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Effect of Reduction Treatment on Microstructure and Mechanical Properties of Fluorite Oxides

HIDE
 Title Page
 Dedication
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Abstract
 Introduction
 Background
 Materials and experimental...
 Microstructural analysis
 Reduction effects on elastic modulus...
 Reduction effect on fracture properties...
 Conclusions and suggested future...
 References
 Biographical sketch
 

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1 EFFECT OF REDUCTION TREATMENT ON MICROSTRUCTURE AND MECHANICAL PROPERTIES OF FLUORITE OXIDES By YANLI WANG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006

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2 Copyright 2006 by Yanli Wang

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3 To my parents

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4 ACKNOWLEDGMENTS I would like first to thank my a dvisor, Dr. Fereshteh Ebrahimi, who introduced me into this great department and has provided me the most va luable training and support for four years. I am deeply impressed by her attitude to science. I re spect her experience and profound knowledge. I enjoy the way she su ccessfully delivers new inform ation to students and inspires students. The amount of time and energy that Dr. Ebrahimi spent on me was invaluable. My professional life and personal life both have bene fited from the discussions with Dr. Ebrahimi, and I believe it will continue to be beneficial for the rest of life. I am grateful to the opportunity working on this project with Dr. Eric D. Wachsman (my committee member) and Dr. Keith L. Duncan. I thank Dr. Wachsman for his advisement throughout the entire time of this research. His encouragement and his belief in me have helped me build up my confidence during the process of this challenging project I thank Dr. Duncan, from whom I received the most help when I firs t stepped into the field of Solid Oxide Fuel Cell (SOFC). Discussions with Dr. Duncan were extr emely inspiring. His generosity to people and openness to science have made th is research enjoyable. I also thank my committee member Dr. John J. Mecholsky, Jr. for his discussions and suggestions on mechanical properties measurem ent and fractography analysis. Dr. Susan B. Sinnott, Dr. Nagaraj K. Arakere (Department of Mechanical and Aerospace) and Dr. Darryl Butt (my former committee member) are acknowledged fo r their sincere help and participation on my supervisory committee. Discussions with Dr. Simon Phillpot on elastic modulus results were very helpful. I am grateful for the numer ous help from Dr. Gerald (Jerry) Bourne for Nanoindentation, Focused Ion Beam (FIB) and Transmission Electron Microscopy (TEM). I appreciate Dr. Hans J. Seiferts generosity in providing thermodynamic data for ceria. I would like to thank Dr. Juan C. Nino, Dr. Valintine Cracium and Dr. Jacob L. Jones for their

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5 suggestions on material characteriza tion. It has also been a great pleasure to work with Sean R. Bishop and Michael Kesler on this project. I would also like to thank Jung Hun Jang, Kerry Siebein, Eric Lambers and Dr. Luisa Amelia De mpere in Major Analytical Instrumentation Center (MAIC), for their instructions and help in this study. A speci al thanks goes to Dr. Richard G. Connell for always bein g nice, helpful and friendly. I would like to thank Dr. Ebrahimis fo rmer and current group members: Eboni Westbrooke, Juhyun Woo, Nichole Wh itney, Brandon Juran, Luis Forero, Hongqi Li, Peng-nan Wang, Samantha Yeates, Krishna Ganesan, Shadab Siddiqui, Michael Kesl er, Ian Liu, Sankara Tatiparti, Mehash Tanniru, Damian Cupid, and S onalika Goyel for providing the best research environment and being helpful. I thank all the Fuel cell group memb ers (Dr. Wachsmans group), especially Dr. Keith Duncan, Sean R. Bishop, Dr. Heesung Yoon, Dr. Abheshek Jaiswal, Dr. Jiho Yoo, Dr. Gongjing Zhang, and Jin Soo Ahn fo r their help on experimental techniques. My second special acknowledgment goes to all my friends in China, as well as my friends here. Their encouragement a nd support throughout these year s have been priceless. I am really lucky to have my husband, Jun He, with me throughout this journey. His love and support is every reason fo r what I have achieved. I can not pick out any words that can expre ss my gratitude to my mother Yuhua Yu, my father Quandao Wang, my brother Guangjun Wang and my sister in-law Li Zhao, to whom I owe the most. Their love and belief in me has shap ed me into who I am today. I can not image having any of my success without my familys st rong support behind me. I also appreciate the support from my husbands parents during this study. Finally, the financial supported by DOE (D E-FC26-02NT41562) is also acknowledged.

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........8 LIST OF FIGURES................................................................................................................ .........9 ABSTRACT....................................................................................................................... ............14 CHAPTER 1 INTRODUCTION..................................................................................................................16 2 BACKGROUND....................................................................................................................20 2.1 Mechanical Requiremen ts for SOFC Components..........................................................20 2.1.1 Introduction to SOFCs...........................................................................................20 2.1.2 Mechanical Requirements.....................................................................................22 2.2 Introduction to Fluorite Oxides.......................................................................................23 2.2.1 Crystal Structure and Predominant Point Defect...................................................23 2.2.2 Phase Diagram of Ce-O System............................................................................25 2.3.3 Relationship between Lattice Parame ter and Nonstoichiometry in Ceria.............26 2.4 Effect of Defects on Mechan ical Properties of Ceramics................................................27 2.4.1 Elastic Modulus.....................................................................................................27 2.4.2 Effect of Point Defects on Fracture Properties of Ceria-Based Materials.............29 2.4 Fracture of Brittle Materials............................................................................................30 2.4.1 Fracture Mechanics for Brittle Materials..............................................................30 2.4.2 Toughening Mechanisms for Brittle Materials......................................................33 3 MATERIALS AND EXPERIMENTAL PROCEDURES.....................................................44 3.1 Sample Fabrication........................................................................................................ ..44 3.2 Heat Treatment............................................................................................................ ....45 3.3 Mechanical Tests.......................................................................................................... ...48 3.3.1 Elastic Modulus Tests............................................................................................48 3.3.1.1 Nanoindentation test....................................................................................48 3.3.1.2 Four-point-bend test....................................................................................50 3.3.2 Hardness Test........................................................................................................51 3.3.3 Flexural Strength Test...........................................................................................52 3.3.4 Fracture Toughness Test........................................................................................52 3.4 Characterization Techniques...........................................................................................54 4 MICROSTRUCTURAL ANALYSIS....................................................................................68 4.1 Characterization of As-Sintered Materials......................................................................68

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7 4.2 Characterization of Reduced Ceria..................................................................................69 4.2.1 Optical Properties..................................................................................................69 4.2.2 Microcracks Formation.........................................................................................70 4.2.3 Phase Identification...............................................................................................71 4.2.4 Phase Transformation upon Cooling.....................................................................73 4.2.5 Aging Effect..........................................................................................................75 4.3 Phase Transformation of Reduced Ceria at Room Temperature.....................................77 4.3.1 Reduced Ceria Powder..........................................................................................77 4.3.2 Reduced Bulk Ceria...............................................................................................78 4.3.3 Effect of Ambient Environment............................................................................81 4.4 Microstructure of Fully Reoxidized Ceria.......................................................................82 4.5 Degradation of Ordered Ceria Phases in Water...............................................................83 4.6 Summary................................................................................................................... .......85 5 REDUCTION EFFECT S ON ELASTIC MODU LUS AND HARDNESS.........................108 5.1 Reduction Effect on Elastic Modulus............................................................................108 5.1.1 Intrinsic Elastic Modulus.....................................................................................108 5.1.1.1 Evaluation of crystallographic anisotropy.................................................108 5.1.1.2 Effect of oxygen partial pressu re on intrinsic elastic modulus.................110 5.1.1.3 Theoretical analysis...................................................................................111 5.1.1.4 Effect of fine pores....................................................................................115 5.1.2 Bulk Elastic Modulus..........................................................................................116 5.2 Reduction Effects on Hardness......................................................................................118 5.3 Effect of Room Temperature Holding...........................................................................120 5.4 Summary................................................................................................................... .....122 6 REDUCTION EFFECT ON FRACTURE PROPERTIES OF PURE CERIA....................131 6.1 Flexural Strength......................................................................................................... ..131 6.2 Fracture Toughness Test Results...................................................................................132 6.3 Fractographic Analysis..................................................................................................134 6.4 Pore-Crack Interaction...................................................................................................136 6.5 Discussion................................................................................................................ ......137 6.5.1 Strength................................................................................................................137 6.5.2 Fracture Toughness and Toughening Mechanisms for Reduced Ceria...............138 6.5.4 Other Important Factors......................................................................................140 6.6 Summary................................................................................................................... .....141 7 CONCLUSIONS AND SUGGES TED FUTURE WORK...................................................156 7.1 Conclusions............................................................................................................... .....156 7.2 Suggested Future Work.................................................................................................159 LIST OF REFERENCES.............................................................................................................161 BIOGRAPHICAL SKETCH.......................................................................................................168

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8 LIST OF TABLES Table page 3-1 Sample dimensions for mechanical tests...........................................................................58 3-2 Oxygen partial pressure ranges (2OPs) of different gas mixtures......................................58 4-1 Comparison of the XRD data for the as -received ceria powder and the as-sintered ceria sample with JCPDS #43-1002 standard....................................................................87 4-2 Grain sizes and densi ties of the materials..........................................................................87 5-1 Elastic modulus results for heat treatments under different 2OP evaluated by nanoindentation................................................................................................................124 5-2 Effect of reduction in H2 on the intrinsic elastic modulus of two ceria samples with different porosities (with 49 indents each test)................................................................124 5-3 Bulk elastic modulus results fo r heat treatments under different 2OP evaluated by four-point-bend tests........................................................................................................124 5-4 Hardness results for heat treatments under different 2OP evaluated by nanoindentation................................................................................................................125 5-5 Room temperature holding effect on the in trinsic elastic modulus and hardness of a reduced ceria sample (with 49 indents each test).............................................................125 5-6 Room temperature holding effect on th e bulk elastic modulus of reduced ceria samples........................................................................................................................ .....125 6-1 Room temperature flexural strength test results..............................................................143 6-2 Room temperature fracture toughness test results...........................................................143 6-3 Pore-crack interaction for Brazilian disc test samples.....................................................143

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9 LIST OF FIGURES Figure page 2-1 Schematic diagram for the princi ple of a solid oxide fuel cell..........................................38 2-2 Fracture of the electrolyte after the half -cell (nickel/yttria stabilized zirconia (or Ni/YSZ) anode and YSZ electrolye) expe rienced reduction and reoxidation cycles........38 2-3 Schematic drawing of the atomic structure for fluorite oxides..........................................39 2-4 Predicted dependence of oxygen vacancy concentration on oxygen partial pressure (2OP) at 800 oC for pure ceria, GDC (gadolinium doped ceria) and YSZ from theoretical modeling...........................................................................................................39 2-5 Dependence of CO/Ccation atom ration on oxygen partial pressure at 800 oC for Ce0.9Gd0.1O1.95-x..................................................................................................................40 2-6 Themogravimetric measurement results (800 oC) of oxygen vacancy concentration as a function of oxygen partial pressure for pure ceria..........................................................40 2-7 Phase diagram for CeO2-x.[16]...........................................................................................41 2-8 Expansion of ceria versus nonstoichiometric composition at 900 oC................................41 2-9 Fracture toughness of doped ceria materials......................................................................42 2-10 Three basic modes for fracture..........................................................................................42 2-11 Crack deflection process by (A) tilt and (B ) twist [45].....................................................43 2-12 Stress-strain curve (A) and the corr esponding crack resistance curve (B) for a microcrack toughening mechanism...................................................................................43 3-1 Flow chart of the samp le fabrication process....................................................................59 3-2 Schematics of the procedures of achie ving two bending samples before machining from one as-sintered bar.....................................................................................................59 3-3 Schematic of the heat treatment experiments set up..........................................................60 3-4 Temperature-time curve for the heat treatment.................................................................60 3-5 Comparison of Nanoindents with abnormal shapes due to (A) a nearby pore or (B) underneath pore and a successful nanoindent....................................................................61

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10 3-6 (A) A digital image of 810 Material Te st System (810MTS) used for the flexural tests. (B) The details of the fixture setup for four point bending test with one ceria sample and the extensormeter in position. (C) Schematics of the fully articulating four-point-bend fixture.......................................................................................................62 3-7 The load-displacement curve of a steel sample with a cross section of 3.145 mm .145 mm...................................................................................................................... ...63 3-8 Scanning electron microscopic (SEM) image of the Vikers indent at 200 g for an assintered ceria sample..........................................................................................................63 3-9 Geometry of the chevron-notched Brazili an disc samples used in the fracture toughness test................................................................................................................. ....64 3-10 (A) Schematics of an ideal chevron notch and (B) two chevron notches with different dimensions..................................................................................................................... ....64 3-11 Schematics of the unsuccessful chevron notches...............................................................66 3-12 Images of the pure ceria transmission electron microscopic (TEM) samples during the preparation process by focused ion beam (FIB)..........................................................67 4-1 X-ray diffraction pattern (XRD ) of the as sintered ceria...................................................88 4-2 Images to show grain sizes of the materials.......................................................................88 4-3 Color change of ceria samples after heat treatment under various oxygen partial pressure....................................................................................................................... .......89 4-4 Digital image taken after four ceria di scs with a diameter of 26 mm exploded during the reduction at 800 o under and oxygen partial pressure of 8.5-26 atm...........90 4-5 SEM images of ceria sample reduced under 4.5-22 atm (at 800 oC for 15 hours) show large macrocrakcs (~100 m) at the top surface layer.............................................90 4-6 SEM images of the microcracks in the mi ddle of the ceria sample after reduction in 2OP =4.5-22 atm (at 800 oC for 15 hours)......................................................................91 4-7 XRD patterns for ceria samples af ter heat treatmen t (A) in air (2OP =0.21 atm) and (B) in H2/H2O mixture (2OP =4.6-22 atm)......................................................................92 4-8 The (311) XRD peak of pure ceria sample at various depths from the surface, as indicated by the numbers on the cu rves, after heat treatment under 2OP = 4.6-22 atm............................................................................................................................ ..........92 4-9 (A) XRD pattern of ceria after reduction under 7.1-24 atm (800 oC for 15 hours). (B) shows the details of 2 range of 54 to 60 degrees.......................................................93

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11 4-10 Theoretical XRD pattern for ceria w ith 2/3 volume fraction of hexagonal Ce2O3 phase (indicated by arrows) and 1/3 volume fraction of cubic CeO2................................94 4-11 (A) XRD pattern of bulk ceria sample after aging at 500 oC. (B) shows the details of 2 range of 52 to 60 degrees..............................................................................................94 4-12 XRD pattern of powder ceria sample after aging at 500 oC..............................................95 4-13 (A) and (B) are XRD patterns as a functi on of time for the ceria powder that were reduced aged at 500 oC for 30 hours after reduction at 800 oC for 15 hours.....................96 4-14 XRD patterns as a function of time for th e ceria bulk sample that were reduced at 800 oC for 15 hours under oxygen partial pressure of 3.6-22 atm................................97 4-15 (A) shows the XRD patterns as a function of time for the bulk ceria sampler that were reduced at 800 oC for 15 hours and then aged at 500 oC for 30 hours. (B) shows the details of the XRD pattern with 2 range of 53 to 61 degree...........................98 4-16 Comparison of the peak ( 311) and peak (420) for CeO2 powder with a bulk and powder ceria sample after room te mperature phase transformation..................................99 4-17 TEM bright field (BF) image (A) and dark field (DF) image (B) along with the selected area diffraction (SAD) pattern (C ) for the bulk ceria sample reduced under 3.6-22 atm....................................................................................................................100 4-18 XRD pattern of a reduced bulk ceria samp le after the sample was held under dry hydrogen at room temperature for 55 hours....................................................................101 4-19 A digital image (A) and an SEM image (B ) of one fully reoxidized ceria Brazilian disc sample.................................................................................................................... ...102 4-20 Low magnification SEM image (A) of the thermo-etched ceria sample that exploded at 800 oC under 8.5-26 atm. (B) High magnification SEM image of the boxed area in (A).................................................................................................................... ....103 4-21 Digital image of the redu ced ceria sample after hold ing in hydrogen/water vapor environment for 4 days....................................................................................................104 4-22 The (311) and (420) XRD peaks of a reduced ceria sample after holding in hydrogen/water vapor environment for 4 days................................................................104 4-23 (A) Low magnification SEM image of a pi ece of sample from Figure 4-21. (B) High magnification image of the boxed area in (A).................................................................105 4-24 Digital images of a reduced ceria before the surface phase tran sformation. (A) After soaking in water for 12 days and (B) after soaking in water for 17 days........................106 4-25 Digital images of a reduc ed ceria 12 days after the surface phase transformation..........107

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12 4-26 Digital image of an as-sintered ceria after soaking in water for 38 days.........................107 5-1 Nanoindent image on the as-sintered pur e ceria sample (A) and the corresponding load-displacement curve (B)............................................................................................126 5-2 Change of the elastic modulus as a function of oxygen partial pressure.........................126 5-3 Experimental results showing the va riation of normalized elastic modulus ( E/E* ) as a function of oxygen partial pressure for pure ceria and GDC...........................................127 5-4 The normalized elastic modulus ( E/E* ) as a function of the normalized lattice parameter (a/a*) for pure ceria and GDC........................................................................127 5-5 Schematics of the preparation procedur e for samples with different porosities..............128 5-6 SEM images of the microstructure fo r dense surface (A) and the less dense middle part (B)....................................................................................................................... ......128 5-7 Relative elastic modulus ( E/Eair) as a function of oxygen partial pressure for ceria (A), GDC (B) and YSZ (C)..............................................................................................129 5-8 Room temperature hardness as a function of oxygen partial pressure for pure ceria and GDC samples............................................................................................................130 5-9 Mechanism of the reduction treatment e ffect on the hardness of ceria and GDC...........130 6-1 Load-displacement curve for (A) air treated sample(2OP =0.21 atm, ) with a cross section of 2.600 mm.985 mm and that for (B) H2/Ar treated sample (2OP =8.820 atm) with a cross section of 2.615 mm.985 mm......................................................144 6-2 Load-displacement curves for fracture of sa mple (A) directly load ing to fracture after heat treatment in air, (B) with precrack process after heat treat ment in air and (C) with precrack process after heat treatment under 2OP = 4.5-22 atm............................145 6-3 Low magnification SEM images showing th e fracture surface within the chevronnotched section for the sample heat treated (A) in air (2OP =0.21 atm) and (B) in H2/ H2O (2OP =1.5-20 atm). (C) shows a unsuccessful precrack for a sample heat treated under 2OP =1.5-20 atm.....................................................................................146 6-4 (A) Low magnification SEM image of the fracture surface of an as-sintered bending sample. (B) Higher magnification image of the box area in (A) showing the crack initiation site................................................................................................................ .....147 6-5 SEM images of the fracture surface for a bending sample heat treated in air.................148

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13 6-6 SEM images of the fracture surface fo r a bending sample heat treated in H2/H2O/Argon (2OP =8.8-20 atm)................................................................................149 6-7 Comparison of the fracture surface roughne ss for samples heat treated (A) in air (2OP =0.21 atm) and (B) in H2/H2O/Argon (2OP =8.8-20 atm).....................................150 6-8 Comparison of the fracture surface for samples heat treated in air (2OP =0.21 atm) (image A and image B) and in H2/H2O/Argon (2OP =1.5-20 atm) (image C and image D)....................................................................................................................... ....151 6-9 SEM images of the Brazilian disc sample heat treated under H2/H2O (2OP =1.5-20 atm) with KIC=1.27 MPam1/2..........................................................................................152 6-10 The six positions relative to crack su rface for pore-crack interaction analysis...............153 6-11 Typical images taken for pore-crack inte raction evaluation with (A) for air treated sample and (B) for the sample heat treated in 2OP = 4.5-22 atm.................................153 6-12 Schematics of fracture deflection pro cess for the sample with pre-existing microcracks: (A) tilting mechan ism and (B) twisting mechanism..................................154 6-13 SEM images of the fractured surface for a Brizilian disc sample after heat treatment under 2OP =1.5-20 atm show the microstructure di scontinuity and the evidence of the secondary phases (shown with arrows)......................................................................155

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14 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy EFFECT OF REDUCTION TREATMENT ON MICROSTRUCTURE AND MECHANICAL PROPERTIES OF FLUORITE OXIDES By Yanli Wang December 2006 Chair: Fereshteh Ebrahimi Major Department: Materials Science and Engineering Ceria based materials because of their high ionic conductivity at low temperatures are potential candidates as the electrolyte component in the new generation of low temperature solid oxide fuel cells (SOFCs). The effects of ope ration conditions in SOFC s on microstructure and mechanical integrity of ceria-based materials ar e evaluated in this research. Pure ceria and gadolinium doped ceria (GDC) were selected to perform this inve stigation. The state-of-art electrolyte material, yttria-stabilized zirconia (YSZ), was also studied for comparison purposes. The samples were heat treated at 800 oC under various oxygen partial pressures (2OP s) until equilibrium was reached. The defect concentrati ons were conserved to room temperature by fast cooling. The crystal structure a nd the lattice parameter were ev aluated by the x-ray diffraction method. Microstructural evaluati ons and fractographic analyses were conducted using electron microscopy techniques. The in trinsic elastic modulus was ev aluated using nanoindentation techniques. The bulk elastic modul us and fracture strength were measured using the four-pointbend testing method and fracture toughness was evaluated using ch evron-notched Brazilian disc samples loaded under the mode I condition.

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15 The result of this study revealed that micr ocracks were formed during the reduction heat treatment in ceria and GDC when the 2OP was lower than 10-19 atm. It was also found that ceria samples upon cooling experienced phase transforma tion that led to the formation of several ordered pseudo-cubic phases. The intrinsic elastic modulus of both ceria and GDC decreased drastically when heat treated at very low 2OP s while the effect was insignificant in YSZ. These results correlate well with our theoretical modeling. Further analysis suggests that an increas e in the point defect concentration weakens the attractive forces betw een atoms. The degradation of bulk elastic modulus of ceria was more pronounced at low 2OP s due to the presence of microcracks caused by the reduction treatments. The results on fracture properties of ceria show ed that the flexural strength decreased significantl y after reduction in very low 2OP s; however, in contrast, fracture toughness was increased by 30% when the 2OP was decreased to the range of 10-20-22 atm. Fractographic studies showed that the microcra cks developed during re duction treatment are responsible for the decreased strength. In this dissertation, the enhan cement in toughness was explained by crack deflection and microcrack toughening mechanisms.

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16 CHAPTER 1 INTRODUCTION A single solid oxide fuel cell (SOFC) unit is a ceramic multiple layer system which consists of two electrodes (anode and cathode) separated by the el ectrolyte. The components are in close contact with each other a nd the entire cell is exposed to high temperatures with reducing fuel running through the anode si de and air running through the cat hode side. Electric power is generated electrochemically. Presently, yttria-sta bilized zirconia (YSZ) is the state-of-the-art electrolyte material used for SOFCs. Cells based on YSZ have to operate at very high temperatures (700 oC oC) to exhibit sufficient ionic co nductivity [1]. The high operating temperature requires expensive and durable elec trodes, sealing material s and interconnects. Therefore, it has been of great interest to decr ease the operation temperature to a lower level to enable the long-term cell stability and the use of low cost metallic interconnects [2, 3]. However, this low operating temperature increase s the ohmic loss at the solid-state electrolyte and the polarization loss at both electrodes. One possible solu tion to these problems is to identify other alternative metal oxides, such as ceria-based materials, which possess high ionic conductivity at much lower temperatures [4]. Stoichiometric ceria has a cubic fluorite crystal structure. At elevated temperatures and in reducing atmospheres, ceria can deviate from its stoichiome tric composition to an oxygendeficient composition, CeO2-x, by reduction of Ce4+ to Ce3+ without changing its fluorite structure. As the lattice expa nds after reduction [5, 6], the int act fluorite structure provides a relatively open path for higher oxygen ionic conduc tivity, which is the most attractive aspect for low/intermediate temperature a pplication in SOFCs. At 800 oC, ceria can accommodate up to ~14% oxygen vacancies, providing the opportunity to study the effects of large vacancy concentrations on a variety of propert ies of fluorite-structured oxides.

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17 There has been extensive research on the thermo-chemical properties [5, 6], defect structural properties [7-19], oxygen diffusion prope rties [20-22] and electri cal properties [23-32] of ceria based materials because of their app lications as catalysts [33-35], high dielectric capacitors [36, 37] and components of SOFCs and sensors [4, 26-32]. However, there has been limited investigation into mechanical properties of ceria-based materials [38-44]. Mechanical failure is an important design fact or for most applications of these materials. In case of their applications in the field of SOFCs, the main sour ce of mechanical failure is due to the build up of stresses arising from expansion/contrac tion mismatches between components [45]. During the operation of SOFCs, the partial pres sure of oxygen varies across the electrolyte, which induces a gradient of latti ce defects in the mate rial. For fluorite-st ructured oxides, oxygen lattice vacancies are known to be the major s ource of nonstoichiometry at low oxygen partial pressure and high temperature re gion [44, 46]. The lattice expans ion caused by the formation of oxygen vacancy and the associated lower valance Ce3+ for ceria-based materials will lead to the mechanical stress gradient between the reduced surface and the unreduced interior. Atkinson studied this issue [39] theo retically and found that the ma ximum tensile stress caused by nonstoichiometry increases as the oxygen partial pressure decreases, resulting in differential strain across the thickness of th e electrolyte, and for the worst case scenario, cause fracture [3840]. Unfortunately, so far, no e xperimental work in literature has systematically studied the effect of nonstoichiometry cau sed by reduction on mechanical properties of ceria-based materials. Based on the above brief discu ssion, there is a need, to sy stematically study mechanical properties of ceria based materials because of their application in SO FCs. In this dissertation, we chose pure ceria and 10 mol % gadolinium doped ceria for the investigation. Both of these two

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18 materials have fluorite structure. In addition, the most popular electrol yte material, fluoritestructured 8 mol % yttria doped zirconia, is also selected fo r the comparison purpose. The objective of this work was to evaluate the eff ects of oxygen partial pressu re on intrinsic elastic modulus, bulk elastic modulus, hardne ss, strength and fracture toughness. It has been shown theoretica lly that introducing oxygen vaca ncy in ceria significantly decreases the intrinsic elastic modulus owing to the expansion of the Ce-O bond length [43, 44]. We employed nanoindentation technique in this re search to confirm and quantify the effect of oxygen partial pressure on the intr insic elastic modulus of ceria-b ased oxides. Nanoindents can be introduced into single grains, and therefor e, the contribution of pores, grain boundaries and other macroscopic defects on elastic modulus can be minimized. However, nanoindentation is limited to room temperature tests only. In or der to investigate the effect of oxygen vacancy concentration on mechanical properties at room temperature, the samples were equilibrated at 800 oC under various oxygen partial pre ssures and then the point def ects were conserved to room temperature through fast cooling. The microstructure change upon this type of heat treatment was systematically studied as a function of oxygen partial pressure using X-ray diffraction, optical microscope and electron microscopy. In addition to elastic modulus, nanoidentation also provided information regarding th e hardness of the samples. To be consistent with these measurements, the same heat treatment plan wa s applied for all other mechanical property evaluations. The bulk elastic modulus as well as the flexural strength wa s evaluated using fourpoint-bend testing technique. Th e fracture toughness of differen tly heat treated samples was measured using chevron-notched Brazilian discs loaded in mode I. Scanning Electron Microscope (SEM) was utilized to characterize the fracture surfaces. The ultimate goal was to

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19 investigate the effects of the reduction treatm ent process on microstructure and mechanical integrity of ceria-based materials.

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20 CHAPTER 2 BACKGROUND Because this research is focusing on the partic ular application conditions of fluorite oxides in solid oxide fuel cell (SOFC), the fundamental aspects of SOFC are firstly reviewed in this chapter. The related literature s on the fundamentals of point def ect formation and point defect structure in fluorite oxides are summarized. In order to pr ovide basic information about mechanical testing, this chapter will also review the basics of fracture mechanics as well as the toughening mechanisms. Finally, th e effects of point defect on m echanical properties of ceriabased oxides will be reviewed. 2.1 Mechanical Requirements for SOFC Components 2.1.1 Introduction to SOFCs A solid oxide fuel cell (SOFC) is a ceramic multiple layer system working at high temperature using gaseous fuel and oxidant, which electrochemically generates electric power. As SOFCs operate without combustion and movi ng parts, they have many advantages over conventional power-generating systems in terms of efficiency, reliab ility, modularity, fuel flexibility, and environmental friendliness [1, 47] There are many differ ent types of SOFC in terms of cell configuration. Figure 2-1 schematica lly shows a planar type SOFC to explain the operation principle. A single SOFC unit cons ists of two electrode s (anode and cathode) separated by the electrolyte. The cell component s are in close contact with each other and the entire cell is exposed to high te mperatures with reducing fuel running through the anode side and air running through the cathode side. Each of the components carries out a specific electrochemical function. Oxygen combines w ith electrons and becomes oxygen ion at the cathode side. The oxygen ions travel through the electrolyte membrane and combine with the hydrogen on the anode side and create an elec tric current, water and heat. The corresponding

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21 reactions at each electrode are also shown in Fi gure 2-1. The output voltage then comes from the chemical potential difference in terms of oxyge n partial pressure across the electrolyte. Presently yttria-stabilized zirconia (YSZ) is the state-of-the-art electrol yte material used for SOFCs. The basic requirements for the electr olyte include a high ioni c conductivity and no (or minimal) electrical conductivity with low ohmic loss. The electrolyte must also be dense to prevent short-circuiting of the reactive gases and be stable in both reducing and oxidizing atmospheres at operating temperatures ranging from 700 oC to 1000 C. The electrodes should have good electrical conductivit y, proper porosity and long term stability in the operation atmosphere (i.e., reducing atmosphere at the a node size and oxidizing atmosphere at the cathode side). Currently, nickel/yttria-stabilized zirconi a (Ni/YSZ) cermets are chosen as anode material according to these requirements. The state-of-the-a rt cathode material used in conjunction with YSZ electrolytes is lanthanum manganate (LaMnO3), which has similar requirements as the anode. Individual cells produce a maximum voltage of one volt at 800oC when hydrogen and air are used for the gas supply, therefore, in order to generate a reasonable voltage, fuel cells are arranged in series to create c ell stacks providing power to oper ate various devices. The anodes and cathodes of adjacent units are joined togeth er using fully dense doped lanthanum chromite (e.g., La0.8Ca0.2CrO3) interconnects with glass sealing to separate gase s from mixing. In addition to the above basic requirements, matching ther mal expansion coefficients (CTEs) of all the components becomes very important as far as the seal is concerne d. On top of these physical/chemical requirements, fuel cell materi als and components must be cost-effective and compatible with mass-production processes. Cells based on YSZ have to operate at very high temperatures (700 oC-1000 oC) to exhibit sufficient ionic conductivity [1]. The high opera ting temperature requires expensive and durable

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22 electrodes, sealing materials and interconnects. Therefore, it ha s been of great interest to decrease the operation temperature to enable the long-term cell stab ility and the use of low cost metallic interconnects [2, 3]. However, this lo w operating temperature increases the ohmic loss at the solid-state electrolyte a nd the polarization loss at both electrodes. There are two possible solutions for this issue. The first is to optimize the electrodes and make the thickness of electrolyte from 100 m range in conventional electro lyte-supported cells to 5 m in anode supported cells [48-50] to achieve the abov e situation. The second possible solution is to investigate other alternative metal oxides, such as ceria-based materials, which possess high ionic conductivity at much lower temperatures [4]. 2.1.2 Mechanical Requirements Besides the above described ba sic requirements for the SOFC components, the mechanical properties are also important for the reliabl e cell design. The fundamental mechanical requirements can be summarized to be their st ability at the operation conditions and their stability for long term application. It is vital that no damage of the electrolyte layer occur during handling and fabrication of the stacks or duri ng the operation conditions where sudden external impacts or vibrations may exist. Therefore, it requires the components to have good strength and fracture toughness under the severe operation conditi ons. When it comes to long term stability, the cell must withstand a significan t number of thermal cycles wit hout degradation or build-up of internal stresses. If we take creep as an exam ple, a long term creep of the porous electrode may cause failure or degradation of the cell in terms of unwanted de nsification of the electrodes, cracking or delamination of the thin electrolyte layer and da mage to the seals [50]. The main source of mechanical failure due to the build up of stresses arises from expansion/contraction mismatches between compone nts [45]. For example, experimental work on a half cell (Ni/YSZ anode a nd YSZ electrolyte) shows the mechanical failure of the

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23 electrolyte (shown in Figure 2-2) after reduction and re-oxidation cy cles [51]. The tensile stress that caused this fracture comes from the extens ive expansion of the anode due to a Ni to NiO transformation during reoxidation cycle. Therefore, it is necessary and important to study the material mechanical properties for their application in SOFCs. The focus of this wo rk is to investigation the effects of the operating conditions of SOFCs on two fl uorite-structured oxides, ceri a and 10 mol % gadolinium doped ceria (GDC). In addition, the most popular el ectrolyte material, fluor ite-structured 8 mol % yttria doped zirconia (YSZ), is also selected for comparison purposes. 2.2 Introduction to Fluorite Oxides 2.2.1 Crystal Structure and Predominant Point Defect The fluorite oxide structure has a space group of Fm3m, with eight-coordinate cations (large quadrivalent M4+, e.g., Ce4+ Zr4+) and 4-coordinate anions (O2-). In the unit cell the cations occupy the FCC lattice sites, while oxygen atoms are located at eight tetrahedral sites. The unit cell is schematically shown in Figure 2-3, from which we can see that there are two MO2 molecules per unit cell. At high temperatures and under reducing atmospheres (or low oxygen partial pressure, 2OP), the process of creating oxyge n vacancies in the fluorite oxides by exchange of oxygen between the crystal lattice and the gas can be written in Krger-Vink notation as 2 O2e V (gas) O O O. (2-1) The equilibrium constant, rK, for the above reaction can be expressed as ] [ ] ][ [2 / 1 22 O O O rO P e V K. (2-2)

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24 At 800 oC, a typical SOFC operation temperature, rK was found to be ~1072 for pure ceria and GDC by extrapolating the informa tion in reference [52], and for YSZ Kr~1060 referring to K. Sasaki and J. Maier [53]. These values indicat e that less oxygen vacancies are generated in YSZ at a given temperature and for a given oxygen partial pressure. For GDC and YSZ, there are pre-existing oxygen lattice vacancies due to the effect of acceptor doping according to Equations 2-3 and 2-4, respectively. O O Ce CeOV O Gd O Gd3 2' 2 3 22. (2-3) O O Zr ZrOV O Y O Y3 2' 2 3 22. (2-4) K. Duncan et. al. [44, 54] have shown the relationship between OVC and the partial pressure of oxygen for fluorit e-structured oxides as 3 2 2 3 4 1 2 2 1 22 1 O 4 3 O] [ ) (A r O VC P K V P CO (2-5) where, AC is the dopant concentration. From this equation, one can see clearly that oxygen vacancy concentration increases as oxygen partia l pressure decreases. Based on this model, Figure 2-4 shows the predicted variation in the oxygen vacancy concentration as a function of 2OP at 800 C for ceria, GDC and YSZ. Note that the initial oxygen vacancies in GDC and YSZ are due to the pre-existing vacancies caused by ac ceptor doping. It can be seen that at the practical testing temperature and 2OP range (0.21 atm-25 atm), no significant change in the vacancy concentration of YSZ is expected, howev er, ceria and GDC should develop a significant amount of defects when 2OP is lower than 10-17 atm. Because the total number of oxyge n vacancy sites and oxygen atoms in ceria is twice of the number of cerium atoms, rewrit ing Equation 2-5 yields [44]

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25 cation a r cation OC c P K C C3 2 2 3 4 1 2 2 12 1 O 4 32 (2-6) where, OC is the concentration of oxygen atoms and cationC is the concentration of cerium atoms. This models prediction shows a good agreement w ith gravimetrically measured results for GDC (see Figure 2-5) [44, 55]. In the case of ceria, extensive experimental work has been done on the nonsoichiometric measurement [11, 12]. Figure 2-6 shows the representative th eromgravimetric measurement results by two research groups. Comparing Fi gure 2-4 and Figure 2-6, one can see that experimental results indicate that the process of oxygen vacancies formation is gradually slowed down (showing by the convex curvature) at very low oxygen partial pressure (lower than 10-22 atm), but the theoretically mode ling does not predict this effect This discrepancy can be attributed to the theoretical modeling inability to incorporate any structural changes resulting from high oxygen vacancy concentration. 2.2.2 Phase Diagram of Ce-O System At room temperature, there are two very stab le intermediate phases known in Ce-O system, Ce2O3 and CeO2, which have type-A rare earth struct ure [7] and cubic fluorite structures, respectively. Brauer et.al. [13,14] and Bevan [7, 11] detected four more intermediate phases between Ce2O3 and CeO2, a disordered C-type rare-earth -oxide phase stable above 600 oC between CeO1.67 and CeO1.714 a nearly stoichiometric triclinic structured phase Ce7O12 (CeO1.714) stable up to 1023 oC and two rhombohedral st ructured phases at CeO1.812 and CeO1.782. These intermediate compounds are thought to occu r as a result of ordering in the cation and anion sub-lattices. There has been an extensive work thereafter on other intermediate phases of the Ce-O system, but there exist some discrepanc ies [7, 15] in terms of composition and crystal

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26 structure. Investigations including specifi c heat measurement [16], thermogravimetric measurement [11], electromotive force [17], elect ron microscopy [8], neutron diffraction [18] and X-ray diffraction measurements [18, 19] ha ve provided valuable information to understand Ce-O system. Figure 2-7 shows the CeO pha se diagram that is generally accepted by researchers [16]. It is shown that at room temperature a miscibility gap exists between CeO2 and CeO1.818 (Ce11O20), which contract with increasi ng temperature and closes at 685 oC (958K) at a composition of approximately CeO1.918. Above the miscibility gap, ceria can ceria can accommodate up to significant amount of oxygen vacancies without changing of the fluorite structure. 2.3.3 Relationship between Lattice Para meter and Nonstoichiometry in Ceria The lattice parameter of ceria-based material s has been shown to be dependent on dopant concentration and oxygen vacancy concentration crea ted by reduction [5, 6, 9, 56-59]. In case of pure ceria, when oxygen vacancies are introduced at low oxygen partial pressures in to the material, the charge neutrality is restored by creating Ce3+ defects. In case of doped ceria, substitution of Ce4+ with a lower valance cation thr ough acceptor doping causes formation of oxygen vacancies in the lattice. Experimental work [5, 6, 9, 56-59] on ceria-based materials has shown that both of the above pr ocesses result in a lattice expa nsion. The reason for lattice expansion is believed to be the fo rmation of larger ioni c radii of the lower va lance cations [59]. Mogensen [6] has considered ceria with various vacancy concentrations as a simple solid solution of Ce2O3 and CeO2, to apply Vegards rule to the lat tice parameter [60], i.e., that a linear relationship exists between lattic e parameter and the concentrati on of the solute. He found out that for homogeneous ceria sample at r oom temperature, the lattice parameter, a as a function of vacancy concentration, x in CeO2-x should follow

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27 nm x nm a 04612 0 5413 0 (2-7) Figure 2-8 shows the good agreement of this prediction and expe rimental expansion measurement results [5, 6, 58]. 2.4 Effect of Defects on Mechanical Properties of Ceramics 2.4.1 Elastic Modulus Material elastic modulus ( E ) (also known as the Young s Modulus or modulus of elasticity) is an important material property because it is in nature a measure of the stiffness of atomic bonds. The material elastic modulus can be related to inter atomic forces, F and inter atomic potential, enet through [61] 0) ( 1 12 2 0 0 r r netdr e d r dr dF r E (2-8) where, r is the inter atomic distance, and r=ro is the equilibrium distance at 0 K, which is determined as the interatomic distance where the attractive force component is equal to the repulsive force, which point corresponds to the minimum interatomic potential. ro is directly related to the lattice constant, a While the intrinsic elastic modulus is dependent on the interatomic forces, the macroscopic Youngs modulus can significantly be reduced by the presence of processing defects. For example, it has been observed for some ceramic materials that macroscopic defects such as porosity and microcracks will significantly decrease the elastic modulus [62, 63]. For example, in case of alumina, the relationship betw een the magnitude of the elastic modulus, E and volume fraction of porosity, p can be expressed as [62] ) 9 0 9 1 1 (2 0p p E E (2-9) where, E0 is the elastic modulus of a material with zero porosity.

