Perovskite and Pyrochlore Tantalum Oxide Nitrides: Synthesis and Characterization

Home , Fergusonite, Perovskite, Perovskite (structure), Pyrochlore

Thesis

Presented in Partial Fulﬁllment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University

by Spencer Hampton Porter, B.S.

Graduate Program in Chemistry Ohio State University 2012

Thesis Committee Dr. Patrick Woodward, Advisor Dr. Joshua Goldberger Copyright

Spencer Porter 2012 Abstract

Oxide nitrides are an emerging class of compounds. Perovskite RETaN2O

[RE = La (Imma), Ce (Pnma), Pr (Pnma)] as well as ATaO2N[A = Ca

(Pnma), Sr (I 4/mcm), Ba (Pm3¯m)] and pyrochlore RE 2Ta2N2O5 where RE = Ce, Pr (both: Fd3¯m) have been synthesized by solid state and solution-based methods. Crystal structures solved by powder XRD and NPD for all the rare earth analogs (La, Ce, Pr) are reported for the first time. Studies on the preparation techniques of oxide nitrides in both, bulk powder and film format, has shown that solution based precipitation techniques decrease crystallite size, increase reactivity, and enable isomorphic films by sedimentation processes. Computational studies on anion ordering generated a library of ordering models herein and finds that, like O2N compounds, an ordered cis orientation and out-of-center tantalum displacement provide the most stable model for perovskites with an -N2O anion stoichiometry. UV-Vis diffuse reflectance reveals band gaps for CeTaN2O (2.0 eV), PrTaN2O (2.0 eV), Ce2Ta2N2O5 (3.0 eV) and Pr2Ta2N2O5 (3.3 eV). Structure-property relations from calculations elucidate that valence band maximum positions within the compound series is affected by bond lengths and f-orbital contributions. Calculated band gaps decrease as dispersion at the conduction band minimum decreases due to octahedral tilting. These insights shed light on why photocatalytic studies on these perovskite oxide nitrides do not yield appreciable oxygen evolution rates.

ii To my family

iii Acknowledgements

Thank you to all the people along the way who have taken their time to shape and mold me. I am grateful for your efforts and hope this work will show that it was not in vain. To my parents, for always being proud when I share with them my accomplishments, and for being supportive during my failures. They have imbued in me all of the Porter Principles: persistence, patience, and precaution. Life would be much more difficult without these principles. To Dr. Patrick Woodward for his sage advice, fiscal support, and hospitality during my stay in his lab. Thank you. I am grateful for everything he has done for me. Often times research discussions with him translated into real world survival tips, for instance: ...like a good beer, knowledge deserves to be shared with all who can handle it, though too much can make your stomach upset! I appreciate his balance in life and clairvoyance in the field of science (not just chemistry). To Ohio State University Chemistry for awarding me the William Lloyd and Cora Roberts Evans Fellowship and the Department ”Excellence in Chemistry” Scholarship. Likewise, I am grateful for the support during my time here as a graduate teaching assistant. Young minds are the catalyst for driving innovation. Dr. Leonard Brillson and Dr. Snezjana Balaz for hard work and countless hours with instrumentation during our collaboration. Dr. Paris Barnes, Dr. Yi-Hsin Liu and Dr. Joshua Goldberger for seeing in me the potential to aid your endeavors. Dr. Zhenguo Huang for insightful discussions on compound solubility and precipitation methods. Teamwork! To Dr. Gordon Renkes, for countless hours of bestowing your XRD tips and tricks upon me. I never knew string, binoculars and a flashlight could do so much. To my dear friends, who provided solace and refuge during down time. For always being down for adventure regardless of where the rabbit hole may lead, some foliage in Columbus may never properly recover.

iv To my previous advisors, Dr. Douglas Keszler (Oregon State University) and Dr. Shane Snyder (SNWA/University of Arizona), for encouraging and supporting me in my endeavors then and now. To the Woodward group past and present. Specifically, thank you to Dr. Harry Seibel for taking me under his wing upon first joining the lab. Also, Dr. Graham King, Dr Rebecca Ricciardo, Allyson Fry, Tricia Meyer, and Jennifer Soliz for bestowing copious amounts of Topas Academic magic into my fingertips. To Dr. Matthew Stoltzfus for being a night owl and CASTEP guru. To Ryan Morrow, for being a purebred. Dr. Michael Lufaso for writing SPuDs and TUBERS. Thank you, United States Government, for deciding science is important enough to subsidize tuition in the sciences and for funding grants for research i.e. (NSF DMR - 0907356). Thank you, Oak Ridge National Laboratory Research scientists, Ashfia Huq and Olivier Gourdon, for your help and guidance during my time on campus. Got Neutrons? Thank you Dr. Ram Shehadri for creating furthered learning experiences via ICMR’s Preparative Strategies in Solid State Chemistry and Materials Science at UCSB. Thank you American Physics Society and the International Union of Crystallographers for allowing me to share my work to broad audiences in Portland, Oregon, USA and Madrid, Spain. And lastly, to Ohio State University for facilities and research support staff (Larry, Judy, Jennifer, and Francis, Brittany) that enabled my research. I now truly understand what it is like to be part of a world class institution.

v Contents

List of Figures ix

List of Tables xii

1 Introduction 1 1.1 Perovskite Oxide Nitrides ...... 1 1.2 Other Oxide Nitrides ...... 2

2 Synthesis and structural characterization of AETaO2N(AE = Ca, Sr,

Ba), RETaON2 (RE = La, Ce, Pr), and RE 2Ta2O5N2 (RE = Ce, Pr) 6 2.1 Previous work ...... 6 2.2 Synthesis ...... 11 2.2.1 Preparation of Oxide Precursors ...... 11 2.2.2 Chemicals ...... 12 2.2.3 Solid State Technique ...... 13 2.2.4 Solution Based Techniques ...... 16 2.2.5 Methanol-Chloride Co-precipitation Technique ...... 19 2.2.6 Acetic-Acid Nitrate-Chloride Co-precipitation Technique . . . . . 23 2.2.7 Thermal Ammonolysis ...... 24 2.2.8 Selective Oxidation ...... 30 2.3 Octahedral Tilting Symmetry Considerations for Oxide Nitrides . . . . . 33 2.4 Structure Determination of Oxide Nitride Perovskites and Pyrochlores . 37

2.4.1 Pyrochlore Ce2Ta2O5N2 and Pr2Ta2O5N2 ...... 40 2.4.1.1 Rietveld Reﬁnements of the X-Ray Diﬀraction data for

Ce2Ta2O5N2 and Pr2Ta2O5N2 ...... 40

2.4.2 Perovskite CeTaN2O and PrTaN2O ...... 45

vi 2.4.2.1 Rietveld Reﬁnements of the XRD data for CeTaN2O

and PrTaN2O...... 48

2.4.2.2 Rietveld Reﬁnements of NPD data for Perovskite RETaN2O where RE = Ce, Pr ...... 54

2.4.3 Perovskite LaTaN2O...... 62

2.4.3.1 Rietveld Reﬁnements of NPD data for Perovskite LaTaN2O 62

2.5 Comparison of Bond Distances, Angles, and Tilts in RETaN2O(RE =

La, Ce, Pr) and RE2Ta2O5N2 (RE = Ce, Pr) ...... 73

3 Electronic, Optical, and Photocatalytic Properties in the ATa(O,N)x Compound Class 86

3.1 Electronic Structure For The ATaO2N and RETaN2O Systems (A = Ba, Sr, Ca; RE = Pr, Ce, La) ...... 86 3.2 Photocatalytic results ...... 87

3.3 Diﬀuse Reﬂectance of RE 2Ta2(O,N)7 and RETa(O,N)3 where RE = Pr &Ce...... 88

3.4 A Model System: Lattice Energies for Ordering Types in LaTaN2O... 94 3.4.1 Theory vs. Experiment ...... 100

3.5 Calculation of Electronic Structure for the ATaO2N and RETaN2O Sys- tems Where (A = Ba, Sr, Ca and RE = Pr) ...... 106 3.5.1 Conduction and Valence Band Trends ...... 107 3.5.2 Valence Band Positions ...... 110

APPENDIX A: KUBELKA-MONK TRANSFORMED UV-VIS PLOTS OF OXIDE NITRIDES PREPARED BY DIFFERENT SYNTHESIS ROUTES 115

APPENDIX B: GEOMETRY OPTIMIZED STRUCTURES FOR A VA-

RIETY OF LaTaN2O MODELS GENERATED IN CASTEP 120

APPENDIX C: ELECTRONIC BAND STRUCTURES AND PARTIAL

DENSITY OF STATES PLOTS FOR A VARIETY OF LaTaN2O MODELS GENERATED IN CASTEP 123

vii APPENDIX D: CASTEP GENERATED ELECTRONIC AND ATOMIC

PARAMETERS FOR ATaO2N AND RETaN2O(A = Ca, Sr, Ba; RE = Pr) 129

References 136

viii List of Figures

1.1 NaTaO3 to RETaN2O...... 3

2.1 RETa(O,N)x structure types ...... 8

2.2 RETa(O,N)x Structure Type Relations ...... 10

2.3 Flow chart of diﬀerent preparation techniques for ATa(O,N)3 compounds 12 2.4 Typical reaction scheme for co-precipitation ...... 21 2.5 Ammonia decomposition as a function of a) temperature and b) pressure 27 2.6 Optimal ammonolysis conditions ...... 29 2.7 Compound colors post ammonolysis ...... 30 2.8 Equipment setup for selective oxidation ...... 31 2.9 Compounds post selective oxidation ...... 32 2.10 Tilting symmetry for simple perovskites ...... 34 2.11 Octahedral arrangements by anion order ...... 35

2.12 Tilting symmetry for complex perovskites in the RETaN2O and AETaO2N series (RE = La, Ce, Pr; AE = Ca, Sr, Ba) ...... 36

2.13 Trans anion ordering symmetries for the Imma LaTaN2O model . . . . 38

2.14 Cis anion ordering symmetries for the Imma LaTaN2O model ...... 39 2.15 Chekcell calculated peaks for the defect ﬂuorite and pyrochlore structure

types versus an experimental Ce2Ta2N2O5 pattern ...... 41

2.16 Rietveld reﬁnement of Ce2Ta2N2O5 ...... 42

2.17 Rietveld reﬁnement of Pr2Ta2N2O5 ...... 43

2.18 XRD super structure of CeTaN2O ...... 46

2.19 XRD super structure of PrTaN2O ...... 47

2.20 Rietveld reﬁnement of CeTaN2O ...... 49

2.21 Rietveld reﬁnement of PrTaN2O ...... 50

ix 2.22 Waterfall plot comparing reﬂections in RETaN2O NPDs ...... 55

2.23 Neutron Powder Diﬀraction Pattern for CeTaN2O, bank 2 ...... 57

2.24 Neutron Powder Diﬀraction Pattern for CeTaN2O, bank 5 ...... 58

2.25 Neutron Powder Diﬀraction Pattern for PrTaN2O, bank 2 ...... 59

2.26 Neutron Powder Diﬀraction Pattern for PrTaN2O, bank 5 ...... 60

2.27 Optimization of A-site bonding scheme in CeTaN2O...... 63 2.28 Comparing calculated reﬂections for various models to the neutron pow-

der diﬀraction pattern for LaTaN2O...... 64

2.29 Neutron Powder Diﬀraction Pattern for LaTaN2O, bank 5 ...... 66

2.30 Neutron Powder Diﬀraction Pattern for LaTaN2O, bank 2 ...... 67

2.31 Neutron Powder Diﬀraction Pattern for LaTaN2O, bank 5 ...... 68

2.32 Variable temperature lattice parameters for LaTaN2O...... 72 2.33 12-coordinate bond distances for RE-X or AE-X in nonPnma space groups ...... 76 2.34 12-coordinate bond distances for RE-X or AE-X in Pnma space groups 77

2.35 Ce2Ta2O5N2 and Pr2Ta2O5N2 lattice parameters compared to other pyrochlores ...... 82

3.1 Semiconductor conduction band minimum and valence band maximum . 87

3.2 Diﬀuse reﬂectance spectra for RE 2Ta2(O,N)7 (RE = Ce, Pr) and RETa(O,N)3 (RE = La, Ce, & Pr) ...... 90 3.3 Band gap, color, M-X-M angle for perovskite and pyrochlore oxide nitrides 91

3.4 Analysis of the band gap transition in LaTaN2O...... 93

3.5 Space group assignments based on possible LaTaN2O anion conﬁgurations 96 3.6 Lattice energy and band gap in determining the space group ...... 98 3.7 Impact of the number of cell parameter variables on band gap ...... 99

3.8 Geometry optimized Ima2 LaTaN2O which was Reitveld reﬁned versus bank 2 NPD data ...... 103

3.9 Geometry optimized Ima2 LaTaN2O which was Reitveld refined versus bank 5 NPD data ...... 104 3.10 Conduction band narrowing due to octahedral tilting ...... 108 3.11 Band gaps determined by UV-Vis Diffuse Reflectance and CASTEP . . 109 3.12 2p Anion non-bonding interaction due to Ta-X bond distance ...... 113

x A.1 CaTaO2N diffuse reflectance prepared by different methods ...... 116

A.2 SrTaO2N diffuse reflectance prepared by different methods ...... 117

A.3 LaTaN2O diffuse reflectance prepared by different methods ...... 118

A.4 PrTaN2O diffuse reflectance prepared by different methods ...... 119

C.1 LaTaN2O band structure and partial density of states for Imma .... 124

C.2 LaTaN2O band structure and partial density of states for C 2/m .... 125

C.3 LaTaN2O band structure and partial density of states for P1 ...... 126

C.4 LaTaN2O band structure and partial density of states for Ima2 . . . . . 127

C.5 LaTaN2O band structure and partial density of states for I 212121 .... 128

D.1 CaTaO2N band structure and partial density of states for Pmn21 .... 132

D.2 SrTaO2N band structure and partial density of states for Pbcm ..... 133

D.3 BaTaO2N band structure and partial density of states for Pmma .... 134

D.4 PrTaN2O band structure and partial density of states for Pmn21 .... 135

xi List of Tables

2.1 Anion eﬀects on structure type ...... 9

2.2 Ammonolysis reaction conditions for solid state precursors. * La2O3 dried at 1000◦C, cooled, and used immediately thereafter ...... 14 2.3 Tolerance factors for tantulum oxide nitrides ...... 15 2.4 A-site reactant melting points as an indicator for diffusion rates. In air. Compiled from CRC data (34) ...... 16 2.5 Solubility overlap for two tantalum compounds - finding the correct combination of solvent and solute for oxide precursors. For clarity the two solvents used in this study, methanol and acetic acid, are colored blue and yellow, respectively, for the compound most soluable. s = soluble, sl = slightly soluble, i = insoluble, and – = not tested...... 17 2.6 Solubility overlap for a suite of alkali earth compounds - finding the correct combination of solvent and solute for oxide precursors. For clarity the two solvents used In this study, methanol and acetic acid, are colored blue and yellow, respectively for the compound most soluble. s = soluble, sl = slightly soluble, i = insoluble, and – = not tested...... 18 2.7 Ammonolysis conditions for the Ca, Sr, and Ba perovskite oxide nitride analogues using the methanol co-precipitation technique. HTD = heated until dry, MO = Mineral oil, SO = silicone oil, PP = phase pure . . . . 22 2.8 Ammonolysis conditions for Rare earth perovskite oxide nitride analogues using the methanol co-precipitation technique. HTD = heated until dry, MO = Mineral oil, SO = silicone oil, PP = phase pure . . . . 23

xii 2.9 Ammonolysis conditions for Ca, Sr, and Ba perovskite oxide nitride analogues using the acetic acid co-precipitation technique. AA = acetic acid, BP = boiled pure, HTD = heated until dry, MO = Mineral oil, SO = silicone oil, PP = phase pure ...... 25 2.10 Ammonolysis conditions for rare-earth perovskite oxide nitride analogues using the acetic acid co-precipitation technique. AA = acetic acid, BP = boiled pure, HTD = heated until dry, MO = Mineral oil, SO = silicone oil, PP = phase pure ...... 26

2.11 Reitveld reﬁnement results for both Pr2Ta2N2O5 and Ce2Ta2N2O5 where data for the cerium compounds are italicized ...... 44

2.12 XRD determined bonds and angles for Pr2Ta2N2O5 and Ce2Ta2N2O5 . 44

2.13 Reitveld reﬁnement results for both PrTaN2O and CeTaN2O where data for the cerium compound is italicized ...... 51

2.14 Diﬀerent ﬁts to CeTaN2O XRD data:I 4/mcm, Pmn21 and Pnma. rwp

= reﬁned calculated pattern,rexp = ideal theoretical pattern, and GOF

= Goodness Of Fit (rwp/rexp)...... 52

2.15 XRD determined bond and angle parameters for CeTaN2O and PrTaN2O. Bond distances increase down the table. Tilt angle calculated by (57) and (58) ...... 53

2.16 Reitveld reﬁnement results for both PrTaN2O and CeTaN2O at 300 K where data for the cerium compound is italicized ...... 56

2.17 NPD determined bonds and angles in PrTaN2O and CeTaN2O. Tilt angle is calculated by (57) and (58) ...... 61

2.18 LaTaN2O space group reﬁnement comparison ...... 64

2.19 Atomic positions for LaTaN2O at 300K ...... 70 2.20 Models of the types of anion ordering in Imma ...... 70

2.21 NPD determined bonds and angles in LaTaN2O. Octahedral tilt angle is about the cubic [110] (57) ...... 71

2.22 Ta-X bond distances in RETaN2O(RE = La, Ce, Pr) versus other compounds. Compounds broken down into structural class by horizontal lines, with nitrogen content increasing down the table. S.G. = Space Group, Tech. = Technique. * compound gives Imma-type tilting . . . . 74

xiii 2.23 Perovskite oxide nitride A-site ionic radii and M-X-M angles from XRD Rietveld reﬁnements. Ordered from largest 12-coordinate cation radius to smallest, radii obtained from (72). τ = tolerance factor ...... 79 2.24 Tilting angles determined by NPD. Data for this table was generated by NPD data from Reference column. Tilts are calculated by SPuDS method (57) and O’Keeﬀe (58) ...... 79

2.25 Ta-X bond distances in RE 2Ta2N2O5 (RE = Ce, Pr). S.G. = Space Group, Tech. = Technique...... 80

2.26 Ce-X bond distances in CeTaN2O and Ce2Ta2O5N2 compared to other compounds; C.N. = coordination number ...... 84

2.27 Pr-X bond distances in PrTaN2O and Pr2Ta2O5N2 relative to literature; C.N. = coordination number ...... 85

3.1 Band gaps of oxide nitride compounds made via diﬀerent preparation techniques. MeOH = methanol co-precipitation, AA = acetic acid co- precipitation, SS = solid state ...... 92

3.2 CASTEP Geometry optimized parameters for LaTaN2O in the Ima2 structure ...... 100

3.3 Geometry optimized bond parameters for Ima2 LaTaN2O...... 101

3.4 Atomic positions generated for Ima2 LaTaN2O as obtained from Reitveld reﬁnements using NPD data ...... 102

3.5 Bond parameters for geometry optimized Ima2 LaTaN2O that was the Rietveld reﬁned versus NPD data ...... 105 3.6 Space group transitions necessary for DFT calculation. XRD to CASTEP106 3.7 Position of the lowest lying O/N 2p – Ta 5d AB band relative to the

Fermi level for ATaO2N(A = Ba, Sr, Ca) and RETaN2O(RE = La,

Pr). f-orbital contributions ignored. Ef is the Fermi level; AB is anti- bonding...... 108 3.8 Position of the highest lying O/N 2p non-bonding band relative to the

Fermi level for ATaO2N(A = Ba, Sr, Ca) and RETaN2O(RE = La,

Pr). Ef is the Fermi level; NB is non-bonding...... 111 3.9 Tantalum-anion bond distance across the series. Calculated values from CASTEP geometry optimized models ...... 112

xiv 3.10 Enengy separation between the O/N 2p non-bonding band and the Ta 5d – O/N 2p anti-bonding band ...... 114

B.1 CASTEP Geometry optimized parameters for LaTaN2O in the Imma structure ...... 120

B.2 CASTEP Geometry optimized parameters for LaTaN2O in the C 2/m structure ...... 121

B.3 CASTEP Geometry optimized parameters for LaTaN2O in the P1 structure ...... 121

B.4 CASTEP Geometry optimized parameters for LaTaN2O in the Ima2 structure ...... 122

B.5 CASTEP Geometry optimized parameters for LaTaN2O in the I 212121 structure ...... 122

D.1 CASTEP geometry optimized parameters for CaTaO2N in the Pmn21 structure ...... 129

D.2 CASTEP geometry optimized parameters for SrTaO2N in the Pbcm structure ...... 130

D.3 CASTEP geometry optimized parameters for BaTaO2N in the Pmma structure ...... 130

D.4 CASTEP geometry optimized parameters for PrTaN2O in the Pmn21 structure ...... 131

xv 1

Introduction

1.1 Perovskite Oxide Nitrides

Chemical control of electronic band structure has been demonstrated extensively through cation manipulation. The eﬀects of which have implications in the physical properties of materials enabling contributions including but not limited to the ﬁeld of phosphors,(1) giant magnetoresistance,(2) p– and n-type semiconductors,(3, 4, 5) superconductivity,(6) dielectrics,(7, 8) and photocatalysts.(9) Across the entire spectrum of material applications listed above, perovskite is a structure type that can be found in all of them. Using an ANX formula for the stoichiometric representation of atoms arranged in this manner yields ABX3, where the A and B sites are occupied by cations and the X corresponds to an anion site. Perovskites, though varied across the entire periodic table for the cations, are mostly oxide based when anions are considered. Along a similar vein as cation doping, is the notion of anion doping; the replacement of oxygen in the lattice with another charge-negative ion, nitrogen for example. Doing so introduces a class of compounds called oxide nitrides.

