the b axis ( b) is in the same direction with each other ( Figure 6 11). (A) (B) Figure 6 8 ( A ) Approximately [010] view of NbO 6 octahedron at the high and low temperature phases. At the high temperature phase, the position of the centered Nb (black circle) has both 2fold (line and ellipse) and mirror (translucent plane) symmetry. At low temperature phase, Nb displaces away from 2fold a xe but still in the mirror plane. ( B ) Approximately [100] view of NbO 6 octahedron at the high and low temperature phases. In the anion sublattice, due to the loss of the 2fold symmetry the O1 position (mu ltiplicity: 4) splits into O1(1) (multiplicity:2) and O1(2) (multiplicity:2). The neighboring NbO6 octahedra are corner shared alternatively through the O1(1) or the O1(2) ions along the [001] direction. The bond angle of O1(1) Nb O1(2) is 177.4o at 295 K and 171.4o at 100 K. Same as t he O1, the O4 position (16h ) splits into O4(1) (8 f ) and O4(2) (8 f ). The NbO6 polyhedra are more distorted from a regular octahedron due to the loss of symmetry. The geometrical center also shifts. Accounting both the shifts of the Nb5+ ions and the geometric center, the net displacement of the Nb5+ ions from the geometrical center of NbO6 polyhedra is 0.02 at 295 K and 0.15 at 100 K

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132 Figure 6 9 [100] view of Gd3NbO7, rendered s pheres indicate atomic positions at high temperature phase; black circles show atomic positions at low temperature phase. Figure 6 10 [100] view of spacing filling Nb and Gd 1 chains parallel to the [001] direction, black circles show the center positions at high temperature phase, the spacing of which is c/2. The black arrows above the atoms indicate the displacement orientation along [001] from the center positions. The c is the shifting distance of the Nb5+ ions projected on the c axis and the c stands for the shift of the Gd 3+ ions projected on the c axis.

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133 Figure 6 11 [100] view of spacing filling Nb and Gd 1 B lack circles show the center positions at high temperature phase The arrows indicate the displacement along [010]. The b is the shifting distance of the Nb5+ ions projected on the b axis and the b stands for the shift of the Gd3+ ions projected on the b axis. Focusing on the rare earth ions, in the HT phase, one third of the Gd3+ ions (Gd13+) occupy a position with symmetry 2/ m in the center of LnO8 polyhedra. However, in the LT phase, they shift slightly away from the 2 fold axi s which is parallel to [100] to occupy an off center site with in the mirror plane similar to the Nb5+ ions ( Figure 6 12). The mirror plane is perpendicular to [100], and hence there is no shift of Gd3+ along [100]. Edgesharing Gd1O8 p olyhedra align along the [001] direction in both the HT and the LT phases. The distance along [001] between neighboring Gd13+ ions is constant

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134 and equal to c/2 at HT. However, at LT, the distance is alternatively c/ 2 + 2 c' or c/ 2 2 c' ( c' is the proj ected shift ing distance of Gd3+ from the 2/ m site along [001]) The Gd3+ ions shift in the same direction along [010], which is the opposite shifting direction of Nb5+ ( Figure 6 11). At HT, the distance between two neighboring Gd3+ and Nb5+ ions is b /2 ( b being lattice parameter in [010]). By contrast, at LT, the distance becomes alternatively b /2 + b + b' and b /2 b b' ( b and b' is the projected shift of Nb5+ and Gd3+ along [010], respectively). Gd13+ ions are displaced by 0.07 at 295 K and by 0.11 at 100 K from the geometrical center of the GdO8 polyhedra. It is t herefore clear that the phase transition in Gd3NbO7 is chiefly concurrent by the off center shift of both Nb5+ and Gd13+ ions in their corresponding polyhedra. The net dipole per unit cell at 100 K and 295 K was calculated based on the atomic positions. The Gd1 position was chosen to be the reference when calculating the net dipole. The net displacements of all other ions from Gd1 are i n [010] direction. It confirms the polar axis [010] in space group Cm2m As discussed above, there is no displacement of the Nb5+ along [100]. Because of Gd1 is on the mirror plane perpendicular to [100], the net displacements of O2and Gd23+ from the Gd1 are compensated and zeroed out by symmetry. Along [001], the Gd23+ ions do not shift. The shifts of Nb5+ ions as well as O2are antiparallel, respectively, resulting in zero net displacements along [001]. Therefore, there is no net dipole along [100] and [001]. As shown in Figure 6 11, the displacement of the Nb5+ are in the same direction but opposite to those of Gd3+. Since the respective shift distances and net charges of Nb5+ and Gd3+ are different, there is net dipole in the [010] direction. The details of the calculation are shown in Table 6 4 The net dipole per unit cell at 100 K is 0.0503 C/m2

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135 in [010] and at 295 K 0.0045 C/m2 in [0 10]. These values are much lower than the calculated net dipole for tetragonal BaTiO3 (0.16 C/m2), which is reasonable since the permittivity of BaTiO3 is almost two order s of magnitude higher.110 Table 6 4 The net dipole calculation. 100 K 295 K Q (1.610 -19 C) # in the unit cell dy () (C ) dy () (C ) Gd1 +3 4 0 0 0 0 Gd2(1) +3 4 0.0233 2.97 0.0168 2.14 Gd2(2) +3 4 0.0118 1.50 0.0175 2.23 Nb +5 4 0.0064 1.36 0.005 1.06 O1(1) 2 2 0.279 11.86 0.271 11.50 O1(2) 2 2 0.269 11.43 0.268 11.34 O2(1) 2 2 0.0497 2.11 0.0450 1.91 O2(2) 2 2 0.0087 0.37 0.0124 0.525 O3(1) 2 2 0.0377 1.60 0.0514 2.18 O3(2) 2 2 0.0387 1.64 0.0223 0.94 O4(1) 2 8 0.119 20.27 0.134 22.70 O4(2) 2 8 0.139 23.63 0.126 21.37 Net dipole (C/m 2 ) 0.0503 0.0045 (A) (B) Figure 6 12 (A) Approximately [010] view of Gd1O 8 polyhedron at high and low temperature phases. At low temperature phase, Gd1 (rendered sphere in the center of the polyhedral) moves away from 2fold axe (line and ellipse) within the mirror plane (translucent plane). (B) Approximately [100] view of Gd1O8 octahedron at the high and low temperature phases.

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136 Finally, it is quite interesting that in the LT phase the off center distance of both Nb5+ and Gd13+ ions increases with decreasing temperature, and that the relative displacement the Nb5+ and Gd13+ ions is antiparallel but generates net dipole along [010] (see Figure 6 11). This suggests the possibility of ferroelectric behavior (incipient ferroelectric), and while our preliminary tests (piezoelectric act ivity and polarization hysteresis) have not yielded significant insight in this respect, further investigation is warranted. 6.5 Conclusion Seco nd harmonic generation (SHG), heat capacity measurement s and IR indicated a phase transition in Gd3NbO7 at about 340 K. The lambdashape specific heat near the phase transition temperature suggest s a 2nd order nature of the phase transition. High resolution X ray diffraction was conducted at 100 K, 295 K, 345 K and 400 K. The appear ance of (201) reflection upon cool ing confirmed the phase transition. Rietveld refinement was performed on the XRD patterns at four above mentioned temperatures and resolved the controversy regarding the space group of the low ( Cm2m) and high temperature ( Cmcm) phases It was also concluded that t he phase transition upon cooling is mainly due to the off center shifts of Nb5+ and one third of the Gd3+ ions within their corresponding polyhedra. The net dipole per unit cell is 0.0503 C/m2 at 100 K and 0.0045 C/m2 at 295 K along [010]. It suggests the possibility of ferroelectric behavior (incipient ferroelectric) and deserves a further investigation.

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137 CHAPTER 7 PHASE TRANSITION IN La3NbO7 and Nd3NbO7 7.1 Introduction The space group Pnma (No. 62) was first assigned to La3NbO7 and Nd3NbO7.127128 However, when the crystal structure was first reported by Rossell36, the space group Cmcm (No. 63) was used. Rossells description of the crystal structure as well as the space group Cmcm was then the prototype widely accepted for Ln3B O7type compounds including Ln3RuO7 (Ln3+ = La3+, Pr3+, Nd3+, and Sm3+),16,83,90,92,94 95,97100,157 Ln3TaO7 (Ln3+ = La3+, Pr3+, and Nd3+),15,88,158 Ln3IrO7 (Ln3+ = Pr3+, Nd3+, Sm3+, and Eu3+),18,89,91 and Ln3ReO7 (Ln3+ = Pr3+, Nd3+, Sm3+, Gd3+, Tb3+, and Dy3+).17,21,93,96 However, Rossell et al.36,80 also commented on the unexpected very weak h 0 l reflections with odd l in Nd3NbO7, which are forbidden in Cmcm Kahnharari et al.37 claimed the very weak forbidden reflections cannot be neglected and ther efore assigned the space group Pnma to La3NbO7 based on single crystal diffraction. Actually, Cmcm is related to Pnma since Pmcn (another setting of Pnma ) is the subgroup of Cmcm.51 The h 0 l reflections with odd l are forbidden in Cmcm but allowed in Pnma .51 As stated in this study, synchrotron XRD and neutron powder diffraction have been performed on the two powders to clarify the appearance of the h 0 l reflections wi th odd l An interesting phase transition was observed in these two compounds based on heat capacity measurements. It was claimed that the phase transition is due to the displacement of atoms with no change in crystal system and no appreciable change in lattice parameters based on XRD.147 In fact, phase transition is commonly observed in Ln3B O7 family. Consequently, there have been considerable amounts study, especially

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138 in crystallographic aspects, on Ln3IrO7,91 Ln3MoO7,8182,87,148 Ln3OsO7,149 Ln3RuO7,150151 and Gd3NbO7 159 (which is also the topic of Chapter 6). The phase transition in Sm3OsO7, Eu3OsO7, and Gd3OsO7 changes from space group P21nb (No. 33) to Cmcm on heating, maintaining an orthorhombic lattice.149 Nd3RuO7 undergoes a phase transition f rom monoclinic ( P21/m No. 11) with = 90.008o to orthorhombic ( Cmcm).97 Therefore, it is reasonable to assume that above the phase transition temperature the space group of La3NbO7 and Nd3NbO7 is Cmcm, which has the highest symmetry among all space groups reported for Ln3B O7 compounds. Neutron powder diffraction is used to investigate the crystal structure (including space group) of Nd3NbO7 and La3NbO7 before and after the phase transition. 7.2 Heat Capacity and SHG Measurements Klimenko et al.147 firs t measured the heat capacity of Nd3NbO7 and La3NbO7 from 295 K to 1100 K. In this study, the heat capacity was remeasured. The measuring temperature was extended down to 170 K as shown in Figure 7 1 The heat capacity plot showed an anomalous divergence between 340 K and 370 K for La3NbO7 and between 430 K and 470 K for Nd3NbO7. The results confirmed a phase transition, similar to the results of Klimenko's study.147 Figure 7 2 shows the real part of permittivity of La3NbO7 and Nd3NbO7 at 1 MHz. The temperature where the maximum of permittivity occurs is close to the phase transition temperature for both compounds. Therefore, the origin of the dielectric relaxation correlates to the phase transition. SHG measurements were also perform ed on La3NbO7 and Nd3NbO7. Figure 7 3 shows the SHG signal of La3NbO7 as well as the SHG signal of Gd3NbO7 for comparison. The laser power applied in measuring the SHG signals of La3NbO7 sample

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139 was 20 times higher than that used in measuring Gd3NbO7 sample. Only noise or white light generated by the laser w as detected for La3NbO7. The same response was observed for Nd3NbO7 that is, no SHG signal was detected. Therefore, from these results, it can be inferred that La3NbO7 and Nd3NbO7 have centrosymmetri c structures throughout the measured temperature range. 200 300 400 500 600 700 120 140 160 180 200 220 240 260 280 Nd3NbO7La3NbO7 370 K Heat Capacity ( J/ ( K mol ) )Temperature (K) 340 K 430 K 470 K Figure 7 1 Heat capacity of La 3 NbO 7 and Nd 3 NbO 7 200 300 400 500 600 700 30 35 40 45 50 55 60 65 La3NbO7 Nd3NbO7 rTemperature (K) Figure 7 2 The real part of permittivity of La 3 NbO 7 and Nd 3 NbO 7 The arrows point to the temperature where the maximum permittivity occurs.

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140 300 320 340 360 380 400 420 La 3 NbO 7 SHG (abr. units) Temperature (K) Gd 3 NbO 7 Figure 7 3 SHG of La 3 NbO 7 and Gd 3 NbO 7 7.3 Crystal Structure and Phase Transition of Nd3NbO7 and La3NbO7 7.3.1 Nd3NbO7 High resolution XRD at 100 K and room temperature was performed on Nd3NbO7. The wavelength used was 0.40092 The general reflection conditions for Cmcm are h + k = 2 n ( n stands for integer) for ( hkl) reflection and h l = 2 n for ( h0l ). There are 9 minor peaks that violate the reflection conditions for Cmcm as shown in Figure 7 4 and Table 7 1 By contrast, all the reflections are allowed for the general reflection conditions of Pmcn which are h + k = 2 n for (hk0 ) and l = 2 n for (00l ). Therefore, it is clear that the correct space group of Nd3NbO7 below the phase transition temperature is Pmcn The Rietveld method was used to refine the high resolution XRD pattern with GSAS software.155156 There are a total of 62 refined parameters as shown in Table 7 2 including crystal structure (lattice, atomic positions, and isotropic atomic displacement), diffractometer constants, scale factor, background, and profile function. Figure 7 4

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141 shows the observed intensities, calculated intensities, and their differences for the extra 9 reflections and Figure 7 5 shows observed intensities, calculated intensities, and their differences of the whole pattern at room temperature. The resulting atomic positions and is otropic atomic displacements are listed in Table 7 3 Table 7 1 List of reflections which are forbidden by Cmcm but allowed in Pmcn h k l d () I/Imax (100) 0 1 1 4.288 5.358 1.0 1 2 1 7.077 3.248 0.9 0 3 1 9.646 2.384 0.4 2 1 3 10.440 2.203 0.3 2 3 1 10.531 2.184 1.3 1 4 1 12.771 1.802 1.5 4 3 1 12.827 1.795 0.9 2 5 1 16.163 1.426 0.8 3 4 3 16.504 1.397 0.7 Table 7 2 Crystal data and refinement parameters. Temperature 100 K 295 K Lattice 10.8930(2) 7.5238(2) 7.6179(2) 10.9043(1) 7.5295(1) 7.6271(8) Z 4 4 Space group Pmcn Pmcn ) 0.400919 0.400919 range (deg) 0.5 ~ 29.999 0.5 ~ 29.999 Total no. reflections 29501 29501 No. peaks 759 765 No. Parameters refined 62 62 Rwp 15.31%, 8.68% Rp 15.31%, 6.59% GOF ( 2 ) 9.398 3.348

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142 4.2 4.3 7.0 7.1 7.2 (112) (310) Intensity (arb. units)2 (degrees)(200) (011) (121) 9.6 9.7 9.8 10.4 10.5 10.6 (420) (213) (402) Intensity (arb. units)2 (degrees)(113) (031) (231) (A) (B) 12.7 12.8 16.1 16.2 16.3 16.4 16.5 Observed Calculated Background Obs Calc(334) (514) (025) (251) (712) Intensity (arb. units)2 (degrees)(141) (431) (343) (C) Figure 7 4 Details of the forbidden peaks by Cmcm They are pointed to by the arrows. The red lines and the blue lines are the calculated pattern and the background using the Rietveld method.

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143 0 5 10 15 20 25 30 (400) (021) (224) (004) (422) (022) (220) (202) Obeserved Calculated Background Obs-Calc Peaks Intensity (arb. units)2 (degrees) Figure 7 5 High resolution XRD of Nd3NbO7 at room temperature ( ). Diamond symbols indicate the less intense peaks which are associate with the Nd3NbO7 structure but not indexed. The Rietveld method was used to refine the pattern as shown in the red lines. Neutron powder diffraction (HB2A in HFIR of ORNL) was also performed on Nd3NbO7 at different temperatures. The monochromators are vertically focusing Ge (115). The resolution is 2103 Below the phase transition temperature (~ 450 K), the appearance of reflections (141) and (431) supports the space group Pmcn ( Figure 7 6 ). By contrast, 9 minor reflections in h igh resolution XRD were found to be associated with the space group Pmcn as shown in Table 7 1 The reason why there are two observable extra reflections in neutron diffraction is that the remaining 7 minor reflections are easier to be overlapped or buried in the neighboring peaks in neutron o) is overlapped o approximately equal to the step size (0. 05o) for the neutron diffraction. However, the

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144 step size for high resolution XRD is 0.001o oo) reflections. Table 7 3 Atomic positions of Nd3NbO7 at 100 K, and 295 K, from high resolution XRD. 100 K Wyckoff x y z Uiso Nb 4c 0.25 0.2526(1) 0.0043(3) 0.0020(2) Nd1 4c 0.25 0.7794(1) 0.0082(1) 0.0022(1) Nd2 8d 0.47689(3) 0.45359(5) 0.25164(9) 0.00132(7) O1 8d 0.8722(5) 0.9475(6) 0.9653(8) 0.005(1) O1 8d 0.3828(5) 0.4128(6) 0.9626(8) 0.012(1) O2 8d 0.3821(4) 0.7264(6) 0.2529(11) 0.0007(10) O3 4c 0.25 0.3227(8) 0.2472(13) 0.003(2) 295 K Wyckoff x y z Uiso Nb 4c 0.25 0.2530(1) 0.0032(1) 0.0027(1) Nd1 4c 0.25 0.77569(5) 0.00725(8) 0.0110(1) Nd2 8d 0.47712(2) 0.45425(3) 0.25140(6) 0.00725(5) O1 8d 0.8732(3) 0.0529(4) 0.9640(5) 0.0037(8) O1 8d 0.3830(3) 0.4187(4) 0.9626(5) 0.017(1) O2 8d 0.3817(2) 0.7273(3) 0.2542(6) 0.0049(7) O3 4c 0.25 0.3226(5) 0.2484(8) 0.0069(10) The disappearance of (141) and (431) reflections above 450 K confirms the phase transition as shown in Figure 7 6 The intensities of the (141) and (431) reflections are comparable at 5 K, 295 K, and 310 K and significantly decrease from 310 K to 390 K. These two peaks totally disappear at 450 K, 470 K, and 500 K. Therefore, Nd3NbO7 undergoes a phase transition on heating from the space group Pmcn to Cmcm. The Rietveld refinement method was used to analyze all the neutron diffraction patterns with GSAS software.155156 Table 7 4 and Table 7 5 list the lattice parameters and a summary of refined parameters for the low temperature phase and the high temperature phase, respectively. Figure 7 7 shows the observed intensities, calculated

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145 intensities, and their difference at 500 K. Figure 7 8 shows the detailed fitting on the o to 54.5o between 295 K and 500 K. The refined atomic positions are listed in Table 7 6 for the low temperature phase an d Table 7 7 for the high temperature phase. 49 50 51 52 53 295 K 500 K (512) (041) (141) (431) (133) (241)Intensity (arb. units)2 (degrees) (A) 49 50 51 52 53 5 K 295 K 310 K 390 K 450 K 470 K 500 K (512) (041) (141) (431) (133) (241)Intensity (arb. units)2 (degrees) (B) Figure 7 6 Neutron diffraction patterns ( ) (A) at 295 K and 500 K, (B) at 5 K, 295 K, 310 K, 390 K, 450 K, 470 K, and 500 K. The lines are the patterns below the phase transition and the scattered points are the patterns above the phase transition temperature. Two extra reflections at the low temperature phase are pointed by the arrows.

