|UFDC Home||myUFDC Home | Help|
This item has the following downloads:
1 NOVEL SYNTHESIS AND PROCESSING OF ELUSIVE SINTERED CERAMICS : THE CASE OF SiC AND Bi2Ti2O7 By JOS ROBERTO ESQUIVEL ELIZONDO A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2011
2 2011 Jos Roberto Esquivel Elizondo
3 To my beloved family
4 ACKNOWLEDGMENTS I would like to express my deepest gratitude to my parents for their unconditiona l love and support which gave me the strength to accomplish this important goal. I want to thank my sister Sof a because she encouraged me to pursue a m asters degree in a foreign countr y, and for her advice and support through this journey towards a higher education. A very special recognition needs to be given to my advisor Dr. Juan C. Nino ; this thesis could not have been written without his guidance and supervision. It was thanks to his constant challenges and pursuit of excellence that I was able t o do things better than I expected or I thought I could do. His help, and more importantly, his trust i n me played a very important role in this achievement. I would like to acknowledge warmly Christopher Turner, Donald Moore, and Beverly Hinojosa for their enormous contribution to this work and for their help inside and outside the labs. I am also thankful to Wei Qiu and Chunghao Shih for their guidance in my first attempts with research. In addition, I extend my gratitude to the former and current memb ers of my research group (Edgar Duarte, Andrs Molina, Paul Johns Andrea Deranek Trey Davis Alex Arias, Luping Li, Sara Bermdez, Kai Yao, Brittnee Mound, Jacqueline Martinez, Hyuksu Han, Wei Zhou, Robert Kasse, Marta Giachino, Satyajit Phadke, and Nathan Wysk) for all sort of assistance, from useful scientific discussions to free icecream I am grateful as well to the weird guy who using esoteric methods predicted the week I was going to synthesize phase pure Bi2Ti2O7 and the month I was going to receiv e a scholarship ( I will need to write another thesis to explain that ) Thanks Ricardo for our quite interesting conversations
5 I am proud to say that I participated several times in the King of the Lab Basketball Tournament with Chris and Robert, a sport developed in Rhines Hall laboratory 208, which clearly shows that not only new materials but also new sports can be designed by materials engineers. I also want to thank these two vi sionaries for helping me make La Puerta N egra the official lab anthem. Finally, I need to acknowledge Dr. John Mecholsky, Dr. Anthony Brennan, Dr. Ronald Bane y, and Dr. Gerald Bourne for lending me the use of equipment necessary to carry out important measurements and many thanks to my committee members Dr. Jacob Jones Dr. Simon Phillpot, and Dr. Jennifer Andrew for their time
6 TABLE OF CONTENT S page ACKNOWLEDGMENTS .................................................................................................. 4 LIST OF TABLES ............................................................................................................ 8 LIST OF FIGURES .......................................................................................................... 9 LIST OF ABBREVIATIONS ........................................................................................... 13 1 INTRODUCTION ........................................................................................................ 16 1.1 Statement of Problem and Motivation ............................................................... 16 1.2 Scientific Approach ........................................................................................... 18 2 BACKGROUND .......................................................................................................... 20 2.1 Nuclear Reactors .............................................................................................. 20 2.2 Thermal Analysis .............................................................................................. 22 2.2.1 Thermogravimetric Analysis (TGA) .......................................................... 23 2.2.2 Differential Thermal Analysis (DTA) ........................................................ 23 2.2.3 Differential Scanning Calorimetry (DSC) ................................................. 24 2.3 X ray Diffraction ................................................................................................ 25 2.4 Dielectric Behavior ............................................................................................ 26 3 THE CASE OF SiC ..................................................................................................... 30 3.1 Inert Matrix Fuels .............................................................................................. 30 3.2 Experimental Procedure ................................................................................... 32 3.2.1 Sample Preparation ................................................................................. 32 3.2.2 Synthesis Characterization ...................................................................... 33 3.2.3 Mechanical Characterization ................................................................... 33 3.2.4 Thermophysical Characterization ............................................................ 35 3.2.5 Density Calculations ................................................................................ 35 3.3 Results and Discussion ..................................................................................... 35 3.3.1 Polymer Analysis ..................................................................................... 35 3.3.2 Density of the Pellets ............................................................................... 41 3.3.3 Mechanical Properties ............................................................................. 46 3.3. 4 Thermal Properties .................................................................................. 49 3.4 Chapter Summary ............................................................................................. 52 4 THE CASE OF Bi2Ti2O7 ............................................................................................. 54 4.1 Bismuth Pyrochlores ......................................................................................... 54 4.2 Bismuth Titanate Compounds ........................................................................... 55
7 4.3 Experimental Procedure ................................................................................... 56 4.3.1 Synthesis ................................................................................................. 56 4.3.2 Characterization ...................................................................................... 58 4.4 Results and Discussion ..................................................................................... 58 4.4.1 Bi2Ti2O7 Structure from DFT Simulation .................................................. 58 4.4.2 Synthesis of Cubic Bi2Ti2O7 Pyrochlore ................................................... 62 4.4.3 Phase Purity Identification of Bi2Ti2O7 ..................................................... 67 4.4.4 Phase Stability of Bi2Ti2O7 ....................................................................... 69 4.4.5 Sintering of Bi2Ti2O7 ................................................................................ 71 188.8.131.52 Powder morphology and ceramic microstructure analysis ............. 74 4.4.6 Bi2Ti2O7 Electrical Properties ................................................................... 75 184.108.40.206 Polarization vs. electric field loop behavior .................................... 75 220.127.116.11 Dielectric properties ....................................................................... 77 4.5 Chapter Summary ............................................................................................. 79 5 DIELECTRIC ANALYSIS OF Bi2Ti2O7 ........................................................................ 81 5.1 Chapter Objective ............................................................................................. 81 5.2 Experimental Procedure ................................................................................... 81 5.3 Dielectric Analysis as a Function of Temperature ............................................. 82 5.3 Dielectric Analysis as a Function of Frequency ................................................ 89 5.4 Chapter Summary ............................................................................................. 97 6 CONCLUSIONS AND FUTURE WORK ..................................................................... 99 6.1 The Case of SiC ................................................................................................ 99 6.2 The Case of Bi2Ti2O7 ...................................................................................... 100 APPENDIX A BISMUTH TITANATE COMMON IMPURITIES ....................................................... 103 B THERMODYNAMIC INSTABILITY OF Bi2Ti2O7 ...................................................... 109 C ORIGIN OF REPORTED FERROELECTRICITY IN Bi2Ti2O7 .................................. 111 LIST OF REFERENCES ............................................................................................. 115 BIOGRAPHICAL SKETCH .......................................................................................... 130
8 LIST OF TABLES Table page 3 1 Mechanical properties of the SiC pellets and other inert matrix material candidates. Indentation mass: *100 g, **200 g, and #1000 g. ............................... 48 4 1 Atomic positions predicted by DFT simulations for cubic Bi2Ti2O7 and the lattice parameter calculated by different methods. ................................................ 60 5 1 Temperature of low frequencies loss max ima (Tm) for Arrhenius fit. ..................... 86
9 LIST OF FIGURES Figure page 2 1 Typical components of a nuclear reactor plant. .................................................. 22 2 2 Example of DTA and/or DSC thermograms. ....................................................... 24 2 3 Braggs Law and XRD pattern generation. ......................................................... 26 3 1 XRD patterns of 1 m SiC powder, the green body with 10 wt% of polymer precursor and the sintered pellet at 930C. ........................................................ 36 3 2 TGA and DTA of SMP 10 in nitrogen with a heating rate of 10C/ min. ............... 37 3 3 DTA of the SiC green body (10 wt% of SMP 10) in different environments with a heating rate of 10C/min. .......................................................................... 39 3 4 XRD patterns of 1 m SiC powder and SMP 10 fired at 930 and 1050C. ...... 40 3 5 Raman spectra of pure SMP 10 fired at the sintering temperatures, sintered pellets with 10 wt% SMP 10, and SiC powder. ................................................ 40 3 6 PSD of the SiC fine particles. ............................................................................. 42 3 7 PSD of the SiC coarse particles. ......................................................................... 42 3 8 Density and weight loss of pellets prepared with a bimodal distribution of particles and 10 wt% of SMP 10. ........................................................................ 43 3 9 SEM images of fractured pellets fired at 930C with only 1 m SiC powder, 1 m SiC powder and SMP 10, and 1/16.9 m SiC powder in a 50/50 wt% ratio and SMP 10. ....................................................................................... 44 3 10 SEM image of a polished and thermal etched (800C) pellet with 1/16.9 m SiC p owder in a 50/50 wt% ratio and SMP 10. The firing temperature was 930C ................................................................................................................. 46 3 11 Thermal diffusivity of the SiC pellets. .................................................................. 51 3 12 Specific heat capacity of the SiC pellets. ............................................................ 51 3 13 Thermal conductivity of the SiC pellets and other inert matrix materials. ............ 52 4 1 Predicted displacement pattern for the OBi4 tetrahedron with the O at 48f and the Bi at 96g, and a snapshot of the TiO6 octahedron with Ti at 96g and O at 48f. ............................................................................................................. 61
10 4 2 Theoret ical (using DFT atomic positions) and experimental (powder and pellet) X ray diffraction patterns of Bi2Ti2O7. For visual aid, a dashed line is included at 33 to illustrate the lack of secondary phases. ................................. 64 4 3 Magnification in logarithmic scale of the XRD pattern of the powder around the area where common bismuth titanate impurities (perovskite and monoclinic) would be observed if present. For visual aid, dashed lines are included at 33 0. 5 to illustrate the lack of secondary phases. ......................... 65 4 4 Le Bail structureless fit of the powder XRD pattern. Only peaks ascribed to the pyrochlore phase were detected. .................................................................. 66 4 5 Theoretical XRD pattern of 90 wt% Bi2Ti2O7 plus 10 wt% Bi4Ti3O12. .................. 68 4 6 Phase pure Bi2Ti2O7 powder and pellet. ............................................................. 68 4 7 Bi2Ti2O7 with 0 wt%, 8 wt%, 50 wt% and >70 wt% of secondary phases. XRD patterns are also shown. ............................................................................ 69 4 8 DTA curve of Bi2Ti2O7 powder (10C/min in nitrogen). The insets correspond to the XRD patterns of the sample (after the heat treatment) below 612C and above 729C ............................................................................................... 72 4 9 Phase diagram of the Bi2O3TiO2 system with modificatio ns The horizontal line at 670C, absent in recent works, was reinserted and the phase line of Bi2Ti2O7 (vertical) was dashed to indicate the thermodynamic instability of this phase. .......................................................................................................... 73 4 10 SEM images of the powder and fracture s urfaces under bending and shearing ............................................................................................................. 76 4 11 Polarization vs. electric field response of Bi2Ti2O7 measured with a Sawyer Tower circuit at 50 Hz. ........................................................................................ 77 4 12 Dielectric permittivity of Bi2Ti2O7 as a function of temperature from 500 to 2000 kHz. ........................................................................................................... 79 5 1 Real and imaginary part of the dielectric constant of BZN as a function of temperature from 10 kHz to 2 MHz. .................................................................... 82 5 2 Real and imaginary part of the dielectric constant of Bi2Ti2O7 as a function of temperature from 10 kHz to 2 MHz. .................................................................... 83 5 3 Real and imaginary part of the dielectric constant of Bi2Ti2O7 as a function of temperature from 80 Hz to 2 MHz. ...................................................................... 84 5 4 Low Temperature DSC analysis of Bi2Ti2O7. ...................................................... 86
11 5 5 Arrhenius plot of Bi2Ti2O7 dielectric relaxation using Equation 51 and Table 5 1. Fitting parameters are presented. ............................................................... 87 5 6 Imaginary and real part of the dielectric constant of Bi2Ti2O7 as a function of temperature at 80, 100, 500, and 1000 kHz. ...................................................... 88 5 7 Dissipation factor of Bi2Ti2O7 as a function of frequency from 30 to 290 K. ........ 92 5 8 Imaginary part of the electric modulus of Bi2Ti2O7 as a function of frequency from 30 to 290 K. ................................................................................................ 92 5 9 Imaginary part of the admittance of Bi2Ti2O7 as a function of frequency from 30 to 290 K. ........................................................................................................ 93 5 10 Imaginary part of the impedance of Bi2Ti2O7 as a function of frequency from 30 to 290 K. ........................................................................................................ 93 5 11 Dielectric constant of Bi2Ti2O7 as a function of frequency from 30 to 290 K. ...... 94 5 12 Cole Cole plot of Bi2Ti2O7 at 290 K. .................................................................... 95 5 13 Bode plot of Bi2Ti2O7 at 30 K. ............................................................................. 96 5 14 Bode plot of Bi2Ti2O7 at 290 K. ........................................................................... 97 A 1 Cubic pyrochlore Bi2Ti2O7. ................................................................................ 103 A 2 Monoclinic and Tetragonal Bi4Ti3O12. ............................................................... 104 A 3 Monoclinic Bi2Ti4O11 and Bi2Ti4O11. ............................................................ 105 A 4 Theoretical XRD pattern of Bi2Ti2O7. ................................................................ 106 A 5 Theoretical XRD pattern of monoclinic and tetragonal Bi4Ti3O12. ..................... 107 A 6 Theoretical XRD pattern of Bi2Ti4O11 and Bi2Ti4O11. .................................. 108 B 1 Bi2Ti2O7 sintered pellet heated to 800C and maintained at that temperature for 2 days. ......................................................................................................... 110 B 2 XRD pattern of a Bi2Ti2O7 sintered pellet heated to 800C and maintained at that temperature for 2 days. .............................................................................. 110 C 1 Parameters used to estimate the particle and grain size of the Bi2Ti2O7 powder and sintered pellets, respectively, employing Scherrers formula. ........ 112 C 2 Representative P E hysteresis loop of Bi4Ti3O12. ............................................. 112
12 C 3 Theoretical P E response of a mixture containing 96 wt% Bi2Ti2O7 and 4 wt% Bi4Ti3O12. .......................................................................................................... 113 C 4 Reported P E response of Bi2Ti2O7. ................................................................. 113 C 5 Theoretical XRD pattern of 96 wt% Bi2Ti2O7 plus 4 wt% Bi4Ti3O12. .................. 114
13 LIST OF ABBREVIATIONS DFT Density functional theory DSC Differential scanning calorimetry DTA Differential thermal analysis IMF Inert matrix fuels LWR Light water reactor LTCC Low temperature cofired ceramics M LCC Multilayer ceramic capacitor MOX Mix ed o xide P E P olarization vs. electric field PSD Particle size distribution SEM Scanning electron microscope TGA Thermogravimetric analysis XRD X r ay diffraction
14 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science NOVEL SYNTHESIS AND PROCESSING OF ELUSIVE SINTERED CERAMICS: THE CASE OF SiC AND Bi2Ti2O7 By Jos Roberto Esquivel Elizondo De cember 2011 Chair: Juan Claudio Nino Major: Materials Sci ence and Engineering Ceramic materials are widely used because of the diversity of mechanical, electrical, and optical properties that they exhibit The synthesis of new ceramics with tailored properties for specific applications is a challenge for mater ials scientists and engineers. In this study, novel methods for the synthesis of SiC and Bi2Ti2O7 for nuclear and dielectric applications, respectively, are explored and the obtained properties are discussed. A polymer precursor route was followed in order to sinte SiC at 930 and 1050C. Differential thermal analysis (DTA), thermogravimetric analysis (TGA) Raman spectroscopy, and X ray diffraction of the precursor confirmed the formation of amorphous SiC at 930C. Sintered pellets made of 90 wt% polycrystalline SiC powder and 10 wt% polymer precursor showed a higher average density of 2.42 g/cm3 (77% of theoretical), by usin g a binary mixture of fine and coarse particles. The hardness, fracture strength, and fracture toughness were determined. These result s were compared with those of UO2, MOX, and other inert matrix material candidates for light water reactors The thermal diffusivity, thermal conductivity and heat capacity were measured from 100 to 900C. The resulting density as well as the measured
15 thermophysical and mechanical properties make this process suitable for an inert matrix fuel open porosity concept. Co precipitation synthesis methods followed by microwave si ntering techniques were utilized to obtain dense phase pure Bi2Ti2O7 polycrystalline ceramic pellets. No evidence of secondary phases was found in the powder or pellets. This maiden achiev e ment allowed for primary thermophysical, crystallographic, and dielectric characterization of this ceramic compound. Reported density functional theory results for Bi2Ti2O7 were used to obtain the theoretical X ray diffraction pattern to determine the purity of the experimental compound. Discrepancies among reports in literature regarding the structure, stability, and supposed ferroelectricity of thi s material are discussed and clarified. A modification to the phase diagram of the Bi2O3TiO2 system is proposed based on the results of the present investigation. In addition, and contrary to prior reports, the dielectric character i zation of Bi2Ti2O7 re veals a linear dielectric with high permittivity values at room temperature (115 at 500 kHz), and more remarkably, a temperature and frequency dependent dielectric relaxation.