Relative to simple perovskites, ABX3, there are two, whole number substitutions of nitrogen for oxygen that can be made: a single replacement, -O2N, and a double,

-ON2. Greater complexity is added when cations of variable oxidation state are used. Inquiry into anion doping, speciﬁcally via nitrogen-based substitution occurred as early as 1970.(10) These early examples of oxynitrides were comprised mainly of silicon.(11) Compounds synthesized later, in 1986, were the ﬁrst examples of perovskite oxynitrides, referring to the structure and the anions present.(12) The basis for their

1 research was to start with NaTaO3, a known perovskite, and implement aliovalent replacement simultaneously on both the cation and anion site. This is represented pictorially in Figure 1.1 which has the tantalum on the B site, sodium on the A site and oxygen on the X site. By replacing either the A or B cation with an atom that has a more positive oxidation state, nitrogen can be added to charge compensate. To maintain the structure, similar chemistry and ion size should be selected. Further consideration should be made in selecting a cation that is stable under reducing conditions, because nitrogen is added by decomposition of ammonia at elevated temperatures. The alkali-earth (AE) elements are a good starting place, with calcium, strontium, and barium being front runners after size considerations are made. Rare-earths (RE) also are stable versus reducing atmospheres. Group 6 elements replacing tantalum would be challenging due to redox activity under standard synthesis conditions. In less words, cations with noble gas conﬁgurations or valence shells ﬁlled should be paired with each other to limit reduction to lower valencies. Re-illustrated, with tantalum unchanged, + +2 3+ −2 −3 AM → AE → RE and O –> N . The middle and end result being AETaO2N and RETaN2O. The class of perovskite oxide nitrides expands!

1.2 Other Oxide Nitrides

A sample library of available oxynitrides from the literature has been composed; the number of compounds still low, but even these attempts are not exhaustive.(13, 14) Beyond the perovskite, the next most common structure is the pyrochlore, which can be described as a cation ordered, defect ﬂuorite structure. Property characterization for these structures is an ongoing process with reports including but not limited to superconductivity,(15) dielectrics,(14, 16) and luminescence.(17) We aim to contribute to the literature by providing additional synthetic routes, based on co-precipitation of rare earth/alkali-earth salts with metal salts, and by adding new compounds to the oxynitride library, CeTa(O,N)3, PrTa(O,N)3, Ce2Ta2(O,N)7 and Pr2Ta2(O,N)7. These routes are important because they enable the creation of compounds that are inaccessible on any reasonable or economic timescale by the most common approach: solid state ammonolysis. As demonstrated in this work, these experimental routes are no more complex than solid state synthesis.

2 Figure 1.1: NaTaO3 to RETaN2O - Cation valence changes and their respective aliovalent anions. AE = alkali-earth, and RE = rare-earth

3 In addition to synthesis, structural characterization of compounds provides information that can allow a deeper understanding of the material properties. For instance, anion stoichiometry can influence the local symmetry of the metal octahedra, affecting the polarity and dielectric permittivity. When the -O2N moiety is adopted by a perovskite the coordination environment has two distinct arrangements: nitrogen cis or trans. Geometry optimization calculations show the cis conformation to be the thermodynamically favored product for BaTaO2N.(18) This mannerism cannot be easily represented in the simple cubic perovskite unit cell due to symmetry restrictions. A user generated supercell with this disorder accounted for, however, yields results that better reflect results given for the optical properties of bulk powders.(19) Can a similar argument can be given for the –N2O case, where the oxygen are now arranged cis in a nitrogen dominated octahedra? What cis space group arrangements are the most stable? Within the structural realm of this class of oxide nitride perovskite, space group assignments accounting for anion arrangement have included the full spectrum: ordered (20, 21), partially ordered (22, 23, 24) and completely disordered models. (21, 25) It is then an interesting exercise to include the pyrochlore structure type in this argument. What are the chemical neighbors in this system and what, if anything, drives ordering of the anions? Perhaps the most famous nod towards oxynitrides, and also one that attempts to control the non-constant nitrogen/oxygen stoichiometry by cation doping, has been by Jansen et. al.(26) Non-toxic, chemically inert pigments are made by the solid solution (Ca,La)Ta(O,N)3, yielding brilliantly colored compounds from red to yellow and every shade in between. Their stability in a variety of media including harsh ones, concentrated acid and alkaline solutions, has lead some researchers to postulate that oxynitrides could be good candidates for water splitting catalysts. They are not though. Understanding why would fill a knowledge gap and provide insight for the design of new, better catalysts. Determination of the absolute band structure of these compounds would illuminate a reason for their low activities, but to do this a slew of tests must be done. Analyti- cal methods for this class of compounds, while still straightforward, are not without their challenges. In fact, difficult property diagnosis is one of the things preventing rapid development in this field. For example, the most common synthetic technique employed for the creation of oxynitrides is a solid state method. This approach suffers

4 from poor sintering, (27) charging at grain boundaries,(28) and single crystal growth difficulties.(29) How can these difficulties be over come to enable analysis of the material properties? Through the creation of films that charge less. They are then eligible for an array of analytical tests, in this case: Kelvin probe force microscopy, cathodoluminescence, and X-ray photoelectron spectroscopy. These experiments, paired with a bulk structural characterization will foster an increased understanding of the electronic band structure of the materials studied.

5 2

Synthesis and structural characterization of AETaO2N (AE = Ca, Sr, Ba), RETaON2 (RE = La, Ce, Pr), and RE2Ta2O5N2 (RE = Ce, Pr)

2.1 Previous work

Three structure types have been reported in the lanthanoid-tantalum oxide nitride phase diagram: perovskite, pyrochlore, and defect fluorite. All of these structures were discovered by different members of the research group headed by Dr. Roger Marchand at the Universitéde Rennes in France and are presented in Figure 2.1. In these explorations the relative cation stoichiometries are held constant at 1:1 regardless of chemical formula. The rare-earth pyrochlore, (30) perovskite, (31) and defect fluorite (32) families they reported were all an extension of previous work done in the 1980s with alkali- earth tantalum nitride oxides, ATaNO2 where A = Ca, Sr, Ba. (12, 25) For a combined oxidation number of seven, two oxygen and one nitrogen must be present in the formula unit. Therefore when a +2 alkali-earth cation is replaced by aliovalent substitution of a +3 rare-earth cation the ratio of oxide to nitride goes from 1:2 to 2:1 offering the formula

6 RETaN2O, illustration 2.1a. The additional nitrogen in place of oxygen allows for the higher combined valence of the cations, +8, in the unit cell to be charge balanced. These oxide nitride arrangements are what stabilize the perovskite. In fact, if oxygen were the only anion present, the RETaO4 phase dominates and a perovskite (ABX 3) is not formed. Smaller by number of compounds identified, but still promising for functional materials, is the pyrochlore with the general formula, A2B2X7, Figure 2.1b. For non uniform anionic environments like these nitride oxides, a general formula of RE 2Ta2N2O5 is adopted. Unlike perovskites where all anion sites are chemically similar, there are two chemically distinct anion environments in the pyrochlore structure: 1/7 of the anion sites are coordinated by four A-site cations (e.g. lanthanoids) while the remaining anions sites are coordinated to two A-site cations and two B-site cations (e.g. Ta). Consequently there should be a site preference that acts to (at least partially) order the oxide and nitride ions. The Ta-(O,N)6 octahedra are corner connected to make a tetrahedral-like tetramer, four of which are used as building units to make a trigonal pyramid which accounts for all the octahedra in the unit cell. Relating the two structure types by anion stoichiometry is best understood by division of the pyrochlore molecular formula by 2, yielding RETaNO2.5, which illustrates that the pyrochlore lattice accommodates an additional 0.5 anions per formula unit for the same cation content as a perovskite. The final reported structure type in this system, can be thought of as a disordered pyrochlore and is known as the defect fluorite structure, RETaO4−xN2x/3x/3. This structural analogue varies from the CaF2 parent structure on two merits: the A-site is shared by two cations that are disordered and the X-site is made up of oxygen, nitrogen, or a vacancy that compensates for the surrounding cationic charge. This structure type is depicted in Figure 2.1c. Obeying the electroneutrality rule, a defect fluorite nitride 2− oxide can be made from the RETaO4 oxide parent by requiring that 3 O be replaced by 2 N3− and a vacancy. (32) This rule enables the existence of a continuous, anion solution domain between the fergusonite (0%N) to the perovskite (66%N). One possible explanation for the existence of such similar phases is a geometrical argument: as the radius of the A-site cation decreases and nears the radius of the B-site cation, random arrangement of cations in a crystal lattice become energetically favored. Similarity in cation size makes for interchangeable ions at a lattice site, or in

7 Figure 2.1: RETa(O,N)x structure types - Various structure types in rare earth tantalum oxide nitrides: a) perovskite RETaN2O b) pyrochlore RE 2Ta2N2O5 and c) defect ﬂuorite RETaO4−xN2x/3x/3. In each the yellow atom is a rare earth, tan is tantalum, red is oxide, gray is nitrogen, and white is defect. In parts a) and b) TaN4O2 octahedra have been included to show connectivity.

8 a crystal structure that has only one coordination geometry. These factors are what differentiate the cation-ordered pyrochlore structure from the cation-disordered defect fluorite structure. Another possible cause is anion pressure; that these phases are stabilized by careful control of the anion stoichiometry. Under these circumstances the anion to cation ratio segregates fergusonite, pyrochlore and perovskite structure types. To understand the difference between these structures it may be thought provoking to order the structures by increasing %N: RETaO4 < RETaO4−xN2x/3x/3 < RETaN2O. For defect fluorite, the middle example, there are two limiting cases: fergusonite where x = 0 and pyrochlore where x = 1.5. It then becomes more obvious that these observed structure-types are actually categorized by degree of nitridation. Table 2.1 goes to show that certain structure types are made available by the level of nitrogen incorporated into the lattice. Starting with the oxides these phases increasingly become more nitrogen rich.

Structure type Fergusonite Pyrochlore Defect ﬂuorite Perovskite

Chemical formula RETaO4 RE 2Ta2N2O5 RETaO4−xN2x/3x/3 RETaN2O % Nitrogen 0 29 x 66

Table 2.1: Anion eﬀects on structure type

This is represented pictorially in Figure 2.2, which shows each structure-type and the common routes to each. The starting material for all the compounds begins in the upper-left with the fergusonite. Under ammonolysis conditions there are two possible anion site substitutions that can explain the observed structure types. The ﬁrst involves the replacement of 3 O2− for 2 N3− ions in a zippered fashion across the gap spanning two corner connected octahedral chains which then creates corner sharing connectivity for all the octahedra and yields the perovskite structure. This zipper mechanism is also described elsewhere. (24)(29) Identically, 1.5 O2− for 1 N3− ions per formula unit are replaced by having octahedra on the same side of a chain become corner connected. This creates a trigonal arrangement of corner connected octahedra capped with a fac connected octahedron and is the basic building block for the B-site octahedral framework in the pyrochlore phase. In the second substitution type, an anion is not replaced by an aliovalent anion at all and a defect is left in its place. This can happen to any of the structure types to yield the ﬂuorite structure

9 Figure 2.2: RETa(O,N)x Structure Type Relations - Necessary addition or sub- straction of anions or vacancies necessary to translate from one structure type to another

10 type and is perhaps why this is such a common secondary phase (even primary) in the reactions. Though in our reactions this found to be most favorable when ammonolysis conditions are poorly controlled and atmospheric oxygen is allowed in the system. This allows for an oxidation of the cations, at least partially, to a higher valency i.e. +4 for Ce and Pr. When this occurs, ﬂuorite dominates. These compounds vary in degree of nitridation and cation:anion ratio is another way to classify each structure. No nitridation corresponds to RETaO4 and has a cation:anion ratio of 2:4. The ﬂuorite and the pyrochlore are intermediate with a 2:3.5 ratio, while maximum nitridation (according to our synthetic approach) results in the perovskite which has a 2 cation : 3 anion ratio. Additionally, when the intermediate

RETaO2.5N stoichiometry in considered, order/disorder must be controlled. Order of the cations leads to pyrochlore, while disorder results in the defect fluorite structure. An example of how the dynamics in this system work is as follows: if a pyrochlore or perovskite rare earth ion becomes oxidized more anions needed to be incorporated to balance the charge, pushing the structure toward defect fluorite and eventually fergusonite. Therefore, careful control of the atmospheric conditions (O and N concentrations), temperature, and/or addition of a flux are necessary to achieve phase purity for any of the constituents.

2.2 Synthesis

2.2.1 Preparation of Oxide Precursors

Most solid state reactions in this class of compounds utilize high temperatures and long annealing times to achieve phase pure products. These techniques are employed because they allow adequate time for the atoms to diffuse, arrange, and order in a specific structure type. This process, though, is cost intensive and two approaches are often utilized to hasten the reaction: increase the diffusion rates of the atoms and/or decrease the diffusion distances. To achieve the first goal, a salt flux is often employed, which, enhances diffusion of the cations by (at least partial) solvation of the reactants. The second approach aims to achieve intimate mixing and is done so by using starting materials that are all soluble in a given medium, where the cation to cation distance is molecular and is not limited by solid-solid grain boundaries. Proper utilization of solvents and precipitants can create an atomically-mixed, solid precipitate. Additional

11 efforts can embed flux agents interstitially in the solid precursor, further facilitating the reaction during combustion and ammonolysis. A variety of methods will be covered in the following sections and a flow chart for order of operations is provided in Figure 2.3 as simple introduction to those topics.

Figure 2.3: Flow chart of diﬀerent preparation techniques for ATa(O,N)3 compounds -

2.2.2 Chemicals

LaCl3·7H2O (99.999%, Aldrich), PrCl3 (anh, 99.99%, Sigma Aldrich), TaCl5 (99.99%,

Alfa Aesar) La(NO3)3·6H2O (99.999%, Aldrich), Ce(NO3)3·6H2O (99.5%, Acros Or- ganics), Pr(NO3)3·5H2O (99.9%, Aldrich), CaCl2·2H2O (99+%, JT Baker), SrCl2·6H2O

(99%, Aldrich), BaCl2·2H2O (99+%, JT Baker), Ca(NO3)2·4H2O (99+%, Mallinkrodt),

Sr(NO3)2 (99.995%, Aldrich), Ba(NO3)2 (99.7%, JT Baker), Ta2O5 (99.993%, Alfa

Aesar), La(OH)3 (99.99%, GFS Chemicals), La2O3 (99.99%, GFS Chemicals), Pr6O11

12 (99.999%, Cerac), BaCO3 (Grade 1, Johnson Matthey), SrCO3 (99.9%, Aldrich), CaCO3

(99.99%, Mallinkrodt), W (99.95%, Alfa Aesar), CH3OH (anh., 99.8%, Mallinkrodt), and CH3COOH ( 99.7%, VWR Scientiﬁc) were used as starting materials. Chemicals were used as received except CH3COOH which was heated until the a boiling point of 118+/-3◦C was observed then used; helping to minimize adsorbed water. Distilled water with resistivity of 18.2 Ωcm−1 was used for all ﬂux rinses.

2.2.3 Solid State Technique

Stoichiometric amounts of rare/alkali earth carbonate or oxide and tantalum oxide were ground in a mortar and pestle for 30 min. The reactants for LaTaN2O are an exception though, as Ta3N5 was used instead of Ta2O5. A 1:1 wt % KCl/NaCl salt flux, used in previous work,(28, 33) was added to aid diffusion and enhance reactivity of materials during anneal steps in some of the reactions. Data summarizing the synthetic conditions for solid state ammonolysis reactions are displayed in Table 2.2. Use of flux, sample boat, and bubbler oil can have an effect on the efficacy of the reaction. Flux aids in the diffusion of the cations, sample boat can determine the available surface area of the powder to the reactive gas, and bubbler oil viscosity can change the over pressure of ammonia in the system. These things are secondary to the duration and temperature parameters but nevertheless have an impact on the outcome of a reaction. It should be noted that all of the solid state reactions listed utilized a flux, barring the barium analogue. This can be explained by utilization of the Goldschmidt tolerance factor, which correlates the size differences between the two cations and how well they fit into the perovskite unit cell. The equation is as follows: √ (ra + rx) ÷ 2 (rb + rx) = τ (2.1) where ra = the ionic radii of the A cation (Rare or alkali earth) in 12-fold coordination, rb = the ionic radii of tantalum in 6-fold coordination, and rx = a weighted average of the anions based on stoichiometry. A weighted average for the anions is used to most accurately model the disordered anion arrangement in these compounds. These values are depicted in Table 2.3. BaTaO2N has a tolerance factor near an ideal value of 1, necessary for a simple cubic perovskite (Pm3¯m), and therefore easily adopts this structure type without the need for a salt flux. The other compounds drift away from

13 Compounds CaTaO2N SrTaO2N BaTaO2N

Reagents CaCO3, Ta2O5 SrCO3, Ta2O5 BaCO3, Ta2O5 Heating Parameters: Temperature (◦C) 975 950 950 Duration (hr) 80 10 24 Flux NaCl/KCl 1:1 NaCl/KCl 1:1 none Boat (S,M,L) L L L Bubbling oil mineral oil (MO) MO MO Notes 5g 5g 5g Products: Phase Pure (PP) PP PP

Compounds LaTaN2O CeTaN2O PrTaN2O

Reagents La2O3*, Ta3N5 CeO2, Ta2O5 Pr6O11, Ta2O5 Heating Parameters: Temperature (◦C) 1000 950 950 Duration (hr) 24 60 48 Flux NaCl/KCl 1:1 NaCl/KCl 1:1 NaCl/KCl 1:1 Boat (S,M,L) L M L Bubbling oil MO MO MO Notes 5g 1g 5g Products: PP PP PP

Table 2.2: Ammonolysis reaction conditions for solid state precursors. * La2O3 dried at 1000◦C, cooled, and used immediately thereafter

14 this ideal value, are more likely to adopt tilting, and therefore require longer times to reach equilibrium.

Compound Tolerance Factor

BaTaO2N 1.03

NaTaO3 1.00

SrTaO2N 0.97

CaTaO2N 0.94

LaTaN2O 0.93

CeTaN2O 0.93

PrTaN2O 0.91

Table 2.3: Tolerance factors for tantulum oxide nitrides

In fact, the tolerance factors for Ce, Pr, La, and Ca based oxide nitride compounds are close to each other. Contrast comes with the introduction of oxidation state. Here the oxidation states for Ca and La are fixed at +2 and +3, respectively. Ce is most stable in the +4 oxidation state while Pr has a +3/+4 mixed valency as the most stable configuration. This is apparent by the oxides used as starting materials: CeO2 and Pr6O11. The +3 oxidation state however is needed for RETaN2O structure type. Therefore the compounds must first undergo a reduction to the +3 oxidation state, or +3 starting materials should be used. Both approaches initially did not react to form perovskite; starting materials were found instead. Rates of diffusion increase as a compound nears the melting point. Table 2.4 shows that the oxides all have similar melting points well above the reaction conditions. Carbonates have much lower values, however, and instead of melting decompose to the binary oxides. This decomposition creates nascent atoms that are more reactive and more likely to diffuse. Where a forward reaction still does not occur in the reaction temperature, diffusion and hence reactivity can be further coaxed by use of a flux. Even with this agent the compounds do not become phase pure until > 80hrs of thermal ammonolysis. Is it possible that the perovskite structure can be formed for all the rare earths, though only under time scales that are not economical and difficult to maintain? That question is difficult to answer. Development of another approach to synthesize these compounds at shorter time scales is definitely justified.

15 Compound Melting point (◦C)

BaCO3 1555

SrCO3 1494

CaCO3 700-900 BaO 1973 SrO 2531 CaO 2613

La2O3 2304

Ce2O3 2210

CeO2 2480

Pr2O3 2183

Table 2.4: A-site reactant melting points as an indicator for diﬀusion rates. In air. Compiled from CRC data (34)

Additionally, annealing temperatures for all of these compounds range from 850 to 1000◦C. In general, ammonolysis occurs at temperatures near or above 850◦C. This assures full decomposition of the ammonia and also gives adequate thermal energy for reactants to overcome the activation needed to form the products. Duration at these elevated temperatures varies as well, from 10 to 80 hours. This dwell time scales in- versely with tolerance factor with times increasing as the tolerance factor decreases below 1.00. Keeping a reaction at an elevated temperature for 80 hours under a ﬂow- ing reactive atmosphere is electricity intensive and also expensive for the amount of gaseous ammonia used. An approach that can minimize both the temperature and time variables should be taken.

2.2.4 Solution Based Techniques

One approach to achieve lower reaction temperatures and times is through intimate mixing. This can be achieved by getting all cations of the reactions into the liquid phase and then precipitating them concatenated. In order to do this, solubility of the cations in a variety of media were tested. The CRC Handbook of Chemistry and Physics was used as an initial reference.(34) It was found, though, that the solubility data reported was occasionally misleading or too general, e.g. the solubility being in- consistent with observations. A variety of salts of the alkali-earth cations were screened

16 for solubility as a benchmark; the rare-earth cations will likely have similar properties. Carbonates, chlorides, oxides, and nitrates were subjected to solvents with varying degrees of polarity and acid/base behavior. The results for tantalum are in Table 2.5 while the alkali earth compounds are in Table 2.6. Few salts of tantalum were available for solubility testing, with TaCl5 being the most heavily studied. This salt is not stable in air or water (decomposes to TaOCl3 then Ta2O5) where degradation pathways are well known. Therefore, TaCl5 was handled under argon. Reactivity in the systems studied is discussed in the proceeding discussion. In this table, salts are either (-) untested, (I) insoluble, (s) soluble, (sl) slightly soluble, and (δs) soluble upon heating in the scope of our reactions; this normalized the solubilities of the cations to our desired reaction conditions, which were not present in the CRC handbook.

solute

Ta2O5 TaCl5 solvent Water i react Methanol – s Ethanol i s

conc. HNO3 i –

NH3 (l) i sl Acetic Acid – s

Table 2.5: Solubility overlap for two tantalum compounds - ﬁnding the correct combination of solvent and solute for oxide precursors. For clarity the two solvents used in this study, methanol and acetic acid, are colored blue and yellow, respectively, for the compound most soluable. s = soluble, sl = slightly soluble, i = insoluble, and – = not tested.