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146 20 40 60 80 100 120 (224) (004) (422) (132) (330) (421) (222) (312) (130) (220) Observed Calculated Background Obs-Calc Peaks Intensity (arb. units)2 (degrees)(202) Figure 7 7 Neutron diffraction of Nd 3 NbO 7 at 500 K ( ). 50 52 54 500 K (241) (133) (431) (141) (041) (512) Observed Calculated Background 2 (degrees)Intensity (arb. units)295 K Figure 7 8 Detailed fitting from 2 48.5 o to 54.5 o between 500 K and 295 K. The arrows point to the extra reflections at low temperature

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147 Table 7 4 Crystal data for the low temperature phase and refinement parameters for neutron diffraction Temperature 5 K 295 K 310 K 390 K Lattice 10.8815(2) 7.5208(2) 7.6162(1) 10.8988(3) 7.5285(2) 7.6270(2) 10.8971(3) 7.5292(2) 7.6257(2) 10.9048(3) 7.5262(2) 7.6342(2) Z 4 4 4 4 Space group Pmcn Pmcn Pmcn Pmcn ) 1.5378 1.5378 1.5378 1.5378 range (deg) 10 ~ 130 10 ~ 130 10 ~ 130 10 ~ 130 Total no. reflections 1832 1832 1832 1832 No. peaks 574 573 573 573 No. Parameters refined 64 64 64 64 Rwp 8.06% 7.94% 8.14% 8.96% Rp 6.12% 6.01% 6.29% 6.80% GOF ( 2 ) 2.872 2.845 2.933 7.129 Table 7 5 Crystal data for the high temperature phase and refinement parameters for neutron diffraction. Temperature 450 K 470 K 500 K Lattice 10.9075(3) 7.5240(2) 7.6397(2) 10.9083(3) 7.5250(2) 7.6405(2) 10.9100(3) 7.5272(2) 7.6421(2) Z 4 4 4 Space group Cmcm Cmcm Cmcm ) 1.5378 1.5378 1.5378 range (deg) 10 ~ 130 10 ~ 130 10 ~ 130 Total no. reflections 1832 1832 1832 No. peaks 312 312 312 No. Parameters refined 53 53 53 Rwp 7.39% 6.71% 7.22% Rp 5.68% 4.91% 5.5% GOF ( 2 ) 2.435 4.054 4.393

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148 Table 7 6 Atomic positions and isotropic atomic displacement of Nd3NbO7 at 5 K, 295 K, 310 K, and 390 K from neutron diffraction. 5 K Wyckoff x y z U iso Nb 4c 0.25 0.2550(10) 0.0015(15) 0.0063(10) Nd1 4c 0.25 0.7783(8) 0.0104(10) 0.0096(12) Nd2 8d 0.4775(2) 0.4538(4) 0.2500(9) 0.0041(5) O1 8d 0.8717(5) 0.9504(6) 0.9652(7) 0.0066(10) O1 8d 0.3844(7) 0.4163(8) 0.9590(10) 0.0230(17) O2 8d 0.3817(4) 0.7267(5) 0.2563(12) 0.0119(9) O3 4c 0.25 0.3256(7) 0.252(2) 0.0131(12) 295 K Wyckoff x y z U iso Nb 4c 0.25 0.2542(11) 0.0029(11) 0.006(1) Nd1 4c 0.25 0.7734(8) 0.0092(10) 0.0093(11) Nd2 8d 0.4779(3) 0.4551(4) 0.2522(10) 0.0072(6) O1 8d 0.8718(6) 0.9502(7) 0.9680(8) 0.013(1) O1 8d 0.3826(7) 0.4208(9) 0.9561(9) 0.019(1) O2 8d 0.3823(4) 0.7267(5) 0.2462(13) 0.0087(10) O3 4c 0.25 0.3236(8) 0.252(2) 0.0115(12) 310 K Wyckoff x y z U iso Nb 4c 0.25 0.2539(12) 0.005(2) 0.012(1) Nd1 4c 0.25 0.7747(10) 0.0085(12) 0.016(1) Nd2 8d 0.4782(3) 0.4542(4) 0.2506(12) 0.0111(8) O1 8d 0.8727(7) 0.9493(8) 0.9633(10) 0.011(1) O1 8d 0.3829(8) 0.4193(9) 0.9538(13) 0.034(2) O2 8d 0.3827(4) 0.7261(6) 0.255(2) 0.014(1) O3 4c 0.25 0.3245(8) 0.255(2) 0.018(1) 390 K Wyckoff x y z U iso Nb 4c 0.25 0.2501(15) 0.003(2) 0.017(1) Nd1 4c 0.25 0.7658(14) 0.009(2) 0.0238(17) Nd2 8d 0.4781(3) 0.4535(5) 0.2532(14) 0.0153(7) O1 8d 0.8720(8) 0.9498(9) 0.9650(13) 0.019(2) O1 8d 0.3834(11) 0.4204(12) 0.9610(17) 0.041(3) O2 8d 0.3828(5) 0.7268(7) 0.250(2) 0.020(2) O3 4c 0.25 0.3218(9) 0.249(3) 0.026(2) Figure 7 9 indicates the lattice parameters after the refinements from both high resolution XRD and neutron diffraction. At room temperature, the lattice parameters

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149 calculated from high resolution XRD matches well with those from neutron diffraction. There is an anomalous decrease of the lattice parameter c from 310 K to 450 K, which may be evidence for the phase transition. As discussed in Chapter 6, Gd3NbO7 also exhibits a decrease in one lattice parameter from room temperature to the phase transition temperature. A summary of the unit cell volume at different temperatures is shown in Figure 7 10. At room temperature, the difference between the volume from the neutron diffraction and from the high resolution XRD is about 0.6%, which is considered a reasonable match. The unit cell volume at 295 K and 310 K are comparable, only less than 0.2% difference. In general, the unit cell volume increase with increa sing temperature though there is anomalous decrease in the lattice parameter c. 0 100 300 400 500 7.5 7.6 10.8 10.9 11.0 c bLattice parameter (A) Temperature (K)oa Figure 7 9 Lattice parameters (with errors) of Nd 3 NbO 7 at different temperatures. The solid square symbols indicate the la ttice parameters from neutron diffraction. The open triangle symbols are from high resolution XRD.

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150 0 100 200 300 400 500 622 624 626 628 Temperature (K)Unit Cell Volume ( A3)O Figure 7 10 Unit cell volume (with errors) of Nd 3 NbO 7 at different temperatures. The solid square sym bols are calculated from neutron diffraction. The open square symbols are from high resolution XRD. Above 450 K, Nb5+ ions occupy Wyckoff position 4b with site symmetry 2/m in the center of NbO6 polyhedra (distorted octahedra). Each Nb5+ ion is bonded to four O1 (site symmetry 1 ) and two O3 (site symmetry m2m) with O3 being corner shared by neighboring NbO6 polyhedra. The bond angle of O3Nb O3 is 180o ( Figure 7 11). The NbO6 polyhedra align in a zigzag manner along [001] and the Nb5+ i ons are separated with constant distance ( c/2, c being the lattice parameter). When cooling down to the transition temperature, the Nb5+ ions shift away from the center of the NbO6 as well as the 2fold axis, which is parallel to the [100] direction. The shifts of ions are confined in the mirror plane, which is parallel to (100) and occupy a site with only mirror symmetry (Figure 7 12). The off center displacement of Nb3+ decreases as the increasing temperature as shown in Figure 7 13.

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151 Table 7 7 Latt ice parameters and atomic positions of Nd3NbO7 at 450 K, 470 K, and 500 K from neutron diffraction. 450 K Wyckoff x y z Uiso Nb 4b 0 0.5 0 0.011(1) Nd1 4a 0 0 0 0.016(1) Nd2 8g 0.2287(3) 0.2949(4) 0.25 0.0067(6) O1 16h 0.1265(3) 0.3118(5) 0.9633(4) 0.0229(8) O2 8g 0.1332(4) 0.0239(6) 0.25 0.0079(9) O3 4c 0 0.4282(8) 0.25 0.018(1) 470 K Wyckoff x y z Uiso Nb 4b 0 0.5 0 0.012(1) Nd1 4a 0 0 0 0.0182(10) Nd2 8g 0.2287(3) 0.2949(4) 0.25 0.0090(6) O1 16h 0.1263(3) 0.3119(4) 0.9635(4) 0.0250(7) O2 8g 0.1328(4) 0.0237(5) 0.25 0.0104(9) O3 4c 0 0.4284(8) 0.25 0.020(1) 500 K Wyckoff x y z Uiso Nb 4b 0 0.5 0 0.016(1) Nd1 4a 0 0 0 0.019(1) Nd2 8g 0.2288(3) 0.2956(4) 0.25 0.016(6) O1 16h 0.1264(3) 0.3116(5) 0.9639(4) 0.0274(8) O2 8g 0.1331(4) 0.0236(6) 0.25 0.014(1) O3 4c 0 0.4288(8) 0.25 0.023(1) The vectors between two neighboring Nb5+ ions are alternatively 0.5] and [0, 0.5] ( is the shift ing distance along [010] of Nb5+ ions). The shift of the Nb5+ ions away from the 2fold axis also gives more freedom to the O2ions. As a result, the O3 ions shift away from the 2fold axis parallel to [010] and the mirror plane parallel to (001) resulting in a site on the mirror plane parallel to (100). The O1 i ons at the site symmetry 1 (Wyckoff position 16h) split into two unequal 8d with site symmetry 1 indicated as O1 and O1. Therefore, the NbO6 polyhedra are more distorted since the O2ions have more degrees of freedom. The bond angle of O3Nb O3 cannot maintain 180o.

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152 (A) (B) Figure 7 11 (A) The Nb 5+ ions align along [001]. The separate between two neighboring Nb5+ along the [001] direction is c/2. The O3 ions are shared by two neighboring Nb5+ ions (B) Polyhedra view of the NbO6 octahedra. The NbO 6 octahedra align in a zigzag manner along [001].

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153 (A) (B) Figure 7 12 (A) Approximately [001] view of NbO 6 octahedra. At the high temperature phase, the position of the centered Nb (black sphere) has both 2fold (line and ellipse) and mirror (translucent plane) symmetry. At low temperature phase, Nb displaces away from 2fold axe but still in the mirror plane. (B) Approximately [301] view of NbO6 octahedra. The black circles show the oxygen positions at high temperature

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154 Similar to Nb5+, for the high temperature phase, the Nd13+ ions are in the center of Nd1O8 polyhedra with site symmetry 2/m and connected to four O1 ions and four O2 ions. Below the phase transition temperature, the Nd13+ ions shift away from the 2fold axis, which is parallel to the [100] direction. The shifts of the ions are confined to the mirror plane, which is parallel to (100). The Nd13+ ions are no longer at the center of the Nd1O8 polyhedra ( Figure 7 14 ). The off center displacement of Nd13+ is shown in Figure 7 13 as a function of temperature. It is worth mentioning that due to the limitation of XRD, the atomic positions of oxy gen ions may not be accurate. This is probably the reason why the calculated off center displacement at 100 K from high resolution XRD is higher than that at 5 K from neutron diffraction. 0 100 200 300 400 500 0.0 0.1 0.2 0.3 NbO6 Nd1O8 Temperature (K)Off-center Displacement (A)o Figure 7 13 Off center displacements of Nb 5+ inside NbO 6 and Nd1 3+ inside Nd1O 8 at different temperatures. The solid symbols are calculated from neutron diffraction and the open symbols are from high resolution XRD.

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155 Figure 7 14 Nd1O 8 polyhedra. At the high temperature phase, the position of the centered Nd (black sphere) has both 2fold (line and ellipse) and mirror (translucent plane) symmetry. At low temperature phase, Nb displaces away from 2 fold axe but sti ll in the mirror plane. As a result of losing 2fold symmetry of Nd13+, the connected O2ions have more degrees of freedom. As discussed above, the O1 ions split into O1 and O1. The O2 ions move away from the mirror plane parallel to [001], resulting in 8d of Pmcn with site symmetry 1 Accordingly, the Nd1O8 polyhedra are more distorted. Figure 7 15 shows the [001] view of the Nd13+ and Nb5+ ions both above and below the phase transition temperature. In the high temperature phase, the Nd13+ ions as well as the Nb5+ ions align perfectly along the [001] direction. In the low temperature phase, the neighboring Nd13+ ions in the [001] direction shifts alternatively in [010] and [0 10]. The neighboring Nb5+ ions in the [001] direction also moves away from the 2-

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156 folder axis alternatively in [010] and [010]. There is no displacement along [100] for both types of the ions. (A) (B) Figure 7 15 The [001] view of the Nd1 3+ and Nb 5+ ions for (A) the high temperature phase (B) the low temperature phase. The blue lines stand for unit cell. The origin of the high temperature phase is (0.25, 0.25, 0) different from the low temperature phase. The ions in the second layer of (B) are in dicated as solid black circle for better visual comparison. A more detailed comparison between the high temperature and low temperature phases is shown in Figure 7 16. The high temperature phase indicated as the black circles are overlapped with the low temperature phase shown as the rendered spheres. It is clear that two neighboring Nb5+ ions or two adjacent Nd13+ ions along [001] displace

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157 in an antiparallel manner parallel to [010]. Because of the antiparallel manner, the net dipoles produced by the off center displacement are compensated to zero. The neighboring Nb5+ and Nd13+ ions along [010] displace in the same direction, either in [010] or [010]. Figure 7 16 [100] view of space filling Nb and Nd1 chains parallel to the [001] direction, black circles show the center positions at high temperature phase. The black arrows above the atoms indicate the displacement orientation from the center positions along [010 ]. It is worth mentioning that there is one extra peak at d = 2.17 which cannot be indexed based on the orthorhombic lattice. This peak appears above and below the phase transition temperature. The relative intensity is about 7% for neutron diffrac tion

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158 The theoretical diffraction patterns of possible compounds like Nd2O3, Nd(OH)3, NdNbO4, LaNb5O14 (given the similarity of possible NdNb5O14), and PrNb3O9 (given the similarity of possible NdNb3O9) were compared with the unindentified peak, but no clear match was obtained. The structure of Nd3RuO7 with a monoclinic lattice was also used as an initial crystal structure for Rietveld refinement.97 However, it resulted in a poor refinement because the calculated pattern did not have a corresponding reflection for the unindentified peak and also had several strong extra reflections which did not exist in the observed pattern. Therefore, it is reasonable to assume the unidentified peak comes from an unreported neodymium niobate. 7.3.2 La3NbO7 The same phase transition occurring in Nd3NbO7 has also been found in La3NbO7. Figure 7 17 shows that the two extra reflections (141) and (431) appear below the phase trans ition temperature and disappear above the temperature. It is strong evidence for the occurrence of a phase transition. The phase transition is between the space group Cmcm and Pmcn as in Nd3NbO7. The Rietveld refinement method was also used to analyze the neutron diffraction patterns. Figure 7 18 shows an example of refinement including the observed pattern, the calculated pattern by refinement, the background, the difference between the observed pattern and the calculated one. All reflections associated with La3NbO7 are indexed by diamond symbols. It is worth mentioning that traces of LaNbO4 and La2O3 were also found in the neutron diffraction pattern. The lattice parameters and refinement parameter are listed in Table 7 8 for the low temperature phase and Table 7 -

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159 9 for the high temperature phase, respectively. The atomic positions and isotropic atomic displacement are list in Table 7 10 for the low temperature phase and Table 7 11 for the high temperature phase. 48 49 50 51 52 53 20 K 100 K 290 K 352 K 380 K 470 K Intensity (arb. units)(512) (431) (141) (041)2 (degrees)(133) (241) Figure 7 17 Neutron diffraction patterns of La 3 NbO 7 at different temperatures ( 1.5378 ). The patterns below the phase transition temperature are plotted in lines. The patterns above the phase transition tem perature are plotted in scattered points. Two extra reflections at the low temperature phase are pointed by the arrows. 20 40 60 80 100 120 Observed Calculated Background Difference Peaks (224) (004) (422) (220) (202)Intensity (arb. units)2 (degrees) Figure 7 18 Neutron diffraction of La 3 NbO 7 at 290 K ( ).