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28 In general, the effect of point defects on elastic modulus is of great in terest. The formation of point defects can modify the inter-atomic forces, and hence the el astic modulus will be affected. Recent studies indicate that the influence of lattice v acancies on elastic modulus can be significant. For instance it has been shown experimentally th at the elastic m odulus of group IVb nitrides with rock-salt structure such as TiNx, ZrNx and HfNx decreases as the concentration of the nitrogen lattice vacancy incr eases [64-367]. Guemmaz [68, 69] has shown that in titanium carbides the elastic modulus is reduced as the carbon lattice vacancy c oncentration increases. Theoretically, computer simulation results using full potential-linear muffin tin orbital method [67-69] and ab initio pseudopotential density functional to tal energy method [70] have shown a good agreement with the above-mentioned experimental results. However, the work on the influence of point defects on elastic modulus of ceria-based oxides is limited [41, 43-44, 71]. Sato et.al. [41] studied the effect of dopant concentration on the elastic modulus of ceria based materials usi ng a small punch testing tec hnique (the concept of this technique is similar to fle xural bend testing). They reported the average elas tic modulus of pure ceria as 175 GPa, which was slightly lower than the results reported as approximately 200 GPa through flexural tests by Atkins on and Seluk [71]. Their re sults showed that the elastic modulus of doped ceria ceramics was lower than elastic modulus of pure ceria. The authors attributed the reduction in elastic modulus to the effect to the formation of oxygen vacancies caused by doping process. Furthermore, sin ce oxygen vacancies can also be formed through reduction treatment, our recent theoretical mode ling based on the calculation of oxygen vacancy formation as a function of partial pressure of oxygen and a consideration of classical atomic potential predicts that elastic modulus decrea ses with a reduction of 2OP in fluorite-structured

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29 oxides [44]. In this dissertati on, experimental measurement on elastic modulus are attempted to confirm this effect. 2.4.2 Effect of Point Defects on Fractu re Properties of Ceria-Based Materials Depending on the material fabrication techniqu e and measurement method, the strength of pure ceria reported in literature has a wide range [38, 71, 72]. Using the same standard solid state fabrication technique, the fl exural strength of pure ceria of was reported to be less than 100 MPa by Mashino et.al.[ 72] and about 150 MPa by Atkinson and Seluk [71]. The fracture toughness of pure ceria was repor ted to be about 1.3 MPam1/2 by Sato et.al [41] and 1.5 MPam1/2 by Mashino et.al. [72]. Besides the effect of proce ssing techniques, the effect of point defects on fracture properties of ceria based materials is of great inte rest. As discussed in section 2.3.3, the ceria lattice will expand when oxygen v acancies are formed by the reduction process. In case of SOFCs, as the oxygen partial pressure varies significantly acro ss the electrolyte, the expansion difference across the electrolyte thickn ess will lead to mechanical stresses, which gives rise to differential strain across the thic kness and inevitably causes fracture [38-40]. In detail, Atkinson [38] has studied the relationship between the st resses and various parameters such as doping concentration, temperature and oxygen activity. His analysis relates the maximum tensile stresses to the non-stoichiometry of the electrolyte. A tensile stress is found to be present at unreduced cathode side (air side ) and a compressive stress at reduced anode side (fuel side). The maximum tensile stress is found to increase with the d ecreasing oxygen pressure and dopant concentration or with increasing temperature. The tr ade-off between temperature and oxygen pressure has bought up an interesting topic in order to keep the maximum tensile stresses to a manageable limit. Some experimental [40-44] work has shown doping process affects fr acture properties of ceria based materials. For example, Sato et. al. [41] found that the fractu re strength and fracture

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30 toughness of doped ceria appear to decrease with increasing d opant level when the dopant concentration is less than 20 mol %. The aut hors attributed this decrease to the increase in concentration of oxygen vacancies caused by acceptor doping process. Intere stingly, they also find that the influence of the increasing oxygen vacancy concentration ove rride the strengthening effects caused by finer grain sizes. Further studies [41] on the fracture properties of rare earth (yttrium, gadolinium, and samarium) doped ceria ceramics showed that the fracture toughness was influenced by the dopant con centration rather than the kind of dopants (Figure 2-9). As the increase in dopant concentration is directly associated with the increase in oxygen vacancy concentration, this result again indicates the important role of the oxygen vacancy effects on fracture properties. 2.4 Fracture of Brittle Materials 2.4.1 Fracture Mechanics for Brittle Materials When the applied stress exceed s the theoretical strength, th which is defined as the maximum stress on the force-displacement curve, materials are expected to fracture in an unstable manner. In a simplest approach, this theoretical cleavage stre ss can be expressed as Equation 2-10 [73]. Since cleavage takes place on specific crystallographic planes, the parameters given in this equation refe r to specific crystallographic planes. 0r Eth (2-10) where, is the surface energy for the cleavage plane and r0 is the equilibrium unstressed interplanar spacing, and E is the elastic modulus perpendicula r to the cleavage plane. Using an estimated value, th in Equation 2-8 can be approximated as 10 E At room temperature, the E values for ceramics vary from tens of GPa (e .g., 70 GPa for pyrex glass) to as high as hundreds

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31 of GPa (e.g., 400 GPa for trigonal alumina), ther efore, the theoretical strength ranges from several GPa to tens of GPa. This estimation is obviously much greater than experimental test strength values for ceramics which nor mally is several hundreds of MPa. In 1913, Inglis [74] carried out some pioneer ing work on stress analysis for a uniformly stressed plate with an elliptical cavity in the mi ddle. He showed that the local stresses ahead of an elliptical cavity tip can raise to as high as several times that of the applied stress. Ingliss stress concentration factor concept can provide some information about the difference between the theoretical strength and the e xperimental values. While Inglis s analysis incorporates the stress intensification, it fails to address the effect of crack size. In othe r words, cracks of equal notch radius to crack length ratio would be equall y effective in intensifying the stress. Following this, Griffith proposed in 1920 a mo del, where instead of stress in tensification, th e energetic of crack propagation was considered. It is genera lly considered as the first breakthrough in developing fracture criterion. Griffiths criterion [75] adapted the thermodyna mic equilibrium concept. He considered a static shaper crack as a reve rsible thermodynamic system and sought to minimize the total free energy of the system. In this system, strain energy was the driving force for the crack propagation and surface energy was the resistant component for crack propagation. Based on this assumption, the Griffiths theory implies that the critical stress, f, for a crack to propagate is defined as 2 1 ') 2 ( C Ef (2-11) where E identifies with elastic modulus ( E ) in plane stress and ( E/(12) ) in plane strain with the Poissons ratio. The strength is therefore controlled by three basic parameters, which are the elastic modulus ( E ), the surface energy ( ) and the flaw size ( C ). This relationship demonstrates

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32 that failure occurs when the loss of strain ener gy is sufficient to provide the increase in surface energy. There are two important basic implications of th is relationship. The first is, the critical stress for a crack to propagat e is inversely proportional to C The second is, when the applied stress is greater than this critic al stress, crack will propagate spontan eously without limit. This is the first time in fracture mechanics history on e specified the criterion for crack growth. However, it has been shown that Griffiths theo ry has some practical limitations. For example, in 1930, Griffths theory ran into major obstacles when Obreimoff [76] test ed his theory with a rigid wedge loading condition to cleave mica. Ob reimoff found that the failure for this loading geometry occurs in a stable fashion, which is agai nst the second implication of Griffths concept. Linear Elastic Fracture Mechanics (LEFM) is a further development of Griffiths concept in the history of fracture mechanics. In the vici nity of a crack, the stress fields can be derived from three basic modes of loading, which are tens ile mode or mode I, sliding mode or mode II and tearing mode or mode III respectively (see Figure 2-10). Based on linear elastic theory, Iwirn in 1958 [77] described stresses in the vicinity of a crack tip as ) ( ) 2 (2 / 1 ij ijf r K (2-12) where, r, are the cylindrical polar coordinates of a point with respect to the crack tip; K is the stress intensification factor, which gives the magnitude of the elastic stress field; and ) ( ijf is an angular function. For a given loading mode, K can be expressed as C Y Ki i, (2-13) where, Yi is a dimensionless parameter that depends on geometry of the crack and the loading mode and i represents the loading mode.

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33 Following Griffiths energy ba lance condition concept, Irwi n was able to combine the stress intensification factor K with the the strain energy release rate G. In case of mode I loading condition this relationship is shown as 2E K GI (2-14) The crack propagates when G reaches a critical value GC which is determined by the resistance for crack propagation, R. For the ideally brittle material, R is twice the surface energy, From Equation 2-14, the existence of GC implies there is also a critical value for the stress intensity factor. For example, K1C can be identified to be the cr itical stress intensity factor for a material under mode I loading condition. Here, K1C is a material property and termed as fracture toughness. 2.4.2 Toughening Mechanisms for Brittle Materials Brittle ceramics usually fracture in a catastroph ic or unstable way, wh ich is not desirable for most practical applications. In general, th ere are three alternative steps [73] that one can consider to overcome this problem with the help of understanding the basic equation between strength and fracture toughness. Because the material strength is inversely proportional to C, the first step is to decrease the flaw size to improve the strength. C ontrol of flaw sizes can be achieved through improvements in material processing, surface fi nishing procedure and service conditions. The second step is to decrease applied stresses by a change in component geometry to remove unwanted stress concentrations so that the de sign stress can be decreased. However, improvements through these two step s are most of the times difficult due to practical limitations. This leads to the advantage of third step, whic h is the enhancement of fracture toughness or flaw insensitivity from material sc ience aspects. Several toughening mechanisms have been

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34 successfully developed over the last severa l decades. A summary of the major toughening mechanisms for brittle materials are summarized in the following. Firstly, toughening can be cau sed by crack tip perturbations. The basic concept of this mechanism is to impede the crack by obstacles in form of second phase. The magnitude of perturbations of crack front by th e second phase depends on the char acter of the particles and the nature of the crack interaction. There are two dominant perturbations in brittle materials, i.e., crack bowing [78-79, 81] and crack deflecti on [82-84], which may operate simultaneously during crack propagation. The following revi ews the development of both processes. In case of crack bowing, the process originates from the s econd phase in the path of a propagating crack and produces a no n-linear crack front. The materi al strength of is determined by the stress to propagate these secondary cracks. This stress is usually greater than the stress to extend the primary crack except the case when the ratio between phase spacing and second phase dimensions is relatively large. Lange [78] sugge sts that the increase in both the strength and the fracture surface energy may be similar to a line tension effect observed for dislocation motion [85]. Evans [79] calculated this line tension effect and found a good correlation with the experimental results [80] for the fracture surf ace energy of glass/alumina system. The fracture surface energy includes all the re sistance to form new surfaces by crack propagation. Crack bowing is found to be the major contribution to the strength increase for brittle second phase (impenetrable second phase) in brittle matrix co mposites, but a minor cont ribution to the strength increase for fiber composites or ductile second phase [79]. Unlike crack bowing process, crack defl ection creates a non-pl anar crack during propagation, which leads to lower stress intensity than that expe rienced by corresponding planar crack. The sources of crack deflection can be either residual strain presented in the material [84]

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35 or the existence of weakened interface. Fi gure 2-11 schematically shows two types of crack deflection mechanisms, i.e., crack tilt and crack twist [82, 83]. The twisted and tilted cracks are subjected to a mixed-mode loading. In case of crack tilt (Figure 211A), the local stress intensities have a mixed mode I and mode II co mponents, and combined mode I and mode III for crack twist (Figure 2-11B). It is clearly to see that crack deflecti on is accompanied by an increased roughness of the fracture surface. Base d on Faber and Evanss calculations [82], the increase in toughness only depends on the shape and volume fraction of the second phase. The most effective morphology for deflecting crack is pred icted to be the rod of high aspect ratio (the ratio of length divided by the diameter). The major toughening increment by crack deflection appears to develop volume fraction of second phase less than 0.2. Secondly, crack tip shielding mechanism can also improve fracture toughness. Some microstructural change in brittle material under deformation may cause the stress intensity factor in front of the crack tip ,tip IK, is less than the applied stress intensity factor, app IK, and shielding occurs. Failure occurs when tip IK=0IcK, the fracture toughness of local highly stressed portion at the crack tip, or the process zone. If this stat ement is expressed in an equation for the critical situation, i.e., the situation when failure occurs, the shielding criterion becomes 0IC c app ICK K K (2-15) where cK is the value of shielding effect at the point of fracture. The measured fracture toughness app ICK is therefore higher than the fracture toughness of the process zone material by the amount of cK It has been proven that there ar e three types of dominant shielding mechanism [86], transformation toughening [87-89] crack bridging [90, 91] and microcrack

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36 toughening [92-102]. The basic concept behind each of these toughening mechanisms is explained in the following contexts. The majority work on transformation toughening is on using metastable tetragonal zirconia as toughening agent [87, 88]. When the stress le vel around the crack tip reaches a critical value, the metastable tetragonal zircon ia tends to transform into the stable monoclinic phase. This transformation is accompanied by a volume incr ease, and the result is the creation of compressive stress around the crack tip, which tends to shield the crack. Crack bridging toughening occurs when the prim ary crack front by-passes obstacles. For composite materials, the bridging process may come from the second phase. If the bridges are elastic, failure may occur when the bridges are pulled out of the matrix [90]; or if the bridges are ductile, failure occurs through plastic deformation. The in crease in toughness by crack bridging can be attributed to the d ecrease of the stress intensity factor at the crack tip. The microcrack toughening mechanism [92-102] has been proven to cause crack tip shielding effect by amount of K through redistributing and re ducing the average near-tip stresses. There are two sources of this redistribu tion effect [92, 97]. On e is due to the reduction in the effective elastic moduli resulting from microcracking formation and extension in the process zone. The other is the strain arising from the release of re sidual stresses or the dilatational effect when microcracks are formed Between these two sources, the dilatational effect is found to be more substantial. Figure 2-12 schematically shows these two effects in the stress-strain curve along with th e rising crack resistance curve, KR curve, for a microcracked material [97]. Frontal zone micr ocrack causes minor increase in K and dilatation toughening will occur when microcracks enter the crack wake Because of the importance of nucleation and extension of microcraks for this mechanism to operate, the control of microcracking sites

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37 becomes essential. These sites are expected to be weak interf aces between the matrix and the second phase for composites or the grain boundaries fo r single phase polycrystals. It needs to be pointed out that toughening by mi crocracking is normally accom panied by reduction of strength of ceramic materials [103]. The challenge for successfully applying this mechanism will involve minimum sacrificing of strength.

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38 Figure 2-1. Schematic diagram for the principle of a solid oxide fuel cell. Figure 2-2. Fracture of the elec trolyte after the half-cell (nickel/yttria stabilized zirconia (or Ni/YSZ) anode and YSZ electrolye) experi enced reduction and reoxidation cycles. (A) Cross section and (B ) electrolyte surface[45] Porous cathode Dense electrolyte Porous anode Electric p ower Fuel: 2H2 +2O2 2 H2O + 4eAir: O2 + 4e 2O2Excess Air Reaction product e e -O2 Anode Electrolyte (A) (B)

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39 Figure 2-3. Schematic drawing of the atomic structure for fluorite oxides. Figure 2-4. Predicted dependence of oxygen vaca ncy concentration on oxygen partial pressure (2OP) at 800 oC for pure ceria, GDC (gadolinium doped ceria) and YSZ from theoretical modeling [44]. O2M4+

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40 Figure 2-5. Dependence of CO/Ccation atom ration on oxygen partial pressure at 800 oC for Ce0.9Gd0.1O1.95-x. ( ) Themogravimetric data fr om Wang et al.[55] and ( ) model [44]. 0 0.1 0.2 0.3 0.4 -30 -25 -20 -15 -10 log Po2x in CeO2-x Bevan Panlener Figure 2-6. Themogravimetric measurement results (800 oC) of oxygen vacancy concentration as a function of oxygen partial pressure for pure ceria [14, 15].

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41 Figure 2-7. Phase diagram for CeO2-x.[16] Figure 2-8. Expansion of ceria vers us nonstoichiometric composition at 900 oC. ( ) Chiang et al. [5]. (-) Theoretical slope; () best fit slope; () Mogensen and Mogensen [6,58].

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42 Figure 2-9. Fracture toughness of doped ceria materials [41]. Figure 2-10. Three basic modes for fracture. Mode I Mode II Mode III

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43 Figure 2-11. Crack deflection process by (A) tilt and (B) twist [45]. Z-X plan is the primary fracture plan. Y is the loading direction. X is the crack propagation direction [82] Figure 2-12. Stress-strain cu rve (A) and the corresponding crack resistance curve (B) for a microcrack toughening mechanism [97]. (A) (B) (A) (B)

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44 CHAPTER 3 MATERIALS AND EXPERIMENTAL PROCEDURES This chapter explains the materials fabrica tion and experimental procedures that were applied in this research. As the nanoindentation technique for intrinsic elastic modulus and hardness evaluation is limited only for room temp erature tests, we designed a heat treatment process that allowed the effect of defect concentration on mechanical properties to be evaluated at room temperature. The strategy was to create defects by equilibrating the samples in various oxygen partial pressures (2OPs) at a high temperature and then conserve them to room temperature by fast cooling. To be consiste nt with nanoindentation tests, all the other mechanical tests were performed at room temperat ure as well, i.e., the mechanical tests are not in-situ tests but post evaluations. In this chapte r, each procedure will be explained in detail. 3.1 Sample Fabrication Three types of fluorite-structu red oxides, pure ceria or CeO2, 10 mol % gadolinium doped ceria (GDC) or Gd0.1Ce0.9O1.95, and 8 mol % yttria stab ilized zirconia (YSZ) or (Y2O3)0.08(ZrO2)0.92, were selected for this research, The materials were prepared with solid state method using commercial powders, i.e., pur e ceria (99.9% pure, Alfa Aesar, 5 m powder), GDC (99.9% pure, Rhodia Inc., USA and Anan Kase i Co., Ltd., Japan ) and YSZ (TZ-8Y, TOSOH Co., Japan). Depending on the type of mechanical tests, the sample size requirements are different. However, the fabrication process of the samples wa s kept same for each material in order to limit microstructure variations. It n eeds to be pointed out that numer ous fabrication methods, such as electrochemical vapor deposition, tape casting, plasma spraying or colloidal/electrophoretic deposition are used to prepare el ectrolyte materials. These met hods are adopted to achieve thin electrolyte (as explained in 2.1.1). However, the samples prepared by these methods have

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45 dimension limitations for mechanical tests in this research. Therefore, we used the conventional solid state method to prepare samples with desire d dimensions. Figure 3-1 shows the flow chart of fabrication processes used in this study, which were slightly different for each material. Pure ceria powder was ball milled with 3 wt% polyvinyl butyral (PVB) ethanol al cohol solution for 24 hours. After drying, the powder was milled and si eved. The ceria samples were then prepared by two step of pressing. The first was uniaxial pressing at pr essure about 35 MPa for 4 mins, and the second was cold isosta tic pressing at 250 MPa pressure for 5 minutes. Because the uniaxial pressing procedure defi nes the shape of the green body, a proper sized dies were adapted, i.e., inch, inch and 1 inch diameter dies were used for disc shaped samples, and 10 mm mm rectangular die was used for bar samples. The pure ceria samples were held at 400 oC for one hour to burn out the PVB binder and then sintered at 1550 oC for 20 hours. The heating and cooling rate was 5 oC/min. The GDC and YSZ samples were prepared similarly as pure ce ria sample, but without the addition of binder and the burn out procedure. As a result, the final size of the ceria samples for nanoindentation tests was about 6 mm mm. The final size for GDC and YSZ samples was 10 mm mm. The Br azilian disc ceria samples for fracture toughness te sts had the dimensions of 26 mm.6 mm. Because the bar samples after firing had a size of approximate ly 3.1 mm mm mm, two bending samples with dimensions of 2.6 mm mm 45 mm were obtained from one or iginal bar. The schematic in Figure 3-2 shows the procedur es how the bar samples were ach ieved. The materials and the size of the samples are summarized in Table 3-1. 3.2 Heat Treatment The heat treatment temperature was chosen to be 800 oC, which is typical operating temperature for Solid Oxide Fuel Cells (SOFCs). The amount of time that was needed for the

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46 heat treatment was decided from two approaches. The idea was to achieve equilibrium. Firstly, in order to calculate the equili brium distance, oxygen self-diffusi vities in these materials are needed. From literature, given by R. Devanathan, et. al.[104] and P.S. Manning, et.al. [105], the oxygen self-diffusivity coefficient in YSZ is ~10-7 cm2s-1, given by B.C.H. Steele [27], oxygen self-diffusivity coefficient in ceria system is one order of magnitude higher with a value of ~10-6 cm2s-1. Because the absolute equilibrium is ve ry difficult to reach in real experiment, equilibrium distance in this research is considered as the depth where the sample has reached 90% or higher of the equilibrium concentration. Using the available information (diffusivity and material dimension values), the equilibrium dist ance for each materials as a function of time was directly read from the plots of the diffusion solution given by J. Crank [106]. As a result, it shows that within 15 hours, the ceria samples and GDC samples has reached equilibrium at a depth larger than 1.3 mm and YSZ has reached equilibrium at a depth larger than 0.6 mm. Secondly, based on thermal-chemical expa nsion experiments conducted by S. Bishop, et.al.[107] for the same materials and experi mental conditions as this re search, the amount of time of 15 hours was sufficient enough for the these materials to reach the maximum expansion, i.e., the equilibrium condition. In order to achieve different defect concentra tion, the samples were heated at a rate of 5 oC/min to 800 oC and equilibrated in various oxygen partial pressures for 15 hours. The various oxygen partial pressures were obtained by c hoosing different gas mixtures (i.e., N2, Ar, H2 and H2/H2O). The gas flow rate was 10 sccm. Figure 3-3 shows the schematics of the heat treatment setup. The samples were heat treated inside a quartz tube. There was an oxygen sensor connected to the out gassing line of the tube furnace for measuring the oxygen partial pressures of the controlling gas or gas mixtures. The oxygen sensor was a galvanic cell with the type of

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47 Pt, air(reference OP,2)/ziroconia electrolyte/ Pt, controlling gas(2OP). The voltage difference between the electr odes is given by the Nernst equation as reference O gas OP P zF RT E, ,2 2ln (3-1) where, R is the universal gas constant, T is the absolute temperature in degrees Kelvin, z is the charge number of the electrode reaction (which is the number of moles of electrons involved in the reaction, in this case, z equals to 4), and F is the Faraday constant (96,500 C mole-1). The reference gas was dry air in this study, therefore reference OP,2=0.21 atm. By measuring the voltage difference across the zirconia electrolyte, the oxyge n partial pressure for the controlling gas at the heat treating temperature can be calculat ed from Equation 3-1. The corresponding oxygen partial pressure ranges of different gases or gas mixtures are listed in Table 3-2. After 15 hours at 800 oC, the samples were then fast cooled to room temperature to maintain the defect concentrations achieved at the elevated temperature. The average cooling rate was about 16 oC/min for the first 200 oC, and 9 oC/min for the range from 600 oC oC. The total time for the samples to cool down to 300 oC was about 50 minutes. Figure 3-4 presents the temperature-time curve for this heat treatment. In order to distinguish between the therma l vacancies and those created by a reduced atmosphere, one sample of each mate rial was heat treated in air (2OP=0.21 atm) for the same amount of time at 800 oC and then fast cooled to room temperature. To prevent reoxidation during cooling, the controlling gas mixture was c ontinually flowed throughout the fast cooling period.

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48 3.3 Mechanical Tests 3.3.1 Elastic Modulus Tests Two sets of tests were designed for elastic modulus measurement, namely, nanoindentaion and four-point-bend tests. For nanoindentation te sts, the indent size is small (submicron) and therefore the indents could be fit inside the grains. Also, by anal yzing the images of each indent, the indents with abnormal shapes resulting from the nearby pores or microcracks were further eliminated, and Figure 3-5 is examples of such indents and a successful indent. Therefore, nanoindentation is able to meas ure the intrinsic elastic modulus, i.e., independent of the influence of pores, grain boundari es and other microscopic def ects such as microcrakcs. However, elastic modulus evaluated by bending test s requires bulk samples where the effects of porosity, grain boundaries and other mi crostructural features contribut ed to the test results. The details of these two testing methods ar e explained in the following sections. 3.3.1.1 Nanoindentation test Due to the sensitivity of nanoindentation test to the sample surface conditions, all samples were carefully polished to 0.25 m using alumina powder and di amond paste prior to heat treatments. In order to minimize the microstructu ral variations (such as porosity, pore size, grain size, ect.) from one sample to another, the same batch of the as-sintered samples was used for nanoindentation tests as a func tion of oxygen partial pressure. Preliminary nanoindentation results conducted on the surface of the as heat treat ed samples showed a larg e scatter in the data. Further analysis using SEM suggested a surface effect upon heat treatment. Therefore, the samples were further mechanically polished after heat treatment and prior to nanoindentation in order to remove the top layer (<10m) altered by the thermal etching and by reoxidation. The nanoindentation was carried out using a Hysitron TriboI ndenter. The triangular pyramid Berkovich indenter was used for all th e measurements. The Hysitron TriboIndenter has

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49 a capability of recording load-displacement curv e during the test. The contact area function of the indenter (i.e., the contact area vs. contact de pth) was generated by testing a standard sample with known elastic modulus. The standard used for this research was fused quartz with an elastic modulus of 72 GPa. The details of generating area vs. contact depth function followed reference [108]. After series of indent s on the standard sample, a power law curve fit was performed on the unloading portion of each curve. A tangent lin e to the power law curve was used to find the stiffness, from which an area was calculated b ecause the elastic modulus of the standard was known. The calculated area versus displacement fo r all the indents was f it in a curve and the area versus displacement function was generated. The machine compliance, sample tilt and thermal drift were all consider ed and calibrated following the in struction in reference [108]. Because of the availability contact area vers e displacement function, the reduced modulus (Er) was then calculated from the slope of the unloa ding segment of the load-displacement curve. This reduced elastic modulus combines the modulus of the indenter and the specimen according to Equation 3-2, which is given in the Hysitron TriboIndenter Naomechanical Test Instruments manual. sample sample indenter indenter rE E E ) 1 ( ) 1 ( 12 2 (3-2) where, indenter and sample are the poisson ratios and Eindenter and Esample are the elastic modulus of the diamond indenter and the sample, respectivel y. The elastic modulus of the sample was calculated using indenter=0.07 and Eindenter=1140 GPa for the diamond indenter and assuming sample=0.3 [6].

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50 All the tests in this research were under load control. The samples were loaded to 5000 N and held for 5 seconds and then unloaded. The loading and unloading rates were the same and equal to 1000 N/s. A total of 4900 indents were performed on each sample. 3.3.1.2 Four-point-bend test For the purpose of comparison with the nanoi ndentation results, th e elastic modulus of bulk samples by four-point-bending was also conduc ted at room temperature. Prior to heat treatment, the bending bar samples were sent to be machined (PremaTech Advanced Ceramics, USA) according to the ASTM C 1161 standard [ 109]. The bulk elastic modulus was measured using an MTS810 mechanical testing system desi gned for controlling small displacements. The displacement was measured using MTS model 632. 06B-20 extensometer at 0.016 inch full scale range. The load was measured using MTS 661.192200 lbs load cell at 200 lbs full scale range. A digital image of the MTS810 system is shown as Figure 3-6A and the details of the bend test setup is shown as Figure 3-6B. The four-poi nt-bending fixture (MTS model 642.05A-02) used in this research was a fully-articulating fixture de signed to be used either with flat and parallel specimens or with uneven or nonparallel specimens. The con cept of fully-articulating is explained in ASTM C 1161 standard (also see Fi gure 3-6C) [109]. As s hown in Figure 3-6B, the fixture allows full independent articulation of a ll rollers about the speci men long axis to match the specimen surface. The upper pairs are free to pivot to distribute force evenly to the bearing cylinders on either side. The support span was 30 mm, and a one-third loading span was used. The loading speed was calculated according to ASTM D 6272 [110] as d ZL R2185 0, (3-3) where, R is the displacement rate; L is the support span (30 mm), d is the depth of the beam (2.6 mm); Z is the strain rate of the outer potion of the sample and equals to 0.01 s-1. Therefore, the

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51 displacement rate was then determined to be 0.6 mm/min. A computer (LabView 7, National Instruments software) was used for the data acquisition. The elastic modulus was calculated from [110] 3 321 0bd m L EB, (3-4) where, EB is the modulus of elasticity in bending; m is the slope of the loading segment of loaddisplacement curve; b is the width of the bending bar. At least two samples for each heat treatment condition were tested fo r the bulk elastic modulus. It is common to see researchers in the literature to do seve ral loading unloading cycles and then evaluate the elastic modulus from the unloading segment of the curves. The reas on we did not perform loading cycles to our sample is because of the sensitivity of the micr ostructure to loading cycles, and this will be addressed later in sectio n 5.1.2. However, the validity and reliability of our method can be shown through the dummy tests on a steel samp le. The steel (which has a known elastic modulus of 200GPa) bar sample with a cross-se ction of 3.145 mm 3.146 mm was tested using the same parameter as described above. The corresponding load verses displacement curve is shown in Figure 3-7. The initial part of the loading curve (approximately 20 N) was omitted due to the nonlinearity caused by friction contact between the sample and the fixture. From the slope of this curve, the elastic modulus calculated through Equation 3-4 was 197.1 GPa, which is very close to the elastic modulus of st eels. In fact, multiple cycling tests were performed using this sample and the variation from one test to another re mained within 6 %. Therefore, it is reliable to use this technique to evaluate elastic modulus. 3.3.2 Hardness Test The hardness was also evaluated at the same time as the intrinsic elastic modulus by the nanoindnetation test from

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52 A P Happ, (3-5) where, H is the hardness; Papp is the maximum applied indentation force; and A is the resultant projected contact area at that load. These cont act areas were determined from the contact area function that was described in section 3.3.1.1. 3.3.3 Flexural Strength Test The flexural strength was also evaluated usi ng four-point-bend test. The number of the samples tested in this research will be revealed later in Chapter 6. The test parameters, fixtures and sample preparation were the same as the a bove mentioned test for evaluating bulk elastic modulus. The flexural stre ngth can be expressed as 2bd L Pf f, (3-6) where, Pf is the fracture load L, d and b are defined the same as in Equation 3-4. 3.3.4 Fracture Toughness Test The initial attempt to evaluated fracture toughness using Vikers microhardness tester was not successful. As shown in Figure 3-8, the inde ntation pattern of the as-sintered ceria sample was severely disrupted (at load of 200 g) and th erefore not suitable for measurement using this method. In this study, chevron-notched Brazilia n disc tests under the mode I loading condition was successfully applied to measure the fracture toughness. The reason that we chose disc shape sample testing instead of the standard bending ba r sample [111] is that we were not able to produce high quality bending bar samp les at the moment that this te st was carried out. Figure 39 schematically shows the dimensions of the Brazilian disc samples. The samples were manually polished using 600 grit si licon carbide sand paper prior to heat treatment. Chevron notches were cut in the Brazilian disc samples prior to their heat trea tment using a low speed

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53 diamond saw with a 0.2 mm-thick blad e. The radius of the blade was R0=12.7 mm. The notch length (2a), the sharpness of the chevron-notched sect ion and the distance between the notch tips (2a0) are not independent parameters, and all of them depend on the penetration depth (see Figure 3-10A) of the blade into the sample. The deeper the penetration depth of the blade, the larger values of these two parameters are, but wi th shorter and shaper chevron-notched section. For samples with same thickness, Figure 3-10B shows a chevron notch with notch to diameter ratio of 0.5 and Figure 3-10C for ratio of 0.6 to visualize the difference. It depends on several parameters to su ccessfully make a chevron notch. During the notching process, the alignments between the di ametric lines of the blade from both cuts, the center line of disc sample and the normal of the disc sample are essential for a symmetric notch. Also, the penetration depth of the blade from bot h sides of the sample has to be same. The schematics of the unsuccessful chev ron notches experienced at the in itial stage of this work are schematically shown in Figure 3-11. The testing method for the KIC measurement using Brizilian disk samples followed the procedure explained by Shetty, et.al. [112, 113]. The final geometry of the ceria samples with a notch to diameter ratio (2a/2R) of 0.5 was comparable to the sample geometry used in their research. The loading and unloading of the fracture test was done unde r displacement control with a cross head speed of 0. 002 in/min using Instron 1125. A precrack procedure proposed by Shetty, et.al.[112] was performed on Brazilian disc sample to achieve a sharp crack tip. A sharp cr ack tip is necessary for valid fracture toughness. In addition, the scattering of the data will be limited because the fracture would be dominated by the sharp crack tip created by precrack procedure, not by the roughness of the notch edges. Firstly, the fracture load of a Brazilian disc sa mple was directly loaded to fracture under mode I

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54 condition, i.e., by loading in compression along a diameter through the chevron notch. The load for precrack for was then determined to be about 90~95% of this fracture load (the precrack was also conducted mode I). The sample was held at this load level for 6 or 12 mins and then unloaded. Crack propagation within the chevron notch (in our case when a/R=0.5) is stable because the effective thickness is increased cont inuously owing to the shape of the notch. The stress-intensity factors at the point of fracture for mode I loading of Brazilian disc samples were calculated using th e solutions given by Atkinson, et. al. [114] as 1 2 / 1 2 / 1 maxN RB a P KC, (3-7) where, Pmax is the fracture load, a is the half crack length, B is the thickness, (see Figure 3-9), and N1 is a non-dimensional coefficient that is a function of the relative crack size (a/R). The relative crack size (a/R) in this study has a rang e of 0.48.51. Atkinson, et. al. [9] provided the numerical solutions for the cracks in the size range a/R=0.1.6, which were used in this study for calculating K1C. Furthermore, Shetty, et.al.[112] calculated the stress state (plain strain condition and biaxial stress state condition) effect s on the stress intensity factor based on strainenergy-density theory and found that stress state did not affect the stress intensity factor for pure mode I condition. In another words, the effect of the sample thickness should not affect the KIC results for brittle materials. 3.4 Characterization Techniques The densities of the as-sintered samples were measured by the immersion technique with pure water as the immersion solution. Assumi ng that the density for pure water at room temperature is 1 g/cm3, then the density of the samples was calculated by Equation 3-8 according to Archimede's principle as

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55 wet dry dryw w w (3-8) where, is the density of the test sample; wdry is the weight measured in air and wwet is the weight of the sample in pure water. The grain boundaries for all three materials used in this research wa s revealed after being thermo-etched at 1550 oC for 12 mins. Optical microscopy and scanning electron microscopy (SEM, JEOL JSM 6400 and FEG-SEM, JEOL JSM-6335F) were both used to image the microstructure. All the samples prior to SEM an alysis were coated with Au-Pd. After taking images with proper magnification, the standard linear-interception method was used to determine the grain sizes [115]. After nanoindentation tests, high resolution naoindent topography images were recorded using scanning probe microscopy, which is one of the function of the TriboIndenter. These images are helpful to verify the quality of the indents. The crystal structure and the texture of the samples were studied using the X-ray diffraction (XRD) method with Cu K radiation (XRD, Philips APD 3720). The XRD patterns for powder samples as well as bulk samples were recorded and compared to the standards to identify the crystal structure. When bulk samples were tested for XRD pattern using this machine, it was very important to adjust the sample height to be aligned with the sample holder for valid 2 values. The amount of time to conduct an XRD test depends on the parameters of the XRD experiment, i.e., step size in terms of 2 and time per step, in another words, the smaller the step size or the longer time per st ep during XRD scanning re sults in longer XRD experiment time. For example, for a 2 range of 20 degree, if the step size was 0.02 degree and time per step was 2 seconds, the total time for XRD scanning was about 2 hours 13 mins.

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56 Based on Bragg law (Equation 3-9), the interplana r spacing for planes w ith Miller indices (h, k, l), or dhkl, was calculated through Equation 3-10. ) sin( 2 hkld (3-9) ) sin( 2 hkld, (3-10) where, is the wavelength of radiati on source, and in this case, Cu Ka (wavelength=1.54). As the materials selected in this research we re all cubic structured materials, the lattice parameter, a, was then calculated through 2 2 2l k h d a (3-11) Scanning electron microscope (SEM) was also employed for fractographical analysis. Fractographic images of bend bar and Brazilian di sc samples were used to identify the crack initiation sites and crack propagation process. In order to investigate the interaction between pores and propagating cracks, a quantitative metallogr aphy analysis method was used on the fractographic images of Brazilian disc fracture samples. The accuracy of the crack length measurement is crucial for the validation of the fracture toughness results. In this research, the crack length was measured usi ng a Unitron Microgoniometer with the accuracy of 0.01 mm. The crack length was also verified later in SEM. In order to study pore-crack interaction, th e pore area densities on the polished surfaces and the fracture surfaces were measured for sa mples heat treated under different conditions. Images used for this analysis were taken at a magnification of 2000X. The pore area density (AA) was measured using point-count method [115 ] The total number of points was 864 (27) and they were uniformly distributed on th e areas of interest (an area of approximately 45 m52 m for each image). AA is equal to number of the points that fall on the pores divided by

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57 the total number of the points. The difference of pore area density between the fracture surface and the polished surface indicates the pore-crack interaction. If the pore area density was higher on the fracture surface than the polished surface, th e crack was attracted by the pores; or if the pore area density was lower on the fracture surf ace than the polished surface, the crack was repulsed by the pores. Transmission electron microscope (TEM Joel 200 CX) was used for observations of microstructure and phase characterizations. Th e TEM samples were prepared using focused ion beam instrument (FIB, FEI Strata DB235). The sa mples used in FIB were triple times coated with carbon. Prior to the ion milling process, a 1.2 m thick Pt layer was also deposited onto the area of interest to protect the sample from i on damaging. As shown in Figure 3-12A, the thin TEM sample (a thin slice of ceria material) is hanging between the two tren ches that were first dug off at the beginning of the proce ss. The bottom of the sample is also cut free at this stage of the process. After further thin ning and when the desired thickne ss is reached, the sample is ready to be cut free from the bulk material (Fi gure 3-12B shows this si tuation for another TEM sample with one shoulder cut free). The TEM samples were lifted out using an ex-situ MicroOptic manipulator and then were put onto a Cu grid. The final size of the TEM sample prepared by this method was about 15 m5 m with a thickness of 100 nm.