Choice of solvent was made where greatest solubility was obtained. It should be noted that the two solvents employed for further experimentation are methanol and acetic acid. Methanol, which has properties closest to water, was able to dissolve all of the alkali-earth nitrates in addition to being stable versus TaCl5. This balance between polarity and reactivity was not matched by any other solvent tested. Acetic acid is an interesting choice because it is a polar protic solvent and was thought to be a good complement to studies with a polar aprotic solvent. Also, if thin ﬁlms were to be made from the solutions, it is understood that these solvents would

17 solute

BaCO3 Ba(NO3)2 BaCl2 solvent Water i s s Methanol – – s Ethanol – sl i Acetone – sl – Acid s s i

NH3 (l) – s – Acetic Acid s i i

solute

SrCO3 Sr(NO3)2 SrCl2 solvent Water i s s Methanol – – s Ethanol – sl s Acetone – sl – Acid i sl s

NH3 (l) – s – Acetic Acid i sl s

solute

CaCO3 Ca(NO3)2 CaCl2 solvent Water i s s Methanol – s s Ethanol – s vs Acetone – s – Acid s s –

NH3 (l) – s – Acetic Acid – s –

Table 2.6: Solubility overlap for a suite of alkali earth compounds - ﬁnding the correct combination of solvent and solute for oxide precursors. For clarity the two solvents used In this study, methanol and acetic acid, are colored blue and yellow, respectively for the compound most soluble. s = soluble, sl = slightly soluble, i = insoluble, and – = not tested.

18 be non-volatile leaving groups which is important for maintaining ﬁlm smoothness.(35) This same feature leaves the amorphous solid preserved and free of residual during subsequent annealing. The requisites for the preparation of acetic acid solutions were a little more stringent. For example, in the case of the barium carbonate compound, heating liberated CO2 gas to form barium acetate in excess acetic acid. Additionally, to facilitate a stable tantalum complex, the glacial acetic acid was pre-heated to a rapid boil for 10 minutes to drive oﬀ any water that may have condensed in the solution.

This was then added to TaCl5 (s). Care was necessary here. If water or moisture was present in the solvent, cloudy solutions indicative of Ta2O5 precipitation were observed, and in more extreme cases, white powder settled at the bottom of the vessel. Of the counter anions and polyatomic anions studied it was found that the alkali– earth nitrates were suitable for solubility in methanol. With exception to the barium compound, the chlorides were determined to be the best counter ion for solubility in acetic acid. Both of these rules are extended without exception to the rare-earth compounds used in this study. It bears mention that both the nitrates and the chlorides for the alkali and rare-earths come in varying states of hydration from anhydrous praseodymium chloride to lanthanum and praseodymium chloride heptahydrates. Pre- viously, special mention was made about the reactivity of TaCl5 to water and moisture.

This beset begs the question: do these hydrates react to oxidize TaCl5? Probably, though the eﬀects of this hydrolysis were mitigated by creating each cationic solution separately and combining thereafter. Ta(OMe)5 or Ta(OAc)5, the species in solution after initial ligand exchange between TaCl5 and solvent, are more stable against hydrolysis than TaCl5, and therefore do not preferentially react with solvated water present. This was apparent by the persistence of a clear solution. Regardless of degree of hydration, this method prevented any observable cloudiness or diﬀerence in precipitation rate.

2.2.5 Methanol-Chloride Co-precipitation Technique

Protic, polar solvents allow solvation and ligand exchange with chloride salts and chloride salt hydrates; in this case yielding alkoxides (methoxy group coordinated to the metal) and solvated hydrochloric acid. One of the ﬁrst reports on tantalum alkoxides (36) has been adapted to create the binary precursors we work with. Further experimental framework was provided by Katayama et. al.(37) A general reaction scheme

19 is:

T aCl + A3+Cl · xH O + xsMeOH → 5 (s) 3 2 (s) (2.2) T a(OMe)5 (MeOH) + A(OMe)3 (MeOH) + 8HCl(g) + xH2O (MeOH)

Complete ligand exchange, however, is not favored under the conditions used in previous work. A tantalum dimer is the major species in solution. Because of air stability issues with TaCl5, it was handled under argon until methanol was added. The complimentary alkali or rare earth compound is solvated in methanol separately and then combined with the dissolved tantalum species. All solutions were clear and colorless, barring the praseodymium which was still clear but green. The clarity is an indication of the purity of the starting materials. White solids found in the solution are oxidized metals, namely Ta2O5. Concentrated NH4OH, the precipitating agent, was added dropwise by syringe (Hamilton,10 mL gas tight [Reno, Nevada]) to equimolar cation concentrations of the precursor solution under rapid stirring. During the precipitation the solutions turn into a white solution for all the compound combinations except for cerium and praseodymium, which are dull red/orange and pastel green. The resulting sol-gel products were evaporated to dryness at 130 ◦C by hotplate. Powder X-Ray Diffraction (XRD) showed the resulting powders to be amorphous with the exception of crystalline NH4Cl, a side product of the hydrolysis. As the solution is driven off at 130 ◦C there are no changes in colors except for the cerium which transitions from red/orange to yellow. This decomposition may enhance reactivity by breaking apart agglomerates to increase surface area. A summary of the above protocol is provided pictorially in Figure 2.4. A summary of the preparation conditions has been compiled in Table 2.7 and Table 2.8 below. Variables reported are similar to the solid-state table (2.2), though it is worth mention that the outcomes have changed. Most importantly, it is shown that intimate mixing is indeed achieved by this solution route as all compounds have been made without the aid of a flux. Furthermore, the reaction time necessary for a completed reaction has also been decreased for all of the compounds studied.

A complication to this is provided by the BaTaO2N compound, which was plagued by secondary phases, mostly BaCl2 and Ta3N5. When BaCl2 is hydrolyzed to Ba(OH)2 and heated to dryness, a portion of this is converted to BaCO3 from CO2 absorption from air as evidenced by XRD. Additionally, a Ba(OH)2 to BaCl2 back reaction occurs. During the solvent evaporation/drying stage of processing the ratio of MeOH:water

20 Figure 2.4: Typical reaction scheme for co-precipitation - top row is solution processing, bottom row is powder prep and ammonolysis decreases as the MeOH volatilizes, the solution becoming more aqueous in nature. This has implications: Ba(OH)2 is more soluble in water, especially as temperature increases.

In fact, down the alkali-earth group A(OH)2 solubility increases and explains why this phenomena is most pronounced in the barium compound. As the MeOH concentration diminishes, the driving force for the continued precipitation of NH4Cl also lessens, and becomes dissolved again. In this solution NH4OH (aq) concentration is low because at 2+ − higher temperatures it degases as NH3. Ba and Cl are all that is left in solution.

This supersaturation and subsequent precipitation creates amorphous BaCl2. This

Ba(OH)2 to BaCl2 conversion process often does not go to completion because it is limited by the maximum solubility of Ba2+ in the available water aﬀorded during the precipitation stage. The BaCO3 and Ba(OH)2 that are not converted back to starting material go on to participate in the later ammonolysis reaction to give end product.

The BaCl2 side product remains inert and shows up as a secondary phase. Regardless, the result is a nonstoichiometric reaction. In the literature this is compensated for by use of excess barium. (38) The above statements clarify why this phenomena occurs during sample processing. BaTaO2N samples of high purity can be prepared by rinsing and drying the ﬁnal sample post ammonolysis, because BaCl2 has moderate solubility

21 in water. This phenomena was also found for the lanthanum and strontium analogues to a lesser extent. It was found that a 2 % molar excess of lanthanum was necessary to get phase pure LaTaN2O. Adjustment of SrTaO2N stoichiometry removed an initial secondary phase which comprised approximately 3 % of bulk. Complete phase purity was achieved by an approach similar to the lanthanum case. In addition to these compounds not needing a flux, the reaction finished in a reduced amount of time. Oxide nitride compounds can be made without flux, though the ammonolysis required longer times plus intermediate grinding with a mortar and pestle between each 48, 24 and 24 hour heating was necessary. When finished reacting, all the compounds are colored similarly to their solid-state counterparts when evaluated by eye.

Compounds CaTaO2N SrTaO2N BaTaO2N

Reagents TaCl5, TaCl5, TaCl5,

CaCl2·2H2O SrCl2·6H2O BaCl2·2H2O Solvent MeOH MeOH MeOH

Precipitant Conc. NH4OH, Conc. NH4OH, NaOH, HTD HTD HTD Heating Parameters: Temperature (◦C) 850 850 850 Duration (hr) 24x3=72 18 12 Flux none none none Boat (S,M,L) S S S Bubbling oil MO MO MO Notes 0.75 g, 0.75 g, 0.75 g, 1.4x10−3 mol/ 1.4x10−3 mol/ 1.4x10−3 mol/ 30mL solvent 30mL solvent 30mL solvent

Products: PP PP BaTaO2N,

BaCl2,

Ta3N5

Table 2.7: Ammonolysis conditions for the Ca, Sr, and Ba perovskite oxide nitride analogues using the methanol co-precipitation technique. HTD = heated until dry, MO = Mineral oil, SO = silicone oil, PP = phase pure

22 Compounds LaTaN2O CeTaN2O PrTaN2O

Reagents TaCl5, TaCl5, TaCl5,

LaCl3·7H2O CeCl3·7H2O PrCl3 Solvent MeOH MeOH MeOH

Precipitant NH4OH, NH4OH conc, NH4OH conc, HTD HTD HTD Heating Parameters: Temperature (◦C) 850 1000 850 Duration (hr) 24 48 24 Flux none none none Boat (S,M,L) S S S Bubbling oil MO MO MO Notes 0.75 g, 0.75 g, 0.75 g, 1.4x10−3 mol/ 1.4x10−3 mol/ 1.4x10−3 mol/ 30mL solvent 30mL solvent 30mL solvent Products: PP PP PP

Table 2.8: Ammonolysis conditions for Rare earth perovskite oxide nitride analogues using the methanol co-precipitation technique. HTD = heated until dry, MO = Mineral oil, SO = silicone oil, PP = phase pure

2.2.6 Acetic-Acid Nitrate-Chloride Co-precipitation Technique

Soft (vs hard) interactions can be attained by changing the ligands. In this case acetic acid replaces methanol. This method was ﬁrst reported for the ligand exchange of

NbCl5 with acetic acid by Funk et. al. (39) and has been expanded to tantalum by Marchetti et. al..(40) Accommodations similar to those reported previously were made for the compounds in this study. The method in which a ligand leaves its coordination sphere can affect the morphology of an annealed powder. (41) Acetic acid as a solvent allows for intermediate diffusion of cations versus co-precipitation in methanol and solid-state techniques. Extra caution should be taken to ensure purity of acetic acid and absence of water during the addition to TaCl5, limiting early precipitation of the tantalum precursor. For this reason, the acetic acid goes through a purifica- tion step where it is boiled until the correct boiling point of acetic acid is observed

23 (118 ◦C). This boiling process takes about 10 minutes and upon removal of heat from the system the acid is added to the reactants. Procedure deviates from the methanol method is the precipitation step. Instead of using an aqueous base to onset precipitation, evaporation of solvent causes the dissolved species to exceed saturation levels and precipitation is forced. This process, done in air, also hastens the oxidation and subsequent precipitation of the cations in solution. Order of operations is the same as the methanol technique, but differs in the aim: the methanol route is designed to achieve an amorphous hydroxide precursor, where as with acetic acid as an amorphous precursor, the anion would largely be acetate. The colors observed at different stages of processing are identical to the methanol method, although, acetic acid solutions are more prone to cloudiness. It is not fully understood why this is, but may be due to the poor stability of the acetic acid coordinated metals and their subsequent high reactivity towards any other water source (glacial acetic acid not dry enough). The acetic acid method produced results that were intermediate of the solid state and methanol approaches, which have been summarized in Table 2.9 and Table 2.10. Samples had reduced reaction times without a flux. If a flux was used, a significant decrease in reaction time was observed. Moreover, the temperatures necessary for the reactions were decreased to the lower threshold of the ammonolysis window for tantalum. Transfer of these compounds from drying to the ammonolysis step was more tedious due to their hygroscopic nature. Movement of the precursor powder to the alumina sample boat was done as hastily as possible without compromising the sample.

2.2.7 Thermal Ammonolysis

When ﬂowing ammonia is heated up there are a variety of things that can happen to it. It can react with itself to form hydrazine, decompose, react with its surroundings, or not react at all. (42, 43) Careful control of these phenomena can facilitate the addition of nitrogen to an oxide compound and even play a role in what type of compound is formed. This can be explained by thinking about the thermal break down of ammonia, which was studied extensively during the development of the Haber process. Figure 2.5a shows that as the temperature of the ammonia increases, decomposition to elemental constituents will also increase. It is known from the Le Chatelier principle that elevated

24 Compounds CaTaO2N SrTaO2N BaTaO2N

Reagents TaCl5, TaCl5, TaCl5,

Ca(NO3)2·4H2O Sr(NO3)2 Ba(NO3)2 Solvent AA AA AA Precipitant HTD, HTD, HTD, Notes BP BP BP Heating Parameters: Temperature (◦C) 850 850 850 Duration (hr) 48 12 12 Flux none NaCl/KCl 1:1 none Boat (S,M,L) S S S Bubbling oil MO MO MO Notes 0.75 g, 0.75 g, 0.75 g, 1.4x10−3 mol/ 1.4x10−3 mol/ 1.4x10−3 mol/ 30mL solvent 30mL solvent 30mL solvent

Products: PP PP BaTaO2N,

Ta3N5

Table 2.9: Ammonolysis conditions for Ca, Sr, and Ba perovskite oxide nitride analogues using the acetic acid co-precipitation technique. AA = acetic acid, BP = boiled pure, HTD = heated until dry, MO = Mineral oil, SO = silicone oil, PP = phase pure

25 Compounds LaTaN2O CeTaN2O PrTaN2O

Reagents TaCl5, TaCl5, TaCl5,

La(NO3)3·6H2O Ce(NO3)3·6H2O Pr(NO3)3·6H2O Solvent AA AA AA Precipitant HTD HTD HTD Notes BP BP BP Heating Parameters: Temperature (◦C) 850 1000 1000 Duration (hr) 24 48 48 Flux none none none Boat (S,M,L) S S S Bubbling oil MO MO MO Notes 0.75 g, 0.75 g, 0.75 g, 1.4x10−3 mol/ 1.4x10−3 mol/ 1.4x10−3 mol/ 30mL solvent, 30mL solvent 30mL solvent

low NH3 ﬂow, 1bubble/s Products: PP PP PP

Table 2.10: Ammonolysis conditions for rare-earth perovskite oxide nitride analogues using the acetic acid co-precipitation technique. AA = acetic acid, BP = boiled pure, HTD = heated until dry, MO = Mineral oil, SO = silicone oil, PP = phase pure

26 temperatures, hence increased entropy, shift the reaction to favor the product side where

4 molar equivalents of product (3H2 + N2) dominate versus 2 molar equivalents of the reactant (2NH3). Similar arguments can be made for Figure 2.5b, as pressure increases the equilibrium shifts from 4 moles of product to favor 2 moles reactant, which relieves stress on the system. In thermal ammonolysis, the desire is to engineer the reverse direction of the Haber process with emphasis on optimization of the location for the decomposition reaction of ammonia.

Figure 2.5: Ammonia decomposition as a function of a) temperature and b) pressure - Adapted from (44)

As ammonia passes though the tube furnace, Figure 2.6, heat from the furnace

27 is transferred to the ammonia. At some time, t, which corresponds to some distance down the tube, the ammonia thermally dissociates into N2 and H2. It is during this decomposition reaction that the intermediates are responsible for integration of nitride ions into the powder sample at the solid-gas interface. Sample placement in the furnace is critical in determining the outcome of solid products, as the reactive intermediate concentration is dynamic throughout the tube. For example, if the sample boat is upstream near the inlet of the furnace the gas composition is primarily ammonia because it hasn’t thermally decomposed yet, nitridation of the sample in this region is possible. Far down stream near the exhaust, and the ammonia atmosphere has mostly been decomposed, and is mainly H2 and N2. This gaseous mixture is equivalent to forming gas and can perform a reduction on the solid oxide, but incorporation of nitrogen into the sample is unlikely due to the low reactivity of diatomic nitrogens. Therefore, these two types of reaction conditions play a role in determining what the final phase will be. Pyrochlore structure types require an intermediate amount of nitride substitution, while the fluorite requires vacancies. Both of these outcomes are favored downstream. The perovskite, however, dominates under the full ammonolysis conditions afforded upstream placement. A typical heating occurred as follows: alumina boats (5-50 mL) were placed in a tube furnace where flowing ammonia was passed over the precursor samples at a rate of, 20-200 mL/min. Mineral and silicone oil were used in the bubbler to vary the ammonia overpressure due to the viscosity difference between the two oils; here use of the silicon oil favors the formation of the perovskite structure-type. A ramp rate of 10 ◦C/min raised temperatures to 700-1000 ◦C, dwelled for 10-96 hrs, and finally cooled at 20 ◦C/min to room temperature. During annealing, compounds that had poor reactivity were given a NaCl/KCl 1:1 weight percent flux that was supplemented at a 1:1 weight percent versus the sample e.g. 1 g KCl, 1 g NaCl, 2 g sample. This flux is utilized to increase the mobility of the cations by partial solvation. Furthermore, the NH4Cl created during the precipitation and the subsequent gel formation phase is hypothesized to occupy a portion of the amorphous solid matrix. During ammonolysis this interstitial ammonium chloride decomposes to yield NH3 and HCl, breaking apart agglomerates and also aiding in ammonolysis by contribution of in situ ammonia. This should increase the available surface area of the reactants further increasing the reactivity of the solids. These two techniques aid the solid-gas reaction between the oxide precursor and the

28 Figure 2.6: Optimal ammonolysis conditions - Gibbs reaction coordinate (top) corresponding to a cut away of a tube furnace (bottom). The decomposition zone (red line) should encompass the sample boat. Blue to red gradient shows thermal heating of ammonia from inlet to outlet. When a nitride replaces an oxide at the sample the outgas is water.

29 reactive gas atmosphere. Samples were then triple rinsed with water and acetone post- reaction to remove any ﬂux agent remaining. These compounds had bright colors and are best displayed in Figure 2.7.

Figure 2.7: Compound colors post ammonolysis - pictures taken under incandescent light with an LG 3.2Mpixel camera

2.2.8 Selective Oxidation

The pyrochlore oxide nitride class of compounds, RE2Ta2O5N2 where RE = rare earth, have not been observed for atomic radii larger than neodymium. Is neodymium the upper limit for which the class of compounds is stabilized? There are two possible approaches that can be taken to attempt to synthesize these compounds: add a stoichiometric amount of nitrogen to replace oxygen in RETaO4 or add a stoichiometric amount of oxygen to replace nitrogen in RETaN2O. The approach taken was the latter; adding oxygen at elevated experimental temperatures to replace nitrogen. This can be more readily understood by examination of the typical reactions for rare-earth oxide nitride related compounds: Full oxidation - perovskite to fergusonite; 3 RET aN O − N + O → RET aO (2.3) 2 2 (g) 2 2 (g) 4 The above equation can be rewritten to include intermediate phases that may form in the full oxidation pathway: Partial oxidation - perovskite to pyrochlore; 1 3 2RET aN O − N + O → RE T a O N (2.4) 2 2 2 (g) 2 2 (g) 2 2 5 2 Partial oxidation - pyrochlore to fergusonite; 3 RE T a O N − N + O → 2RET aO (2.5) 2 2 5 2 2 (g) 2 2 (g) 4

30 A similar approach can be taken to arrive at equations for the nitridation pathway. It is left to the reader to evoke them, however. These oxidation equations aid a Gibbs free energy analysis. Certain conditions must be manipulated to cause the formation of the pyrochlore. Examining the partial oxidation of the perovskite to pyrochlore, the entropy term of this reaction is negative. As demonstrated by Equation 2.4, the number of moles of gas decreases as the reactants transition to products. As temperature increases, change in the Gibbs free energy term increases due to the T∆S term. From calculations, most reactions between oxides and ammonia are associated with a positive standard Gibbs energy change. (45) The opposing direction, the reaction of oxide nitrides with oxygen then, must have a negative standard Gibbs energy change. The equilibrium of the reaction from perovskite to pyrochlore, therefore, can be manipulated by adjustment of the partial pressure of O2. Assuming the activities of each compound are one, the nitridation of the oxides becomes favorable when the partial pressure of O2 is minimized, while the oxidation of the oxide nitrides becomes favorable when the partial pressure of O2 is maximized. A caveat arises when examining Equation 2.5. The transition from the pyrochlore to the fergusonite involves the loss of nitrogen as well as the addition of oxygen. To create conditions that allow for the pyrochlore to be made from the perovskite and the fergusonite denied, nitrogen loss and oxygen incorporation must be controlled.