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160 Table 7 8 Crystal data for the high temperature phase and refinement parameters for neutron diffraction. Temperature 20 K 100 K 295 K Lattice 11.1478(3) 7.6413(3) 7.7407(2) 11.1487(3) 7.6398(3) 7.7407(2) 11.1593(4) 7.6309(3) 7.7522(2) Z 4 4 4 Space group Pmcn Pmcn Pmcn ) 1.5378 1.5378 1.5378 range (deg) 10 ~ 130 10 ~ 130 10 ~ 130 Total no. reflections 1832 1832 1832 No. peaks 608 608 608 No. Parameters refined 64 64 64 R wp 10.80% 11.21% 10.19% R p 8.07% 8.2% 7.36% GOF ( 2 ) 7.240 7.806 6.566 Table 7 9 Crystal data for the high temperature phase and refinement parameters for neutron diffraction. Temperature 380 K 470 K Lattice 11.1667(4) 7.6275(3) 7.7588(2) 11.1726(4) 7.6336(3) 7.7636(3) Z 4 4 Space group Cmcm Cmcm ) 1.5378 1.5378 range (deg) 10 ~ 130 10 ~ 130 Total no. reflections 1832 1832 No. peaks 330 330 No. Parameters refined 53 53 R wp 9.74% 10.24% R p 7.02% 7.61% GOF ( 2 ) 5.968 6.642

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161 Table 7 10. Lattice parameters and atomic positions of La3NbO7 at 20 K, 100 K, 295 K, and 390 K from neutron diffraction. 20 K Wyckoff x y z U iso Nb 4c 0.25 0.2584(15) 0.0067(19) 0.008(1) La1 4c 0.25 0.7762(9) 0.0073(12) 0.0079(15) La2 8d 0.4748(3) 0.4498(5) 0.2528(13) 0.0063(7) O1 8d 0.1296(8) 0.4462(9) 0.5247(10) 0.010(2) O1 8d 0.3805(7) 0.4147(9) 0.9619(9) 0.0031(14) O2 8d 0.3806(5) 0.7252(7) 0.253(2) 0.0074(11) O3 4c 0.25 0.3206(9) 0.255(3) 0.0052(17) 100 K Wyckoff x y z U iso Nb 4c 0.25 0.2601(16) 0.005(2) 0.0126(14) La1 4c 0.25 0.7751(11) 0.0066(14) 0.018(2) La2 8d 0.4750(4) 0.4487(5) 0.2515(15) 0.0157(8) O1 8d 0.8698(8) 0.9465(10) 0.9650(12) 0.020 (2) O1 8d 0.3806(8) 0.4156(9) 0.9621(11) 0.0126(17) O2 8d 0.3807(5) 0.7258(7) 0.252(2) 0.0140(12) O3 4c 0.25 0.3211(10) 0.253(3) 0.0143(18) 295 K Wyckoff x y z U iso Nb 4c 0.25 0.2614(19) 0.001(2) 0.0132(15) La1 4c 0.25 0.7696(14) 0.0086(17) 0.0179(18) La2 8d 0.4754(4) 0.4492(5) 0.2512(18) 0.0169(9) O1 8d 0.8681(9) 0.9439(11) 0.9661(13) 0.021 (2) O1 8d 0.3797(8) 0.4196(10) 0.9615(13) 0.014(2) O2 8d 0.3803(5) 0.7259(8) 0.250(3) 0.0150(13) O3 4c 0.25 0.3196(10) 0.254(3) 0.0129(19) A summary of lattice parameters at different temperatures are shown in Figure 7 19. The lattice parameter c shows anomalous extraction for the low temperature phase, the same as Nd3NbO7 and Gd3NbO7. After the phase transition temperature, the lattice parameter increases with increasing temperature. A summary of the unit cell volume at different temperatures are also plotted in Figure 7 20. Due to the anomalous decrease with increasing temperature in c, the unit cell volume at 20 K is slightly larger than that

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162 at 100 K. However, it is clear that the general trend of the unit cell volume is increasing with temperature. Table 7 11. Lattice parameters and atomic positions of La3NbO7 at 380K and 470 K from neutron diffraction. 450 K Wyckoff x y z U iso Nb 4b 0 0.5 0 0.0132(14) La1 4a 0 0 0 0.0211(14) La2 8g 0.2258(3) 0.3012(5) 0.25 0.0125(8) O1 16h 0.1233(4) 0.3175(6) 0.9645(5) 0.0186(9) O2 8g 0.1308(5) 0.0262(7) 0.25 0.0103(12) O3 4c 0.25 0.4327(10) 0.25 0.0052(17) 470 K Wyckoff x y z U iso Nb 4b 0 0.5 0 0.0171(17) La1 4a 0 0 0 0.0241(17) La2 8g 0.2262(4) 0.3009(5) 0.25 0.0163(9) O1 16h 0.1233(4) 0.3177(6) 0.9652(6) 0.0245(11) O2 8g 0.3699(6) 0.5267(8) 0.25 0.0149(14) O3 4c 0 0.4336(11) 0.25 0.02(2) 0 50 100 300 400 500 7.60 7.65 7.70 7.75 11.0 11.1 11.2 Lattice parameter (A) oTemperature (K)a b c Figure 7 19 Lattice parameters (with errors) of La 3 NbO 7 at different temperatures.

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163 0 100 200 300 400 500 659 660 661 662 663 Temperature (K)Unit Cell Volume ( A3)O Figure 7 20 Unit cell volume of La 3 NbO 7 at different temperatures. Similar to Nd3NbO7, for the high temperature phase, both Nb5+ ions and 8 coordinated La13+ (account for 1/3 of total La3+) are in the center of their corresponding polyhedra with site symmetry 2/m Below the phase transition temperature, both ions shift away from the 2 fold axis, which is parallel to the [100] direction. The shifts of ions are confined in the mirror plane, which is parallel to (100). The site symmetry of La13+ and Nb5+ results in m for the low temperature phase. The La13+ and Nb5+ ions are no longer at the center of their corresponding polyhedra. The off center shifts are shown in Figure 7 21. The off center displacement of Nd13+ decreases with increasing temperature As mentioned before, phase transition is commonly observed in Ln3B O7 compounds. The phase transition temperatures for Ln3B O7 are summarized in Figure 7 22. It is based on the summary by Nishimine et al.91 The phase transition temperatures for La3NbO7 and Nd3NbO7 are also added to Figure 7 22.

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164 0 100 200 300 400 500 0.0 0.1 0.2 0.3 NbO6 Nd1O8 Off-center Displacement (A)oTemperature (K) Figure 7 21. Off center displacements of Nb 5+ inside NbO6 and La1 3+ inside La1O8 at different temperatures. 1.04 1.06 1.08 1.10 1.12 1.14 1.16 200 400 600 Ln3RuO7 Ln3OsO7 Ln3ReO7 Ln3IrO7 Ln3MoO7 Ln3NbO7 Phase transition temperature (K)Ionic radius of Ln3+ (A)Gd Eu Sm Nd Pr Lao Figure 7 22. Phase transition temperature for Ln3B O7. The figure is based on the summary by Nishimine et al.91 and adds Ln3NbO7 points based on this work. The phase transition temperature of Ln3RuO7 and Ln3OsO7 is after Gemmill et al.149,157, Ln3MoO7 and Ln3IrO7 after Nishimine et al.18,91, Ln 3 ReO 7 after Hinatsu et al. 96

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165 It is clearly seen that the phase transition temperature is related to the ionic radius of Ln3+. Within the same B5+ ion, the phase transition temperature decreases with increasing the ionic radius of Ln3+. It is worth mentioning that the phase transition in Gd3NbO7 occurs at 340 K, which does not follow the general trend. It is because Gd3NbO7 b elongs to another weberitetype structure. In addition, all the phase transitions in Figure 7 22 except Gd3NbO7 are from a P type lattice to the orthorhombic lattice with space group Cmcm The phase transition in Gd3NbO7 is from Cm2m (No. 38) to Cmcm. 7.4 Conclusion Heat capacity measurements and neutron diffraction confirmed a phase transition in Nd3NbO7 at about 450 K as well as in La3NbO7 at about 360 K. SHG measurements indicate that Nd3NbO7 and La3NbO7 have a centrosymmetric structure both below and above the phase transition temperature. Based on high resolution X ray diffraction and neutron diffraction of Nd3NbO7 and La3NbO7 at room temperature, the correct space group below the phase transition temperature was determined to be Pmcn as there are som e minor peaks that violate the reflection conditions for Cmcm The disappearance of (141) and (413) reflections above the phase transition temperature confirmed the phase transition from Pmcn to Cmcm The Rietveld refinement method was performed on the XRD patterns and neutron diffraction at different temperatures. It was also concluded that the phase transition upon cooling is mainly due to the off center shifts of Nb5+ and one third of the La3+ and Nd3+ ions within their corresponding polyhedra. As a result, two neighboring Nb5+ ions or two adjacent Nd13+ ions along [001] displace in an antiparallel manner parallel to [010]. Because of

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166 the antiparallel manner, the net dipoles produced by the off center displacement are compensated to zero since the s pace group is centrosymmetric

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167 CHAPTER 8 INFRARED SPECTROSCOPY OF Gd3NbO7 8.1 Introduction Infrared spectroscopy (IR) is a powerful tool for providing information like phonon modes, bonding, orientation of dipoles, etc As already shown in Chapter 6, IR confirm s t he phase transition in Gd3NbO7 as the mode at 450 cm1 disappears above the phase transition temperature. A vibrational mode will absorb IR electromagnetic radiation only if the natural frequency of vibration is the same as the frequency of the radiation and the stimulated vibration produces a change in the dipole moment. The normal vibrational modes can be determined by nuclear site group analysis. In this method, the number of allowed modes of a specific structure is derived based on the symmetry of ea ch atomic site composing the crystal as introduced in Chapter 2.117 The first part of the study was to determine the IR active modes by the above method below and above the phase transition temperature of Gd3NbO7. It is important to note that only one art icle about IR spectrum of Gd3NbO7 has been published and that study was mainly focused on the crystallographic aspects.123 In this study, the IR spectra of Gd3NbO7 were collected at various temperatures using a Fourier transform spectrometer (Bruker IFS 113v) covering the frequency range between 20 cm1 and 650 cm1 (0.6 THz to 19 THz). A custom made timedomain terahertz transmission spectrometer was used to obtain the complex dielectric response in the range from 12 cm1 to 40 cm1 (0.36 THz to 1.2 THz) This spectrometer uses a femtosecond Ti : sapphire laser and a biased largeaperture antenna from a low temperature grown GaAs as a THz emitter, and an electrooptic sampling detection technique.160161 The collected data was analyzed using dispersion analysis to elucidate

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168 the different contribution of the phonon modes to the reflectivity, which is normalized by the experimental THz data. From these results, the dielectric properties at phonon frequenc ies were calculated. The chapter represents the collaborative work with Professor Stanislav Kambas group and Professor David Tanners group on the subject of IR. The infrared spectra between 10 K and 600 K and dielectric properties at THz were collected in Professor Kambas lab. The infrared spectra at 50 K, 300 K, and 360 K were also collected in Professor Tanners lab independently for comparison. The comparison of the IR spectra from the two independent experiments will be in Appendix B 8.2 Normal Mode Determination In Chapter 6, the atomic positions of Gd3NbO7 at different temperatures were determined by the phase refinements. Based on the symmetry of atomic site from Chapter 6, normal mode determination tables at the low temperature phase and the hi gh temperature phase are presented in Table 8 1 and Table 8 2 Based on the site symmetry, there are in total 20 A1, 10 A2, 18 B1, and 18 B2 modes. The acoustic modes are 1A1 + 1B1 + 1B2. The A2 is Raman active, and the A1, B1, and B2 are both Raman and IR active. Therefore, the irreducible representation for the low temperature phase can be written as IR) (R, 17B + IR) (R, 17B + (R) 10A + IR) (R, 19A = 2 1 2 1 ( 8 1 ) As for the high temperature phase, the irreducible representation is (IR) 9B (R) 7B (IR) 11B (R) 4B (IR) 10B (R) 8B (-) 6A (R) 8A 3u 3g 2u 2g 1u 1g u g ( 8 2 ) where (R), (), (IR), (R,IR) stand for the Raman active, silent, infrared active, and both the Raman and IR active modes, respectively. In summary, there are 53 IR active

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169 modes in the low temperature phase and 30 IR active modes in the high temperature phase. Table 8 1 Normal mode determination for the low temperature phase of Gd3NbO7 with space group Cm2m. Site Symmetry A 1 A 2 B 1 B 2 Gd1 C s xz (4 c ) 2 1 2 1 Gd2(1) C s yz (4 e ) 2 1 1 2 Gd2(2) C s yz (4 d ) 2 1 1 2 Nb C s xz (4 c ) 2 1 2 1 O1(1) C 2v (2 a ) 1 0 1 1 O1(2) C 2v (2 b ) 1 0 1 1 O2(1) C 2v (2 a ) 1 0 1 1 O2(2) C 2v (2 b ) 1 0 1 1 O3(1) C 2v (2 a ) 1 0 1 1 O3(2) C 2v (2 b ) 1 0 1 1 O4(1) C 1 (8 f ) 3 3 3 3 O4(2) C 1 (8 f ) 3 3 3 3 Acoustic Modes 1 0 1 1 Lattice Modes 19 10 17 17 Selectrion Rules Raman IR Raman Raman IR Raman IR Table 8 2 Normal mode determination for the high temperature phase of Gd3NbO7 with space group Cmc m Site Symmetry Ag Au B1g B1u B2g B2u B3g B3u Gd1 C 2h x (4 b ) 0 1 0 2 0 2 0 1 Gd2 C s xy (8 g ) 2 1 2 1 1 2 1 2 Nb C 2h x (4 a ) 0 1 0 2 0 2 0 1 O1 C 2v y (4 c ) 1 0 1 1 0 1 1 1 O2 C 2v y (4 c ) 1 0 1 1 0 1 1 1 O3 C 2v y (4 c ) 1 0 1 1 0 1 1 1 O4 C 1 (16 h ) 3 3 3 3 3 3 3 3 Acoustic Modes 0 0 0 1 0 1 0 1 Lattice Modes 8 6 8 10 4 11 7 9 Selectrion Rules Raman Inactive Raman IR Raman IR Raman IR

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170 8.3 Infrared Spectra Experimental IR reflectivity data for Gd3NbO7 was fitted with the generalized factorized four parameter oscillator model in the following162: 2 *1 ) ( 1 ) ( ) ( R ( 8 3 ) Tj Tj Lj Lj n j i i + + ) ( = ) (2 2 2 2 1 = *( 8 4 ) where () is the high frequency permittivity from electronic polarization, Tj and Lj are the eigenfrequencies of the transverse and longitudinal jth phonon mode and Tj and Lj are their corresponding damping constants. Dielectric contribution j of the jth mode to static permittivity can be calculated by ) ( ) ( ) ( = 2 2 2 2 2 Tj Tk j k Lj Lk k Tj j ( 8 5 ) For the 600 K spectrum, 18 oscillators yielded a good fitting with mean square deviation 0.00634. Meanwhile, 24 oscillators were used to fit the 300 K spectrum, and 33 oscillators for the 10 K spectrum. It is expected that the number of oscillators used is less than t he number of modes predicted by nuclear site group analysis (30 for the high temperature phase and 53 for the low temperature phase). One requirement for a successful fitting is that the number of oscillators used is the minimum number. Fitting routine of the experimental reflectivity followed least squares minimization techniques using the ASF program developed in Professor Kambas lab. The complete lists of all j of each mode for different temperatures are in Table 8 3 Table 8 4 and Table 8 5 Figure 8 1 and Figure 8 2

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171 show comparison between the experimental reflectivity and the fitting based on the parameters listed in Table 8 3 and Table 8 4 at 10 K and 600 K. The experimental reflec tivity match well with the oscillator fit. Table 8 3 List of fitting parameters for 33 oscillators at 10 K No. T(cm1) T (cm1) L (cm1) L (cm1) 1 5.94 18.72 5.97 18.20 0.31 2 78.30 60.90 79.67 46.48 2.036 3 83.56 10.70 84.02 11.02 0.54 4 91.58 6.15 101.42 10.22 4.64 5 100.28 2.58 96.84 5.74 0.41 6 111.27 5.94 113.10 8.56 1.1 7 126.38 13.82 131.87 3.45 3.02 8 146.07 12.68 149.27 6.14 1.7 48 9 166.97 19.92 197.81 20.38 6.9 46 10 170.33 10.13 169.88 5.38 1.04 11 204.68 5.14 221.62 13.34 0.6 27 12 207.88 13.48 207.88 13.22 0.00 0 13 211.70 5.91 210.17 9.79 0.16 14 217.75 5.65 216.12 6.98 0.09 15 234.90 9.56 239.47 11.19 0.659 16 249.09 17.74 272.90 12.76 1.337 17 255.96 10.50 254.42 9.33 0.416 18 276.56 3.41 293.96 23.75 0.266 19 299.46 9.16 313.19 117.68 0.169 20 323.27 10.93 326.93 16.54 0.084 21 339.95 11.70 342.50 9.73 0.138 22 350.74 8.47 367.22 25.53 0.407 23 374.55 9.53 375.88 11.82 0.024 24 385.44 12.71 387.37 18.89 0.063 25 403.86 13.82 423.09 20.32 0.517 26 447.81 13.42 462.47 13.19 0.396 27 480.78 17.63 541.23 22.55 0.373 28 490.85 9.56 488.11 6.40 0.142 29 511.92 41.67 508.25 41.10 0.07 0 30 551.75 18.32 557.42 20.03 0.023 31 605.99 54.03 608.30 39.03 0.123 32 615.40 28.50 708.00 17.57 0.369 33 675.38 32.62 673.06 32.85 0.008 55

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172 Table 8 4 List of fitting parameters for 19 oscillators at 600 K No. T (cm 1 ) T (cm 1 ) L (cm 1 ) L (cm 1 ) 1 61.021 30.5424 64.7379 20.7648 6.164 2 92.8806 31.1139 119.7191 30.3628 15.616 3 147.8207 14.0218 147.9071 13.9462 0.04 4 162.4217 40.587 184.8965 55.3917 5.387 5 202.1392 30.7635 214.6063 25.6496 1.476 6 230.2851 32.7406 239.3042 43.3296 0.99 7 259.9987 34.8091 291.3617 35.8644 2.31 8 296.2362 25.2799 311.3698 65.346 0.21 9 317.3912 38.8237 325.5188 81.6835 0.1058 10 349.1298 34.7643 366.5566 36.2629 0.5078 11 380.3553 24.5661 382.67 34.5537 0.07198 12 400.9602 41.4127 427.75 45.6446 0.61338 13 473.1506 64.9387 543.7183 36.4062 0.905 14 511.0153 33.849 508.846 30.623 0.038 15 550 22.3663 552.538 27.7063 0.00637 16 592.0126 50.7997 607.8256 49.9398 0.244 17 617.4507 48.0348 688.396 22.752 0.136 18 674.5646 59.5725 670.2173 53.3285 0.00589 100 200 300 400 500 600 0.0 0.2 0.4 0.6 0.8 1.0 Experimental Data Oscillator Fit10 KReflectivityWavenumber ( cm-1) Figure 8 1 IR reflectivity of Gd 3 NbO 7 at 10 K. Solid lines show experimental data. Dot ted lines show fit curves to a sum of 33 oscillators