16 CHAPTER 1 INTRODUCTION 1.1 Statement of Problem and Motivation The development of new and better technologies is usually related to the synthesis of improved materials In the last two decades a lot of effort has gone into the investigation of materials that could allow for the more effective use of energy. In the nuclear field, generation of electricity has been carried out mainly in light water reactors (LWR) using the well known mixed oxide (MOX) fuel .1 Although this fuel has been used for years, intense investigation has been carried out in order to replace MOX with a better material, capable of higher burnups (fuel utilization) and a more effective plutonium transmutation.25 Stockpiles of plutonium from dismantled nuclear weapons and from spent nuclear fuel are a threat to international security and to the environment. It has been reported th at the total inventory of Pu had reached the order of 1200 tons by the end of last century.6 Besides minor actinides such as 237Np, 241Am, 243Am, and 244Cm, by products of nuclear power are a major concern for environmental safety because of their radiotoxicity and decay heat generation.7 The MOX fuel, made of a mixture of UO2 and P uO2, contains 238U which is a fertile material that adsorbs thermal neutrons and converts into fission material 239Pu through beta decays after irradiation in nuclear reactors. Therefore, burning MOX fuel in a LWR is inefficient and does not allow a rapi d reduction of stocked Pu.3 Silicon carbide is one of the candidates to replace MOX through the concept of inert matrix fuels (IMF), materials that avoid the undesir able effect of neutron capture (239Pu generation) .8 H owever, complications with the sintering (densification) of SiC ceramic s represent a
17 major challenge that has to be overcome before SiC can be considered more seriously for nuclear applications (very high temperatures and/or pressures, and sintering aids are usually required912) In this work a novel l ow temperature sintering method of SiC is explored and the resulting properties of the ceramic are studied to determine the potential of this material to replace MOX. Another area that has been extensively studied in the last decades is that of dielectrics The storage of energy in materials is of great interest because of the current boom in electronics. E fforts are now concentrated in the miniaturization of the electric components which requires the synthesis of materials with improved properties.13,14 Capacitors, used to store energy in an electric field, are composed of two conductive surfaces separated by a dielectric (insulator) material. Materials with superior dielectric properties would allow capacitors to significantly decrease in size.15,16 Multilayer ceramic capacitors (MLCC) and low temperature cofired ceramics (LTCC) are acquiring popularity due to their small size and high capacitance, and can be found in computers, telecommunication devices and i ndustrial controls .1722 Bismuth based pyrochlores have been studied due to their compositiondependent dielectric properties including high permittivity and low dielectric loss which in combination with low sintering temperatures make them suitable for MLCC and LTCC technologies .23 26 A key compound in the study of t hes e pyrochlores is Bi2Ti2O7; however, the synthesis and sintering of this material has represented a major problem for more than 40 years .27 In this work a coprecipitation method followed by microwave sintering allowed for the syn thesis and sintering of the phase pure compound for the first time. Measured
18 electrical properties are discussed in detail in order to provide a better understanding of the dielectric behavior of bismuth based pyrochlores. 1.2 Scientific Approach Before SiC can be seriously considered as an option for nuclear fuel applications, it is necessary to develop a low temperature sintering method to avoid potential undesirable reactions with the fuel (plutonium ) For this purpose, the present investigation starts with a thermal analysis of allylhydridopolycarbosilane, a polymer precursor of SiC commercialized with the name SMP 10, which allows for the formation of SiC below 1000C The thermal analysis is mainly used to identify the most convenient sintering temperatures The polymer is then fired at those temperatures in order to study the formation of SiC using analytical methods. Different mixtures of SiC powder and polymer precursor are pressed into pellets and fired to find the combination that yields the highest density The mechanical properties of the SiC pellets made with the best composition are studied, including Vickers hardness, fracture strength and fracture toughness. Finally, thermophysical properties of the pellets such as specific heat capacit y, thermal conductivity, and thermal diffusivity are measured and discussed to establish the potential of SiC to be employed in nuclear reactors. In the other study, the analysis starts with the synthesis of Bi2Ti2O7 employing a novel coprecipitation method. The investigation continues with the comparison of the experimental result with the predictions of density functional theory (DFT) to determine the purity of the ceramic powder obtained. A guide to help with the identification of the purity of Bi2Ti2O7 synthesized with the proposed method is developed, and the origin of detection problems of common impurities i s investigated using crystallographic
19 software The stability of the pyrochlore is later studied using a thermoanalytic technique and correcti ons to the phase diagram of the Bi2O3TiO2 system are discussed. With aid of the improved phase diagram microwave sintering is selected to produce a dense bulk ceramic for the first time. The electrical properties of the bulk Bi2Ti2O7 are then evaluated. In the next chapter, a brief background of topics useful to better understand and analyze th e investigation presented in subsequent chapters is given Chapter 3 comprises the work carried out on SiC, while Chapter s 4 and 5 deal with the research on Bi2T i2O7. Conclusions and futur e work are presented in Chapter 6.
20 CHAPTER 2 BACKGROUND The present chapter presents a brief summary of some of the theoretical background required for understanding and analyzing the investigation presented in the subsequent chapters. The material under investigation in Chapter 3 is a possible candidate for nuclear fuel applications as will be later discussed, so that a summary on the topic of nuclear reactors is offered as background in section 2.1. In Chapter s 2 and 3 thermoanalytic techniques are a key part of the analysis which led to important findings. Therefore, a brief introduction is given in section 2.2 to better understand how these techniques work and how they result useful in this investigation. In addition, X ray diffraction (XRD) analysis is one of the most commonly used techniques among materials scientists and will be employed several times in the following chapters. A short explanation of the basis of this technique is in consequence offered i n section 2.3 Finally, understanding the dielectric properties of materials is fundamental to follow the discussion presented in Chapters 4 and 5. The dielectric behavior and related concepts are commented in section 2.4. As a summary, it is not intended to cover the background of the research areas in their entirety, but rather to present a work frame for the rest of the thesis. 2.1 Nuclear Reactors The core of this section is chiefly based on Chapter 2 of Nuclear Energy Today,28 a publication of the Nuclear Energy Agency. Due to t he increasing global demand for energy and the knowledge that fossil fuel reserves will be depleted in the close future, the exploration of alternative energy
21 sources has been encouraged. Nuclear reactors have been successfully used to generate electricity since the 1950s and their popularity as a reliable energy producing option has been rising since then. To produce electric energy nuclear reactors follow a similar procedure to that of fossil fueled plants, the difference being the ene rgy source. In nuclear plant s, h eat released from the fission (splitting) of atoms is used to produce steam which drives a turbine that powers electric generators as shown in Figure 21. Typical components are: Fuel. It is usually uranium and plutonium based. Pellets containing the fuel are arranged in tubes or fuel rods made of stainless steel or a zirconium alloy (Zircaloy) assembled in the reactor core. Reactor core. W here the fission reactions take place. Moderator. A material (usually water or gr aphite) located in the reactor core in order to slow down the neutrons released from the fission reactions. Slowing down neutrons will produce more fission events in a sustained chain reaction (235U fissions through slow or thermal neutrons). Control rods Are made from neutron absorbing material s (e.g. Cd, Hf and B ) They are inserted and removed from the core to control the reaction rates. Coolant. The fluid circulating inside the core absorbs the heat generated and produces steam Vessel. It contains the reactor core and the coolant The most common type of nuclear reactor is the light water reactor (LWR), which uses water as coolant and moderator. According to the International Atomic Energy Agency (IAEA) 359 LWRs are currently in operation across 27 countries and 27 more are under construction; so this technology is growing. Most of the efforts are focused on improving the performance of LWRs through better designs and/or enhanced fuels. The mixed oxide fuel (MOX) composed of uranium oxide and plutonium oxide has been used as an alternative to low enriched uranium (LEU, formed of 238U and <20wt% of
22 235U) because it offers a way to get rid of plutonium (239Pu is fissile like 235U) which is advantageous due to the risks that 239Pu represents (weapons and damage to the environment). However, substitutes for MOX are desirable as will be further discussed in Chapter 3. Figure 21. Typical components of a nuclear reactor plant. The nuclear reactor vessel (1) contains the fuel rods (green), the cont rol rods (gray) and the coolant/moderator (2). The steam generator (3) feeds a turbine generator (4) to produce electricity. A condenser (5) converts steam back to water and a cooling tower (6) removes heat from the cooling water to return it to near ambient temperature.28 2.2 Thermal Analysis The core of this section is chiefly based on Chapter 5 of Polymer Chemistry: An Introduction.29 All the techniques employed to determine properties of materials based on temperature changes are grouped in what is called thermal analysis. The differ ence
23 between the techniques depends on the property trying to be determined. The most widely used are the following: 2.2.1 Thermogravimetric A nalysis (TGA) In this technique a change in the mass of the sample is obtained as a function of temperature. The method consists of the continuous weight measurements on a sensitive balance while temperature is increased in air or inert atmospheres like nitrogen or argon. The data is plot ted as weight (usually weight fraction) versus temperature. It is commonly u sed to determine the thermal stability of polymers. The weight loss indicates evaporation of solvents or polymer decomposition. TGA in combination with other thermoanalytic techniques is used to study ceramics (oxidation can be easily identified when TGA is combined with differential thermal analysis ). 2.2.2 Differential Thermal A nalysis (DTA) DTA is used to detect thermal transitions in materials A standard material used as a reference and the sample are heated by the same heat source under a chosen a tmosphere. When a transition occurs in the sample a voltage change, interpreted as a variation in temperature, is observed with respect to the reference. This temperature difference temperature plot or thermogram as shown in Figure 22 The peak will point up or down depending on the chemical reaction. If it is exothermic (e.g. crystallization) it will point up, if endothermic (melting) it will po int down. Second order transitions ( continuous in a first but discontinuous in a second derivative of the free energy), such as glass transitions, are manifested as changes of slope. DTA is commonly used in combination with TGA to analyze polymers, metal s and ceramics for different applications.
24 2.2.3 Differential Scanning C alorimetry (DSC) DSC is a similar technique to DTA and the same type of information can be obtained; the difference is the setup of the instrument. In DSC both the sample and the ref erence have individual heaters which maintain a constant temperature. Therefore, instead of measuring corresponding thermogram heat flow vs temperature, is used to identify phase transitions and also calculate the specific heat capacity of the sample. Figure 22. Example of DTA and/or DSC thermogram s.
25 2.3 X ray Diffraction The core of this section is chiefly based on Chapter 4.1 of Enc yclopedia of Materials Characterization.30 XRD is a technique used to identify crystalline phases present in materials and to measure the structural properties of these phases. The sensitivity of the technique depends o n the material of interest; XRD is more sensitive to materials composed of highZ elements. In an XRD the incident and diffracted X rays. The diffraction pattern is built by plotting the Crystals consist of planes of atoms spaced a distance d apart; however, many atomic planes, each with different dspacings, can be distinguished within the crystal. In order to simplify the analysis, a coordinate system was introduced where the unit vectors a, b, and c represents the edges of a unit cell. Atomic planes can then be differentiated using its Miller indices (hkl). The dspacing between (hkl) planes is denoted as dhkl, and in the case of cubic crystals it is calculated as follows: 2 2 2 0 hkll + k + h a = d ( 2 1 ) where a0 is the lattice constant of the crystal. When there is constructive interference from diffracted X rays (electromagnetic waves) by the atomic planes in a crystal, a diffraction peak is observed. The condition for constructiv e interference from planes with spacing dhkl is given by Braggs law: hkl hkl sin d 2 = n ( 2 2 )
26 where n is a rays (usually 1.54 when Cu k hkl is the angle between the atomic planes and the incident X ray beam. The X rays of the incident beam remain in phase and parallel until the top beam str ikes the atom 1 of the top layer. The second beam continues to the next layer where atom 2 produces its scattering. In order to satisfy Braggs law, the second beam must travel an extra distance AB+BC equal to an integral multipl e of the wavelength. When this occurs both beams continue in phase and parallel so constructive interference is produced as shown in Figure 23 Figure 23 Braggs Law and XRD pattern generation. 2.4 Dielectric Behavior The core of this section is chiefly based on Chapter 7 of Principles of Electronic Materials and Devices.31 D ielectric behavior takes place in all insulators independently of their state (solid, liquid or gas). Under the influence of an electric field charges inside a dielectric at
27 atomic and molecular level s are oriented in specific directions giving rise to the so called dielectric polarization. The degree of polarization in response to the applied field e). A quantity used to meas ure the resistance of a material to an applied field is known as the re as follows: 1 -r e ( 2 3 ) The complex relative permittivity can be related to the polarization and the electric field through: 1 E P 0 r ( 2 4 ) where P is the polarization, E is 0 is the permittivity of vacuum which has the value of 8.854 x 1012 F/m. The complex relative permittivity is obtained from the complex absolute permittivity 0 r ( 2 5 ) The complex relative permittivity is a complex number composed of a real part, known as the relative permittivity or dielectric conr), and an imaginary part or r): j r r r ( 2 6 ) where j is the square root of 1. The dielectric constant represents the stored energy when the material is exposed to an electric field while the dielectric loss factor influences energy absorption or losses. A material with a high dielectric constant indicates a better insulator than a different
28 material wi th a low dielectric constant. In the case of capacitors, dielectrics with high relative permittivity and low dielectric loss factors are desirable because they allow the best storing energy capability. An important number derived from rr is the tanr r ( 2 7 ) The dielectric loss factor i s maximized at a frequency where the applied field has the same period of the relaxation process in a material. Hence, the frequency at which a dielectric material is utilized will depend on the relaxation times of its polarization contributors (dipoles, ions, or space charges). Losses will be small if the period of the applied electric field differs considerably from the relaxation time. There are four main types of polarization mechanisms in materials:31 A tomic polarization. It corresponds to displacement of the electrons in an atom relative to the nucleus. The mechanism is active up to a frequency of 1015 Hz and its contribution to the relative permittivity can go up to ~5. I onic polarization. I nvolves relative displacement of the cation and anion sublattices from their equil ibrium positions giving rise to ionic dipoles Their response can go up to 1013 Hz and their contribution to the dielectric constant is found between 10 and 60. D ipolar polarization. It occurs due to reorientation and alignment of permanent dipoles becaus e of an applied external field. It can respond up to 1011 Hz, and can have contributions to r ranging from 102 to 104. S pace charge polarization. A limited transport of charge carriers takes place until they are stopped at a potential barrier which could be a grain boundary an interphase boundary or a dislocation. The result is a spatial d istribution of charge centers over the microstructure. Depending on conductivity (mobility) and barrier contribution (distances) it can respond in most ceramics up to 106 Hz and can contribute to the relative permittivity ~ 105.
29 Usually more than one activ e polarization mechanism can be found in a material. Therefore, the total permittivity is a contribution of the different mechanisms: Charge Space Dipolar Ionic electronic Total (2 8 ) w here is the permittivity at frequencies above 1015 Hz typically corresponding to 1 .
30 CHAPTER 3 T HE CASE OF SiC 3.1 I nert Matrix Fuels The core of this chapter is chiefly based on the journal article ( Journal of Nuclear Materials, 2011, submitted) titled Low Temperature Sintering (930C ) of SiC for Inert Matrix Fuels Using a Polymer Precursor by J. Roberto Esquivel Elizondo, Donald T. Moore, and Juan C. Nino. It is well known that plutonium (Pu) from dismantled nuclear weapons and spent nuclear fuel represents a problem of environmental safety due to its radiotoxicity and decaying heat generation. In addition, minor actinides such as americium (Am), neptunium (Np), and curium (Cm), by products of nuclear power, are also a concern for the same reasons. The half life of most of the radioactive isotopes of these elements is in the range of thousands of years so disposal of them in repositories is a major challenge.2 In an effort to reduce the stockpiles of these actinides, their transmutation to non/less radioactive nuclei has been carried out in LWRs while generating electricity. For this purpose, a mixture of plutonium oxide and uranium oxide ( MOX ) is used as fuel. The problem with MOX is the neutron absorption of 238U (the most abundant isotope of uranium), which upon capturing a neutron changes to 239U and after two beta decays becomes 239Pu. Therefore, this is not an efficient process for burning plutonium.3,4 In order to increase the efficiency of the plutonium transmutation process in the LWRs, a neutron transparent material replacing UO2 is needed. The fuel resulting from the inclusion of this non fertile material has received the name of inert matrix fuel (IMF).