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58 Table 3-1. Sample dimensi ons for mechanical tests. Table 3-2. Oxygen part ial pressure ranges (2OPs) of different gas mixtures. Sample Size Materials Nanoindentation samples Samples for flexural tests Brazilian disc samples for K1C tests Pure ceria (CeO2) 6 mm mm 2.6 mm mm mm 26 mm.6 mm GDC (Gd0.1Ce0.9O1.95) 10 mm mm 2.6 mm mm mm ---YSZ ((Y2O3)0.08(ZrO2)0.92) 10 mm mm 2.6 mm mm mm ----Gas Compositions Oxygen Partial Pressure, atm air 0.21 N2 or Ar 10-6~10-4 H2/H2O/N2 or H2/H2O/Ar 10-19~10-23 Dry H2 <10-24

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59 Figure 3-1. Flow chart of the sample fabrication process. Figure 3-2. Schematics of the procedures of achieving two bending samples before machining from one as-sintered bar. 3wt.% polyvinyl butyral (PVB) Sintering process (1550 oC for 20 hours) Uniaxial pressing 400oC (1 hour) Ball milling (24 hrs) Cold isostatic pressing Powder ceria GDC, YSZ Drying and milling Green body: 4 mm 10 mm 60mm As-fired bar: ~ 3.1 mm 8.5 mm 48 mm Two bending samples before machining: ~ 3.1 mm 4 mm 48 mm Sintering Cut in the middle

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60 Figure 3-3. Schematic of the heat treatment e xperiments set up. The gas flow direction is showing by the arrows. 5 oC / m i nF a s t c o o l i n g 5 oC / m i nF a s t c o o l i n g Figure 3-4. Temperature-time cu rve for the heat treatment.

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61 Figure 3-5. Comparison of Nanoi ndents with abnormal shapes due to (A) a nearby pore or (B) underneath pore and a successful nanoindent. ( A ) ( B ) ( C ) 1 m 1 m 1 m

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62 Figure 3-6. (A) A digital image of 810 Material Test System (810MTS) used for the flexural tests. (B) The details of the fixture setup for four point bending test with one ceria sample and the extensormeter in position. (C) Schematics of the fully articulating four-point-bend fixture [6]. ( C ) ( B ) ( A )

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63 slope= 3401.0 N/mm 0 40 80 120 160 00.010.020.030.040.05 Displacement, mmLoad, N Figure 3-7. The load-displacement curve of a st eel sample with a cross section of 3.145 mm .145 mm. is the experimental data; is the best linear fit. The resulting elastic modulus from this test is 197.1 GPa. Figure 3-8. Scanning electron microscopic (SEM) im age of the Vikers indent at 200 g for an assintered ceria sample. (Hardness with Vikers number 599, or 5.9 GPa).

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64 Figure 3-9. Geometry of the chevron-notched Brazilian disc samples used in the fracture toughness test. The main crack propagation direction is defined as X-direction and the crack opening direction is Y-direction. The fracture surface lies on X-Z plane. The final dimensions of a t ypical sample were R=13.03 mm, B=2.62 mm, ao=3.67 mm, a=6.45 mm, M=0.24mm. Figure 3-10. (A) Schematics of an ideal chev ron notch and (B) two chevron notches with different dimensions. ((B) for a/R =0.5 and (C) for a/R=0.6) depending on the penetration depth, h, of the blade into the disk sample. A A M a0 a R Section A-A B R X Y X Z h R0 R0 R0 (A)

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65 Figure 3-10. ctd. 1mm 1mm (B) (C)

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66 Figure 3-11. Schematics of the unsuccessful ch evron notches. These outcomes are due to (A) misalignment of sample and the blade, (B) misalignment between the two cuts, (C) misalignment of the two cuts to the normal of the sample and (D) uneven penetration depth. (D) (A) (B) (C)

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67 Figure 3-12. Images of the pure ceria transm ission electron microscopi c (TEM) samples during the preparation process by focused ion beam (FIB). (A) A sample was prepared before cut free from the bulk material. (B ) Another sample with one shoulder cut off from the bulk material. (A) (B) The sample Underneathcut

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68 CHAPTER 4 MICROSTRUCTURAL ANALYSIS Because material properties are directly related to microstr ucture, it is important to characterize and understand microstr uctural conditions prior to mech anical property evaluations. The objectives of the microstructural characteri zations are to answer the following questions. Did the oxygen vacancies created at high temperatur e conserve to room temperature? Did phase transformation occur during the cooling process? Did ordering of oxygen vacancies take place? Was the reoxidation at room temperature signi ficant? Were there any other factors that contributed to microstructural va riation? These questions will be answered in detail for pure ceria in the following sections. 4.1 Characterization of As-Sintered Materials The X-ray diffraction (XRD) patterns of the as-received ceria powder and the as-sintered ceria sample are shown in Figure 4-1. The XRD patterns were comparable to the standard XRD file of JCPDS #43-1002 in terms of 2 peak positions. The relative XRD intensity of the powder and the as-sintered sample was also compared to the standard and the results are shown in Table 4-1. The relative intensity of each planes were f ound to be comparable to the standard, therefore, the powder and the as-sintered sample are consid ered to be fluorite structure with no obvious texture present. This fluorite oxide has a space group of Fm3m (225). Using the 2 values found for each sets of planes, the lattice parame ter was calculated through Equations 3-9 and 310 for the powder as well as the as-sintered ceria sample. The average lattice parameter was calculated for 0.5400 nm0.0005 nm. The average grain sizes for ceria and gadolin ium doped ceria (GDC) were measured using linear interception method from SEM images or optic al images after thermal etching process. In case of the yttria stabilized zi rconia (YSZ) samples, images of a fractured cross section were

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69 used to estimate the grain size. Although this is not the standard method to measure grain size, it is reasonable for estimation. Images in Figure 42 are presented to show the grain sizes of these materials. The densities of each material were measured by immersion tec hnique as explained in section 3.4. Based on the theoreti cal density values (i.e., 7.22g/cm3 for ceria and GDC, 5.96g/cm3 for YSZ), the relative densities for each materi al were also calculated. The results of the grain size measurements along with th e densities are summarized in Table 4-2. 4.2 Characterization of Reduced Ceria 4.2.1 Optical Properties After the heat treatments, th e ceria and GDC samples became noticeably darker as the applied oxygen partial pressure (2OP) was decreased. This is an indication that the vacancy concentrations were conserved. The color change on the surface was strongest immediately after heat treatment for ceria and GDC However, it decayed somewhat over time, even at room temperature. The color fading rate for GDC wa s very fast and took only several hours for the surface color to change from black (after H2 reduction) to a light brow nish color. However, the process was very sluggish in the pure ceria samples. Figure 4-3 shows the digital images of the color change of ceria samples as a function of o xygen partial pressure. These images were taken within several hours after the heat treatment. There are three important points regarding the validity of color comparison. The fist point is as the color depends on the surface conditions of the samples, all the samples shown in this image were polished down to 0.25 m to limit the variation of the surface r oughness. The second is that, during h eat treatment, the heating/cooling rate was kept constant for all the samples. Th e third is that there should be no contamination from the environment. During the heat treat ment, the quartz tube furnace was cleaned using ethanol alcohol and the controlli ng gases were high purity grade, therefore, the contamination

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70 sources were limited. For YSZ samples, the co lor did not change noti ceably even under very low oxygen partial pressure environments, which s uggests that the defect concentration was not increased significantly upon heat treatment. 4.2.2 Microcracks Formation After reduction under low oxygen partial pressure microcracks appeared on the ceria and GDC sample surfaces. However, the focus of th is section is on ceria only. The lowest oxygen partial pressure applied in this study without formation of microcrack s in ceria was about 10-19 atm, i.e., all ceria samples that were reduced under an oxygen partial pr essure lower than 10-19 atm experienced microcracking. The microcrack ing process was initiated during reduction at high temperature. When oxygen partial pressure wa s very low, indeed the samples fracture into small pieces. Figure 4-4 shows a digital image of the situation after four ceria Brazilian disc samples with a diameter of 26 mm were reduced at 800 oC for 15 hours under an oxygen partial pressure of 8.5-26 atm. All samples were cracked in to pieces. In another words, the microcracks were extended/developed to be big m acrocracks so that the original samples fell apart. The cracking process was recognized due to a relatively la rge noise within half an hour after 800 oC was reached. The development of microc racks under severe reduction is thought to be caused by the internal stresses resulting from the lattice expansion difference between the reduced surface and the unre duced interior [38]. In order to investigat e the distribution of the microcracks (several m to 20 m) throughout the thickness of the sample, the cross s ection of a ceria sample after heat treatment under an oxygen partial pressure of 4.5-22 atm (at 800 oC for 15 hours) was polished and imaged using the scanning electron microscope (SEM). Microcracks were observed throughout the entire thickness. It was noticed that re latively larger macrocracks (hundreds of m) were formed on the surfaces that were exposed to the ambient gas. This phenomenon was more

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71 pronounced at the edges, and images of which are presented in Figure 4-5. As shown in this figure, large processing pores were usually acco mpanied by these large macrocracks and their presences extended to a de pth of approximately 100 m. This 100 m surface layer is an insignificant fraction considering that the sample thickness was 2.6 mm. After passing this top surface layer, there was no obvious difference in th e size and distribution of the microcracks as a function of the distance up to the middle. Figure4-6 presents typical SEM im ages of the interior part of the reduced sample with the presence of microcracks. The arrows in the figure indicate the positions of the microcracks. As shown in this figure, the microcracks were located very near to the pores and the size of the microcracks was about several m to 20 m. The appearance of the large macrocracks on the su rface is believed to be related to such environmental effects as the formation of water dur ing the reduction treatment (this effect will be indicated in section 4.3.3). The formation of the microcracks inside the sample can be attributed to development of internal stresses due to th e expansion difference between the reduced outer part and the unreduced inner center of the samples during th e high temperature reduction process. The microcracks are expected to be firstly originated subsurface where the maximum tensile stresses are generated at the beginning of the reduction process. The inside microcracks are developed along with the re duction process, progressing across the sample thickness. 4.2.3 Phase Identification The heat treatment under in 2OP=4.6-22 atm at 800 C is expected to result in a composition of CeO1.92 according to reference [12]. Based on the phase diagram of CeO2-x [16], slow cooling to room temperature should introduce a phase separation by spinodal decomposition in the composition range up to CeO1.846 at temperature between 424oC and 685 oC (see Figure 2-6) which would re sult in the splitting of the XRD peaks. Phase separation below

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72 this temperature would result in a solid solu tion of two phases with compositions close to stoichiometric ceria and CeO2-x phase (possibly CeO1.818 ), respectively. Therefore, XRD tests were performed on the surface of this reduced sa mple. Figure 4-7 presents the XRD results of this reduced sample and an air treated sample. The same fluorite-structured XRD patterns were observed for both samples, and more interest ingly, the XRD peaks for both sample had approximately the same 2 positions. These 2 peak positions were consistent with the lattice parameter of stoichiometric ceria. As we know from section 2.2.1 that the increase in oxygen vacancy concentration should have increased the lattice parameter, according to Equation 2-7, we expected to see lower 2 peak positions for the reduced samp le. Therefore, the question is why there was no lattice expansion shown on the XRD pattern for a reduced ceria sample. Is it because of shrinkage of the lattice parameter by reoxidation at room temper ature or is it because of other factors? In order to answer these ques tions, the first step we took was to investigate the phase transformation as a function of depth by polishi ng the surface and conducting XRD at different distances from the surface for the sample reduced in 2OP=4.60-22 atm. Figure 4-8 presents the (311) peak at various depths from the surface. Single peaks were observed down to 40 m. However, at the depth of 60 m a broadened unsymmetrical extra peak at lower 2 angles appeared. In addition, as shown in Figure 4-8, the (311) peak init ially shifts to greater and then to lesser angles with the increase in depth. Th is observation demonstrates that the surface of the sample was in compression and therefore a slightly smaller apparent lattice parameter was measured. However, the shape of this extra peak suggests there was possible several peaks present underneath. Although it was very difficult to find out the exact lattice parameters of these peaks underneath, a ll of them had larger lattice para meters than air treated sample.

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73 Therefore, these peaks corresponded to phases w ith greater oxygen vacancy concentrations. However, this result does not explain the reason for the presence of the stoichiometric peak. There are two ways to form stoichiometric phase in a reduced sample, i. e., phase transformation at temperature below 424 oC (see Figure 2-6) or reoxi dation. This leads to the next step of this research, i.e., to identify the extra peak and answer how and why the stoichiometric phase appeared in a reduced ceria sample. 4.2.4 Phase Transformation upon Cooling After reduction of in 7.1-24 atm at 800 oC, a bulk ceria sample was immediately taken for the XRD test. Note that, the process of pr eparing the XRD was about 15 minutes (including taking sample out of the furnace, preparing it for XRD scanning and XRD experiments setting up), 2 hours and 13 minutes were ne eded for the XRD scanning (explai ned in 3.4), therefore, at least 2.5 hours was needed to conduct the XRD test. Also note that according to Bevan and Kordis [11], the equilibrium compositi on obtained after re duction in 7.1-24 atm at 800 oC is close to CeO1.83. Prior to any analysis to the XRD pattern, it needs to be pointed out that since the controlling gases for the reduction treatment wa s continuously flowing throughout the cooling process, no reoxidation should take place during the cooling process. Figure 4-9A shows the XRD pattern for this sample and two sets of peaks matching fluorite structure were observed Figure 4-9B shows the details of the XRD pattern in the 2 range of 54 to 60 degrees with a dashed line showing the stoichio metric ceria (311) peak. In terms of peak positions or 2 values and peak intensity ratios, the fluorite phase designated with letter a had similar lattice parameter of shoichiometirc ceria. It was identified that the extra peak shown in Figure 8 had the similar 2 peak position of the sec ond set of peaks designated with letter b. Although b matc hed fluorite structure in terms of the peak intensity ratios, it

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74 had a larger lattice parameter than stoichiometric ceria because of the lower 2 peak position. In literature [116], this b phase is called the pseu do-cubic fluorite phase or ordered phase and the corresponding lattice parameter calculated for this pseudo-cubic phase from the 2 values is called pseudo lattice parameter. It can be vi ewed as a derivation ceria phase with ordered oxygen vacancies. From the shape of the peak for b phase, it can be clearly seen that b phase was actually a mixture of several pseudo-cubic fluorite-stru ctured phases with pseudo lattice parameters ranging from 0.548 nm to 0.552 nm (calculated fr om the underneath peaks marked with arrows in Figure 4-8B). Based on the linear relati onship between the lattice parameter and oxygen vacancy concentration given by Equation 2-7, the nonsoichiometric values (x in CeO2-x) were then calculated to be within 0.19 to 0.24, i.e., the compositions of these phases are CeO1.81.76. If there are only these two types of phases pres ent, a simple mixture rule can be used to calculate the volume fraction of the CeO2 phase. In order to get a composition of CeO1.82 at this oxygen partial pressure, the volume fraction of CeO2 phase is assumed to be f, then 25 0 05 0 82 1 ) 1 ( 76 1 81 1 2 f or f f or f. (4-1) Therefore, less than 25 % volume fraction of CeO2 phase should be present. However, simply considering the peak intensity ratio of CeO2 phase and the b phases in Figure 4-9A, the result of this calculation obviously shows an opposite conclusion. Th is leads back to the initial assumption, it can not be true to a ssume that only two phases exist. To identify the other phases is almost impossi ble without the help of other techniques. However, triclinic Ce11O20-y phase is not possible to co-exist with cubic ceria phase according to the result of J.P. Nair et. al. [116], the other most possible phase should be hexagonal Ce2O3+ It is not surprising that these hexagonal phases do not show up in the XRD pattern when the cubic

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75 CeO2 is present, because of its low XRD intensity due to their lower symmetry structure. In order to visualize this statement, a theoretical XRD pattern of a sample with 2/3 volume fraction of hexagonal Ce2O3 phase and 1/3 volume fraction of cubic CeO2 phase are shown in Figure 410. In this plot, most of the peaks of the Ce2O3 phases overlap with that of the CeO2 phase, the extra peaks for Ce2O3 phases (blue lines, peaks shown with arrows) are too weak to be identified, even though hexagonal Ce2O3 is the major component. It needs to be pointed out that these pse udo-cubic phases are metast able and therefore do not exist on the phase diagram (at room temperature). In another words, our heat treatment and cooling procedure did not allow the equilibrium phases to appear. Firstly, the samples after heating at the elevated temperature were cooled under hydrogen gas flow. Secondly, the samples were fast cooled to room temp erature and did not allow phase transformation to be fulfilled. Based on these results and discussion, we stil l could not completely answer the questions brought up above. Since the presence of diff erent phases may depend on the heat treatment temperature and cooling rate, an intermediate te mperature aging test wa s designed as described in the following in order to further inves tigate the causes for different phases. 4.2.5 Aging Effect Considering that there may be a surface effect existing in th e reduction process, both ceria powder (more surface area) and bulk samples (t he size of half of the Brazilian disc ( 26 mm.6 mm)) were studied in this experiment. These ceria samples were held at 500 oC for 30 hours, instead of direct cooling down to room temperature, following the reduction process of 15 hours in 8.5-25 atm at 800 oC. The cooling rate was similar to what is described in Chapter 3 except this aging step was added in the middle of the cooling process. Cons istent with previous experiments, the controlling gas was continually flowed throughout the entire heat treatment process until the samples were taken out for XR D tests. The XRD scan took about 2.5 hours for

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76 the bulk ceria sample and 20 minutes for the (311) and (420) peaks of the powder sample. The reason that only these two peaks were chosen for the powder sample is because we want to shorten the amount of time that the powder sample ha d to be exposed in air. In another words, we want to minimize the reoxidation process of the reduced powder. The XRD results are shown in Figure 4-11 for the bulk sample and Fi gure 4-12 for the powder sample, respectively. The 2 position for stoichiometric ceria (311) peak is shown with dashed lines in Figure 4-11B and Figure 4-12. As shown in Figure 4-11A, the XRD pattern of bulk sample consists of the aforementioned pseudofluorite phase indicated as b and an new extra phase indicated with *. Because of the distinct underneath peaks (ind icated by the arrows) for the (311) (Figure4-11B), at least four distinct lattice parameters were identified for b phases. Thes e lattice parameters were 0.556 nm, 0.553 nm, 0.552 nm and 0.551, which correspond to the nonstoichiometric values (x in CeO2-x) of 0.32, 0.26, 0.24 and 0.21. Due to the low peak intensity of the asterisk phase, the detailed structure information coul d not be identified by this work. Comparing the XRD patterns of reduced bulk ce ria sample with and without aging process (Figure 4-11B and Figure 4-9B), the stoichiometric phases appear ed in the directly cooled sample but not in the aged sample. This indicates three pieces of important information. The first is that the stoichiometric phase that appeared in the directly cooled sample was due to phase transformation and not reoxidation at room temperature. The second is that the 500 oC aging process stabilized the pseudo-cubic phases and th erefore no stoichiometric phase was separated out. The third is that, the volum e ratio of the pseudo-cubic phases and the stoichiometric phases was affected significantly by the cooling rate. According to the information given by the aging

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77 experiment, it is suspected that the pseudo-cubic phases will be more pronounced if the samples are cooled slowly in hydrogen environment. However, comparing the XRD pattern for the aged powder sample (Figure 4-12) and the bulk sample (Figure 4-11B), it is obvious that the stoichiometric ceria (311) peak was present for the powder XRD but absent for the bulk sample. The strongest pseudo-cubic peak, i.e., b with a lattice parameter of 0.551 nm was present in the powder XRD pattern. As the powder and the bulk sample were heat treated simultaneously, th e XRD pattern should have similar features, or at least, same type of phases should be present. The difference in the XRD patterns between the powder and the bulk samples brings up the next question about the stability of the pseudo-cubic phase at room temperature. 4.3 Phase Transformation of Reduced Ceria at Room Temperature 4.3.1 Reduced Ceria Powder The powder ceria samples that were held at 500 oC for 30 hours after its reduction (under 8.5-25 atm at 800 oC for 15 hours) were systematically st udied for XRD patterns as a function of time at room temperature in air using XRD t echnique. The results ar e presented in Figure 413 in two different styles for be tter visualization. The peak co rresponding to the ordered ceria phases or b phases (marked with arrows) disapp eared relatively fast. In fact, the ordered phases were no longer present in XRD pattern after 36 hours of exposur e to air at room temperature. There were two distinct features for the decay ing process of the ordered phases. The first feature was that the decaying of the order phases was companied by the growing of the stoichiometric ceria phase. In another words, these two processes happened simultaneously. The second feature was, the decaying of the orde red phases with larger lattice parameter (the underneath peak at lower 2 ) was faster than the ones with smaller lattice parameter (the

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78 shoulder of the peak at higher 2 ). The second point is better seen from the change of the shape of the (311) peak of the ordered phases (See Figure 4-13B). In f act, the underneath peak at lower 2 of the ordered phase disappeared much faster so that the shape of the peak became less asymmetrical. In addition, after this room te mperature transformation, the color of the ceria powder turned noticeably lighter. Now the question is what causes the disappearan ce of the ordered phases. There are two possible mechanisms. The fist is the reoxidati on process. Reoxidation of these pseudo-cubic phases causes the larger Ce3+ ions (128.3 pm) transform into smaller Ce4+ ions Ce4+ (111 pm) ions [117], hence the lattice shri nks and the enhancement of the stoichiometric ceria peak at larger 2 values. The second mechanism is room temperature phase transformation. The pseudo-cubic phases with ordered oxygen vacancies are not stable at room temperature. Some phase transformation process of order ceria phase s such as order-disorder transition has been proved to be a relatively easy process (very low activation energy) and ca n happen very fast at room temperature [116, 118]. The exposure of reduced powder to air somehow might have triggered this transition. It is inevitable for both mechanism to operate, however, the dominate mechanism will be further discussed in th e following sections and section 4.3.3. 4.3.2 Reduced Bulk Ceria The XRD pattern for the bulk ceria sa mple after heat treatment at 800 oC under 3.6-22 atm for 15 hours was recorded as a function of time. The results are presented in Figure 4-14. Consistent with the observation for the XRD pa ttern in Figure 4-9, the ordered pseudo-cubic ceria phase was present at the initial stage. Even thought the XRD pa ttern in Figure 4-9 was taken 1.5 hours earlier than th e first XRD in Figure 4-14, th e former showed much more significant ordered phase peaks. If we consider the sample in Figure 4-9 was heat treated under 7.1-24 atm, it is understandable that the lower oxygen partial pressure created more oxygen

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79 vacancies, and hence the larger volume fraction of the ordered phase were formed. After 49 hours exposure to air at room temperature, the pseudo-cubic phases almost totally transformed (shown in Figure 4-14). The XRD patterns as a function of time were also recorded for the bulk sample with 500 oC aging process (the sample of Figure 4-11), and the results are presented in Figure 4-15A. The details of the 2 range from 53 to 61 degree can be better seen in Figure 4-15B. There are two important points observed from the XRD evolution profiles. On one hand, the entire asterisk phase and the majority ordered phases disappe ared after 40.2 hours expos ure to air at room temperature, this amount of time is comparable to the time need for the transformation of the sample in Figure 4-14. Considering the much lower oxygen partial pressure was used to reduce the sample for Figure 4-15 than that for Figure 4-14 (8.5-25 atm instead of 3.6-22 atm), a much higher vacancy concentration was expected fo r the sample in Figure 4-15. Therefore, if the reoxidation process was dominating, much l onger reoxidation time would be expected for more oxygen atoms to diffuse into the material fo r the sample in Figure 4-15. This controversy indicates reoxidation was not the major reason for the formation of stoichiometric ceria peaks. On the other hand, the decaying of the ordered phas es was not a progressive process. In another words, the decaying of the pseudo-cubic phase with larger lattice parame ter did not increase the volume fraction of the pseudo-cubic phase with sm aller lattice parameter, which is consistent with the observation for reduced ceria powder in Figure 4-13. All the pseudo-cubic phases simultaneously transformed into the stoichiometric ceria phase. Both of these two points indicate that the disappe aring the pseudo-cubic phases were caused by a room temperature phase transformation mechanism. The products of this transformation of the pseudo-cubic phases are expected to be the stoichiometric ceria phases and Ce2O3+ phase. However, the extra peaks for

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80 the hexagonal phases were too weak to be identified. After the transformation, the color of the bulk ceria after this transition did not change as significant as the powder. A comparison is made on the details of the XRD peaks of (311) and (420) in Figure 4-16 for a bulk ceria sample and a powder sample th at experienced the room temperature phase transformation (the bulk ceria and po wder ceria were reduced under 1.4-24 atm and 3.6-22 atm respectively). The XRD pattern for the stoi chiometric ceria powder is also shown in the figure for comparison purposes. After the transfor mation, the reduced bulk ceria sample and the powder sample both showed the larger FWHM (Full Width at Half Maximum) than the stoichiometric powder. In addition, purely from the shape of the peaks, the bulk ceria and the powder ceria sample with the transf ormation did not show distinct Cu K 2 peak. The broadened (311) peak indicates there were other phases present for the sample after room temperature phase transformation. The hexagonal Ce2O3 is considered to be the most stab le and possible phase [116] at room temperature for reduced ceria. An effort was made to find this phase through transmission electron microscopy (TEM). A TEM sample was made using focused ion beam (FIB) from a ceria bulk sample that was reduced under 3.6-22 atm. The TEM images were taken days after the samples were made to make sure the disorder ing transition was indeed finished in the TEM sample. The bright field (BF) and dark field (DF) images are shown in Figure 4-17 along with selected area diffraction pattern (SAD) with zo ne axis of [113]. The two beam condition used for the imaging (g=[242]) was imbedded into the pictur es. Although the SAD did not show extra diffraction spots, a second phase showed up in the BF and DF images. This secondary phase was about nanometer size. Although one can not draw an ab solute conclusion about the

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81 nature of the extra phase(s) from this limited TEM work, the existence of the extra phase(s) confirmed the previous arguments. 4.3.3 Effect of Ambient Environment From the above observations and discussion, it seems that the presence of oxygen is very important for the transformation of the pseudo-c ubic phases in ceria. The following experiment was designed to prove this point. One bul k ceria sample was firstly reduced at 800 oC under dry hydrogen (oxygen partial pressure of 1.7-25 atm) for 15 hours, then the sample was held in the dry hydrogen environment for 55 hours at room temperature before it was taken for XRD experiment. Because of the dry hydrogen environment, the reduced sample did not have access to oxygen prior to XRD experiment. The result of the XRD pattern is shown in Figure 4-18. The pseudo-cubic ceria phases b as well as the stoichiometric ceri a phase(s) a was both present. The peak ratio of these two sets of the phases was consistent to that of the XRD pattern in Figure 4-9 (reduced in oxygen partial pressure of 7.1-24 atm). Since the XRD pattern in Figure 4-9 was directly taken af ter the sample was cooled to room temperature and this XRD was taken after 48 hours of holding in H2 environment, the similar XRD profile of Figure 4-18 with Figure 4-9 indicate that dry H2 environment is not favorable for the room temperature transformation of the order phases. In order to understand the progr ess of this transformation in bulk ceria, we combined all the above XRD information and compared with th e reoxidation process to revisit the controlling mechanism for the decaying of the pseudo-cubic pha ses. If the disappearance of the order phase was caused by reoxidation, there should be so me relationship between the depth of the reappearance of the order phase and time. Th e reoxidation process can be considered as the oxygen on the surface diffuse into a 2.6 mm thick cer ia plate. Since the sample was exposed to air, the surface oxygen concentration was constant. Assuming the reduced sample had an initial

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82 uniform oxygen vacancy concentration, the diffusi on solution for this situation can therefore be calculated by J. Crack [106]. The diffusion distance can be simply considered to be approximately proportional to Dt, with D the oxygen diffusion coefficient in ceria at room temperature and t the diffusion time. However, as we know from the above results, the order phase disappeared from the XRD pattern in two days. Considering the interaction volume of XRD is about 5 m and the depth of the transformation was about 60 m after 220 days [Figure 4-8], the depth and the time had a linear relationship, not a square root relationship. Therefore, this estimation again confirms that the decay ing of the pseudo-cubic ceria phase was phase transformation process, not a reoxidation process. As we mentioned earlier, the exposure of reduced powder to air triggered the transformation of the ordered phase. We suspect this trigger comes from the relief of internal stress. Effects of stress on phase transformati on have been widely studied for variety of materials [90, 119-122]. It was also seen in ceria thin film system [116, 118]. However, we can not draw conclusions purely based on our results, future work is need to investigate this issue. 4.4 Microstructure of Fully Reoxidized Ceria Because the radius of the Ce4+ ion is much smaller than that of Ce3+, reoxidation of the reduced ceria shrinks the lattice [6]. If oxygen vacancies were the only products of the reduction process, ceria would go back to the stoichiome tric condition by reoxidati on [33]. However, the ceria samples experienced micros tructural changes when they we re reduced under oxygen partial pressure lower than 10-19 atm, i.e., microcracks were formed during the reduction, and phase separation happened during the cooling process. If reoxidation of ceria were carried out at a high enough temperature and in the single phase region (a bove the miscibility gap) the phases due to nonstoichiometry could be eliminated. The problem is the microcracks. In fact, because of the

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83 shrinkage effect of reoxidation process, these microcracks tended to extend and open up, and they eventually extended/developed into macrocracks. In order to demonstrate this behavior, a ceria Brazilian disc sample was fully reoxidized in air at 800 oC for 15 hours after its reduction heat treatment under oxygen partial pressure 1.7-22 atm. The sample was polished by 600 grit silicone carbide sand paper and th en painted with red ink. A digital image of this reoxidized sample is shown in Figure 4-19A (note that, th e redness on the sample came from the red ink and it was not the true color of the sample). The macrocracks are clearly shown (as the lines) in this image. The cracks formed a so-called mud pa ttern. If we recall th e microcacks in Figures 4-5 and 4-6 for the sample reduced under simila r oxygen partial pressure, the cracks for the fully reoxidized ceria were much larger and pronounced in terms of crack opening and crack length. The features of the cracks afte r reoxidation can be better seen through the SEM image presented in Figure 4-19B. In order to identify the positions of these cr acks, a piece of ceria sample from Figure 4-6 was thermo-etched at 1550 oC for 12 mins. In addition to the thermo-etch effect, this process also acted as reoxidation proce ss. The low magnification and hi gh magnification SEM images as a result of reoxidation are shown in Figure 4-20. Some macrocracks joined each other to form continuous crack net works. These joints are mark ed with arrows in Figure 4-20A. The core of the opening for the macrocr ack was as big as 3-5 m. The majority of the macrocracks overlapped the grain boundaries, suggesting that reoxidation process pr ogressed through grain boundaries. 4.5 Degradation of Ordered Ceria Phases in Water So far, all the reduced samples underwent the room temperature phase transformation were exposed to dry air. However, the reduced ceria was found to be very sensitive to the presence of water vapor during the handling of the sample. It is worth menti oning that the transformation of

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84 powder samples (see section 4.3.1) did not take the same amount of time. In fact, another experiment with similar schedule was repeated, but the powder completely transformed as soon as it was taken out of the furnace. The fast transformation was companied by a fast color changing. This inconsistency is believed to be associated with the ambient moisture level, in another words, the kinetics of this transition seemed to be very sensitive to the presence of water. Therefore, the following series of experiments we re performed in order to address this issue. One ceria bulk sample was heat treated at 800 oC under hydrogen/water vapor environment (oxygen partial pressure of 3.6-22 atm) for 15 hours. After it was fast cooled down to room temperature, the sample was kept in the furn ace with the hydrogen/water vapor flowing through for four days. The water vapor was condensed on the surface of the sample at room temperature and water moisture was visible on furnace inner wa ll. After the sample was taken out of the hydrogen/water vapor environment, the sample wa s found to be corroded into pieces (Figure 421). The XRD pattern of these pieces showed broadened peaks without the aforementioned pseudo-cubic ordered phases (Figure 4-22). It is suspected that the ordered phases transformed with the help of the water. Further SEM image analysis of these pieces (Figure 4-23) revealed the manner that the sample shattered. High ma gnification SEM image (Figure 4-23B) shows that the reduced ceria cracked through series of para llel planes, i.e., the water corrosion process followed a certain crystallographic planes. As the pseudo-cubic ceria phases have a structure with ordered oxygen vacancies, in another wo rds, the oxygen vacancies sit on particular crystallographic planes, the unique features of cracked planes due to the water corrosion process indicate that this process has a close connection with the disappearance of the ordered phases. In order to prove the above hypothesis, th e dry hydrogen reduced bulk ceria samples whose XRD pattern was present in Figure 4-18 were further st udied through the following two

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85 sets of experiments. One of the samples with the presence of the ordered phase was immediately soaked into water at room temperature after the XRD pattern was taken. After soaking in water for 12 days, the sample was noticeably cracked through water corrosion (Figure 4-24A). The corrosion crack progressed significantly for the following 5 days and the sample virtually cracked into pieces (Figure 4-24B). In contrast the second sample was exposed in dry air for 12 days before it was put into wate r (Figure 4-25A). From the prev ious results (section 4.5.2), 12 days was enough for the transformation process of ordered phases on the sample surface to finish. The sample did not start to crack until it was soaked in water for as long as 26 days. It was also noticed that the crack started at the sharp edges (Figure 4-25B). The much slower corrosion process for the second sample again indi cates that the order phases are susceptive to water corrosion. However, the mechanism for the decaying of the ordered phases in this case may be different than what described above in s ections 4.2 and 4.3 because of the involvement of water molecules. For comparison purpose, one as-sintered ceria sa mple was also soaked in water for a long time (38 days) at room temperature, and no corro sion damage was observed (Figure 4-26). This proves that the stoichiometric fluorite phase is very stable in water 4.6 Summary In summary, the behavior of ceria after reduction treatment at 800 oC and under low oxygen partial pressure is reported in this ch apter. Ceria samples developed microcracks (several m to 20 m) when the oxygen partial pressure was less than 10-19 atm. Some microcracks further developed into macroscopic level cracks (hundreds of m) during the reduction when the oxygen partial pressure level reached as low as 10-24 atm, resulting in broken samples. The reoxidation of the low oxygen partial pressure reduced ceria caused the microcracks to develop much larger in length with larger openning.

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86 Pseudo-cubic fluorite phases were present in the reduced ceria samples, these phases were derivatives of the fluorite st ructure with ordered oxygen vaca ncies. These order phases automatically transformed into stoichichiometric phases and Ce2O3+ at room temperature when the samples were exposed to dry air. These or dered phases were also found to be susceptive to water corrosion cracking.