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173 Table 8 5 Fitting parameters for 24 oscillators at 300 K No. T (cm 1 ) T (cm 1 ) L (cm 1 ) L (cm 1 ) 1 61.58 35.71 65.24 24.94 5.66 2 92.23 9.97 109.00 13.19 5.63 3 98.30 15.18 94.60 8.60 6.12 4 113.91 13.70 119.41 13.26 1.23 5 125.00 11.46 128.00 11.28 0.56 6 146.29 12.25 147.03 9.87 0.34 7 163.64 25.95 182.72 35.13 4.85 8 167.11 10.52 166.70 9.87 0.56 9 204.69 21.83 218.57 15.68 2.57 10 230.14 26.24 239.39 34.55 1.06 11 260.21 25.01 291.43 26.45 2.82 12 296.56 15.21 312.25 55.37 0.30 13 316.97 26.09 324.67 58.55 0.11 14 348.10 26.17 372.38 29.56 0.83 15 380.08 22.55 382.39 34.98 0.05 16 400.14 26.09 429.05 34.40 0.66 17 452.18 24.94 460.27 20.24 0.27 18 476.00 34.55 545.85 25.59 0.63 19 487.00 10.66 486.87 10.63 0.0814 20 511.06 27.18 509.95 26.31 0.02 21 550.00 18.00 552.79 23.92 0.0459 22 592.11 44.52 608.00 46.84 0.23 23 622.18 35.13 708.00 17.85 0.2054 24 675.38 32.16 673.06 31.01 0.0076 During this type of fitting routines, it is good practice to use the combined data from THz and/or MW and/or low frequency range if available to establish boudary conditions.6,162 Therefore, the dielectric properties data at THz frequency range were used to normalize the reflectivity spectra. The room temperature real and imaginery parts of permittivity measured by time domain terahertz transmission spectrometer and from the oscillateor fit are shown in Figure 8 3 and Figure 8 4 The real and imaginary parts of permittivity from the normalized reflectivity match well with the low frequency values measured by LCR as shown in Chapter 5: The real part of permittivity is 39 and

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174 the imaginary part is 0.02 from IR at the wavenumber ~ 0, while the corresponding value is 45 and 0.04 at 1 MHz from LCR. 100 200 300 400 500 600 0.0 0.2 0.4 0.6 0.8 1.0 ReflectivityWavenumber ( cm-1) Experimental Data Oscillator Fit600 K Figure 8 2 IR reflectivity of Gd3NbO7 at 600 K. Solid lines show experimental data. Dot ted lines show fit curves to a sum of 19 oscillators 1 10 100 -20 -10 0 10 20 30 40 50 60 70 Wavenumber ( cm-1) Experimental Data Oscillator Fit300 Kr' Figure 8 3 The real part of permittivity obtained from the time domain THz spectrometer (dots) combined with th e result of the IR reflectivity spectra

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175 1 10 100 0 10 20 30 40 50 60 Experimental Data Oscillator Fit300 Kr" Wavenumber ( cm-1) Figure 8 4 The imaginary part of permittivity obtained from the time domain THz spectrometer (dots) combined with th e result of the IR reflectivity spectra T he real and imaginary parts of permittivity from the oscillator fit at 10 K and 600 K are presented in Figure 8 5 and Figure 8 6 The calculated real part of permittivity is 32.4 at the temperature of 10 K and wave number close to 0. The measured real part of permittivity is 32 at the temperature of 20 K and 1 MHz frequency. Considering the variation real part of permittivity is small below 100 K as shown in Chapter 5. It is expected the 10 K permittivity should near 32. Therefore, the lower limit of t he real part of permittivity from IR is in a good match with the value by LCR. The static permittivity can be calculated by the summation of each phonon contribution by ) ( + = ) 0 ( j ( 8 6 )

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176 The fitted () is 4.17 for all temperatures since the electronic polarization is temperatureinsensitive as described in Chapter 2. The calculated static permittivity is shown in Figure 8 7 The experimental measured dielectric permittivity from 1 kHz to 1 MHz by LCR in Chapter 5 are also included in Figure 8 7 for comparison. The static permittivity maintain the same variation as function of temperature as that measured by LCR. The permittivity increases with increasing temperature until 340 K, then decreasing with a smaller slope with increasing temperature. The static permittivty is about 10% lower than the 1 MHz permittivity, which may be due to the errors created by different methods. 0 40 80 r' T = 10 K Gd3NbO7r"Wavenumbers ( cm-1)1 10 100 0 40 80 Figure 8 5 Calculations of the real and imaginary parts of the permittivity at 10 K.

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177 0 40 r' T = 600 K Gd3NbO7r"Wavenumbers ( cm-1)1 10 100 0 20 40 Figure 8 6 Calculations of the real and imaginary parts of the permittivity at 600 K. There is not much change between the dielectric behavior at 300 K and that at 600 K (the phase transition temperature is 340 K). As discussed in Chapter 6 and also mentioned above, in reflectivity spectra, there is a mode at 450 cm1 appearing below 340 K and disappearing above 340 K. However, there i s not much difference in dielectric behavior at 450 cm1 between 300 K and 600 K. As in Table 8 3 and Table 8 4 j) from the mode at 450 cm1j is

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178 0.396 at 10 K and 0.27 at 300 K, which are both less than 2% of the total dielectric permittivity. The major dielectric contribution is from the modes below 200 cm1. 0 100 200 300 400 500 600 25 30 35 40 45 50 55 r'Temperature (K) Decreasing frequency from 1 MHz to 1 kHzStatic Figure 8 7 Dielectric permittivity of Gd 3 NbO 7 from 1 kHz to 1 MHz by LCR meter and static permittivity. 8.4 Conclusion Normal mode determination was used to calculate possible IR active modes below and above the phase transition temperature (340 K). The low temperature phase of Gd3NbO7 has 53 IR active modes and the high temperature phase has 30 IR active modes. A four parameter oscillator model was used to fit the reflectivity. Total 33 oscillators were used to fit the 10 K spectrum, 24 oscillators were modeled for the 300 K spectrum, and only 19 oscillators were applied in the 600 K spectrum. The dielectric properties measured by terahertz transmission spectrometer were used to normalize the reflectivity. The dielectric properties at three temperatures were calculated from the fit up to 650 cm1. The calculated static permittivity as a func tion of temperature maintains the same shape as the 1 MHz permittivity and reaches the maximum at 340 K.

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179 One mode at 450cm1 disappears above the phase transition temperature (340 K), supporting the phase transiton. However, the dielectric contribution f rom the mode is small, less than 2% at both 10 K and 300 K. Therefore, comparing the dielectric behavior at 300 K and 600 K, there is not much change.

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180 CHAPTER 9 STRUCTUREDIELECTRIC PROPERT Y RELATIONSHIPS IN FLUORITERELATED Ln3NbO7 AND Ln2LnNbO7 9.1 Introduction The previous chapters presented a study on a series of fluoriterelated Ln3NbO7 and Ln2LnNbO7 compounds based on crystallography as well as dielectric properties. The current chapter aims at establishing correlations between the crystal structure and the dielectric properties observed in these compounds. In order to accomplish this, two additional compounds (Sm2YbNbO7 and Gd2YbNbO7) are introduced. Despite the fact that the crystal structure of these two compounds is not completely resolved, it will be shown that their inclusion greatly helps in realizing general trends and correlations. 9.2 Summary of the Crystal Structure of Investigated Compounds It is important to recall that one characteristic feature of the XRD patterns for the orthorhombic weberite ty pe structure is the peak splitting of the most intense fluorite peaks, for example, the (111) reflection of cubic fluorite split into (202) and (220) of orthorhombic weberite type. The peak splitting decreases with decreasing ionic radius of Ln3+ for Ln2Y bNbO7 compounds as shown in Figure 9 1 As for Gd2YbNbO7, the peak splitting is greatly depressed. The XRD pattern of Gd2YbNbO7 indicates a tetragonal lattice unlike the orthorhombic lattice observed in all other Ln2LnNbO7 in this study ( Figure 9 2 ). The XRD pattern of Gd2YbNbO7 contains less minor reflections comparing to that Gd3NbO7. Therefore, though t he peak splitting of Gd3NbO7 is depressed at 295 K and 100 K as discussed in Chapter 6, the lattice of Gd3NbO7 is orthorhombic

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181 27 28 29 55 56 57 58 59 (440) (404) (220)Gd2YbNbO7Sm2YbNbO7Nd2YbNbO7 La2YbNbO7Intensity (arb. units)2 (degrees)(202) Figure 9 1 XRD of Ln 2 YbNbO 7 (Ln 3+ = La 3+ Nd 3+ Sm 3+ and Gd 3+ ) showing the peak splitting between (202) and (220), and between (404) and (440). 10 20 30 40 50 60 70 (206) (044) (040) (115) (230) (032) (031) (220) (022)Intensity (arb. units)2 (degrees)Gd2YbNbO7 Figure 9 2 The XRD pattern of Gd 2 YbNbO 7 As discussed in Chapter 4, the crystal structure of Ln3NbO7 is mediated by the ionic radius of Ln3+. Ln3NbO7 compounds with large Ln3+ ionic radius of such as La3+, Nd3+, and Gd3+ all crystallize with an orthorhombic weberi te type structure, whereas Dy3NbO7, Y3NbO7, Er3NbO7, and Yb3NbO7 all crystallize with a cubic fluorite structure.

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182 The average ionic radius of Ln3+ (2/3rGd + 1/3rYb) for Gd2YbNbO7 is between the ionic radius of Dy3+ (1.027 ) and Gd3+ (1.053 ) as shown in Figure 9 3 (A), especially close to Dy3NbO7.27 Therefore, the tetragonal lattice of Gd2YbNbO7 may be an intermediate between cubic fluorite and orthorhombic weberitetype. (A) (B) Figure 9 3 (A) The formula volume of Ln 3 NbO 7 and Ln 2 Ln NbO 7 as a function of the (average) ionic radius of rare earth element.27 (B) APF as a function of ionic radius The red line is the linear fitting. The grey lines are the 95% confidence limit of the linear fitting. The formula volume is calculated by the unit cell volume divided by the formula number. For Ln2Ln NbO7 compounds r average = 2/3r Ln + 1/3r Ln Formula volume(3) 1.16 1.12 1.08 1.04 1.00 0.96130 140 150 160 170 GdYb SmYb NdYb LaYb LaEr LaDy La Nd Gd Dy Er Ybweberite-type defect fluoriteY Ionic radius () Ionic radius ()

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183 A su mmary of lattice parameters, formula volume (Vunit cell/Z as defined in Chapter 5) and atomic packing factor (APF) is listed in Table 9 1 The details of the lattice parameter calculation for Ln3NbO7 and La2LnNbO7 were discussed in Chapter 4. The latti ce parameters for Nd2YbNbO7, Sm2YbNbO7, and Gd2YbNbO7 were calculated by the Checkcell program.163 APF was calculated by the summation of the individual ion volume in a formula unit divided by the formula volume. Table 9 1 Summary of the lattice param eters, formula volume, and atomic packing factor (APF) of Ln3NbO7 and Ln2LnNbO7.86,120,159 a () b () c () Formula volume ( 3 ) APF (%) La 3 NbO 7 11.1593(4) 7.6309(3) 7.7522(2) 165.0356 58.08% La 2 DyNbO 7 10.921(2) 7.5646(12) 7.7060(13) 159.1539 59.32% La 2 ErNbO 7 10.9220(8) 7.5915(5) 7.7189(5) 160.0019 58.87% Nd 3 NbO 7 10.8988(3) 7.5285(2) 7.6270(2) 156.4519 59.74% La 2 YbNbO 7 7.5623(13) 10.767(2) 7.6619(13) 155.9643 60.25% Nd 2 YbNbO 7 10.624(4) 7.482(4) 7.582(3) 150.671 62.37% Gd 3 NbO 7 7.5324(1) 10.6185(2) 7.5476(1) 150.9195 60.58% Sm 2 YbNbO 7 10.566(8) 7.443(5) 7.528(8) 148.0056 61.77% Gd 2 YbNbO 7 10.5440(11) 7.443(12) 146.0298 62.96% Dy 3 NbO 7 5.2701(6) 146.3715 62.70% Y 3 NbO 7 5.253(4) 144.9513 63.09% Er 3 NbO 7 5.232(2) 143.2198 63.45% Yb 3 NbO 7 5.194(5) 140.1218 64.35% The ionic radius of 7 coordinated Nd 3+ is average of that of 6 coordinated and 8 coordinated Nd 3+ The ionic radii are after Shannon.27 The Nb5+ is 6 coordinated. For weberite type Ln3NbO7 (Ln3+ = La3+, Nd3+, and Gd3+), 1/3 of Ln3+ are 8 coordinated and 2/3 are 7 coordinated. For Ln2LnNbO7 (except Gd2YbNbO7), the Ln3+ ions are considered to be 8 coordinated and Ln3+ are 6 coordinated. For Gd 2 YbNbO 7 and defect fluorite Ln 3 NbO 7 the Ln 3+ ions are considered to be 8 coordinated. It can be seen that t he formula volume and APF of Ln3NbO7 and Ln2Ln NbO7 has a nearly linear relationship with the (average) ionic radius of the rare earth element ( Figure 9 3 (A) and (B) ) The formula volume of Gd3NbO7 and La2ErNbO7 is slightly outside the upper 95% confidence limit, which may indicate structural openness. APF of Gd3NbO7 and La2ErNbO7 is outside the bottom limit of 95% confidence limit. It

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184 confirms that Gd3NbO7 and La2ErNbO7 have more open structures. The openness of the structure may indicate easier movement of the ions ( i.e. polarization) under the external field. 9.3 Weberitetype Ln3NbO7 The real part of the relative dielectric permittivity of Gd3NbO7 as a function of temperature and frequency is shown in Figure 9 4 The permittivity at 9 GHz was measured by composite dielectric resonator technique. The details of the setup and experiment can be found elsewhere.164 The permittivity at 630 GHz was obtained by a custom made timedomain terahertz transmission spect rometer. The experimental setup and the measuring technique are described in Chapter 8. The static permittivity is calculated from IR fitting in Chapter 8. It is clear that the shape of the permittivity at different frequencies is well maintained. The transition temperature (T( m)), where the slope of the permittivity curve changes from positive to negative, is almost the same at different frequencies. T( m) is also close to the phase transition temperature as discussed in Chapter 6.159 The transition at 630 GHz is as sharp as that at frequencies in the kHz range. By contrast, in Bi1.5Zn0.92Nb1.5O6.92 pyrochlore, which has no phase transition near T( m), T(m) increases with increasing frequency and the transition is already greatly smoothed at 1.8 GHz.6 Therefore, it is clear that the origin for the dielectric relaxation in Gd3NbO7 is the phase transition. Since the static permittivity was calculated from IR, it only contains the permittivity contribution from the ionic polarization and electronic polarization. The difference between the measured permittivity at low frequency and the static permittivity indicates the permittivity contribution from the dipolar mechanism as shown in Figure 9 -

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185 4. On heating from 50 K, the dipolar contribution reaches a maximum near the phase transition (~ 340 K) In dipolar polarization, t he average residence time ( ) of an atom or ion at any given site decreases with increasing temperature (Equation 213). Debye equations indicate that the dipolar contribution increases with decreasing as 2 2 '1 (dipolar) -sr (9 1) where is the frequency of an external field, is the sum of the ionic and electronic contribution, and s is the sum of the dipolar, ionic and electronic contribution under the static field ( s = s(dipolar) + s(ionic) + s(electronic)). On the other hand, as in Equation 212, s(dipolar) 1 is proportional to 1/T. Therefore, at low temperature, the dipolar contribution increases with increasing temperature because of reduce in ; at high temperature, thermal randomization begins to play a role. The dielectric response of Gd3NbO7 is plotted as a function of frequency in Figure 9 5 The real part of the permittivity decreases slightly with increasing frequency from 1 kHz to 1 MHz. There is a sh arp decrease in permittivity between 1 MHz and 9 GHz. There is an associated peak in the dielectric loss. The peak position at 380 K is at higher frequency than that at 293 K. The behavior of permittivity and dielectric loss respective to frequency conf irms dielectric relaxation. The permittivity at 630 GHz is higher than that at 9 GHz. This may be due to the different measuring techniques used at these two frequencies. It may also be because that 630 GHz is approaching the resonating region for ionic polarization. As shown in Figure 2 23, the resonance process for ionic polarization occurs at about 1013 Hz.

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186 0 100 200 300 400 500 600 700 24 32 40 48 56 r'9 GHz r'Temperature (K) Decreasing from 1 MHz to 1 kHz 630 GHz static 5 10 15 20 25 Figure 9 4 Dielectric properties of Gd 3 NbO 7 at 1 kHz, 3 kHz, 8 kHz, 10 kHz, 30 kHz, 80 kHz, 100 kHz, 300 kHz, 800 kHz, 1 MHz, 9 GHz, and 630 GHz ( left axis ) Dielectric permittivity difference between dielectric permittivity at 1 MHz and the static permittivity ( right axis ) The dielectric response does not exactly follow the Debye type relaxation. Following Debye equations (Equation 92 and 93), when is at 1/ r is at an inflection point and r is at a peak position. There is a MHz should be far below 1/ ) at both 295 K and 380 K. Since Debye type relaxation does not take into consider ation phase transition effects it is expected that there would be discrepancies between the dielectric behavior of Gd3NbO7 and the Debye model. In order to better understand t he dielectric relaxation as a function of frequency more data points between 1 MHz and 9 GHz are needed.