31 Considering the aggressive conditions in a nuclear reactor the desirable characteristics of an inert matrix (IM) material include a low neutron absorption cross section, high melting point, high thermal conductivity, good irradiation stability, good chemical stability, and good mechanical properties ;8 charac teristics difficult to find a single material. Silicon carbide is one of the possible IM candidates but its sintering step represents a major drawback by reason of the typically required high temperatures (usually above 1700C) and pressures, and the util ization of sintering aids (TiO2, Al2O3 or Y2O3) .32 Therefore, the synthesis of SiC at lower temperatures is highly desired to avoid potential chemical reactions w ith Pu and the loss of minor actinides due to their volatility at high temperature. An approach that has been successfully used to lower the sintering temperature of SiC is the polymer precursor route. Yajima et al .33 reported in 1975, for the first tim e, the conversion of a polycarbosilane to silicon carbide fibers upon heat treatment. A year later, Yajima succeeded again, but this time working with SiC rectangular pellets, which were sintered between 1000C and 1400C using a polycarbosilane as binder .34 The conversion of polycarbosilane to silicon carbide occurs in three stages: (1) loss of low molecular mass components and crosslinking of the polymer, (2) organic to inorganic t ransition which involves the formation of amorphous silicon carbide, and (3) conversion of amorphous to crystalline silicon carbide.3539 A recently developed polymer precursor of SiC, the allylhydridopolycarbosilane (commercialized with the name SMP 10), known for producing near stoichiometric SiC, has been investigated by different authors because compared to polycarbosilane it
32 possess higher densification ef ficiency, superior rheological characteristics, and greater mass yield (7075%) .40 42 The allylhydridopolycarbosilane (AHPCS) has been used to make SiC composit es40,43 and has already been utilized for inert matrix fuel purposes ;44, 45 nevertheless, in most of the cases the firing temperature exceeded the 1300C. In a recent study, Shih et al .45 sintered SiC pellets using SMP 10 and CeO2 as a surrogate for Pu at a low tem perature (1050C), apparently solving the latent problem of chemic al reactions between SiC and Pu Nonetheless, at that processing temperature, they showed that only amorphous SiC resulted from the precursor. This might have a deleterious effect on the mec hanical and thermophysical properties of the pellets. Hence, further studies are needed to determine the potential of SiC made in this manner as an IM material. In the present investigation, the synthesis was carried out at temperatures as low as 930C. Furthermore, the thermal and mechanical properties of the obtained material were determined and compared with those of UO2, MOX, and other inert matrix material candidates. 3.2 Experimental Procedure 3.2.1 Sample P reparation In order to prepare the samples SiC powder of nominal sizes 1 m (Alfa Aesar, Ward Hill, MA) and 16.9 m (Superior Graphite, Chicago, IL) was mixed with 10 wt% of SMP10 (Starfire Systems Inc, Schenectady, NY). A 1:1 weight percent ratio of nHexane 99+% pure (Acros Organics, New Jersey, US) to powder was added as a solvent. The slurry was then manually shaken for 10 min in a 2 cm3 stainless steel comminution vial with a 5 mm stainless steel ball (Chemplex Industries Palm City, FL).
33 The slurry was dried overnight in a fume hood for the solvent evaporation. The dried mixture was gr ound with a corundum mortar and pestle and sieved through a 150 m stainless steel wire mesh. The powder was uniaxially pressed at 200 MPa and isostatically pressed at 250 MPa. The obtained pellets were placed on an alumina tray with sacrificial powder and sintered under a vacuum of 15 mTorr in a tube furnace (CM Inc, Bloomfield, NJ) with the following schedule: room temperature250C (2C/min), 250650C (1C/min), 650sintering temperature (2C/min), hold for 1 hour, sinteringroom temperature (3C/min). 3.2.2 Synthesis Characterization XRD (Philips 3720, Westorough, MA ) patterns of the pellets and powder w ere analyzed to verify phase purity and the scanning electron microscope (SEM) images were obtained with a JEOL JCM 5000 NeoScope and a JEOL SEM 6400. For the TGA and DTA, samples of 10 mg were set on an alumina pan in nitrogen and air with a heating rate of 10C/min in a Seiko Instruments TGA/DTA 320 SSC/5200 series. Raman spectra were c ollected at room temperature using a Horiba LabRAM Aramis Raman spectrometer with a 532 nm diode lase r. 3.2.3 Mechanical Characterization Sintered pellets were polished to a 1200 grit finish with aid of a polishing wheel. T he Vickers hardness was then measured with a conventional Vickers indentation method usi ng a load of 1 kg and applying E quation 3 1: 2 Vd F 852 1 H ( 3 1 ) where F is the load ( kgf ) and d is the average length ( millimeters ) of the indentation
34 diagonals Three indents per sample were measured (4 samples per sintering temperature) For the fracture strength and fracture toughness tests a Vickers hardness indent of 10 kg was made on the cent er of the pellets to follow the indentation/strength technique.46 The samples were later loaded on a threeball fixture with the indent pointing down towards the threeball arrangement ( pistonon3 ball method) A test frame (Instron m odel 1350, Instron Corporation, Norwood, MA) was employed and a pin speed of 0.3 mm/min was maintained (1.6 mm in diameter) until the specimen failed. The load at the rupture was recorded and the fracture strength was calculated using E quations 3 2, 33, and 34:47 Y X d P 4 3 S2 ( 3 2 ) 2 2C B 2 1 C B ln 1 X ( 3 3 ) 2 2C A 1 C A ln 1 1 Y ( 3 4 ) where is the Poissons r atio, B is the radius (m) of the loaded area, A is the radius (m) of the support circle, C is the radius (m) of the specimen, P is the load (N) and d is the thickness (m) of the specimen. Four pellets were measured per sintering temperature. The fracture toughness was obtained from E quation 3 5 using the strength indentation method:46 4 3 3 1 ICSP 88 0 K ( 3 5 ) where S is the fracture strength (Pa) and P is the indent load (N).
35 3.2.4 Thermophysical Characterization Thermal conductivity, thermal diffusivit y, and specific heat capacity of sintered pel lets were measured from 100 to 900C at 100C increments in nitrogen using an Anter Flashline 4010 Thermal Properties Analyzer Pellets were ground flat and parallel with 320 grit SiC paper so the surfaces were not reflective. One of the highest density pellets of each sintering temperature were measured three times per temperature and the values averaged. For the thermal diffusivity measurements, a Clark and Taylor correction48 was used while for the thermal conductivity and heat capacity, a certified thermographite (Anter Corp., Pittsburgh, PA) sample was taken as a reference.49 3.2.5 Density Calculations The volume of the pellets was measured geometrically with a caliper and the weight was later use to cal culate the experimental density. The recorded weight loss of each pellet was assigned to the polymer precursor only, which represented 10 wt% of the original mixture. The remaining of the precursor after firing was assumed to be amorphous SiC according to the discussion of the next section. The theoretical density was then calculated using a rule of mixtures of the density specified by the manufacturers, 3.21 g/cm3 for crystalline and 2.4 g/cm3 for amorphous SiC (Chunghao and cow o r kers confirmed this value for amorphous SiC45). 3.3 Results and Discussion 3.3.1 Polymer Analysis The XRD patterns of the SiC powder, green body, and sintered pellet are shown in F ig ure 31 O nly SiC is present after the sintering step and no oxidation or other
36 reactions took place. The low intensity peak located between the (110) and (200) planes corresponds to hexagonal SiC. The amorphous phase is clearly observed in the broader peaks of the fired pellet in contrast with those of the powder and green body. Concentrations of SMP 10 greater than 10 wt% were attempted but during pressing the excess SMP 10 were forced out from the pellet, indicating that the pellet is saturated with polymer at 10 wt%. Figure 3 1. XRD patterns of 1 m SiC powder, the green body with 10 wt% of polymer precursor and the sintered pellet at 930C. The DTA and TGA curves of the polymer are shown in Fig ure 3 2 The onset of a reaction can be found around 120C in accordance to the data obtained by Sreeja et al ,42 who explained that at this temperature the cross linking of the allyl bonds starts. The maximum cure (cross linking) observed in this work is located at 177C. The
37 exothermic reaction found at 244C has been previously associated with the self crosslinking due to the loss of hydrogen.42 A weight loss of 8% was measured from 30C to 300C Between 300 and 600C several reactions take place and a weight loss of 16% is observed (24% cumulative) mainly as a result of the loss of CH4. After 600C no more reactions were detected, only a change in the slope in the DTA curve at 850C which represents the formation of amorphous SiC (the manufacturer of the polymer claims the formation of amorphous SiC between 850 and 1200C). The ceramic yield at 1200C was found to be 72% so the weight loss in the last 600C was small (4%). Figure 32. TGA and DTA of SMP 10 in nitrogen with a heating rate of 10C /min. The same thermal analysis was carried out for the green body containing 10 wt% of SMP 10 with the DTA results shown in Fig ure 33 The DTA showed similar cure
38 temperatures for all ambient conditions, slightly lower than the value obtained for the p olymer alone. None of the reactions observed between 200 and 600C in the pure SMP10 were seen in the SiC green body; the reason could be the relative s mall amount of polymer used. Above 800C a change of slope is seen in pure nitrogen and the onset of an endothermic reaction can be identified in the presence of oxygen with a maximum at ~930C. T he change of slope in pure nitrogen is due to the formation of amorphous SiC. The endothermic reaction in air would suggest the o xidation of SiC to SiO2; howev er, this reaction is exothermic ,50 ruling out this possibility The oxidation of amorphous SiC to form amorphous silicon oxycarbide (SiCO) is an endothermic reaction, which would take place between 800 and 1000C,51,52 explaining the observed broad peak in the DTA of Figure 33. Because of the similar formation temperatures, in this case it is assumed that oxidation of amorphous SiC to SiCO occurs immediately after the formation of the first one. At 930C the amorphous SiCO finds its maximum formation rate. Hence 930C was chosen as the sintering temperature in addition to 1050C, the temperature suggest ed by the polymer manufacturer company The XRD pattern of the polymer fired at both sintering temperatures is shown in Fig ure 3 4 It is seen that in the SMP 10 fired at 1050C the peaks at ~60 and ~71 start to be visible, while at 930C they are not yet differentiated, indicating that at this last temperature the material is more amorphous. The amount of amorphous SiC was calculated to be between 6 and 7% independently of the firing temperature (refer to experimental section for details). The Raman spectra in Fig ure 3 5 are of pure SMP 10 (fired at both sintering temperatures), sintered pellets with 10 wt% SMP 10, and SiC powder A strait line
39 background subtract was performed on the spectra. SiC has a peak reported at ~795 cm1 and is attributed to the Si C transverse optical (TO) mode. There are also peaks at ~1315 cm1 for disordered carbon (D) and at ~1600 cm1 for ordered graphite (G).53,54 Fig ure 3 3. DTA of the SiC green body (10 wt% of SMP 10) in different envi ronments with a heating rate of 10C/min. SiC powder has the Si C TO peak whereas the pure SMP 10 only has the D and G peaks meaning the sintering temperatures did not form crystalline SiC from the SMP10. Raman spectra of the pure SMP 10 confirms the amorphous SiC after firing at 930 and 1 050C with increased intensity of the D and G bands at 1050C. The same effect is seen for the pellets with SMP 10 except that the Si SiC powder
40 Fig ure 34. XRD patterns of 1 m SiC powder and SMP 10 fired at 930 and 1050C Fig ure 35. Raman spectra of pure SMP 10 fired at the sintering temperatures, sintered pellets with 10 wt% SMP 10, and SiC powder.
41 3.3.2 Density of the Pellets After preparing 2 batches of 4 pellets each, the s intered pellets with 1 m SiC powder and 10 wt% of the polymer precursor were found to have ~71% of the theoretical density (3.21 g/cm3 for crystalline and 2.4 g/cm3 for amorphous SiC as specified by manufacturers). In comparison, fired pellets with only powder are ~59.5% dense. A negligib le shrinkage of the pellet was observed while the cold isostatic pressing was seen to increase the final density by 1.5%. In order to increase the density, and therefore, improve the thermal and mechanical properties of the pellets, a bimodal mixture of particles was used. According to McGeary55 the mechanical packing of spheric al particles reaches the highest density around a particle size ratio of 10. Above the previous value the packing density versus particle size ratio curve behaves as a plateau where improvements in the packing density are negligible. Considering the size availability on the market, a 16.9 m SiC powder was chosen as the coarse particles. The particle size distribution (PSD) of both the fine and the coarse particles is shown in Figure 36 and Figure 37, respectively. The results of using a bimodal mixt ure of particles are presented i n Fig ure 3 8 The highest average density (2.42 g/cm3, 77% of the theoretical) was located at a weight ratio of 50/50, the density corresponding to the next ratio measured was smaller so it was not necessary to try 75 wt% o f coarse particles (each point represent 4 pellets from two different batches) Taking into account the error bars, the weight loss ranges between 3 and 4% with higher average values at 930C This accounts for the 67 wt% of the amorphous phase present in t he pellets (refer to section 3. 2.5 for calculation details).
42 Fig ure 36. PSD of the SiC fine particles Fig ure 37 P SD of the SiC coarse particles
43 Fig ure 3 9 shows the SEM images of the different fractured pellets at the same magnification for comparison purposes. There is not much difference observed between the pellet that contains only powder and the pellet that contains powder and amorphous SiC as expected due to the anticipated nanometer size of the SiC particles from the SMP10. In the SEM image with the bimodal mixture it can be observed how the coarse particles are surrounded by the smaller ones closing pores and increasing density, this is more clearly seen in the SEM image of the polished and thermal etched pellet in Figure 3 10 Fig ure 3 8 Density and weight loss of pellets prepared with a bimodal distribution of particles and 10 wt% of SMP 10.
44 ( A ) ( B ) ( C ) Fig ure 39 SEM images of fractured pellets fired at 930C with A) only 1 m SiC powder; B ) 1 m SiC powder and SMP 10; C ) 1/16.9 m SiC powder in a 50/50 wt% ratio and SMP 10.