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87 Table 4-1. Comparison of the XRD data for the as-received ceria powde r and the as-sintered ceria sample with JCPDS #43-1002 standard. Intensity, % Peaks Standard As-sintered ce ria As received powder (111) 100 100 100 (200) 27 27 30 (220) 46 36 57 (311) 34 26 44 (222) 6 4 8 (400) 6 4 7 (331) 12 8 15 (420) 7 5 9 (422) 10 6 13 (511) 9 5 10 Table 4-2. Grain sizes and densities of the materials. Materials Grain size, m Density, g/cm3 Relative density, % Ceria Nanoindentation samples Bending samples Brazilian disc samples 13 24 30 6.81 94%% GDC Nanoindentation samples 5 7.10 98%% YSZ Nanoindentation samples 4 5.95 >99%

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88 255075100 Intensity, (a.u.)2 theta, degree as-sinted ceria as-received powder Figure 4-1. X-ray diffraction pattern (XRD) of the as sintered ceria. Figure 4-2. Images to show grain sizes of the materials. (A) SEM image for ceria nanoindentation sample. (B) Optical imag e for GDC nanoindentation sample. (C) SEM image for YSZ nanoindentation sample. (A) (111) (200) (220) (311) (222) (400) (331) (420) (422) (511)

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89 Figure 4-2 ctd. Figure 4-3. Color change of ceria samples after heat treatment unde r various oxygen partial pressure. The diameter of each sampled was about 6 mm. P O2= 0 2 2 a t mP O2= 9 5 x 1 05a t mPO2=1.8x10-17atmP O2= 4 5 x 1 02 2a t mP O2= 5 1 x 1 02 5a t mA B C D E F P O2= 0 2 2 a t mP O2= 9 5 x 1 05a t mPO2=1.8x10-17atmP O2= 4 5 x 1 02 2a t mP O2= 5 1 x 1 02 5a t mA B C D E F P O2= 0 2 2 a t mP O2= 9 5 x 1 05a t mPO2=1.8x10-17atmP O2= 4 5 x 1 02 2a t mP O2= 5 1 x 1 02 5a t mA B C D E F (B) (C)

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90 Figure 4-4. Digital image take n after four ceria discs with a diameter of 26 mm exploded during the reduction at 800 o under and oxygen partial pressure of 8.5-26 atm. Figure 4-5. SEM images of ceria sample reduced under 4.5-22 atm (at 800 oC for 15 hours) show large macrocrakcs (~100 m) at the top surface layer. Quartz tube furnace Pieces of ceria Alumina plate Ruler (A) (B)

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91 Figure 4-6. SEM images of the microcracks in th e middle of the ceria samp le after reduction in 2OP=4.5-22 atm (at 800 oC for 15 hours). The arrows in the images indicate the positions of the microcracks. (C) (B) (A)

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92 Figure 4-7. XRD patterns for ceria samp les after heat treatment (A) in air (2OP=0.21 atm) and (B) in H2/H2O mixture (2OP=4.6-22 atm). XRD patterns were taken one week after the heat treatment. Figure 4-8. The (311) XRD peak of pure ceria sa mple at various depths from the surface, as indicated by the numbers on the cu rves, after heat treatment under 2OP= 4.6-22 atm. The arrow indicates the extra peak of the ordered phase. These XRD patterns were taken 220 days after the reduction treatment. (A) (B)

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93 20406080100 Intensity, (a.u.)2 theta, degree 2.5 hours 54555657585960 Intensity, (a.u.)2 theta, degree 2.5 hours Figure 4-9. (A) XRD pattern of ceria after reduction under 7.1-24 atm (800 oC for 15 hours). (B) shows the details of 2 range of 54 to 60 degrees a indicates the CeO2 phase, b indicates pseudo-cubic nonstoichiomet ric fluorite phases. The dashed line indicates the stoichiometric CeO2 peak position for (311). (A) (B) a a a a a a a a a a b b b b b b b b b b a b b a

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94 204060801002 theta, degreeIntensity, (a.u.) 2/3 Ce2O3 1/3 CeO2 Figure 4-10. Theoretical XRD pattern for cer ia with 2/3 volume fraction of hexagonal Ce2O3 phase (indicated by arrows) and 1/3 volume fraction of cubic CeO2. The extra peaks of the hexagonal phase shows very weak in tensity even though hexagonal phase is the major component. 2030405060708090100 Intensity, (a.u.)2 theta, degree 2.5 hours Figure 4-11. (A) XRD pattern of bul k ceria sample after aging at 500 oC. (B) shows the details of 2 range of 52 to 60 degrees. b i ndicates pseudo-cubic nonstoichiometric fluorite phases, * indicates another unidentified phase. b b b b b b b b b b * * * * * (A)

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95 54565860 Intensity, (a.u.)2 theta, degree 2.5 hours Figure 4-11. ctd. 54565860 Intensity, (a.u.)2 theta de g ree 20 mins Figure 4-12. XRD pattern of powde r ceria sample after aging at 500 oC. a indicates the CeO2 phase; b indicates pseudo-cubi c nonstoichiometric fluorite phases. The dashed line indicates the stoichiometric CeO2 peak position for (311). b a b b(B) b

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96 54565860 2 theta, de g ree 20 mins 40 mins 36 hours Intensity, (a. u.) stoichiometric ceria 545556575859602 theta, degreeIntensity, (a.u.) stoichiometric ceria 36 hours 40 mins 20 mins Figure 4-13. (A) and (B) are XRD patterns as a f unction of time for the ceria powder that were reduced aged at 500 oC for 30 hours after reduction at 800 oC for 15 hours. The XRD pattern for CeO2 powder is also presented for comparison. The dashed lines indicate the stoichiometric CeO2, peak positions. b indicates the ordered phases. (A) (B) b a b a a a b

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97 54565860 2 theta, degreeIntensity, (a.u.) 4 hours 49 hours Figure 4-14. XRD patterns as a function of time fo r the ceria bulk sample that were reduced at 800 oC for 15 hours under oxygen partial pressure of 3.6-22 atm. a indicates the stoichiometric ceria phase(s); b is the ordered phases. b b a a a a

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98 20406080100 2 theta, degree 2.5 hours Intensity, (a.u.) 40.2 hours 56.2 hours Figure 4-15. (A) shows the XRD patterns as a f unction of time for the bulk ceria sampler that were reduced at 800 oC for 15 hours and then aged at 500 oC for 30 hours. (B) shows the details of the XRD pattern with 2 range of 53 to 61 degree. The dashed lines indicate the CeO2 peak positions; b is the ordered phases. (A) b b b b b b b b b a a a a a a a b b b a a a a a a a

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99 54565860 56.2 hours 40.2 hoursIntensity, (a.u.) 14.6 hours 2 theta, degree 2.5 hours Figure 4-15. ctd. 5455565758596061 2 theta, de g reeIntensity, (a.u.) Reduced bulk ceria RT for 56.2 hours Reduced powder ceria RT 30 hours Stoichiometric ceria Figure 4-16. Comparison of the pe ak (311) and peak (420) for CeO2 powder with a bulk and powder ceria sample after room temp erature phase transformation. (B) b b b a a a

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100 Figure 4-17. TEM bright field (BF) image (A) and dark field (DF) image (B) along with the selected area diffraction (SAD) pattern (C) for the bulk ceria sample reduced under 3.6-22 atm. Zone axis is [113] with g=[242] for the two beam condition. (A) (B) (C)

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101 525456586062 Intensity, (a.u.)2 theta, degree 20mins Figure 4-18. XRD pattern of a reduced bulk ceri a sample after the sample was held under dry hydrogen at room temperature for 55 hours. a represents the st oichiometric ceria phase(s) and b represents the pseudo-cubic ceria peaks. b b a a

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102 Figure 4-19. A digital image (A) and an SEM im age (B) of one fully re oxidized ceria Brazilian disc sample. The Brazilian disc had a diam eter of 26 mm and thickness of 2.6 mm. (A) (B)

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103 Figure 4-20. Low magnification SEM image (A) of the thermo-etched ceria sample that exploded at 800 oC under 8.5-26 atm. (B) High magnification SEM image of the boxed area in (A). (A) (B)

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104 Figure 4-21. Digital image of the reduced ceria sample after holding in hydrogen/water vapor environment for 4 days. These pie ces come from one bulk sample. 5455565758596061 Intensity, (a.u.)2 theta, degree 20 mins Figure 4-22. The (311) and (420) XRD peaks of a reduced ceria sample after holding in hydrogen/water vapor environment for 4 days.

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105 Figure 4-23. (A) Low magnificat ion SEM image of a piece of sa mple from Figure 4-21. (B) High magnification image of the boxed area in (A). (A) (B)

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106 Figure 4-24. Digital images of a reduced ceria before the surface phase transformation. (A) After soaking in water for 12 days and (B ) after soaking in water for 17 days. (A) (B)

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107 Figure 4-25. Digital images of a reduced ceria 12 days after the surf ace phase transformation. (A) On the first day soaking in water and (B) after soaking in water for 26 days. Figure 4-26. Digital image of an as-sintered ceria after soaking in water for 38 days. (A) (B)

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108 CHAPTER 5 REDUCTION EFFECTS ON ELAS TIC MODULUS AND HARDNESS This chapter reports the elastic modulus te st results by nanoindentation and four point bending as well as the hardness re sults also evaluated by nanoinde ntation. As mentioned earlier in Chapter 2, because the nanoindentation test is limited to room temperature, the bending modulus for polycrystalline materials was also evaluated at room temperature for comparison purposes. The samples used for nanoindentation a nd four point bending we re all heat treated under various oxygen partial pressure and fast cooled to room te mperature prior to mechanical testing. As reported in Chapter 4, reduced ceria samples experienced microstructural changes at room temperature. We manage to limit this effect by conducting the tests shortly after the reduction process. The elastic modulus (section 5.1) and hardness (section 5.2) for all three types of materials were then evaluated as a f unction of oxygen partial pr essure within 2 days after reduction. The effect of reduction trea tment on the elastic modulus was related to the defect concentration using an empirical model. In addition, in order to investigate the significance of room temperature microstructu re transformation on el astic modulus, the time dependence of the elastic modulus for redu ced ceria is reported in section 5.3. 5.1 Reduction Effect on Elastic Modulus 5.1.1 Intrinsic Elastic Modulus 5.1.1.1 Evaluation of crystallographic anisotropy As nanoindentation technique wa s applied to measure the in trinsic elastic modulus, the first question we need to answer is the effect of crystallographic anisotropy on the test results. In Chapter 3, it has been shown that the material s used in this resear ch had a random fluorite structure, i.e., no texture was obs erved in the bulk samples. Si nce the size of the indents during nanoindentation is much smaller than the grain size of materials investigated here, several

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109 indents could be applied within one single gr ain. Considering each grain has different crystallographic orientation, the first effort was to identify the crystallorgraphic orientation dependence of the elastic modul us for all three materials. Nanoindentation tests with the same loading function were performed on the air treated samples. These samples were selected for this test for two reasons. Firstly, the oxygen vacancies inside air treated samples are purely du e to thermal effects, th erefore, the amount of the vacancies is so small that these air tr eated samples have a composition close to the stoichiometric CeO2 condition. Therefore, the elastic m odulus for schoichiometric condition can be conveniently compared to l iterature reported data. Sec ondly, since the only difference between other heat treated samples and the ai r treated was the oxygen partial pressure for reduction, comparison between the elastic modulus of those samples with the elastic modulus of air treated sample will pr ovide the information of reduction tr eatment effect on elastic modulus. In another words, the result of air treated sample s will be served as the comparison basis for the effects of oxygen partial pre ssure on elastic modulus The nanoindents were distributed in a 10 or a 7 pattern with 5 m separation from each other. Considering the grain sizes (see Table 4-2), a total area with more than 16 grains was covered for ceria and with 45 to 70 grains wa s covered for gadolinium doped ceria (GDC) and yttria stabilized ziconia (YSZ) samples. All the indents were made using maximum load of 5 mN for 5 seconds. The loading a nd unloading rate was kept at 1 mN /s. A typical in dent with the associated load-displacement curve for air treated ceria is shown in Figure 5-1. This indent is about 0.6 m in length with a contact depth of 120 nm. No cracks were observed at this indentation load level. The mean elastic modulus for the air treated samples was 264.15.5GPa for pure CeO2, 254.66.4GPa for GDC and 243.37.5 for YSZ. The small variation in the

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110 elastic modulus for each sample (less than 6%) in dicates that the tested oxides with the fluorite structure are elastically isotropic. In comparison to elastic moduli measured us ing bulk specimens, na noindentation results are usually higher because the former includes th e effects of process defects such as pores. Therefore, we find that the el astic modulus values for pure ce ria and GDC measured are both approximately 33% higher than the bulk material values reported by K. Sato et al. [41]. In the case of YSZ, our data are 18% lower than th e nanoindentation result s on single crystal YSZ reported by B. Savoini [123] but 10% higher than the dynamic bulk elastic modulus of 222 GPa for porosity-corrected 6.5 mol % YSZ reported by J.W. Adams et al. [124] and A.J.A. Winnubst [125]. Besides the composition and microstr ucture differences, bulk elastic modulus measurements using conventional mechanical test methods have limitations of strain measurement and fixture/sample contact, which normally yield lower values. 5.1.1.2 Effect of oxygen partial pressu re on intrinsic elastic modulus The relationship between elastic modulus and ox ygen partial pressure is an important piece of information for the application of these materials in SOFCs. The purpose of this section is to quantify this relationship. The importance of the sample preparation for consistent nanoindentation results was addressed earlier in Chapter 3. The oxygen range used in this evaluation was 0.22 atm to 10-25 atm. The detailed elastic modulus values along with the standard deviation for all three materials are listed in Table 5-1. It is obvious that the elastic moduli for both pure ceria and GDC were drastic ally decreased after reduction in low oxygen partial pressure atmosphere; however, the variati on of oxygen partial pressure for the test range did not create much effect on the elastic modulus of YSZ. This trend can be better seen by plotting the relative modulus (the elastic modulus for various oxygen partia l pressures divided by the elastic modulus for air treated sample) vs. ox ygen partial pressure (Figure 5-2). The elastic

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111 moduli for pure ceria and GDC remained almost constant when oxygen partial pressure was higher than 10-17 atm, but decreased approximately 28% as the oxygen partial pressure was reduced down to 5.1-25 atm. The trends of the elastic modulus versus oxygen partial pressure for all three materials are consistent with the change in the concentration of defects (the defect concentrations are shown in Figures 2-4, 2-5 and 2-6), i.e., the elastic modulus decreased as the defect concentration was increased. When the oxygen partia l pressure is reduced below 10-17 atm, the defect concentration significantly increases in ceria and GDC, however the defect concentration in YSZ was not affected noticeably within the tested oxygen par tial pressure range. The insignificant amount of defects created in YSZ was not enough to cause noticeable changes in the elastic modulus this material. 5.1.1.3 Theoretical analysis Oxygen vacancy is the major s ource of defects when fluorit e oxides are reduced at low oxygen partial pressure [11, 12, 46]. This relation ship was addressed previously in Chapter 2. The formation of the oxygen vacancy and concomitant presence of lower valent cations can cause an increase in average inter-atomic bond length [6, 60]. This change in bond length is expected to result in a re duction in the intrinsic elasti c modulus [43, 44, 126]. In order to relate the elastic modulus to this bond length change the theoretical net potential, enet, between two neighboring atoms is expresse d by the classic potential format as m n net r B r A e (5-1) where, A, B, n and m are empirically determined constants (m < n); 1 m and 9 n for ionic bonding [61]; r is the distance between two atoms. At the equilibrium state,

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112 m n netr m B r n A dr de F0 00 (5-2) where, r=ro is the equilibrium distance at 0 K, which is directly related to the lattice constant. In Chapter 2, we have discussed that there is linear relationship between lattice constant and vacancy concentration (Equation 2-7), we can generalize this relationship as x a a 0, or 10 0 x a a a (5-3) where, 0a and a0 are the lattice parameters in the stoichiometric and nonstoichiometric conditions, respectively; is the slope of expansion versus nonstoichiometry curve, which in case of ceria, is nm 04612 0(Equation 2-7)[6], x is the vacancy concentration, i.e., x in CeO2-x. The elastic modulus, E, can be estimated from th e second derivative of the enet, relative to r as Equation 2-7. Combining Equations 2-7, 5-2 and 5-3, the elastic modulus in a nonstoichiometric oxide can be expressed as [43, 44] 3 0 ) 3 ( 01 ] ) ( [ n nx a r m n An E (5-4a) or 3 0 ) 3 ( 01 ] ) ( [ m mx a r m n Bm E. (5-4b) For the stoichiometric compound the elastic modulus is defined as E* and is given as ] ) ( [ *) 3 ( 0 nr m n An E ] ) ( [) 3 ( 0 mr m n Bm (5-5) where, 0r is the equilibrium distance in the stoichiometric CeO2 condition. Consistent with the experimental observation, Equation 5-4 predicts that elastic modulus should decrease with increasing lattice parameter owing to the introduction of defects. However, experimentally it is

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113 easier to measure lattice parameter than vacancy concentration. Ther efore, we rearrange Equation 5-3 and it yields [43] ) 3 ( 0 0 ) 3 ( 0) / ]( ) ( [ n na a r m n An E (5-6a) or ) 3 ( 0 0 ) 3 ( 0) / ]( ) ( [ m ma a r m n Bm E (5-6b) where, 0a and ao is the lattice parameters in the stoi chiometric and nonstoichiometry conditions, respectively. When defects are introduced into the lattice, it is expected that n and m values do not change significantly but both A and B values may vary with the defect concentration. Equations 5-6a or 5-3a is applic able if we assume that the repulsive force is not significantly changed but the attractive for ce is noticeably decreased as de fects are introduced. However, Equation 5-6b or 5-3b would hold, if B remains unchanged, but the repulsive force, i.e. A would be altered. The general relationship between the elastic modulus in stoichiometric and nonstoichiometric states can be expressed as [43] ) 3 ( 0 0 *) / ( / qa a E E (5-7) Assuming that temperature has insignificant e ffect on elastic modulus and lattice parameter ratios, an evaluation of Equation 5-7 would sh ed light on the nature of bond modification. Since YSZ samples were not affected by the heat treatment, we analyzed the data for pure ceria and GDC in the following. The vari ation of the normalized elastic modulus (E/E*) for both ceria and GDC as a function of oxygen partial pressu re is shown in Figure 5-3. Considering that 0.5 mole oxygen vacancies are created when 0.1 mole Gd3+ are doped into ceria system, the lower elastic modulus value (~4% lower) of air treated GDC than ai r treated pure ceria is due to the pre-existing oxygen vacancies by doping. Beside s this initial differen ce, the variation of normalized elastic modulus for ceria and GDC follows the same trend as described above.

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114 Another useful comparison is to plot the normalized elastic modulus as a function of normalized lattice parameter. This plot in loga rithmic scale will yield used information about the q value in Equation 5-7. However, since our samples were heat treated in the bulk form and cooled fast to room temperature, several issu es including phase transf ormation and microcracks developed during heat treatment were addressed in chapter 4, the accurate measurement of the lattice parameter changes due to nonstoichiomet ry could not be evalua ted from my own room temperature XRD data. In order to make this ev aluation, we used the lattice parameter values from studies by Chiang et al. [5] and Wang et al [127], where powder materials were heat treated under conditions similar to ou r experiments. The values for E* and 0a were the values for stoichiometric conditions, in this case, they were taken as the elastic modulus and lattice parameter for air treated pure ceria, re spectively. Under this treatment, Gd3+ and Ce3+ were essentially considered to create the same effect on lattice para meter when they were introduced into the ceria system by the same amount to create oxygen vacancies. Since the lattice parameters in references [5] a nd [127] were measure at the 800 C (in-situ measurement), we corrected the values to room temperature usi ng the expansion coefficient parameter given by Mogensen et al. [6], i.e., (12.160.5)-6 K-1 for ceria based materials. However, this correction did not change the latt ice parameter ratio noticeably. The variation of the normalized elastic modulus ( E/E*) as a function of the normalized lattice parameter ( a/ 0a) are shown in Figure 5-4. The plots fit very well with the line corresponding to q =9. Since q value is equal to the n value in Equation 5-1, it suggests that the introduction of the defects modifies the attractive forces in the fluorite-structured oxides, but the effect on the repulsive compone nt is insignificant [43].

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115 5.1.1.4 Effect of fine pores Although the size of the nanoindents is small, th e results are still suspec ted to be affected by fine pores when the pore size is comparable to or smaller than the indent size. In order to address this issue, one ceria sample was prepared similarly as the procedure described in Chapter 3 but without adding PVB binder an d the cold isostatic pressing (CIP) procedure. The absence of binder and CIP procedure resulted in non-uni formly distributed porosities. Although the overall density was achieved to be about 94% afte r sintering, the outer surface of the sample was relatively much denser than the middle portion. This sample was cut in the middle to form two samples. The procedure is schematicly showi ng in Figure 5-5. The typical microstructure features on these two samples are shown as scanning electron microscopic (SEM) images (Figure 5-6). Sample B (middle part) showed the presence of fine pores in addition to the large pores observed in sample A (dense surface). Na noindentation tests were conducted for these two samples. The dense surface sample showed an elastic modulus of 248.1 8.0 GPa and the less dense middle part (sample B) show ed an elastic modulus of 204.0 16.0 GPa (see Table 5-2). This difference in the elastic modulus can be attr ibuted to the presence of the fine pores in the latter sample. During the data analysis stage, the indent data that were on or close to big pores were discarded by observing the topographic im age of each indent (shown in Figure 3-5). However, when much finer pores in the microstr ucture were on the order of sub-microns, it is impossible to recognize them especially when they were underneath the indents. Furthermore, the larger standard deviation of the elastic modulus for sample B (l ess dense) is also indicative of the probability of the indents encountering th e fine pores. These finer pores inevitably contributed to the nanoindentation results, and in this case, 18% lower elastic modulus value was measured when the fine pores were present. In addition, the lower hardness values of sample B

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116 (less dense sample) than sample A (denser sample) confirms the presence of fine pores. Unfortunately, the porosity and por e size distribution for the sample s prepared by this procedure was not quantified for further analysis. The question here is how the reduction treatment affects samples with different porosities. In another words, if we can quantify the change s of the elastic modulus after different heat treatment, do we need to accommodate another micr ostructure related para meter? In order to answer this question both above sa mples were reduced under the dry H2 for the same length of time following the heat treatment procedure describe d in Chapter 3. The oxygen partial pressure measured during the heat treatment was about 10-26 atm. The reduced samples were then prepared for their second nanoindent ation tests. The results are al so summarized in Table 5-2. The dense surface (sample B) show ed an elastic modulus of 155.7 15.5 GPa and the less dense middle part (Sample A) showed an elastic modulus of 133.2 13.4 GPa. These results tell us two important facts. First, elastic modulus of cer ia was decreased significan tly after reduction in H2. Second, after H2 reduction treatment, elastic modulus for the two samples with different porosity both decreased about same amount (35%). This re sult confirms that the degradation of elastic modulus due to the presence of vacancies is an intrinsic prop erty and nanoindentation is a reliable technique to evaluate this relationship. Thus, to give a clear answ er to the question that was brought up above, the effect of reduction on elastic modulus should not be varied by the initial microstructure state. 5.1.2 Bulk Elastic Modulus In order to evaluate the elastic modulus fo r bulk samples, four-point-bend tests were applied according to the procedure explained in Ch apter 3. As explained previously, due to the nature of nanoindentation tests, the effect of porosity and microcracking on elastic modulus was

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117 minimized. It needs to be pointed out that in the absence of elastic an isotropy, the presence of grain boundary in polycrystalline bu lk samples is not expected to affect the elastic modulus as significant as pores and microcracks. All the tests were carried out within two days after the heat treatment process to minimize the reoxidation effects as discusse d in Chapter 4. The results of bending tests for elastic modulus as well as the number of samples tested are show n in Table 5-3. The elastic modulus values were reproducible among several tests from sample to sample for each condition with the maximum variation of 7% for the air treated ce ria. Comparing the average elastic modulus measured by bending tests with those measured by nanoindentation for the air treated condition, the bending test results were 30% lower for pure ceria, 26% lower for GDC and 20% lower for YSZ. This difference is related to be the eff ects of porosity and possibl y experimental errors. However, the bulk elastic modulus results measured by bending tests of this work are comparable to the literature reported bending mo dulus values for both ceria and GDC [41]. As shown in Table 5-3, bulk elastic modulus could not be evaluated in bending when the oxygen partial pressure was higher than 10-20 atm due to severe microcracking. Most of the bending samples for ceria and GDC did not surv ive the reduction treatment for oxygen partial pressure of 10-22 atm and 10-24 atm. The survival rate became less as the oxygen partial pressure was decreased. Furthermore, the fracture loads fo r the ceria and GDC samples that survived the reduction treatment were too low (less than 2 lbs) for evaluating the elastic moduli. It should be mentioned that it was very difficult to control the oxygen partial pressure within one order of magnitude accurately using th e available facilities. In another words, although 10-20 atm may not be the lowest oxygen partial pressure we coul d achieve for bending samples, any other heat

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118 treatment with oxygen partial pressure between 10-20 atm and 10-22 atm became practically unreasonable. Consistent with the intrinsic elastic m odulus obtained by nanoindentation, the bulk bending modulus results reveal that the elastic m odulus for ceria is significantly decreased after reduction treatment under 8.8-20 atm, and the reduction did not significant affect the YSZ samples. Figure 5-7 presents a detailed comparis on of the oxygen partial pres sure on the elasetic modulus as evaluated by both techniques for all three materials. The moduli measured by these two methods were normalized by the respective el astic modulus for air treated samples for the purpose of comparison. The reduction treatment di d not create much effect for YSZ. Ceria and GDC behaved similarly to the reduction treatment. The reduction treatment effect on the elastic modulus of bulk ceria was more pronounced (Figur e 5-7) than the effect on elastic modulus by nanoindentation. This difference can be attribut ed to the microcrack formation during the low oxygen partial pressure reduction pr ocess. Since the decrease of the elastic modulus values by nanoindentation tests was not sign ificantly affected by microcrack ing, it can be concluded that the variation of the intrinsic elastic modulus w ith oxygen partial pressure is mainly due to the point defects formation. However, the decrea se of the bulk elastic modulus after reduction treatment measured by bending includes the effe ct of both point defects formation and the microcracks and hence the more pronounced de crease in elastic modulus was observed. 5.2 Reduction Effects on Hardness The room temperature hardness values of cer ia, GDC and YSZ evalua ted as a function of the oxygen partial pressure by nanoindentation tests are listed in Table 5-4. The hardness value for YSZ changed from 17.9 0.4 GPa for air treated condition to 16.2 1.8 GPa for dry hydrogen treated condition. Thus, reduction treatment did not affect the hardness of the YSZ significantly

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119 considering the test errors. The heat treatments under various oxygen partial pressures higher than 10-17 atm did not create much effect on the hardne ss for ceria and GDC either. In general, the variation of the test results for ceria a nd GDC increased as the oxygen partial pressure decreased. The trend of the hardness for ceria and GDC as a function of oxygen partial pressure is plotted in Figure 5-8. Ceri a and GDC behaved similarly within the tested range. It is important to point out that th ese curves indicate a maximum hardness for the samples heat treated at 2OP =4.5-22 atm for both materials. This interesting phenomenon is absolutely different with the trend observed previously fo r the reduction effects on elastic modulus. Here, the question is what causes this difference. Hardness is a material property that measures the resistance to both elastic and plastic deformation. It should be noted that nanoindentation results are not being affect significantly by the presence of microcracking and pores. The effect of oxygen partial pressure on hardness is mainly due to the effects of point defect conc entration. The effects of reduction in various oxygen partial pressures on hardness of ceria and GDC can be ther efore explained in terms of two components, i.e., the elastic and the plas tic components. These two components behave differently as a function of oxygen partial pressure The point defect conc entration in ceria and GDC significantly increases as th e oxygen partial pressu re is decreased [11-12, 44]. On one hand, the increase in point defect concentration decrease d the elastic modulus as explained in the previous section [43]. The w eakening of the elastic modulus causes the resistance to elastic deformation to decrease. On the other hand, as the point defect concentration increases, the interactions between dislocations and point defects become more prevalent, and hence enhance the resistance to plastic deformation. This strengthening effect is anticipated to increase hardness. As a result of these two opposing e ffects caused by the increase in point defect

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120 concentration, a maximum appeared in the ha rdness values in the region where the oxygen partial pressure was most effective in reduc ing the elastic modulus. This mechanism is schematically shown as Figure 5-9. 5.3 Effect of Room Temperature Holding So far, all the tests were conducted within two day after the reducti on process to minimize the contributions of room temp erature microstructure change. In order to understand the significance of room temperature microstructure change on elastic modulus measurement, the following experiments were also conducted. As we have shown in Chapter 4, reduced cer ia samples experience phase transformation at room temperature. It would be very relevant to evaluate this transformation effect on elastic modulus. If this transition affects elastic modulus, we expect to see variation of test results from nanoindentation as a function of time. Since th e XRD results showed that the transformation was completed within two days, we designed two test s to investigate this issue (the sample used in this test did not experience CI P procedure, the porosity might be different than those in used in Table 5-1). We tested a reduced ceria sample immediately after reduction treatment (oxygen partial pressure of 1.8-24 atm), and then tested the same sample again after one week and after 64 days. Note that, the XRD signals come from a depth of 5 m, which is similar magnitude of the interaction depth of the nanoide ntation (usually 5 times of cont act depth) of this research. Therefore, the results of these te sts should reveal the effect of th is phase transformation in ceria. The results of these three tests are listed in Table 5-5. As we can see, the average elastic modulus decreased 18% after 64 days of room temp erature holding. In addition, the hardness, also summarized in Table 5-5, showed the same trend as well. In order to see the significance of the time de pendence of bulk elastic modulus of reduced ceria, four ceria samples were reduced in oxygen partial pressure of 8.8-20 atm

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121 simultaneously, two of then were tested in bendi ng within 2 days after re duction (test 1, which is the data point in Figure 5-7A). In contrast the other two samples we re tested in bending modulus after 24 days (test 2). The results are listed in Table 56. The elastic modulus of the two samples for each tests showed consistent re sults. Although the average fracture load for each sets of tests remained the same, the aver age elastic modulus for test 1 was 154.1 GPa and dropped down to 123.4 GPa for test 2 (decreased 20%). This trend is consistent with intrinsic elastic modulus test results shown previously. Applying the same calcula tion that was used to determine the equilibrium time for reduction treatm ent (section 3.2), we can estimate the depth of reoxidation. Although the oxygen self diffu sivity in ceria can be as high as 10-12 cm2/s at room temperature by extrapolate the diffusivity data given by B.C.H. Steele [128], fully reoxidation in the samples (cross section of 2.6 mm mm) only took place in the thin top layer (less than 200 m). As discussed in 4.3.3, the decaying of the ordered phase was very sensitive to ambient condition and size of the sample. Th erefore, we measured the XRD pattern for the cross section of samples used in the test 2, a nd it was found that no ordered phases were present. In another words, the entire sample already transformed into stoichiometric phase(s) and Ce2O3+ phases. Now let us consider the pro cesses that took place in th e reduced ceria during room temperature holding and evaluate their contributions to the elas tic modulus. There are overall three processes. The first process was that oxygen vacancy concentration decreased due to reoxidation. The second process wa s the increase in microcrack de nsity by reoxidation. And the third process was the aforementioned room temper ature phase transformation. We know from section 5.1 and 5.2 that, the first process in creases elastic modulus and the second process decrease the elastic modulus. Now the question is how room temperature phase transformation

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122 affects the elastic modulus. As we discussed previously in Chapter 3, the contribution of microcrack to the intrinsic elastic modulus was mi nimized, therefore, only the effects of the first process and the third process cont ributed to the nanoindentation resu lts. The fact that the overall effect of room temperature holdi ng decreased the intrinsic elastic modulus indicates that phase transformation process decreased th e elastic modulus, which is consis tent with the observation of bulk elastic modulus. In summary, the decrease in elastic modulus after room temperature holding suggests that the macroscopic microstructure variations (mic rocracking and phase tran sformation) on elastic modulus override the effect of poi nt defects and decrease the elas tic modulus of reduced ceria. Based on these results, we can conclude that it is very important to pay special attentions to the details of the ex-situ tests for ceria based materi al due to their room temperature microstructural instability 5.4 Summary Three fluorite-structured oxide s, pure ceria, gadolinium doped ceria (GDC) and yttria stabilized ziconia (YSZ) were heat treated at 800 oC for 15 hours in an oxygen partial pressure range of 0.21-24.atm. The point defect concentration was conserved to room temperature by fast cooling. After these reduction treatments, the elastic modulus a nd hardness as a function oxygen partial pressure of were successfully eval uated. The bulk elastic modulus was measure by four-point-bend test and th e intrinsic elastic modulus wa s measured by nanoindentation, which was not affected by the presence of large pores and microcracks. The intrinsic elastic modulus for ceria and GDC decreased signifi cantly when the oxygen partial pressure was reduced below 10-18 atm. This phenomenon was explained by an increase in oxygen vacancy concentration, which weakens the Ce-O bond by increasing the bond length. The elastic modulus of YSZ within the stud ied oxygen partial pres sure range remained unchanged owing to

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123 the negligible deviation from stoichiometry. The bulk elastic modulus was lower than the intrinsic elastic modulus for air treated samples, which is due to the contribution of porosity to the bulk elastic modulus. The degradation of bul k elastic modulus of ceria was more significant due to the presence of microcracks caused by redu ction treatment. In another words, the preexisting microcracks significantly affected bulk elastic modulus of the low oxygen partial pressure reduced ceria. The hardness of YSZ did not show significan t change within the oxygen partial pressure range tested. However, the hardness of ceria and GDC showed a maximum as a function of oxygen partial pressure, which can be explaine d by two opposing effects caused by the increase in defects concentration.

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124 Table 5-1. Elastic modulus results for heat treatments under different 2OP evaluated by nanoindentation. Elastic modulus, GPa, after heat treatment under various oxygen partial pressure 2OP atm Materials 0.22 9.5-05 1.8-17 4.5-22 6.0-24 5.1-25 CeO2 264.1 5.5 251.5 11.1261.0 12.4235.7 8.8 ----190.4 14.9 Gd0.1Ce0.9O1.95 254.6 6.4 259.2 4.9 250.5 6.5 239.3 7.5204.7 3.8 ---(Y2O3)0.08(ZrO2)0.92 243.3 7.5 ----------------246.2 11.7 Table 5-2. Effect of reduction in H2 on the intrinsic elastic modulus of two ceria samples with different porosities (with 49 indents each test). As-sintered condition After Reduction in H2 Samples Elastic modulus, GPa Hardness, GPa Elastic modulus, GPa Hardness, GPa Overall changes in elastic modulus, % Sample A (dense surface) 248.1 8.0 9.5 1.2 155.7 15.5 8.8 1.4 37.2% Sample B (middle part with fine pores) 204.0 16.8 8.5 0.7 133.2 13.4 7.3 1.4 34.5% Table 5-3. Bulk elastic modulus results for heat treatments under different 2OP evaluated by four-point-bend tests. Various oxygen partial pressure 2OP atm Materials 0.22 3.4-04 8.8-20 CeO2 183.8 12.6 (6 samples) 196.3 (2 samples) 151.4 (2 samples ) Gd0.1Ce0.9O1.95 188.8(2 samples) 180.3 (2 sample) ---(Y2O3)0.08(ZrO2)0.92 192.3 (2 samples) 189.0 (1 sample) 177.9 2.3 (3 samples)

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125 Table 5-4. Hardness results fo r heat treatments under different 2OP evaluated by nanoindentation. Various oxygen partial pressure 2OP atm Materials 0.22 9.5-05 1.8-17 4.5-22 6.0-24 5.1-25 CeO2 9.4 0.14 9.5 0.9 10.2 0.5 11.6 1.1 -----9.2 1.2 Gd0.1Ce0.9O1.95 11.8 0.3 12.1 0.4 11.9 0.5 13.9 1.1 13.1 0.5 (Y2O3)0.08(ZrO2)0.92 17.9 0.4 ----------------16.2 1.8 Table 5-5. Room temperature holding effect on the intrinsic elastic m odulus and hardness of a reduced ceria sample (with 49 indents each test). Reduced ceria Immediately after reduction After 7 days After 64 days Elastic modulus 160.7 11.2 149.5 20.1 131.7 19.6 Hardness 9.6 1.3 8.9 1.3 8.2 2.0 Table 5-6. Room temperature holding effect on the bulk elastic modulus of reduced ceria samples. Tests Time after reduction test Number of samples Average bending modulus, GPa Fracture load, N Test 1 2 days 2 151.4 37.5 Test 2 24 days 2 123.4 35.8

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126 Figure 5-1. Nanoindent image on the as-sinte red pure ceria sample (A) and the corresponding load-displacement curve (B). 0.6 0.7 0.8 0.9 1 1.1 -30 -25 -20 -15 -10 -5 0log(PO2), atmE/Eair Nanoindentation results for ceria Nanoindentation results for YSZ Nanoindentation resutls for GDC Figure 5-2. Change of the elastic modulus as a function of o xygen partial pressure. 1 m (B) (A)

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127 Figure 5-3. Experimental results showing th e variation of normalized elastic modulus ( E/E* ) as a function of oxygen partial pressure for pure ceria and GDC. Figure 5-4. The normali zed elastic modulus ( E/E* ) as a function of the normalized lattice parameter (a/a*) for pure ceria and GDC. The symbols represent the experimental data with the elastic modulus measured in this work the and lattice parameter extrapolated from references [28, 29]. The dashed line has a slope of -12 and corresponds to q= 9 in Equation 5-7.

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128 Figure 5-5. Schematics of the preparation proced ure for samples with different porosities. The center dark circles on each surface indicat e where the indentation took place. Figure 5-6. SEM images of the microstructure for dense surface (A) and the less dense middle part (B). 10 m 10 m (B) (A) Surface: A Middle: B

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129 0.4 0.6 0.8 1-25 -20 -15 -10 -5 0log(PO2), atmE/EairNanoindentation results for ceria 4 point bending results for ceria 0.6 0.8 1 -25 -20 -15 -10 -5 0log(PO2), atmE/Eair Nanoindentation results for GDC 4 point bending results GDC 0.4 0.6 0.8 1 -2 5 -20 -15 -10 -5 0log(PO2), atmE/Eair 4 point bending results for YSZ Nanoindentation results for YSZ Figure 5-7. Relative elastic modulus ( E/Eair) as a function of oxygen partial pressure for ceria (A), GDC (B) and YSZ (C). (A) (B) (C)

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130 4 8 12 16 -25 -20 -15 -10 -5 0 log(PO2), atmH, GPa Hardess-GDC Hardness-Ceria Figure 5-8. Room temperature hardness as a fu nction of oxygen partial pressure for pure ceria and GDC samples. Figure 5-9. Mechanism of the reduction treatme nt effect on the hardness of ceria and GDC. Strengthening due to defect/dislocation interaction (plastic component) Hardness high low Weakening due to the decrease of E (elastic component)

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131 CHAPTER 6 REDUCTION EFFECT ON FRACTURE PROPERTIES OF PURE CERIA Since the variation of elastic modulus with def ect concentration is an ticipated to directly affect fracture properties, this chapter follows the previous work and is focused on the reduction treatment effects on the flexural strength and fracture toughness. Being consistent with the study on elastic modulus and hardness in Chapter 5, the same type of heat treatment method was adapted for the evaluation of fracture properties. However, almost all gadolinium doped ceria (GDC) samples were found to break during high temperature heat treatment at low oxygen partial pressure (2OP ) or during handling after the heat treatment, which made it impossible to conduct reliable mechanical property evaluati ons. Also, within the testing oxygen partial pressure range, there is no significant difference in the oxygen vacancy concentrations in the yttria stabilized zirconia (YSZ) samples, and this was confirme d by the insignificant changes of elastic modulus results. Thus, the fracture prope rties of YSZ samples are not expected to be influenced by the heat treatments under different oxygen partial pressure either. Therefore, fracture tests were only conducted on pure ceria in this study. 6.1 Flexural Strength Flexural strength was evaluated using fourpoint-bend testing met hod as explained in Chapter 3. Two examples of th e load-displacement curves obtained by flexural strength tests are shown in Figure 6-1. These curves are for samples treated in air (Figure 6-1A, 2OP =0.21 atm) and in H2/Ar (Figure 6-1B, 2OP =8.8-20 atm), respectively. Note that, the initial part of the loading curve (approximately 20 N) was omitted due to the nonlinearity caused by the contact friction between the sample and the fixture. Based on Equation 3-6, th e calculated strength values are 144 MPa (Figure 6-1A ) and 43 MPa (Figure 6-1B), resp ectively. In order to get a good statistics of strength values, multiple tests were attempted for certain heat treatment

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132 conditions. However, when the samples were heat treated under very low oxygen partial pressures, some of them broke during the heat tr eatment as explained in Chapter 4. Therefore, fewer samples were tested for lower oxygen par tial pressure heat treatment conditions. The flexural strength as a function of the oxyge n partial pressure, is given in Table 6-1. The corresponding oxygen partial pressure, approxi mate composition and number of samples tested are also listed in this table accordingly. The results show that the variation in the flexural strength test results was small (less th an 10%) for samples heat treated at low 2OP as well as for those heat treated under Ar. Howe ver, the strength of the air treated samples varied noticeably from sample to sample (more than 20% variation). Based on the test results given in Table 6-1, the flexural strength was reduced significantly as a result of the reduction process. The average flexural strength dropped from 127 MPa for air treated samples to almost no strength (<4 MPa) for dry hydrogen (2OP =4.8-24 atm) reduced samples. 6.2 Fracture Toughness Test Results Fracture toughness was evaluate d using pre-cracked Brazilian disc samples with chevron notches as explained in Chapte r 3. Pre-cracking was conducted by holding samples at a load below the fracture stress for a certain time to gua rantee the complete precracking of the chevron notch. Examples of load-time curves for Brazilian disc samples with notch to diameter ratio of approximate 0.5 are presented in Figure 6-2. The load per thickness values is shown in these plots for comparison purposes. Figure 6-2A show s the situation where the sample was directly loaded to fracture after treatment in air. From the linear loading curve, the fracture took place in an unstable manner. From the load level determ ined by Figure 6-2A, a second sample with the same heat treatment condition was loaded accordi ngly as shown in Figure 6-2B. In this case, sample was precracked at 857 lbs/in for 6 minutes unloaded and the loaded to fracture. Figure

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133 6-2C presents an example of the loadtime curve for a sample heat treated under 2OP =4.5-22 atm, which had a greater fracture toughness. As can be noted in Figure 6-2B and Figure 6-2C, the load decreased during the holding period. Since the precrack was under displacement control, the relaxing of the load during this process indi cates stable crack growth. The crack length used for calculating the fracture toughness was determined by studying the fracture surfaces of the chevron-notched sample s. The fracture surfaces showing the extent of stable precracks for the sa mple heat treated in air (2OP =0.21atm) and H2/H2O (2OP =1.5-20 atm ) are presented in Figure 6-3. The transition of stable precrack to unstable fracture for the sample heat treated in air is not as distinct as the sample heat treated in hydrogen. The transition front (dashed line in Figure 6-3A) of the air treated sample was distinguished from the low magnification scanning electron microscopic (S EM) image based on the distinct contrast between the two regions when the ar ea within the notch was in focu s. The stable precrack front for the hydrogen treated sample was easily identified as shown in Figure 6-3B. Within the stable crack region, the sample heat treated in hydroge n showed significant r oughness in comparison to the sample heat treated in air. For comparis on purposes, an unsuccessful precrack is shown in Figure 6-3C, where the stable to unstable transition happened within the notch. In this situation, this sample can not be used for fracture toughness evaluation. After determining the crack length, the fract ure toughness was then calculated to be 0.96 MPam1/2 and 1.36 MPam1/2 through Equation 3-7 using the fracture loads shown on Figure 62B and C, i.e., surprisingly, the KIC increased as much as 30 to 40% for the samples heat treated in a reduced atmosphere (2OP =1.5-20 atm.5-22 atm). Following the same procedure, multiple tests were attempted. The fracture toughness values for various oxygen partial pressures tested are shown in Table 6-2. The re sults were consistent for each heat treatment

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134 condition and KIC values deviated within 6% for multip le tests. The fracture toughness data showed that the as-sintered, air treated and N2 treated samples have similar room temperature KIC values with variations within the test error. 6.3 Fractographic Analysis The fracture surfaces of the flexural test samp les showed distinct differences between air treated and low 2OP treated samples. The as-sintered samples and the samples heat treated in air or N2 exhibited the classic brittle fracture patter n. Examples of these fracture surfaces are presented in Figure 6-4 for an as-sintered sample and Figure 6-5 for an air treated sample. Both samples fractured with one crack initiation site followed by a mirror zone (dotted regions in Figure 6-4B and Figure 6-5B) and a hackle zone spreading outward from the crack origin (Figure 6-4A and Figure 6-5A). SEM images of the crac k initiation sites (Figure 6-4B and Figure 6-5C.) reveal that both primary cracks were originated from processing defects such as large processing pores. The processing defects were located on the surface (Figure 6-5C ) or near the surface (Figure 6-4B) that were under tensile stress. However, no single distinct crack initiation or igin was found on the fracture surface of the samples heat treated in low 2OP atmospheres (2OP <10-19 atm). As shown in Figure 6-5A and B, for the two matching fracture surfaces of a sample heat treated under 8.8-20 atm, although crack propagation direction can be identified through the river marks, no distinct crack origin can be identified. On the other hand, near the edge, where crack was initiated, several fracture zones that had developed on different levels were dis tinguished. These zones are marked as A, B, C and D in Figure 6-5A and a higher magnification of zone A is given in Figure 6-5B. The size of these zones is approximately 200 to 800 m, which is much larger than the grain size or the microcracks (several micron to 20 m) formed upon heat treatmen t (see Figures 4-2 and 4-4).