Figure 2.8: Equipment setup for selective oxidation - Baruim peroxide upstream for the formation of pyrochlores

Synthetic design achieves this by using ammonolysis as the reducing over-atmosphere and by decompositon of BaO2 as the oxygen adding component to the reaction scheme. This enables the ability to synthesize compounds with oxygen-nitrogen ratios that are in between the thermodynamic end products of oxidation (RETaO4) and ammonolysis

31 (RETaN2O). Two different approaches were taken to make these intermediate compounds. The first procedure used to make pyrochlore oxide nitrides was through the addition of oxygen via in situ BaO2 up stream in flowing ammonia, as seen in Figure 2.8. When

BaO2 is heated it decomposes, forming nascent oxygen and BaO1+x. (46, 47) XRDs of the end product in this work match literature accounts of BaO1.3. The liberated oxygen reacted with downstream perovskite oxide nitride to increase the oxygen to nitrogen ratio. Pr2Ta2N2O5 was made in this manner: amorphous PrTaO4 precursor was ammonolyzed at 800 ◦C for 24 hours followed by a 12 hour heating at 900 ◦C resulting in a mixed phase powder, perovskite and defect fluorite. 20 times molar ◦ excess BaO2 was added upstream and was heated at 825 C for 6 hours. This oxidation ◦ step was repeated at 775 C for 6 hours which resulted in the Pr2Ta2N2O5 pyrochlore presented in this work. The other way pyrochlores of this type were prepared is as follows: oxide precursors were ammonolyzed for a short time, locking in some intermediate compound of unknown oxide and nitride ratio. Because the oxide and oxynitride are usually a lighter vs darker color, e.g. CeTaO4 is yellow and CeTaN2O is a grey brown, an approximation of the nitrogen content can be gauged and either further ammonolysis can occur or oxidation via air can be executed. Ce2Ta2N2O5 was made in this way. The amorphous ◦ CeTaO4 precursor was ammonolyzed at 850 C for 24 hours. A mixed phase product of perovskite and pyrochlore was verified by XRD. The sample was then heated under low ammonia flow (20 mL/min) at 750 ◦C for 24 hours. Attempts are underway in our lab to create routes to these compounds that are more reproducible The compounds that were made were pastel colored and are better represented in Figure 2.9.

Figure 2.9: Compounds post selective oxidation - pictures taken under incandescent light with an LG 3.2Mpixel camera

32 2.3 Octahedral Tilting Symmetry Considerations for Ox- ide Nitrides

A standard simple cubic perovskite unit cell has an edge length of approximately 4A˚. As tilting is introduced, however, the dimensions of the unit cell and the symmetry allowed for the space group are altered. Often symmetry elements are lost which lower the symmetry, or reduce translational symmetry which makes the unit cell larger. This is covered in great depth for oxide perovskites, (48, 49, 50) oxide double perovskites, (51) and ferroelectric oxide perovskites. (52) Having a double or a ferroelectric perovskite adds additional complexity to the analysis in much the same way as going from an oxide to an oxide nitride perovskite does. A walkthrough chronicling the symmetry changes from an oxide to an oxide nitride perovskite is established below. First, symmetry changes in response to tilting must be understood. Symmetry as tilting is added, as mentioned above, has already been solved. It is reformatted in Figure 2.10 to facilitate a discussion relevant to this work. Starting with a simple

ABX3 perovskite (Pm3¯m) two types of tilts can be added: in-phase or out-of-phase. Cooperative or in-phase tilting adds octahedra that are all tilted the same direction down a tilting axis while out-of-phase tilting adds alternating tilts of the octahedra (clockwise then counterclockwise). Both elements change the symmetry of a group. To grossly over simplify, when atoms are arranged by in-phase tilting, mirror planes and rotation axes are adequate to map the unit cell, where as when out-of-phase tilting occurs mirror planes are transformed to glide planes and rotation axes to screw axes. Initial work on octahedral tilting developed a notation that utilizes a superscript to denote the type of tilting down an axis and a letter (usually a, b, or c) to denote relative magnitude of the tilt. Superscript “+” indicates in-phase tilting, while “–” means out-of-phase tilting. Summarized in an example: a+b−b− creates a lattice that has two out-of-phase tilting axes that are equal to each other (b−b−) and diﬀerent than the remaining tilt down the in-phase axis (a+). These groups are adequate for modeling oxide nitrides where anions are statistically distributed (disordered). In fact, if the anions were completely disordered tantalum perovskite oxide nitrides (Ca, Sr, Ba, La, Ce, Pr), they would reside in one of the green boxes. What happens when the anions order?

33 Figure 2.10: Tilting symmetry for simple perovskites - Green tiles represent the symmetry descent found for the ATa(O,N)3 series. Top to bottom tilting increases (number of tilts separated by tiers in the left column). In general, if the line is slanting left an out- of-phase tilt is being added and if the line is slanting to the right an in-phase tilt is added.

34 Second, ordering types for anions must be determined. In this work, the anion stoichiometry is limited to –O2N and –N2O and dictates the ratios of anions in an average octahedron. From this arrangement there can be 2 types of conﬁgurations: trans and cis, as in Figure 2.11.

Figure 2.11: Octahedral arrangements by anion order - cis and trans

As tilting is added the cis and trans arrangements can alter based on how they are placed relative to either a tilting axis, tilting plane, or coordinate axis. A complete catalog for these variants is still in progress. Some of the ones relevant to this work have been worked out (green tiled parent groups in Figure 2.10). These are presented in Figure 2.12, and shows that as number of tilting axes increases the number of variants increases. Starting with no tilts, as a tilting axis is added the anion arrangements, cis or trans, can be placed perpendicular or parallel to said axis. In one-tilt systems there are 5 diﬀerent conformations that can be achieved. As an additional tilting axis is allowed (e.g. Imma) the addition of cis or trans elements are placed relative to the plane that the two tilting axes make up. Furthermore, in that plane, coordinate axis length determines which way the octahedron buckle; order of the axis lengths must be reported to help distinguish between subtle buckling diﬀerences. This distinction allows for one additional and 6 total conformations for two tilt systems. These same 6 are available for three tilt systems where two of the tilts are of equal magnitude (e.g.

35 Pnma). Some new naming conventions have been devised to help explain these new anion ordering specimens. For each of the illustrations the space group is given followed by additional descriptors. The symbols used describe orientations and are explained as follows: “//” means parallel and “ | ” is perpendicular to the main tilting axis or plane. Furthermore, for more complicated (3 tilt) systems, a subscript (a,b,c,d) notes the coordinate axis that symmetry occurs along.

Figure 2.12: Tilting symmetry for complex perovskites in the RETaN2O and

AETaO2N series (RE = La, Ce, Pr; AE = Ca, Sr, Ba) - Key = red box

These notations are better understood if they are paired with a structural picture.

This is done via a two part example using Imma LaTaN2O. Figure 2.13 shows the trans variants while Figure 2.14 yields the cis models in this study. The trans disorder iteration is self explanatory. The trans parallel has linear Ta-O-Ta chains that run down the long axis (a). The trans parallel has linear chains with that orient along the [011] direction. In the second ﬁgure, the cis parallel has cis octahedron that are

36 rock salt ordered up and down with a zig-zagging Ta-O-Ta chain that cuts down the body diagonal. The perpendicular variants also have rock salt ordering left and right with zig-zagging Ta-O-Ta chains that run along the indicated axis. It should be noted that, additional ordering patterns have been found (anti and inline) and will be further developed in a later work. Lastly, account for out-of-center octahedral displacements must be accounted for.

Calculations involving compounds of the composition AETaO2N where AE = Ca, Sr, Ba suggest that the most stable configuration in a fully anion-ordered perovskite is one where cation displacements are allowed and when a cis conformation is adopted. (18) Out-of-center displacements found in ferroelectric compounds have been incorporated into the Glazer notation as subscripts. Subscript + denotes a displacement of the atom in the positive direction along that axis and subscript – defines the direction of the displacement as negative. (52) In this work though, out-of-center displacement is controlled by the orientation of the cis environment (i.e., either toward or away from the cis-edge). As such it is possible to have displacements that are anti to each other. Luckily, when assigning cis octahedron symmetry it already accounts for out- of-center displacements and no space group changes apply. It is therefore subscripts are not necessary to indicate the out-of-center displacement if the octahedral anion configuration is known. In these compounds and from a chemical stand point, the direction of the displacement is assumed to be towards the stronger interaction. In the case of the Ta-(O,N)6 octahedron, displacement towards the nitrogen is favored due to a stronger covalent interaction between Ta and N.

2.4 Structure Determination of Oxide Nitride Perovskites and Pyrochlores

Knowledge of all the possible space groups that could be achieved for a given chemical system guides interpretation of both experimental results and density functional theory calculations. Two structural techniques, x-ray and neutron powder diﬀraction, are used here to experimentally determine the space groups of the compounds in this study. Using the symmetry guide in tandem, provides a basis of comparison for later theoretical calculations. In experimental structural determination, the characteristic features of a

37 Figure 2.13: Trans anion ordering symmetries for the Imma LaTaN2O model - Key = bottom right

38 Figure 2.14: Cis anion ordering symmetries for the Imma LaTaN2O model - Key = bottom right

39 perovskite and pyrochlore are discussed followed by application of these principles in real data.

2.4.1 Pyrochlore Ce2Ta2O5N2 and Pr2Ta2O5N2

Though both are cubic space groups, the fluorite structure can be differentiated to the pyrochlore by ordering of the cations and the anion vacancies. When cations pos- sess enough size difference to ensure ordering, the unit cell is doubled and creates super structure peaks characteristic of the pyrochlore space group. Crystallographically within the pyrochlore system, a complete vacancy is observed at one of two Wyckoff sites (8b or 8a). Deviation from this results in a defect pyrochlore. This has conse- quences on peak intensities. Lattice reflections in powder diffraction data are the best way to determine either a pyrochlore or fluorite structure type. Chekcell (53) was used to simulate and match theoretical peaks to rare-earth tantalum oxynitride samples over the 10-100 ◦2θ region. The pyrochlore space group, Fd3m¯ (#227), was compared to the fluorite space group, Fm3m¯ (#225). Headway is made when comparison of the experimental plots yields 2 unique peaks at 14.5 and 27.9 ◦ 2θ, seen in Figure 2.15. Here a generic fluorite (top row) with edge length, a = 5.3 A˚, and generic pyrochlore (bottom row) with a = 10.6 A˚ are tiled with the pattern for comparison. This clearly shows the failure of the fluorite structure type to account for the two early peaks in the powder pattern. These correspond to <111> and <311> respectively, and are crystallographically tied to the doubling of the fluorite cell as a result of cation ordering.

2.4.1.1 Rietveld Reﬁnements of the X-Ray Diﬀraction data for Ce2Ta2O5N2

and Pr2Ta2O5N2

The similarities between the cerium and praseodymium perovskites are also found when comparing the XRD spectra of the pyrochlores. The XRD Rietveld fits for Ce2Ta2N2O5 and Pr2Ta2N2O5 are in sequence below, Figure 2.16 and Figure 2.17. The single special position available in the pyrochlore structure type makes refinement straightforward. For each compound, refinement of the thermal parameters (Beq) at each anion position trends negative from an initial start equal to two. To obtain the most reasonable value, the positions are constrained to refine together; a positive value is obtained. In this process they were allowed to refine freely with all the other

40 Figure 2.15: Chekcell calculated peaks for the defect ﬂuorite and pyrochlore

structure types versus an experimental Ce2Ta2N2O5 pattern - Miller indicies are labeled for each stucture type. parameters, and are displayed in Table 2.11 for both Ce and Pr pyrochlore analogs. It should be noted, however, that the estimated standard deviations for these thermal parameters are large. This is mainly due to the limitations of XRD (poor electron scatter of oxygen and nitrogen) and the sample (broad peaks). Reﬁnement data was used to generate bond lengths for both the rare-earth-anion and the tantalum-anion distances as well as octahedral tilt characteristics. This data is compiled in Table 2.12. The praseodymium analog shows an increase in the Ta-X - Ta angle as well as a decreasing Ta-X bond distance. These result from decreases in the ionic radii across the series. The scalenohedron distances adjust to accommodate the surrounding environment. In the praseodymium pyrochlore, the six axial anion distances are elongated and the two axial anions are shortened versus the cerium analog. These octahedral bond values will be important later when they are compared to similar compounds (e.g, NaTaO3 and CaTaO2N) from the literature. Unlike simple perovskites where all anion sites are chemically equivalent, there are two chemically distinct anion environments in the pyrochlore structure: 1/7 of the anion sites are coordinated by four A-site cations (e.g. Ce, Pr) while the remaining anions sites are coordinated to two A-site cations and two B-site cations (e.g. Ta). Consequently there should be a site preference that acts to (at least partially) order the oxide and

41 Figure 2.16: Rietveld reﬁnement of Ce2Ta2N2O5 - green dots = data, red line = calculated pattern, gray line = diﬀerence curve, hash marks = indexed peaks

42 Figure 2.17: Rietveld reﬁnement of Pr2Ta2N2O5 - green dots = data, red line = calculated pattern, gray line = diﬀerence curve, hash marks = indexed peaks

43 2 Compound rwp χ Lattice Parameter(s)

Pr2Ta2N2O5 15.273 1.093 a = 10.5724(4) A˚

Ce2Ta2N2O5 17.085 1.065 a = 10.5832(8) A˚

Source 2θ range S.G. # Lab X-ray, = 1.5406 A˚ 10-110◦ Fd3m¯ 227

Atomic Position(s) ion site x y z occ Beq Ta+5 16c 0 0 0 1 0.83(8) 0.77(8) Pr+3 16d 0.5 0.5 0.5 1 1.9(1) Ce+3 1.2(1) O−2/N−3 48f .324(2) 0.125 0.125 0.833/.167 0.2(6) .328(2) 0.6(7) N−3 8b 0.375 0.375 0.375 1 0.2(6) 0.6(7)

Table 2.11: Reitveld reﬁnement results for both Pr2Ta2N2O5 and Ce2Ta2N2O5 where data for the cerium compounds are italicized

Compound dA-X (A˚) dTa-X (A˚)

Pr2Ta2O5N2 6x 2.64(1) 6x 2.02(1) 134.6(5) 2x 2.2890(5)

Ce2Ta2O5N2 6x 2.61(1) 6x 2.045(9) 132.4(5) 2x 2.2913(1)

Table 2.12: XRD determined bonds and angles for Pr2Ta2N2O5 and Ce2Ta2N2O5

44 nitride ions. If the 8b site is coordinated to nitrogen exclusively, the tantalum octahedra are –O5N on average. Where as if the site is oxygen, the octahedra are O4N2 on average. Each of these hypothetical arrangements about the tantalum would correspond to different bond lengths, which as stated above, can be compared to relevant literature. From a XRD perspective, though, refinement of the anion occupancies from x-ray data is not possible as a direct result of the similarity of the x-ray scattering powers between oxygen and nitrogen. They are therefore, fixed with the same precedence set by the literature: nitrogen fully in the 8b site with Ta-O5N octahedra. (30) Alternatively, attempts to understand the ordering dynamics were also made using the bond valence sums and Madelung site potentials. In both cases though, the results were ambiguous. Grasp of the ordering is limited using currently available techniques. How can anion ordering, if any, on the 8b site be determined? Examination of these compounds using NPD may provide answers.

2.4.2 Perovskite CeTaN2O and PrTaN2O

Rietveld reﬁnement and structure solution for the perovskites followed guidelines laid out in Barnes et. al.(51) In brief, a hypothetical unit cell is constructed from a doubled (in 3 dimensions) simple cubic perovskite cell enabling the analysis of octahedral tilting contributions. A review of this phenomena can be found in the literature. (49, 54) Nonetheless, Miller indices recorded as having integer values corresponding to are realized as subcell peaks, denotes in-phase (+) tilting, is out-of-phase (-) tilting, and lastly, implies both in and out-of-phase tilting.

Amongst supercell peaks, the CeTaON2 sample has weak indicators for both in- phase tilting at 24.7◦ and 52◦ 2θ and out-of-phase tilting at 37◦ 2θ. These peaks when indexed indeed match the convention noted above. In increasing 2θ: 24.7◦ equaling <201> corresponds to even-even-odd, 37◦ equaling <113> matches odd-odd-odd, and 52◦ equaling <412> indicates even-even-odd indices. Note: even or odd labels in the hkl indicies are not syntax sensitive (i.e. <103> =<031> = <301>). These types of super structure peaks narrow the number of probable space groups to ones that contain both types of tilting. After winnowing the pool of candidates, Pnma was the clear front runner and as such groups that are commonly related to it in the perovskite family were also included. These were fully evaluated in Topas Academic

45 (55) and are given by their Glazer notation: a0a0c−, a0a0c+, and a−b+a−. These correspond to space group I 4/mcm (140), P4/mbm (127), and Pnma (62). Of those groups listed, Pnma is the only one that indexes the superstructure peaks mentioned in the XRD pattern. The region of interest has been enlarged as Figure 2.18 and Figure 2.19 for the cerium and praseodymium analogues, respectively. While the splittings responsible for the splitting are weak, and are difficult to resolve versus the baseline noise, they are present nonetheless and allow the best assignment available by XRD data. Furthermore, Rietveld refinement yields the best fit when lattice parameters are given the additional freedom of the Pnma, orthorhombic cell, although a pseudo- tetragonal cell is maintained when lattice parameters are allowed to refine freely.

Figure 2.18: XRD super structure of CeTaN2O - Miller indicies of super structure peaks are in brackets. Tick marks (bottom) show where calculated peaks are expected.

Parallels between both Ce and Pr in size, redox, and electron configuration afford identical space group assignments. In fact, the refinement process described above was

46 Figure 2.19: XRD super structure of PrTaN2O - Miller indicies of super structure peaks are in brackets. Tick marks (bottom) show where calculated peaks are expected.

47 identical for the Pr case. A notable diﬀerence between the two patterns that doesn’t become apparent until Figure 2.19 and Figure 2.18 is that superstructure peaks in the

PrTaN2O analogue are weaker than the CeTaN2O counterpart. In fact, the <311> peak was not well resolved above background noise for PrTaN2O. This makes a space group assignment to the XRD more difficult. Rietveld Refinements are in order, but neutron diffraction is necessary for making unambiguous assignments of the tilt system.

2.4.2.1 Rietveld Reﬁnements of the XRD data for CeTaN2O and PrTaN2O

Phase purity of all products were verified by XRD. Patterns were collected on a Bruker D8 diffractometer (40 kV / 50 mA / CuKα1) equipped with a Ge <111> monochro- mator and a Lynx-eye detector. Scan parameters were: 10-110 ◦ 2θ, 0.015 ◦ step size, and 0.75 second dwell time. Structure solution and refinements were completed using the Topas Academic software. (55) Experimental data afforded the assignment of the cerium compound in the Pnma space group. Refinement of the data was done using the Rietveld technique and was typically done in this sequence: the lattice parameters are optimized, followed by the atomic positions, and lastly the thermal parameters are allowed to refine. Once a global minimum is believed to have been found all optimized parameters are allowed to refine freely. Rietveld refinements yield Pnma as the most favorable designation. The final plots of the XRD data showing the refinement fit for cerium, Figure 2.20, and praseodymium, Figure 2.21, are found below.

For both cases, CeTaN2O and PrTaN2O, the thermal parameters refine to negative values, likely the cause of theta dependent experimental error unaccounted for in the data. The theoretical implications of negative thermal parameters is that abnormal amount of electron density are being placed on the sites. This allotment is more than what is realistically possible for each anion. Because this is unconventional and also unlikely in the actual structure, a more realistic value for the beq, 0.5, was fixed in the calculations. The remaining cation thermal parameters were then allowed to refine freely. The full refinements are summarized in Table 2.13. The fit for the praseodymium compound yields a rwp is much higher than the cerium analog. This is due to noise, presumably associated with Pr luminescence. The result of this diminishes the signal to noise ratio of the supercell peaks, which, in Pnma is largely determined be A-site

48 Figure 2.20: Rietveld reﬁnement of CeTaN2O - blue dots = data, red line = calculated pattern, gray line = diﬀerence curve, hash marks = indexed peaks

49 Figure 2.21: Rietveld reﬁnement of PrTaN2O - blue dots = data, red line = calculated pattern, gray line = diﬀerence curve, hash marks = indexed peaks

50 shifts. This is further evidenced by the larger estimated standard deviation for the praseodymium atomic position (versus the Ce).

2 Compound rwp χ

PrTaN2O 27.226 1.142

CeTaN2O 16.632 1.052

Compound Lattice Parameter(s)

PrTaN2O a = 5.6853(8) A˚ b = 8.0132(4) A˚ c = 5.6814(7) A˚

CeTaN2O a = 5.6968(2) A˚ b = 8.0333(2) A˚ c = 5.7078(2) A˚

Compound S.G. #

PrTaN2O Pnma 62

CeTaN2O Pnma

Atomic Position(s) ion site x y z occ beq Ta+5 4b 0.5 0 0 1 0.62(7) 0.57(4) Pr+3 4c .0249(8) 0.25 .006(2) 1 0.8(1) Ce+3 .0171(5) .994(1) 0.64(5) O−2/N−3 4c .50(1) 0.25 .09(2) 0.5/0.5 0.5 .476(7) .107(8) O−2/N−3 8d .28(1) .042(6) .72(2) 0.25/0.75 0.5 .289(6) .032(3) .736(8)

Table 2.13: Reitveld reﬁnement results for both PrTaN2O and CeTaN2O where data for the cerium compound is italicized

The preliminary results of peak indexing and superstructure analysis (discussed in the previous section) identified Pnma as the most likely solution to the pattern. However, it also identified other systems that could possibly offer solutions for this system, I 4/mcm (a0a0c−) P4/mbm (a0a0c+). Early refinements yielded two nearly equivalent lattice parameters in this system. This could indicate a pseudo-tetragonal structural motif and therefore a tetragonal lattice, I4/mcm and I4/m, were attempted

51 as a solution to the structure, though, the overall fit of the refinement worsens for each. The freedom allowed by lowering the symmetry to orthorhombic better suits the peak positions and intensities. DFT calculations (18, 56) have identified 2 other orthorhombic systems (Pmn21 and Pmc21) in addition to Pnma that are energetically more favorable. These groups maintain the same tilt system as Pnma (a−a−c+) and differ by allowing out-of-center tantalum distortions and/or anion ordering. These too were evaluated but did not allow for a better fit, either. See Table 2.14 to compare the top three fits.