45 A key physical characteristic of a low density material, like the SiC pellets investigated here, is porosity. In the case of nuclear applications, s pecifically, light water reactors, porosity plays a major role. It is well known that fission gas released f rom the fuel pellets induces an increment of the internal pressure of the fuel rod, leading to higher temperatures of the fuel and eventually to the failure of the rod.56 This will limit the achievable burnup, considering that such release increases with temperature. In consequence, fission gas liberation would represent a major drawback of the porous SiC pellets, given that most of their porosity is open as shown by Shih and his collaborators45 who wo rked with SiC made from a polymer precursor fired at low temperature as in this study. Closed porosity is typically then desirable to avoid the pressurization problem, as it would retain the fission gases. However, on the other hand, swelling of the pell ets will take place due to accumulation of fission gas bubbles, increasing the mechanical interaction between the pellets and the cladding, leading to deformation of the latter.57 In this case, open porosity would be preferred. These contrasting implications as a result of a pellet with extended porosity require further analysis and solutions. An option proposed by Shih et al .45 is the utilization of polymer infiltration and pyrolysis cycles to cl ose the open pores. This proposal opens the possibility to find and optimize the amount of both types of porosity that would reduce pellet swelling and, at the same time, internal pressurization of the rod. Recently, in mid2010, a vented fuel pellet/gett er concept has been proposed to enable higher burnups of the nuclear fuel.58 The proposal is the enhancement of the fission gas release employing vented pellets and the collection of those gases in a getter material located in a fuel pin plenum in order to avoid the undesirable effects
46 already discussed. The use of nanoporous carbon and nanoparticles of carbon (nanotubes and bucky balls) as possible getter materials is being studied. A reduction on the grain size of the fuel pellets has been proposed to enhance the rele ase of gaseous fission products. The open porosity of the SiC pellets studied here would be ideal for the vented fuel pellet approach and represents a good alternative worth of fu rther studies. Therefore, in the next sections, the mechanical and thermophysical properties of the SiC pellets are explored. Fig ure 3 10 SEM image of a polished and thermal etched (800C) pellet with 1/16.9 m SiC powder in a 50/50 wt% ratio and SMP 10. The firing temperature was 930C. 3.3.3 Mechanical Properties Table 3 1 summarizes the measured mechanical properties of the SiC pellets as well as data obtained from literature of UO2, MOX, other IM candidat es such as MgAl2O4, Y3Al5O12, 59 and yttria stabilized zirconia.60 In addition, CeO2 commonly used
47 as a surrogate for PuO2, and MgO, which has the requirements for an ideal IM material, except hot water corrosion resistance, were included. The SiC pellets sintered at the two temperatures of interest exhibit very close values of both fracture strength and toughness so the more amorphous SiC fired at 930C does not affect the microstructure. The Vickers hardness of SiC fired at 930C was noticeably higher indicating that the interfacial strength between the amorphous and the crystalline forms is affected with increasing temperature. This can be explained by the fact that when the amorphous SiC turns into a more crystalline form, the volume reduction due to densification l eaves enough porosity to affect the boundary strength. With respect to fully dense SiC, the values obtained for the pellets in this study are around four times smaller for hardness and fracture strength, as expected due to the low density achieved. On the other hand, the fracture toughness was found to be very close, albeit, the testing methods vary in literature. For different sintering additives and methods, values ranging from 3.5 to 4.5 MPa m(1/2) are reported.32 Compared to the other IMF candidates and simulated MOX the hardness of the SiC pellets was found to be low er. Neeft et al .59 points out that the interaction between the pellets and the cladding diminishes with decreasing hardness making it more difficult for the fuel rod to fail. The fracture toughness, by contrast was higher than the other candidates and the simulated MOX leading to a lower risk of pellet fragmentation during normal operation or accidents.59 Considering that the temperature of the SiC pellets in operation inside the nuclear reactor will be above the sintering temperature of this work, SiC pellets were heat treated to 1500C in argon atmosphere and kept at that temperature for 2 hours. It is
48 clear that fuel pellets stay in the reactor for much longer periods of time; however, the objective was to determine if the thermal and mechanical properties were improved, deteriorated or stayed the same given that the amorphous material will crystallize. The results showed a decrease in hardness and inferior values of fracture strength and toughness, which could be explained by the increased porosity left by further densification of the amorphous material. It is important to note, that in spite of these morphology changes, the properties remain superior than most of the other materials. Table 31. Mechanical properties of the SiC pellets and other inert matrix material candidates. Indentation mass: 100 g, **200 g and #1000 g. Hv (kgf/mm 2 ) S (MPa) K I C (MPa m (1/2) ) SiC 930C # 542.71 46.7 89.52 4.90 2.55 0.10 SiC 1050C # 446.65 66.4 93.31 10.60 2.63 0.22 SiC 1 5 0 0C # 344.57 84.1 73.59 3.68 2.20 0.08 SiC 32 2150.87 2436.29 362 2.6 3 CeO 2 59 532 155 1.2 0.2 MgO 59 760 1.6 1.8 MgAl 2 O 4 ** 59 1615 113 2.5 0.4 Y 3 Al 5 O 12 ** 59 1446 67 2.5 0.4 ZrO2 based IMF** 60 774.72 71.36 57.7 8.3 1.5 0. 2 UO 2 61 632.00 20.39 76 0.87 0.14 Simulated MOX 61 625 680 40 50 0.7 0.9 An issue regarding the interaction between the SiC pellets and the cladding is worth a com ment here. The pellets fired at 930C and 1050C will still release gases (although in small amounts, ~1 wt% of the polymer, or 0.1 wt% of the pellet) as a result of the polymer decomposition as can be observed on the TGA of Figure 3 2 The hydrogen embr ittlement of steels has been extensively investigated62,63 and is a subject to consider in this study because failure of the cladding could be a concern due to hydrogen release from the pellets. The hydrogen loss is known to take place during the crosslinking of the polymer as already discussed, but some amounts will still be
49 released along with other out gassi ng products (e.g. methane) above 1050C .41 Tiwari et al .63 measured an average content of 5 ppm of hydrogen in the bulk of steels at the time of fracture, although the actual value is much higher according to the authors (reported equilibrium solubility of stainless steels at 350C ranges from 43 to 118 ppm56). Z irconium alloys on the other hand, could absorb larger amounts of hydrogen before the precipitation of zirconium hydrides, which are responsible for the embrittlement of the material .64 Between 260 and 300C, the solubility limit of irradiated Zircaloy 4 has been determined in 150380 ppm .57 The very low diffusivity of hydrogen in zirconium alloys (2.5 x 1013 m2/s65) and the presence of pressurized helium gas in the fuel rods, which would diminish considerably the partial pressure of out gassing products, make it unlikely for the small amount of hydrogen released from the SiC pellets (<1000 ppm) to diffuse completely in to the cladding. Therefore, it is safe to assume that the hydrogren released would not represent a problem for the Zircal oy cladding. Moreover, it has been found that the deleterious effect of hydrogen on the mechanical properties of Zircaloys decreases with increasing temperature,66,67 probably because of the improved ductility of the zirconium matrix.67 3.3.4 Thermal Properties The measured thermal properties of the SiC pellets are presented in Fig ure 3 11, Figure 312 and Fig ure 313 (polynomial curves were fitted to the data points). The thermal diffusivity ( Figure 311) increases wi th increasing firing temperature. The observed behavior is consistent with the increasing atomic ordering as indicated in Fig ure 34 and 3 5 from 930 to 1050C and subsequent crystallization of SiC when fired
50 at 1500C. The specific heat capacity present ed in Fig ure 312 matches well with literature ,32 which is expected given that the pellets are 93SiC regardless of the heat treatment here employed. Fig ure 3 13 shows the calculated thermal conductivity (E quation 3 6) of the SiC samples compared to UO2, MOX, and potential inert matrix materials C kp, ( 3 6 ) where k is the thermal conductivity, is the thermal diffusivity, Cp is the specific heat capacity, and is the density. Even though the SiC pellets are low density and its thermal conductivity is considerably lower than dense SiC,32 it is still higher than that of UO2 and MOX. A high conductivity is beneficial because it leads to a lower operating temperature, important for safety considerations,68 and allows for higher burnups.56,64 The reported yttria stabilized zirconia (YSZ)69 used i n the comparison is tetragonal with 5.8 wt% yttria and is fully dense but with a conductivity lower than UO2 which is in accordance to data p resented by other authors.70 T he thermal conductivity of SiC is greater than the spinel MgAl2O4 71 at higher temperatures. The thermal conductivity of Y3Al5O12 (not shown)72 wa s found to be lower than that of the spinel and the SiC of this work. By using SMP10 polymer infiltration of the SiC pellets the density and resulting conductivity could be increased even further The UO2 is 95% dense and is polynomial fit from a revie w of thermal conduc tivity measurements of UO2.73 M OX is U0.94Pu0.06O2 x with an oxygen to metal ratio of 2.00 a nd a density 95% of the theoretical.74
51 Fig ure 3 11 Thermal diffusivity of the SiC pellets Fig ure 3 12 Specific heat capacity of the SiC pellets
52 Figure 313 Thermal conductivity of the SiC pellets and other inert matrix materials. 3.4 Chapter Summary Sintered SiC pellets with a density of 2.42 g/cm3 (77% of the theoretical) were successfully made at 930C, temperature low enough to avoid a potential reaction with Pu and the loss of minor actinides due to volatilization. The mechanical properties showed to be superior to simulated MOX, UO2, and other candidates for inert matrix material s such as MgAl2O4 and YSZ. In addition, the measured thermophysical properties of the SiC pellets resulted in higher thermal conductivity values than the mentioned compounds. These results indicate that the mechanical and thermophysical properties of the porous pellets composed of amorphous and polycrystalline SiC prepared in this work, are convenient for inert matrix fuel applications, particularly in a vented fuel pellet/getter concept. Hence, SiC is a promising candidate for inert matrix
53 material to be used in LWRs, albeit more investigation is necessary. Irradiation tests should be performed to determine the swelling of the pellets at working conditions as well as the effect on the mechanical and thermal properties.
54 CHAPTER 4 THE CASE OF Bi2Ti2O7 4.1 Bismuth Pyrochlores The core of this chapter is chiefly based on the journal article (Chemistry of Materials, DOI: 10.1021/cm202154c, 2011) titled Bi2Ti2O7: It Is Not What You Have Read by J. Roberto Esquivel Elizondo, Beverly Brooks Hinojosa, and Juan C. Nino.27 Compounds with the nominal composition A2B2O7 containing the B2O6 octahedral and the A2O tetrahedral substructure s are known as pyrochlores. Bismuth based pyrochlores have been extensively studied due to their at tractive compositiondependent dielectric properties .7583 A combination of high permittivity values (usually above 100) low dielectric losses and low sinterin g temperatures (1000C 150) makes them good candidates for dielectric components in MLCC and LTCC applications. Over the last 10 years, extensive research has been done to explain a phenomenon that is common to several pyrochlores and all Bi pyrochlores: a temperature and frequency dependent dielectric relaxation consistent with glassy like dipolar mechanisms.7779,81,84 ,85 On cooling below room temperature, these materials exhibit a steplike decrease in the real part of the dielectric constant accompanied by a broad frequency depende nt peak in the imaginary part As a consequence of this relaxation, at microwave frequencies the temperature at which the dielectric loss peaks (Tm) displace s towards room temperature as has been observed for Bi1.5Zn1.0Nb1.5O7 (BZN) ,78,85 limiting possible applications. Several potential explanations for the observed relaxation in Bi pyroc hlores have been proposed including the hopping of the disordered cations at the A equivalent sites ,78 reorientation of unstable dipoles due to interactions in the A2O sub structure ,86
55 and chain rotation modes .79 I t is considered though that chemical disorder (more than one cation species sharing the A or B sites) highly polarizable lone pair cations such as Bi3+, and atomic displacement ar e responsible for the relaxor behavior. The measurement of the dielectric properties of Bi2Ti2O7, a cubic pyrochlor e without substitutions on both the A and B site, is extremely desirable because this com pound would help to isolate possible causes of relaxation. Atomic simulations have shown that inherent displacive disorder is expected in this bismuth based pyrochlore,27,8789 meaning that the pr esence of substitutional cations is not necessarily a requirement for the dis placive disorder observed in these compounds The presence of energy barriers of ion hopping mechanisms on the order of 0.10.2 eV (similar to those of BZN83) suggests dielectric relaxation may occur in bismuth titanate.88 If this prediction is confirmed atomic displacement (displacive disorder) would essentially be the origin of the relaxation behavior However, difficulties in the synthesis and densification (sintering) of Bi2Ti2O7 hav e impeded the dielectric study of this k ey material as will be discussed in the following sections 4.2 Bismuth Titanate Compounds The phase diagram of Bi2O3TiO2 was first published in 1965 by Speranskaya and coworkers ,90 and since then, the bismuth compounds reported there have been extensively studied due to their unique set of properties. Combi n ing the ens uing work by Bruton91 and Masuda et al .92 a total of five bismuth titanate co m pounds h a ve been identified: Bi4Ti3O12, Bi2Ti4O11, Bi12TiO20, Bi8TiO14, and Bi2Ti2O7. The well known Aurivillius phase ( layered perovskitelike ) Bi4Ti3O12 is a ferroelectric compound that has been synthe sized by different methods such as solid-
56 phase reaction,93 co precipitation,94 and mechanochem ical activation.95 Bi2Ti4O11 is antiferroelectric at low temperature ( Bi2Ti4O11) and tran sforms into paraelectric ( Bi2Ti4O11) at 233C.96 The crystal structure of both phases w as studied by Kahlenberg and Bhm97 who used a flux m e thod to grow single crystals The optical properties of Bi12TiO20 are a subject of much interest and many authors have studied t hem The compound has been synthesized by solid state reaction98 and coprecipitation.99 Moreover, single cry s tals have been grown by the Czochralski method.100,101 The existence of Bi8TiO14 is controversial since it was reported by M a suda et al .92 but not by Bruton91 or Lopez Martinez et al .102 The case of the pyrochlore Bi2Ti2O7 is different from the pr e vious ones and rather interesting. Ev en 42 years after Knop et al .103 a t tempted to make the compound using the solid state reaction method, it is not possible to say with cer tainty, the chemical and physi cal properties of this material due to the large differences within literature. The existence, stability, crystal structure, bulk densification (sintering), and diel ectric properties of the pyrochlore, often (wrongfully) reported as ferroe lectric,86,92,104107 have been subject of di scussion for many years. In the following sections a comprehensive study was carried out in order to clarify these issues concerning the synthesis, crystal structure, thermal stability, sinte r ing, and electrical properties of Bi2Ti2O7. 4.3 Experimental Procedure 4.3.1 Synthesis T o prepare 0.01 mol of Bi2Ti2O7, g lacial acetic acid (Alfa Ae sar, 99+%), bismuth nitrate pentahydrate (Fisher, certified), ammonium hydroxide (Acros Organics, 2830% solution of NH3 in water), and titanium (IV) isopropoxide (Acros Organ ics, 98+%) were
57 used as starting materials Bismuth nitrate (0.02 mol) was dissolved in acetic acid (25 mL) after approximately 20 min of stirring. The ammonium hydroxide (33 mL) was kept in a freezer below 0C, while the bismuth ni trate was dissolved. Titanium isopropoxide ( 0.02 mol plus an excess of 23% which has been found to be the optimum ratio to obtain a pure Bi2Ti2O7 phase108) w as later added to the bismuth nitrate sol u tion followed by 5 min of stirring. The ammonium hydroxide was poured in th is mixture (a strongly exothermic reaction) and after vigorous (manual) agitation a white precipitate was formed (the pH of the solution at this point wa s ~ 7). The precipitate was filtered, rinse d with abun dant water and dried overnight. S lightly yellow chunks were obtained and were gr ou nd with a mortar and a pestle until a hom o geneous white fine powder was observed. An alternative method consisted of following the same procedure just described but with the next changes : bismuth subnitrate (Fisher USP, 0.02/5 mol) was used instead of bismuth ni trate, and acetic acid was replaced with nitric acid 35% v/v (Ricca Chemical Company, 40 mL). The rest r e mained the same (but 40 mL of NH3OH substituted 33 mL). A calcination step was carried out at 550C for 16 h with a heating and cooling rate of 200C/h in a zirconium oxide crucible. The powder was pressed (50 MPa) into pellets of 7 and 13 mm in diameter. The pellets were microwave sintered in a ThermWAVE 1.3 furnace using silicon n i tride susceptors to attain a heating rate of 80C/min and a holding temper a ture of 1200C for 45 min. The samples were ambient cooled to room temperature inside the microwave furnace. F or d i electric and polarization vs electric field measurements si n tered samples were polished to a 1200 grit (SiC) finish, son i cated in water for 10 min and then electroded with gold (sputter