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135 However, the microcracks on or close to the surface under maximum tensile stress are anticipated to act as crack init iation sites of these fracture zo nes. During loading, the preexisting microcracks with favorable size (largest) and orientation (perpend icular to the loading direction) will initiate fracture. The effect of these microcracks overrides the effects of processing defects. Since fracture zones developed by the propagation from different microcracks may lie on different planes, eventually they will join each other by fracturing the ligament left between them. This process causes th e formation of ridges that identify each zone. A comparison of the fracture surfaces of the sa mples heat treated in air versus those heat treated in the 2OP =8.8-20 atm, revealed that in addition to the crack initiation differences, the fracture surface roughness was affect ed significantly by the environment. The bending sample heat treated in the reduced at mosphere (Figure 6-7A) exhibite d a much rougher fracture surface than the sample heat treated in air (an image from the hackle zone shown in Figure 6-7B). Considering that the grain size of these samples were about 30 m, the roughness we see in Figure 6-7A (2OP =8.8-20 atm) is much greater than the grain size scale. This result is consistent with the observation made for the Brazilian disc samples. As shown in Figure 6-8, the fracture surfaces of ai r treated samples (Figure 6-8A and Figure 6-8B) are compared with the fracture surface of those heat treated 2OP =1.5-20 atm (Figure 6-8C and Figure 6-8D). Here, by observations of the imag es of the fracture surfaces with different magnification, two levels of roughness are revealed by observations of these images. The first level shown on the fracture surf ace (Figure 6-8B) of the low 2OP treated sample is much greater than grain size level, which is consistent with Figure 6-7A. By comparing the higher magnification images, the second level of roughness (F igure 6-8D) is revealed to be within the grain size scale. The greater roughness level on th e fracture surface is consistent with the higher

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136 fracture toughness results because a rougher frac ture surface can dissipate more mechanical energy than a smother surface. Further observations of the fracture surface of a Brazilian disc sample heat treated under H2/H2O (2OP =1.5-20 atm) with KIC=1.27 MPam1/2 revealed the presence of multiple secondary cracks (marked with arrows in Figur e 6-9A). As shown in a higher magnification image of one of the secondary cracks (Figure 69B), these secondary cr acks were actually extended to the fracture surface af ter the primary crack had passed through, as evidenced by the continuity of the river marks. 6.4 Pore-Crack Interaction In order to investigat e the reason for the toughening effect of heat treating in reduced atmospheres, the interaction between pores a nd propagating primary cracks was evaluated using a quantitative metallography anal ysis method for the Brazilian disc samples. The pore area densities on the polished surfaces and the fractur e surfaces were measured for samples heat treated under different conditions. Images from six different areas were measured for each type of surface (the six positions are approximately s hown on a digital image of the fracture surface in Figure 6-10). Typical images taken for this evaluation are shown in Figure 6-11 (Figure 6-11A for air treated sample and Figure 6-11B for the sample heat treated in 2OP =4.5-22 atm). The pore area fraction calculated on the polished surfaces i.e., ~6%, was consistent with the density of the material. Since the pore-crack interact ion may be size dependent the calculations were conducted also for the pores with sizes less than 2.5 m. The results of the measurements are shown in Table 6-3. The air treated samples showed a slightly higher area density on the fracture surf ace than on the polished surface, particularly for the smaller pores, indicating that the crack was at tracted to the pores. However, the results for

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137 the H2 treated sample suggest that the crack does not interact with fi ne pores or the larger ones. Based on this analysis, the pore-crack interactio n is not responsible fo r the higher toughness of the samples heat treated in a reduced atmosphere. 6.5 Discussion This work shows an interesti ng opposite effect of heat trea tment on flexural strength and fracture toughness when ceria was heat treated under 2OP <1.5-19 atm. Similar phenomenon was seen in composites of Al2O3 with unstablized ZrO2 dispersion [66], which was attributed to the effects of microcracks. In this section, an attempt will be made to interpret this phenomenon. 6.5.1 Strength The basic equation for fracture strength of ceramics, f based on Griffiths theory is shown as Equation 2-11 [75]. From the equation, we can see that the strength is therefore controlled by three basic parameters which are the elastic modulus ( E ), the fracture surface energy ( ) and the flaw size ( C ). From our previous results in Chapter 5, the elastic modulus of pure ceria decreased about 11% after reduction under 2OP =4.5-22 atm comparing to the value af ter heat treatment in air. This drop alone obviously can not explain the 90% strength reduction given in Table 6-1. On the other hand, the presence of macroscopic level defects particular ly on the surface is crucial to the results of flexural tests. The fl exural strength is controlle d by the crack initiation process through and defect size C The toughness resu lts suggest that may indeed increase after reduction treatment. Therefore, the change in fracture strength must be associated with the initial defect size. For the air treated samples, the processing def ects (such as pores) on or near the surface control the measured strength. Depending on the size of the processing defects ( C ), the strength may vary significantly from one sa mple to another. Heat treatment in low 2OP

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138 conditions causes the formation of many microc racks, much larger and sharper than the processing defects. Therefore, the decreased flexur al strength of ceria after heat treatment in a reduced atmosphere can be expl ained by the increase in the C value. Furthermore, f varies inversely with the square root of C and therefore the variation in f with defect size decreases as C increases. In air treated samples, the defect size is relatively small and consequently the strength may vary significantly from one sample to another (see Table 6-1). In contrast, the multiple crack initiation behavior (see Figure 6-6) and the consistency of the flexural strength values (see Table 6-1) for samples heat treated in low 2OP are associated with the presence of relatively sharp microcracks in these samples. 6.5.2 Fracture Toughness and Toughening Mechanisms for Reduced Ceria For the fracture toughness tests with Brazilian disc samples, crack initiation is not as crucial as in flexural tests a nd crack propagation controls the te st results. The fracture toughness can be expressed in terms of the critical elastic energy release rate, GC, and elastic modulus, E through Equation 2-13. Since the elastic modulus decreased about 11% [43, 44] and microcracks were present prior after reduction treatment under 2OP =10-22 atm, it is rather surprising to see the 37% improvement of the fracture toughness. In ideally brittle materials, GC is approximately equal to the twice that of th e fracture surface energy, However, in real materials, other factors may result in a higher elastic energy release rate valu e at the point of crack instability. Assuming the effect of defect formation through heat treatment on surface energy is insi gnificant, there has to be some microstructural reasons for the impr oved fracture toughness. In this case, the mechanical energy can be released through forma tion of new surfaces as well as any other terms that can dissipate part of strain energy. Th e following discussion is presented to explain the

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139 increase in toughness upon heat treatment in re ducing atmospheres based on the observations of the fracture surfaces, i.e., attempt to find microstruc tural features than can dissipate strain energy during crack propagation. One possible mechanism is the microcrack toug hening. The concept of crack tip shielding in the fracture process zone by microcrack fo rmation and extension wa s explained in section 2.4.2 [92-102]. Here, similar concept can be adopted We also have demonstrated the fact (see Figure 6-9) that upon crack propagation the pre-ex isting microcracks extend in the wake of the crack. Firstly, the extension of microcracks in creases the material compliance (see Figure 2-12) and thus contributes to the crack tip shieldi ng effects. Secondly, the extension of the microcracks can redistribute the ne ar-tip stresses and act as an ex tra source of releasing of the strain energy [92]. In another words, the mechan ical energy is released not only by formation of new fracture surfaces, but also by the extension of the pre-existing microcracks. Therefore, a greater apparent toughness will be measured. Crack deflection [82-84] is also suspected to be a mechanism for the enhanced fracture toughness of the reduced ceria. In this case, both tilt and twist effects for the 2OP <10-19 atm reduced samples come from the random oriented pre-existing microcracks. This concept is schematically shown in Figure 6-12. In this figure, the loading di rection (direction of app ) is defined as the Y-direction, consistent with Figur e 3-9. The tilt process (Figure 6-12A) gives the roughness level along the primary crack propagation direction, i.e. th e X-direction, and the twist (Figure 6-12B) explains the r oughness along the Z-direction. As shown in the schematics, the roughness level on the fracture surfa ce does not directly correlate with the distri bution of the microcracks shown in Figure 4-6. The overa ll roughness represents th e probability of the primary crack front meeting the microcracks. The fact that the roughne ss level for the fracture

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140 surface of the samples heat treated in low 2OP (shown in Figure 6-7A and Figure 8C) is much greater than the grain size level confirms thes e mechanisms. Therefore, during the propagation the crack front is anticipated to be deflected by the pre-existing microcracks, resulting in an improved toughness. 6.5.4 Other Important Factors As discussed in Chapter 4, after low oxygen partial pressure reduction treatment, ceria samples experienced phase transf ormations during cooling, re sulting in the presence of the pseudo-cubic ordered phases. The evidence fo r these phases can be found through Figure 6-13, which is an image of the fracture su rface for a sample heat treated under H2/H2O environment (2OP =1.5-20 atm). The geometric features indicate microstructure discontinuity. These features are much finer than grain size and in a range of several hundred s of nanometers (shown as arrows). In another words, the existence of second phases may also cause an improvement in toughness. We have shown that reduced ceria experienced microstructural cha nges, including phase transformation, at room temperature; however, th e effect of these changes on the measurements of fracture properties (see Table 5-6) was insignificant within th e time that these tests were conducted. However, this issue needs to be taken into consideration in the future. It is a common phenomenon for brittle material s to develop internal stress during heat treatment or during fast cooling. In our case, th e major internal stress is caused by the expansion difference between the reduced part and the unredu ced part. This issue has been addressed in detail by Atkinson, et.al. [38-40]. As discussed in Chapter 4, the microcracks were mainly developed during the high temperature reduction pr ocess, not the cooling process confirms this point. On one hand, although internal stresses ca n be partially released through the formation of

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141 the microcracks, the possibility of the effect of th e remaining internal stresses can not be ignored. On the other hand, the ordering process mentioned in Chapter 4 can also cause internal stresses because ordering can cause uneven expansion fo r different crystal or ientations [129]. Unfortunately, purely based on our current results, it is impossible to quantify this effect. The internal stress left inside the material could be under a complex state and the significance of their contribution to toughness measurement results is not clear from this work. Future work on theoretical calculations of th e development of internal stre sses and corresponding experimental investigations are suggested for better understanding. In addition, from Equation 2-11, we can see that it is very helpful to evaluate and compare the fracture toughness values from strength measurement. For example, in case of Figure 6-5, the main crack was suspected to be develope d from region A and B by observing the fracture surfaces at a higher magnification, but unfortunately the attempt of evalua tion of exact value of flaw size was not successful due to the irregular shap e of the initiation sites. Future work is also suggested to look in to this issue. 6.6 Summary In summary, the flexural st rength and fracture toughness of ceria was measured as a function of oxygen partial pressure using four-p oint-bend test and chevron-notched Brazilian disc under mode I condition, respectively. For the samples heat treated under very low 2OP it is clear that pre-existing microcr acks significantly decrease the flexural strength. When the samples were reduced in an oxygen partial pressure of 10-22 atm, the strength decreased more than 90%. Detailed fractographic analysis sh owed because of the presence of microcracks, multiple crack initiation was found on the fracture surface of the sample with low oxygen partial pressure reduction. Therefore, we conclude that the low flexural strength, which is controlled by

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142 crack initiation, is associated with the enhanced probability of fracture due to the large size and the sharpness of the microcracks formed during heat treatment in the reducing atmosphere. However, interestingly, the fracture toughness is increased by 30% when the oxygen partial pressure was decreased to 10-20 to 10-22 atm range. SEM analysis revealed that the greater toughness was accompanied with much rougher fractur e surfaces. In addition, secondary cracks were also observed on the fracture surfaces of low oxygen partial pressure reduced samples. Based on these observations and analysis, we conc lude that the increase in the fracture toughness in low 2OP atmosphere was associated with micr ocrack toughening and crack deflection mechanisms.

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143 Table 6-1. Room temperature fl exural strength test results. Heat Treatment Condition 2OP, atm. Number of Samples Tested Approximate composition f, MPa H2 4.8-24 1a) CeO1.825 c) <4 MPa H2 /H2O 2.3-22 2b) CeO1.877 c) 8 H2 /H2O/Argon 8.8-20 4 CeO1.991 c) 414 Argon 3.4-4 3 CeO2 c) 1378 Air 0.21 4 CeO2 12730 a) 5 samples were heat treated, 4 sample s broke during high temp erature reduction and only one sample could be tested. b) 3 samples were heat treated, however one sample broke during the high temperature reduction. c) The composition is extrapol ated from Bevan and Kordis [37]. The heat treatment under argon do not create significant am ount of oxygen vacancies [14,32]. Table 6-2. Room temperature fr acture toughness test results. Heat Treatment Condition 2OP, atm. Number of Samples Tested Approximate composition KIC, MPam1/2 H2 /H2O a) 4.5-22 2c) CeO1.899 d) 1.32 H2 /H2O b) 8.8-20 2 CeO1.981 d) 1.40 N2 4.5-6 1 CeO2 d) 0.92 Air 0.21 3 CeO2 0.960.05 As-sintered ------1 CeO2 0.91 a) and b) used same gases with different gas ratio. c) A total of 3 samples were heat treated, one sample broke during the high temperature reduction. d) The composition is extrapol ated from Bevan and Kordis [37], heat treatment in N2 and air does not significantly increase the oxygen concentration [14, 32]. Table 6-3. Pore-crack interacti on for Brazilian disc test samples. Heat Treatment Environment Sample Conditions Average on Six Positions AA, % Polished 6 1 H2 Fractured 5 1 Polished 5 1 All pores Air Fractured 6 1 Polished 2 H2 Fractured 2 Polished 3 Fine pores (2.5.5 m) Air Fractured 4

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144 0 20 40 60 80 100 120 140 00.010.020.030.040.050.06Displacement, mmLoad, N P f = 129 N 0 20 40 60 00.0050.010.0150.020.0250.03Displacement, mmLoad, N P f = 39 N Figure 6-1. Load-displacement cu rve for (A) air treated sample(2OP =0.21 atm, ) with a cross section of 2.600 mm.985 mm and that for (B) H2/Ar treated sample (2OP =8.8-20 atm) with a cross section of 2.615 mm. 985 mm. The fracture loads for fracture are indicated on the plots. (A) (B)

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145 0 400 800 1200 1600 200001020304050 Time, SLoad/thickness,lbs/inPmax/t = 964 lbs/in 0 400 800 1200 1600 2000 0100200300400500600Time, SLoad/thickness,lbs/inPmax/t = 1153 lbs/in P/t = 857 lbs/in 0 400 800 1200 1600 2000 0100200300400500600Time, SLoad/thickness,lbs/inPmax/t = 1604 lbs/in P/t = 956 lbs/in Figure 6-2. Load-displacement curves for fractur e of sample (A) direct ly loading to fracture after heat treatment in air, (B) with precrack process after heat treatment in air and (C) with precrack process after heat treatment under 2OP = 4.5-22 atm. The horizontal dash lines in (B) and (C) are used to show the relaxing of the load during the precracking process. (A) (B) (C)

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146 Figure 6-3. Low magnification SEM images show ing the fracture surface within the chevronnotched section for the sample heat treated (A) in air (2OP =0.21 atm) and (B) in H2/ H2O (2OP =1.5-20 atm). (C) shows a unsuccessful precrack for a sample heat treated under 2OP =1.5-20 atm. The dotted lines show the stable to unstable crack transition fronts. 1 mm 1 mm (A) (B) (C)

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147 Figure 6-4. (A) Low magnificati on SEM image of the fracture surface of an as-sintered bending sample. (B) Higher magnification image of the box area in (A) showing the crack initiation site. The dotted line in (B) iden tifies the typical mirror zone. The large processing pore (shown with an arrow) acted as the crack initiation origin. (A) (B)

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148 Figure 6-5. SEM images of the fracture surface fo r a bending sample heat treated in air. (A) Low magnification SEM image of the fract ure surface. (B) Higher magnification image of the box area in (A) s howing the crack initiation site The dotted line in (B) identifies the typical mirror zone. (C) The processing defects that acted as the crack initiation origin. 2mm (A) (B) (C)

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149 Figure 6-6. SEM images of the fracture su rface for a bending sample heat treated in H2/H2O/Argon (2OP =8.8-20 atm). (A) is a low magnification image showing the development of several fracture zones, a nd (B) is the matching fracture surface of (A), the crack propagation direction is shown with arrows next to (A) and (B). (C) is a higher magnification image of the fract ure zone marked as A in (A). A A B C D A B C D (C) (A) (B) 2 mm

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150 Figure 6-7. Comparison of the fracture surface roughness for samples heat treated (A) in air (2OP =0.21 atm) and (B) in H2/H2O/Argon (2OP =8.8-20 atm). (A) (B)

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151 Figure 6-8. Comparison of the fracture su rface for samples heat treated in air (2OP =0.21 atm) (image A and image B) and in H2/H2O/Argon (2OP =1.5-20 atm) (image C and image D). The primary crack propagation direction is from left to right. 2mm 2mm (C) (A) (B) (D)

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152 Figure 6-9. SEM images of the Brazili an disc sample heat treated under H2/H2O (2OP =1.5-20 atm) with KIC=1.27 MPam1/2. The secondary cracks are marked with arrows in (A). (B) is the higher magnification im age of the boxed area in (A). (B) (A) 20 m 5 m

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153 Figure 6-10. The six positions relative to crack surface for pore-crack in teraction analysis. Figure 6-11. Typical images take n for pore-crack interaction eval uation with (A) for air treated sample and (B) for the sample heat treated in 2OP = 4.5-22 atm. 1 2 3 4 5 6 (A) (B)

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154 Figure 6-12. Schematics of fracture deflection process for the sample with pre-existing microcracks: (A) tilting mechanism and (B) twisting mechanism. The dotted line represents the predicted fracture contour on the fracture surface. The dashed lines present the fracture surface without deflection process. The solid line segments represent the pre-existed microcracks and th e ones that assist deflection process are thickened. (A) Y Z appapp (B) app app Y X

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155 Figure 6-13. SEM images of the fr actured surface for a Brizilian di sc sample after heat treatment under 2OP =1.5-20 atm show the microstructure discontinuity and the evidence of the secondary phases (shown with arrows). (A) (B)

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156 CHAPTER 7 CONCLUSIONS AND SUGGESTED FUTURE WORK 7.1 Conclusions The effects of oxygen partial pressure on micros tructure and mechanical properties of three fluorite-structured materials, pure ceria, 10 mol % gadolinium doped ceria (GDC) and 8 mol% yttria stabilized zirconia (YSZ), were systematically investigat ed. By equilibrating the samples under various oxygen partia l pressures in the ra nge of 0.21 atm to 10-26 atm at 800 0C, different oxygen vacancy concentrations were created. Th e defects were conserved to room temperature through a fast cooling process to enable room temperature mechanical property evaluations. As a result of reduction process, ceria a nd GDC samples developed microcracks at the reduction temperature when the oxygen partial pressure was less than 10-19 atm. Detailed study on pure ceria shows that microc racks extended into macroscopi c level cracks during the high temperature reduction when the oxygen partia l pressure level reached as low as 10-22 atm, resulting in broken samples. Low oxygen partial pressure reduced ceria experienced phase series of phase transformation upon cooling that led to the form ation of pseudo-cubic ordered phases. These ordered phases were not stable at room temper ature. The decaying of these ordered phases at room temperature was confirmed to be a phase transformation process and not a reoxidation process. The transformation the ordered phases was found to be se nsitive to ambient atmosphere as well as the stress state. Th is type of transformation was sl ower in dry hydrogen environment than in air and slower in bulk form than in pow der form. Water vapor wa s found to be a crucial factor that contributed to the de gradation of reduced cer ia at room temperature. By comparing two reduced ceria samples, with and without or dered phases respectively, it was shown that the sample with ordered phases experienced water co rrosion at room temperature, which eventually

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157 shattered the samples into small pieces. Sca nning electron microscopi c (SEM) observations of these shattered pieces confirmed the environmenta l effect. Further more, the reoxidation of the low oxygen partial pressure reduced ceria samp les caused the pre-existing microcracks to develop much larger in lengt h with larger opening. Because of the microstructural instability of reduced ceria at room temperature, the mechanical properties were evaluated as a func tion of oxygen partial pressure and also as a function of time for ceria. When the samples were tested within two days after reduction, the variation of the intrin sic elastic modulus tested by nanoi ndentation showed a good correlation with the defects concentration for all three ma terials. As the oxygen partial pressure was decreased, the defect concentration was increa sed and the elastic modulus of ceria and GDC decreased. The elastic modulus of YSZ within the studied oxygen partial pr essure range remained unchanged owing to the negligible deviati on of defect concentrati on. For bulk elastic modulus tested by four-point-be nding, the degradation in elasti c modulus of ceria was more significant due to the presence of microcracks cau sed by the development of internal stresses at low oxygen partial pressure. However, because the microstructure continuously changed at room temperature, the elastic modulus testing re sults were found to be time dependent. In fact, the elastic modulus further decreased after holding the reduced samples at room temperature for a long time. This degradation was mainly due to the room temperature phase transformation process. In contrast to the intrin sic elastic modulus, the hardness (also measured by nanoindentation) of ceria and GDC showed a maximum as a function of oxygen partial pressure. This interesting phenomenon was explained by th e competition of two processes caused by the increase in defect concentration when the oxygen partial pressure was decreased. On one hand,

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158 the weakening of the elastic modulus caused by the increased point defect concentration decreases the resistance to deformation. On th e other hand, as the poin t defect concentration increases, the interactions between dislocations and point defects become more prevalent, and hence the resistance to plastic deformation is increased. A maximum in hardness was obtained when the oxygen partial pressure was most eff ective in reducing the elastic modulus. In addition, the hardness of YSZ, c onsistent with the elastic modulus results, did not change within the tested range. The flexural strength of ceria tested by four-point-bending was found to decrease dramatically as a functio n of the oxygen partial pressure. When the samples were reduced in an oxygen partial pressure of 10-22 atm, the strength decreased more than 90%. Detailed fractographic analysis showed that the air treated samples exhibit classic brittle fracture pattern with one single crack initiation origin. Howeve r, because of the pres ence of microcracks, multiple crack initiation sites were found for the samples treated at low oxygen partial pressures. Therefore, we conclude that the low flexural strength, which is controlled by the crack initiation process, is associated with the enhanced proba bility of fracture due to the large size and the sharpness of the microcracks formed during he at treatment in the reducing atmosphere. Interestingly, the fracture toughness values measured using Brazilian disc samples under mode I condition, increased 30-40% after samples were reduced in oxygen partial pressures of 10-20 to 10-22 atm. SEM analysis revealed that the higher toughness was accompanied with much rougher fracture surfaces. The greater roughness cam e from the deflection of the primary crack during the crack propagation. S econdary cracks were also observ ed to extend onto the fracture surfaces. Residual strain energy released by exte nding of pre-existing microcrakcs is the source of micracking toughening. Based on these observa tions and analyses, we conclude that the

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159 enhancement of the fracture toughness was attrib uted to crack deflection and microcracking toughening mechanisms. 7.2 Suggested Future Work We have shown in this dissertation that th e mechanical property is important for the application of ceria based material s in solid oxide fuel cells (SOFCs). The results of this study gives insights into how reduction processes under different oxygen partial pressure affect the microstructure and mechanical properties of ceria based materials. However, several unsolved issues were developed during the progress of this research. In order to fully understand these materials, further investigations of phase tran sformation and mechanical properties as functions of temperature and partial pres sure of oxygen are needed. For example, phenomena such as room temperature phase transformation and wate r corrosion of reduced ceria-based materials need to be better understood in order to evaluate the long term application of these materials in SOFCs. In addition, as disc ussed in Chapter 6, the relatio nships between the amount of microcracks and the internal stresses developed during reduction treatment will be worth investigating due to its importance to the applic ation in SOFCs. Furthermore, in-situ evaluation of high temperature mechanical properties is recommended for elucidating the roles of point defect versus various microstructural compone nts on mechanical inte grity of ceria-based materials. Based on our discussions in Chapter 5, the relationship between intrinsic elastic modulus and oxygen vacancy concentration should be able to apply successfully to the high temperature in-situ tests. A lthough the development of microcr acks at very low oxygen partial pressure is still inevitable for the ceria samples during in-situ high temperature mechanical testing, the major advantage of these in-situ e xperiments is that the ceria samples will have single-phase (see phase diagram in Figure 2-7) for the oxygen partial pressure range of this

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160 study. Thus, the contribution of phase transforma tion to mechanical properties results will be eliminated for high temperature mechanical tests.

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166 [109] C 1161, Standard Test Me thod for Flexural Strength of Advanced Ceramics at Ambient Temperature, 2002 Book of ASTM Standards [110] D6272, Standard Test Me thods for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials by Four-Point Bending, 1998 Book of ASTM Standards [111] C1421, Standard Test Methods for Dete rmination of Fracture Toughness of Advanced Ceramics at Ambient Temperature, 1999 Book of ASTM Standards [112] D. Singh, D. K. Shetty, J. Am. Ceram. Soc. 72[1] (1989), p. 78. [113] D.K. Shetty, A.R. Rosenfield and W.H. Duckworth, Eng. Fract. Mecha. 26 (1987), p. 825. [114] C. Atkinson, R.E. Smelser and J. Sanchez, Int. J. Fract. 18 (1982), p. 279. [115] E112, Standard Methods for Estima ting the Average Grain Size of Metals, 1981 Book of ASTM Standards. [116] J. P. Nair, E.Wachtel, I. L ubomirsky, J. Fleig and J. Maier, Adv. Mater. 15[24] (2003), p. 2077. [117] R.D. Shannon, Acta Crystallogr A32 (1976), p. 751. [118] A.Kossoy, J. P. Nair, E.Wachtel, I. Lubomirsky, J. Fleig and J. Maier, J. Electroceram 13 (2004), p. 605. [119] D. Halley, B. Gilles, P. Bayle-Guillemaud, R. Arenal, A. Marty, G. Patrat and Y. Samson, Phys. Rev. B 70 (2004), p. 174437. [120] S. H. Whang, Q. Feng and Y.-Q. Gao, Acta Mater. 46[18](1998), p. 6485. [121] M. Salluzzo, G. M. de Luca, D. Marr, M. Putti, M. Tropeano, U. Scotti di Uccio and R. Vaglio, Phys. Rev. B 72(2005), p. 134521. [122] J. Kondoh, S. Kikuchi, Y. Tomii and Y. Ito, Physica B 262 (1999), p. 177. [123] B. Savoini, D. Cceres, I. Vergar a, R. Gonzlez and J. E. M. Santiuste, J. Nucl. Mater. 277 (2000), p. 199. [124] Jane W. Adams, Robert Ruh and K. S. Mazdiyasni, J. Am. Ceram. Soc 80 (1997), p. 903. [125] A. J. A.Winnubst, K. Keizer and A. J. Burggraaf, J. Mater. Sci. 18 (1983), p. 1996. [126] C.S.Montross, J. Eur. Ceram. Soc. 18(1997), p. 353. [127] S. Wang, M. Katsuki, T. Hashimoto and M. Dokiya J. Elecctrochem. Soc. 150 (2003), p. A952.

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167 [128 ] B.C.H. Steele, in: High Conductivity So lid Ionic Conductors, ed. T. Takahashi, World Scientific Singapore, (1989). [129] B. Hofmann and H. Kronmller, J. Magnetism and Magnetic Mater 152 (1996), p. 91.

PAGE 168

168 BIOGRAPHICAL SKETCH Yanli Wang was born on October 1, 1977 in Di ngzhou, Hebei, P.R.China. Accepted by University of Science and Technology Beijing in 1995, Yanli received her B.S. in Materials Science and Engineering department in 1999 w ith the first place honor. She continued her graduate study and achieved her masters degr ee under the advisement of Professor Yonglin Kang from the same department in 2002. Yanli joined in the Materials Science and Engineering department of the University of Florida in th e spring of 2003 for her Ph.D under the guidance of Professor Fereshteh Ebrahimi. Yanli r eceived her Ph.D. in December of 2006.


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Title: Effect of Reduction Treatment on Microstructure and Mechanical Properties of Fluorite Oxides
Physical Description: Mixed Material
Copyright Date: 2008

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Source Institution: University of Florida
Holding Location: University of Florida
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Table of Contents
    Title Page
        Page 1
        Page 2
    Dedication
        Page 3
    Acknowledgement
        Page 4
        Page 5
    Table of Contents
        Page 6
        Page 7
    List of Tables
        Page 8
    List of Figures
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
    Abstract
        Page 14
        Page 15
    Introduction
        Page 16
        Page 17
        Page 18
        Page 19
    Background
        Page 20
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    Materials and experimental procedures
        Page 44
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    Microstructural analysis
        Page 68
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    Reduction effects on elastic modulus and hardness
        Page 108
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    Reduction effect on fracture properties of pure ceria
        Page 131
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    Conclusions and suggested future work
        Page 156
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    References
        Page 161
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    Biographical sketch
        Page 168
Full Text





EFFECT OF REDUCTION TREATMENT ON MICROSTRUCTURE AND MECHANICAL
PROPERTIES OF FLUORITE OXIDES























By

YANLI WANG


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2006

































Copyright 2006

by

Yanli Wang



































To my parents









ACKNOWLEDGMENTS

I would like first to thank my advisor, Dr. Fereshteh Ebrahimi, who introduced me into this

great department and has provided me the most valuable training and support for four years. I

am deeply impressed by her attitude to science. I respect her experience and profound

knowledge. I enjoy the way she successfully delivers new information to students and inspires

students. The amount of time and energy that Dr. Ebrahimi spent on me was invaluable. My

professional life and personal life both have benefited from the discussions with Dr. Ebrahimi,

and I believe it will continue to be beneficial for the rest of life.

I am grateful to the opportunity working on this project with Dr. Eric D. Wachsman (my

committee member) and Dr. Keith L. Duncan. I thank Dr. Wachsman for his advisement

throughout the entire time of this research. His encouragement and his belief in me have helped

me build up my confidence during the process of this challenging project. I thank Dr. Duncan,

from whom I received the most help when I first stepped into the field of Solid Oxide Fuel Cell

(SOFC). Discussions with Dr. Duncan were extremely inspiring. His generosity to people and

openness to science have made this research enjoyable.

I also thank my committee member Dr. John J. Mecholsky, Jr. for his discussions and

suggestions on mechanical properties measurement and fractography analysis. Dr. Susan B.

Sinnott, Dr. Nagaraj K. Arakere (Department of Mechanical and Aerospace) and Dr. Darryl Butt

(my former committee member) are acknowledged for their sincere help and participation on my

supervisory committee. Discussions with Dr. Simon Phillpot on elastic modulus results were

very helpful. I am grateful for the numerous help from Dr. Gerald (Jerry) Bourne for

Nanoindentation, Focused Ion Beam (FIB) and Transmission Electron Microscopy (TEM). I

appreciate Dr. Hans J. Seifert's generosity in providing thermodynamic data for ceria. I would

like to thank Dr. Juan C. Nino, Dr. Valintine Cracium and Dr. Jacob L. Jones for their









suggestions on material characterization. It has also been a great pleasure to work with Sean R.

Bishop and Michael Kesler on this project. I would also like to thank Jung Hun Jang, Kerry

Siebein, Eric Lambers and Dr. Luisa Amelia Dempere in Major Analytical Instrumentation

Center (MAIC), for their instructions and help in this study. A special thanks goes to Dr.

Richard G. Connell for always being nice, helpful and friendly.

I would like to thank Dr. Ebrahimi's former and current group members: Eboni

Westbrooke, Juhyun Woo, Nichole Whitney, Brandon Juran, Luis Forero, Hongqi Li, Peng-nan

Wang, Samantha Yeates, Krishna Ganesan, Shadab Siddiqui, Michael Kesler, Ian Liu, Sankara

Tatiparti, Mehash Tanniru, Damian Cupid, and Sonalika Goyel for providing the best research

environment and being helpful. I thank all the Fuel cell group members (Dr. Wachsman's

group), especially Dr. Keith Duncan, Sean R. Bishop, Dr. Heesung Yoon, Dr. Abheshek Jaiswal,

Dr. Jiho Yoo, Dr. Gongjing Zhang, and Jin Soo Ahn for their help on experimental techniques.

My second special acknowledgment goes to all my friends in China, as well as my friends

here. Their encouragement and support throughout these years have been priceless.

I am really lucky to have my husband, Jun He, with me throughout this journey. His love

and support is every reason for what I have achieved.

I can not pick out any words that can express my gratitude to my mother Yuhua Yu, my

father Quandao Wang, my brother Guangjun Wang and my sister in-law Li Zhao, to whom I owe

the most. Their love and belief in me has shaped me into who I am today. I can not image

having any of my success without my family's strong support behind me. I also appreciate the

support from my husband's parents during this study.

Finally, the financial supported by DOE (DE-FC26-02NT41562) is also acknowledged.