Space group rwp rexp GOF I 4/mcm 16.851 15.769 1.068 Pnma 16.690 15.820 1.055

Pmn21 16.878 15.758 1.071

Table 2.14: Diﬀerent ﬁts to CeTaN2O XRD data:I 4/mcm, Pmn21 and Pnma. rwp =

reﬁned calculated pattern,rexp = ideal theoretical pattern, and GOF = Goodness Of Fit

(rwp/rexp)

Of space groups evaluated, the best fit is provided by the Pnma model. This conclusion is further solidified by examination of the atomic positions. Comparison of the refined values and their proximity to a general position are usually within 5% of each other. Slight distortions of the atoms from these positions are additional evidence for the assignment of lower symmetry space group. However, the small differences in goodness of fit between all of the models suggests that the statistics afforded by neutron diffraction experiments would be beneficial.

Arguments made for the CeTaN2O are congruent for the praseodymium case, though a notable difference between the CeTaN2O and PrTaN2O is the GOF, how well the refinement fit. Solved in the Pnma space group, the fit for each compound is 1.06 and 1.14, respectively. Even though identical space groups are assigned, the cerium compound was better accounted for versus a theoretical fit. Remember, though, the background in the praseodymium compound was noisier and had a much higher rwp value. This also translates to the disconnect here. The refinements enable the determination of XRD bond distance, angle and tilt data for both of the compounds and have been compiled in Figure 2.15. Both these

52 compounds crystallize in the same space group, Pnma, which enables a strong basis for comparison. The maximum and minimum A-X bond distances for each compound are similar with a the cerium favoring a bimodal distribution, with a higher proportion of shorter bonds and longer bonds versus its praseodymium analogue. Praseodymium rather has a bond distance distribution that is more normal, centering around the average. These are correlated to how the Ta-X bond distances behave. Praseodymium again has a tighter distribution about the average while the cerium requires two short bonds followed by four longer bonds. While these distances suggest distorted octahedra with 4 short and 2 long bonds, the estimated standard deviations of the atomic positions are high. NPD data is needed to conﬁrm or refute this conclusion. Less octahedral tilt is observed in the cerium system though both lie within the range expected for a Pnma perovskite.

Compound dA-X (A˚) dM-X (A˚)

PrTaN2O 2.3(1) 2x 2.05(8) 151(1) About the 2x 2.52(7) 2x 2.07(3) 157(1) cubic [011]:¯ 2.74(6) 2x 2.1(1) 14(1) 2x 2.74(8) 2x 2.86(7) [001]: 3.02(6) 0.85(7) 2x 3.30(7) 3.4(1)

CeTaN2O 2.29(5) 2x 1.94(4) 145.4(6) About the 2x 2.55(3) 2x 2.10(1) 161.1(6) cubic [011]:¯ 2.69(4) 2x 2.14(4) 11.5(5) 2x 2.76(3) 2x 2.87(3) [001]: 3.15(4) 0.55(2) 2x 3.25(3) 3.44(5)

Table 2.15: XRD determined bond and angle parameters for CeTaN2O and PrTaN2O. Bond distances increase down the table. Tilt angle calculated by (57) and (58)

53 2.4.2.2 Rietveld Reﬁnements of NPD data for Perovskite RETaN2O where RE = Ce, Pr

Outside of LaTaON2 there are no detailed structure determinations on RETa(O,N)3 perovskites or RE 2Ta2(O,N)7 pyrochlores using neutron powder diffraction (NPD). However, neutrons are essential, not only to accurately locate the anion positions, but to differentiate between oxygen and nitrogen, due to the large difference in neutron scattering lengths (O 5.805 fm vs. N 9.36 fm). The question of anion ordering is of particular interest because the anion distribution is closely tied to the properties, par- ticularly the dielectric properties. Previous studies on the (related) AMO2N (A = Ca, Sr, Ba; M = Nb, Ta) perovskites have reached conclusions on the presence of O/N order ranging from fully ordered, to partially ordered, to short range ordered, to disordered. (18, 20, 22, 25, 28, 59) Recent studies of SrTaO2N using variable temperature

NPD provide the most compelling evidence to date of local cis-ordered TaO4N2 units connecting to make zig-zag chains. (24) Time-of-ﬂight (TOF) powder neutron diﬀraction data were collected using 5.44 g

PrTaN2O, 5.55 g CeTaN2O, and 4.90 g LaTaN2O, each contained within an 8 mm diameter vanadium sample can at 12 and 300 K. LaTaN2O was examined up to 1073 K in a vacuum furnace at 10−6 Torr until decomposition of the sample occurred. The POWGEN (BL-11A) neutron powder diffractometer at the Spallation Neutron Source at Oak Ridge National Laboratory, Oak Ridge, TN enabled diffraction profiles with d-spacings from 0.26 to 6.15 A˚. Rietveld refinements were performed on the data using GSAS via the EXPGUI macro.(60) (61) Peaks and background were modeled by peak- profile function number 3 and a reciprocal interpolation function. Diffraction peaks were indexed and analyzed according to the procedure set forth in octahedral tilting symmetry section.

Superstructure reflections for CeTaN2O and PrTaN2O yield definitive , , and indicies, which confirms those observed in the XRD analysis of these compounds. The similar sized CaTaO2N perovskite has been reported in this structure, Pnma (a+b−b− glazer notation), provides a starting model. For comparison versus

LaTaN2O, the reflections specific to the cerium and praseodymium analogues are high- lighted in Figure 2.22. In fact, all of the additional peaks are equal the or indicies, are fit by the Pnma model, and therefore can be attributed to in-phase tilting.

54 Figure 2.22: Waterfall plot comparing reﬂections in RETaN2O NPDs - Vertical red lines show existence of the most obvious peaks observed by cerium and praseodymium analogues but not LaTaN2O. * denotes and + denotes reﬂections

55 Other similar space groups, C 2/m, Imma, C 2/c, Pmn21 and Pmc21 are investigated as possibilities as well but none parallel the fit achieved by Pnma. A summary of the refined parameters is found in Table 2.16. When refining the anion occupancy, a disordered model provided the best fit. In this process, when fully ordered models are refined they diverge or refine to disorder. A tandem bank, bank 2 and bank 5, structure solution Rietveld refinement is employed that generates a calculated pattern for the entire d-spacing region examined. Overlapping regions result in refining atomic positions to give the best fit for both data sets.

Compound PrTaN2O CeTaN2O Space group Pnma Pnma Temperature (K) 12 300 12 300 a (A˚) 5.6829(1) 5.6866(1) 5.69306(8) 5.69689(9) b (A˚) 8.0027(1) 8.0152(1) 8.02373(9) 8.0327(1) c (A˚) 5.67177(9) 5.68061(9) 5.79294(8) 5.70888(9) V(A˚3) 257.945(9) 258.919(9) 260.467(8) 261.245(9) Rp (%) 3.48 3.52 3.70 4.12 Rwp (%) 2.66 2.66 2.96 2.93 χ2 7.256 7.409 9.746 9.793

Atomic Position(s)

ion site x y z occ Uiso Ta+5 4b .5 0 0 1 .0066(1) .0076(2) Pr+3 4c .0240(3) .25 -.0019(7) 1 .0112(2) Ce+3 .0174(4) .9977(5) .0109(2) O−2/N−3 4c .4869(3) .25 .0796(3) .48(1)/.52(1) .0065(3) .4908(3) .0759(2) .46(1)/.54(1) .0087(2) O−2/N−3 8d .2820(2) .0400(1) .7204(2) .382(9)/.618(9) .0108(2) .2761(1) .03912(8) .7246(1) .413(8)/.587(8) .0119(2)

Table 2.16: Reitveld reﬁnement results for both PrTaN2O and CeTaN2O at 300 K where data for the cerium compound is italicized

The final Reitveld refinement fits in the Pnma space group using bank 2 and 5 of

56 the NPD data for CeTaN2O are compiled in Figure 2.23 and Figure 2.24, respectively. Similarly, the final Reitveld refinement fits in the Pnma space group using bank 2 and 5 of the NPD data for PrTaN2O are arranged in Figure 2.25 and Figure 2.26, respectively.

Figure 2.23: Neutron Powder Diffraction Pattern for CeTaN2O, bank 2 - Blue circles are observed, red line is calculated pattern, gray line corresponds to difference curve, green and cyan hash marks are allowed Bragg reflections for Pnma and vanadium, respectively

Neutron powder diffraction data allows for a better resolution of anion type and positions which in turn helps further define the bonding relationships in the solids. The results in Table 2.17 confirm the trends identified in the XRD analysis. The increased certainty of atomic positions lend itself to more precise bond lengths. The tantalum octahedra in the praseodymium compound are now determined to have tight distribution around the average with just a 0.009 A˚ standard deviation. The disparity between the degree of the tilts in the two systems is resolved in the NPD case where

57 Figure 2.24: Neutron Powder Diffraction Pattern for CeTaN2O, bank 5 - Blue circles are observed, red line is calculated pattern, gray line corresponds to difference curve, green and cyan hash marks are allowed Bragg reflections for Pnma and vanadium sample holder, respectively

58 Figure 2.25: Neutron Powder Diffraction Pattern for PrTaN2O, bank 2 - Blue circles are observed, red line is calculated pattern, gray line corresponds to difference curve, green and cyan hash marks are allowed Bragg reflections for Pnma and vanadium sample holder, respectively

59 Figure 2.26: Neutron Powder Diffraction Pattern for PrTaN2O, bank 5 - Blue circles are observed, red line is calculated pattern, gray line corresponds to difference curve, green and cyan hash marks are allowed Bragg reflections for Pnma and vanadium sample holder, respectively

60 ◦ ◦ both compounds center in at 11.8 for PrTaN2O and 10.5 for CeTaN2O.

Compound dA-X (A˚) dM-X (A˚)

PrTaN2O 2.408(4) 2x 2.040(1) 154.2(1) About the 2x 2.503(2) 2x 2.0556(4) 157.2(1) cubic [011]:¯ 2.673(2) 2x 2.060(1) 11.81(1) 2x 2.734(3) 2x 2.866(2) [001]: 3.090(2) 0.5762(6) 3.288(4) 2x 3.315(2)

CeTaN2O 2.439(3) 2x 2.0551(2) 155.47(9) About the 2x 2.524(2) 2x 2.0532(6) 158.83(7) cubic [011]:¯ 2x 2.733(2) 2x 2.0491(6) 10.455(8) 2.734(3) 2x 2.908(2) [001]: 3.033(3) 0.4509(3) 2x 3.272(2) 3.278(3)

Table 2.17: NPD determined bonds and angles in PrTaN2O and CeTaN2O. Tilt angle is calculated by (57) and (58)

When evaluating the A-X bond distance for both compounds it is clear that the Pnma space group affords the octahedra to tilt in a manner that enables optimized bonding with the f-orbitals. The four longest bonds in the 12-coordinate system are arranged in a curved “Y” shape, Figure 2.27, which align well with LUMO f-orbital. The orbital given in the figure is specific to the Ce3+ 4f1 electron count. However, the occupied orbital for the Pr3+ is completely different in shape and symmetry but quite similar in terms of overlap with the anion positions/orbitals. The overlap and A-X bond distances for the all twelve of the coordinating anions is optimized to overlap based on the f-orbital bonding, anti-bonding or non-bonding interaction. In the figure, the longest bonds have been shown to minimize overlap, presumably with an anti-bonding lobe. This design applies oppositely to the shortest bonds which maximize overlap, and the 4 middle bonds which are oriented to vacant regions and express a non-bonding-

61 type interaction. This scheme helps to understand both, how this Pnma structure tilts to enable the best anion overlap aﬀorded by the structure for these compounds.

2.4.3 Perovskite LaTaN2O

2.4.3.1 Rietveld Reﬁnements of NPD data for Perovskite LaTaN2O

The starting model for this compound in a previous report was disordered Imma

(BaPbO3-type). (20) Upon refinement, one of the Wyckoff positions became fully occupied by a single anion, effectively lowering the symmetry at that site. This yielded the conclusion: a fully ordered, trans oxygen C 2/m space group designation. This was our starting model, however it did not account for all peaks in the spectrum. Fur- thermore, the refinement of the anion thermal parameters in C 2/m for our LaTaN2O required large amounts of damping, diverging often. This lead to a more thorough investigation of the data set.

Superstructure reflections based on a doubled perovskite unit cell for LaTaN2O were observed at . These reflections are indicative of octahedra that are out-of-phase (ooo). In an effort to get a better fit in the refinement model, Imma was evaluated. It did not suffer from divergence. When refining the anion thermal parameters, though, it favored a statistically disordered model over all anion sites. Some questions remain though, some weak peaks in the spectrum are still unfit by the model. Pnma was able to place calculated reflections at some of these peaks in the spectrum. In fact, reasonable calculated reflections for the data can be made in Pnma, C 2/m, and Imma which are best contrasted in the following figure 2.28. Of bank 2 and bank 5 for the data collected, the latter had a more stable background in this region and therefore provided excellent resolution for all the unidentified peaks in the spectrum. Signal to noise for the weakest peak is still 2:1 and in turn enables the selected window of data to present the subtle differences between each space group. The averaged fits of each refinement are presented in Table 2.18. While each refinement in those space groups is good enough to be reported correct, only one of them (or possibly another lower symmetry group) is actually the proper assignment. An evaluation of the differences between the three models is in order. Does the allowed freedom ensure a better fit of the data? No, Imma maintains a better fit to the data and, in fact, does so with a lower number of allowed reflections. In

62 Figure 2.27: Optimization of A-site bonding scheme in CeTaN2O - black dots indicate the 4 longest bonds in the A-X 12-coordinate system where they make a curved “Y” shape. Bottom: phase matching of the orbitals to the anion positions

63 Figure 2.28: Comparing calculated reflections for various models to the neutron powder diffraction pattern for LaTaN2O - Blue dotted line are observed, green, purple, and red hash marks are allowed Bragg reflections for Pnma, C 2/m, and Imma, respectively. Light blue stars indicate reflections not allowed in any of the models.

Space group Rp (%) Rwp (%) χ2 variables Imma 3.56 2.83 8.307 10 Pnma 3.66 2.69 7.695 16 C 2/m 3.76 2.89 8.645 14

Table 2.18: LaTaN2O space group reﬁnement comparison

64 order to fully gauge differing magnitudes, the peaks associated with the tilting superstructure of the out-of-phase peaks (ooo) must be evaluated. Odd-odd-odd reflections were visually analyzed at 2.44, 1.85 and 1.55 A˚ for each model. The Imma model was equivalent to the C 2/m model except for slightly worse fit at 2.44 A˚. Based on the overall fit of the two models and accounting for the out-of-phase tilting regions, tilting magnitudes should be assigned equivalent, as in the Imma model. This coincides well with Linus Pauling’s 5th law: parsimony. What remains to be discussed is what level of impact the addition of an in-phase tilt along the a-axis provides to the overall fit. Quickly referencing Table 2.18 it can be determined that Pnma provides the better fit versus the others. Upon closer examination, however, the “better fit” is false and exists because the allowed reflections for Pnma coincidently, partially fit the weak peaks that were not previously fit by the other models. This is best depicted by Figure 2.29. In addition to that, the refined magnitude of tilting is only 2.2 ◦, less than what is typically observed in tilted perovskites. It was not possible to correctly align the in-phase tilting superstucture peaks allowed by the Pnma model to the unidentified peaks, though some intensity is allowed in the refinements because peak position is similar. Attempts to manually adjust the lattice parameters to accurately fit these positions were not successful. In-phase tilting peaks that do not adequately fit data paired with the fact that the tilting angle is close to zero indicates that Pnma does not actually provide a better fit. + + − Other tilting models that could be correct are a a c (P42/nmc) and one that 0 − − allows out-of-center octahedral distortions to the Imma model, a0 b+ b+ (Ima2). The first alternate is viable because there is a very weak, though possibly coincidental superstructure peak at ca. 1.56 A˚ that might indicate some in-phase tilting. The fit did account for the weak superstructure peak positions, but peak intensities could not be refined to give a improvement in the rwp. The latter model did not pick up any of unaccounted for peaks and increased the number of variables in the calculation to yield the same fit. Both alternative models are ruled out. It has been shown that this system contains only out-of-phase tilts which can only be accounted for by a Imma model. The final simultaneous Rietveld refinement fit to the neutron diffraction patterns can be found for bank 2 in figure 2.30 and for bank 5 in figure 2.31.

65 Figure 2.29: Neutron Powder Diffraction Pattern for LaTaN2O, bank 5 - green line is Pnma calculated pattern, green hash marks are allowed Bragg reflections for Pnma, green stars are reflections that due to in-phase tilting, red * are peaks still unaccounted for, blue dotted line is observed

66 Figure 2.30: Neutron Powder Diffraction Pattern for LaTaN2O, bank 2 - Blue circles are observed, red line is calculated pattern, gray line corresponds to difference curve, green and cyan hash marks are allowed Bragg reflections for Pnma and vanadium, respectively

67 Figure 2.31: Neutron Powder Diffraction Pattern for LaTaN2O, bank 5 - Blue circles are observed, red line is calculated pattern, gray line corresponds to difference curve, green and cyan hash marks are allowed Bragg reflections for Pnma and vanadium, respectively

68 Some very weak peaks in the spectrum, indexed at d-spacings of 2.92, 2.69, 2.23, 2.065, 1.49, 1.46 A˚, are unaccounted for by any of the reﬁnement models suggested. Some of them are found marked in Figure 2.29. To verify that these are part of the sample that it is indeed phase pure, attempts were made to match these peaks to common secondary phases (LaTaO4, La2Ta2O5N2, LaTaO4−xN2x/3x/3, Ta3N5, and

La2O3) and were unsuccessful. A survey of XRD data (not presented) from this same compound shares similar peaks and one at high d-spacing (6.86 A˚) that was not within the window of bank 2 or 5 in the NPD data taken. The peaks are persistent. An ongoing investigation of the cause of these peaks continues beyond the scope of this work, but it is believed by the author that a superstructure arising from anion ordering, that conserves the tilting afforded by Imma, is the cause of the extra peaks. Table 2.19 displays final refinement parameters in the system. In order to realize these values, anisotropic libration thermal motion matrices, Lxx were utilized in the peak profiles functions. Anion thermal parameters, Uaniso, were also attempted to better the fit but divergence, even under maximum damping, occurred. Specifically,

U11 skewed to values > 0.05 while U22 and U33 became close to zero or negative suggesting an almost flat ellipsoid. Poor fitting conditions continued when U12,U 13, and U23 were invoked. Combined anion occupancies were constrained to equal one on the mixed site but were allowed to refine freely. There is no statistical difference between the complete disorder model (67 % N and 33 % O) versus the refined values. However, when anion ratios were set to be fully ordered, e.g. oxygen on 4e site and nitrogen on the 8g site or nitrogen on the 4e site and nitrogen with oxygen 50/50 on the 8g site, refinements give an inferior fit. Further evidence for this is provided by the data in Table 2.20. NPD refined positions allow for the generation of bond length, angle and octahedral tilt data, which are presented in Table 2.21. In the Imma group the 12-coordinate A-site has two sets of four equivalent bond lengths, creating a distribution of bond lengths similar to the Pnma CeTaN2O and PrTaN2O cases. The Ta-X bond distance is anchored at ca. 2.045 A˚ due to the four equivalent anion sites (8g) in the octahedron. The M-X-M angles differ by 6 ◦ but does not result in a deviant tilt, which is calculated to be 10.09 ◦. This tilt being the smallest of the rare earth compounds presented is expected based on ionic radii arguments. The larger the radii of the A-site cation,

69 Compound LaTaN2O Space group Imma Temperature (K) 12 300 1073 a (A˚) 5.7037(2) 5.7093(1) 5.7489(8) b (A˚) 8.0506(2) 8.0593(2) 8.129(1) c (A˚) 5.7334(2) 5.7384(2) 5.7614(9) V(A˚3) 263.26(2) 264.04(2) 269.23(4)

Rp (%) 3.66 3.55 8.48

Rwp (%) 3.05 2.88 4.34 χ2 9.638 8.597 1.874

Atomic Position(s) 2 ion site x y z occ Uiso A˚ Ta+5 4a 0 0 0 1 .0058(2) La+3 4e 0 0.25 0.5 1 .0110(3) O−2/N−3 4e 0 0.25 .0685(3) .33/.66 .0090(3) O−2/N−3 8g .25 -0.0352(1) .25 .33/.66 .0190(4)

Table 2.19: Atomic positions for LaTaN2O at 300K

2 Order model Anion Ratios Rwp Rp χ Disordered 67% N: 33% O, all sites 2.88 3.55 8.597 Partial order N on 4a site, 50% N: 50% O on 8g 3.15 3.8 10.28 Ordered O on 4a, N on 8g 3.58 4.33 13.3

Table 2.20: Models of the types of anion ordering in Imma

70 the less tilt the octahedral network must undergo to obtain orbital interactions which stabilize the structure.