58 coated) and silver paste. They were then dr ied over night at 120C. Before the polarization vs electric field test s, the samples were poled at 140C under a voltage of 30 kV/cm for 30 min. 4.3.2 Characterization X ray diffraction (XRD) patterns of the pellets ( Philips APD 3720 Cu Kalpha source) and powder ( INEL CPS 120, Cu Kalpha source) w ere collected to verify phase purity and the scanning electron microscope (SEM) i m ages were obtained with a field emission JEOL 6335F FEG SEM For differential thermal analysis (DTA), 15 mg powder samples were set on a platinum pan in nitrogen atmosphere with a heating rate of 10C/min in a Seiko Instruments TGA/DTA 320 SSC/5200 s e ries The dielectric measurements were computer controlled with a closed cycle cryogenic workstation (CTI Cryogenics, Model 22) in the temperature range of 248C to 22C and a Delta 9023 oven from 22C to 200C. The measurements were conducted during cooling and heating cycle. Since no ther mal hysteresis was observed, only the data from the heating cycle are presented here. The polarization electric field (P E) loop was measured with a Sawyer Tower circuit with a sin u soidal wave at 50 Hz. 4.4 Results and Discussion 4.4.1 Bi2Ti2O7 Structure from DFT S imulation The bismuth titanate pyrochlore phase has been studied in several comput ational investigations.89,109113 Recent investigations based on first principles have reported lattice i nstability for the cubic bismuth titanate pyroc h lore when considering the atoms on the ideal high symmetry sites, which resulted in lattice distortions converging towards
59 a monoclinic Cm or orthor hombic 1Pna2 space groups.109,111,113 However, it is well known that t he Bi within Bi2Ti2O7 will displace off the high symmetry positions in the m 3 Fd space group.110,114,115 When atomic displacements were cons i dered, bismuth titanate was stable within the m 3 Fd space group and no lattice instabilities were found from phonon dispers ion ca l culations.88 Early DFT simulations on the Bi2Ti2O7 found Bi, Ti, and O atoms displaced with various positions identified.110 Briefly, in these results Bi occupied three positions (96g 96h and 192i ), O occupied the 192i centered at (1/8,1/8,1/8), and Ti also occupied the 192i position centered at (1/2,1/2,1/2). A recent study focused on expanding these results to examine the symmetry equivalent displacement sites for the Bi cations and a new energetic minimum was found.88 Using that result the Wyckoff positions for the Bi, Ti, O, and O atoms have been identified27 ( Table 41 ). The Bi atoms were found to exclusively occupy the 96g ( x, x, z) Wyckoff position result ing in 6 symmet r ically equivalent pos itions for each of the 16 Bi cations. The O anions exclusively bond to the Bi cations and occupy the 48f position, differing from previous reports where the O anions di s place to the 32e position114 or the 192i position.110 The O anions within the 48f position displace t o wards the six edges of the OBi4 tetrahedra27, as illustrated in Figure 41 A (o ne of the actual di splacement patterns of the O and Bi cations is highlighted as the black atoms ) Remarkably, it was found that the Ti atoms also occupy the 96g ( x, x, z) Wyckoff position but the resulting 6 equivalent pos i tions are centered around the 16d (1/2,1/2,1/2) .27 The 96g pos i tion for Ti has the Ti atoms displacing towards each of the vertices of the TiO6 oct a hedra, as seen in Figure 41 B One of the six possible
60 displacement pat t erns is highlighted i n green and results in a shorter Ti O bond length (distinguished in Figure 41 B ) The reported di s placement pattern for Ti also differs from the previously reported 192i position.110 For the case of the 192i position, the Ti displaced by a smaller magnitude and not di rectly towards one of the six O atoms within the octahedron. The difference between the two displacement patterns is attr i buted to the Bi displ acement.27 The details of the Bi occupying the 96g or 96h position have been discussed previously by Hector and Wiggin114 and R adosavljevic,115 respectively. Briefly, when Bi occupies the 96g site it displaces directly towards one O atom and simultaneously away from another O atom, resul t ing in an under coordinated O atom. It was observed that with the Ti occupying the 96g site, the Ti atom displaces t o wards this under coordinated O atom.27 For aid in viewing this displac e ment pattern, the magnitudes of both the Ti and O displac e ments shown in Figure 41 were exaggerated and the atomic radii were modified for all the atoms. Table 41. Atomic positions predicted by DFT simulations for cubic Bi2Ti2O7 and the lattice parameter calculated by different methods.27 Atom Wyckoff Pos i tion x y z Uiso Occupancy Bi 96 g 0.015 0.015 0.964 0.001 1/6 Ti 16 d 1/2 1/2 1/2 0.023 1 O 48 f 0.431 1/8 1/8 0.010 1 O 48 f 0.136 1/8 1/8 0.003 1/6 a ( ) 10.335 0.005 (DFT) 10.335 0.008 (CPS XRD) 10.327 0.002 (Le Bail) By a linear extrapo lation for curved position sensitive (CPS) detectors116
61 DFT captures snapshots of t he material without thermal co n siderations and experimental efforts have not i dentified static Ti displacement .27 Therefore, in the absence of experimen tal evidence, the Ti displacement is reinterpreted as an isotropic displacement about the high symmetry 16d site.27 Figure 4 1 Predicted displacement pattern for the (A ) OBi4 tetrah e dron with the O at 48f and the Bi at 96g and (B ) a snapshot of the TiO6 octahedron with Ti at 96g and O at 48f. The displacement magni tudes were exaggerated for the O and Ti for visual aid.27 A) B)
62 With the stability of the m 3 Fd space group confirmed, the lattice parameter, and the atomic positions and thermal parameters identified by DFT27 ( Table 41 ), the theoretical X ray diffraction pattern was generated and it is pr e sented in Figure 42 The theoretical pattern based on the DFT pr e dicted structure is compared with the observed XRD from the experimentally synthesized bismuth titanate in the following se ction. 4.4. 2 Synthesis of C ubic Bi2Ti2O7 P yrochlore In 1969 Knop and collaborators103 studying pyrochlore tit a nates attem pted to make the compound using the solid state reaction method but did not succeed. Instead, t hey made Y1xBixTi2O7 with different compositions and extrapolated the data to give an estimate of the lattice parameter (10.354 ), but con cluded that Bi2Ti2O7 was not a cubic pyrochlore. Later in 1977, Shimada et al .117 claime d t he grow th of Bi2Ti2O7 single crystals w hich were described as reddish brown crystals. The structure was simply defined as a face centeredcubic with a unit cell of 20.68 Masuda et al .92 worked with the Bi2O3TiO2 system and the flux method to grow single crystals and stated in 1992 that Bi2Ti2O7 was part of the phase diagram of the system and its melting point was 1210C. Three years later, Kahlenberg and Bhm ,118 determined that the crystal grown by Shidama et al .117 years before, was actually a different compound. That year (1995) the same authors pub lished another paper119 in which they tried to make the stoichiometric Bi2Ti2O7 by means of solid state reactions. They synthesized a mixture of Bi4Ti3O12, Bi2Ti4O11, and the pyrochlore, instead of isolating a single phase. After multiple phase analysis with the Rietveld method, they
63 concluded that the pyrochlore was Bi3+ and O2deficient with a compos i tion of Bi1.833Ti2O6.75 (a = 10.354 ) In 1998, Yordanov et al ,107 claimed the synthesis of Bi2Ti2O7 via solid state reactions but no proof (e.g. XRD pattern) was give n. The same year, Radosavljevic et al .115 published for the first time the synthesis of the single phase Bi2Ti2O7 obtained with a precipitation method ( although very weak peaks of Bi2Ti4O11 and TiO2 we re still observed in the XRD pattern according to the authors). From neutron diffraction, the compound was identified as Bi1.74Ti2O6.62, with a lattice param e ter of 10.352 and a density of 6.771 g/cm3. In 2002, Hou et al .86 prepared nanocrystals of Bi2Ti2O7 via metallorganic decomposition; however, their XRD pattern clearly shows the presence of the ferroelectric Bi4Ti3O12 phase. One year later, Su and Lu108 showed a convincing XRD pattern of a phase pure Bi2Ti2O7 made from a sol gel method. Non e theless, the complexity of the synthesis method (more than 10 different substances were used through several steps in combi nation with nitrogen purges and vacuum distillations) described by the authors makes it nonideal for possible applications and in cons e quence less attractive to researchers. In a latter wor k (2004), Hector and Wiggin114 were able to synthesize the com pound via coprecipitation. They reported that Bi2T i2O7 was very sensitive to temperature, and therefore, pure phase powder could only be obtained up to 470C. Using the coprecipitation method described in the S ection 2.1, in this work, phase pure cubic Bi2Ti2O7 pyrochlore was successfully synthesized only after calcination at 550C In Figure 42 a comparison between the experimental XRD pa t tern of the
64 calcined samples and the theoretical pattern o b tained from the parameters of Table 41 is presented. It can be noticed that the experimental pattern matches well the prediction from DFT Ad ditionally, the calculated lattice parameter from the experimental pattern, 10.335 0.008 (using a linear extrapo lation for curved position sensitive detectors116), is in excellent agree ment with the DFT value (10.335 0.005). Figure 42. Theoretical (using DFT atomic positions) and exper i mental (powder and pellet) X ray diffraction patterns of Bi2Ti2O7. For visual aid, a dashed line is included at 33 to illustrate the lack of secondary phases In addition to the agreement between the XRD patterns in Figure 42 comparing the DFT and experimental pat terns shows no unassigned peaks that would be due to
65 the presence of secondary phases. For visual ai d, a dashed line was added at 33, where peaks ascribed to Bi4Ti3O12 ( monoclinic or tetragon al) and the monoclinic Bi2Ti4O11 ( or ) would be observed (0.5) if any of these phases were present (refer to Appendix A for details ) Again, the absence of peaks associated with the secondary phase(s) and the excellent agreement with the DFT predictions gives strong evidence of the purity of the bismuth titanate pyrochlore. To further illustrate this, a magnification in log a rithmic scale of the XRD pattern area around 33 (where impurity peaks would appear if present) is depicted in Figure 43 with dashed lines shown at 33 0.5, and again no sign of impurity peaks is observed. Figure 4 3. Magnification in logarithmic scale of the XRD pattern of the powder around the area where common bismuth titanate impurities (pe rovskite and monoclinic) would be observed if present. For vis u al aid, dashed lines are included at 33 0.5 to illustrate the lack of secondary phases.
66 In order to further verify single phas e purity a Le Bail refinement (structureless fit) was per formed on the powder XRD pattern using the software Rietica. The resulting fit is shown in Figure 4 4 where it is evident that the sample is composed of a single phase. The small difference between the Le Bail fit and the experimental data corresponds to slight discrepancy in the peak intensities as ex pected. The calculated lattice parameter after the refinement was 10.327 0.002 ( Table 4 1 ) Furthermore, given the pervasive failure to synthes ize or is o late phase pure Bi2Ti2O7 reported in literature, a detailed d e scription on phase purity identification is presented in the next section. Figure 4 4. Le Bail structureless fit of the powder XRD pattern. Only peaks as cribed to the pyrochlore phase were detected.
67 4.4.3 Phase Purity I dentification of Bi2Ti2O7 S ingle phase purity is not often reported in literature, since typical ly the Aurivillius type phase ( Bi4Ti3O12) is present as an impurity. In Figure 45 the theoretical XRD patterns of a m i x ture composed of 90 wt% Bi2Ti2O7 and 10 wt% Bi4Ti3O12 (structural parameters obtained from Hervoches and Lightfoot120) are shown. It is possible to notice that the main peak of the secondary phase, (117)A (near 30), is overlapped and hidden by the main peak of the pyroc h lore (222)P Thus, detection of the ferroelectric phase depends on the identification of less intense peaks that even at this relatively high secondary phase concentration are difficult to see. In cons e quence, low intensity XRD patterns will give the impression of a phase pure compound, when it may not be the case. This could be the reason of the misleading ferroelectricity reports di scussed in section 18.104.22.168. Perhaps a more practical and direct observation in the ident i fication of the purity of the powder when employing the sy n thesis method proposed in this w ork is the color. It was found that the phase pure Bi2Ti2O7 powder calcined at 550C is white ( Figure 46 ). With increasing amount of the secondary phases it turns from white to yel low and finally to orange when the concentration of this phases is above 70% (even small amounts as low as 8% which would be hard to detect via standard XRD, make a big difference in color as evidenced in Figure 4 7 ). D e picted in Figure 46 the phase pure sintered pellets are shown to be light yellow. Since the purity of t he pellet was previously established through discussion of Figure 42 it should be noted t his difference in color b e tween the pellet and the powder can be explained by the nanosize nature of the latter (it is known that nanoparticles may exhibit different optical proper ties ,121 e.g. gold and silver122)
68 Figure 4 5 Theoretical XRD pattern of 90 wt% Bi2Ti2O7 plus 10 wt% Bi4Ti3O12. Figure 4 6 Phase pure Bi2Ti2O7 powder and pellet
69 Figure 47 Bi2Ti2O7 with 0 wt% (top left), 8 wt% (top right), 50 wt% (bottom left) and >70 wt% (bottom right) of secondary phases XRD patterns are also shown in the same order 4.4.4 Phase S tability of Bi2Ti2O7 Speranskaya et al .90 reported in 1965 the presence of only Bi4Ti3O12 and Bi2Ti4O11 in the phase di a gram of the Bi2O3TiO2 system. Masuda et al .92 published 27 years later, based on differential thermal analysi s, the existence of Bi2Ti2O7 in addi tion to the other two compounds. The three phases were stable in all ranges of temperature up to their i n congruent melting points In recent work, Lopez Martinez et al .102 obtained the phase di a gram by means of thermodynamic calculations The results are in agreement with the data ob tained experimentally by Masuda et al .92 However, researchers familiar with Bi2Ti2O7 would question the temperature stability. Jiang et al .105 determined in 1992 that Bi2Ti2O7 is an unstable phase since it decomposed to form Bi4Ti3O12 at 650C according to X ray diffraction analysis The same result was o b served by Toyoda et al .123 and Nakamura et al .124 Su and Lu108 obtained a single Bi2Ti2O7 phase and studied
70 the phase transformations at different temperatures They found that the pyrochlore started t o disappear at 700C d e composing to Bi4Ti3O12 and Bi2Ti4O11. Hector and Wiggin114 reported the transition at 480C, but it is possible that what they actually saw was not a phase trans ition, but the crystalliz a tion of Bi4Ti3O12, which might have been amorphous in the sample. It s hould be noted that Speranskaya et al .90 identified a transformation at 670C linking Bi4Ti3O12 and Bi2Ti4O11, but did not observe the p yrochlore phase. Based on this history of bismuth titanate, it is expected the cubic Bi2Ti2O7 will undergo a phase transition at elevated te m perature. Therefore, to locate the phase transition tem perature of Bi2Ti2O7, DTA was performed on the powder. The result shown in Figure 48 reveals the onset of a secondorder transition tak es place at 612C, which extends up to 729C, as the change of slope of the DTA curve reveals The absence of a well defined peak indicates a continuous trans i tion which explains the difference in the phase transformation temperature observed by different au thors. An alysis of the data, like that used for glass transitions ( following ASTM E1356), yields a transition temperature of 670C Curiously, it is the same temperature at which Bi4Ti3O12 starts a phase transform a tion from orthorhombic to tetragonal125 (although the low temperature phase has been reported to be monoclinic and not orthorhombic126128). The observed transition in the DTA result de monstrates the need to modify the phase diagram of the Bi2O3TiO2 system. Accordingly, the phase diagram of Speranskaya et al .90 based on experimental observations was here combined with the experimental work of Masuda et al .92 and the thermodynamic predictions of Lopez Martinez et al .102 The merged phase diagram with two proposed corrections is shown in Figure 49 First,
71 the horizontal temperature line of 670C was reinserted from the Bi2Ti4O11 phase (0.2 m ol fra ction Bi2O3) to the Bi4Ti3O12 phase (0.4 mol fraction Bi2O3). Second, Bi2Ti2O7 phase line at 0.33 mol fraction Bi2O3 thermodynamic instability (and dependence on processing history) of the pyrochlore phase (for mo re information on this topic refer to Appendix B) 4.4.5 Sintering of Bi2Ti2O7 Obtaining large single crystals or a dense polycrystalline c e ramics is essential for determining key bulk thermophysical and electrical properties of Bi2Ti2O7. Unfortunately, until now, it is precisely t he instability of the pyrochlore phase what has impeded the successful growth of large single crystals or the sintering of the compound. The consequence has been the inaccurate determination of properties, such as dielectric.129 This is one of the re a sons why most of the interest has shifted to the study of thin films prepared with different methods.130138 However, the key to solving the sinteri ng issue was found in the revised phase diagram presented in Figure 49 As discussed in Section 4.4.4, the Bi2Ti2O7 phase is stable up to 670C. This effectively precludes the use of any conventional sintering method. How ever, recognizing that the phas e diagram represents thermodynamic equilibrium, i t should be possible, in principle to heat the pyrochlore rapidly to 1200C (or near the appearance of liquid) to move away from thermal equilibrium and prevent the formation of the more stable secondary phases above 670 C Such process of sintering kinetics en hancement while limiting the phase transformation kinetics obviously requires very fast heat ing rates. The necessary heating rates were achieved by microwave sintering (80 C/min) which exposed t he pe llets to 1200 C with in 15 min. The obtained density (measured by
72 the Archimedes m e thod) was 6. 93 g/cm3. This would correspond to roughly 92% of the theoretical density, 7.53g/cm3 (assuming a fully stoichiometric compound). The XRD pattern of the pellet is presented in Figure 42 It matches well the theoretical and powder patterns. The lack of additional peaks near the dash line in Figure 42 indicates the secondary phases are not present in the sintered pellet. Figure 4 8 DTA curve of Bi2Ti2O7 powder (10C/min in nitrogen). The insets correspond to the XRD patterns of the sample (after the heat treatment) below 612C (left) and above 729C (right). It is important to note that since liquid phase appears at 1210C according to the phase diagram of Figure 49, there is a very small working window to achieve a sintered
73 pellet and small fluctua tions c an affect the desired outcome. For example, it is clear that even if small amounts of the pyrochlore melt, it would lead to the formation of Bi2Ti4O11 due to the peritectic reaction. In addition, a sintering temperature of 1150C r e sult ed in grey pellets with a density of 6.63 g/cm3 for which XRD analysis revealed the presence of only Bi4Ti3O12 and Bi2Ti4O11 as ex pected. Figure 4 9 Phase diagram of the Bi2O3TiO2 system, with the modif i cations in red. The horizontal line at 670C, absent in recent works, was reinserted and the phase line of Bi2Ti2O7 (vertical) was dashed to indicate the thermodynamic i n stability of this phase.