TABLE OF CONTENTS



A C K N O W L E D G M E N T S ..............................................................................................................4

L IST O F T A B L E S ......................................................................................................... ........ .. 8

LIST OF FIGURES ............................................. ............ ...........................9

A B S T R A C T .......................................................................................................... ..................... 14

CHAPTER

1 INTRODUCTION .................................. .. ........... ..................................... 16

2 BACKGROUND ......................................... .......... ............................. 20

2.1 Mechanical Requirements for SOFC Components.....................................................20
2 .1.1 Introduction to SO F C s.......................................... ......................... ................ 20
2.1.2 M echanical R equirem ents ....................................... ...................... ................ 22
2.2 Introduction to Fluorite O xides ............................................... ............ ....... ................ 23
2.2.1 Crystal Structure and Predominant Point Defect..............................................23
2.2.2 Phase D iagram of C e-O System ...................................................... ................. 25
2.3.3 Relationship between Lattice Parameter and Nonstoichiometry in Ceria ..........26
2.4 Effect of Defects on Mechanical Properties of Ceramics...........................................27
2 .4 .1 E plastic M odulu s ................................................ .... .... ... .......... ... .... ........... .. 27
2.4.2 Effect of Point Defects on Fracture Properties of Ceria-Based Materials ..........29
2.4 F racture of B rittle M materials ..................... .................................................. ................ 30
2.4.1 Fracture M echanics for Brittle M materials ......................................... ................ 30
2.4.2 Toughening Mechanisms for Brittle Materials.................................................33

3 MATERIALS AND EXPERIMENTAL PROCEDURES ................................................44

3 .1 S am p le F ab ricatio n ............................................................. ............................................. 4 4
3 .2 H eat T reatm en t ................................................................................................................ 4 5
3 .3 M ech an ical T ests ............................................................................................................. 4 8
3 .3 .1 E plastic M odulu s T ests........................................... ......................... ................ 4 8
3.3.1.1 N anoindentation test................................... ...................... ................ 48
3.3.1.2 F our-point-bend test ...................................... ...................... ............... 50
3 .3 .2 H ard n ess T est ........................................................................................................ 5 1
3.3.3 F lexural Strength T est .......................................... ......................... ................ 52
3.3.4 Fracture T oughness T est........................................ ........................ ............... 52
3.4 C haracterization T techniques .......................................... ......................... ................ 54

4 M ICRO STRU CTURAL AN ALY SIS ...................................... ...................... ................ 68

4.1 Characterization of A s-Sintered M materials ................................................. ................ 68









4.2 C haracterization of R educed C eria............................................................. ................ 69
4.2.1 O ptical Properties .................................................. .............. ................ 69
4.2.2 M icrocracks F orm ation ......................................... ........................ ................ 70
4.2.3 Phase Identification .................... ................ 71
4.2.4 Phase Transform ation upon Cooling ................................................ ................ 73
4.2.5 Aging Effect .......................................................................... 75
4.3 Phase Transformation of Reduced Ceria at Room Temperature...............................77
4.3.1 R educed C eria Pow der .................. ............................................................. 77
4 .3.2 R educed B ulk C eria................ ........................................................... ................ 78
4.3.3 Effect of A m bient Environm ent ....................................................... ................ 81
4.4 M icrostructure of Fully R eoxidized Ceria.................................................. ................ 82
4.5 Degradation of Ordered Ceria Phases in W ater.......................................... ............... 83
4 .6 Su m m ary ......................................................................................................... ........ .. 8 5

5 REDUCTION EFFECTS ON ELASTIC MODULUS AND HARDNESS .........................108

5.1 R education Effect on Elastic M odulus ............................. .................... ..................... 108
5.1.1 Intrinsic Elastic M odulus................ .............................. ............... 108
5.1.1.1 Evaluation of crystallographic anisotropy........................................... 108
5.1.1.2 Effect of oxygen partial pressure on intrinsic elastic modulus ...............110
5.1.1.3 T heoretical analysis .................................... .. ..................... .............. .. 111
5.1.1.4 E effect of fine pores ................................... ...................... ............... 115
5.1.2 Bulk Elastic M odulus ....................................................... 116
5.2 R education Effects on H ardness.................................... ....................... ............... 118
5.3 Effect of Room Temperature Holding...... .......... ........ ..................... 120
5 .4 Su m m ary ....................................................................................................... ........ .. 12 2

6 REDUCTION EFFECT ON FRACTURE PROPERTIES OF PURE CERIA .................... 131

6 .1 F lex u ral S tren g th ......................................................... .................................................. 13 1
6.2 Fracture Toughness Test R results .................................. ...................... ............... 132
6.3 Fractographic A analysis ...................... ................................................................ 134
6.4 Pore-C rack Interaction .... .................................................................... ............... 136
6 .5 D iscu ssion ...................................................................................................... .......... 13 7
6.5.1 Strength................... ...................................... ......... ... .. ............... 137
6.5.2 Fracture Toughness and Toughening Mechanisms for Reduced Ceria .............138
6.5.4 Other Im portant Factors ................. .......................................................... 140
6 .6 Su m m ary ....................................................................................................... ........ .. 14 1

7 CONCLUSIONS AND SUGGESTED FUTURE WORK..............................................156

7 .1 C o n c lu sio n s .................................................................................................................... 1 5 6
7.2 Suggested Future W ork ...................... ............................................................... 159

L IST O F R E F E R E N C E S ....................................................... ................................................ 16 1

B IO G R A PH IC A L SK E T C H .................................................... ............................................. 168









LIST OF TABLES


Table page

3-1 Sam ple dim tensions for m echanical tests ...................................................... ................ 58

3-2 Oxygen partial pressure ranges (Po2 s) of different gas mixtures .................................58

4-1 Comparison of the XRD data for the as-received ceria powder and the as-sintered
ceria sam ple w ith JCPD S #43-1002 standard............................................... ................ 87

4-2 G rain sizes and densities of the m materials .................................................... ................ 87

5-1 Elastic modulus results for heat treatments under different Po2 evaluated by
nanoindentation ................................................................................. ...................... 124

5-2 Effect of reduction in H2 on the intrinsic elastic modulus of two ceria samples with
different porosities (with 49 indents each test). ...... .......... ....................................... 124

5-3 Bulk elastic modulus results for heat treatments under different Po evaluated by
four-point-bend tests. .......... ... ................... ......... ............ ............... 124

5-4 Hardness results for heat treatments under different Po evaluated by
nanoindentation ................................................................................. ...................... 125

5-5 Room temperature holding effect on the intrinsic elastic modulus and hardness of a
reduced ceria sample (with 49 indents each test)...... .... ...................................... 125

5-6 Room temperature holding effect on the bulk elastic modulus of reduced ceria
sam ples ................................................................................................... 125

6-1 Room temperature flexural strength test results. ......................................... ................ 143

6-2 Room temperature fracture toughness test results. .......................................143

6-3 Pore-crack interaction for Brazilian disc test samples...... .................... ................... 143









LIST OF FIGURES


Figure page

2-1 Schematic diagram for the principle of a solid oxide fuel cell. ....................................38

2-2 Fracture of the electrolyte after the half-cell (nickel/yttria stabilized zirconia (or
Ni/YSZ) anode and YSZ electrolye) experienced reduction and reoxidation cycles ........38

2-3 Schematic drawing of the atomic structure for fluorite oxides....................................39

2-4 Predicted dependence of oxygen vacancy concentration on oxygen partial pressure
(PO ) at 800 C for pure ceria, GDC gadoliniumm doped ceria) and YSZ from
th eoretical m o d elin g ........................................................................................................... 3 9

2-5 Dependence of C., Ccaton atom ration on oxygen partial pressure at 800 C for
C e o0.9G d o. 0 1.95-x.................................................................................................................. 4 0

2-6 Themogravimetric measurement results (800 C) of oxygen vacancy concentration as
a function of oxygen partial pressure for pure ceria. .................................... ................ 40

2-7 P hase diagram for C eO 2-x.[16] .......................................... ......................... ................ 4 1

2-8 Expansion of ceria versus nonstoichiometric composition at 900 C...............................41

2-9 Fracture toughness of doped ceria m aterials................................................. ................ 42

2-10 Three basic m odes for fracture ..................................................................... ................ 42

2-11 Crack deflection process by (A) tilt and (B) twist [45] ...............................................43

2-12 Stress-strain curve (A) and the corresponding crack resistance curve (B) for a
m icrocrack toughening m echanism ..................................... ...................... ................ 43

3-1 Flow chart of the sam ple fabrication process ............................................... ................ 59

3-2 Schematics of the procedures of achieving two bending samples before machining
from one as-sintered bar ................. ............. ........................... .. 59

3-3 Schematic of the heat treatment experiments set up..................................... ................ 60

3-4 Temperature-tim e curve for the heat treatment ............................................ ................ 60

3-5 Comparison of Nanoindents with abnormal shapes due to (A) a nearby pore or (B)
underneath pore and a successful nanoindent............................................... ................ 61









3-6 (A) A digital image of 810 Material Test System (810MTS) used for the flexural
tests. (B) The details of the fixture setup for four point bending test with one ceria
sample and the extensormeter in position. (C) Schematics of the fully articulating
four-point-bend fixture ................... .. ........... ............................. 62

3-7 The load-displacement curve of a steel sample with a cross section of 3.145 mm
x 3 .14 5 m m ...................................................................................................... ....... .. 6 3

3-8 Scanning electron microscopic (SEM) image of the Vikers indent at 200 g for an as-
sintered ceria sam ple .............. .. .................... ................. .............. ........ ... ........... 63

3-9 Geometry of the chevron-notched Brazilian disc samples used in the fracture
to u g h n e ss te st .................................................................................................................. ... 6 4

3-10 (A) Schematics of an ideal chevron notch and (B) two chevron notches with different
d im e n sio n s. ........................................................................................................................ 6 4

3-11 Schem atics of the unsuccessful chevron notches.......................................... ................ 66

3-12 Images of the pure ceria transmission electron microscopic (TEM) samples during
the preparation process by focused ion beam (FIB) ..................................... ................ 67

4-1 X-ray diffraction pattern (XRD) of the as sintered ceria .............................................88

4-2 Im ages to show grain sizes of the m aterials.................................................. ................ 88

4-3 Color change of ceria samples after heat treatment under various oxygen partial
p re ssu re ........................................................................................................... ........ .. 8 9

4-4 Digital image taken after four ceria discs with a diameter of 26 mm "exploded"
during the reduction at 800 under and oxygen partial pressure of 8.5 x 10-26 atm. ..........90

4-5 SEM images of ceria sample reduced under 4.5 x 10-22 atm (at 800 C for 15 hours)
show large macrocrakcs (-100 [tm) at the top surface layer ........................................90

4-6 SEM images of the microcracks in the middle of the ceria sample after reduction in
Po, =4.5 x 10-22 atm (at 800 C for 15 hours) ................................................. ................ 91

4-7 XRD patterns for ceria samples after heat treatment (A) in air (P2 =0.21 atm) and
(B) in H 2/H 20 m ixture (P0 =4.6 x 1022 atm )................................................. ................ 92

4-8 The (311) XRD peak of pure ceria sample at various depths from the surface, as
indicated by the numbers on the curves, after heat treatment under P0 = 4. 6x 1022
atm .......................................................................................................... .................. 9 2

4-9 (A) XRD pattern of ceria after reduction under 7.1 x 10-24 atm (800 C for 15 hours).
(B) shows the details of 20 range of 54 to 60 degrees ................................. ................ 93









4-10 Theoretical XRD pattern for ceria with 2/3 volume fraction of hexagonal Ce203
phase (indicated by arrows) and 1/3 volume fraction of cubic CeO2 ..............................94

4-11 (A) XRD pattern of bulk ceria sample after aging at 500 C. (B) shows the details of
20 range of 52 to 60 degrees ........................................................................... ................ 94

4-12 XRD pattern of powder ceria sample after aging at 500 C.. ....................... 95

4-13 (A) and (B) are XRD patterns as a function of time for the ceria powder that were
reduced aged at 500 C for 30 hours after reduction at 800 C for 15 hours..................96

4-14 XRD patterns as a function of time for the ceria bulk sample that were reduced at
800 C for 15 hours under oxygen partial pressure of 3.6x 1022 atm ..............................97

4-15 (A) shows the XRD patterns as a function of time for the bulk ceria sampler that
were reduced at 800 C for 15 hours and then aged at 500 C for 30 hours. (B)
shows the details of the XRD pattern with 20 range of 53 to 61 degree ........................98

4-16 Comparison of the peak (311) and peak (420) for CeO2 powder with a bulk and
powder ceria sample after room temperature phase transformation...............................99

4-17 TEM bright field (BF) image (A) and dark field (DF) image (B) along with the
selected area diffraction (SAD) pattern (C) for the bulk ceria sample reduced under
3 .6 x 1 0 -22 a tm ....................................................................................................................1 0 0

4-18 XRD pattern of a reduced bulk ceria sample after the sample was held under dry
hydrogen at room temperature for 55 hours. ..................................101

4-19 A digital image (A) and an SEM image (B) of one fully reoxidized ceria Brazilian
d isc sa m p le ................................................................................................................... .... 1 0 2

4-20 Low magnification SEM image (A) of the thermo-etched ceria sample that exploded
at 800 C under 8.5x 10-26 atm. (B) High magnification SEM image of the boxed
a re a in (A ). ....................................................................................................................... 1 0 3

4-21 Digital image of the reduced ceria sample after holding in hydrogen/water vapor
environment for 4 days .................... ............ ........................... 104

4-22 The (311) and (420) XRD peaks of a reduced ceria sample after holding in
hydrogen/water vapor environment for 4 days. ...... .......... ....................................... 104

4-23 (A) Low magnification SEM image of a piece of sample from Figure 4-21. (B) High
m agnification im age of the boxed area in (A). ...... ........... ........................................ 105

4-24 Digital images of a reduced ceria before the surface phase transformation. (A) After
soaking in water for 12 days and (B) after soaking in water for 17 days ..................... 106

4-25 Digital images of a reduced ceria 12 days after the surface phase transformation..........107









4-26 Digital image of an as-sintered ceria after soaking in water for 38 days...................... 107

5-1 Nanoindent image on the as-sintered pure ceria sample (A) and the corresponding
load-displacem ent curve (B) ....................... ...................................................... 126

5-2 Change of the elastic modulus as a function of oxygen partial pressure .......................126

5-3 Experimental results showing the variation of normalized elastic modulus (E E*) as a
function of oxygen partial pressure for pure ceria and GDC................ ....................127

5-4 The normalized elastic modulus (E E*) as a function of the normalized lattice
parameter (a/a*) for pure ceria and GDC .....................................127

5-5 Schematics of the preparation procedure for samples with different porosities............128

5-6 SEM images of the microstructure for dense surface (A) and the less dense middle
part (B ) ........................................................................................ ........... 128

5-7 Relative elastic modulus (E Ear) as a function of oxygen partial pressure for ceria
(A ), G D C (B ) and Y SZ (C) ................................................................. ............... 129

5-8 Room temperature hardness as a function of oxygen partial pressure for pure ceria
and GDC samples. ........................................... ............................. 130

5-9 Mechanism of the reduction treatment effect on the hardness of ceria and GDC .........130

6-1 Load-displacement curve for (A) air treated sample(P2 =0.21 atm, ) with a cross
section of 2.600 mmx3.985 mm and that for (B) H2/Ar treated sample (P =8.8x10-
20 atm) with a cross section of 2.615 mmx3.985 mm ....... ................. ................... 144

6-2 Load-displacement curves for fracture of sample (A) directly loading to fracture after
heat treatment in air, (B) with precrack process after heat treatment in air and (C)
with precrack process after heat treatment under P =4.5 x 1022 atm ..........................145

6-3 Low magnification SEM images showing the fracture surface within the chevron-
notched section for the sample heat treated (A) in air (P0 =0.21 atm) and (B) in H2/
H20 (P =1.5 x 10-20 atm). (C) shows a unsuccessful precrack for a sample heat
treated under P = 1.5x 10 20 atm .................................................................................... 146

6-4 (A) Low magnification SEM image of the fracture surface of an as-sintered bending
sample. (B) Higher magnification image of the box area in (A) showing the crack
in itiatio n site .................................................................................................................. ... 14 7

6-5 SEM images of the fracture surface for a bending sample heat treated in air ...............148









6-6 SEM images of the fracture surface for a bending sample heat treated in
H2/H20/Argon (Po2 =8.8x1 0-20 atm). ................................................................ 149

6-7 Comparison of the fracture surface roughness for samples heat treated (A) in air
(Po2 =0.21 atm) and (B) in H2/H20/Argon (P" =8.8x10-20 atm)................................150

6-8 Comparison of the fracture surface for samples heat treated in air (Po =0.21 atm)
(image A and image B) and in H2/H20/Argon (P2 =1.5 x 10-20 atm) (image C and
im ag e D ) ............................................................................... ..... ............. .................. 15 1

6-9 SEM images of the Brazilian disc sample heat treated under H2/H20 (P =1.5x 10-20
atm) with Kic=1.27 MPa*m1l2........................... .............................. 152

6-10 The six positions relative to crack surface for pore-crack interaction analysis .............153

6-11 Typical images taken for pore-crack interaction evaluation with (A) for air treated
sample and (B) for the sample heat treated in Po2 =4. 5x 10-22 atm. ..............................153

6-12 Schematics of fracture deflection process for the sample with pre-existing
microcracks: (A) tilting mechanism and (B) twisting mechanism ................................154

6-13 SEM images of the fractured surface for a Brizilian disc sample after heat treatment
under P0 =1.5 x 10-20 atm show the micro structure discontinuity and the evidence of
the secondary phases (shown with arrows)........... .............................................. 155









Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

EFFECT OF REDUCTION TREATMENT ON MICROSTRUCTURE AND MECHANICAL
PROPERTIES OF FLUORITE OXIDES

By

Yanli Wang

December 2006

Chair: Fereshteh Ebrahimi
Major Department: Materials Science and Engineering

Ceria based materials because of their high ionic conductivity at low temperatures are

potential candidates as the electrolyte component in the new generation of low temperature solid

oxide fuel cells (SOFCs). The effects of operation conditions in SOFCs on microstructure and

mechanical integrity of ceria-based materials are evaluated in this research. Pure ceria and

gadolinium doped ceria (GDC) were selected to perform this investigation. The state-of-art

electrolyte material, yttria-stabilized zirconia (YSZ), was also studied for comparison purposes.

The samples were heat treated at 800 C under various oxygen partial pressures (P0 s) until

equilibrium was reached. The defect concentrations were conserved to room temperature by fast

cooling. The crystal structure and the lattice parameter were evaluated by the x-ray diffraction

method. Microstructural evaluations and fractographic analyses were conducted using electron

microscopy techniques. The intrinsic elastic modulus was evaluated using nanoindentation

techniques. The bulk elastic modulus and fracture strength were measured using the four-point-

bend testing method and fracture toughness was evaluated using chevron-notched Brazilian disc

samples loaded under the mode I condition.









The result of this study revealed that microcracks were formed during the reduction heat

treatment in ceria and GDC when the P2 was lower than 10-19 atm. It was also found that ceria

samples upon cooling experienced phase transformation that led to the formation of several

ordered pseudo-cubic phases.

The intrinsic elastic modulus of both ceria and GDC decreased drastically when heat

treated at very low P2 s while the effect was insignificant in YSZ. These results correlate well

with our theoretical modeling. Further analysis suggests that an increase in the point defect

concentration weakens the attractive forces between atoms. The degradation of bulk elastic

modulus of ceria was more pronounced at low P0 s due to the presence of microcracks caused

by the reduction treatments. The results on fracture properties of ceria showed that the flexural

strength decreased significantly after reduction in very low P0 s; however, in contrast, fracture

toughness was increased by 30-40% when the P0 was decreased to the range of 10-2-10-22 atm.

Fractographic studies showed that the microcracks developed during reduction treatment are

responsible for the decreased strength. In this dissertation, the enhancement in toughness was

explained by crack deflection and microcrack toughening mechanisms.









CHAPTER 1
INTRODUCTION

A single solid oxide fuel cell (SOFC) unit is a ceramic multiple layer system which

consists of two electrodes (anode and cathode) separated by the electrolyte. The components are

in close contact with each other and the entire cell is exposed to high temperatures with reducing

fuel running through the anode side and air running through the cathode side. Electric power is

generated electrochemically. Presently, yttria-stabilized zirconia (YSZ) is the state-of-the-art

electrolyte material used for SOFCs. Cells based on YSZ have to operate at very high

temperatures (700 'C-1000 C) to exhibit sufficient ionic conductivity [1]. The high operating

temperature requires expensive and durable electrodes, sealing materials and interconnects.

Therefore, it has been of great interest to decrease the operation temperature to a lower level to

enable the long-term cell stability and the use of low cost metallic interconnects [2, 3].

However, this low operating temperature increases the ohmic loss at the solid-state electrolyte

and the polarization loss at both electrodes. One possible solution to these problems is to

identify other alternative metal oxides, such as ceria-based materials, which possess high ionic

conductivity at much lower temperatures [4].

Stoichiometric ceria has a cubic fluorite crystal structure. At elevated temperatures and in

reducing atmospheres, ceria can deviate from its stoichiometric composition to an oxygen-

deficient composition, CeO2-x, by reduction of Ce4+ to Ce3+ without changing its fluorite

structure. As the lattice expands after reduction [5, 6], the intact fluorite structure provides a

relatively open path for higher oxygen ionic conductivity, which is the most attractive aspect for

low/intermediate temperature application in SOFCs. At 800 C, ceria can accommodate up to

-14% oxygen vacancies, providing the opportunity to study the effects of large vacancy

concentrations on a variety of properties of fluorite-structured oxides.









There has been extensive research on the thermo-chemical properties [5, 6], defect

structural properties [7-19], oxygen diffusion properties [20-22] and electrical properties [23-32]

of ceria based materials because of their applications as catalysts [33-35], high dielectric

capacitors [36, 37] and components of SOFCs and sensors [4, 26-32]. However, there has been

limited investigation into mechanical properties of ceria-based materials [38-44]. Mechanical

failure is an important design factor for most applications of these materials. In case of their

applications in the field of SOFCs, the main source of mechanical failure is due to the build up of

stresses arising from expansion/contraction mismatches between components [45].

During the operation of SOFCs, the partial pressure of oxygen varies across the electrolyte,

which induces a gradient of lattice defects in the material. For fluorite-structured oxides, oxygen

lattice vacancies are known to be the major source of nonstoichiometry at low oxygen partial

pressure and high temperature region [44, 46]. The lattice expansion caused by the formation of

oxygen vacancy and the associated lower valance Ce3+ for ceria-based materials will lead to the

mechanical stress gradient between the reduced surface and the unreduced interior. Atkinson

studied this issue [39] theoretically and found that the maximum tensile stress caused by

nonstoichiometry increases as the oxygen partial pressure decreases, resulting in differential

strain across the thickness of the electrolyte, and for the worst case scenario, cause fracture [38-

40]. Unfortunately, so far, no experimental work in literature has systematically studied the

effect of nonstoichiometry caused by reduction on mechanical properties of ceria-based

materials.

Based on the above brief discussion, there is a need, to systematically study mechanical

properties of ceria based materials because of their application in SOFCs. In this dissertation, we

chose pure ceria and 10 mol % gadolinium doped ceria for the investigation. Both of these two









materials have fluorite structure. In addition, the most popular electrolyte material, fluorite-

structured 8 mol % yttria doped zirconia, is also selected for the comparison purpose. The

objective of this work was to evaluate the effects of oxygen partial pressure on intrinsic elastic

modulus, bulk elastic modulus, hardness, strength and fracture toughness.

It has been shown theoretically that introducing oxygen vacancy in ceria significantly

decreases the intrinsic elastic modulus owing to the expansion of the Ce-O bond length [43, 44].

We employed nanoindentation technique in this research to confirm and quantify the effect of

oxygen partial pressure on the intrinsic elastic modulus of ceria-based oxides. Nanoindents can

be introduced into single grains, and therefore, the contribution of pores, grain boundaries and

other macroscopic defects on elastic modulus can be minimized. However, nanoindentation is

limited to room temperature tests only. In order to investigate the effect of oxygen vacancy

concentration on mechanical properties at room temperature, the samples were equilibrated at

800 C under various oxygen partial pressures and then the point defects were conserved to room

temperature through fast cooling. The microstructure change upon this type of heat treatment

was systematically studied as a function of oxygen partial pressure using X-ray diffraction,

optical microscope and electron microscopy. In addition to elastic modulus, nanoidentation also

provided information regarding the hardness of the samples. To be consistent with these

measurements, the same heat treatment plan was applied for all other mechanical property

evaluations. The bulk elastic modulus as well as the flexural strength was evaluated using four-

point-bend testing technique. The fracture toughness of differently heat treated samples was

measured using chevron-notched Brazilian discs loaded in mode I. Scanning Electron

Microscope (SEM) was utilized to characterize the fracture surfaces. The ultimate goal was to









investigate the effects of the reduction treatment process on microstructure and mechanical

integrity of ceria-based materials.









CHAPTER 2
BACKGROUND

Because this research is focusing on the particular application conditions of fluorite oxides

in solid oxide fuel cell (SOFC), the fundamental aspects of SOFC are firstly reviewed in this

chapter. The related literatures on the fundamentals of point defect formation and point defect

structure in fluorite oxides are summarized. In order to provide basic information about

mechanical testing, this chapter will also review the basics of fracture mechanics as well as the

toughening mechanisms. Finally, the effects of point defect on mechanical properties of ceria-

based oxides will be reviewed.

2.1 Mechanical Requirements for SOFC Components

2.1.1 Introduction to SOFCs

A solid oxide fuel cell (SOFC) is a ceramic multiple layer system working at high

temperature using gaseous fuel and oxidant, which electrochemically generates electric power.

As SOFCs operate without combustion and moving parts, they have many advantages over

conventional power-generating systems in terms of efficiency, reliability, modularity, fuel

flexibility, and environmental friendliness [1, 47]. There are many different types of SOFC in

terms of cell configuration. Figure 2-1 schematically shows a planar type SOFC to explain the

operation principle. A single SOFC unit consists of two electrodes (anode and cathode)

separated by the electrolyte. The cell components are in close contact with each other and the

entire cell is exposed to high temperatures with reducing fuel running through the anode side and

air running through the cathode side. Each of the components carries out a specific

electrochemical function. Oxygen combines with electrons and becomes oxygen ion at the

cathode side. The oxygen ions travel through the electrolyte membrane and combine with the

hydrogen on the anode side and create an electric current, water and heat. The corresponding









reactions at each electrode are also shown in Figure 2-1. The output voltage then comes from the

chemical potential difference in terms of oxygen partial pressure across the electrolyte.

Presently yttria-stabilized zirconia (YSZ) is the state-of-the-art electrolyte material used for

SOFCs. The basic requirements for the electrolyte include a high ionic conductivity and no (or

minimal) electrical conductivity with low ohmic loss. The electrolyte must also be dense to

prevent short-circuiting of the reactive gases and be stable in both reducing and oxidizing

atmospheres at operating temperatures ranging from 700 C to 1000 C. The electrodes should

have good electrical conductivity, proper porosity and long term stability in the operation

atmosphere (i.e., reducing atmosphere at the anode size and oxidizing atmosphere at the cathode

side). Currently, nickel/yttria-stabilized zirconia (Ni/YSZ) cermets are chosen as anode material

according to these requirements. The state-of-the-art cathode material used in conjunction with

YSZ electrolytes is lanthanum manganate (LaMnO3), which has similar requirements as the

anode. Individual cells produce a maximum voltage of one volt at 800C when hydrogen and air

are used for the gas supply, therefore, in order to generate a reasonable voltage, fuel cells are

arranged in series to create "cell stacks" providing power to operate various devices. The anodes

and cathodes of adjacent units are joined together using fully dense doped lanthanum chromite

(e.g., Lao.sCao.2CrO3) interconnects with glass sealing to separate gases from mixing. In addition

to the above basic requirements, matching thermal expansion coefficients (CTEs) of all the

components becomes very important as far as the seal is concerned. On top of these

physical/chemical requirements, fuel cell materials and components must be cost-effective and

compatible with mass-production processes.

Cells based on YSZ have to operate at very high temperatures (700 TC-1000 C) to exhibit

sufficient ionic conductivity [1]. The high operating temperature requires expensive and durable









electrodes, sealing materials and interconnects. Therefore, it has been of great interest to

decrease the operation temperature to enable the long-term cell stability and the use of low cost

metallic interconnects [2, 3]. However, this low operating temperature increases the ohmic loss

at the solid-state electrolyte and the polarization loss at both electrodes. There are two possible

solutions for this issue. The first is to optimize the electrodes and make the thickness of

electrolyte from 100-500 [tm range in conventional electrolyte-supported cells to 5-20 [tm in

anode supported cells [48-50] to achieve the above situation. The second possible solution is to

investigate other alternative metal oxides, such as ceria-based materials, which possess high

ionic conductivity at much lower temperatures [4].

2.1.2 Mechanical Requirements

Besides the above described basic requirements for the SOFC components, the mechanical

properties are also important for the reliable cell design. The fundamental mechanical

requirements can be summarized to be their stability at the operation conditions and their

stability for long term application. It is vital that no damage of the electrolyte layer occur during

handling and fabrication of the stacks or during the operation conditions where sudden external

impacts or vibrations may exist. Therefore, it requires the components to have good strength and

fracture toughness under the severe operation conditions. When it comes to long term stability,

the cell must withstand a significant number of thermal cycles without degradation or build-up of

internal stresses. If we take creep as an example, a long term creep of the porous electrode may

cause failure or degradation of the cell in terms of unwanted densification of the electrodes,

cracking or delamination of the thin electrolyte layer and damage to the seals [50].

The main source of mechanical failure due to the build up of stresses arises from

expansion/contraction mismatches between components [45]. For example, experimental work

on a half cell (Ni/YSZ anode and YSZ electrolyte) shows the mechanical failure of the









electrolyte (shown in Figure 2-2) after reduction and re-oxidation cycles [51]. The tensile stress

that caused this fracture comes from the extensive expansion of the anode due to a Ni to NiO

transformation during reoxidation cycle.

Therefore, it is necessary and important to study the material mechanical properties for

their application in SOFCs. The focus of this work is to investigation the effects of the operating

conditions of SOFCs on two fluorite-structured oxides, ceria and 10 mol % gadolinium doped

ceria (GDC). In addition, the most popular electrolyte material, fluorite-structured 8 mol %

yttria doped zirconia (YSZ), is also selected for comparison purposes.

2.2 Introduction to Fluorite Oxides

2.2.1 Crystal Structure and Predominant Point Defect

The fluorite oxide structure has a space group of Fm 3 m, with eight-coordinate cations

(large quadrivalent M4+ e.g., Ce4+, Zr4+) and 4-coordinate anions (02-). In the unit cell the

cations occupy the FCC lattice sites, while oxygen atoms are located at eight tetrahedral sites.

The unit cell is schematically shown in Figure 2-3, from which we can see that there are two

M02 "molecules" per unit cell.

At high temperatures and under reducing atmospheres (or low oxygen partial pressure,

Po2 ), the process of creating oxygen vacancies in the fluorite oxides by exchange of oxygen

between the crystal lattice and the gas can be written in Kroger-Vink notation as

O =2 1/02 (gas) + Vo" + 2e'. (2-1)

The equilibrium constant, Kr, for the above reaction can be expressed as

S[Vo ][e']2Po1 2
[0o] (2-2)









At 800 C, a typical SOFC operation temperature, K, was found to be -1072 for pure ceria

and GDC by extrapolating the information in reference [52], and for YSZ Kr~1060 referring to K.

Sasaki and J. Maier [53]. These values indicate that less oxygen vacancies are generated in YSZ

at a given temperature and for a given oxygen partial pressure.

For GDC and YSZ, there are pre-existing oxygen lattice vacancies due to the effect of

acceptor doping according to Equations 2-3 and 2-4, respectively.

Gd203 2ce2 > 2Gdce + 30 + Vo (2-3)

Y203 2 > 2Yz + 30 + Vo' (2-4)

K. Duncan et. al. [44, 54] have shown the relationship between C;.. and the partial

pressure of oxygen for fluorite-structured oxides as


C, (Po2)= [V']= KPo + (C (2-5))

where, CA is the dopant concentration. From this equation, one can see clearly that oxygen

vacancy concentration increases as oxygen partial pressure decreases. Based on this model,

Figure 2-4 shows the predicted variation in the oxygen vacancy concentration as a function of

Po at 800 C for ceria, GDC and YSZ. Note that, the initial oxygen vacancies in GDC and YSZ

are due to the pre-existing vacancies caused by acceptor doping. It can be seen that at the

practical testing temperature and Po2 range (0.21 atm-10-25 atm), no significant change in the

vacancy concentration of YSZ is expected, however, ceria and GDC should develop a significant

amount of defects when Po2 is lower than 10-17 atm.

Because the total number of oxygen vacancy sites and oxygen atoms in ceria is twice of the

number of cerium atoms, rewriting Equation 2-5 yields [44]









I K 1 ) 3 h0
CO= 2 -[ f o (c Y2 (2-6)
C C
cation cahon

where, Co is the concentration of oxygen atoms and Ccalon is the concentration of cerium atoms.

This model's prediction shows a good agreement with gravimetrically measured results for GDC

(see Figure 2-5) [44, 55].

In the case of ceria, extensive experimental work has been done on the nonsoichiometric

measurement [11, 12]. Figure 2-6 shows the representative theromgravimetric measurement

results by two research groups. Comparing Figure 2-4 and Figure 2-6, one can see that

experimental results indicate that the process of oxygen vacancies formation is gradually slowed

down (showing by the convex curvature) at very low oxygen partial pressure (lower than 10-22

atm), but the theoretically modeling does not predict this effect. This discrepancy can be

attributed to the theoretical modeling inability to incorporate any structural changes resulting

from high oxygen vacancy concentration.

2.2.2 Phase Diagram of Ce-O System

At room temperature, there are two very stable intermediate phases known in Ce-O system,

Ce203 and CeO2, which have type-A rare earth structure [7] and cubic fluorite structures,

respectively. Brauer et.al. [13,14] and Bevan [7, 11] detected four more intermediate phases

between Ce203 and CeO2, a disordered C-type rare-earth-oxide phase stable above 600 C

between CeO1.67 and CeO1.714, a nearly stoichiometric triclinic structured phase Ce7012

(CeO1.714) stable up to 1023 C and two rhombohedral structured phases at CeO1.812 and CeO1.782.

These intermediate "compounds" are thought to occur as a result of ordering in the cation and

anion sub-lattices. There has been an extensive work thereafter on other intermediate phases of

the Ce-O system, but there exist some discrepancies [7, 15] in terms of composition and crystal









structure. Investigations including specific heat measurement [16], thermogravimetric

measurement [11], electromotive force [17], electron microscopy [8], neutron diffraction [18]

and X-ray diffraction measurements [18, 19] have provided valuable information to understand

Ce-O system. Figure 2-7 shows the Ce-O phase diagram that is generally accepted by

researchers [16]. It is shown that at room temperature a miscibility gap exists between CeO2 and

CeO1.818 (Cen020), which contract with increasing temperature and closes at 685 C (958K) at a

composition of approximately CeO1.918. Above the miscibility gap, ceria can ceria can

accommodate up to significant amount of oxygen vacancies without changing of the fluorite

structure.

2.3.3 Relationship between Lattice Parameter and Nonstoichiometry in Ceria

The lattice parameter of ceria-based materials has been shown to be dependent on dopant

concentration and oxygen vacancy concentration created by reduction [5, 6, 9, 56-59]. In case of

pure ceria, when oxygen vacancies are introduced at low oxygen partial pressures in to the

material, the charge neutrality is restored by creating Ce3+ defects. In case of doped ceria,

substitution of Ce4+ with a lower valance cation through acceptor doping causes formation of

oxygen vacancies in the lattice. Experimental work [5, 6, 9, 56-59] on ceria-based materials has

shown that both of the above processes result in a lattice expansion. The reason for lattice

expansion is believed to be the formation of larger ionic radii of the lower valance cations [59].

Mogensen [6] has considered ceria with various vacancy concentrations as a simple solid

solution of Ce203 and CeO2, to apply Vegard's rule to the lattice parameter [60], i.e., that a linear

relationship exists between lattice parameter and the concentration of the solute. He found out

that for homogeneous ceria sample at room temperature, the lattice parameter, a, as a function of

vacancy concentration, x, in CeO2-x should follow









a = 0.5413nm + xx 0.04612nm (2-7)

Figure 2-8 shows the good agreement of this prediction and experimental expansion

measurement results [5, 6, 58].

2.4 Effect of Defects on Mechanical Properties of Ceramics

2.4.1 Elastic Modulus

Material elastic modulus (E) (also known as the Young's Modulus or modulus of

elasticity) is an important material property because it is in nature a measure of the stiffness of

atomic bonds. The material elastic modulus can be related to inter atomic forces, F, and inter

atomic potential, enet, through [61]

E 1= dF d )' e(2-8)
E dr /X net dr) (2

where, r is the inter atomic distance, and r=ro is the equilibrium distance at 0 K, which is

determined as the interatomic distance where the attractive force component is equal to the

repulsive force, which point corresponds to the minimum interatomic potential. ro is directly

related to the lattice constant, a

While the intrinsic elastic modulus is dependent on the interatomic forces, the macroscopic

Young's modulus can significantly be reduced by the presence of processing defects. For

example, it has been observed for some ceramic materials that macroscopic defects such as

porosity and microcracks will significantly decrease the elastic modulus [62, 63]. For example,

in case of alumina, the relationship between the magnitude of the elastic modulus, E, and volume

fraction of porosity, p, can be expressed as [62]

E = E(1-1.9p + 0.9p2), (2-9)

where, Eo is the elastic modulus of a material with zero porosity.









In general, the effect of point defects on elastic modulus is of great interest. The formation

of point defects can modify the inter-atomic forces, and hence the elastic modulus will be

affected. Recent studies indicate that the influence of lattice vacancies on elastic modulus can be

significant. For instance, it has been shown experimentally that the elastic modulus of group IVb

nitrides with rock-salt structure such as TiNx, ZrNx and HfNx decreases as the concentration of

the nitrogen lattice vacancy increases [64-367]. Guemmaz [68, 69] has shown that in titanium

carbides the elastic modulus is reduced as the carbon lattice vacancy concentration increases.

Theoretically, computer simulation results using full potential-linear muffin tin orbital method

[67-69] and ab initio pseudopotential density functional total energy method [70] have shown a

good agreement with the above-mentioned experimental results.

However, the work on the influence of point defects on elastic modulus of ceria-based

oxides is limited [41, 43-44, 71]. Sato et.al. [41] studied the effect of dopant concentration on

the elastic modulus of ceria based materials using a small punch testing technique (the concept of

this technique is similar to flexural bend testing). They reported the average elastic modulus of

pure ceria as 175 GPa, which was slightly lower than the results reported as approximately 200

GPa through flexural tests by Atkinson and Selguk [71]. Their results showed that the elastic

modulus of doped ceria ceramics was lower than elastic modulus of pure ceria. The authors

attributed the reduction in elastic modulus to the effect to the formation of oxygen vacancies

caused by doping process. Furthermore, since oxygen vacancies can also be formed through

reduction treatment, our recent theoretical modeling based on the calculation of oxygen vacancy

formation as a function of partial pressure of oxygen and a consideration of classical atomic

potential predicts that elastic modulus decreases with a reduction of P, in fluorite-structured









oxides [44]. In this dissertation, experimental measurement on elastic modulus are attempted to

confirm this effect.

2.4.2 Effect of Point Defects on Fracture Properties of Ceria-Based Materials

Depending on the material fabrication technique and measurement method, the strength of

pure ceria reported in literature has a wide range [38, 71, 72]. Using the same standard solid

state fabrication technique, the flexural strength of pure ceria of was reported to be less than 100

MPa by Mashino et.al.[72] and about 150 MPa by Atkinson and Selguk [71]. The fracture

toughness of pure ceria was reported to be about 1.3 MPa*m12 by Sato et.al [41] and 1.5

MPa*m12 by Mashino et.al. [72]. Besides the effect of processing techniques, the effect of point

defects on fracture properties of ceria based materials is of great interest. As discussed in section

2.3.3, the ceria lattice will expand when oxygen vacancies are formed by the reduction process.