Compound dA-X (A˚) dM-X (A˚)

LaTaN2O 2.477(2) 2x 2.0526(3) 158.0(1) 10.099(3) 4x 2.6631(5) 4x 2.0435(1) 164.0(9) 2x 2.8814(2) 4x 3.0624(6) 3.261(2)

Table 2.21: NPD determined bonds and angles in LaTaN2O. Octahedral tilt angle is about the cubic [110] (57)

The high temperature structural transition to cubic for perovskite oxide nitrides has been shown to allow a better understanding of anion ordering. (24) It lowers the anion site degrees of freedom and eliminates octahedral tilting axes, which can complicate the interpretation of diﬀraction patterns. A survey of compounds that have similar chemistry, electronic conﬁguration, or space group assignment to LaTaN2O under go structural transitions in the 300 - 1000 K range. Comparison with the nearest oxide perovskite analog, NaTaO3, would suggest that octahedral tilting transitions are expected near 703 K (Pbnm to Cmcm), 833 K (Cmcm to P4/mbm) and 883 K

(P4/mbm to Pm3¯m).(62) SrTaO2N, an oxide nitride that is similar in ionic radius to

LaTaN2O, transitions from I 4/mcm to (pseudo) cubic near 473 K. (24) Lastly, SrTcO3 has transitions at 375 K (Pnma to Imma), 615 K (Imma to I 4/mcm), and 800 K

(I 4/mcm to Pm3¯m). (63) A variable temperature study on LaTaN2O from 12 K to 1073 K is summarized by figure 2.32. Lattice parameters in this plot are normalized to a simple cubic perovskite, where the refined lattice parameters a, b, and c are transformed √ √ by a/ 2, b/ 2 and, c/2. One striking conclusion is that, aside from the changes due to thermal lattice expansion, there is no apparent phase transition observed. The Imma structure is stable over a very wide range of the temperatures, contrary to any indications from the survey study. At low temperatures all the reflections observed at room temperature are conserved. At higher temperatures, also, they appear to stay present though they become more difficult to resolve as background noise increases with increased thermal

71 Figure 2.32: Variable temperature lattice parameters for LaTaN2O - cell egdes are normalized to a simple cubic perovskite

motion. Furthermore, the selected window to collect data, bank 2, did not have as high a resolution in the region where the Imma superstructure peaks are most easily resolved. It should be noted that heating was stopped at 1073 K because the sample began to degas, presumably losing nitrogen. The vacuum chamber pressure went from 10−6 to 10−3 Torr. Extrapolating the slopes of the a and b lattice parameters in the plot hints at a possible structural transition at much higher temperatures but attaining this value may be out of practical range, both instrumentally and compound stability- wise. It is unclear how the Imma LaTaN2O structure is robust under a wide range of temperatures and why it diﬀers from the survey set derived from the literature survey.

2.5 Comparison of Bond Distances, Angles, and Tilts in

RETaN2O(RE = La, Ce, Pr) and RE2Ta2O5N2 (RE = Ce, Pr)

Experimentally determined data via XRD and NPD methods provide insight to the structure at long time scales (> 10 minutes) resulting in atom positions that are averaged over time. In simple perovskites relevant to photophysical processes there are two main bond distances of interest: tantalum to the anions and A-site cation to anions. Similarly for the pyrochlore system the A-site is an 8-coordinate scalenohedron while the B-site is an octahedron. A way to better understand the compounds in this study is to compare bond distances for each class and bond type to literature values of similar compounds/analogues. Perovskites We begin with the Ta-X bonds, Table 2.22, which are arranged to include a full breadth of compounds from oxides to nitrides. In the compound classes that have only Ta-O bonds the distances are all close to 1.99 A˚. As nitrogen replaces oxygen in the

Ta-X 6 octahedra, such as the oxide nitride pyrochlore and perovskites, an elongation of the average bond distance is observed. This is explained by three things: the increased ionic radii of a nitride, tolerance factor, and trans eﬀect. As nitrogen is added to the octahedron, a more covalent bond interaction (versus oxygen) with tantalum occurs about the coordination sphere, but the increases in ionic radii correspond with increases in the Ta-X 6 bond distance. Upon close examination the The Ta-X bond distance,

BaTaO2N may seem like an outlier, but this elongated bond distance is observed for

73 Ba in the (Ca, Sr, Ba)TiO3 series as well. It results from barium having the largest ionic radii of the cations surveyed and is reﬂected by having the largest tolerance factor observed (1.03). Barium is too large for the cavity it resides in, and therefore the bonds about tantalum must elongate to accommodate it. Having a small tolerance factor, and hence, heavy octahedral tilting can also play a role. These geometries can induce nonstandard bonding arrangements often changing coordination number and yielding irregular polyhedra. When comparing the bond lengths of perovskite nitrides, oxide nitrides, and oxides, it becomes apparent that the hybrids have the longest average

Ta-X 6 bond distances. This is the result of a structural trans-effect and is discussed at length later, though quick reference can be found by Table 3.9. This phenomena has been shown to affect octahedral complexes, where a strong trans-influencing ligand can increase a bond distance 0.2 A˚. (64) These concepts explain the phenomena observed for the Ta-X bond distances for all the oxide nitrides presented in this study.

Compound Bond type Avg. B-X (A˚) S.G. Tech. Ref.

LaTaO4 Ta-O 1.9925 P21/c XRD (65)

PrTaO4 Ta-O 1.9941 P21/c XRD (66)

CeTaO4 Ta-O 1.9898 P21/c XRD (66)

LaRuO3 Ru-O 2.0465 Pnma XRD (67)

PrRuO3 Ru-O 2.0475 Pnma XRD (67)

KTaO3 Ta-O 1.9942 Pm3¯m XRD (68)

NaTaO3 Ta-O 1.9843 Pcmn NPD (69)

CaTaO2N Ta-O/N 2.0268 Pnma NPD (20)

SrTaO2N Ta-O/N 2.0220 I 4/mcm NPD (24)

BaTaO2N Ta-O/N 2.0564 Pm3¯m NPD (25)

LaTaN2O Ta-O/N 2.0465(1) Imma* NPD This work

CeTaN2O Ta-O/N 2.0524(3) Pnma NPD This work

PrTaN2O Ta-O/N 2.0519(5) Pnma NPD This work

ThTaN3 Ta-N 2.01 Pm3¯m XRD (70)

Table 2.22: Ta-X bond distances in RETaN2O(RE = La, Ce, Pr) versus other compounds. Compounds broken down into structural class by horizontal lines, with nitrogen content increasing down the table. S.G. = Space Group, Tech. = Technique. * compound gives Imma-type tilting

The ARuO3 series is included because it was the only perovskite-type compound

74 that gave similar radii to the perovskite oxide nitrides, though only the lanthanum and praseodymium ruthenium compounds have been synthesized. Both, LaRu3 and

PrRuO3 like CeTaN2O and PrTaN2O adopt the Pnma space group. LaTaN2O does not and gives a0b−b− system of tilts. Of the perovskite compounds involved in this study, A-site lanthanum perovskites from the literature have been shown to adopt complex structure or low symmetry types. (71) Regarding comparison to the perovskite nitrides, a limited ternary compound library yields just one example of a perovskite nitride, ThTaN3. Regardless, the Ta-N6 average bond distance is greater than the oxide equivalent. 12-coordinate bond distances at the A-site are also a metric worth examining and are collected in Figure 2.33 and Figure 2.34. These depictions are intended to be tiled sequentially to create a waterfall of compounds with decreasing ionic radii. In each of the plots the axes are held constant so global or local shifts, if any, can be observed. As a general trend, when the tolerance factor decreases resulting in a space group of lower symmetry, the distribution of bond lengths becomes more disperse. This is indicated by a decrease in the height of the data and an increase in the width down the cascade of plots. Variable A-site radii is allowed by the flexibility (tilts) of the corner connected octahedral network. The uniformity of the bond distribution is regular in the first figure but begins to skew in the second. The compound with the largest maximum-minimum bond length difference is observed in CaTaO2N, at 0.977 A˚. Within the range there is also a void region of bond lengths in the 2.8 to 3.1 A˚ region. The calcium seems to favor 8 shorter bonds in a pseudo-8-coordination at the cost of the remaining 4 bonds being elongated. This can be rationalized because this compound has the most pronounced tilting of the compounds presented, and also has the least regular spacing of the A-site bonds. A progression to this phenomena is observed within the Pnma structure going from a more uniform distribution of bond lengths in Ce, to the intermediate Pr, and Ca, where the bond angles are most distorted from 180 ◦. All of these phenomena observed at the A-site can be explained by effects due to tolerance factor and tilting, which is further expanded below. One of the symmetry ascents often observed upon heating perovskites is Pnma

→ Imma) → I 4/mcm) → Pm3¯m. This was the case earlier for SrTcO3 (63) when it was used as an indicator for the possible route LaTaN2O might take. The exact same order in SrTcO3 is now observed in this series when the compounds are sorted

75 Figure 2.33: 12-coordinate bond distances for RE-X or AE-X in nonPnma space groups - Compounds ordered by decreasing tolerance factor

76 Figure 2.34: 12-coordinate bond distances for RE-X or AE-X in Pnma space groups -

77 by the ionic radii of the A-site, Table 2.23. The symmetry ascent could not be done without the correct tilting assignment of LaTaN2O in Imma. The table shows that radii trends are governing the structural transitions of the compounds through the series, down the alkali-earth group, radii increase and across the rare-earth period radii decrease each causing structure changes. The symmetry ascent cannot be accomplished if the compounds are sorted by tolerance factor which is also included in the table. This may indicate that the ionic radii used for N3− or O2− is not adequate for oxide nitrides. Also, the limited structural characterization of the CaTaO2N, speciﬁcally by modern NPD techniques, leaves some uncertainty in the space group assignment. Nonetheless, according to the table there is an overlap in the progression of the alkali earth and rare earth radii compound series: the calcium and lanthanum analogues. The radii also play a strong role in the deviation of the M-X-M angle from 180 ◦.

As the radii decrease versus the ideal case, BaTaO2N, the averaged M-X-M angle also decreases. As discussed throughout, tilting has implications on the symmetries allowed. Increases in ionic radii lessen the octahedral tilting maximum which then requires less energy to overcome a lower symmetry by obtaining a fluxional tilting (net tilt = 0). Similar to heating the compound, where increased thermal motion allows compounds to overcome the energetic double well necessary to have fluxional tilting, again raising the symmetry. This oxide nitride series is an example of cation/anion substitutions showing a symmetry ascent for the full breadth of the tilting spectrum, from no tilts to tilts about all three axes. In addition to the M-X-M angles, the magnitude of tilts can be extracted, as was shown in the NPD analysis of RETaN2O where RE = La, Ce, Pr. All of the tilts in this series are arranged in Table 2.24. Tilts were calculated using the formula laid out in Woodward et. al. (57), and were affirmed by comparison with the TUBERS program. The systems, when they do have tilting, tilt in the 3.8-11.8 ◦ range. The strongest is observed for Pnma PrTaN2O and the weakest is found in I 4/mcm SrTaO2N. The remaining compounds presented in Table 2.24 lie at intermediate values within that range. All of the orthorhombic compounds (Ca, La, Ce, Pr) show similar tilting magnitudes, due to similarity of ionic radius. The degree of tilting, however, decreases from Ca > Pr > Ce. This is a result of different cation overlap interactions between the anions for calcium (s orbital) and the rare-earths (f orbital). Pyrochlores

78 Compound A-site radii (A˚) τ M-X-M angles (◦)

BaTaO2N 1.61 1.03 180

SrTaO2N 1.44 0.97 171.718(2)

LaTaN2O 1.36 0.93 157.98(9) 167.04(1)

CaTaO2N 1.34 0.94 153.3(1) 155.131(1)

CeTaN2O 1.34 0.93 155.48(9) 158.83(3)

PrTaN2O 1.29 0.91 154.24(9) 157.19(6)

Table 2.23: Perovskite oxide nitride A-site ionic radii and M-X-M angles from XRD Rietveld reﬁnements. Ordered from largest 12-coordinate cation radius to smallest, radii obtained from (72). τ = tolerance factor

Compound Tilt system Tilt (◦) Tilt about the cubic: Ref. + − − CaTaO2N a b b ˜14.6 [011]¯ (20) 0.882 [001] 0 0 − SrTaO2N a a c ˜3.8 [001] (24) 0 0 0 BaTaO2N a a a 0 N/A (25) 0 − − LaTaO2N a b b 10.099(3) [110] this work + − − CeTaO2N a b b 10.455(8) [011]¯ this work 0.4509(3) [001] + − − PrTaO2N a b b 11.81(1) [011]¯ this work 0.5762(6) [001]

Table 2.24: Tilting angles determined by NPD. Data for this table was generated by NPD data from Reference column. Tilts are calculated by SPuDS method (57) and O’Keeﬀe (58)

79 Compound Bond type Avg. B-X (A˚) S.G. Tech. Ref.

Ce2Ta2O5N2 Ta-O/N 2.045(9) Fd3¯m XRD This work

Pr2Ta2O5N2 Ta-O/N 2.02(1) Fd3¯m XRD This work

Sm2Ta2O5N2 Ta-O/N 1.9690 Fd3¯m XRD (30)

Table 2.25: Ta-X bond distances in RE 2Ta2N2O5 (RE = Ce, Pr). S.G. = Space Group, Tech. = Technique.

Table 2.25, the pyrochlores are all assigned to the same space group; sorting by bond distance is mute. In this class of compounds the A-X bond distance increases as the ionic radii decreases. Because the pyrocholore framework is more rigid than the perovskite, “tilting” cannot occur in the same sense as with perovskites. There is ﬂexing that can occur to accommodate cation radii changes but it is minimal. In the compounds studied then, the ionic radii decrease is not accompanied by anion sublattice changes and results in the lengthening of the A-X 8 scalenohedron bonds.

Within the oxide nitride series, the pyrochlore Ta-X 6 octahedra are more contracted versus the perovskite analogue when comparing between RE 2Ta2O5N2 and RETaN2O (RE = Ce, Pr). In the pyrochlore series, the bond distances decrease with the ionic radii of the rare earth. This trend is not conserved in the oxide nitride perovskite series, or if it is, the magnitude of the bond distance change with the ionic radii change is damped. The Ta-X 6 bond lengths can shed some light on an earlier question regarding the site preference of the anions in the two chemically diﬀerent Wyckoﬀ sites, 48f and 8b, of a pyrochlore. The cerium (2.045 A˚) and praseodymium (2.02 A˚) Ta-X 6 lengths match that of BaTaO2N and CaTaO2N which both have tantalum coordinated octahedra that correspond to -O4N2. If the octahedral coordination was -O5N1 or -O6 then bond distances would be expected to be more in line with the 1.98-1.99 A˚ Ta-

O6 average bond distance observed in other tantalum oxides. The implications then yield an 8b site that must be oxygen. This is contrary to the previous report made by Pors et. al. (30) for the Sm2Ta2O5N2, but makes chemical sense. The 8b Wyckoﬀ site is coordinated by four rare-earth atoms, all with 3+ valence, whereas the 48f site contains bonds to two 5+ cations and two 3+ cations. The higher charge density of the 48f site should attract anions of higher charge, encouraging a more covalent bond, in this case nitrogen. Further evidence for the existence of this ordering is provided

80 by the RE-X bond distance as presented later in Table 2.27 and Table 2.26. There is only one example of a 3,4 pyrochlore with cerium 3+, Ce2Zr2O7. The data gives a very long RE-X bond distances after account is made for the zirconium ionic radii. It is believed that other factors that are unaccounted for are at play here as evidenced by: the lack of cerium compounds in the pyrochlore space group and the fact that cerium 3+ is difficult to stabilize under high temperature oxidizing conditions needed for the pyrochlore phase to crystallize. As a worthy side note, Ce2Ta2O5N2 is an addition to this cerium pyrochore class, now totaling two examples. Praseodymium, however, has a larger library of compounds available by contrast. Comparison is drawn to the Pr2Sn2O7 and Pr2Zr2O7 compounds, which have RE-X bond distances that are very similar to those observed for Pr2Ta2O5N2. In fact, the RE-X bond distances for each, when account is made for the differing ionic radii, are the same; the oxide nitride compound geometry about the rare-earth is the same as in oxide compound pyrochlores. The 8b site must be composed of oxygen to conserve a RE-X bond distance that matches those obtained for pyrochlore oxides, and therefore to maintain the charge balance necessary to stabilize the pyrochlore phase (-O5N2), the nitrogen would be placed about the tantalum octahedra (-O4N2). To convey the bonding arrangement then, a way to write the oxide nitride pyrochlore compounds would be: REOTaN2O4. The pyrochlore oxide nitrides show similar lattice parameters to the homologous oxide pyrochlore. This is illustrated by Figure 2.35 where comparison is made to group 4 (Ti, Zr, Hf) oxide pyrochlores. All of the series have a similar slope when progressing down the lanthanide block. The tantalum series yields lattice parameters that are better compared to hafnium and zirconium oxide pyrochlores. However, the Shannon radii of 6-coordinate tantalum (0.64 A˚) is closer to titanium (0.61 A˚) in the same configuration. The lattice expansion is then directly a result of the addition of the a larger anion, nitrogen, now incorporated into the pyrochlore lattice. The compounds contributed by this work extend the tantalum oxide nitride work done by Maillard et. al. to the larger rare-earths and fit well if the trends observed the series are extrapolated to include the aforementioned cerium and praseodymium analogs. The rare earth compounds presented in this work on pyrochlores can be included in a survey of compounds to gain knowledge of RE-X bond distances. Table 2.26 contains cerium compounds and Table 2.27 is composed of praseodymium compounds. Com- paring pyrochlore bond distances and accounting for the 0.05 A˚ ionic radii difference

81 Figure 2.35: Ce2Ta2O5N2 and Pr2Ta2O5N2 lattice parameters compared to other pyrochlores - Arrows denote compounds presented in this work. Pyrochlore data were generated from Subramanian (73) for the Ti, Zr, and Hf series barring Ce2Hf2O7 and Ce2Zr2O7 which were provided by Brixner (74) and Raison (75), respectively. Late lanthanide tantalum oxide nitrides are derived from Maillard (32)

82 between zirconium and tantalum shows that A-X bond lengths going from an oxide to oxide nitride are static. As mentioned previously the pyrochlore lattice is fairly rigid. This accounts for the lack of changes in the values. It was previously mentioned that cerium pyrochlore examples are lacking. In CeTaO4 the 8-coordinate cerium has irregular polyhedra. Addition of the nitrogen and, hence adoption of the pyrochlore phase normalizes the bond distances to two lengths: 2 short axial bonds and 6 long equatorial bonds. The two short bonds are related to the 8b site, discussed above. The two short Ce-X distances in the oxide nitride pyrochlore are quite instructive. In both the cerium and praseodymium analogues the distances are approximately the same length as their oxide counterparts. The long distances which are associated with the 48f Wyckoﬀ site are elongated versus the oxide compounds compared to. The ionic radii of the tin (0.69 A˚) and zirconium (0.72 A˚) in Pr2Sn2O7 and Pr2Zr2O7 are greater than tantalum (0.65 A˚) but the Pr-X distances don’t reﬂect that trend. The largest

6-long-bond-site length is held by Pr2Ta2O5N2 followed by the zirconium and tin oxide pyrochlores. The elongation of the six equatorial bonds must be due to the nitrogen being exclusively localized about this site, furthering the evidence that the 8b site is populated by only by oxygen.

83 Compound Bond type C.N. Ce-X (A˚) Technique Reference

CeO2 Ce-O 8 8x 2.3430 XRD (76)

CeTaO4 Ce-O 8 2.36053 XRD (66) 2.37263 2.37722 2.46172 2.51625 2.54215 2.68577 2.82504

Ce2Zr2O7 Ce-O 8 2.31497 NPD (77) 2.52658

Ce2Ta2O5N2 Ce-O/N 8 2x 2.2913(1) XRD This work 6x 2.61(2) CeN Ce-N 6 6x 2.51 XRD (78)

Table 2.26: Ce-X bond distances in CeTaN2O and Ce2Ta2O5N2 compared to other compounds; C.N. = coordination number

84 Compound Bond type C.N. Pr-X (A˚) Technique Reference

PrO2 Pr-O 8 8x 2.3348 NPD (79)

PrTaO4 Pr-O 8 2.33749 XRD (66) 2.35054 2.35467 2.46718 2.47102 2.53778 2.68181 2.8114

Pr2Zr2O7 Pr-O 8 2x 2.28674 ED (80) 6x 2.62726

Pr2Sn2O7 Pr-O 8 2x 2.29505 NPD (81) 6x 2.589

Pr2Ta2O5N2 Pr-O/N 8 2x 2.28899(5) XRD This work 6x 2.64(2) PrN Pr-N 6 2.5845 XRD (78)

Table 2.27: Pr-X bond distances in PrTaN2O and Pr2Ta2O5N2 relative to literature; C.N. = coordination number

85 3

Electronic, Optical, and Photocatalytic Properties in the

ATa(O,N)x Compound Class

3.1 Electronic Structure For The ATaO2N and RETaN2O Systems (A = Ba, Sr, Ca; RE = Pr, Ce, La)

Most work regarding these compounds has been exploratory synthesis with material properties not well explored or chronicled. Pioneering the ﬁeld in oxynitride characterization has been Fuertes et. al. and Marchand et. al.. Reports include but are not limited to: superconductivity,(82) luminescence, (83) dielectrics, (28) and photocatalysis. (27)

Tantalum perovskite oxide nitrides (ATaO2N and RETaN2O where [A = Ba, Sr, Ca and RE = La]) have stimulated significant interest as possible visible light driven, overall water splitting photocatalysts using a variety of different reaction schemes. (84, 85, 86, 87) The end result for all approaches was that these compounds, while able to reduce water to evolve hydrogen, do not efficiently evolve oxygen. Water oxidation is suppressed and therefore the water redox reaction is unstoichiometric. It is not clear why the compounds do not evolve oxygen, but X-ray photospectroscopy (XPS), Kelvin probe force microscopy (KPFM), UV-visible diffuse reflectance (UV-vis DR), and depth resolved cathodoluminescence spectroscopy (DRCLS) have provided an experimental picture with absolute positions for band states near the Fermi level. (88) This has

86 been compiled with other data from the literature to create Figure 3.1. This collection will serve as a frame of a reference for the subsequent calculations. Understanding what happens to the electronic structure as you progress from Ba → Sr → Ca → lanthanoid is necessary for explaining photocatalytic rates in these compounds. How do tilts, bond angles, and bond lengths play a role in the electronic structure? What types of contributions do each of these compounds have to the valence band maximum or the conduction band minimum? What happens when the anion stoichiometry goes from –O2N to –N2O? Density Functional Theory (DFT) oﬀers a theoretical method to explore this series and when paired with experimental data may provide a powerful explanation of the compound series. Answers about atomic interactions like bonding, overlap, and octahedral tilting, may provide an explanation of the phenomena observed when probed through DFT calculations.