74 Furthermore, it is clear that, starting with nanometer sized powder, which coprecipitation yields, is essential to maximize the driving force for sintering (surface area) and obtaining a dense polycrystalline ceramic. Therefore, details on the powder morphology and sinter ed ceramic are provided in the following subsection. 4.4. 5.1 Powder morphology and ceramic microstructure anal y sis In order to study the powder morphology and ceramic microstructure, SEM images were collected. As can be noticed from Figure 410A the powder obtained from the coprecipitation method is comprised of round 100 nm clusters (hard aggl o merates) of smaller ~ 15 nm particles. Figure 104 B (at lower magnific a tion) also shows that these clusters result in powder of homoge neous round shape with very few soft agglomerates, this also very important to assure the densification of the ceramic Gi ven the fast firing employed, after sintering, no grain growth was ob served as can be inferred from the fractured pellet (under bending) of Figure 10 4 C Additi onal co n firmation wa s observed in a lower magnification image ( Figure 104 D ) that showed the hom o geneous grain distribution of the sample. The effective conser vation of the nanograins has been previously observed in microwave sintering.139,140 The image of the surface of a pellet fractured under shear stress is presented in Figure104 E and r e veals a transgranular fracture with a compacted structure where the nanograins cannot be easily differentiated, unlike the case in Figure 104 D At a lower magnification, Figure 104 F exhibits the dense nature of the pel let but also illustrates the presence of some isolated porosity
75 4.4.6 Bi2Ti2O7 Electrical Properties 22.214.171.124 Polarization vs. electric field loop behavior The believed ferroelectricity of Bi2Ti2O7 has been especially con troversial. Several authors have published this supposed characteristic of Bi2Ti2O7,86,92,104107 but o n the other hand, the com pound has been repor ted as a cubic pyrochlore,114,115, 117 thereby ruling out the poss i bility of a ferroelectric behavior. Moreover, Su and Lu108 did not find the hysteresis lo op characteristic of the ferroelectric mat e rials, but a single line. In addition, the DFT calculations previously discussed predict a cubic structure. Therefore, the obtained si n tered pellets of phase pure Bi2Ti2O7 reported here are ideal to help clarify the disagreement. In Figure 411 the p olarization vs. electric field (P E) response o b tained for Bi2Ti2O7 is illustrated Clearly n o ferroelectricity was observed and the small loop, which does not exhibit concave regions was understandably ascribed to dielectric loss. It is i m portant to note that incorrect data interpretation has led to at least one report of ferroelectric behavior of Bi2Ti2O7 when it was clearly not the case106,141 ( for more information regarding proper identif i cation of ferroelectrics from hysteresis loops, please refer to the work by Scott142) More importantly, the calculated relative permittivity from the polarization and the electric field at 50 Hz and room temperature was ~ 162 ( Eq uation 4 1) As will be seen in the next section, this matches very well with the dielectric permittivity of Bi2Ti2O7 here measured. 1 E P 0 r 4 1 w here r is the relative permittivi ty, P is the polarization, E is the electric field and o is
76 the permittivity of vacuum. In Appendix C the previously reported ferroelectricity of Bi2Ti2O7 and its relationship with impurities and grain size is discussed. Fi gure 410 SEM images of the powder (A and B ) and fracture sur faces under bending (C and D ) and shear ing (E and F)
77 Figure 4 11 Polarization vs. electric field response of Bi2Ti2O7 measured with a Sawyer Tower circuit at 50 Hz 126.96.36.199 Dielectric pr operties Bismuth pyrochlores have desirable dielectric properties, i n cluding high dielectric constant, low dielectric loss and low temperature coefficients of capacitance which help to decrease the size of the capacitors, as well as lower the material cos ts In fact, bismuth titanate was combined with bismuth hafnate to form solid solutions in an effort to improve the overall dielectric properties .129 An other example of this is BZN (Bi1.5Zn0.92Nb1.5O6.92) which also shows dielectric relaxation.83 The dielectric relaxation observed in pyrochlores is often attri buted to multiple features such as the highly polarizable A site cation, chemical substitution, and large ion displacement from the ideal m 3 Fd (space group No. 227) sites of the cubic pyrochlore structure.143,144 The sintered phasepure Bi2Ti2O7 pellet presents an opportunity to understand the di electric properties of a pyrochl ore without the chemical substitution on the A or B site, the reby
78 helping to isolate the features necessary to observe dielectric relaxation. The dielectric beha vior of Bi2Ti2O7 was investigated and the results are presented in Figure 412. The dielectri c constant of 115 at 500 kHz and room temperature is rel a tively high and the dielectric loss is small with the imaginary part of the permittiv i ty <1 (i.e. tan < 0.01). The relative permittivity indirectly calculated from the hysteresis loop at room temperature and 50 Hz (presented in Figure 411) is in good agreement with the direct measurements in Figure 412 when considering that the permittivity increases with decreasing fr e quency, as expected. Further, although it is not included in Figure 412, at 1 kHz the permittivity was 128. More remarkably, i t is clear that bi smuth titanate exhibits a form of dielectric relaxation commonly observed in pyroc h lores.83, 85,144146 In a typical bismuth pyrochlore relaxation, t he maxima in the real part of the dielectric permittivity (r) is relatively sharp and the curves at different frequen cies tend to converge at higher temperature to the same permittivity value. As seen in Figure 412, for bismuth titanate this be havior is not exactly followed Instead, the curves remain separated and the peak in permittivity is softened. The shape of the ass o ciated dielectric loss peak is rather interesting and deserves fur ther investigation since it does not follow the typical peak from relaxation processes. Additionally, r ecent computational work examining atomic hopping mechanisms i n bismuth titanate suggested the occur rence of dielectric relaxation due to Bi/O transitioning between equivalent displacement positions.88 The observat ion of dielectric relaxation in bismuth titanate suggests of the multiple fea tures proposed to be necessary, atomic displacement is key. Clearly, further analysis of the nature of the
79 dielectric response of bismuth titanate is needed and it is the focus of the discussion in the following chapter. Figure 4 12 Dielectric permittivity of Bi2Ti2O7 as a function of tem perature from 500 to 2000 kHz 4.5 Chapter Summary Cubic pyrochlore Bi2Ti2O7 was synthesized by a coprecipitation route. The powder was m icrowave sintered at 1200C to avoid the formation of the thermodynamically more favorable secondary phases, Bi4Ti3O12 and Bi2Ti4O11. The XRD pattern of the compound, also modeled by DFT, confirmed the phase purity of both the powder and the densified cer amic. In the phase pure sintered Bi2Ti2O7 compound, ferroelectricity was not found and it is not believed to exist in this stratum altogether. It was clarified that given the difficulty in making a single phase of the pyrochlore structure, ferroelectrici ty might have been incorrectly ascribed to this compound. In
80 order to help r e searchers avoid confusions of this sort, a brief description of how to identify the presence of impurities based on the color of the powder was offered. In addition, theoretical X ray diffraction patterns were shown to explain why the ferroelectric Bi4Ti3O12 commonly goes unnoticed in the experimental pat terns, which is a possible reason of the misleading properties attributed to Bi2Ti2O7. The synthesized cubic pyrochlore is not a ferroelectric as proven by the polarization vs. electric field response of the sintered pellets made here. The relative permittivity of ~ 162, calculated from the slope of the hysteresis loop, is in good agreement with the results obtained from the diel ectric measurements, from which dielectric re laxation was apparently observed. The fact that this phenomenon takes place in a pyrochlore with no substit u tion on the A or B site, strongly suggests, altogether with recent computational work, that atomic di s placements from the high symmetry sites is sufficient condition for the appearance of dielectric relaxation behavior in bismuth pyroc h lores.
81 CHAPTER 5 DIELECTRIC ANALYSIS OF Bi2Ti2O7 5.1 Chapter Objective Preliminary dielectric properties of Bi2Ti2O7 wer e reported in the previous Chapter; nonetheless, it was still unclear if the relaxation behavior was exhibited by this compound and further analysis is required. In this Chapter the dielectric properties of Bi2Ti2O7 are studied comprehensively as a functi on of temperature and frequency in order to clarify the presence of relaxation in this material and in turn, better understand t he nature of the dielectric relaxation phenomenon observed in Bi pyrochlores. 5.2 Experimental Procedure The dielectric measurements as a function of temperature were collected with an Agilent E4980A Precision LCR Meter using a computer controlled closed cycle cryogenic workstation (CTI Cryogenics, model 22) for the temperature ranges between 246C to 27C a nd a Delta 9023 ov en from 27C to 227C in the fre quency range between 40 Hz and 2 MHz Data at higher temperatures (100450C) was obtained placing the samples in a quartz tube reactor located in side a tube furnace. The thermocouple was placed in close proximity to the pellets in order to have accurate temperature control. Measurements in the frequency range from 1 kHz to 1 MHz were carried out using the Agilent system. Impedance data as a function of frequency was collected using an Agilent 4294A Precision Impedance Analyzer wi th measurements collected at 10C intervals between the temperature and frequency ranges of 20C 500C and 40 Hz to 1 MHz, respectively
82 5.3 Dielectric Analysis as a Function of Temperature The measured relative permittivity at 100 kHz and 25C was 115 (dielectric loss) was 0.0064. The obtained dielectric constant is in agreement with the reported value of 118 measured at the same frequency and temperature for thin films with strong (111) orientation;147 is an order of magnitude lowe r in this work Cagnon and coworkers130 reported the relative permittivity for thin films of Bi2Ti2O7 in the range of 140150 and the loss around 4x103. In this last case better agreement was found for the loss tangent but the difference in the dielectric constant is high. The real and the imaginary part of the dielectric constant at fixed frequency values against temperature are illustrated in Figure 51 for BZN and in Figure 52 for Bi2Ti2O7. Figure 51 Real and imaginary part of the dielectric constant of B ZN as a function of te m perature from 10 kHz to 2 MHz.
83 Figure 52 Real and imaginary part of the dielectric constant of Bi2Ti2O7 as a function o f te m perature from 10 kHz to 2 MHz. The dielectric behavior of BZN is characteristic of Bi pyrochlores, i.e., a low temperature frequency dispersive dielectric relaxation is observed where Tm shifts to higher temperatures with increasing measuring frequency. Also, the loss value at Tm and the width and magnitude of the loss peak increases with measuring frequency. In addition, the dielectric constant of BZN at different frequencies seems to converge to the same value as temperature is increased. However bismuth titanate, despite being a Bipyrochlore, does not have the same behavior. Even though it is clear that close to room temperature the relative permittivity of Bi2Ti2O7 changes its increasing tendency (except at low frequency as seen at 10 kHz) i t is not accompanied by a response in the imaginary part as in the case of BZN. This points to the possibility of a phase transition
84 being responsible for the permittivity change in Bi2Ti2O7. A similar phenomenon is observed in Gd3NbO7, a dielectric with a weberitetype structure, an anion deficient fluorite superstructure, similar to the pyrochlore structure.148,149 The measurement was extended up to 210C looking for indications of dielectric relaxation but it was not observed. From Figure 52 it is also noticed that t he dielectric constant of Bi2Ti2O7 at different frequencies does not converge as in BZN. At 10 kHz (the lowest frequency in Figure 52 ) the onset of a peak in the imaginary part is observed but the increasing conductivity does not allow seeing it clearly. Therefore, another measurement was carried out including frequencies as low as 80 Hz. The resulting plot is depicted in Figure 53 Figure 53 Real and imaginary part of the dielectric constant of Bi2Ti2O7 as a function of te m perature from 80 Hz to 2 MHz.
85 From this plot it is evident that at low frequencies (<10 kHz) a type of dielectri c relaxation is taking place. Nonetheless, the shape of the loss curves does not follow the observed pattern in BZN, more specifically, in Bipyrochlores the loss peaks seem to appear at the same low temperature, which is not the case for Bi2Ti2O7, sugges ting a different origin for the relaxation. Differential scanning calorimetry (DSC) performed on a Bi2Ti2O7 sample from 2 to 200 K ( 271 to 73C) only reveals a slight change of slope at 127 K ( 146C) as illustrated in Figure 54 It is important to me ntion that the relaxation in Bi2Ti2O7, where the dielectric constant dispersion starts, occurs at higher temperatures than in BZN (and any other Bi pyrochlore studied so far). Employing the Arrhenius equation, the Debye model corresponding to a single rela xation time was followed to determine the activation energy (Ea) and the attempt jump frequency or characteristic frequency ( 0) of the relaxation phenomenon in Bi2Ti2O7: m B a 0 rT k E exp ( 5 1 ) w here r is the frequency of the relaxation peak in the loss spectra, and kB is the Boltzman constant. The behavior of the loss peaks obeyed correctly the selected model as shown in Figure 55 (with data from Table 51 ). The calculated activation energy of 0.162 eV (equivalent to 1881.3 K) is in agreement with calculated values from DFT (0.110.2188) and is similar to that of BZN (0.136 eV ,83 0.202 eV78). However, the attempt jump frequency (9.91 x 105 Hz = ~1 MHz) is several orders of magnitude lower (1012 Hz), which makes the comparison of activation energies pointless since different relaxation mechanisms should be taking place.
86 Table 5 1. Temperature of low frequencies loss maxima (Tm) for Arrhenius fit. Frequency (Hz) Tm (K ) 100 203.666 200 222.717 500 247.525 800 264.550 1000 271.739 Figure 54 Low Temperature DSC analysis of Bi2Ti2O7. The very low attempt jump frequency suggests the presence of space charge polarization within the grain boundaries or an interaction between the surface of the sample and the electrode. Otherwise, if one assumes that the observed phenomenon is a typical dielectric relaxation, such low frequency would imply the involvement of a large vibrating mass or a cooperative displacement in the form of rigid unit modes.150,151 In
87 BZN the characteristic frequency in the order of 1012 Hz is normally attributed to the attempt jump frequency of the hopping of A ions within the A2O substructure that is governed by the O AO phonon vibration.152 If a rough calculation is used considering harmonic oscillators (m2/m1 = 1 2/ 2 2), a mass difference of 12 orders of magnitude is obtained between BZN and Bi2Ti2O7. In that case, the low frequency dielectric relaxation in Bi2Ti2O7 requires a vibrating mass in the order of several lattices or unit cells (4.81 x 1010 unit cells) which means that cooperative displacement w ould be occurring. Given this unlikely event, space charge polarization in the form of electrode interfacial polarization would seem more reasonable. Figure 55 Arrhenius plot of Bi2Ti2O7 dielectric relax ation using Equation 5 1 and Table 5 1 Fitting parameters are presented. In order to verify the possible interaction between the electrodes and the sample, three different electrodes were used for the dielectric analysis, silver paste, platinum ink
88 and gold (sputter coated). In all the three cases the same dielec tric response was obtained ( Figure 53 ). In addition, current voltage tests revealed similar curves with a behavior that rules out the possibility of Schottky barriers.153,154 Also a 15V field bias was applied during capacitance measurements giving as a result horizontal lines in a capacitance versus voltage plot confirming the absence of a Schottky contact A lack of tunability of Bi2Ti2O7 has been reported for thin films by Cagnon et al .130 which contrast with the tunability observed for BZN thin films.155 Cagnon and co workers attributed this to a possible dielectric relaxation above room temperature. To confirm that possibility a higher temperature analysis was carried out here with the results shown in F igure 5 6 Figure 56 Imaginary and real part of the dielectric constant of Bi2Ti2O7 as a function of temperature at 80, 100, 500, and 1000 kHz
89 No sign of relaxation was found in the imaginary part; however, there is a clear change in the relative permittivity around 239C It is remarkable that at 1 MHz the loss only 0.0097 at 273C and finally to 0.0317 at 376C where conductivity is evident Furthermore, the dielectric constant ranges from 113.59 at room temperature to 122.85 at 376C This result implies that at this (1 MHz) and at higher frequencies Bi2Ti2O7 does not have the deleterious effect of highly increasing loss due to dielectric relaxation or conductivity up to 273C. 5.3 Dielectric Analysis as a Function of Frequency Frequency dependent properties of materials are commonly described using 4 mai admittance (Y), and complex modulus function (M). These four basic immittance functions are related as follows: j ( 5 2 ) 1 jM M M ( 5 3 ) 1 1 jZ Z Z ( 5 4 ) jY Y Y ( 5 5 ) w here = j c, is the angular frequency ( f ) Cc is the capacitance without the dielectric material and j is the square root of 1 .156 When a single relaxation process is occurring the dielectric response can be represented by various relaxation models known as the Debye relaxation,157 the ColeCole relaxation,158 the DavidsonCole
90 relaxation,159 and the Havriliak Negami relaxation.160 The permittivity takes the following forms for each model, respectively: j 1 s ( 5 6 ) 1 s j 1 ( 5 7 ) s j 1 ( 5 8 ) 1 s j 1 ( 5 9 ) where s is the real permittivity when =0 and is the real permittivity as is the angle offset in the complex permittivity plot, and represents a nonlinearity in the high frequency region of the real imagi nary plane. Using the relationships in E quations 5 2 to 5 5 and E quations 5 6 to 59, all of the dielectric functions will result in semicircles when plotted in the complex plane, and sigmoidal and peak curves will be obtained for the real and imaginary parts of the function. However, not all of these features can be observed experimentally depending on the strength of the relaxation and the value of the distribution parameters .161 It is important to note that a single physical process can be represented by several relaxation times, depending on which dielectric function one chooses for the same physical process .162
91 The ratio r = s plays a key role in determining the relaxation time for a particular dielectric function, therefore determining at what frequency the imaginary formalism of a particular dielectric function will display a peak resulting from the same physical process .161 As shown in the work by Cao and Gerhardt162 conductivity will result in M = Z therefore both the M and the Z peaks will overlap throughout the entire frequency range, giving a clear indication that conduction is present. Because of the relatively high temperature dielectric relaxation exh ibited by Bi2Ti2O7 it is complicated to establish the boundary between localized relaxation and long range conductivity. In order to differentiate between the two events, frequency explicit plots of the dissipation factor (tan electric modulus, admitt ance, and impedance are shown in Figures 5 7,8,9, and 10, respectively T he dissipation factor is plotted ( Figure 57 ) along the frequency plane where it is evident that at temperatures >120 K a dielectric loss peak is observed. When tan is compared w ith the imaginary component of the complex modulus ( M ), complex admittance ( Y ), and complex impedance ( Z ) ( Figure 58,9, and 10) it is clear that there are no visible peaks in Y and Z while the tan and M plots both display peaks at nearly the same frequency range which is predicted for materials with a small relaxation ratio (r = s) .161 Materials with small relaxation ratios also exhibit two plateaus visible in the real part of the die r plot ; this is verified in Bi2Ti2O7 as depicted in Figure 511
92 Figure 57 Dissipation factor of Bi2Ti2O7 as a function of frequency from 30 to 290 K Figure 58 Imaginary part of the electric modulus of Bi2Ti2O7 as a function of frequency from 30 to 290 K
93 Figure 59 Imaginary part of the admittance of Bi2Ti2O7 as a function of frequency from 30 to 290 K Figure 510 Imaginary part of the impedance of Bi2Ti2O7 as a function of frequency from 30 to 290 K
94 Figure 511 Dielectric constant of Bi2Ti2O7 as a function of frequency from 30 to 290 K By plotting these dielectric formalisms as a function of frequency it is evident that there is dielectric relaxation occurring in Bi2Ti2O7 a t a relativ ely low frequency range from ~12 0 K to room temperature. T he ColeCole plot of Figure 512 shows a shape that is close to a semicircle which means that the relaxation follows the Debye model ( 0). The approximate values of s (129) and (111) were obtained from which a small relaxation ratio was calculated ( r = s = 1.16) 105s. To finish the dielectric spectroscopy analysis Bode plots at 30 and 290 K are shown in Figures 5 13 and 514, respectively. In a Bode plot a perfect capacitance is obtained when the Bodemagnitude diagram (log |Z| versus log ) show s a straight line with a slope of 1 and the Bodeversus log ) has a phase angle of
95 90.163 This is almost the case for Bi2Ti2O7 at 30 K where the slope of the magnitude is close to 1 and the phase remains at 89.7 until a small deviation towards 89.5 at 200 kHz takes place. On the other hand, at 290 K the phase moves away from the ideal value forming a peak with a maximum in 87.12 because of the relaxation taking place at low frequency (the slope of the magnitude, however, remains close to 1) Figure 512 Cole Cole plot of Bi2Ti2O7 at 290 K After the frequency and temperature dependent dielectric analysis the origi n of the dielectric relaxation observed at low frequency in Bi2Ti2O7 is still unclear. So far it seems that the phenomenon is structural rather than dipolar or ionic as seen in BZN. The dielectric study of Bi2Ti2O7 makes it evident that chemical substitution affects the relaxation mechanisms of Bi pyrochlores. For those with substitution on both sites (A
96 and B) similar activation energies and characteristic frequencies have been calculated (0.1120.259 eV and 10121015 Hz77,152,164 166) from the Arrhenius equation; nevertheless, the pyrochlores with substitution only on the B site show different values than the previous group (0.3190.559 eV and 101 61020 Hz76,79). The frequencies for these compounds are so unlikely that authors had to use a different model to fit the relaxation behavior. Bismuth titanate, a compound without chemical substitution (substitutional disorder), has an activation energy that fits well in the fir st group, nonetheless, 0 differs orders of magnitude than any other Bi pyrochlore. Figure 513 Bode plot of Bi2Ti2O7 at 30 K The recent observation of dielectric relaxation in the CaTi (Nb,Ta) O pyrochlores144 discards the presence of lone pair electrons or highly polarizable cations
97 such as Bi3+ as the origin of the phenomenon. Nevertheless, atomic displacements and substitutional cations are present in those Capyrochlores. In this work the dielectric analysis of Bi2Ti2O7 has revealed that combined atomic displacement and high polarizability in the A site are not enough to lead to the onset of dielectric relaxation. This result in combination with the observations in Capyrochlores suggests that substitutional cations play a major role in the mechanism that triggers the relaxation behavior in these compounds. Figure 514 Bode plot of Bi2Ti2O7 at 290 K 5.4 Chapter Summary A dielectric analysis of Bi2Ti2O7, a bismuth pyrochlore without substitutional disorder, revealed considerable differences with respect to the common dielectric
98 behavior exhibited by this family of compounds. The dielectric relaxation observed in BZN is absent in Bi2Ti2O7; however, a relaxation of a different nature was found at low frequencies (<10 kHz) and at relatively high temperature (125 K) in Bi2Ti2O7. The calculated activation energy and characteristic frequency of this behavior using the Arrhenius model were 0.162 eV and ~1 MHz, respectively. The low attempt jump frequency is consistent with space charge polarization and not the result of dipolar or ionic disorder. The relaxation behavior at low frequency was confirmed with a study of The atypical dielectric response of Bi2Ti2O7 suggests that substitutional cations play a major role in the origi n of the dielectric relaxation in Bi pyrochlores.