In case of SOFCs, as the oxygen partial pressure varies significantly across the electrolyte, the

expansion difference across the electrolyte thickness will lead to mechanical stresses, which

gives rise to differential strain across the thickness and inevitably causes fracture [38-40]. In

detail, Atkinson [38] has studied the relationship between the stresses and various parameters

such as doping concentration, temperature and oxygen activity. His analysis relates the

maximum tensile stresses to the non-stoichiometry of the electrolyte. A tensile stress is found to

be present at unreduced cathode side (air side) and a compressive stress at reduced anode side

(fuel side). The maximum tensile stress is found to increase with the decreasing oxygen pressure

and dopant concentration or with increasing temperature. The trade-off between temperature and

oxygen pressure has bought up an interesting topic in order to keep the maximum tensile stresses

to a manageable limit.

Some experimental [40-44] work has shown doping process affects fracture properties of

ceria based materials. For example, Sato et. al. [41] found that the fracture strength and fracture









toughness of doped ceria appear to decrease with increasing dopant level when the dopant

concentration is less than 20 mol %. The authors attributed this decrease to the increase in

concentration of oxygen vacancies caused by acceptor doping process. Interestingly, they also

find that the influence of the increasing oxygen vacancy concentration override the strengthening

effects caused by finer grain sizes. Further studies [41] on the fracture properties of rare earth

yttriumm, gadolinium, and samarium) doped ceria ceramics showed that the fracture toughness

was influenced by the dopant concentration rather than the kind of dopants (Figure 2-9). As the

increase in dopant concentration is directly associated with the increase in oxygen vacancy

concentration, this result again indicates the important role of the oxygen vacancy effects on

fracture properties.

2.4 Fracture of Brittle Materials

2.4.1 Fracture Mechanics for Brittle Materials

When the applied stress exceeds the theoretical strength, 0th, which is defined as the

maximum stress on the force-displacement curve, materials are expected to fracture in an

unstable manner. In a simplest approach, this theoretical cleavage stress can be expressed as

Equation 2-10 [73]. Since cleavage takes place on specific crystallographic planes, the

parameters given in this equation refer to specific crystallographic planes.


ath E- (2-10)


where, y is the surface energy for the cleavage plane and ro is the equilibrium unstressed inter-

planar spacing, and E is the elastic modulus perpendicular to the cleavage plane. Using an

E
estimated y value, o-th in Equation 2-8 can be approximated as -. At room temperature, the E
10

values for ceramics vary from tens of GPa (e.g., 70 GPa for pyrex glass) to as high as hundreds









of GPa (e.g., 400 GPa for trigonal alumina), therefore, the theoretical strength ranges from

several GPa to tens of GPa. This estimation is obviously much greater than experimental test

strength values for ceramics which normally is several hundreds of MPa.

In 1913, Inglis [74] carried out some pioneering work on stress analysis for a uniformly

stressed plate with an elliptical cavity in the middle. He showed that the local stresses ahead of

an elliptical cavity tip can raise to as high as several times that of the applied stress. Inglis's

stress concentration factor concept can provide some information about the difference between

the theoretical strength and the experimental values. While Inglis's analysis incorporates the

stress intensification, it fails to address the effect of crack size. In other words, cracks of equal

notch radius to crack length ratio would be equally effective in intensifying the stress. Following

this, Griffith proposed in 1920 a model, where instead of stress intensification, the energetic of

crack propagation was considered. It is generally considered as the first breakthrough in

developing fracture criterion.

Griffith's criterion [75] adapted the thermodynamic equilibrium concept. He considered a

static shaper crack as a reversible thermodynamic system and sought to minimize the total free

energy of the system. In this system, strain energy was the driving force for the crack

propagation and surface energy was the resistant component for crack propagation. Based on

this assumption, the Griffith's theory implies that the critical stress, of, for a crack to propagate is

defined as

2 1
cr = ( ) (2-11)


where E' identifies with elastic modulus (E) in plane stress and (E/(1-v2)) in plane strain with v

the Poisson's ratio. The strength is therefore controlled by three basic parameters, which are the

elastic modulus (E), the surface energy (y) and the flaw size (C). This relationship demonstrates









that failure occurs when the loss of strain energy is sufficient to provide the increase in surface

energy.

There are two important basic implications of this relationship. The first is, the critical

stress for a crack to propagate is inversely proportional to -VC. The second is, when the applied

stress is greater than this critical stress, crack will propagate spontaneously without limit. This is

the first time in fracture mechanics history one specified the criterion for crack growth.

However, it has been shown that Griffith's theory has some practical limitations. For example,

in 1930, Griffth's theory ran into major obstacles when Obreimoff [76] tested his theory with a

rigid wedge loading condition to cleave mica. Obreimoff found that the failure for this loading

geometry occurs in a stable fashion, which is against the second implication of Griffth's concept.

Linear Elastic Fracture Mechanics (LEFM) is a further development of Griffith's concept

in the history of fracture mechanics. In the vicinity of a crack, the stress fields can be derived

from three basic modes of loading, which are tensile mode or mode I, sliding mode or mode II

and tearing mode or mode III respectively (see Figure 2-10). Based on linear elastic theory,

Iwirn in 1958 [77] described stresses in the vicinity of a crack tip as

K
-, W = )12 (0), (2-12)

where, r,0 are the cylindrical polar coordinates of a point with respect to the crack tip; K is the

stress intensification factor, which gives the magnitude of the elastic stress field; and f, (0) is an

angular function. For a given loading mode, K can be expressed as

K, = cr (2-13)

where, Y, is a dimensionless parameter that depends on geometry of the crack and the loading

mode and i represents the loading mode.









Following Griffith's energy balance condition concept, Irwin was able to combine the

stress intensification factor K with the the strain energy release rate G. In case of mode I loading

condition this relationship is shown as


G =K (2-14)
E

The crack propagates when G reaches a critical value Gc, which is determined by the

resistance for crack propagation, R. For the "ideally" brittle material, R is twice the surface

energy, y. From Equation 2-14, the existence of Gc implies there is also a critical value for the

stress intensity factor. For example, Kjc can be identified to be the critical stress intensity factor

for a material under mode I loading condition. Here, K1c is a material property and termed as

fracture toughness.

2.4.2 Toughening Mechanisms for Brittle Materials

Brittle ceramics usually fracture in a catastrophic or unstable way, which is not desirable

for most practical applications. In general, there are three alternative steps [73] that one can

consider to overcome this problem with the help of understanding the basic equation between

strength and fracture toughness.

Because the material strength is inversely proportional to -\C, the first step is to decrease

the flaw size to improve the strength. Control of flaw sizes can be achieved through

improvements in material processing, surface finishing procedure and service conditions. The

second step is to decrease applied stresses by a change in component geometry to remove

unwanted stress concentrations so that the design stress can be decreased. However,

improvements through these two steps are most of the times difficult due to practical limitations.

This leads to the advantage of third step, which is the enhancement of fracture toughness or flaw

insensitivity from material science aspects. Several toughening mechanisms have been









successfully developed over the last several decades. A summary of the major toughening

mechanisms for brittle materials are summarized in the following.

Firstly, toughening can be caused by crack tip perturbations. The basic concept of this

mechanism is to impede the crack by obstacles in form of second phase. The magnitude of

perturbations of crack front by the second phase depends on the character of the particles and the

nature of the crack interaction. There are two dominant perturbations in brittle materials, i.e.,

crack bowing [78-79, 81] and crack deflection [82-84], which may operate simultaneously

during crack propagation. The following reviews the development of both processes.

In case of crack bowing, the process originates from the second phase in the path of a

propagating crack and produces a non-linear crack front. The material strength of is determined

by the stress to propagate these secondary cracks. This stress is usually greater than the stress to

extend the primary crack except the case when the ratio between phase spacing and second phase

dimensions is relatively large. Lange [78] suggests that the increase in both the strength and the

fracture surface energy may be similar to a line tension effect observed for dislocation motion

[85]. Evans [79] calculated this line tension effect and found a good correlation with the

experimental results [80] for the fracture surface energy of glass/alumina system. The fracture

surface energy includes all the resistance to form new surfaces by crack propagation. Crack

bowing is found to be the major contribution to the strength increase for brittle second phase

(impenetrable second phase) in brittle matrix composites, but a minor contribution to the strength

increase for fiber composites or ductile second phase [79].

Unlike crack bowing process, crack deflection creates a non-planar crack during

propagation, which leads to lower stress intensity than that experienced by corresponding planar

crack. The sources of crack deflection can be either residual strain presented in the material [84]









or the existence of weakened interface. Figure 2-11 schematically shows two types of crack

deflection mechanisms, i.e., crack tilt and crack twist [82, 83]. The twisted and tilted cracks are

subjected to a mixed-mode loading. In case of crack tilt (Figure 2-11A), the local stress

intensities have a mixed mode I and mode II components, and combined mode I and mode III for

crack twist (Figure 2-11B). It is clearly to see that crack deflection is accompanied by an

increased roughness of the fracture surface. Based on Faber and Evans's calculations [82], the

increase in toughness only depends on the shape and volume fraction of the second phase. The

most effective morphology for deflecting crack is predicted to be the rod of high aspect ratio (the

ratio of length divided by the diameter). The major toughening increment by crack deflection

appears to develop volume fraction of second phase less than 0.2.

Secondly, crack tip shielding mechanism can also improve fracture toughness. Some

microstructural change in brittle material under deformation may cause the stress intensity factor

in front of the crack tip, K,", is less than the applied stress intensity factor, K" and shielding

occurs. Failure occurs when KP = KO, the fracture toughness of local highly stressed portion at

the crack tip, or the process zone. If this statement is expressed in an equation for the critical

situation, i.e., the situation when failure occurs, the shielding criterion becomes

Kf'P= AK,+KYe, (2-15)

where AKA is the value of shielding effect at the point of fracture. The measured fracture

toughness Kj,'P is therefore higher than the fracture toughness of the process zone material by

the amount of AK,. It has been proven that there are three types of dominant shielding

mechanism [86], transformation toughening [87-89], crack bridging [90, 91] and microcrack









toughening [92-102]. The basic concept behind each of these toughening mechanisms is

explained in the following contexts.

The majority work on transformation toughening is on using metastable tetragonal zirconia

as toughening agent [87, 88]. When the stress level around the crack tip reaches a critical value,

the metastable tetragonal zirconia tends to transform into the stable monoclinic phase. This

transformation is accompanied by a volume increase, and the result is the creation of

compressive stress around the crack tip, which tends to shield the crack.

Crack bridging toughening occurs when the primary crack front by-passes obstacles. For

composite materials, the bridging process may come from the second phase. If the bridges are

elastic, failure may occur when the bridges are pulled out of the matrix [90]; or if the bridges are

ductile, failure occurs through plastic deformation. The increase in toughness by crack bridging

can be attributed to the decrease of the stress intensity factor at the crack tip.

The microcrack toughening mechanism [92-102] has been proven to cause crack tip

shielding effect by amount of AK through redistributing and reducing the average near-tip

stresses. There are two sources of this redistribution effect [92, 97]. One is due to the reduction

in the effective elastic moduli resulting from microcracking formation and extension in the

process zone. The other is the strain arising from the release of residual stresses or the

dilatational effect when microcracks are formed. Between these two sources, the dilatational

effect is found to be more substantial. Figure 2-12 schematically shows these two effects in the

stress-strain curve along with the rising crack resistance curve, KR curve, for a microcracked

material [97]. Frontal zone microcrack causes minor increase in AK, and dilatation toughening

will occur when microcracks enter the crack wake. Because of the importance of nucleation and

extension of microcraks for this mechanism to operate, the control of microcracking sites









becomes essential. These sites are expected to be weak interfaces between the matrix and the

second phase for composites or the grain boundaries for single phase polycrystals. It needs to be

pointed out that toughening by microcracking is normally accompanied by reduction of strength

of ceramic materials [103]. The challenge for successfully applying this mechanism will involve

minimum sacrificing of strength.









Air: 02 + 4e 202-


Dense electrolyte


Porous anode

Fuel: 2H2 +20 -2 H20 + 4e


Excess Air


- Reaction product


Figure 2-1. Schematic diagram for the principle of a solid oxide fuel cell.

(A)












(B)












Figure 2-2. Fracture of the electrolyte after the half-cell (nickel/yttria stabilized zirconia (or
Ni/YSZ) anode and YSZ electrolye) experienced reduction and reoxidation cycles.
(A) Cross section and (B) electrolyte surface[45]


e

Electric
power

e


I















@ 02-


O M4+





Figure 2-3. Schematic drawing of the atomic structure for fluorite oxides.



10

E8 -
r Ceria
86 --YSZ
S GDC

> 4
I
2-

0 -----------------
0 -10 -20 -30 -40 -50
log(Po), atm


Figure 2-4. Predicted dependence of oxygen vacancy concentration on oxygen partial pressure
(Po2 ) at 800 C for pure ceria, GDC gadoliniumm doped ceria) and YSZ from
theoretical modeling [44].























-24


-22 -20 -18 -16 -14 -12
log PN (atm)


Figure 2-5. Dependence of Co. Ccaon atom ration on oxygen partial pressure at 800 C for
Ceo0.9Gdo.101.95-x. (e) Themogravimetric data from Wang et al.[55] and (-) model
[44].


-15 -20 -25


log Po2

Figure 2-6. Themogravimetric measurement results (800 C) of oxygen vacancy concentration
as a function of oxygen partial pressure for pure ceria [14, 15].



























Figure 2-7. Phase diagram for CeO2-x.[16]


0.0 -
2000


1900
N in CeON


Figure 2-8. Expansion of ceria versus nonstoichiometric composition at 900 oC. (o, *) Chiang et
al. [5]. (- -) Theoretical slope; (- ) best fit slope; (E) Mogensen and Mogensen
[6,58].













o-
2






CD
Y203

S --- Gd2O
O Sm 203
LL 0 I I I I ,
0 10 20 30 40 50

Dopant (mol%)

Figure 2-9. Fracture toughness of doped ceria materials [41].













Mode I Mode II Mode III


Figure 2-10. Three basic modes for fracture.




















V


Figure 2-11. Crack deflection process by (A) tilt and (B) twist [45]. Z-X plan is the primary
fracture plan. Y is the loading direction. X is the crack propagation direction [82]


(A)








(B)


Figure 2-12. Stress-strain curve (A) and the corresponding crack resistance curve (B) for a
microcrack toughening mechanism [97].









CHAPTER 3
MATERIALS AND EXPERIMENTAL PROCEDURES

This chapter explains the materials fabrication and experimental procedures that were

applied in this research. As the nanoindentation technique for intrinsic elastic modulus and

hardness evaluation is limited only for room temperature tests, we designed a heat treatment

process that allowed the effect of defect concentration on mechanical properties to be evaluated

at room temperature. The strategy was to create defects by equilibrating the samples in various

oxygen partial pressures (Po2 s) at a high temperature and then conserve them to room

temperature by fast cooling. To be consistent with nanoindentation tests, all the other

mechanical tests were performed at room temperature as well, i.e., the mechanical tests are not

in-situ tests but post evaluations. In this chapter, each procedure will be explained in detail.

3.1 Sample Fabrication

Three types of fluorite-structured oxides, pure ceria or CeO2, 10 mol % gadolinium doped

ceria (GDC) or Gdo.1Ceo.901.95, and 8 mol % yttria stabilized zirconia (YSZ) or

(Y203)0.o08(ZrO2)0.92, were selected for this research, The materials were prepared with solid state

method using commercial powders, i.e., pure ceria (99.9% pure, Alfa Aesar, 5tm powder), GDC

(99.9% pure, Rhodia Inc., USA and Anan Kasei Co., Ltd., Japan ) and YSZ (TZ-8Y, TOSOH

Co., Japan).

Depending on the type of mechanical tests, the sample size requirements are different.

However, the fabrication process of the samples was kept same for each material in order to limit

microstructure variations. It needs to be pointed out that numerous fabrication methods, such as

electrochemical vapor deposition, tape casting, plasma spraying or colloidal/electrophoretic

deposition are used to prepare electrolyte materials. These methods are adopted to achieve thin

electrolyte (as explained in 2.1.1). However, the samples prepared by these methods have









dimension limitations for mechanical tests in this research. Therefore, we used the conventional

solid state method to prepare samples with desired dimensions. Figure 3-1 shows the flow chart

of fabrication processes used in this study, which were slightly different for each material. Pure

ceria powder was ball milled with 3 wt% polyvinyl butyral (PVB) ethanol alcohol solution for 24

hours. After drying, the powder was milled and sieved. The ceria samples were then prepared

by two step of pressing. The first was uniaxial pressing at pressure about 35 MPa for 4 mins,

and the second was cold isostatic pressing at 250 MPa pressure for 5 minutes. Because the

uniaxial pressing procedure defines the shape of the green body, a proper sized dies were

adapted, i.e., 3 inch, 12 inch and 114 inch diameter dies were used for disc shaped samples, and

10 mmx60 mm rectangular die was used for bar samples.

The pure ceria samples were held at 400 C for one hour to burn out the PVB binder and

then sintered at 1550 C for 20 hours. The heating and cooling rate was 5 C/min. The GDC and

YSZ samples were prepared similarly as pure ceria sample, but without the addition of binder

and the burn out procedure.

As a result, the final size of the ceria samples for nanoindentation tests was about 06 mm

x4 mm. The final size for GDC and YSZ samples was 010 mmx4 mm. The Brazilian disc ceria

samples for fracture toughness tests had the dimensions of D26 mmx2.6 mm. Because the bar

samples after firing had a size of approximately 3.1 mmx8 mmx48 mm, two bending samples

with dimensions of 2.6 mmx4 mmx45 mm were obtained from one original bar. The schematic

in Figure 3-2 shows the procedures how the bar samples were achieved. The materials and the

size of the samples are summarized in Table 3-1.

3.2 Heat Treatment

The heat treatment temperature was chosen to be 800 C, which is typical operating

temperature for Solid Oxide Fuel Cells (SOFCs). The amount of time that was needed for the









heat treatment was decided from two approaches. The idea was to achieve equilibrium. Firstly,

in order to calculate the equilibrium distance, oxygen self-diffusivities in these materials are

needed. From literature, given by R. Devanathan, et. al.[104] and P.S. Manning, et.al. [105], the

oxygen self-diffusivity coefficient in YSZ is 10-7 cm2S-1, given by B.C.H. Steele [27], oxygen

self-diffusivity coefficient in ceria system is one order of magnitude higher with a value of 10-6

cm s -1. Because the absolute equilibrium is very difficult to reach in real experiment,
"equilibrium distance" in this research is considered as the depth where the sample has reached

90% or higher of the equilibrium concentration. Using the available information diffusivityy and

material dimension values), the equilibrium distance for each materials as a function of time was

directly read from the plots of the diffusion solution given by J. Crank [106]. As a result, it

shows that within 15 hours, the ceria samples and GDC samples has reached "equilibrium" at a

depth larger than 1.3 mm and YSZ has reached "equilibrium" at a depth larger than 0.6 mm.

Secondly, based on thermal-chemical expansion experiments conducted by S. Bishop, et.al. [107]

for the same materials and experimental conditions as this research, the amount of time of 15

hours was sufficient enough for the these materials to reach the maximum expansion, i.e., the

equilibrium condition.

In order to achieve different defect concentration, the samples were heated at a rate of 5

C/min to 800 C and equilibrated in various oxygen partial pressures for 15 hours. The various

oxygen partial pressures were obtained by choosing different gas mixtures (i.e., N2, Ar, H2 and

H2/H20). The gas flow rate was 10 sccm. Figure 3-3 shows the schematics of the heat treatment

setup. The samples were heat treated inside a quartz tube. There was an oxygen sensor

connected to the out gassing line of the tube furnace for measuring the oxygen partial pressures

of the controlling gas or gas mixtures. The oxygen sensor was a galvanic cell with the type of









Pt, air(Porefrence .....)/ziroconia electrolyte/Pt, controlling gas(Po, ).

The voltage difference between the electrodes is given by the Nernst equation as


E = RT In Pogas (3-1)
zF P
zF P0 ,reference

where, R is the universal gas constant, Tis the absolute temperature in degrees Kelvin, z is the

charge number of the electrode reaction (which is the number of moles of electrons involved in

the reaction, in this case, z equals to 4), and F is the Faraday constant (96,500 C mole-'). The

reference gas was dry air in this study, therefore Po reference =0.21 atm. By measuring the voltage

difference across the zirconia electrolyte, the oxygen partial pressure for the controlling gas at

the heat treating temperature can be calculated from Equation 3-1. The corresponding oxygen

partial pressure ranges of different gases or gas mixtures are listed in Table 3-2.

After 15 hours at 800 C, the samples were then fast cooled to room temperature to

maintain the defect concentrations achieved at the elevated temperature. The average cooling

rate was about 16 C/min for the first 200 C, and 9 C/min for the range from 600 C-400 C.

The total time for the samples to cool down to 300 C was about 50 minutes. Figure 3-4 presents

the temperature-time curve for this heat treatment.

In order to distinguish between the thermal vacancies and those created by a reduced

atmosphere, one sample of each material was heat treated in air (Po =0.21 atm) for the same

amount of time at 800 C and then fast cooled to room temperature. To prevent reoxidation

during cooling, the controlling gas mixture was continually flowed throughout the fast cooling

period.









3.3 Mechanical Tests


3.3.1 Elastic Modulus Tests

Two sets of tests were designed for elastic modulus measurement, namely, nanoindentaion

and four-point-bend tests. For nanoindentation tests, the indent size is small (submicron) and

therefore the indents could be fit inside the grains. Also, by analyzing the images of each indent,

the indents with abnormal shapes resulting from the nearby pores or microcracks were further

eliminated, and Figure 3-5 is examples of such indents and a successful indent. Therefore,

nanoindentation is able to measure the intrinsic elastic modulus, i.e., independent of the

influence of pores, grain boundaries and other microscopic defects such as microcrakcs.

However, elastic modulus evaluated by bending tests requires bulk samples where the effects of

porosity, grain boundaries and other microstructural features contributed to the test results. The

details of these two testing methods are explained in the following sections.

3.3.1.1 Nanoindentation test

Due to the sensitivity of nanoindentation test to the sample surface conditions, all samples

were carefully polished to 0.25 ptm using alumina powder and diamond paste prior to heat

treatments. In order to minimize the microstructural variations (such as porosity, pore size, grain

size, ect.) from one sample to another, the same batch of the as-sintered samples was used for

nanoindentation tests as a function of oxygen partial pressure. Preliminary nanoindentation

results conducted on the surface of the as heat treated samples showed a large scatter in the data.

Further analysis using SEM suggested a surface effect upon heat treatment. Therefore, the

samples were further mechanically polished after heat treatment and prior to nanoindentation in

order to remove the top layer (<10tm) altered by the thermal etching and by reoxidation.

The nanoindentation was carried out using a Hysitron Tribolndenter. The triangular

pyramid Berkovich indenter was used for all the measurements. The Hysitron Tribolndenter has









a capability of recording load-displacement curve during the test. The contact area function of

the indenter (i.e., the contact area vs. contact depth) was generated by testing a standard sample

with known elastic modulus. The standard used for this research was fused quartz with an elastic

modulus of 72 GPa. The details of generating area vs. contact depth function followed reference

[108]. After series of indents on the standard sample, a power law curve fit was performed on

the unloading portion of each curve. A tangent line to the power law curve was used to find the

stiffness, from which an area was calculated because the elastic modulus of the standard was

known. The calculated area versus displacement for all the indents was fit in a curve and the

area versus displacement function was generated. The machine compliance, sample tilt and

thermal drift were all considered and calibrated following the instruction in reference [108].

Because of the availability contact area verse displacement function, the reduced modulus (Er)

was then calculated from the slope of the unloading segment of the load-displacement curve.

This reduced elastic modulus combines the modulus of the indenter and the specimen

according to Equation 3-2, which is given in the Hysitron Tribolndenter Naomechanical Test

Instruments manual.


1 (1 Videnter ) 1 vsple )
Er Eindenter Esample (3-2)

where, Vindenter and Vsampie are the poisson ratios and Emndenter and Esampie are the elastic modulus of

the diamond indenter and the sample, respectively. The elastic modulus of the sample was

calculated using vOndenter=0.07 and Ejenter =1 140 GPa for the diamond indenter and assuming

Vsample=0.3 [6].









All the tests in this research were under load control. The samples were loaded to 5000 aN

and held for 5 seconds and then unloaded. The loading and unloading rates were the same and

equal to 1000 aN/s. A total of 49-100 indents were performed on each sample.

3.3.1.2 Four-point-bend test

For the purpose of comparison with the nanoindentation results, the elastic modulus of

bulk samples by four-point-bending was also conducted at room temperature. Prior to heat

treatment, the bending bar samples were sent to be machined (PremaTech Advanced Ceramics,

USA) according to the ASTM C 1161 standard [109]. The bulk elastic modulus was measured

using an MTS810 mechanical testing system designed for controlling small displacements. The

displacement was measured using MTS model 632.06B-20 extensometer at 0.016 inch full scale

range. The load was measured using MTS 661.19-2200 lbs load cell at 200 lbs full scale range.

A digital image of the MTS810 system is shown as Figure 3-6A and the details of the bend test

setup is shown as Figure 3-6B. The four-point-bending fixture (MTS model 642.05A-02) used

in this research was a fully-articulating fixture designed to be used either with flat and parallel

specimens or with uneven or nonparallel specimens. The concept of fully-articulating is

explained in ASTM C 1161 standard (also see Figure 3-6C) [109]. As shown in Figure 3-6B, the

fixture allows full independent articulation of all rollers about the specimen long axis to match

the specimen surface. The upper pairs are free to pivot to distribute force evenly to the bearing

cylinders on either side. The support span was 30 mm, and a one-third loading span was used.

The loading speed was calculated according to ASTM D 6272 [110] as

0.185ZL2 (33)
d

where, R is the displacement rate; L is the support span (30 mm), dis the depth of the beam (2.6

mm); Z is the strain rate of the outer potion of the sample and equals to 0.01 s-1. Therefore, the









displacement rate was then determined to be 0.6 mm/min. A computer (LabView 7, National

Instruments software) was used for the data acquisition.

The elastic modulus was calculated from [110]

E 0.21L3m (34)
B bd3 '3

where, EB is the modulus of elasticity in bending; m is the slope of the loading segment of load-

displacement curve; b is the width of the bending bar. At least two samples for each heat

treatment condition were tested for the bulk elastic modulus. It is common to see researchers in

the literature to do several loading unloading cycles and then evaluate the elastic modulus from

the unloading segment of the curves. The reason we did not perform loading cycles to our

sample is because of the sensitivity of the microstructure to loading cycles, and this will be

addressed later in section 5.1.2. However, the validity and reliability of our method can be

shown through the dummy tests on a steel sample. The steel (which has a known elastic

modulus of 200GPa) bar sample with a cross-section of 3.145 mm x 3.146 mm was tested using

the same parameter as described above. The corresponding load verses displacement curve is

shown in Figure 3-7. The initial part of the loading curve (approximately 20 N) was omitted due

to the nonlinearity caused by friction contact between the sample and the fixture. From the slope

of this curve, the elastic modulus calculated through Equation 3-4 was 197.1 GPa, which is very

close to the elastic modulus of steels. In fact, multiple cycling tests were performed using this

sample and the variation from one test to another remained within 6 %. Therefore, it is reliable

to use this technique to evaluate elastic modulus.

3.3.2 Hardness Test

The hardness was also evaluated at the same time as the intrinsic elastic modulus by the

nanoindnetation test from









P
H = app (3-5)
A

where, H is the hardness; Papp is the maximum applied indentation force; and A is the resultant

projected contact area at that load. These contact areas were determined from the contact area

function that was described in section 3.3.1.1.

3.3.3 Flexural Strength Test

The flexural strength was also evaluated using four-point-bend test. The number of the

samples tested in this research will be revealed later in Chapter 6. The test parameters, fixtures

and sample preparation were the same as the above mentioned test for evaluating bulk elastic

modulus. The flexural strength can be expressed as

PL
c bd (3-6)
bd2

where, Pf is the fracture load L, d and b are defined the same as in Equation 3-4.

3.3.4 Fracture Toughness Test

The initial attempt to evaluated fracture toughness using Vikers microhardness tester was

not successful. As shown in Figure 3-8, the indentation pattern of the as-sintered ceria sample

was severely disrupted (at load of 200 g) and therefore not suitable for measurement using this

method. In this study, chevron-notched Brazilian disc tests under the mode I loading condition

was successfully applied to measure the fracture toughness. The reason that we chose disc shape

sample testing instead of the standard bending bar sample [111] is that we were not able to

produce high quality bending bar samples at the moment that this test was carried out. Figure 3-

9 schematically shows the dimensions of the Brazilian disc samples. The samples were

manually polished using 600 grit silicon carbide sand paper prior to heat treatment. Chevron

notches were cut in the Brazilian disc samples prior to their heat treatment using a low speed









diamond saw with a 0.2 mm-thick blade. The radius of the blade was R0=12.7 mm. The notch

length (2a), the sharpness of the chevron-notched section and the distance between the notch tips

(2ao) are not independent parameters, and all of them depend on the penetration depth (see

Figure 3-10A) of the blade into the sample. The deeper the penetration depth of the blade, the

larger values of these two parameters are, but with shorter and shaper chevron-notched section.

For samples with same thickness, Figure 3-10 OB shows a chevron notch with notch to diameter

ratio of 0.5 and Figure 3-10C for ratio of 0.6 to visualize the difference.

It depends on several parameters to successfully make a chevron notch. During the

notching process, the alignments between the diametric lines of the blade from both cuts, the

center line of disc sample and the normal of the disc sample are essential for a symmetric notch.

Also, the penetration depth of the blade from both sides of the sample has to be same. The

schematics of the unsuccessful chevron notches experienced at the initial stage of this work are

schematically shown in Figure 3-11.

The testing method for the Kic measurement using Brizilian disk samples followed the

procedure explained by Shetty, et.al. [112, 113]. The final geometry of the ceria samples with a

notch to diameter ratio (2a/2R) of 0.5 was comparable to the sample geometry used in their

research. The loading and unloading of the fracture test was done under displacement control

with a cross head speed of 0.002 in/min using Instron 1125.

A precrack procedure proposed by Shetty, et.al. [112] was performed on Brazilian disc

sample to achieve a sharp crack tip. A sharp crack tip is necessary for valid fracture toughness.

In addition, the scattering of the data will be limited because the fracture would be dominated by

the sharp crack tip created by precrack procedure, not by the roughness of the notch edges.

Firstly, the fracture load of a Brazilian disc sample was directly loaded to fracture under mode I









condition, i.e., by loading in compression along a diameter through the chevron notch. The load

for precrack for was then determined to be about 90-95% of this fracture load (the precrack was

also conducted mode I). The sample was held at this load level for 6 or 12 mins and then

unloaded. Crack propagation within the chevron notch (in our case when a R=0.5) is stable

because the effective thickness is increased continuously owing to the shape of the notch.

The stress-intensity factors at the point of fracture for mode I loading of Brazilian disc

samples were calculated using the solutions given by Atkinson, et. al. [114] as


K = 'axa N (3-7)


where, Pmax is the fracture load, a is the half crack length, B is the thickness, (see Figure 3-9),

and N, is a non-dimensional coefficient that is a function of the relative crack size (a R). The

relative crack size (a R) in this study has a range of 0.48-0.51. Atkinson, et. al. [9] provided the

numerical solutions for the cracks in the size range a/R=0.1-0.6, which were used in this study

for calculating Kjc. Furthermore, Shetty, et.al. [112] calculated the stress state (plain strain

condition and biaxial stress state condition) effects on the stress intensity factor based on strain-

energy-density theory and found that stress state did not affect the stress intensity factor for pure

mode I condition. In another words, the effect of the sample thickness should not affect the Kic

results for brittle materials.

3.4 Characterization Techniques

The densities of the as-sintered samples were measured by the immersion technique with

pure water as the immersion solution. Assuming that the density for pure water at room

temperature is 1 g/cm3, then the density of the samples was calculated by Equation 3-8 according

to Archimede's principle as










p= wd (3-8)
W dry -Wwet

where, p is the density of the test sample; wdry is the weight measured in air and Wwet is the weight

of the sample in pure water.

The grain boundaries for all three materials used in this research was revealed after being

thermo-etched at 1550 C for 12 mins. Optical microscopy and scanning electron microscopy

(SEM, JEOL JSM 6400 and FEG-SEM, JEOL JSM-6335F) were both used to image the

microstructure. All the samples prior to SEM analysis were coated with Au-Pd. After taking

images with proper magnification, the standard linear-interception method was used to determine

the grain sizes [115].

After nanoindentation tests, high resolution naoindent topography images were recorded

using scanning probe microscopy, which is one of the function of the Tribolndenter. These

images are helpful to verify the quality of the indents.

The crystal structure and the texture of the samples were studied using the X-ray

diffraction (XRD) method with Cu Ka radiation (XRD, Philips APD 3720). The XRD patterns

for powder samples as well as bulk samples were recorded and compared to the standards to

identify the crystal structure. When bulk samples were tested for XRD pattern using this

machine, it was very important to adjust the sample height to be aligned with the sample holder

for valid 20 values. The amount of time to conduct an XRD test depends on the parameters of

the XRD experiment, i.e., step size in terms of 20 and time per step, in another words, the

smaller the step size or the longer time per step during XRD scanning results in longer XRD

experiment time. For example, for a 20 range of 20-100 degree, if the step size was 0.02 degree

and time per step was 2 seconds, the total time for XRD scanning was about 2 hours 13 mins.









Based on Bragg' law (Equation 3-9), the interplanar spacing for planes with Miller indices (h, k,

/), or dhkl, was calculated through Equation 3-10.

A = 2dhki sin(O), (3-9)


dhki 2 (3-10)


where, X is the wavelength of radiation source, and in this case, Cu Ka (wavelength=1.54A).

As the materials selected in this research were all cubic structured materials, the lattice

parameter, a, was then calculated through

a= d 4h2 k2 (3-11)

Scanning electron microscope (SEM) was also employed for fractographical analysis.

Fractographic images of bend bar and Brazilian disc samples were used to identify the crack

initiation sites and crack propagation process. In order to investigate the interaction between

pores and propagating cracks, a quantitative metallography analysis method was used on the

fractographic images of Brazilian disc fracture samples. The accuracy of the crack length

measurement is crucial for the validation of the fracture toughness results. In this research, the

crack length was measured using a Unitron Microgoniometer with the accuracy of 0.01 mm.

The crack length was also verified later in SEM.

In order to study pore-crack interaction, the pore area densities on the polished surfaces

and the fracture surfaces were measured for samples heat treated under different conditions.

Images used for this analysis were taken at a magnification of 2000X. The pore area density

(AA) was measured using point-count method [115] The total number of points was 864

(27x32) and they were uniformly distributed on the areas of interest (an area of approximately 45

amx52 tm for each image). AA is equal to number of the points that fall on the pores divided by









the total number of the points. The difference of pore area density between the fracture surface

and the polished surface indicates the pore-crack interaction. If the pore area density was higher

on the fracture surface than the polished surface, the crack was attracted by the pores; or if the

pore area density was lower on the fracture surface than the polished surface, the crack was

repulsed by the pores.

Transmission electron microscope (TEM Joel 200 CX) was used for observations of

microstructure and phase characterizations. The TEM samples were prepared using focused ion

beam instrument (FIB, FEI Strata DB235). The samples used in FIB were triple times coated

with carbon. Prior to the ion milling process, a 1.2 tm thick Pt layer was also deposited onto the

area of interest to protect the sample from ion damaging. As shown in Figure 3-12A, the thin

TEM sample (a thin slice of ceria material) is hanging between the two trenches that were first

dug off at the beginning of the process. The bottom of the sample is also cut free at this stage of

the process. After further thinning and when the desired thickness is reached, the sample is

ready to be cut free from the bulk material (Figure 3-12B shows this situation for another TEM

sample with one shoulder cut free). The TEM samples were lifted out using an ex-situ

MicroOptic manipulator and then were put onto a Cu grid. The final size of the TEM sample

prepared by this method was about 15 [tmx5 [tm with a thickness of 100-150 nm.









Table 3-1. Sample dimensions for mechanical tests.

Sample Size
Materials Nanoindentation Samples for flexural tests Brazilian disc
samples samples for Kic tests
Pure ceria (6 mmx4 mm 2.6 mmx4 mmx45 mm (026 mmx2.6 mm
(CeO2)
GDC 010 mmx4 mm 2.6 mmx4 mmx45 mm ----
(Gdo 1Ceo0 901 95)

YSZ 010 mmx4 mm 2.6 mmx4 mmx45 mm --
((Y203)0 o08(ZrO2)o 92)



Table 3-2. Oxygen partial pressure ranges (Po2 s) of different gas mixtures.

Gas Compositions Oxygen Partial Pressure, atm
air 0.21
N2 or Ar 10-6_10-4
H H O/N2 or H- HO/Ar 10-19-10-23
Dry H2 <10-24





































Figure 3-1. Flow chart of the sample fabrication process.







Green body: 4 mm x 10 mm x 60mm


Sinteringj


As-fired bar: 3.1 mm x 8.5 mm x 48 mm


Two bending samples before machining:
-3.1 mm x 4 mm x 48 mm


Figure 3-2. Schematics of the procedures of achieving two bending samples before machining
from one as-sintered bar.


V 'A


'-Cut in the middl











Gas Supply:H2,
112/f120, Ar, N2, Air


Sample


Figure 3-3. Schematic of the heat treatment experiments set up. The gas flow direction is
showing by the arrows.


800


o 600


. 400
E
I-

200


0


0 200 400 600
Time, mins


Figure 3-4. Temperature-time curve for the heat treatment.























(B)













(C)












Figure 3-5. Comparison of Nanoindents with abnormal shapes due to (A) a nearby pore or (B)
underneath pore and a successful nanoindent.











Load cell


MTS control console





Data acquisition system




Setup for bending tests






4 point bending fixtures



Ceria sample

Extensometer


T fMlit MANWOS
AfRltATfO
AND FA
TO ROLL INWARDN


NOT AfICULATI
BUT FREE TO RiLL


ARfICULATie
AND FPUe
TO ROLL OUTWARDS


FULLY-ARTICULATING. The two imnIr barmigs eln to il ionwanis, d tmey cn lndq iu dy
Uticulam to mWl& fa. tpeciam wop aUM. Tie two auer bmlahp I re tee to roll, and one bearing cn
Mnicuae to asmil On p punn bornm urtasm.


Figure 3-6. (A) A digital image of 810 Material Test System (810MTS) used for the flexural
tests. (B) The details of the fixture setup for four point bending test with one ceria
sample and the extensormeter in position. (C) Schematics of the fully articulating
four-point-bend fixture [6].






















40 -



0
0 0.01 0.02 0.03 0.04 0.05
Displacement, mm


Figure 3-7. The load-displacement curve of a steel sample with a cross section of 3.145 mm
x3.145 mm. -- is the experimental data; --is the best linear fit. The
resulting elastic modulus from this test is 197.1 GPa.


Figure 3-8. Scanning electron microscopic (SEM) image of the Vikers indent at 200 g for an as-
sintered ceria sample. (Hardness with Vikers number 599-608, or 5.9 GPa).



