Figure 3.1: Semiconductor conduction band minimum and valence band maximum - % derived from Schoonen et. al.,(89) * from Domen et. al., (27) # from Serpone et. al.,(90) and @ from Balaz et. al.(88) Black hash marks are Fermi levels

3.2 Photocatalytic results

Reactions were executed in a quartz bottom-irradiation vessel connected to a closed gas circulation system. 1 % w/w platinum was photodeposited as a co-catalyst on the

87 surface of the oxide nitride compounds (ATaNO2 where A = Ba, Sr, Ca and RETaN2O where RE = La, Ce, Pr) over a 20 hour time span. To analyze hydrogen production, 100 mg of powder was suspended using a magnetic stirrer in 100 mL of a 10 % aqueous methanol (sacriﬁcial e− donor) solution. Tests to exact the oxygen production were not employed. Reactant solutions were purged of air by bubbling argon through the system until background GC spectra were featureless. Irradiation was performed with a 150W Xe lamp (Newport Oriel, Stratford, CT). Gases evolved were separated by a tandem Shimadzu GC-14A gas chromatograph equipped with a 60/80 molecular sieve 5A (Sigma Aldrich, St. Louis, MO) and quantiﬁed by a internal thermal conductivity detector.

PrTaN2O, CeTaN2O, LaTaN2O, and BaTaNO2 did not result in evolution of hydrogen above the detection limit (465 nmol) in the photacatalytic chamber over a time span of 13-22 hours. SrTaNO2 also did not evolve hydrogen but a shorter time scale was used, 5 hours. CaTaNO2 did produce quantiﬁable hydrogen when sampled at the 8 and 15 hour intervals. The quantities, 470 and 530 nmol respectively, were −1 used to determine a H2 evolution rate of 0.05 µmol hr per 100 mg of sample. This data indicates similar performance to previous work done on the alkali-earth analogues, −1 ATaO2N where A = Ca, Sr, Ba and LaTaN2O equaling approximately 20 µmol hr −1 of evolved H2 or 0 µmol hr of evolved O2 per 200-400 mg of sample in 200 mL of sariﬁcial reagent (10 vol. % methanol in water and 0.01 M AgNO3, respectively) under a 300 W xenon light source.(91) These runs were calibrated versus an external standard curve for hydrogen. A known catalyst, Pt:TiO2 (Degussa P25), which exhibited an H2 evolution rate of 120 µmol hr−1 100 mg−1 of sample, was used as a control.

3.3 Diﬀuse Reﬂectance of RE 2Ta2(O,N)7 and RETa(O,N)3 where RE = Pr & Ce

Simple precursors that can be used to create an entire spectrum of colored compounds is desirable to the pigment industry. Portions of the spectrum, yellow to red (26) and yellow to green, (92) can be realized by solid solutions of oxynitride compounds. One technique to examine electronic phenomena in the UV-Visible region is through diﬀuse reﬂectance.

88 UV-Vis diffuse reflectance data were collected for all compounds using an Ocean Optics (Dunedin, Florida) USB4000-UV-Vis spectrometer equipped with a standard reflectance probe and a DH-2000-BAL deuterium/tungsten halogen light source. Data in the 250-750 nm range were initially analyzed using SpectroSuite software, and transformed using the Kuebelka-Munk method to a function of reflectance for subsequent interpretation. Spectra, compiled in Figure 3.2, coupled with the Shapiro method (93) enables qualitative determination of the energy necessary to excite an electron from the valence band (VB) to the conduction band (CB). These band gaps are listed along with observed color in Figure 3.3. Compounds show strong correlation between Eg and observed color, where deviations can be accounted for by trap states between the conduction band minimum and the valence band maximum, as evidenced by cathodoluminescence spectra. (88) These defect states allow for excitation of the electrons from the valence band into energy states below the conduction band. This phenomena of excitation at wavelengths less than Eg yields non-zero absorbance values which explains why, at low energies the spectra gives a plateau parallel to the x-axis. Three routes for achieving the same phase of oxide nitride have been described in this work: solid-state, acetic acid co-precipitation, and methanol co-precipitation. Previously we have shown that these approaches can give different material properties such as crystallite size. This begs the question, does the preparation technique have an impact on the diffuse reflectance? Yes. The complete library of spectra have been assembled in Appendix A 3.5.2 for simplicity, but will be discussed here. Also, for additional clarity, Table 3.1 presents the band gap of all the compounds for some of the synthesis techniques in this study. These gaps are calculated by the Shapiro method mentioned previously. Except for the SrTaO2N case, all of the oxide nitrides prepared by the methanol co-precipitation route have higher band gaps. It is not understood why SrTaO2N is as exception. The solid state and the acetic acid co-precipitation techniques may have defects near the conduction band edge, effectively lowering the band energy. The methanol co-precipitation technique does not observe this phenomena and therefore yields wider gaps. When paired with the evidence presented by the cathodoluminescence data, (88) a strong case can be made in favor of this conclusion. The acetic acid co-precipitation method having non-zero values at lower energies is also another outcome yielded from careful examination of the spectra. A non-zero value can be obtained by adsorption of a photon which has lower energy than that of the band

89 Figure 3.2: Diﬀuse reﬂectance spectra for RE 2Ta2(O,N)7 (RE = Ce, Pr) and

RETa(O,N)3 (RE = La, Ce, & Pr) - Reﬂectance values are Kuebelka-Munk transformed

90 Figure 3.3: Band gap, color, M-X-M angle for perovskite and pyrochlore oxide nitrides - Arranged by decreasing band gap. M-X-M calculated from XRD data. Pictures of colors taken with 3.2Mpixel camera under incandescent light.

91 gap. This can occur if the compounds have low lying defect states in the bulk that are consequence of anion vacancies or O:N oﬀ-stoichiometry both of which could be induced by a reduced Ta4+ species.

Compound Technique Eg (eV)

CaTaO2N SS 2.57 AA 2.59 MeOH 2.63

SrTaO2N SS 2.23 AA 2.13 MeOH 2.18

LaTaN2O SS 2.03 AA 2.04 MeOH 2.10

PrTaN2O SS 1.92 MeOH 2.02

CeTaN2O MeOH 2.00

Table 3.1: Band gaps of oxide nitride compounds made via diﬀerent preparation techniques. MeOH = methanol co-precipitation, AA = acetic acid co-precipitation, SS = solid state

The VB to CB electronic transition has been defined but is the transition direct or indirect? LaTaN2O prepared be the AA method was chosen because it possessed features at lower energies that made it most likely to have an indirect gap, if it was observed at all. Evaluation for these characteristics was done in Figure 3.4. It is known that for an indirect semiconductor, a ”hockey stick”-shape plot is obtained for (α*hω)1/2 vs hω. As this is not the case here, a procedure for evaluation of the direct band gap is achieved by plotting (α*hω)2 vs hω. This yields a value (2.02 eV) in agreement with the Shapiro method (2.04 eV). This approach does not produce a convincing evidence that allows for the conclusion that the transition is direct. It can, however show that the direct gap method matches band gap extrapolations for the adsorption onsets found via the Shapiro method. No changes were observed in any of the UV-Vis diffuse reflectance plots that could be directly correlated to the anion transition from –O2N to –N2O stoichiometry. Changes were found on going from –O2N

92 to –N2O stoichiometry. For instance, CaTaO2N, CeTaN2O and PrTaN2O should all have the same Eg based on Ta-X -Ta bond angles but this is not observed, instead the

RETaN2O compounds have band gaps that are ca. 0.6 eV smaller.

Figure 3.4: Analysis of the band gap transition in LaTaN2O - black lines show ideal ﬁts for each type of transition

Discussion Blue shift in the compounds, the progression of reﬂectance onset towards higher energies, can be understood as a function of octahedral tilting. In the Figure 3.3, corner connected tantalum octahedra are listed with increasing tilt, which must occur to better occupy void space created by decreases in ionic radii for the accompanying A-cation in the series (Ba, Sr, La, Ce, Pr, and Ca). This helps relieve charge-charge repulsion and under/overbonding at any particular site in the crystal lattice. The conduction band minimum falls at the Γ point, because at that point in k-space, translational symmetry dictates that the net interaction between oxygen 2p π orbitals and the Ta t2g orbitals is non-bonding. (94) As the tilt increases at Γ, the Ta5d – O2p anti-

93 bonding orbital overlap term, S, increases. This localizes the electrons in the orbital and constricts the Ta t2g based conduction band (discussed in a proceeding section) eﬀectively making orbitals that were non-bonding incrementally more anti-bonding in character with respect to octahedral tilt. A subtle conclusion one can draw from this data is that the energetics driving orbital overlap are less than the need to minimize charge repulsion. More succinctly, the M-X orbital overlap at Γ due to tilting results in band gap increases after account is made for Ta-O/N bond distances or f-orbital eﬀects.

For instance, the tilt angles in CaTaO2N are similar in magnitude to PrTaN2O but the band gaps diﬀer by ˜0.6 eV. The anion ratio however in these compounds goes from

2O:1N to 1O:2N. This changes the Ta-X 6 bond distances and also adds f-electrons.

Additionally, the fact that RETaN2O compounds all have similar band gaps yet go 0 1 2 from f – f – f suggests that the 4f orbitals are not important for Eg.

3.4 A Model System: Lattice Energies for Ordering Types

in LaTaN2O

One of the limitations of Density Functional Theory (DFT) calculations is that band structure diagrams produced yield an arbitrary energy axis with the Fermi level set at zero. Band positions are generated relative to that and can be compared within the realm of the calculation for a given compound. Absolute correlation of bands (conduction, valence, core) from one compound to another within a series requires stringent control of experimental parameters. Nonetheless, trends can be identified across the series that do not necessitate knowledge of the absolute positions of the bands, e.g. changes in band width or gap. Creating a model that can normalize the differences in space groups between each system is desired. Success in this task is challenging because disordered anions are difficult to model computationally. As stated previously, cis configurations are energetically more favorable that trans configurations. Experimental evidence for short range order helps skirt this issue. Design of our cis configurations was assisted by a starting model provided by the reported, calculated structure for CaTaO2N. (18, 56) This model which incorporates both tilting modes and out-of-center displacements was determined to be the most thermodynamically favorable space group at ground state. To evaluate whether this

94 model still applies to –N2O perovskites, LaTaN2O was used because it provides the least complex calculations. That is, no f-electrons need to be accounted for, which would be necessary for the cerium and praseodymium cases. Lanthanum, therefore, was used in the initial studies.

The crystallographic information file for the CaTaO2N compound was imported to Materials Studio 5.5 (95) and adjusted accordingly. Symmetry of the crystal was reduced to P1, lanthanum replaced calcium, and the nitrogen/oxygen ratio was balanced. The initial unit cell was maintained prior to optimization because the ionic radii of calcium and lanthanum are similar. Different cis arrangements were created by moving the locations of the oxygens on the two Ta-N4O2 octahedron available in the unit cell. When an acceptable configuration was found, symmetry was imposed. There are 3 distinct lineages that become apparent: disorder, cis order, and trans order. These pairings have been proposed by extending work done on group theoretical analysis of tilting in perovskites (49, 52) to anion ordering. To understand the differences between all of the different arrangements, Figure 3.5, was created. Within each lineage there can be equatorial or axial arrangements with respect to a given tilting plane and/or coordinate axis. Currently, the only reported assignment for the LaTaN2O is in the C 2/m space group and was arrived at by Rietveld analysis of neutron powder diffraction (NPD) data. (20) This assignment designates a trans equatorial arrangement of the oxygen relative to the b−b− plane however no computational analysis of the lattice energy of the chosen group was done. This work will show the relative stability of cis and trans ordering phenomena in the LaTaN2O subgroups of the Imma parent. The disordered model of Imma however, requiring an adequate superstructure with sufficient randomness and not afforded easily by DFT methods, was not attempted. DFT related calculation were executed using Cambridge Serial Total Energy Pack- age (CASTEP), a subprogram of the Materials Studio suite. A norm-conserving non- local pseudo-potential generated by the Kerker scheme with an energy cutoff of 400 eV was utilized. An energy charge per atom convergence criterion of 0.00002 eV, a root- mean-square displacement of 0.001 A˚, and a root-mean-square residual force on movable atoms of 0.05 eV/ A˚ was chosen. Electron exchange interactions and correlation were developed by Perdew and Wang via a generalized gradient approximation (PW91). Each structure was geometry optimized using the Broyden-Fletcher-Goldfarb-Shanno

95 Figure 3.5: Space group assignments based on possible LaTaN2O anion configurations - Red box = legend scheme, which enabled optimization of both the lattice parameters and the atomic coordinates. These geometry optimized structure results are compiled in APPENDIX B 3.5.2 but will be discussed here. How the computer algorithm refines the atomic positions can shed light on what displacements are most favorable under the symmetry conditions imposed. The most notable examples are usually found when an atom is allowed to move freely on a general position but drifts towards a special position. This can help confirm a higher symmetry as well as what type of operations may need to be applied to the system. Geometry optimized C 2/m provides an example of this. The lanthanum is placed on the 4i Wyckoff site which has coordinates (x,0,z). When optimized to the positions that generate the most stable structure, it places La at (0.749(1), 0, 0.02(3)). This indicates that a special position at (3/4, 0, 0), and hence a higher symmetry space group assignment might provide a better fit while also increasing the degrees of freedom available (decreasing the number of variables in use) in the calculation. The aim of this work is to determine which atomic arrangement is most favorable for the lattice to adopt. CASTEP optimization provides a lattice enthalpy and band gap for a given atomic arrangement. To achieve the lowest enthalpy or lattice energy, the atoms should be placed in a crystal in such a manner that the bonding interactions are maximized and the anti-bonding overlap is minimized. This provides a stable structure.

96 However, in semiconductor band structure calculations using density functional theory, there is a well know problem: the program will underestimate the band gap. (96) This is due to the exchange-correlation potential not properly accounting for the energetics of the conduction and valence band. When comparing polymorphs it is generally found that the sturcture that maximizes the band gap is the most stable. (97, 98, 99) Figure 3.6 shows these data for the compounds in this study which are ordered by space group on the x-axis. Z varies per structure so enthalpy values are scaled to normalize the data. The space groups are ordered by decreasing lattice enthalpy. The two highest, Imma and C 2/m are both trans conﬁgurations while the lowest three,

I 212121, Ima2, and P1, all hail from cis groups. This brings about an important point: cis configurations are energetically more stable than trans configurations. Similarly for the band gaps, the trans models all have band gaps that smaller than the cis models, reinforcing the idea that cis-configuration is more stable. Accounting for lattice energy and band gap alone is not enough to determine the theoretically most stable structure. An analysis of the number variables in the cell parameter must occur. It can be shown in Figure 3.7, that increasing the number of variables used in the determination of cell parameters lowers the total energy. This has limitations though. There are diminishing returns when adding variables; the band gap given by the P1 group is equivalent to the Ima2 but is achieved at a cost of 3x more variables. For Ima2, the 11 variables used presents the minimum number of variables necessary in the cis geometry to fully model all the components in the system.

Therefore, if lattice energy, the number of cell parameters, and the calculated Eg are then taken into consideration, Ima2 appears to be the most favorable assignment. The implications of this when paired with the NPD data presented earlier in this work is that a trans model is not possible by NPD or by calculations. The long range order of the anions in RETaN2O is shown to be disordered but calculations show that a cis model is favored. Therefore, local cis octahedron are present but do not suﬃciently order on a length that can be realized by diﬀraction techniques. Partial density of states (PDOS) and band structure plots generated by CASTEP for each space group are listed in APPENDIX C 3.5.2 but are explained below. All of the PDOS plots show similar orbital contributions associated with the conduction band (d and p orbitals) and the valence band (p orbitals). These are the tantalum 5d – O/N 2p anti-bonding orbitals in the CB and O/N 2p non-bonding orbitals in the VB.

97 Figure 3.6: Lattice energy and band gap in determining the space group -

Red line is the calculated band gaps for LaTaN2O in speciﬁed space groups. Blue line corresponds to the lattice enthalpy.

98 Figure 3.7: Impact of the number of cell parameter variables on band gap -

Red line is the calculated band gaps for LaTaN2O in speciﬁed space groups. Green line corresponds to the number of variables used in the cell parameters.

99 In general for these calculations the conduction band minimum does not have a large density of states population, but increases with energy, while the valence band is the opposite and has a large density of states population at the valence band maximum that persists at lower energies. Electrons in the valence band are therefore localized, while the conduction band electrons are more delocalized. Ima2 is related to the the space group determined by NPD (Imma). This work shows a course of action for modeling this class of compounds by DFT: (1) Use the space group assignment by XRD and or NPD as a starting model. (2) Account for local octahedra geometry, out-of-center distortions, and tiltings. This process can be aided by use of Figure 2.12 and Figure 2.10 (3) Choose the group that has optimal agreement between cell parameters (least) / degrees of freedom (most), calculated band gap (largest), and lattice energy (lowest).

3.4.1 Theory vs. Experiment

As was just discussed, Ima2 was selected as the imminent anion ordering pattern based on a variety of metrics. A visual representation of this system has been presented previously but can be referenced at Figure 2.14. Geometry optimized data for the atomic parameters of this compound are present here, Table B.4, as well as in Appendix 3.5.2 with all the other model systems. When compared to the lattice parameters of the NPD determined Imma system the values are inﬂated by about 3, 4, and 5 % for the short, medium and long axes, respectively.

Space group Ima2 SG# 46 Unit cell (A˚) a = 5.8616 b = 5.9361 c = 8.4332 (◦) α = 90 β = 90 γ = 90 Atom Site x y z La 4b 0.25 0.2344 0.6579 Ta 4b 0.25 0.7597 0.8999 N 4b 0.25 0.6549 0.6730 N 4a 0.5 0.5 0.3718 O 4a 0 0.5 0.9808

Table 3.2: CASTEP Geometry optimized parameters for LaTaN2O in the Ima2 structure

100 From this atomic position data a slew of bond parameters can be determined, which are displayed in Table 3.3. Trends herein do not match experiment. Because this is an ordered model individual Ta-N and Ta-O bond distances are generated, showing that within Ta-X 6 octahedra bonding between Ta-N forms three short followed by one long bond. The three short bonds give values that are approximately equivalent to the one experimental perovskite nitride, ThTaN3. The two Ta-O bonds are intermediate to the short and long Ta-N values, though bond length far exceeds the reported value of a

Ta-O bond length in a perovskite Ta-O6 octahedron. These discrepancies carry over into the La-X and Ta-X -Ta bond angles. The angles calculated deviate far from what is observed in these systems experimentally (nominally, 160 ◦).

Bond type Ta-X bond distance (A˚) La-X bond distance (A˚) Ta-X-Ta (◦) Ta-N 2.012 2.499 149.5 2x 2.058 2x 2.708 166.7 2.358 2x 3.006 2x 3.233 3.442 Ta-O 2x 2.233 2x 2.512 144.4 2x 3.471

Table 3.3: Geometry optimized bond parameters for Ima2 LaTaN2O

In an attempt to yield values that better align with experimental data, the CASTEP geometry optimized positions in the Ima2 system were input to GSAS and were subjected to simultaneous Rietveld refinement of both banks using the data generated by the neutron diffraction experiment on LaTaN2O. Identical procedure as previous was enlisted with the lattice parameter and atomic position results compiled in Table 3.4. The lattice parameters that were suggested by the geometry optimized CASTEP model were tapered back through the iterative Rietveld process and now maintain similar con- 2 stants to those suggested by the disordered Imma model. The Rp,Rwp, and χ values are higher than those obtained for the disordered Imma space group model, however, and is explained by examination of the fits themselves. The Rietveld refinement fits in the Ima2 space group using the NPD data are displayed for bank 2 in Figure 3.8 and bank 5 in Figure 3.9. The calculated pattern

101 Compound LaTaN2O Space group Ima2 a (A˚) 5.7089(2) b (A˚) 5.7388(2) c (A˚) 8.0597(2) V(A˚3) 264.05(2)

Rp (%) 4.26

Rwp (%) 3.35 χ2 11.64

Atomic Position(s) 2 atom site x y z occ Uiso (A˚ ) Ta 4b 0.25 0.749(1) 0.9144(6) 1 .0058(2) La 4b 0.25 0.2484(5) 0.6698(4) 1 .0025(3) N(1) 4b 0.25 0.6832(3) 0.6708(6) 1 .0142(4) N(2) 4a 0.5 0.5 0.3770(2) 1 .0136(9) O 4a 0 0.5 -0.0555(5) 1 .011(1)

Table 3.4: Atomic positions generated for Ima2 LaTaN2O as obtained from Reitveld reﬁnements using NPD data

102 fits well in the low d-spacing regions but poorly at higher values. Specifically, the calculated pattern for bank 5 generates a peak at 4.7 A˚ in d-space that is not present in the experimental data and could not be “refined” out. The fact that the fit is good for some regions is, at least partially, a result of the model for the local cis environment and tilting order being correctly accounted for. What is lacking is a long range anion order that still remains to be elucidated.

LATAN2OIMA2V2PLAY cycle 135 Hist 1

diff Obs 7 Calc bckgr

3 Intensity

-1

0.5 1 1.5 2 2.5 3 Dspace

Figure 3.8: Geometry optimized Ima2 LaTaN2O which was Reitveld refined versus bank 2 NPD data - Magenta hash marks = indexed Ima2 reflections, baby blue hash marks = indexed V can reflections

The geometry optimized, Rietveld reﬁned Ima2 system generates bond parameters that suﬀer from less extreme data sets than the CASTEP generated data initially discussed in this section. Table 3.5 summarizes this. Ta-N bond distances are more in-line with literature values and have a more coherent range, 2.037 A˚ to 2.102 A˚. The oxide distances decrease to within the reported margins as well. This has implications

103 LATAN2OIMA2V2PLAY cycle 135 Hist 2

8 diff Obs Calc bckgr 7

Intensity 3

-1

2 3 4 5 6 Dspace

Figure 3.9: Geometry optimized Ima2 LaTaN2O which was Reitveld refined versus bank 5 NPD data - Magenta hash marks = indexed Ima2 reflections, baby blue hash marks = indexed V can reflections

104 on the Ta-X -Ta values; they show angles that are observed in the Pnma CeTaN2O and

PrTaN2O compounds reported in this work.