99 CHAPTER 6 CONCLUSIONS AND FUTURE WORK 6 .1 The Case of SiC Silicon carbide was successfully sintered at 930C which is a temperature low enough to avoid potential reactions with the nuclear fuel. The achievement was possible because of the use of a polymer precursor that allows the formation of amorphous SiC as the thermal analysis, Raman spectroscopy and XRD revealed. The SiC pellets were prepared using a mixture of 90 wt% polycrystalline SiC powder (bimodal) and 10 wt% polymer precursor. The average density of the sintered pellets was 2.42 g/cm3, which represents 77% of theoretical value. The high porosity of these pellets was found to be suitable for an inert matrix fuel open porosity concept as their mechanical and thermophysical properties demonstrated. The hardness, fracture strength, and fracture toughness, in spite of being lower than those of dense SiC, proved more appropriate than the same properties exhibited by UO2 and MOX for use in LWRs The thermal diffusivity, thermal conductivity and heat capacity of the SiC pellets were better as well Hence, SiC is a promising candidate for inert matrix material to be used in LWRs, albeit more investigation is necessary. Irradiation tests should be performed to determine the swelling of the pellets at working conditions as well as the effect on the mechanical and thermal properties. The utilization of polymer infiltration and pyrolysis cycles to close the open pores would be useful t o find and optimum amount of both open and closed por es that would reduce pellet swelling and, at the same time, internal pressurization of the fuel rods. Also, the microstructure and porosity of the SiC pellets can be controlled through the
100 use of sacrif icial templates or via the direct foaming method to produce various properties for numerous applications as has been recently shown for BaTiO3.167, 168 Finally, in order to evaluate the potential of the SiC pellets as Americium bearing compounds nonradioactive surrogates for Am such as Mn ( for its similar high vapor pressure with Am) and lanthanides ( for their crystallochemical similarity with Am) can be tested. 6.2 The Case of Bi2Ti2O7 Cubic pyrochlore Bi2Ti2O7 was synthesized phase pure by a coprecipitation route. The XRD pattern of the powder did not reveal t he presence of secondary phases, which have been present in many reports in literature. In order to clarify confusions regarding the purity of this compound, a description of how to identify the presence of impurities based on the color of the powder was offered. It was also found that the ferr oelectric Bi4Ti3O12 commonly goes unnoticed in the experimental pat terns because of overlapping of the main peaks of both the perovskite and the pyrochlore. This issue le d to several mistaken reports of observed ferroelectricity in Bi2Ti2O7. A thermal analysis of the powder was employed to correct the phase diagram of the Bi2O3TiO2 system The horizontal line at 670C, absent in recent works, was reinserted and the phase line of Bi2Ti2O7 (vertical) was dashed to indicate the thermodynamic i n stability of t his phase. The synthesized powder was microwave sintered at 1200C to avoid the formation of the thermodynamically more favorable secondary phases, Bi4Ti3O12 and Bi2Ti4O11. This is the first time that Bi2Ti2O7 is successfully sintered allowing the study of this compound. The cubic pyrochlore was proven to be a linear dielectric and not a
101 ferroelectric as the polarization vs. electric field response of the sintered pellets revealed. A dielectric analysis of Bi2Ti2O7 exposed considerable differences with respect to the common dielectric behavior exhibited by Bipyrochlores The dielectric relaxation observed in BZN was not found in Bi2Ti2O7, instead, a low frequency (<10 kHz) and relatively high temperature (125 K) relaxation was observed. The relaxation was confirmed by plotting function of frequency The relaxation behavior was then modeled using a single Debye relaxation through the Arrhenius equation. An activation energy of 0.162 eV and a characteristic frequency of 9.91 x 105 Hz were calculated. The low attempt jump frequency is consistent with space charge polarization and not the result of dipolar or ionic disorder. After the dielectric spectroscopy analysis and the literature survey it was concluded that t h e atypical dielectric response of Bi2Ti2O7 suggests that substitutional cations play a major role in the origin of the dielectric relaxation in Bi pyrochlores. Future work include s neutron diffraction analysis to confirm the atomic displacements predicted by DFT and to obtain a more accurate lattice parameter Also, the stoichiometry of the synthesized bismuth titanate powder has to be confirmed. X ray fluorescence or mass spectroscopy could be a viable option to determine the exact composition of the pyr ochlore, necessary to obtain important information such as the correct theoretical density of the ceramic. To complete the dielectric study a Raman and infrared analysis of Bi2Ti2O7 can be performed for comparison with previous reports in literature for BZN which would allow a better understanding of the dielectric properties of these materials. Efforts to explain
102 the origin of the dielectric relaxation in Bi pyrochlores can focus on the synthesis and sintering of Bi2Zr2O7 and/or Bi2Hf2O7. The dielectric properties of these materials is desirable since Zr and Hf belong to the same group as Ti in the periodic table so a similar behavior to that of Bi2Ti2O7 would be expected. Finally, given the difficulty in literature to obtain a bulk dense ceramic of B i2Ti2O7, thermophysical, optical and chemical properties have not yet been reported for this material. Thus, the door is opened for the characterization of this bismuth based pyrochlore.
103 APPENDIX A BISMUTH TITANATE COMMON IMPURITIES As discussed in Chapter 4, there are 2 impurities usually found in the synthesized cubic pyrochlore Bi2Ti2O7 ( Figure A 1) One of them is the layered Perovskite (Aurivillius type phase) Bi4Ti3O12, which can be present in the low temperature monoclinic phase ( Figure A 2 A ) or the high temperature tetragonal phase ( F igure A 2B ). The phase transition takes place at 670C ,125 the Curie temperature, which has been reported to be reversible,169 so it is e xpected to observe the monoclinic phase (ferroelectric space group B1a1170) in the calcined Bi2Ti2O7 powder and sintered pellets. It has been reported, however, that the tetragonal phase (space group I4/mmm120) can be obtained at room temperature through coprecipitation.171, 172 Figure A 1. Cubic pyrochlore Bi2Ti2O7 (Bi = blue, Ti = green, O = red)
104 ( A ) ( B ) Figure A 2. Monoclinic170 (A) and t etragonal120 (B) Bi4Ti3O12.
105 The other common impurity is the monoclinic Bi4Ti3O12 ( Figure A 3) which has a phase transition at 233C f rom antiferroelectric ( Bi2Ti4O11, space group C2/C97) to paraelectric ( Bi2Ti4O11, space group C2/m97). ( A ) ( B ) Figure A 3. Monoclinic Bi2Ti4O11 (A) and Bi2Ti4O11 97 (B).
106 The transition is reported to be reversible so the alpha phase is expected to be found in the Bi2Ti2O7 powder and pellets. However, it is possible to have a similar situation as that described for Bi4Ti3O12 where, depending on the synthesis method, the usually high temperature phase can be obtained instead of the low temperature one. The theoretical XRD pattern of Bi2Ti2O7 shows the main peak at around 30 as observed in Figure A 4. In the case of Bi4Ti3O12 (Figure A 5) and Bi2Ti4O11 (Figure A 6) the main peaks are also found at ~30 for all the phases. Because of this overlapping, identification of bismuth titanate impurities in a Bi2Ti2O7 sample depends on the detection of lower intensity peaks of the secondary phases. Analysis of the theoretical XRD patterns reveals that after the main peak, Bi2Ti2O7 has anot her one at 34.66. In the case of Bi4Ti3O12 and Bi2Ti4O11 (all phases), relative high intensity peaks are located at 33 0.5. Hence, for a quick analysis, it is possible to determine the purity of a Bi2Ti2O7 sample looking at 2 between 30 and ~35, where no peaks should appear. Figure A 4. Theoretical XRD pattern of Bi2Ti2O7.
107 (A) (B) Figure A 5. Theoretical XRD pattern of monoclinic (A) and t etragonal (B) Bi4Ti3O12.
108 (A) (B) Figure A 6. Theoretical XRD pattern of Bi2Ti4O11 (A) and Bi2Ti4O11 (B).
109 APPENDIX B THERMODYNAMIC INSTABILITY OF Bi2Ti2O7 The DTA of Bi2Ti2O7 (Figure 48) in Chapter 4 revealed a phase transition between 612 and 729C which leads to the formation of Bi4Ti3O12 and Bi2Ti4O11. The phase diagram of the Bi2O3TiO2 system (Figure 4 9 ) indicates that the pyrochlore phase appears again at 1200C where a peritectic reaction occurs, allowing the sintering of the ceramic at this temperature. In previous attempts, sintering of coprecipitated powder at 1000C under vacuum (20 mTorr) and argon atmosphere were not successful because the pyrochlore phase underwent the mentioned phase transition. Solid state processing and quenching failed as well. In the case of quenching, crucibles of different material s (alumina, zirconia, quartz, and platinum) had to be used due to reactions between the liquid ( mixture of Bi2O3 and 2TiO2 powder ) and the crucible. Platinum was the only material that allowed the quenching ( in water ) of the liquid mixture through sealed (welded) tubes from 1 250 1350, and 1450C; however the obtained compound was a mixture of bismuth titanates with no evidence of the pyrochlore phase. With one of the phase pure Bi2Ti2O7 sintered pellets an experiment was carried out to further proof the thermodynamic instability of the cubic pyrochlore above the transition temperature of 670C (so far, only powder has been observed to exhibit the phase transformation) The phase pure yellow pellet ( Figure 46) was heated up to 800C and kept at that temperature for 2 days. As observed in Figure B 1, after the heat treatment the pel let changed color to gray. The XRD pattern of this pellet, presented in Figure B 2, reveals the presence of Bi4Ti3O12, Bi2Ti4O11, and a small amount of Bi2Ti2O7, showing the t hermodynamic instability of the pyrochlore phase at this temperatures.
110 Figure B 1. Bi2Ti2O7 sintered pellet heated to 800C and maintained at that temperature for 2 days. Figure B 2. XRD pattern of a Bi2Ti2O7 sintered pellet heated to 800C and m aintained at that temperature for 2 days.
111 APPENDIX C ORIGIN OF REPORTED FERROELECTRICITY IN Bi2Ti2O7 In section 188.8.131.52 the P E response of the sintered Bi2Ti2O7 reveals a linear dielectric and not a ferroelectric as previously reported. However, it is known that ferroelectricity can be suppressed below a critical grain size. In Bi4Ti3O12 this value is 44 nm,173 while in BaTiO3 it is 48 nm174 (it is also reported to be <30 nm175,176) Using Scherrers formula (E quation C 1) a particle size of 113 nm is obtained for the calcined Bi2Ti2O7 powder ( Figure C 1) which is in good agreement with the SEM image of Figure 4 10. The calculated grain size of the sint ered pellet is 159 nm, and compared to the critical grain size of Bi4Ti3O12 and BaTiO3 is much larger and makes it very unlikely to be below the critical value of a ferroelectric cubic pyrochlore. Hence, it is almost certain that Bi2Ti2O7 is not a ferroel ectric material. cos B 9 0 tB ( C 1 ) where t is the thickness of the crystal, the wavelength of the X ray source (1.5406 for Cu K emission), B (measured in radians) the full width at half maximum (FWHM) corrected for instrumental effects with a Si (004) single crystal (Binst = 0.05) and B is the angle that exactly satisfies Braggss law.177 In order to demonstrate that the reported ferroelectricity of Bi2Ti2O7 is due to the presence of Bi4Ti3O12 as an unnoticed impurity the characteristic P E hysteresis loop of Bi4Ti3O12 (Figure C 2) was combined with the P E response obtained for Bi2Ti2O7 in Figure 411 using a volume ratio of 2: 98. The obtained theoretical r esponse is illustrated in Figure C 3 and compared with an example of a reported loop ( Figure C 4 )
112 Figure C 1. Parameters used to estimate the particle and grain size of the Bi2Ti2O7 powder and sintered pellets, respectively, employing Scherrers formul a Figure C 2 Representative P E hysteresis loop of Bi4Ti3O12.178
113 Figure C 3. Theoretical P E res ponse of a mixture containing 96 wt% Bi2Ti2O7 and 4 wt% Bi4Ti3O12. Figure C 4. Reported P E response of Bi2Ti2O7.86 From the comparison, it is clear that the P E loop from literature is composed of a mixture o f the layered perovskite and the cubic pyrochlore. In addition, Figure C 5 100 Hz
114 shows the theoretical XRD pattern of the mixture in Figure C 3 which illustrates that detection of the ferroelectric impurity requires high quality XRD patterns. Figure C 5 T heoretical XRD pattern of 96 wt% Bi2Ti2O7 plus 4 wt% Bi4Ti3O12.
115 LIST OF REFERENCES 1. J. Edwards and D. Powell, "Mixed oxide fuel A valuable energy source," Nucl. Energy J. Br. Nucl. Energy Soc., 35  25356 (1996). 2. S. J. Yates, "Processing thermal Conductivity Relationships in MgO pyrochlore Composite Inert Matrix Materials," pp. 179. in Department of Materials Science and Engineering, Ph.D. University of Florida, Gainesville, 2009. 3. P. Xu, "Potential I nert Matrix Materials: Materials Synthesis and Evaluation of Inservice Engineering Parameters pp. 203. in Department of Materials Science and Engineering, Ph.D. University of Florida, Gainesville, 2009. 4. C. Shih, "Fabrication and Characterization of Silicon Carbide Inert Matrix Fuels Through a Polymer Precursor Route," pp. 152. in Department of Materials Science and Engineering, Ph.D. University of Florida, Gainesville, 2010. 5. S. J. Yates, P. Xu, J. Wang, J. S. Tulenko, and J. C. Nino, "Processing of magnesiapyrochlore composites for inert matrix materials," Journal of Nuclear Materials, 362 [2 3] 33642 (2007). 6. C. Degueldre and J. M. Paratte, "Concepts for an Inert Matrix Fuel, an Overview," Journal of Nuclear Materials, 274 [1 2] 1 6 (1999). 7. W. J. Weber, R. C. Ewing, C. R. A. Catlow, T. D. de la Rubia, L. W. Hobbs, C. Kinoshita, H. Matzke, A. T. Motta, M. Nastasi, E. K. H. Salje, E. R. Vance, and S. J. Zinkle, "Radiation effects in crystalline ceramics for the immobilization of highlevel nuclear waste and plutonium," J. Mater. Res., 13  143484 (1998). 8. H. Matzke, V. V. Rondinella, and T. Wiss, "Materials research on inert matrices: a screening study," Journal of Nuclear Materials, 274 [1 2] 47 53 (1999). 9. A. G. Evans and E. A. Charles, "Fracture Toughness Determinations by Indentation," J. Am Ceram Soc 59 [7 8] 37172 (1976). 10. H. Kodama and T. Miyoshi, "Study of Fracture Behavior of Very FineGrained Silicon Carbide Ceramics," J. Am Ceram Soc 73  308186 (1990). 11. M. J. Slavin and G. D. Quinn, "Mechanical property evaluation at elevated silicon carbide," International Journal of High Technology Ceramics, 2  4763 (1986). 12. Y. Zhou, K. Hirao, M. Toriy ama, Y. Yamauchi, and S. Kanzaki, "Effects of Intergranular Phase Chemistry on the Microstructure and Mechanical Properties of Silicon Carbide Ceramics Densified with RareEarth Oxide and Alumina Additions," J. Am Ceram Soc 84  164244 (2001).