Section A-A


-A


Figure 3-9. Geometry of the chevron-notched Brazilian disc samples used in the fracture
toughness test. The main crack propagation direction is defined as X-direction and
the crack opening direction is Y-direction. The fracture surface lies on X-Z plane.
The final dimensions of a typical sample were R=13.03 mm, B=2.62 mm, ao=3.67
mm, a=6.45 mm, M=0.24mm.




(A)














Figure 3-10. (A) Schematics of an ideal chevron notch and (B) two chevron notches with
different dimensions. ((B) for a/R =0.5 and (C) for a R=0.6) depending on the
penetration depth, h, of the blade into the disk sample.


Z




























.a,- (C)







22







Figure 3-10. ctd.












- --- --- - -


Figure 3-11. Schematics of the unsuccessful chevron notches. These outcomes are due to (A)
misalignment of sample and the blade, (B) misalignment between the two cuts, (C)
misalignment of the two cuts to the normal of the sample and (D) uneven penetration
depth.


(A)









(B)










(C)









(D)












(A)
The sample


Underneath cut








(B)













Figure 3-12. Images of the pure ceria transmission electron microscopic (TEM) samples during
the preparation process by focused ion beam (FIB). (A) A sample was prepared
before cut free from the bulk material. (B) Another sample with one shoulder cut off
from the bulk material.









CHAPTER 4
MICROSTRUCTURAL ANALYSIS

Because material properties are directly related to microstructure, it is important to

characterize and understand microstructural conditions prior to mechanical property evaluations.

The objectives of the microstructural characterizations are to answer the following questions.

Did the oxygen vacancies created at high temperature conserve to room temperature? Did phase

transformation occur during the cooling process? Did ordering of oxygen vacancies take place?

Was the reoxidation at room temperature significant? Were there any other factors that

contributed to microstructural variation? These questions will be answered in detail for pure

ceria in the following sections.

4.1 Characterization of As-Sintered Materials

The X-ray diffraction (XRD) patterns of the as-received ceria powder and the as-sintered

ceria sample are shown in Figure 4-1. The XRD patterns were comparable to the standard XRD

file of JCPDS #43-1002 in terms of 20 peak positions. The relative XRD intensity of the powder

and the as-sintered sample was also compared to the standard and the results are shown in Table

4-1. The relative intensity of each planes were found to be comparable to the standard, therefore,

the powder and the as-sintered sample are considered to be fluorite structure with no obvious


texture present. This fluorite oxide has a space group ofFm3 m (225). Using the 20 values

found for each sets of planes, the lattice parameter was calculated through Equations 3-9 and 3-

10 for the powder as well as the as-sintered ceria sample. The average lattice parameter was

calculated for 0.5400 nm+0.0005 nm.

The average grain sizes for ceria and gadolinium doped ceria (GDC) were measured using

linear interception method from SEM images or optical images after thermal etching process. In

case of the yttria stabilized zirconia (YSZ) samples, images of a fractured cross section were









used to estimate the grain size. Although this is not the standard method to measure grain size, it

is reasonable for estimation. Images in Figure 4-2 are presented to show the grain sizes of these

materials. The densities of each material were measured by immersion technique as explained in

section 3.4. Based on the theoretical density values (i.e., 7.22g/cm3 for ceria and GDC,

5.96g/cm3 for YSZ), the relative densities for each material were also calculated. The results of

the grain size measurements along with the densities are summarized in Table 4-2.

4.2 Characterization of Reduced Ceria

4.2.1 Optical Properties

After the heat treatments, the ceria and GDC samples became noticeably darker as the

applied oxygen partial pressure (Po2) was decreased. This is an indication that the vacancy

concentrations were conserved. The color change on the surface was strongest immediately after

heat treatment for ceria and GDC. However, it decayed somewhat over time, even at room

temperature. The color fading rate for GDC was very fast and took only several hours for the

surface color to change from black (after H2 reduction) to a light brownish color. However, the

process was very sluggish in the pure ceria samples. Figure 4-3 shows the digital images of the

color change of ceria samples as a function of oxygen partial pressure. These images were taken

within several hours after the heat treatment. There are three important points regarding the

validity of color comparison. The fist point is, as the color depends on the surface conditions of

the samples, all the samples shown in this image were polished down to 0.25 |tm to limit the

variation of the surface roughness. The second is that, during heat treatment, the heating/cooling

rate was kept constant for all the samples. The third is that there should be no contamination

from the environment. During the heat treatment, the quartz tube furnace was cleaned using

ethanol alcohol and the controlling gases were high purity grade, therefore, the contamination









sources were limited. For YSZ samples, the color did not change noticeably even under very

low oxygen partial pressure environments, which suggests that the defect concentration was not

increased significantly upon heat treatment.

4.2.2 Microcracks Formation

After reduction under low oxygen partial pressure, microcracks appeared on the ceria and

GDC sample surfaces. However, the focus of this section is on ceria only. The lowest oxygen

partial pressure applied in this study without formation of microcracks in ceria was about 10-19

atm, i.e., all ceria samples that were reduced under an oxygen partial pressure lower than 10-19

atm experienced microcracking. The microcracking process was initiated during reduction at

high temperature. When oxygen partial pressure was very low, indeed the samples fracture into

small pieces. Figure 4-4 shows a digital image of the situation after four ceria Brazilian disc

samples with a diameter of 26 mm were reduced at 800 C for 15 hours under an oxygen partial

pressure of 8.5 x 10-26 atm. All samples were cracked into pieces. In another words, the

microcracks were extended/developed to be big "macrocracks" so that the original samples fell

apart. The cracking process was recognized due to a relatively large noise within half an hour

after 800 C was reached. The development of microcracks under severe reduction is thought to

be caused by the internal stresses resulting from the lattice expansion difference between the

reduced surface and the unreduced interior [38].

In order to investigate the distribution of the microcracks (several [am to 20 [am)

throughout the thickness of the sample, the cross section of a ceria sample after heat treatment

under an oxygen partial pressure of 4.5x10-22 atm (at 800 C for 15 hours) was polished and

imaged using the scanning electron microscope (SEM). Microcracks were observed throughout

the entire thickness. It was noticed that relatively larger "macrocracks" (hundreds of [am) were

formed on the surfaces that were exposed to the ambient gas. This phenomenon was more









pronounced at the edges, and images of which are presented in Figure 4-5. As shown in this

figure, large processing pores were usually accompanied by these large "macrocracks" and their

presence extended to a depth of approximately 100 [am. This 100 [am surface layer is an

insignificant fraction considering that the sample thickness was 2.6 mm. After passing this top

surface layer, there was no obvious difference in the size and distribution of the microcracks as a

function of the distance up to the middle. Figure4-6 presents typical SEM images of the interior

part of the reduced sample with the presence of microcracks. The arrows in the figure indicate

the positions of the microcracks. As shown in this figure, the microcracks were located very

near to the pores and the size of the microcracks was about several |tm to 20 |tm. The

appearance of the large "macrocracks" on the surface is believed to be related to such

environmental effects as the formation of water during the reduction treatment (this effect will be

indicated in section 4.3.3). The formation of the microcracks inside the sample can be attributed

to development of internal stresses due to the expansion difference between the reduced outer

part and the unreduced inner center of the samples during the high temperature reduction

process. The microcracks are expected to be firstly originated subsurface where the maximum

tensile stresses are generated at the beginning of the reduction process. The inside microcracks

are developed along with the reduction process, progressing across the sample thickness.

4.2.3 Phase Identification

The heat treatment under in Po2 =4.6x 10-22 atm at 800 C is expected to result in a

composition of CeO1.92 according to reference [12]. Based on the phase diagram of CeO2-x [16],

slow cooling to room temperature should introduce a phase separation by spinodal

decomposition in the composition range up to CeO1.846 at temperature between 424C and 685 C

(see Figure 2-6) which would result in the splitting of the XRD peaks. Phase separation below









this temperature would result in a solid solution of two phases with compositions close to

stoichiometric ceria and CeO2-x phase (possibly CeOi.8i8 ), respectively. Therefore, XRD tests

were performed on the surface of this reduced sample. Figure 4-7 presents the XRD results of

this reduced sample and an air treated sample. The same fluorite-structured XRD patterns were

observed for both samples, and more interestingly, the XRD peaks for both sample had

approximately the same 20 positions. These 20 peak positions were consistent with the lattice

parameter of stoichiometric ceria. As we know from section 2.2.1 that the increase in oxygen

vacancy concentration should have increased the lattice parameter, according to Equation 2-7,

we expected to see lower 20 peak positions for the reduced sample. Therefore, the question is

why there was no lattice expansion shown on the XRD pattern for a reduced ceria sample. Is it

because of shrinkage of the lattice parameter by reoxidation at room temperature or is it because

of other factors?

In order to answer these questions, the first step we took was to investigate the phase

transformation as a function of depth by polishing the surface and conducting XRD at different

distances from the surface for the sample reduced in P2 =4.6x 10-22 atm. Figure 4-8 presents the

(311) peak at various depths from the surface. Single peaks were observed down to 40 |tm.

However, at the depth of 60 |tm a broadened unsymmetrical extra peak at lower 20 angles

appeared. In addition, as shown in Figure 4-8, the (311) peak initially shifts to greater and then

to lesser angles with the increase in depth. This observation demonstrates that the surface of the

sample was in compression and therefore a slightly smaller apparent lattice parameter was

measured. However, the shape of this extra peak suggests there was possible several peaks

present underneath. Although it was very difficult to find out the exact lattice parameters of

these peaks underneath, all of them had larger lattice parameters than air treated sample.









Therefore, these peaks corresponded to phases with greater oxygen vacancy concentrations.

However, this result does not explain the reason for the presence of the stoichiometric peak.

There are two ways to form stoichiometric phase in a reduced sample, i.e., phase transformation

at temperature below 424 C (see Figure 2-6) or reoxidation. This leads to the next step of this

research, i.e., to identify the extra peak and answer how and why the stoichiometric phase

appeared in a reduced ceria sample.

4.2.4 Phase Transformation upon Cooling

After reduction of in 7.1 x 10-24 atm at 800 C, a bulk ceria sample was "immediately" taken

for the XRD test. Note that, the process of preparing the XRD was about 15 minutes (including

taking sample out of the furnace, preparing it for XRD scanning and XRD experiments setting

up), 2 hours and 13 minutes were needed for the XRD scanning (explained in 3.4), therefore, at

least 2.5 hours was needed to conduct the XRD test. Also note that according to Bevan and

Kordis [11], the equilibrium composition obtained after reduction in 7.1 x 10-24 atm at 800 C is

close to CeO1.83.

Prior to any analysis to the XRD pattern, it needs to be pointed out that since the

controlling gases for the reduction treatment was continuously flowing throughout the cooling

process, no reoxidation should take place during the cooling process.

Figure 4-9A shows the XRD pattern for this sample and two sets of peaks matching

fluorite structure were observed. Figure 4-9B shows the details of the XRD pattern in the 20

range of 54 to 60 degrees with a dashed line showing the stoichiometric ceria (311) peak. In

terms of peak positions or 20 values and peak intensity ratios, the fluorite phase designated with

letter "a" had similar lattice parameter of shoichiometirc ceria. It was identified that the extra

peak shown in Figure 8 had the similar 20 peak position of the second set of peaks designated

with letter "b". Although "b" matched fluorite structure in terms of the peak intensity ratios, it









had a larger lattice parameter than stoichiometric ceria because of the lower 20 peak position. In

literature [116], this "b" phase is called the pseudo-cubic fluorite phase or ordered phase and the

corresponding lattice parameter calculated for this pseudo-cubic phase from the 20 values is

called pseudo lattice parameter. It can be viewed as a derivation ceria phase with ordered

oxygen vacancies.

From the shape of the peak for "b" phase, it can be clearly seen that "b" phase was actually

a mixture of several pseudo-cubic fluorite-structured phases with pseudo lattice parameters

ranging from 0.548 nm to 0.552 nm (calculated from the underneath peaks marked with arrows

in Figure 4-8B). Based on the linear relationship between the lattice parameter and oxygen

vacancy concentration given by Equation 2-7, the nonsoichiometric values (x in CeO2-x) were

then calculated to be within 0.19 to 0.24, i.e., the compositions of these phases are CeO1.81- 1.76.

If there are only these two types of phases present, a simple mixture rule can be used to

calculate the volume fraction of the CeO2 phase. In order to get a composition of CeO1.82 at this

oxygen partial pressure, the volume fraction of CeO2 phase is assumed to bef then


2 x f +1.81 or 1.76x(1- f) = 1.82->f = 0.05 or f = 0.25. (4-1)


Therefore, less than 25 % volume fraction of CeO2 phase should be present. However,

simply considering the peak intensity ratio of CeO2 phase and the "b" phases in Figure 4-9A, the

result of this calculation obviously shows an opposite conclusion. This leads back to the initial

assumption, it can not be true to assume that only two phases exist.

To identify the other phases is almost impossible without the help of other techniques.

However, triclinic CenO20-y phase is not possible to co-exist with cubic ceria phase according to

the result of J.P. Nair et. al. [116], the other most possible phase should be hexagonal Ce203+a. It

is not surprising that these hexagonal phases do not show up in the XRD pattern when the cubic









CeO2 is present, because of its low XRD intensity due to their lower symmetry structure. In

order to visualize this statement, a theoretical XRD pattern of a sample with 2/3 volume fraction

of hexagonal Ce203 phase and 1/3 volume fraction of cubic CeO2 phase are shown in Figure 4-

10. In this plot, most of the peaks of the Ce203 phases overlap with that of the CeO2 phase, the

extra peaks for Ce203 phases (blue lines, peaks shown with arrows) are too weak to be identified,

even though hexagonal Ce203 is the major component.

It needs to be pointed out that these pseudo-cubic phases are metastable and therefore do

not exist on the phase diagram (at room temperature). In another words, our heat treatment and

cooling procedure did not allow the equilibrium phases to appear. Firstly, the samples after

heating at the elevated temperature were cooled under hydrogen gas flow. Secondly, the samples

were fast cooled to room temperature and did not allow phase transformation to be fulfilled.

Based on these results and discussion, we still could not completely answer the questions

brought up above. Since the presence of different phases may depend on the heat treatment

temperature and cooling rate, an intermediate temperature aging test was designed as described

in the following in order to further investigate the causes for different phases.

4.2.5 Aging Effect

Considering that there may be a surface effect existing in the reduction process, both ceria

powder (more surface area) and bulk samples (the size of half of the Brazilian disc (QD26 mmx2.6

mm)) were studied in this experiment. These ceria samples were held at 500 C for 30 hours,

instead of direct cooling down to room temperature, following the reduction process of 15 hours

in 8.5x 10-25 atm at 800 C. The cooling rate was similar to what is described in Chapter 3 except

this aging step was added in the middle of the cooling process. Consistent with previous

experiments, the controlling gas was continually flowed throughout the entire heat treatment

process until the samples were taken out for XRD tests. The XRD scan took about 2.5 hours for









the bulk ceria sample and 20 minutes for the (311) and (420) peaks of the powder sample. The

reason that only these two peaks were chosen for the powder sample is because we want to

shorten the amount of time that the powder sample had to be exposed in air. In another words,

we want to minimize the reoxidation process of the reduced powder. The XRD results are

shown in Figure 4-11 for the bulk sample and Figure 4-12 for the powder sample, respectively.

The 20 position for stoichiometric ceria (311) peak is shown with dashed lines in Figure 4-11B

and Figure 4-12.

As shown in Figure 4-11A, the XRD pattern of bulk sample consists of the aforementioned

pseudo-fluorite phase indicated as "b" and an new extra phase indicated with "*". Because of

the distinct underneath peaks (indicated by the arrows) for the (311) (Figure4-1 1B), at least four

distinct lattice parameters were identified for "b" phases. These lattice parameters were 0.556

nm, 0.553 nm, 0.552 nm and 0.551, which correspond to the nonstoichiometric values (x in

CeO2-x) of 0.32, 0.26, 0.24 and 0.21. Due to the low peak intensity of the asterisk phase, the

detailed structure information could not be identified by this work.

Comparing the XRD patterns of reduced bulk ceria sample with and without aging process

(Figure 4-11B and Figure 4-9B), the stoichiometric phases appeared in the directly cooled

sample but not in the aged sample. This indicates three pieces of important information. The

first is that the stoichiometric phase that appeared in the directly cooled sample was due to phase

transformation and not reoxidation at room temperature. The second is that the 500 C aging

process stabilized the pseudo-cubic phases and therefore no stoichiometric phase was separated

out. The third is that, the volume ratio of the pseudo-cubic phases and the stoichiometric phases

was affected significantly by the cooling rate. According to the information given by the aging









experiment, it is suspected that the pseudo-cubic phases will be more pronounced if the samples

are cooled slowly in hydrogen environment.

However, comparing the XRD pattern for the aged powder sample (Figure 4-12) and the

bulk sample (Figure 4-11B), it is obvious that the stoichiometric ceria (311) peak was present for

the powder XRD but absent for the bulk sample. The strongest pseudo-cubic peak, i.e., "b" with

a lattice parameter of 0.551 nm was present in the powder XRD pattern. As the powder and the

bulk sample were heat treated simultaneously, the XRD pattern should have similar features, or

at least, same type of phases should be present. The difference in the XRD patterns between the

powder and the bulk samples brings up the next question about the stability of the pseudo-cubic

phase at room temperature.

4.3 Phase Transformation of Reduced Ceria at Room Temperature

4.3.1 Reduced Ceria Powder

The powder ceria samples that were held at 500 C for 30 hours after its reduction (under

8.5x 1025 atm at 800 C for 15 hours) were systematically studied for XRD patterns as a function

of time at room temperature in air using XRD technique. The results are presented in Figure 4-

13 in two different styles for better visualization. The peak corresponding to the ordered ceria

phases or "b" phases (marked with arrows) disappeared relatively fast. In fact, the ordered

phases were no longer present in XRD pattern after 36 hours of exposure to air at room

temperature.

There were two distinct features for the decaying process of the ordered phases. The first

feature was that the decaying of the order phases was companies by the growing of the

stoichiometric ceria phase. In another words, these two processes happened simultaneously.

The second feature was, the decaying of the ordered phases with larger lattice parameter (the

underneath peak at lower 20) was faster than the ones with smaller lattice parameter (the









shoulder of the peak at higher 20). The second point is better seen from the change of the shape

of the (311) peak of the ordered phases (See Figure 4-13B). In fact, the underneath peak at lower

20 of the ordered phase disappeared much faster so that the shape of the peak became less

asymmetrical. In addition, after this room temperature transformation, the color of the ceria

powder turned noticeably lighter.

Now the question is what causes the disappearance of the ordered phases. There are two

possible mechanisms. The fist is the reoxidation process. Reoxidation of these pseudo-cubic

phases causes the larger Ce3+ ions (128.3 pm) transform into smaller Ce4+ ions Ce4+ (111 pm)

ions [117], hence the lattice shrinks and the enhancement of the stoichiometric ceria peak at

larger 20 values. The second mechanism is room temperature phase transformation. The

pseudo-cubic phases with ordered oxygen vacancies are not stable at room temperature. Some

phase transformation process of order ceria phases such as order-disorder transition has been

proved to be a relatively easy process (very low activation energy) and can happen very fast at

room temperature [116, 118]. The exposure of reduced powder to air somehow might have

triggered this transition. It is inevitable for both mechanism to operate, however, the dominate

mechanism will be further discussed in the following sections and section 4.3.3.

4.3.2 Reduced Bulk Ceria

The XRD pattern for the bulk ceria sample after heat treatment at 800 C under 3.6x 10-22

atm for 15 hours was recorded as a function of time. The results are presented in Figure 4-14.

Consistent with the observation for the XRD pattern in Figure 4-9, the ordered pseudo-cubic

ceria phase was present at the initial stage. Even thought the XRD pattern in Figure 4-9 was

taken 1.5 hours earlier than the first XRD in Figure 4-14, the former showed much more

significant ordered phase peaks. If we consider the sample in Figure 4-9 was heat treated under

7.1 x 10-24 atm, it is understandable that the lower oxygen partial pressure created more oxygen









vacancies, and hence the larger volume fraction of the ordered phase were formed. After 49

hours exposure to air at room temperature, the pseudo-cubic phases almost totally transformed

(shown in Figure 4-14).

The XRD patterns as a function of time were also recorded for the bulk sample with 500

C aging process (the sample of Figure 4-11), and the results are presented in Figure 4-15A. The

details of the 20 range from 53 to 61 degree can be better seen in Figure 4-15B. There are two

important points observed from the XRD evolution profiles. On one hand, the entire asterisk

phase and the majority ordered phases disappeared after 40.2 hours exposure to air at room

temperature, this amount of time is comparable to the time need for the transformation of the

sample in Figure 4-14. Considering the much lower oxygen partial pressure was used to reduce

the sample for Figure 4-15 than that for Figure 4-14 (8.5 x 10-25 atm instead of 3.6 x 10-22 atm), a

much higher vacancy concentration was expected for the sample in Figure 4-15. Therefore, if

the reoxidation process was dominating, much longer reoxidation time would be expected for

more oxygen atoms to diffuse into the material for the sample in Figure 4-15. This controversy

indicates reoxidation was not the major reason for the formation of stoichiometric ceria peaks.

On the other hand, the decaying of the ordered phases was not a progressive process. In another

words, the decaying of the pseudo-cubic phase with larger lattice parameter did not increase the

volume fraction of the pseudo-cubic phase with smaller lattice parameter, which is consistent

with the observation for reduced ceria powder in Figure 4-13. All the pseudo-cubic phases

simultaneously transformed into the stoichiometric ceria phase. Both of these two points

indicate that the disappearing the pseudo-cubic phases were caused by a room temperature phase

transformation mechanism. The products of this transformation of the pseudo-cubic phases are

expected to be the stoichiometric ceria phases and Ce203+6 phase. However, the extra peaks for









the hexagonal phases were too weak to be identified. After the transformation, the color of the

bulk ceria after this transition did not change as significant as the powder.

A comparison is made on the details of the XRD peaks of (311) and (420) in Figure 4-16

for a bulk ceria sample and a powder sample that experienced the room temperature phase

transformation (the bulk ceria and powder ceria were reduced under 1.4x 10-24 atm and 3.6 x 1022

atm respectively). The XRD pattern for the stoichiometric ceria powder is also shown in the

figure for comparison purposes. After the transformation, the reduced bulk ceria sample and the

powder sample both showed the larger FWHM (Full Width at Half Maximum) than the

stoichiometric powder. In addition, purely from the shape of the peaks, the bulk ceria and the

powder ceria sample with the transformation did not show distinct Cu Ka2 peak. The broadened

(311) peak indicates there were other phases present for the sample after room temperature phase

transformation.

The hexagonal Ce203 is considered to be the most stable and possible phase [116] at room

temperature for reduced ceria. An effort was made to find this phase through transmission

electron microscopy (TEM). A TEM sample was made using focused ion beam (FIB) from a

ceria bulk sample that was reduced under 3.6x 1022 atm. The TEM images were taken days after

the samples were made to make sure the disordering transition was indeed finished in the TEM

sample. The bright field (BF) and dark field (DF) images are shown in Figure 4-17 along with

selected area diffraction pattern (SAD) with zone axis of [113]. The two beam condition used

for the imaging (g=[24 2 ]) was imbedded into the pictures. Although the SAD did not show

extra diffraction spots, a second phase showed up in the BF and DF images. This secondary

phase was about nanometer size. Although one can not draw an absolute conclusion about the









nature of the extra phase(s) from this limited TEM work, the existence of the extra phase(s)

confirmed the previous arguments.

4.3.3 Effect of Ambient Environment

From the above observations and discussion, it seems that the presence of oxygen is very

important for the transformation of the pseudo-cubic phases in ceria. The following experiment

was designed to prove this point. One bulk ceria sample was firstly reduced at 800 C under dry

hydrogen (oxygen partial pressure of 1.7x 10-25 atm) for 15 hours, then the sample was held in the

dry hydrogen environment for 55 hours at room temperature before it was taken for XRD

experiment. Because of the dry hydrogen environment, the reduced sample did not have access

to oxygen prior to XRD experiment. The result of the XRD pattern is shown in Figure 4-18.

The pseudo-cubic ceria phases "b" as well as the stoichiometric ceria phase(s) "a" was both

present. The peak ratio of these two sets of the phases was consistent to that of the XRD pattern

in Figure 4-9 (reduced in oxygen partial pressure of 7.1 x 10-24 atm). Since the XRD pattern in

Figure 4-9 was directly taken after the sample was cooled to room temperature and this XRD

was taken after 48 hours of holding in H2 environment, the similar XRD profile of Figure 4-18

with Figure 4-9 indicate that dry H2 environment is not favorable for the room temperature

transformation of the order phases.

In order to understand the progress of this transformation in bulk ceria, we combined all

the above XRD information and compared with the reoxidation process to revisit the controlling

mechanism for the decaying of the pseudo-cubic phases. If the disappearance of the order phase

was caused by reoxidation, there should be some relationship between the depth of the

reappearance of the order phase and time. The reoxidation process can be considered as the

oxygen on the surface diffuse into a 2.6 mm thick ceria plate. Since the sample was exposed to

air, the surface oxygen concentration was constant. Assuming the reduced sample had an initial









uniform oxygen vacancy concentration, the diffusion solution for this situation can therefore be

calculated by J. Crack [106]. The diffusion distance can be simply considered to be

approximately proportional to DDt, with "D" the oxygen diffusion coefficient in ceria at room

temperature and "t" the diffusion time. However, as we know from the above results, the order

phase disappeared from the XRD pattern in two days. Considering the interaction volume of

XRD is about 5 [tm and the depth of the transformation was about 60 tm after 220 days [Figure

4-8], the depth and the time had a linear relationship, not a square root relationship. Therefore,

this estimation again confirms that the decaying of the pseudo-cubic ceria phase was phase

transformation process, not a reoxidation process.

As we mentioned earlier, the exposure of reduced powder to air triggered the

transformation of the ordered phase. We suspect this trigger comes from the relief of internal

stress. Effects of stress on phase transformation have been widely studied for variety of

materials [90, 119-122]. It was also seen in ceria thin film system [116, 118]. However, we can

not draw conclusions purely based on our results, future work is need to investigate this issue.

4.4 Microstructure of Fully Reoxidized Ceria

Because the radius of the Ce4+ ion is much smaller than that of Ce3+, reoxidation of the

reduced ceria shrinks the lattice [6]. If oxygen vacancies were the only products of the reduction

process, ceria would go back to the stoichiometric condition by reoxidation [33]. However, the

ceria samples experienced microstructural changes when they were reduced under oxygen partial

pressure lower than 10-19 atm, i.e., microcracks were formed during the reduction, and phase

separation happened during the cooling process. If reoxidation of ceria were carried out at a high

enough temperature and in the single phase region (above the miscibility gap), the phases due to

nonstoichiometry could be eliminated. The problem is the microcracks. In fact, because of the









shrinkage effect of reoxidation process, these microcracks tended to extend and open up, and

they eventually extended/developed into "macrocracks". In order to demonstrate this behavior, a

ceria Brazilian disc sample was fully reoxidized in air at 800 C for 15 hours after its reduction

heat treatment under oxygen partial pressure 1.7x 10-22 atm. The sample was polished by 600 grit

silicone carbide sand paper and then painted with red ink. A digital image of this reoxidized

sample is shown in Figure 4-19A (note that, the redness on the sample came from the red ink and

it was not the true color of the sample). The "macrocracks" are clearly shown (as the lines) in

this image. The cracks formed a so-called "mud pattern". If we recall the microcacks in Figures

4-5 and 4-6 for the sample reduced under similar oxygen partial pressure, the cracks for the fully

reoxidized ceria were much larger and pronounced in terms of crack opening and crack length.

The features of the cracks after reoxidation can be better seen through the SEM image presented

in Figure 4-19B.

In order to identify the positions of these cracks, a piece of ceria sample from Figure 4-6

was thermo-etched at 1550 C for 12 mins. In addition to the thermo-etch effect, this process

also acted as reoxidation process. The low magnification and high magnification SEM images as

a result of reoxidation are shown in Figure 4-20. Some macrocracks joined each other to form

continuous crack net works. These joints are marked with arrows in Figure 4-20A. The core of

the opening for the macrocrack was as big as 3-5 [tm. The majority of the macrocracks

overlapped the grain boundaries, suggesting that reoxidation process progressed through grain

boundaries.

4.5 Degradation of Ordered Ceria Phases in Water

So far, all the reduced samples underwent the room temperature phase transformation were

exposed to dry air. However, the reduced ceria was found to be very sensitive to the presence of

water vapor during the handling of the sample. It is worth mentioning that the transformation of









powder samples (see section 4.3.1) did not take the same amount of time. In fact, another

experiment with similar schedule was repeated, but the powder completely transformed as soon

as it was taken out of the furnace. The fast transformation was companies by a fast color

changing. This inconsistency is believed to be associated with the ambient moisture level, in

another words, the kinetics of this transition seemed to be very sensitive to the presence of water.

Therefore, the following series of experiments were performed in order to address this issue.

One ceria bulk sample was heat treated at 800 C under hydrogen/water vapor environment

(oxygen partial pressure of 3.6x 10-22 atm) for 15 hours. After it was fast cooled down to room

temperature, the sample was kept in the furnace with the hydrogen/water vapor flowing through

for four days. The water vapor was condensed on the surface of the sample at room temperature

and water moisture was visible on furnace inner wall. After the sample was taken out of the

hydrogen/water vapor environment, the sample was found to be corroded into pieces (Figure 4-

21). The XRD pattern of these pieces showed broadened peaks without the aforementioned

pseudo-cubic ordered phases (Figure 4-22). It is suspected that the ordered phases transformed

with the help of the water. Further SEM image analysis of these pieces (Figure 4-23) revealed

the manner that the sample shattered. High magnification SEM image (Figure 4-23B) shows that

the reduced ceria cracked through series of parallel planes, i.e., the water corrosion process

followed a certain crystallographic planes. As the pseudo-cubic ceria phases have a structure

with ordered oxygen vacancies, in another words, the oxygen vacancies sit on particular

crystallographic planes, the unique features of cracked planes due to the water corrosion process

indicate that this process has a close connection with the disappearance of the ordered phases.

In order to prove the above hypothesis, the dry hydrogen reduced bulk ceria samples

whose XRD pattern was present in Figure 4-18 were further studied through the following two









sets of experiments. One of the samples with the presence of the ordered phase was immediately

soaked into water at room temperature after the XRD pattern was taken. After soaking in water

for 12 days, the sample was noticeably cracked through water corrosion (Figure 4-24A). The

corrosion crack progressed significantly for the following 5 days and the sample virtually

cracked into pieces (Figure 4-24B). In contrast, the second sample was exposed in dry air for 12

days before it was put into water (Figure 4-25A). From the previous results (section 4.5.2), 12

days was enough for the transformation process of ordered phases on the sample surface to

finish. The sample did not start to crack until it was soaked in water for as long as 26 days. It

was also noticed that the crack started at the sharp edges (Figure 4-25B). The much slower

corrosion process for the second sample again indicates that the order phases are susceptive to

water corrosion. However, the mechanism for the decaying of the ordered phases in this case

may be different than what described above in sections 4.2 and 4.3 because of the involvement of

water molecules.

For comparison purpose, one as-sintered ceria sample was also soaked in water for a long

time (38 days) at room temperature, and no corrosion damage was observed (Figure 4-26). This

proves that the stoichiometric fluorite phase is very stable in water

4.6 Summary

In summary, the behavior of ceria after reduction treatment at 800 C and under low

oxygen partial pressure is reported in this chapter. Ceria samples developed microcracks

(several [tm to 20 [tm) when the oxygen partial pressure was less than 10-19 atm. Some

microcracks further developed into macroscopic level cracks (hundreds of tm) during the

reduction when the oxygen partial pressure level reached as low as 10-24 atm, resulting in broken

samples. The reoxidation of the low oxygen partial pressure reduced ceria caused the

microcracks to develop much larger in length with larger opening.









Pseudo-cubic fluorite phases were present in the reduced ceria samples, these phases were

derivatives of the fluorite structure with ordered oxygen vacancies. These order phases

automatically transformed into stoichichiometric phases and Ce203+, at room temperature when

the samples were exposed to dry air. These ordered phases were also found to be susceptive to

water corrosion cracking.









Table 4-1. Comparison of the XRD data for the as-received ceria powder and the as-sintered
ceria sample with JCPDS #43-1002 standard.
Intensity, %
Standard As-sintered ceria As received powder
(111) 100 100 100
(200) 27 27 30
(220) 46 36 57
(311) 34 26 44
(222) 6 4 8
(400) 6 4 7
(331) 12 8 15
(420) 7 5 9
(422) 10 6 13
(511) 9 5 10


Table 4-2. Grain sizes and densities of the materials.
Materials Grain size, |tm Density, g/cm3 Relative density, %
Ceria Nanoindentation samples 13 6.81 94%-95%
Bending samples 24
Brazilian disc samples 30
GDC Nanoindentation samples 5 7.10 98%-99%
YSZ Nanoindentation samples 4 5.95 >99%











as-rceived pwder


as-sinted ceria

JL-JJLJJ


2 theta, degree

Figure 4-1. X-ray diffraction pattern (XRD) of the as sintered ceria.


(A)








Figure 4-2. Images to show grain sizes of the materials. (A) SEM image for ceria
nanoindentation sample. (B) Optical image for GDC nanoindentation sample. (C)
SEM image for YSZ nanoindentation sample.





88


It
















4. ~I


(c)








Figure 4-2 ctd.

B



yO c
A PO2 1.8x0-7 atm .D

.5 10-22






Figure 4-3. Color change of ceria samples after heat treatment under various oxygen partial
pressure. The diameter of each sampled was about 6 mm.











Quartz tube furnace






S A, Pieces of ceria

.. .Alumina plate







Figure 4-4. Digital image taken after four ceria discs with a diameter of 26 mm "exploded"
during the reduction at 800 under and oxygen partial pressure of 8.5x 10-26 atm.


(A)



S .- ., . .
-io

,. ", .k -. .

;"" '













I










Figure 4-5. SEM images of ceria sample reduced under 4.5x 10-22 atm (at 800 C for 15 hours)
show large macrocrakcs (-100 [am) at the top surface layer.









(A)


(B)















-4. .












Figure 4-6. SEM images of the microcracks in the middle of the ceria sample after reduction in
P, =4.5 x 10-22 atm (at 800 TC for 15 hours). The arrows in the images indicate the
positions of the microcracks.
























60
2 theta (degrees)


100


Figure 4-7. XRD patterns for ceria samples after heat treatment (A) in air (Po2 =0.21 atm) and
(B) in H2/H20 mixture (Po2 =4.6x 10-22 atm). XRD patterns were taken one week after
the heat treatment.





C 60Pm

40pm



__ _20pm




55 56 57 58
2 theta (degrees)

Figure 4-8. The (311) XRD peak of pure ceria sample at various depths from the surface, as
indicated by the numbers on the curves, after heat treatment under Po2 = 4.6x 10-22
atm. The arrow indicates the extra peak of the ordered phase. These XRD patterns
were taken 220 days after the reduction treatment.


1-1
I-I
1.1






^su __1JLL-L-L


(A)
(A) iL i~ i I~A



















CO

S b |2.5 hours
-a

bb
a-a


b b I I I


20 40 60 80 100
2 theta, degree


(B)
a









bb

a



54 55 56 57 58 59 60
2 theta, degree

Figure 4-9. (A) XRD pattern of ceria after reduction under 7.1 x 10-24 atm (800 C for 15 hours).
(B) shows the details of 20 range of 54 to 60 degrees. "a" indicates the CeO2 phase,
"b" indicates pseudo-cubic nonstoichiometric fluorite phases. The dashed line
indicates the stoichiometric CeO2 peak position for (311).














-2/3 Ce203
-1/3 Ce02








) 40 60 80 1
2 theta, degree


Figure 4-10. Theoretical XRD pattern for ceria with 2/3 volume fraction of hexagonal Ce203
phase (indicated by arrows) and 1/3 volume fraction of cubic CeO2. The extra peaks
of the hexagonal phase shows very weak intensity even though hexagonal phase is the
major component.


(A)




b
b b b


1 |2.5 hours|




b b



I I I I I I I I
20 30 40 50 60 70 80 90 100
2 theta, degree

Figure 4-11. (A) XRD pattern of bulk ceria sample after aging at 500 C. (B) shows the details
of 20 range of 52 to 60 degrees. "b" indicates pseudo-cubic nonstoichiometric
fluorite phases, "*" indicates another unidentified phase.










(B)









b
_-2.5 hours


56 58


2 theta, degree


Figure 4-11. ctd.


54 56 58 60
2 theta, degree

Figure 4-12. XRD pattern of powder ceria sample after aging at 500 C. "a" indicates the CeO2
phase; "b" indicates pseudo-cubic nonstoichiometric fluorite phases. The dashed line
indicates the stoichiometric CeO2 peak position for (311).









(A)



a ^20 mins

I I I







Ca


a
c(B
_c- 36 hours

I I I, I





I I I











54 56 57 8 9 60
2 theta, degree
the stoichiometric Ce02, peak positions "b" indicatestoichiometric ceria














54 55 56 57 58 59 60
2 theta, degree





the stoichiometric CeO2, peak positions. "b" indicates the ordered phases.


















4 hours


a





49 hours


I I I
54 56 58 60
2 theta, degree


Figure 4-14. XRD patterns as a function of time for the ceria bulk sample that were reduced at
800 C for 15 hours under oxygen partial pressure of 3.6x 1022 atm. "a" indicates the
stoichiometric ceria phase(s); "b" is the ordered phases.









b

Sb b (A)



II
II
II 2.5 hours

IbI
I I





a) 40.2 hours







a 156.2 hours



20 40 60 80 100

2 theta, degree

Figure 4-15. (A) shows the XRD patterns as a function of time for the bulk ceria sampler that
were reduced at 800 C for 15 hours and then aged at 500 C for 30 hours. (B) shows
the details of the XRD pattern with 20 range of 53 to 61 degree. The dashed lines
indicate the CeO2 peak positions; "b" is the ordered phases.













12.5 hours


al
b 140.2 hours






I I I I
156.2 hours


54 56 58 60
2 theta, degree


Figure 4-15. ctd.







R-
3

In


54 55 56 57 58 59 60 61
2 theta, degree

Figure 4-16. Comparison of the peak (311) and peak (420) for Ce02 powder with a bulk and
powder ceria sample after room temperature phase transformation.








(A)












(B)












(C)












Figure 4-17. TEM bright field (BF) image (A) and dark field (DF) image (B) along with the
selected area diffraction (SAD) pattern (C) for the bulk ceria sample reduced under
3.6x 10-22 atm. Zone axis is [113] with g=[24 2 ] for the two beam condition.