Bond type Ta-X bond distance (A˚) La-X bond distance (A˚) Ta-X-Ta (◦) Ta-N 2.037 2.494 158.4 2x 2.047 2x 2.619 163.0 2.102 2x 2.881 2x 3.112 3.244 Ta-O 2x 2.037 2x 2.713 166.3 2x 3.004

Table 3.5: Bond parameters for geometry optimized Ima2 LaTaN2O that was the Rietveld reﬁned versus NPD data

Shortcomings of the Ima2 model suggest that an additional modifications that need to be added to the course of action outlined at the end of the last section. NPD- DFT tandem structure solution shoud therefore be carried out as follows: (1) Use the space group assignment by XRD and or NPD as a starting model. (2) Account for local octahedra geometry, out-of-center distortions, and tiltings. This process can be aided by use of Figure 2.12 and Figure 2.10 (3) Choose the group that has optimal agreement between cell parameters (least) / degrees of freedom (most), calculated band gap (largest), and lattice energy (lowest). (4) Import modeling solution to Rietveld refinement software and check model (5) repeat until theory and experiment converge Though this structure solution model did not provide the correct solution (yet), this work has generated an excellent framework for the systematic discovery of anion ordering systems. With continued efforts to generate alternative anion ordering models, this algorithm pioneers the process and foundations necessary for solving many more anion ordering systems that are as of yet, undetermined or undiscovered.

105 3.5 Calculation of Electronic Structure for the ATaO2N

and RETaN2O Systems Where (A = Ba, Sr, Ca and RE = Pr)

Explanation of the electronic structure is dependent on knowledge of the underlying atomic structural features that each analogue has. Following the methodology stated above, the remainder of the oxide nitride compounds were generated and calculated. Each compound started in the space group assigned by XRD or NPD, symmetry was reduced to P1, atoms were arranged into a cis fashion, the most likely out of center displacement direction was input, and symmetry was imposed. To arrange anions in a cis manner around the tantalum octahedron, occasionally the unit cell centering had to be adjusted. Similarly, the initial out-of-center distortion was assumed to be towards nitrogen, due to (an assumed) more covalent interaction between Ta and N, so that when the space group was assigned it would allow for the correct distortions. Of the generated structures, (depicted earlier in Figure 2.12) the structure with the lowest lattice enthalpy, and subsequently largest band gap was chosen. Table 3.6 summarizes the new assignments used to model the atom arrangements in DFT calculations. After a geometry optimization was performed, band structure and density of states diagrams were generated.

Compound XRD CASTEP CASTEP Ordering

BaTaO2N Pm-3m Pmma c

SrTaO2N I 4/mcm Pbcm c |

CaTaO2N Pnma Pmn21 c | b

LaTaN2O Imma Ima2 c | b

PrTaN2O Pnma Pmn21 c | b

Table 3.6: Space group transitions necessary for DFT calculation. XRD to CASTEP

The outcomes of the band structure diagram calculations provide insight on three characteristics: conduction band narrowing, f-orbital contributions, and valence band positions. The phenomena that arise within the series explain the physical, photocatalytic, and photophysical properties of these materials. Each compound is introduced below as it is relevant to the discussion. For a complete survey, the geometry optimized

106 atomic positions and lattice parameters as well as the band structure and density of states plots are compiled in APPENDIX D 3.5.2.

3.5.1 Conduction and Valence Band Trends

The tantalum oxide nitride series composed of A-site alkali-earths have the same electronic configuration down the group, s0d0. By holding configuration effects constant, properties due to ionic radii, and in-turn, octahedral tilting can be examined. The 12-coordinate size of the cations increases going down the group: Ca < Sr < Ba. This is further exemplified (and supplemented with M-X-M angles) for the remainder of the series by referencing the previously discussed, Table 2.23. The most important correlation is: as ionic radius decreases, the M-X-M angle decreases. The Goldschmidt tolerance factor discussed earlier, is tied to this, and determines how much tilting of the

Ta-X 6 octahedra is necessary to optimize bonding with the A-site cation. This tilting does not come without a cost, however, and drastically aﬀects the bonding (or rather, the anti-bonding) interactions at the conduction band minimum (CBM). In order to fully evaluate these electronic interactions it is best to examine the band structure diagrams of the CaTaO2N(Pmn21), SrTaO2N(Pbcm), and BaTaO2N (Pmma) models. Meticulous collection of data obtains the width of the lowest lying conduction band; attention was given to noting the Brillioun zone contributing to each maximum and minimum. The spoils of this exploration are divulged in Table 3.7. Quite simply, the CBM Brillouin zone for each analogue is the Γ point. This corresponds to a Ta 5d – anion 2p anti-bonding interaction in simple oxide perovskites. (94) The tantalum perovskite oxide nitride case is similar. (91) The calculated PDOS plots show that the conduction band is dominated by d and p character which match this model. In addition, the widths are shown in the table to decrease successively where Ba > Sr > Ca. This can be explained by octahedral tilting.

As the TaX6 octahedra tilt the d-orbitals begin to interact more with the 2p anion orbitals, Figure 3.10. Increased overlap for anti-bonding orbitals increases their energy, pushing the CBM up, which results in an increased band gap. This narrowing of the conduction band from Ba → Sr → Ca also results in a more localized electron upon excitation. These calculations are relative, not absolute, but still enable the identiﬁcation of trends within a set.

107 Compound Bottom of lowest Top of lowest Width (eV) O/N2p-Ta5d AB band O/N2p-Ta5d AB band (E-Ef ) (E-Ef )

BaTaO2N 0.379 2.979 2.6

SrTaO2N 0.734 2.207 1.5

CaTaO2N 1.487 2.685 1.2

LaTaN2O 0.995 2.864 1.9

PrTaN2O 0.070 0.824 0.75

Table 3.7: Position of the lowest lying O/N 2p – Ta 5d AB band relative to the Fermi

level for ATaO2N(A = Ba, Sr, Ca) and RETaN2O(RE = La, Pr). f-orbital contributions

ignored. Ef is the Fermi level; AB is anti-bonding.

Figure 3.10: Conduction band narrowing due to octahedral tilting - As tilting increases, conduction band width decreases due to increased Γ 5d Ta - 2p anion anti- bonding interaction

108 Comparison of the calculated band gaps from CASTEP to experimentally determined UV-visible diﬀuse reﬂectance (DR) in Figure 3.11, demonstrates this. Even though the calculated band gap for each compound is approximately 50 % of DR mea- surements, it still follows the trend of an increasing gap as tilts are introduced.

Figure 3.11: Band gaps determined by UV-Vis Diﬀuse Reﬂectance and CASTEP - Energy scale is relative

Lanthanoids can be included in this trend but f-orbital eﬀects must be taken into account and make interpretation complicated. The rare-earth conduction band positions vary by the number of f-electrons present in the system. In the RETaO4 (RE = La, Ce, Pr, Nd, Sm) system, band structure calculations yield f orbital contributions in the conduction band for the lanthanum case. For the cerium and praseodymium cases they lie in the band gap plus the conduction band. (100) Furthermore, a study on the RE 2Ti2O7 series suggests that the (early) f-orbitals are partially ﬁlled (as op- posed to occupied/unoccupied) and therefore pin the Fermi level at the 4f band in

109 the gap. (101) Regardless, these f-orbital energy assignments are questionable because DFT methods for the selection of a correct U parameter, on-site electron-electron repulsion, is property dependent. (102) CASTEP results for the LaTaN2O, do not show signiﬁcant f-character near the conduction band minimum or valence band maximum. 2 +3 PrTaN2O, however, containing an f Pr , has partially ﬁlled f-orbitals that are calculated to be just below the empty Ta 5d – anion 2p anti-bonding bands. The valence band is pushed up by the addition of the f-orbitals in this compound. This narrows the band gap considerably (to 0.072 eV) and complicates the analysis of the conduction band. Experimentally, though, the UV Vis determined band gaps of LaTaN2O and

PrTaN2O are similar, approximately 2 eV. Accounting for this, the f-orbitals in the praseodymium analog may actually lie lower in the gap than calculated, and thus are not included in band gap calculations. The values reported for the conduction band maximum and minimum of PrTaN2O in Table 3.7 are inclusive of only the s, p, and d orbital contributions. Within the –N2O system, tolerance factor decreases and increases in tilting going from La to Pr, cause for less dispersion of the lowest lying Ta 5d – O/N 2p anti-bonding band. The band narrowing trend is also observed by the anion 2p non-bonding bands, which make up the valence band maximum for the alkali-earth tantalum perovskites. The rare-earth analogues, speciﬁcally praseodymium, have f-orbitals that become involved. Presented in Table 3.8, the highest lying O/N 2p non-bonding widths show that as the ionic radii decreases (also: the M-X-M angle), the band width decreases. The non-bonding O/N 2p orbital overlap is increasingly localized. Again going from the alkali earth to the rare earth compounds require consideration of the anion stoichiometry changing from 2O:1N to N2:1O and f-orbital eﬀects. The stoichiometry changes, increasing the amount of nitrogen in the system increases the density of states at the valence band maximum, due to lower electronegativity on nitrogen versus oxygen.

3.5.2 Valence Band Positions

Conduction band trends and the eﬀects of f-orbitals on the band structure have been evaluated, but what can be learned about the valence band trends? As stated ad in-

ﬁnitum in the literature, the valence band maximum in simple ABO3 perovksites is composed of the oxide 2p non-bonding orbitals. In this work and these compounds, however, the valence band is made up of O/N 2p non-bonding bands. Because the

110 Compound Top of highest Bottom of highest Width (eV) O/N 2p NB band O/N 2p NB band (E-Ef ) (E-Ef )

BaTaO2N 0 -1.55 1.6

SrTaO2N 0 -1.457 1.5

CaTaO2N 0 -0.891 0.9

LaTaN2O 0 -0.707 0.7

PrTaN2O -1.283 -1.561 0.3

Table 3.8: Position of the highest lying O/N 2p non-bonding band relative to the Fermi

level for ATaO2N(A = Ba, Sr, Ca) and RETaN2O(RE = La, Pr). Ef is the Fermi level; NB is non-bonding. nitrogen is less electronegative it dominates the character at the band edge, which is confirmed by atom specific PDOS plots for nitrogen and oxygen. The Ta-N distances are therefore are the most important factor that determines VB position. They are composed in Table 3.9 and show the bond distances for each class of bond about the TaX 6 octahedron as well as the Ta-X -Ta bond angle. The outcome should be ascertained in two parts: compounds that have anion stoichiometry –O2N and –N2O compounds. For the former, the cis nitrogen yield the shortest bonds versus the other coordinated anions. Opposite the nitrogen (i.e., trans to the N), the oxygen are elongated and have the longest bonds. The oxygen not in that plane of atoms has an intermediate distance versus the rest. These effects are conserved for the –N2O compounds as well: Nitrogen that is trans to the oxygen has the shortest bonds, while the cis oxygen has elongated bonds. The non-planar nitrogen is intermediate to those values. The octahehra in these compounds are irregular and match observation for NPD data. However, the bond lengths that are given by CASTEP geometry calculations give, on average, oxygen distances that are longer that nitrogen. This is contrary to the lengths observed when comparing tantalum oxide perovskites with tantalum nitride perovskites. This is phenomena explained in some detail by Dronskowski et. al. (56) but also has to do with lack of well defined ionic radii data for the nitride ion. Accounting for these two phenomena then, enables discussion of the topic at hand: explaining the valence band position changes within the series of compound examined. Calculated bond lengths for each compound shows average Ta-N distance that increases:

111 Compound Bond type Ta-X bond distance Ta-X -Ta (◦)

CaTaO2N Ta-O 2.049 143.3 2.068 Ta-O (trans to N) 2.064 148.6 2.251 Ta-N 2.067 154.1 1.940

SrTaO2N Ta-O 2x 2.039 160.7 Ta-O (trans to N) 2.184 156.6 2.191 Ta-N 2.023 160.6 2.022

BaTaO2N Ta-O 2x 2.055 166.0 Ta-O (trans to N) 2x 2.218 180 Ta-N 2x 2.040 180

LaTaN2O Ta-N 2.012 149.5 2.358 Ta-N (trans to O) 2x 2.058 166.7 Ta-O 2x 2.233 144.4

PrTaN2O Ta-N 2.113 142.9 2.133 Ta-N (trans to O) 2.069 143.9 2.072 Ta-O 2.235 143.3 2.216

Table 3.9: Tantalum-anion bond distance across the series. Calculated values from CASTEP geometry optimized models

112 Ca (2.003 A˚) < Sr (2.022 A˚) < Ba (2.039 A˚) < Pr (2.097 A˚) < La (2.122 A˚). Ta-O average bond distances are as follows: Ca (2.108 A˚) < Ba (2.096 A˚) < Sr (2.113 A˚) < Pr (2.225 A˚) < La (2.233 A˚). As is shown from these series, the values increment for each atom. The two main effects going from –O2N to –N2O are, both Ta-N and Ta-O bond distance increases. Part of these distance increases have to do with the increased nitrogen ratio in the –N2O compounds and hence larger ionic radii. The remaining effect and probably most notable is how nitrogen causes the destabilization of the Ta-O bond via a the structural trans-effect. Though this is most common in square planar compounds it is also well observed in octahedral complexes. (103) The labilization of the oxygen becomes even more pronounced as more nitrogen is added, going from the –O2N to the –N2O case. As the bond lengths comprising the TaX 6 octahedron increase, the anion-anion non-bonding overlap decreases causing a lower energy interaction, which is conveyed by Figure 3.12. The implications of these results on the electronic structure can be understood in this way: lower energy non bonding interaction directly yields a VBM with lower energy.

Figure 3.12: 2p Anion non-bonding interaction due to Ta-X bond distance - Going from Ca to La increases the total bond length

113 Compound Eg

BaTaO2N 0.38

SrTaO2N 0.73

CaTaO2N 1.49

LaTaN2O 1.00

PrTaN2O 1.35

Table 3.10: Enengy separation between the O/N 2p non-bonding band and the Ta 5d – O/N 2p anti-bonding band

114 APPENDIX A: KUBELKA-MONK TRANSFORMED UV-VIS PLOTS OF OXIDE NITRIDES PREPARED BY DIFFERENT SYNTHESIS ROUTES

115 Figure A.1: CaTaO2N diffuse reflectance prepared by different methods - aa = acetic acid co-precipitation, ss = solid-state, cl = methanol co-precipitation

116 Figure A.2: SrTaO2N diffuse reflectance prepared by different methods - aa = acetic acid co-precipitation, ss = solid-state, cl = methanol co-precipitation

117 Figure A.3: LaTaN2O diffuse reflectance prepared by different methods - aa = acetic acid co-precipitation, ss = solid-state, cl = methanol co-precipitation

118 Figure A.4: PrTaN2O diffuse reflectance prepared by different methods - aa = acetic acid co-precipitation, ss = solid-state, cl = methanol co-precipitation

119 APPENDIX B: GEOMETRY OPTIMIZED STRUCTURES FOR A VARIETY OF LaTaN2O MODELS GENERATED IN CASTEP

Space group Imma SG# 74 Unit cell (A˚) a = 8.2523 b = 5.9151 c = 5.9325 (◦) α = 90 β = 90 γ = 90 Atom Site x y z La 4e 0 0.75 0.7665 Ta 4d 0.75 0.75 0.25 N 8f 0.6971 0.5 0.5 O 4e 0 0.75 0.3485

Table B.1: CASTEP Geometry optimized parameters for LaTaN2O in the Imma structure

120 Space group C 2/m SG# 12 Unit cell (A˚) a = 5.8234 b = 5.8234 c = 5.8994 (◦) α = 119.3 β = 119.3 γ = 90.1 Atom Site x y z La 4i 0.7490 0.5 0.0200 Ta 4f 0.25 0.25 0.5 N 4i 0.1828 0.5 0.4260 N 4g 0 0.7801 0 O 4h 0 0.7960 0.5

Table B.2: CASTEP Geometry optimized parameters for LaTaN2O in the C 2/m structure

Space group P1 SG# 1 Unit cell (A˚) a = 5.8905 b = 5.8911 c = 5.9024 (◦) α = 119.5297 β = 60.0987 γ = 89.7785 Atom Site x y z La 1a 0.7615 0.7555 0.5025 La 1a 0.2386 0.2313 0.4985 Ta 1a 0.0207 0.9767 0.9903 Ta 1a 0.4869 0.4788 0.9950 N 1a 0.2211 0.6629 0.9424 N 1a 0.3123 0.1871 0.9935 N 1a 0.2073 0.7930 0.5018 N 1a 0.7914 0.2259 0.5015 O 1a 0.7811 0.3563 0.0632 O 1a 0.6791 0.8324 0.0112

Table B.3: CASTEP Geometry optimized parameters for LaTaN2O in the P1 structure

121 Space group Ima2 SG# 46 Unit cell (A˚) a = 5.8616 b = 5.9361 c = 8.4332 (◦) α = 90 β = 90 γ = 90 Atom Site x y z La 4b 0.25 0.2344 0.6579 Ta 4b 0.25 0.7597 0.8999 N 4b 0.25 0.6549 0.6730 N 4a 0.5 0.5 0.3718 O 4a 0 0.5 0.9808

Table B.4: CASTEP Geometry optimized parameters for LaTaN2O in the Ima2 structure

Space group I 212121 SG# 24 Unit cell (A˚) a = 8.286 b = 5.906 c = 5.9527 (◦) α = 90 β = 90 γ = 90 Atom Site x y z La 4c 0.5 0.75 0.5115 Ta 4b 0.25 0.7694 0 N 4c 0.5 0.75 0.0907 N 4a 0.2955 0 0.75 O 4a 0.1896 0.5 0.25

Table B.5: CASTEP Geometry optimized parameters for LaTaN2O in the I 212121 structure

122 APPENDIX C: ELECTRONIC BAND STRUCTURES AND PARTIAL DENSITY OF STATES PLOTS FOR A

VARIETY OF LaTaN2O MODELS GENERATED IN CASTEP

123 Figure C.1: LaTaN2O band structure and partial density of states for Imma - Top = band structure, bottom = partial density of states

124 Figure C.2: LaTaN2O band structure and partial density of states for C 2/m - Top = band structure, bottom = partial density of states

125 Figure C.3: LaTaN2O band structure and partial density of states for P1 - Top = band structure, bottom = partial density of states

126 Figure C.4: LaTaN2O band structure and partial density of states for Ima2 - Top = band structure, bottom = partial density of states

127 Figure C.5: LaTaN2O band structure and partial density of states for I 212121 - Top = band structure, bottom = partial density of states

128 APPENDIX D: CASTEP GENERATED ELECTRONIC AND ATOMIC PARAMETERS FOR ATaO2N AND RETaN2O (A = Ca, Sr, Ba; RE = Pr)

Space group Pmn21 SG# 31 Unit cell (A˚) a = 7.89 b = 5.78 c = 5.61 (◦) α = 90 β = 90 γ = 90 Atom Site x y z Ca 2a 0 0.2175 0.9836 Ca 2a 0 0.6878 0.5144 Ta 4b 0.2535 0.2550 0.4831 N 4b 0.3000 0.0337 0.2142 O 4b 0.2009 0.4607 0.8016 O 2a 0 0.2873 0.4062 O 2a 0 0.7568 0.0978

Table D.1: CASTEP geometry optimized parameters for CaTaO2N in the Pmn21 structure

129 Space group Pbcm SG# 57 Unit cell (A˚) a = 5.86 b = 5.83 c = 8.04 (◦) α = 90 β = 90 γ = 90 Atom Site x y z Sr 4c 0.7261 0.25 0.5 Ta 4d 0.7679 0.7481 0.75 N 4d 0.0425 0.5419 0.25 O 4d 0.448 0.9465 0.25 O 4c 0.2904 0.25 0.5

Table D.2: CASTEP geometry optimized parameters for SrTaO2N in the Pbcm structure

Space group Pmma SG# 51 Unit cell (A˚) a = 6.01 b = 4.08 c = 6.02 (◦) α = 90 β = 90 γ = 90 Atom Site x y z Ba 2e 0.25 0 0.2709 Ta 2f 0.75 0.5 0.229 N 2b 0 0.5 0 O 2d 0 0.5 0.5 O 2e 0.25 0 0.7293

Table D.3: CASTEP geometry optimized parameters for BaTaO2N in the Pmma structure

130 Space group Pmn21 SG# 31 Unit cell (A˚) a = 8.1242 b = 5.8178 c = 5.7182 (◦) α = 90 β = 90 γ = 90 Atom Site x y z Pr 2a 0 0.1925 0.9906 Pr 2a 0 0.6994 0.4939 Ta 4b 0.2511 0.2674 0.5021 N 2a 0 0.2760 0.4060 N 2a 0 0.7939 0.1033 N 4b 0.2026 0.4358 0.8139 O 4b 0.2974 0.0692 0.1777

Table D.4: CASTEP geometry optimized parameters for PrTaN2O in the Pmn21 structure

131 Figure D.1: CaTaO2N band structure and partial density of states for Pmn21 - Top = band structure, bottom = partial density of states

132 Figure D.2: SrTaO2N band structure and partial density of states for Pbcm - Top = band structure, bottom = partial density of states

133 Figure D.3: BaTaO2N band structure and partial density of states for Pmma - Top = band structure, bottom = partial density of states

134 Figure D.4: PrTaN2O band structure and partial density of states for Pmn21 - Top = band structure, bottom = partial density of states

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140 Declaration

I herewith declare that I have produced this paper without the prohibited assistance of third parties and without making use of aids other than those speciﬁed; notions taken over directly or indirectly from other sources have been identiﬁed as such. This paper has not previously been presented in identical or similar form to any other American or foreign examination board.

The thesis work was conducted from September 2008 to March 2012 under the supervision of PI, Dr. Patrick Woodward, at Ohio State University.

Columbus, Ohio, USA