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187 2 2 '1 ) ( sr (9 2) ) ( 1 ) (2 2 s r (9 3) Figure 9 5 Dielectric response of Gd 3 NbO 7 as a function of frequency at 293 K and 380 K. A summary of the real part of permittivity for weberitetype Ln3NbO7 (Ln3+ = La3+, Nd3+, and Gd3+) at 1 MHz is shown in Figure 9 6 As stated in Chapter 5, 6, and 7, the te mperature (T( m)) where the maximum permittivity occurs as well as the phase transition temperature is approximately 340 K for Gd3NbO7, 360 K for La3NbO7, and 450 K for Nd3NbO7. T( m) may be related to the openness of the structure. Gd3NbO7 has the most open structure among the three compounds as shown in Figure 9 3 It is pr oposed that the structural openness allows for an easier polarization of the material, which in turn results leads to lower temperatures needed to achieve maximum permi ttivity.38 1021041061081010101232 36 40 44 48 tan 'rFrequency (Hz) Gd3NbO7293 K 0.00 0.01 0.02 0.03 0.04 0.05 380 K

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188 0 100 200 300 400 500 30 35 40 45 50 55 60 65 Gd3NbO7 La3NbO7 Nd3NbO7 r'Temperature (K) 'r Figure 9 6 A summary of the real part of permittivity for weberitetype Ln3NbO7 at 1 MHz. The arrows show the difference ( r ) between the maximum permittivity and the minimum permittivity. It is interesting to see that the off center shift of 8coordinated Ln3+ is largest in Nd3NbO7, intermediate in La3NbO7, and smallest in Gd3NbO7 ( Figure 9 7 ). It can be inferred that it will take more thermal energy for Nd3+ to be able to move to the center of the corresponding polyhedra. Therefore, it makes sense that Nd3NbO7 has the highest phase transition temperature, La3NbO7 the second highest, and Gd3NbO7 the lowest ( Figure 9 8 ). It is also important to notice that at 20 K the permittivity of these three compounds is almost the same, about 32. Nd3NbO7 has the highest difference in r in Figure 9 6 ) while Gd3NbO7 has the lowest difference. The r zability of Ln3+) is also presented in Figure 9 8 It also increases with increasing off center shifts of Ln13+.

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189 0 100 200 300 400 500 0.0 0.1 0.2 0.3 Gd3NbO7La3NbO7Ln1O8 Temperature (K)Off-center Displacement (A)oNd3NbO7 Figure 9 7 Off center displacement of 8cooridinated Ln 3+ for Ln3NbO7 at different temperatures. Figure 9 8 T( m ) and normalized dielectric difference from the maximum to the minimum vs. off center displacement of Ln3+ inside Ln1O8 polyhedra. (measured in 3 ) is the polarizability of Ln 3+ 0.08 0.12 0.16 0.20 0.24 0.28200 250 300 350 400 450 T ( m) 3 4 5 6 7 8 9 10 Nd3NbO7Gd3NbO7 'r A-3oLa3NbO7 Off center displacement of Ln3+()

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190 Figure 9 9 shows the off center shifts of Nb5+ within NbO6 polyhedra. The off center distances of Nb5+ in Gd3NbO7 are smaller than that of La3NbO7 at both 100 K and 295 K. Because of the shorter off center displacements of both Ln13+ and Nb5+ ions in Gd3NbO7, it makes sense that Gd3NbO7 has lower T( m) than La3NbO7. As for Nd3NbO7 and La3NbO7, the off center shifts of Nb5+ in Nd3NbO7 are smaller t han that of La3NbO7 at or below RT. The off center shifts of Nb5+ at all measured temperatures are below 0.17 for both compounds. They are smaller than the off center distance of Ln13+ (above 0.19 see Figure 9 10). Since the Ln13+ ions have to trav el farther distance to reach the center of Ln1O8 polyhedra at T( m), it is reasonable to conclude that the off center shift of 8coordinated Ln13+ plays a more important role in determining T( m) in La3NbO7 and Nd3NbO7. 0 100 200 300 400 500 0.0 0.1 0.2 NbO6 Temperature (K)Off-center Displacement (A)oNd3NbO7La3NbO7Gd3NbO7 Figure 9 9 Off center displacement of Nb 5+ for Ln 3 NbO 7 at different temperatures.

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191 0 100 200 300 400 500 0.0 0.1 0.2 0.3 Ln1O8 NbO6La3NbO7 Temperature (K)Off-center Displacement (A)oNd3NbO7 Figure 9 10 Comparison of off center shifts of the Nb 5+ and Ln1 3+ ions in La 3 NbO 7 and Nd 3 NbO 7 9.4 Ln2LnNbO7 It can be expected that the more polarizable Ln3+ ions result in higher real part of permittivity and indeed, the 1 MHz permittivity for the 6 investigated Ln2LnNbO7 compounds at all measured temperatures (from 20 K to 350 K) follow this trend. A summary of the 1 MHz real part of permittivity for the Ln2LnNbO7 compounds at 20 K and room temperature is shown in Figure 9 11 It is clear that the permittivity increases with ionic radius of Ln3+. This is not too surprising since there is a nearly linear relationship between the average ionic radius of Ln3+ and the average polarizability of Ln3+ average Ln Ln) across the rare earth element series. As disc ussed above, Gd2YbNbO7 is an intermediate between cubic fluorite and orthorhombic weberitetype. The real part of permittivity of Gd2YbNbO7 increases with an increase in temperature from 20 K to 350 K ( Figure 9 12). It is interesting to find out that the dielectric behavior of Gd2YbNbO7 resembles the dielectric response of defect fluorite Ln3NbO7, different from the other Ln2YbNbO7 investigated in this study.

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192 Figure 9 11 A summary of the real part of the permittivity for all investigated Ln2LnNbO7 compounds at the frequency of 1 MHz and the temperature of 20 K and room temperature. The average polarizability of Ln3+ is also included. It suggests that the crystal structure of Gd2YbNbO7 is more close ly related to the defect fluorite than the weberitetype, which is reasonable from the point of view of ionic radius. The average ionic radius of Ln3+ for Gd2YbNbO7 is close to the ionic radius of Dy3+ ( Figure 9 3 ). A summary of the real part of permitti vity at 20 K and RT as well as the (average) polarizability of Ln3+ for Gd2YbNbO7 and defect fluorite Ln3NbO7 (Ln3+ = Dy3+, Y3+, Er3+, and Yb3+) is shown in Figure 9 13. It is clear that Gd2YbNbO7 has the highest ion polarizability and the average ionic radius of Ln3+ but the lowest permittivity. As presented in Chapter 5, the experimentally observed dielectric permittivity for defect fluorite compounds is approximately 50% higher than the calculated values from Clausius Mosotti equation at RT. A weak dipolar may be generated by the disorder of Average ionic radius of Ln3+() 1.02 1.04 1.06 1.08 1.10 1.12 20 30 40 50 LaDy LaEr LaYb NdYb SmYb 20 K Room Temperature Polarizabilityr'GdYb4 6 8 10 Ion polarizability of Ln3+ (A)o

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193 the lanthanide and niobium ions. As for Gd2YbNbO7, it is expected that Gd3+ and Yb3+ are less disordered because of the difference in the ionic radius. 0 100 200 300 400 24 27 30 33 36 39 42 Gd2YbNbO7 Er3NbO7Y3NbO7 Yb3NbO7Dy3NbO7 Temperature (K)r' Figure 9 12 The real part of permittivity of Gd 2 YbNbO 7 and defect fluorite Ln 3 NbO 7 at 1 MHz. It is interesting to find out that in Ln2YbNbO7 (except Gd2YbNbO7) the temperature (T( m)), where the maximum permittivity occurs, decrease with decreasing the ionic radius of Ln3+ ( Figure 9 14). The temperature (Tm), where the peak of the imaginary part of permittivity occurs, also decreases with decreasing the ionic radius of Ln3+, following the same trend ( Fig ure 9 15 ). It seems that the dielectric relaxation may be related to the ionic radius of Ln3+ or the ratio of the ionic radius of the Ln3+ cations (rA) over the average ionic radius of Ln3+ and Nb5+ (rB).

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194 Figure 9 13 Summary of the real part of the permittivity for defect fluorite Ln 3 NbO 7 and Gd2YbNbO7 compounds at the frequency of 1 MHz and the temperature of 20 K and room temperature. The average polarizability of Ln3+ is also included. A series of La2LnNbO7 is also presented to show the effect of rB. Figure 9 1 6 shows the real part of the permittivity of La2LnNbO7 (Ln3+ = Yb3+, Er3+, and Dy3+). The T( m) of La2DyNbO7 and La2ErNbO7 is comparable, at about 80 K. The T( m) of La2YbNbO7 is about 140 K. As for Tm, La2YbNbO7 has the highest value, La2DyNbO7 the second, and La2ErNbO7 the lowest ( Figure 9 1 7 ). There is no obvious effect of rB on either T( m) and Tm. Average ionic radius of Ln3+() 0.98 1.00 1.02 1.04 15 20 25 30 35 40 Permittivity at 20 K Permittivity at RT4 6 8 Gd2YbNbO7Dy3NbO7Y3NbO7Er3NbO7 Polarizability r'Ion polarizability of Ln3+ (A)oYb3NbO7

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195 0 50 100 150 200 250 300 350 400 24 26 28 34 36 38 40 42 44 46 Gd2YbNbO7Sm2YbNbO7Nd2YbNbO7 r'Temperature (K) La2YbNbO7 Figure 9 14 Summary of the real part of permittivity for Ln 2 YbNbO 7 compounds. The arrows point to the temperature where the maximum permittivity occurs. 0 50 100 150 200 250 300 350 400 0.0 0.1 0.2 0.3 0.4 La2YbNbO7Sm2YbNbO7 Nd2YbNbO7 r'' Temperature (K) Figure 9 15 The imaginary part of permittivity for Ln 2 YbNbO 7 at 1 MHz.

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196 A summary of Tm for all five compounds is plotted in Figure 9 1 8 to see if there is any trend with respect to rA/rB. The Tm at 1 MHz for Ln2LnNbO7 generally increases with an increasing ratio of rA over rB but with one exception. La2DyNbO7 has a lower rA/rB value but higher Tm than La2ErNbO7. It is worth noting that La2ErNbO7 has a more open structure than La2DyNbO7 Figure 9 3 ). As discussed before, the structural openness in Gd3NbO7 may be one reason for the low T( m). T he structural openness in La2ErNbO7 may also cause an easier polarization of the material, which in turn accounts for the lower Tm than that of La2DyNbO7. Therefore, the Tm generally increases with the increasing rA/rB. It is apparent that structural openness leads to l ower Tm. 0 50 100 150 200 250 300 43 44 50 52 54 La2ErNbO7 La2DyNbO7 r'La2YbNbO7Temperature (K) Figure 9 16 A summary of the real part of permittivity for La 2 LnNbO 7 compounds.

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197 0 100 200 300 400 0.0 0.1 0.2 0.3 0.4 0.5 La2YbNbO7 La2ErNbO7 La2DyNbO7 r'' Temperature (K) Figure 9 17 The imaginary part of permittivity La 2 LnNbO 7 at 1 MHz. 1.40 1.45 1.50 1.55 1.60 0 20 40 60 80 100 Sm2YbNbO7Nd2YbNbO7La2ErNbO7La2DyNbO7 Tm (K)rAVIII/rBVILa2YbNbO7 Figure 9 18 The temperature (T m ) where the peak of the 1 MHz imaginary occurs vs. the ratio of the ionic radius of A cations over that of B cations for Ln2LnNbO7. It is assumed that the Ln3+ ions with larger ionic radius are at A sites and Ln3+ with smaller ionic radius are at B sites. The ionic radius are after Shannon. 27

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198 The real part of the permittivity has almost linear variation as a function of temperature above T( m) for Ln2LnNbO7. As for Gd2YbNbO7, the variation of the real part of the permittivity against temperature is nearly linear from 150 K to 350 K. The temperature coefficient of permittivity (TCC) from 218 K to 350 K was calculated for all Ln2LnNbO7. The TC C increases with increasing average ionic radius of Ln3+. The TCC varies from 137 MK1 to 225 MK1. Ln2LnNbO7 has a negative TC C except Gd2YbNbO7. Nd2YbNbO7 and Sm2YbNbO7 have the most stable TC C (~ 40 MK1) in these compounds. As in Chapter 2, the 18mol% Ca2Nb2O7 + 82mol% Ca2Ta2O7 system is promising since the TCC is compensated to zero. It is also possible that a small amount of Gd2YbNbO7 secondary phase inside Sm2YbNbO7 and Nd2YbNbO7 can compensate TCC to zero, which may have potential applications. Figure 9 19 A summary of the temperature coefficient of permittivity for all Ln 2 LnNbO 7 Average ionic radius of Ln3+() 1.02 1.04 1.06 1.08 1.10 1.12 1.14 -400 -300 -200 -100 0 100 200 300 3 LaDy LaEr LaYb NdYb SmYb TCC( MK-1)GdYb

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199 A summary of the attempt frequencies, activa tion energy, the Tm (1 MHz), the T( m) (1MHz) and frequency dispersion between 10 kHz and 1 MHz is listed in Table 9 2 The corresponding thermal energy of the Tm and the T( m) is also listed. The thermal energy is much lower than the activation energy. It is clearly seen that the dielectric relaxation of Gd3NbO7 is different from the other Ln2LnNbO7. Gd3NbO7 has much higher Tm, activation energy and frequency dispersion. T able 9 2 A summary of T( m), Tm and their corresponding energy at 1 MHz, and the attempt frequency, the activation energy, and frequency dispersion ( m/(l o gf1l o gf2), f1 is 1 MHz, f2 is 10 kHz) of dielectric relaxation. T( m) (K) at 1 MHz E (T( m)) (eV) Tm (K) at 1 MHz E(Tm) (eV) 0 (Hz) Ea (eV) m/(l o gf1l o gf2) (K/Hz) La3NbO7 *1 360 0.031 -----Nd3NbO7 *1 450 0.038 -----Gd3NbO7 340 0.029 442 0.038 1.510 11 0.45 60.32 La2YbNbO7 *2 --90 0.0078 1.210 14 0.14 8.60 La2DyNbO7 *2 --83 0.0072 1.910 13 0.12 8.78 La2ErNbO7 *2 --75 0.0065 1.310 12 0.09 8.98 Nd2YbNbO7 *2 --44 0.0038 2.510 10 0.04 7.03 Sm2YbNbO7* 3 --26 0.0022 ---* 1 The imaginary part of the permittivity increases with increasing temperature due to conduction *2 T( m) is hard to determine due to the smooth transition of r. 3 The T m at lower frequencies is expected beyond the limit of measured temperature range. It is suggested in Chapter 5 that the origin of the dielectric relaxation in Ln2LnNbO7 is due to a phase transition, similar to weberitetype Ln3NbO7, or cation disorder, similar to pyrochlore ( e.g. Ca1.46Ti1.38Nb1.11O7 28, also see APPENDIX A ). Neutron diffraction was collected on Nd2YbNbO7, La2YbNbO7, and La2ErNbO7 below and above the temperature (T( m)) where the maximum permittivity occurs. There are no extra reflections when comparing the patterns below and above T( m), which excludes the possibility of a phase transition. Figure 9 2 0 shows an example

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200 (Nd2YbNbO7) of the neutron diffraction patterns below and above the T( m). Therefore, the origin of the dielectric relaxation of Ln2LnNbO7 compounds is different from weberitetype Ln3NbO7. W hether there is a cation disorder in Ln2LnNbO7 is worth further investigation. 20 40 60 80 100 120 10 K 100 K difference2 (degrees)Intensity (arb. units)Nd2YbNbO7 Figure 9 20 Neutron diffraction of Nd 2 YbNbO 7 at 10 K an 100 K ( = 1.5378 ). 9.5 Conclusion The crystal structure and dielectric property relationships were presented in this chapter. Weberitetype compounds exhibit dielectric relaxation. The real part of the permittivity of defect fluorite compounds just increases with increasing temperature. As shown in Figure 9 2 1 the dielectric relaxation is related to crystal structure. For weberitetype Ln3NbO7, the origin of the dielectric relaxation is due to the phase transition. Gd3NbO7 has the most open structure while Nd3NbO7 has the most condensed. The structural openness may cause an easier polarization and a lower T( m). It is also found T( m r center distance of Ln13+ within their polyhedra.

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201 Figure 9 21 Average ion polarizability vs. average ionic radius of Ln 3+ in Ln 3 NbO 7 and Ln2LnNbO7 It shows that the dielectric relaxation is related to crystal structure. The rectangles on La, Nd, and Gd, identify the phases for which a phase transition was identified. Ln2LnNbO7 with more polarizable Ln3+ ions has a higher real part of permittivity. The crystal structure of Gd2YbNbO7 is intermediate between orthorhombic weberitetype and cubic defect fluorite. The dielectric behavior s of Gd2YbNbO7 resemble that of the defect fluorite Ln3NbO7, other than Ln2LnNbO7. The TC C is negative for orthorhombic Ln2LnNbO7, but positive for Gd2YbNbO7 (~225 MK1). Nd2YbNbO7 and Sm2YbNbO7 have the most stable TC C ~ 40 MK1. TC C increases wi th increasing the average ionic radius of Ln3+. On the other hand, the Tm generally increases with an increasing ratio of rA (Ln3+) over rB (average of Ln3+ and Nb5+). However, the structural openness also plays a role. As for the origin of dielectric relaxation, the possibility of phase transition has been ruled out by neutron diffraction at different temperatures. Ion polarizability (3) Ionic radius ()

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202 W hether there is a cation disorder (like in Ca1.46Ti1.38Nb1.11O7) in Ln2LnNbO7 deserves further investigation.

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203 CHAPTER 10 SUMMARY AND FUTURE WORK 10.1 SUMMARY 10.1.1 Phase Formation and Crystal Structure of Ln3NbO7 and Ln2LnNbO7 A series of Ln3NbO7 and Ln2LnNbO7 were successfully synthesized by conventional solid state processing. The phase formation was relatively easier for the defect fluorite compounds, Nd3NbO7, and Gd3NbO7 since the pure phase was formed after calcination at 1673 K for 8 h (the calcination temperature for Dy3NbO7 was even lower, 1573 K). As for La3NbO7, multiple calcinations with intermediate grinding were needed to eliminate the LaNbO4 phase. La3NbO7 had to be calcined at 1773 K for at least 48 h in total. Multiple and long time calcinations with intermediate grinding were also necessary to reach the equilibrium phase for Ln2LnNbO7. ray diffraction, and neutron diffraction were used to characterize the crystal structure. The crystal structure of Ln3NbO7 at room temperature is defect fluorite if the ionic radius of Ln3+ is equal to or smaller than Dy3+ (1.027 ) which is confirmed by XRD analysis. The lattice parameter of these compounds increases linearly with increasing ionic radius of Ln3+. La3NbO7 and Nd3NbO7 crystallize into a weberitetype structure. The correct space group between Pmcn (No. 62) and Cm cm (No. 63) cannot be discerned by r oom Based on synchrotron XRD and neutron diffraction, the space group was found to be Pmcn at room temperature since a few minor reflections, which violate the reflection conditions for Cmcm, appeared in both synchrotron XRD and neutron diffraction patterns.

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204 The crystal structure of Gd3NbO7 is another weberitetype. Like La3NbO7 and Nd3NbO7, the correct space group The room temperature space group Cm2m was determi ned by synchrotron XRD. As for La2LnNbO7, these compounds have an orthorhombic fluoriterelated structure. La2(Yb0.5Nb0.5)2O7 is orthorhombic pyrochlore, and La2(Er0.5Nb0.5)2O7 and La2(Dy0.5Nb0.5)2O7 are weberite type. Nd2YbNbO7 and Sm2YbNbO7 also have an orthorhombic lattice. However, Gd2YbNbO7 has a tetragonal lattice; it may be an intermediate structure between the cubic defect fluorite and orthorhombic weberitetype. The formula volume, which is defined as the unit cell volume divided by the formula number, has a nearly linear relationship with the (average) ionic radius of Ln3+. However, Gd3NbO7 and La2ErNbO7 have more open structure because these two compounds lie slightly outside the upper 95% confidence limit of the linear fitting. T herefore, there may be an easier ion movement or polarization in these two compounds. 10.1.2 Phase Transition in Weberitetype Ln3NbO7 There is a phase transition in Gd3NbO7 at 340 K, which is confirmed by s eco nd harmonic generation (SHG), heat capacity measurement s, and IR Based on the heat capacity curve and the dielectric susceptibility plot, the phase transition is likely to be a second order phase transition. High resolution x ray diffraction was conducted at 100 K, 295 K, 345 K and 400 K to study the crystal structure before and after the phase transition. The main difference in XRD patterns is t he appear ance of (201) reflection below the phase transition. Rietveld refinement was performed on the XRD patterns of the four mentioned temperatures which has resolved the controversy regarding the

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205 space group of the low ( Cm2m) and high temperature ( Cmcm ) phases It was also concluded that t he phase transition upon cooling is mainly due to the off center shifts of Nb5+ and one third of the Gd3+ ions within their corresponding polyhedra. The off center shift of the Nb5+ ions is in an antiparallel manner with their nearest Nb5+ neighbors along [001]. The same happens for the Gd13+ ions, antiparallel displacement with their nearest Gd3+ neighbor s in [001]. The antiparallel shifts may cause antipolar displacements along [001]. The most interesting finding is that the off center shifts cause net dipole along [010]. The calculated net dipole per unit cell is 0.0503 C/m2 at 100 K and 0.0045 C/m2 a t 295 K. It indicates that Gd3NbO7 is an incipient ferroelectric with [010] being the polar axis. There are correlated antipolar displacements in [001] Nd3NbO7 and La3NbO7 also exhibit phase transition above room temperature, which was proven by heat capacity measurement and neutron diffraction. However, unlike Gd3NbO7, SHG measurements indicate that Nd3NbO7 and La3NbO7 have a centrosymmetric structure both below and above the phase transition temperature. On the neutron diffraction patterns, t he dis appear ance of ( 141 ) and (413) reflections above the phase transition temperature confirmed the phase transition from Pmcn to Cmcm. The Rietveld refinement method was performed on the diffraction patterns at different temperatures. It was concluded that t he phase transition upon cooling is mainly due to the off center shifts of Nb5+ and one third of the La3+ and Nd3+ ions within their corresponding polyhedra. As a result, two neighboring Nb5+ ions along [001] displace in an antiparallel manner parallel to [010]. The same thing also happens in the displacement of 8coor dinated Ln3+. Because of the antiparallel manner, the net dipoles produced by the off center displacement s sum to zero. Therefore, these two materials

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206 may be potential antiferroelectrics. The key difference of these two from Gd3NbO7 is that in the latter there is net dipole moment along [010]. 10.1.3 Dielectric Properties The different structures show different dielectric behavior as a function of temperature. The dielectric permittivity of defect fluorite Ln3NbO7 ( Ln3+ = Dy3+, Er3+, Yb3+, and Y3+) increases with increasing temperature from 20 K to 475 K. The TC C increases with the decreasing ionic radius of Ln3+. Weberitetype Ln3NbO7 (Ln3+ = La3+, Nd3+, and Gd3+) exhibit dielectric relaxation. The temperature where the maximum permittivity occurs is close to the phase transition temperature. Above T( m), the TC C is negative with its value also increasing with decreasing Ln3+ in weberitetype Ln3NbO7. An Arrhenius type function was used to model the relaxation behavior for Gd3NbO7. The resulting activation energy is 0.45 eV and the attempt frequency is 1.51011 Hz. Ln2LnNbO7 (except Gd2YbNbO7) demonstrate dielectric relaxation as well. However, the temperature where the maximum of permittivity occurs in Ln2LnNbO7 is a much lower than in the weberitetype Ln3NbO7. Ln2LnNbO7 has smaller variation of Tm as a function of frequency. The relaxation behavior was modeled by the Arrhenius function for Ln2(LnNb)O7. The ac tivation energy of all the Ln2(LnNb)O7 compounds is lower than that of Gd3NbO7. Nd2(YbNb)O7 has the lowest activation energy, 0.04 eV. The experimentally determined room temperature dielectric permittivity for Ln3NbO7 ranges between 29 and 45, at 1 MHz. Gd3NbO7 has a higher room temperature permittivity than Nd3NbO7, probably because the former has a more open structure. As for Ln2LnNbO7, the compounds with more polarizable Ln3+ ions have higher permittivity at all measured temperatures (from 20 K to 350 K).

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207 10.1.4 IR The low temperature phase of Gd3NbO7 has 53 IR active modes and the high temperature phase has 30 IR active modes based on the nuclear site group analysis. A four parameter oscillator model was used to fit the reflectivity at differ ent temperatures. A total of 33 oscillators were used to fit the 10 K spectrum, 24 oscillators were used for the 300 K spectrum, and only 18 oscillators were required to fit the 600 K spectrum. The dielectric properties measured by terahertz transmission spectrometer were used to normalize the reflectivity. The dielectric properties at three temperatures were calculated from the oscillator fit from 20 cm 1 up to 650 cm1. The calculated static permittivity as a function of temperature maintains the shape with 1 MHz permittivity. The dielectric contribution from the 450 cm1 mode, which disappears above the phase transition temperature, is less than 2% from the total dielectric permittivity. 10.1.5 StructureDielectric Property Relationship For weberitetype Ln3NbO7, the origin of dielectric relaxation is the phase transition. T( m), where the maximum permittivity occurs, increases with the increasing off center shifts of the 8coordinated Ln13+: Nd3NbO7 has the highest T( m) and largest off center shift; La3N bO7 exhibits the intermediate T( m) and intermediate off center displacement; Gd3NbO7 with the shortest off center shift demonstrates the lowest T( m). r increasing off center shifts of the Ln13+. On the other hand, Gd3NbO7 has the most open structure while Nd3NbO7 has the most dense among the three compounds. The structural openness may cause an easier polarization and result in a lower T( m).

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208 The real part of the permittivity of Ln2LnNbO7 follows the trend of the average Ln3+ ion polarizability, i.e. more polarizable ions result in higher permittivity. The crystal structure of Gd2YbNbO7 is intermediate between orthorhombic weberitetype and cubic defect fluorite. The dielectric behaviors of Gd2YbNbO7 resemble that of defect fluorite Ln3NbO7, other than the other Ln2LnNbO7. However, the real part of the permittivity of Gd2YbNbO7 is lower than any other defect fluorite Ln3NbO7 though the former has higher ion pol arizability. For Ln2LnNbO7 (except Gd2YbNbO7), the Tm generally increases with an increasing ratio of rA (Ln3+) over rB (average of Ln3+ and Nb5+). However, the structural openness can lower the Tm because La2ErNbO7, with a more open structure, has a l ower rA/rB but lower Tm than La2DyNbO7. The TCC is negative for all investigated Ln2LnNbO7 except Gd2YbNbO7. The TCC also increases with the decreasing average ionic radius of Ln3+. As for the origin of dielectric relaxation, the possibility of phase t ransition has been ruled out by neutron diffraction at different temperatures. The origin of dielectric relaxation may be due to a cation disorder like in pyrochlores. 10.2 Future Work 10.2.1 Crystallography The phase refinements of weberitetype Ln3NbO7 at different temperatures were conducted. The relationships of the crystal structure and dielectric property as well as the origin of the dielectric relaxation have been studied in more depth. By contrast, the origin of the dielectric relaxation of Ln2L nNbO7 is still somewhat unclear. It would be appealing to perform phase refinements on neutron diffraction patterns of Ln2LnNbO7 to correlate the crystal structure with dielectric relaxation. It would be interesting to see if there is cation disorder ( like in pyrochlores) in Ln2LnNbO7. In addition, TEM and high

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209 resolutionTEM studies may provide additional structural information t o help develop a better understanding of the crystal structure. 10.2.2 Thin films of Ln3NbO7 (Ln3+ = La3+, Nd3+, and Gd3+) In Chapter 6, it indicates that Gd3NbO7 is an incipient ferroelectric with [010] polar axis. There are also correlated antipolar displacements perpendicular to the polar axis. However, some preliminary tests of bulk Gd3NbO7 (piezoelectric activity and polariza tion hysteresis) have not yielded significant insight in this respect. The d33 value measured using Piezoelectric Meter by KCF technologies shows almost zero. The polarization vs. the electric field indicates a linear dielectric, no hysteresis loop. It can be argued that the effect of the net dipole is too small to be detected for bulk Gd3NbO7. The net dipole is only in [010] direction. The fabrication of thin films especially epitaxial films will enable a better control of the domains. It will also be interesting to study the thin films of Nd3NbO7 and La3NbO7. In Chapter 7, there are antiparallel displacements of the Nb5+ and Ln13+ ions. These two materials are potential antiferroelectrics. A typical hysteresis loop for an antiferroelectric material is shown in Figure 101 The polarization undergoes a double hysteresis loop if the applied field above the critical field. It is reasonable to expect that the critical (coercive) field for bulk materials is too high to be realized. Therefore, it will be interesting to grow Nd3NbO7 and La3NbO7 thin films to make the critical field achievable to see whether the antiparallel displacements result in antiferroelectric behavior. 10.2.3 Dielectric Properties Recent development s in electronic technologies extensivel y demand ceramics with good dielectric properties The good properties include high dielectric constant, low

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210 dielectric loss and low temperature coefficient of capacitance (TCC) In general Ln2LnNbO7 has the smallest TCC and weberitetype Ln3NbO7 tends to have highest TCC among the investigated compounds. It will be interesting to delve on why TCC has such a trend, which may give an insight on how to predict or even control TCC. Figure 10 1 A typical hysteresis loop for an antiferroelectric material. 112 E crit is the critical field. There is an increasing need for the applications of dielectric materials at microwave frequencies. The dielectric properties investigated were focused on the frequency range 1 kHz to 1 MHz. Only the dielectric properties of Gd3NbO7 have been studied at GHz range. It would be compelling to investigate the dielectric properties at microwave frequency for the rest Ln3NbO7 and Ln2LnNbO7 to shed light on control ling dielectric properties at microwave frequencies through crystal structure. It will also be interesting to see how frequency will influence the dielectric relaxation.

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211 APPENDIX A D IELECTRIC R ELAXATION IN THE CaO TiO2Nb2O5 P YROCHLORE AND S YNTHESIS OF PYROCHLORE FILMS BY PULSED LASER DEPOSTION Deposition (PLD) The core of the first section of the appendix is chiefly based on the journal article (Journal of the Solid State Chemistry 181(3) 406414 (2008)) titled Pyrochlore formation, phase relations, and properties in the CaO TiO2(Nb,Ta)2O5 systems by R.S. Roth, T.A. Vanderah, P.Bordet, I.E. Grey, W.G.Mumme, L.Cai, and J.C. Nino. It is reprinted with permission from Elsevier Bibased pyrochlores are among the most studied compounds in the family of fluorite related structures due to their interesting dielectric properties. Generally, t hese compounds exhibit dielectric relaxation. Given that bismuth is the dominant element on the A site of Bibased pyrochlores, it was speculated that the observe d relaxor dielectric behavior was associated to the presence of Bi (with its lone electron pair). However, in collaboration with NIST, CNRS, and CSIRO, it was shown that a displacive cubic pyrochlore not containing bismuth, namely Ca1.469Ti1.469Nb1.037O7, also displays dielectric relaxation. The first section of the appendix discusses dielectric properties of Ca1.469Ti1.469Nb1.037O7. The second section s hows the continuing work on Ca1.469Ti1.469Nb1.037O7 pyrochlore; namely, the growth of Ca1.469Ti1.469N b1.037O7 and Bi1.657Fe1.092Nb1.15O7 pyrochlore thin film s by pulsed laser deposition (PLD). A.1 Dielectric Relaxation in CaO TiO2Nb2O5 pyrochlore Preliminary capacitance measurements of CaTi Nb O and CaTi TaO pyrochlores165 suggested that both phases exhibited dielectric relaxation. resembling

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212 that observed in bismuth pyrochlores (e.g. Bi ZnNb O166169 and Bi FeNb O170). The real and imaginary parts of the relative permittivity for a pyrochlore specimen of composition 42.5:42.5:15.0 CaO : TiO2 : Nb2O5 ( Ca1.469Ti1.469Nb1.037O7) are shown in Figure A 1 as a function of temperature and frequency from 1 kHz to 1 MHz. This composition lie s slightly outside the singlephase pyrochlore region. The sample contained a just detectable amount of rutile (on the order of 12%). Remarkably, a dielectric relaxation characteristic of bismuthbased pyrochlores is clearly observed,167 that is, with increasing measuring frequency the peak of the imaginary part of permittivity shifts towards higher temperatures and the width and maximum of the imaginary part of permittivity peak increases. At 1 MHz, the CaTi Nb O pyrochlore exhibits a maximum relative dielectric permittivity of 107 at 200 K, and the peak of the imaginary part of permittivity occurs at Tm 150 K. When compared with the bismuth niobate pyrochlores, the CaTi Nb O analog exhibits a higher Tm but a lower dielectric constant. To better understand the phenomenon, the Arrhenius function was used to model the rel axation behavior Tm was determined for each measuring frequency by fitting the peak of the imaginary part of the relative permittivity to a Gaussian function. The resulting Arrhenius plot is shown in Figure A 2 0 = 4.61014 Hz and the activation energy Ea is 0. 32 eV. Both the attempt jump frequency and the activation energy are higher than those of Bi based pyrochlores .166167 Previously, the attempt jump frequency which drives the relaxation has been correlated with that of the O A O bending phonon mode.168 Since the A site atoms in CaTi Nb O pyrochlore (Ca and Ti) are lighter than those in Bi based pyrochlores (primarily Bi), higher frequencies for the O A O bending phonon mode and the attempt jump frequency are

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213 therefore expected. Although the activation energy for the CaTi Nb O pyrochlore is higher than that observed for the bismuth pyrochlores (e.g. for Bi ZnNb O Ea 0.14 eV), it is lower than that weberitetype Gd3NbO7 (Ea 0.45 eV) as discussed in Chapter 5.171 The CaTi (Nb,Ta) O pyrochlores, like the bismuth analogs, exhibit substantial displacive disorder in their A2O sub networks. Observation of dielectric relaxation in these systems suggests, for the first time, that it arises from the displacive di sorder and is not necessarily associated with the presence of polarizable lonepair cations such as Bi3+. This observation suggests that further investigations may result in a fundamental change in the understanding and analysis of dielectric relaxation i n all fluorite related materials. 100 200 300 400 500 50 60 70 80 90 100 0 2 4 6 8 100 200 300 400 500 r' r"Increasing FrequencyTemperature (K) Figure A 1 The real part ( r) and imaginary parts of permittivity ( r) for a pyrochlore specimen 42.5:42.5:15.0 CaO:TiO2:Nb2O5, measured at (from left to right) 1 kHz, 3 kHz, 8 kHz, 10 kHz, 30 kHz, 80 kHz, 100 kHz, 300 kHz, 800 kHz and 1 MHz.

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214 5.0 5.5 6.0 6.5 7.0 7.5 103104105106 = 4.6 1014 exp(-0.32/kT) Frequency (Hz)103/Temp (1/K)R 2= 0.9997 Figure A 2 Arrhenius plot of measuring frequency and T m The equation for the linear least squares fit is given along with the goodness of the fit. A.2 Ca1.469Ti1.469Nb1.037O7 and Bi1.657Fe1.092Nb1.15O7 pyrochlore films Due to the interesting dielectric properties of Ca1.469Ti1.469Nb1.037O7, deposition and growth of thin films of this material as well as another Bi based pyrochlore, Bi1.657Fe1.092Nb1.15O7, were performed. This section is focused on the film growth using pulsed laser deposition (PLD) and phase formation. Ceramic targets for laser ablation were synthesized by conventional solid state processing as discussed in Chapter 3. The calcination temperature for Ca1.469Ti1.469Nb1.037O7 was 1573 K. Multiple calcinations, each with an extended soaking time, were used but the secondary phases CaTiO3, TiO2, and Ca5Nb4Ti3O21 (CNT) were still present. Figure A 3 shows the XRD of the target which was calcined at 973 K for 4 h, followed by calcinations at 1273 K for 8 h, 1373 K for 8 h, 1473 K for 8 h, 1573 K for 4 h, 1573 K for 12 h, and 1573 K for 24 h. Ca1.469Ti1.469Nb1.037O7 t hin films were grown on the <100> Si wafer under the growth conditions: 673 K 723 K

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215 substrate temperature, 10 Hz laser frequency, energy 600 mJ, and 100 mTorr oxygen pressure ( Figure A 3 ). The phase formation was strongly dependent on the annealing temperature. The films were amorphous when the annealing temperature was below 973 K. Phase pure pyrochlore was formed when annealed at 973 K for 0.5 h. However, the pyrochlore phase decomposed if annealed for longer times. As shown in Figure A 4 after annealing at 973 K for 2 h, the CNT phase appears. 10 20 30 40 50 60 70 Annealing 973 K 0.5 h Annealing 873 K 0.5 h Target Intensity (arb units)2 (degrees)SiCNT (551) (444) (622) (533) (620) (531) (440) CNT (333) or (511) (422) (400) CNT (222) (311) CNT (111) Figure A 3 XRD of the Ca 1.469 Ti 1.469 Nb 1.037 O 7 target and the films annealed at 873 K and 973K, respectively. CNT stands for Ca 5 Nb 4 Ti 3 O 21 The Bi1.657Fe1.092Nb1.15O7 target was also synthesized by solid state processing with a calcination temperature of 1273 K for 12 h. The thin films of Bi1.657Fe1.092Nb1.15O7 with preferred orientations were successfully produced on the <100> Si wafer under growth conditions: 673 K 723 K substrate temperature, 10 Hz laser frequency, energy 250 mJ, and 100 mTorr oxygen pressure. The annealing temperature was 973 K for 0.5 h. As shown in Figure A 5, the preferred orientation is (111).

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216 10 20 30 40 50 60 Annealing 873 K 0.5 h 973 K 0.5 h 973 K 2 h Substrate T 560 C Annealing 973 K 2 h Substrate T 673 723 K Annealing 873 K 0.5 h 973 K 0.5 hCNT (622) (440) (400) (222) (111)Intensity (arb units)2 (degrees) Figure A 4 XRD of the Ca 1.469 Ti 1.469 Nb 1.037 O 7 films at different annealed temperature and time. 10 20 30 40 50 60 70 target(444) (622) (531) (440) (511) (331) (400) (222) (311) (111)filmIntensity (arb units)2 (degrees) Figure A 5 XRD of the Bi 1.657 Fe 1.092 Nb 1.15 O 7 target and film.

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217 APPENDIX B S UPPLEMENT INFORMATION FOR INFRARED SPECTROSCOPY As stated in Chapter 6, t wo independent experiments were performed to measure the IR of Gd3NbO7 by Daniel Arenas in Professor Tanners lab at University of Florida and Veronica Goian in Professor Kambas lab at Institute of Physics of the AS CR, Republic The first part of the appendix is to show the comparison between the two experiments. As shown in Figure B 1 Figure B 2 and Figure B 3 o bservable vibrational modes match well with each other at all three temperatures. 100 200 300 400 500 600 0.0 0.2 0.4 0.6 0.8 1.0 from Prof. Tanner from Prof. Kamba ReflectivityWavenumber ( cm-1)50 K Figure B 1 Infrared reflectivity of Gd 3 NbO 7 at 50 K The normal determination of the fluorite structure was shown in Chapter 2. The normal mode determination table for the RT Ln3NbO7 (Ln3+ = Nd3+ and La3+) phase are presented in Table B 1

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218 Table B 1 Normal mode determination for RT La3NbO7 and Nd3NbO7 phase with space group Pmcn Site Symmetry Ag Au B1g B1u B2g B2u B3g B 3 u Ln1 C 1 (8 d ) 3 3 3 3 3 3 3 3 Ln2 C s xz (4 c ) 2 1 1 2 2 1 1 2 Nb C s xz (4 c ) 2 1 1 2 2 1 1 2 O1 C 1 (8 d ) 3 3 3 3 3 3 3 3 O2 C s xz (4 c ) 2 1 1 2 2 1 1 2 O3 C 1 (8 d ) 3 3 3 3 3 3 3 3 O4 C 1 (8 d ) 3 3 3 3 3 3 3 3 Acoustic Modes 0 0 0 1 0 1 0 1 Lattice Modes 18 15 15 17 18 14 15 17 Selectrion Rules Raman Inactive Raman IR Raman IR Raman IR The irreducible representation for the RT La3NbO7 and Nd3NbO7 phase can be written as (IR) 17B + (R) 15B + (IR) 14B + (R) 18B + (IR) 17B + (R) 15B + (-) 15A + (R) 8A 1 = 3u 3g 2u 2g 1u 1g u g B 1 There are totally 66 Raman modes and 48 IR modes. The infrared spectra of Nd3NbO7 and Sm3NbO7 are shown in Figure B 4 and Figure B 5 Classical damped harmonic oscillator model was used to fit the reflectivity: n j j j j j i 1 2 2 2 ) ( B 2 21 ) ( 1 ) ( ) ( R B 3 where is the permittivity at frequencies much higher than all oscillator eigenfrequencies, and j, j, and j, is the frequency, dielectric strength, and damping constant of the jth phonon mode. The ASF program developed in Professor Kambas lab was used for the fitting. The fitting parameters are listed in Table B 2 and Table B 3

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219 100 200 300 400 500 600 0.0 0.2 0.4 0.6 0.8 1.0 from Prof. Tanner from Prof. Kamba ReflectivityWavenumber ( cm-1)300 K Figure B 2 Infrared refle ctivity of Gd 3 NbO 7 at 300 K 100 200 300 400 500 600 0.0 0.2 0.4 0.6 0.8 1.0 from Prof. Tanner from Prof. Kamba ReflectivityWavenumber ( cm-1)360 K Figure B 3 Infrared reflectivity of Gd 3 NbO 7 at 360 K

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2 20 100 200 300 400 500 600 0.0 0.2 0.4 0.6 0.8 1.0 ReflectivityWavenumber ( cm-1)Nd3NbO7 Figure B 4 Infrared reflectivity of Nd 3 NbO 7 at room temperature. Table B 2 Fitting Parameters for the reflectivity of Nd3NbO7 No. (cm 1 ) (cm 1 ) 1 87.3629 1.1449 6.3491 2 102.6504 2.7107 8.5883 3 124.2524 4.2161 13.1363 4 145.4279 0.9907 7.1971 5 154.2582 1.8858 16.987 6 169.1808 2.676 20.5542 7 188.0656 3.0567 23.9089 8 265.7592 3.6556 19.3056 9 274.9751 2.3809 8.9648 10 300.8369 0.3052 12.6338 11 330.6909 1.6095 66.6918 12 330.9352 3.0274 27.5672 13 362.1505 0.2396 9.8237 14 447.9323 0.5565 22.7981 15 547.5186 0.2411 67.0734 16 577.5773 0.2742 29.2296 17 596.9123 0.2982 17.3937 18 770.0724 0.0555 85.305

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221 100 200 300 400 500 600 0.0 0.2 0.4 0.6 0.8 1.0 ReflectivityWavenumber ( cm-1)Sm3NbO7 Figure B 5 Infrared reflectivity of Sm 3 NbO 7 at room temperature. Table B 3 Fitting Parameters for the reflectivity of Sm3NbO7 No. (cm 1 ) (cm 1 ) 1 58.191 1.4608 13.3498 2 97.4834 7.2269 26.1808 3 119.395 1.1884 15.7315 4 172.7618 1.3772 11.7609 5 194.2726 2.7549 23.4876 6 267.5433 0.9934 20.7065 7 311.418 5.8778 38.4904 8 380.7177 1.618 40.7026 9 457.5484 1.094 53.3473 10 600.7356 0.59 43.3216 11 785.3206 0.0504 89.8245

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222 APPENDIX C T HE TOLERANCE FACTORS OF PYROCHLORE The tolerance factor ( t ) concept, widely used in crystallochemical analysis of perovskites ABO3, is here applied to A2B2O7 fluorite derivative superstructure: pyrochlores. Based on geometrical considerations of the different cation coordination polyhedra two tolerance factors for pyrochlores are introduced in this appendix. The t values were calculated for 315 pyrochlores. A stability field i s proposed to distinguish A2+ 2B5+ 2O7 pyrochlores from A2+ 2B5+ 2O7 weberites. A relationship between the tolerance factors and dielectric properties is also discussed. C.1. Introduction The tolerance factor ( t ) concept was first introduced by Goldschmidt172 in 1926 and it is routinely used analyze structureproperty relations of ceramics with the perovskite crystal structure ( ABO3). The tolerance factor is a geometrical parameter that provides a measure of how well the A site cation fits the twelve fold coordinated space within the corner shared octahedral network formed by the B site cation. Based on the ionic radii and assuming a sphere model where anions and cations are touching, t for perovskites can be expressed as: O B O Ar r r r t 2 1 C 1 where rA, rB, rO are ionic radii of A B and oxygen ions, respectively. The constant 1/ 2 is a geometric factor, which is the rati o of the B O bond length (half of the lattice parameter) over the A O bond length (1/2 of the face diagonal). The tolerance factor is 1.0 for the ideal perovskite structure. The closer t is to unity, the greater is the stability of the structure. The application of the t is not only limited to providing an indication of the

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223 structural stability but also to providing key information about the physical properties. For example, Reaney et al.173 determined there is a relations hip between the t and the temperature coefficient of the dielectric permittivity ( ) in Ba and Sr based perovskites. Suarez et al.174 concluded that the temperature Tc (paraelectric to ferrroelectric phase transition temperature) decreases as the t increases in Aurivillius phases (perovskiterelated). There have been very few attempts to extend the tol erance factor concept ( t ) to other crystal structures. Perhaps more notable, is the attempt at introduc ing it for the pyrochlore structure ( AVIII 2BVI 2O7) by Isupov175 in 1958. O n the assumption that the BO6 were perfect octahedra, h e determined the tolerance factor to be : O B O Ar r r r t 866 0 C 2 However, BO6 octahedra are almost never regular in real pyrochlores. For an ideal pyrochlore, when placing the B site at the origin (space group m 3 Fd origin 2), 6/7 of the oxygen ions are located at Wyckoff position 48f ( x, 1/8, 1/8). The x parameter can vary from 0.3125, leading to perfect BO6 octahedra and distorted AO8 cube to 0.375, leading to distorted BO6 octahedra and regular AO8 cube (see Figure C 1 ). The disregard of the x parameter in Isupovs tolerance factor diminishes important structural features. Therefore, in this appendix a new tolerance factor for pyrochlores is proposed and correlated with physical properties. C.2. Derivation of the Tolerance Factor Following the logic of the tolerance factor for perovskites, the t for pyrochlores is proposed to have a similar format as below:

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224 O B O Ar r r r g t C 3 where g is a geometric factor. In cubic perovskites, it is evident that the g is a constant (1/ 2). (A) (B) (C) Figure C 1 [001] view of pyrochlores when (A) x = 0.3125 (perfect BO 6 octahedra) (B) x = 0.375 (perfect AO8 cube) (C) x is between 0.3125 and 0.375 (both BO 6 octahedra and AO 8 cube distorted).

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225 The pyrochlore structure is more complicated than the perovskite structure since the former contains more ions per unit cell. Therefore, it is easier to relate rA+ rO and rB+ rO in a cationic polyhedra where the oxygen ions lie inside rather than in a unit cell as in perovskites. In ideal pyrochlores, A2B2 tetrahedra are regular, which means the tetrahedral edges have the same length: a l l lB A B B A A4 2 C 4 where l is the distance between the two subscripted ions and a is the lattice parameter. 2 sin 2 AOA l lO A A A C 5 2 sin 2 BOB l lO B B B C 6 2 sin 2 2 sin 2 BOB l AOA lO B O A C 7 In a stable ionic compound, cations should contact anions, i.e. the distance between nearest neighboring cation and anion should be close to the su mmation of the two ionic radii. The tolerance factor t1 is introduced in the following equation based on the equation C 7 : 2 sin ) ( 2 sin ) (1BOB r r t AOA r ro B O A C 8 where r indicates the ionic radius of the subscripted ion. It is evident that sin( AOA/2) and sin( BOB/2) are functions of x: 32 1 2 12 x a lO A C 9 32 1 4 12 x a lO B C 10 32 1 2 1 8 2 2 1 2 sin2 x l l AOAO A A A C 11

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226 32 1 4 1 8 2 2 1 2 sin2 x l l BOBO B B B C 12 Therefore, the t1 is defined as: O B O A O B O Ar r r r x x r r r r BOB AOA t 32 1 2 1 32 1 4 1 2 sin 2 sin2 2 1 C 13 It is important to recall that there are two Wyckoff positions for oxygen ions in ideal cubic pyrochlores ( B cations at the origin): O at 48f ( x, 1/8, 1/8) inside A2B2 tetrahedra and O 8b (3/8, 3/8, 3/8) inside A4 tetrahedra ( Figure C 2 (A)). The discussion above has considered the tolerance factor based on A2B2 tetrahedra ( Figure C 2 (B)). It is reasonable to consider the other tolerance factor corresponding to A4 tetrahedra. In A4 tetrahedra, the edge length ( lA O) is only related to the lattice parameter ( Figure C 2 (C)): 8 3 3'a lO A C 14 The second tolerance factor ( t2) is defined as O A o A o Ar ra r r l t 8 3 3' 2 C 15 In Isupovs tolerance factor( ti), the g is 0.866, which is the ratio of lA O to lB O when BO6 is perfect octahedra ( x = 0.3125).175 The ti ignores the importance of the x and the introduction of 0.866 as geometric factor is rather misleading since lA O and lB O are not directly related to each other.

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227 (A) (B) (C) Figure C 2 (A) 1/8 pyrochlore unit cell showing cation tetrahedra (B) A 2 B 2 tetrahedra with O inside (C) A 4 tetrahedra with O in the center. The involvement of the x makes the t more precise. However, the disadvantage is the limited availability of the x Nikiforov176 developed a mathematical relationship to

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228 calculate the range of the unknown oxygen positional parameter x (O at the origin) based on the ionic radius of A B and O ions. ar x a ro o2 2 2 1 C 16 2 1 2 2 1 232 1 8 3 2 3 8 1 8 3 a r r x r r r rO B O A O B C 17 McCauley177 obtained the x by averaging the smaller of the two larger values and the larger of the two smaller values from the inequalities C 16 and C 17. The x value in above inequalities are for an origin at the O site. The following equation can convert x into B origin lattice. ) ( 8 5 ) ( O x B x C 18 To test Nikiforovs method, in this study, the reported x of 76 pyrochlore compounds not satisfying the inequality C 19 were compared with the calculated x.14,39,58,71,178211 The ionic radii used in the calculation were after Shannon.27 The calculated x and the reported x are in good agreement (71 compounds have less than 4% difference). However, the calculated x of Tl2Pt2O7 (high pressure phase)178 and Pr2Te2O7 179 pyrochlor es have a 7%~8% difference, possibly because the ratio, Tl3+/Pt4+, is small (one of the smallest in pyrochlores) and Te4+ is large. The calculated x of Zr4+based pyrochlores, like Gd2Zr2O7 39,182 (some publications refer this as defect fluorite211212), A m2Zr2O7 181, and Sm2Zr2O7 180,184, differ by 4% 5% from the report values due to relative large ionic radius of Zr4+. Table C 1. Table 104. lists selected pyrochlores comparing the calculated and reported x. It clearly shows that the reported and the calculated values match better for Ti4+based pyrochlores than Sn4+based pyrochlores,

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229 probably due to the smaller ionic radius of Ti4+.27 It is apparent that when the ratio of rA over rB is small or the ionic radius of rB is large, the discrepancy becomes larger. Table C 1 Comparison of the x value from literature with calculated after Nikiforov176 Compound Lattice constant () Reported x Calculated x difference% Tb 2 Ti 2 O7 197 10.1589 0.3281 0.3252 0.89 Dy 2 Ti 2 O 7 14 10.1237 0.323 0.3263 1.02 Y 2 Ti 2 O 7 208 10.0949 0.3282 0.3272 0.30 Er 2 T i2 O 7 14 10.0869 0.3293 0.3274 0.55 Tm 2 Ti 2 O 7 197 10.0638 0.3292 0.3282 0.30 Yb 2 Ti 2 O 7 197 10.0325 0.3309 0.3292 0.51 Lu 2 Ti 2 O 7 14 10.0172 0.3297 0.3297 0.005 Ho 2 Ti 2 O 7 208 10.1041 0.3285 0.3269 0.48 Pr 2 Sn 2 O 7 191 10.6004 0.33148 0.3210 3.15 Nd 2 Sn 2 O 7 194 10.5671 0.3322 0.3220 3.06 Sm 2 Sn 2 O 7 191 10.5099 0.333 0.3238 2.77 Eu 2 Sn 2 O 7 191 10.47526 0.3338 0.3248 2.69 Tb 2 Sn 2 O 7 194 10.4235 0.3356 0.3264 2.75 Dy 2 Sn 2 O 7 194 10.3979 0.3372 0.3271 2.99 Y 2 Sn 2 O 7 191 10.3725 0.338 0.3279 2.99 Ho 2 Sn 2 O 7 194 10.3726 0.3366 0.3279 2.59 Er 2 Sn 2 O 7 194 10.3504 0.3375 0.3287 2.60 Tm 2 Sn 2 O 7 194 10.3262 0.3382 0.3304 2.31 Yb 2 Sn 2 O 7 194 10.3046 0.33908 0.3318 2.14 Lu 2 Sn 2 O 7 194 10.2917 0.3397 0.3330 1.98 Gd 2 Sn 2 O 7 194 10.45438 0.3348 0.3254 2.80 Gd 2 Ru 2 O 7 209 10.2281 0.332 0.3247 2.20 Gd 2 ScNbO 7 210 10.4429 0.334 0.3260 2.38 Gd 2 TiZrO 7 211 10.3772 0.3281 0.3248 1.00 Gd 2 Ti 0.5 Zr 1.5 O 7 211 10.4594 0.3348 0.3254 2.80 Gd 2 Zr 2 O 7 39,182 10.523 0.3411 0.3266 4.25 It is worth noting that Nikiforovs method does not work for some compounds. The inequalities C 19 and C 20 are derived from the assumption that the bond length was equal to the sum of the ionic radii. However, the bond length is less than the sum of the ionic radii for many cases. For example, all 315 of pyrochlores investigated in this work have shorter A O bond length than the sum of rA and rO ( i.e. all the t2 are smaller

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230 than 1). For some compounds, the difference between the bond length and the sum of the ionic radii is not negligible, like BaLaHfNbO7 and PbBiSnTaO7 ( lA O is below 0.86 of rA + rO).39 In these cases, the following inequality results and Nikiforovs method should not be applied177: 2 32 O A O Br r r r C 19 There is however, another way to predict x which is based on the bond valence sum concept : 37 0 exp 6O B O B BR l V C 20 where lB O is B O bond length and RB O is the bondvalence parameter.52,57 For A2(ByB1 y)2O7 (0
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231 shows that all t2 are less than 1. This is expected because the actual bond length is less than the sum of the ionic radii. The number of compounds generally increases with increasing t2 from 0.83 to 0.92. The distribution has a peak when the t2 value is between 0.91 and 0.92 and decreases with increasing t2 afterward. The t2 values of the majority of the compounds lie between 0.89 and 0.93, which is a narrower distribution than the t1. It is interesting to note that t2 shows a clearer trend in its values as a function of rA/ rB when compared with the t1. The t2 weakly decreases with increasing rA/ rB, especially between t2 values of 0.91 and 0.92. By contrast, the t1 is rather scattered against rA/ rB ( Figure C 4 ). 0.84 0.87 0.90 0.93 0.96 0.99 1.02 1.05 0 20 40 60 0 20 40 60 0.84 0.87 0.90 0.93 0.96 0.99 1.02 1.05 Number Number total x from literature calculated xTolerance Factort1(B)t2 (A) Figure C 3 The distribution of pyrochlore compounds with a grouping range of 0.01 based on (a) t1 (distinguishing the x from literature and calculated x from the total) and (b) t 2

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232 One important function for tolerance factors is to determine the stability fiel d. It is important to recall previous work on the stability field of pyrochlores: Subramanian14 used rA vs. rB to define the stability region; Lopatin et al.73,76 successfully utilized A) and rA/ rB to distinguish pyrochlores and weberi tes, another aniondeficient fluoriterelated structure; Sych et al.72 and Cai et al.248 (as stated in Chapter 2) introduced rA/ rB vs. relative ionicity of A O bond, which is a ratio of the ionicity of A O bond to the sum of ionicity of A O and B O bonds. Here, t1 and rA/ rB are used to determine the pyrochlore stability region against the weberite. t1 has been chosen rather than t2 for the stability field because its calculations contain more structural information. As another aniondeficient flu orite related structure, the lattice parameters of orthorhombic weberites are approximately 2/2ap, ap, and 2/2ap ( ap is the lattice parameter of pyrochlores). The converted ap from weberites is (4Vw)0.5 ( Vw is the unit cell volume of weberites). The x is calculated by the bond valence approach. Based on 25 orthorhombic weberite oxides, only 16 have the calculated x in the required pyrochlore range (0.3125 0.375).13,54,58,72,75,100,249 252 Since there are very few, if any, A2 3+B2 4+O7 weberites reported, the stability field is only for A2+ 2B5+ 2O7 pyrochlores and weberites. As seen in Figure C 5 there is a clear separation between weberites and pyrochlores. The dashed line is for visual effect; the weberite region is found above the line. It is interesting to note that Cd2Sb2O7 pyrochlore is close to the weberite region. Actually, Cd2Sb2O7 can form a metastable phase of weberite, which can be fully converted to pyrochlore under high pressure.54 In summary, weberites prefer higher t1 and higher ratio of rA/rB than pyrochlores.

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233 Due to the meaningless value of x for weberites, t1 may not be the best way to distinguish pyrochlores and weberites. Bond ionicity is a more meaningful way to define the stability field for weberites due to the covalent nature of their bonds when compared to pyrochlores.7275 Nevertheless, t1 may serve as a supplement for the calculation of the stability field. 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 0.80 0.85 0.90 0.95 1.00 1.05 1.10 rA/ rBt1 (A) 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 rA/ rBt2 (B) Figure C 4 (A) t 1 as a function of r A / r B the ratio of the ionic radius of A over the ionic radius of B (B) t2 as a function of rA/ rB with a linear regression for observation of the trend.

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234 1.4 1.6 1.8 2.0 2.2 2.4 0.85 0.90 0.95 1.00 1.05 1.10 Pyrochlore Weberite t1rA/ rB Figure C 5 t1 as a function of rA / rB The dashed line is for visual separation between pyrochlore and weberite range. The significance of the tolerance factor in the perovskite or related structures is that t is related to dielectric properties, i.e. and Tc.173174 It will be interesting to see if the t of pyrochlores can also have such indication. Previous work has shown that more than 60% of the total dielectric permittivity is contributed by the O A O bending modes in Bi1.5Zn0.92NbO6.92 pyrochlore.6,139,160 As the t2 is closely related to A O bond length, it is reasonable to classify dielectric permittivity as a function of the t2. The normalized difference in dielectric permittivity ( n, define below) is proposed here to correlate the t2.

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235 In Clausius Mossotti relation, the macroscopic relative dielectric permittivity (r) is related to microscopic polarizability () as follows: 3 4 2 1cgs r rN C 22 cgs is polarizability measured in 3, N is the number of molecules per 3.109 For A2B2O7 pyrochlore, o B A cgs 7 2 2 C 23 A, B, and O can be found from Shannons ion polarizabilities.26 Then, the n is defined as cgs r m n C 24 m is measured permittivity (obtained from literature), r is calculated permittivity based on Clausius Mossotti relation. Figure C 6 (A) shows n vs. t2 of the 16 pyrochlores containing Bi3+, Zn2+, and Nb5+ ions.6,8,234,253256 It indicates that n has a clear correlation to t2, increasing with decreasing the t2. The n as a function of x is also plotted in Figure C 6 (B) and there is no observable trend. It shows that dielectric permittivity may have a closer relationship with t2 than with x, which corresponds to the experim ental results that O A O bending modes contribute more to dielectric permittivity in Bi1.5Zn0.92NbO6.92. It demonstrates the importance of the tolerance factors, not only in the geometric aspect but also in establishing a trend that will allow for the t ailoring of dielectric materials based on the predicted properties.

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236 0.88 0.89 0.90 0.91 0.92 0.93 0.94 0.95 0 2 4 6 Bi1.5Zn0.5Nb0.5Sn1.5O7Bi1.5Zn0.833Sn0.5Nb1.167O7BiZnTiNbO7Bi1.5Zn0.92Nb1.5O6.92Bi1.5Zn0.9167Nb1.333Ti0.25O7Bi1.5Zn0.833Nb1.167Ti0.5O7Bi1.5Zn0.667Nb0.833TiO7Bi1.5Zn0.5Nb0.5Ti1.5O7n t2Bi1.65Zn0.35Ti1.65Nb0.35O7Bi1.5ZnNbTa0.5O7Bi1.5Zn0.9167Sn0.25Nb1.333O7Bi1.5Zn0.5Nb0.5Zr1.5O7Bi1.5Zn0.667SnNb0.8333O7Bi1.5ZnNb0.5TaO7Bi1.5Zn0.5Nb0.5Ce1.5O7 (A) 0.310 0.315 0.320 0.325 0.330 0.335 0 1 2 3 4 5 6 n x-parameterBi1.5Zn0.5Nb0.5Sn1.5O7Bi1.5Zn0.833Sn0.5Nb1.167O7BiZnTiNbO7Bi1.5Zn0.92Nb1.5O6.92Bi1.5Zn0.9167Nb1.333Ti0.25O7Bi1.5Zn0.833Nb1.167Ti0.5O7Bi1.5Zn0.667Nb0.833TiO7Bi1.5Zn0.5Nb0.5Ti1.5O7 Bi1.65Zn0.35Ti1.65Nb0.35O7Bi1.5ZnNbTa0.5O7Bi1.5Zn0.9167Sn0.25Nb1.333O7Bi1.5Zn0.5Nb0.5Zr1.5O7Bi1.5Zn0.667SnNb0.8333O7Bi1.5ZnNb0.5TaO7Bi1.5Zn0.5Nb0.5Ce1.5O7 (B) Figure C 6 (A) The normalized permittivity difference vs. t 2 with a linear regression for the observation of the trend for (Bi,Zn,Nb) based pyrochlore. (B) The normalized permittivity difference vs. the xparameter showing no observable correlation. C.4. Conclusion The concept of the tolerance factor has been reintroduced into the pyrochlore structure. Two tolerance factors ( t ) for pyrochlores were derived from the geometrical aspects and the positional parameter x has been incorporated into the calculation. The

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237 tolerance factors were calculated for 315 pyrochlore compounds. t1, based on the A2B2 cation tetrahedra (O inside), ranges from 0.83 to 1.07 with the majority of compounds lying between 0.9 and 0.99. Together with rA/ rB, it can define the stability field for A2+ 2B5+ 2O7 pyrochlores versus weberites, another f luorite related structure. However, t2 values, based on the lattice parameter and the ionic radius of the A and O ions, are between 0.83 and 0.99, with the majority between 0.88 and 0.93. t2 seems to have clearer trend against rA/ rB than t1. It is now established that the normalized dielectric difference ( n) decreases with increasing t2 and does not have a clear trend with x This provides another way from the structural point of view to predict dielectric properties, thus, increasing the fundamental understanding of structuredielectric property relationships and a creating a more complete picture for the behavior of dielectric materials with the pyrochlore structure.

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238 APPENDIX D R AMAN OF Ln3NbO7 This appendix introduces collaborative and independent work on Raman spectroscopy of Ln3NbO7. Some of issues and problems, which havent been solved or understood, are also presented here. The normal mode determination table for the RT Ln3NbO7 (Ln3+ = Nd3+ and La3+) phase are presented in Appendix B There are totally 66 Raman modes and 48 IR modes. The Raman spectroscopy of Ln3NbO7 is puzzling. One interesting finding of Gd3NbO7 by Kovyazina et. al.121 was that there was one peak at 944 cm1 in Raman spectroscopy at room temperature, which disappears at the spectrum above 373 K. It was claimed to be a proof of phase transition. However, it is not repeatable in this study ( Figure D 1 ). A laser with the same wavelength ( = 514.5 nm) w as uti lized but the peak at about 944 cm1 exists even at 400 K. 100 200 300 400 500 600 700 800 900 1000 100 K 300 K 400 KIntensity (arb. units)Wavenumber ( cm-1)Wavelength 514.5 nm Figure D 1 Raman spectroscopy (wavelength 514.5 nm) of Gd 3 NbO 7 at 100 K, 300 K, and 400 K

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239 Three independent experiments of Gd3NbO7 with green laser were performed by Daniel Arenas, in Professor Reaneys lab, and in Professor Kambas lab. The Raman spectra match well with each other. However, red lasers (632 nm, 785 nm, and 1036 nm) were also used to collect the Raman spectra of Gd3NbO7; oddly, different laser wavelengths result in significantly different spectra ( Figure D 2 ). The same thing also happened in Nd3NbO7. The Raman spectra by the green laser and the red laser are different ( Figure D 3 ). Different Raman spectra with different lasers are probably due to electronic transitions in rare earth. In the case of resonant Raman (i.e. energy of laser is close to band gap) the intensity is completely different. It is worth noting that the Raman spectra of Sm3NbO7 are the same at different laser wavelengths, different from Gd3NbO7 and Nd3NbO7 ( Figure D 4 ). 200 400 600 800 1000 632 nm from Kamba 785 nm 1036 nmIntensity (arb. units) 514 nm from Arenas 514 nm from Kamba 514.5 nm taken in UKWavenumber ( cm-1) Figure D 2 Raman spectroscopy of Gd 3 NbO 7 by different laser wavelengths at room temperature.

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240 200 400 600 800 1000 Intensity (arb. units)Wave Number (cm-1) 514.5 nm 785 nmNd3NbO7 Figure D 3 Raman spectroscopy of Nd3NbO7 at room temperature ( = 514.5 nm or 785 nm) 0 200 400 600 800 1000 514 nm from Arenas 785 nmIntensity (arb. units)Wavenumber ( cm-1)514.5 nm taken in UK Figure D 4 The Raman spectroscopy of Sm 3 NbO 7 at room temperature.

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241 0 400 800 1200 1600 2000 2400 2800 3200 514 nm from Arenas 514 nm from Kamba 632 nm 785 nm 1036 nmIntensity (arb. units)Wavenumber ( cm-1)Gd3NbO7 Figure D 5 Raman spectroscopy of Gd 3 NbO 7 by different laser wavelengths up to 3200 cm 1 at room temperature. 0 500 1000 1500 2000 2500 3000 Intensity (arb. units)Wavenumber ( cm-1)Nd3NbO7La3NbO7Gd3NbO7Sm3NbO7Wavelength 785 nm Figure D 6 The Raman spectra of Ln 3 NbO 7 (Ln 3+ = La 3+ Nd 3+ Sm 3+ and Gd 3+ ). Another confusing phenomena is that there are strong peaks above 900 cm1 at all laser wavelength measured for Gd3NbO7 ( Figure D 5 ), Nd3NbO7, La3NbO7 ( Figure D 6 ), and Y3NbO7 ( Figure D 7 ). Given that the se are ceramic s materials (primarily ionic bonding) their composition, and their crystal structure, it is safe to assume that the

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242 peaks above 900 cm1 should not be related to phonons. Among the four orthorhombic Ln3NbO7 compounds, only Sm3NbO7 d oes not have strong peaks above 900 cm1 ( Figure D 4 ). Also, defect fluorite Er3NbO7, Yb3NbO7, and Dy3NbO7 are shown in Figure D 8 The spectrum of Er3NbO7 is different from Yb3NbO7 and Dy3NbO7, which may indicate the presence of local structure in Er3Nb O7. 500 1000 1500 2000 2500 3000 Intensity (arb. units)Wave Number (cm-1)Y3NbO7 Figure D 7 The Raman spectroscopy of Y 3 NbO 7 at room temperature. Figure D 8 Spectroscopy of defect fluorite Yb 3 NbO 7 Er 3 NbO 7 and Dy 3 NbO 7 200 400 600 800 1000 Dy3NbO7Intensity (arb. units)Wave Number (cm-1) Yb3NbO7 Er3NbO7

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243 APPENDIX E Sm3NbO7 The Sm3NbO7 samples were also synthesized by solid state processing as discussed in Chapter 3. The calcination temperature was 1723 K. Multiple calcinations were needed to reduce SmNbO4. After calcined at 1723 K for totally 48 h, the amount of the secondary phase of SmNbO4 was below than 1% measured by comparing the XRD pattern of Sm3NbO7 with the simulated XRD pattern of Sm3NbO7 and SmNbO4 mixtures using CrystalDiffract software. Figure E 1 shows high resolution XRD pattern of powder Sm3NbO7, the simulated XRD pattern of Sm3NbO7 based on the space group C2221 36, and the simulated XRD pattern of SmNbO4.257 The highest intensity peak of SmNbO4 is about 0.9% relative intensity. 0 5 10 15 20 Theoretical SmNbO4Theoretical Sm3NbO7 2 (degrees)Intensity (arb. units)Experimental Sm3NbO7 Figure E 1. Comparison of High resolution XRD pattern of Sm3NbO7 at RT ( = 0.400919 ), sim ulated XRD pattern of Sm3NbO7 and simulated XRD pattern of SmNbO 4 from CrystalDiffract software. After sintered at 1873 K for 4 h, the Sm3NbO7 pellet was polished and thermal etching for SEM as described in Chapter 3. A secondary phase in the form of particles

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244 was observed (Figure E 2). Chemical analysis was performed using energy dispersive spectroscopy ( EDS). The secondary phase was found t o be a Nb deficient phase with the presence of Al element. The Al element was most likely from the alumina rectangle tray. The Sm3NbO7 powders were used as the sacrificing powders to separate the pellet from direct contacting the Al2O3 tray. The Nb deficient phase was still present. Figure E 2. The SEM picture and the EDS pattern of Sm 3 NbO 7 pellet. Figure E 3. Dielectric properties of Sm 3 NbO 7 from 10 kHz to 1 MHz. 0 50 100 150 200 250 300 350 400 58 60 62 64 66 68 70 10 kHz 30 kHz 80 kHz 100 kHz 300 kHz 800 kHz 1 MHz Temperature (K)r' r" 0.0 0.3 0.6 0.9 1.2

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245 The Sm3NbO7 compound also exhibit s dielectric relaxation as shown in Figure E 3. Unlike other Ln3NbO7 (Ln3+ = La3+, Nd3+, and Gd3+), T(m) is below RT, at about 120 K. Figure E 4 is the reproduction of Figure 9 22 and includes the Sm3NbO7 point. It is clear that dielectric relaxation is related to the crystal structure. Figure E 4 Average ion polarizability vs. average ionic radius of Ln 3+ in Ln 3 NbO 7 and Ln2LnNbO7 including Sm3NbO7. The dielectric relaxation occurs only in weberite type. 1.15 1.10 1.05 1.00 0.953.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 No RelaxationGdYb SmYb NdYb LaYb LaEr LaDy La Nd Gd Dy Er Ybweberite-type defect fluoriteY Dielectric Relaxation Sm Ionic radius ()Ion polarizability (3)

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267 BIOGRAPHICAL SKETCH Lu Cai was born in 1982 in Chengdu, China. She attended Sichuan University, obtaining her B.S. degree in Materials Science and Engineering. She spent one year studying in the Department of Materials Science and Engineering at University of Washington (UW), from 2003 to 2004, as an exchange student. While in UW, she joined Dr. Younan Xias research group. In 2005, she began her Ph.D. study in Dr. Juan C. Ninos research group. After spending almost 5 years at UF in Gainesville, she received her Ph.D. in Spring of 2010.