116 13. R. W. Keyes, "Miniaturization of Electronics and Its Limits," IBM J. Res. Dev., 32  2428 (1988). 14. K. Feldmann, J. Franke, and F. Schler, "Development of micro assembly processes for further miniaturization in electronics production," CIRP Annals Manufacturing Technology, 59  1 4 (2010). 15. Y. Budianto, A. Aoki, and T. Miyashita, "Ultrathin Polymer Film Capacitor Composed of Poly(N Macromolecules, 36  876165 (2003). 16. J. K. Ahn, N. D. Cuong, S. G. Yoon, and C. S. Kim, "Structural and Electrical Properties of Bi1.5Mg1.0Nb1.5O7 Thin films deposited on Pt/TiO2/SiO2/Si Substrates by Rf magnetron Sputtering," Journal of Vacuum Science & Technology B, 26  127780 (2008). 17. O Dernovsek, M. Eberstein, W. A. Schiller, A. Naeini, G. Preu, and W. Wersing, "LTCC glass ceramic composites for microwave application," Journal of the European Ceramic Society, 21 [10 11] 169397 (2001). 18. H. Jantunen, T. Kangasvieri, J. Vahakangas, and S. Leppavuori, "Design aspects of microwave components with LTCC technique," Journal of the European Ceramic Society, 23 14] 254148 (2003). 19. H. Kishi, Y. Mizuno, and H. Chazono, "Basemetal Electrodemultilayer Ceramic Capacitors: Past, Present and Future Perspectives," Jpn. J. Appl Phys 1, 42  1 15 (2003). 20. C. Pithan, D. Hennings, and R. Waser, "Progress in the synthesis of nanocrystalline BaTiO(3) powders for MLCC," International Journal of Applied Ceramic Technology, 2  1 14 (2005). 21. M. T. Sebastian and H. Jantunen, "Low Loss Dielectric Materials for LTCC Applications: A Review," Int. Mater. Rev., 53  5790 (2008). 22. S. Yukio, "Multilayer Ceramic Capacitors," Current Opinion in Solid State and Materials Sc ience, 2  58487 (1997). 23. S. H. Shim, J.W. Yoon, K. B. Shim, J.i. Matsushita, B. S. Hyun, and S. G. Kang, "Low temperature synthesis of the microwave dielectric Bi2O3 MgO Nb2O5 nano powders by metal citrate method," J. Alloy Compd 415 [1 2 ] 234 38 (2006). 24. M. F. Yan, H. C. Ling, and W. W. Rhodes, "Low Firing, TemperatureStable Dielectric Compositions Based on Bismuth Nickel Zinc Niobates," J. Am Ceram Soc 73  110607 (1990).
117 25. S. T. Zhang, Z. Yi, M. H. Lu, Y. F. Chen, and Z. G. Liu, "Structures and dielectric properties of Bi1.5Zn1.0Nb1.5xTixO7 (x=0, 0.05, and 0.10) thin films," Applied Physics Letters, 90  (2007). 26. D. Liu, Y. Liu, S. Q. Huang, and X. Yao, "Phase Structure and Dielectric Properties of Bi2O3ZnO Nb2O5Based Dielectric Ceramics," J. Am Ceram Soc 76  212932 (1993). 27. J. R. Esquivel Elizondo, B. B. Hinojosa, and J. C. Nino, "Bi2Ti2O7: It is not what you have read," Chemistry of Materials (DOI: 10.1021/cm202154c, 2011). 28. N uclear Energy Agency, "Nuclear Energy Today, pp. 112. OECD Publishing: Paris, (2003). 29. M. P. Stevens, "Polymer Chemistry: An Introduction, pp. 574 3rd ed. Oxford Univeristy Press: New York, (1999). 30. R. C. Brundle, C. A. Evans, and S. Wilson, Encyclopedia of Materials Characterization, pp. 800. Elsevier Science & Technology: Oxford, (1992). 31. S. O. Kasap, "Principles of Electronic Materials and Devices, pp. 874 3rd ed. McGraw Hill: Hillsboro, (2006). 32. L. L. Snead, T. Nozawa, Y. Katoh, T. S. Byun, S. Kondo, and D. A. Petti, "Handbook of SiC properties for fuel performance modeling," Journal of Nuclear Materials, 371 [1 3] 32977 (2007). 33. S. Yajima, J. Hayashi, and M. Omori, "Continuous siliconcarbide fiber of hightensile s trength," Chem Lett  93134 (1975). 34. S. Yajima, T. Shishido, H. Kayano, K. Okamura, M. Omori, and J. Hayashi, "Sic Sintered Bodies with 3Dimensional Polycarbosilane as Binder," Nature, 264  23839 (1976). 35. E. Bouillon, D. Mocaer, J. F. Villeneuve, R. Pailler, R. Naslain, M. Monthioux, A. Oberlin, C. Guimon, and G. Pfister, "Composition microstructure property relationships in ceramic monofilaments resulting from the pyrolysis of a polycarbosilane precursor at 800 to 1400C," J. Mater Sci. 26  1517 30 (1991). 36. Y. Hasegawa, M. Iimura, and S. Yajima, "Synthesis of continuous siliconcarbide fiber. Part 2. Conversion of polycarbosilane fiber into siliconcarbide fibers," J. Mater Sci. 15  72028 (1980).
118 37. Y. Hasegawa and K. Okamura, "Synthesis of continuous siliconcarbide fiber. Part 3. Pyrolysis process of polycarbosilane and structure of the products," J. Mater Sci. 18  363348 (1983). 38. A. R. Maddocks, D. J. Cassidy, A. S. Jones, and A. T. Har ris, "Synthesis of nanoporous silicon carbide via the preceramic polymer route," Mater Chem Phys 113 [2 3] 86167 (2009). 39. A. R. Maddocks, J. M. Hook, H. Stender, and A. T. Harris, "Heterogeneously catalysed crosslinking of polycarbosilane with divinylbenzene," J. Mater Sci. 43  266674 (2008). 40. M. Kotani, Y. Katoh, A. Kohyama, and M. Narisawa, "Fabrication and oxidation resistance property of allylhydridopolycarbosilanederived SiC/SiC composites," J. Ceram Soc Jpn. 111  3000 7 (2003). 41. A. R. Puerta, E. E. Remsen, M. G. Bradley, W. Sherwood, and L. G. Sneddon, "Synthesis and ceramic conversion reactions of 9BBNmodified allylhydridopolycarbosilane: A new singlesource precursor to boronmodified silicon carbide," Chemi stry of Materials, 15  47885 (2003). 42. R. Sreeja, B. Swaminathan, A. Painuly, T. V. Sebastian, and S. Packirisamy, "Allylhydridopolycarbosilane (AHPCS) as matrix resin for C/SiC ceramic matrix composites," Mater. Sci. Eng B, 168 [1 3] 20407 (2010). 43. M. Berbon and M. Calabrese, "Effect of 1600 degrees C heat treatment on C/SiC composites fabricated by polymer infiltration and pyrolysis with allylhydridopolycarbosilane," J. Am Ceram Soc 85  189193 (2002). 44. K. H. Sarma, J. Fourcade, S. G. Lee, and A. A. Solomon, "New processing methods to produce silicon carbide and beryllium oxide inert matrix and enhanced thermal conductivity oxide fuels," Journal of Nuclear Materials, 352 [1 3] 32433 (2006). 45. C. H. Shih, J. S. T ulenko, and R. H. Baney, "Low temperature synthesis of silicon carbide inert matrix fuel through a polymer precursor route," Journal of Nuclear Materials, 409  199206 (2011). 46. P. Chantikul, G. R. Anstis, B. R. Lawn, and D. B. Marshall, "A crit icalevaluation of indentation techniques for measuring fracturetoughness. Part 2. strength method," J. Am Ceram Soc 64  53943 (1981). 47. J. B. Wachtman, W. Capps, and J. Mandel, "Biaxial flexure tests of ceramic substrates," J. Mater 7  18894 (1972).
119 48. L. M. Clark and R. E. Taylor, "Radiation loss in flash method for thermal diffusivity," Journal of Applied Physics, 46  71419 (1975). 49. K. D. Maglic and N. D. Milosevic, "Thermal diffusivity measurements of thermographite, Int. J. Thermophys., 25  23747 (2004). 50. M. Di Ventra and S. T. Pantelides, "Atomic scale mechanisms of oxygen precipitation and thinfilm oxidation of SiC," Physical Review Letters, 83  1624 (1999). 51. H. Fukui, H. Ohsuka, T. Hino, an d K. Kanamura, "Influence of polystyrene/phenyl substituents in precursors on microstructures of Si O C composite anodes for lithium ion batteries," J. Power Sources, 196  37178 (2011). 52. G. Das, P. Bettotti, L. Ferraioli, R. Raj, G. Mariotto, L PaveSib, and G. D. Soraru, "Study of the pyrolysis process of an hybrid CH3SiO1.5 gel into a SiCO glass," Vib Spectrosc 45  6168 (2007). 53. A. C. Ferrari and J. Robertson, "Interpretation of Raman spectra of disordered and amorphous carbon," Physical Review B, 61  14095 (2000). 54. Y. Ma, S. Wang, and Z. H. Chen, "Raman spectroscopy studies of the high temperature evolution of the free carbon phase in polycarbosilane derived SiC ceramics," Ceramics International, 36  245559 (2010). 55. R. K. Mcgeary, "Mechanical packing of spherical particles," J. Am Ceram Soc 44  51322 (1961). 56. D. Hardie, J. Xu, E. A. Charles, and Y. Wei, "Hydrogen embrittlement of stainless steel overlay materials for hydrogenators," Corros ion Science, 46  3089100 (2004). 57. P. Vizcano, A. D. Banchik, and J. P. Abriata, "Solubility of hydrogen in Zircaloy 4: irradiation induced increase and thermal recovery," Journal of Nuclear Materials, 304 [2 3] 96 106 (2002). 58. J. Carmack and K. Pasamehmetoglu, "Options study documenting the fast reactor fuels innovative design activity." in. Idaho National Laboratory (INL), 2010. 59. E. A. C. Neeft, K. Bakker, R. L. Belvroy, W. J. Tams, R. P. C. Schram, R. Conrad, and A. van Veen, "Mechanical behaviour of macrodispersed inert matrix fuels," Journal of Nuclear Materials, 317 [2 3] 21725 (2003). 60. Y. W. Lee, H. S. Kim, S. H. Kim, C. Y. Joung, S. C. Lee, S. H. Na, P. Heimgartner, and G. Ledergerber, "Measurement of the mechanical properties of
120 thermally shocked zirconiabased simulated inert matrix fuel," Progress in Nuclear Energy, 38 [3 4] 23136 (2001). 61. Y. W. Lee, S. C. Lee, C. Y. Joung, H. S. Kim, and H. L. Lee, "Analysis of resistance to thermal stress in ceramic oxide nuclear materials," Adv Eng Mater 4  58489 (2002). 62. R. A. Oriani, "Hydrogen embrittlement of steels," Annu. Rev Mater. Sci. 8 32757 (1978). 63. G. P. Tiwari, A. Bose, J. K. Chakravartty, S. L. Wadekar, M. K. Totlani, R. N. Arya, and R. K. Fotedar, "A study of internal hydrogen embrittlement of steels," Mat Sci. Eng a Struct. 286  26981 (2000). 64. A. Zielinski and S. Sobieszczyk, "Hydrogenenhanced degradation and oxide effects in zirconium alloys for nuclear applications," International Journal of Hydrogen Energy, 36  861929 (2011). 65. K. R. F. Silva, D. S. dos Santos, A. F. Ribeiro, and L. H. Almeida, "Hydrogen diffusivity and hydride formation in richzirconium alloys used in nclear reactors," Defect and Diffusion Forum, 297301 72227 (2010). 66. M. Daunys, R. Dundulis, A. Grybenas, and P. Krasauskas, "Hydrogen influence on mechanical and fracture mechanics characteristics of zirconium Zr 2.5Nb alloy at ambient and elevated temperatures," Nuclear Engineering and Design, 238  253645 (2008). 67. H. H. Hsu, "An evaluation of hydrided Zircaloy 4 cladding fracture behavior by X specimen test," J Alloy Compd. 426 [1 2] 25662 (2006). 68. H. R. Trellue, "Safety and neutronics: A com parison of MOX vs UO2 fuel," Progress in Nuclear Energy, 48  13545 (2006). 69. S. Raghavan, H. Wang, R. B. Dinwiddie, W. D. Porter, and M. J. Mayo, "The effect of grain size, porosity and yttria content on the thermal conductivity of nanocrystall ine zirconia," Scripta Materialia, 39  111925 (1998). 70. X. Song, M. Xie, F. Zhou, G. Jia, X. Hao, and S. An, "Hightemperature thermal properties of yttria fully stabilized zirconia ceramics," Journal of Rare Earths, 29  15559 (2011). 71. R. J. M. Konings, K. Bakker, J. G. Boshoven, H. Hein, M. E. Huntelaar, and R. R. van der Laan, "Transmutation of actinides in inert matrix fuels: fabrication studies and modelling of fuel behaviour," Journal of Nuclear Materials, 274 [1 2] 8490 (1999).
121 72. N. P. Padture and P. G. Klemens, "Low thermal conductivity in garnets," J. Am Ceram Soc 80  101820 (1997). 73. J. K. Fink, "Thermophysical properties of uranium dioxide," Journal of Nuclear Materials, 279  1 18 (2000). 74. C Duriez, J. P. Alessandri, T. Gervais, and Y. Philipponneau, "Thermal conductivity of hypostoichiometric low Pu content (U,Pu)O2x mixed oxide," Journal of Nuclear Materials, 277 [2 3] 14358 (2000). 75. J. Banys, M. Ivanov, S. Rudys, J. Li, and H. Wang, "Dielectric properties of cubic bismuth based pyrochlores containing lithium and fluorine," Journal of the European Ceramic Society, 30  38588 (2010). 76. D. P. Cann, C. A. Randall, and T. R. Shrout, "Investigation of the dielectric properties of bismuth pyrochlores," Solid State Commun 100  52934 (1996). 77. H. L. Du, X. Yao, and H. Wang, "Relaxor like behavior of bismuthbased pyrochlores containing Sn," J. Electroceram 21 [1 4] 22225 (2008). 78. S. Kamba, V. Porokhonskyy, A. Pashkin, V. Bovtun, J. Petzelt, J. C. Nino, S. Trolier McKinstry, M. T. Lanagan, and C. A. Randall, "Anomalous broad dielectric relaxation in Bi1.5Zn1.0Nb1.5O7 pyrochlore," Physical Review B, 66  054106 (2002). 79. Y. Liu, R. L. Withers, H. B. Nguyen, K. Elliott, Q. Ren, and Z. Chen, "Displacive disorder and dielectric relaxation in the stoichiometric bismuthcontaining pyrochlores, Bi2MIIINbO7 (M=In and Sc)," Journal of Solid State Chemistry, 182  274855 (2009). 80. M. W. Lufaso, T. A Vanderah, I. M. Pazos, I. Levin, R. S. Roth, J. C. Nino, V. Provenzano, and P. K. Schenck, "Phase formation, crystal chemistry, and properties in the system Bi2O3Fe2O3Nb2O5," Journal of Solid State Chemistry, 179  390010 (2006). 81. M. Valan t, "Dielectric Relaxations in Bi2O3 Nb2O5 NiO Cubic Pyrochlores," J. Am Ceram Soc 92  95558 (2009). 82. T. A. Vanderah, J. Guzman, J. C. Nino, and R. S. Roth, "Stability PhaseFields and Pyrochlore Formation in Sections of the Bi2O3Al2O3Fe2O3Nb2O5 System," J. Am Ceram Soc 91  365962 (2008). 83. J. C. Nino, M. T. Lanagan, and C. A. Randall, "Dielectric relaxation in Bi2O3ZnO Nb2O5 cubic pyrochlore," Journal of Applied Physics, 89  451216 (2001).
122 84. H. B. Nguyen, R. L. Withers, L. Noren, Y. Liu, X. Y. Wei, and M. M. Elcombe, "The disordered structures and low temperature dielectric relaxation properties of two misplaceddisplacive cubic pyrochlores found in the Bi2O3MIIO Nb2O5 (M = Mg, Ni) systems," Journal of Solid State Chemistry, 180  255865 (2007). 85. C. Ang, Z. Yu, H. J. Youn, C. A. Randall, A. S. Bhalla, L. E. Cross, J. Nino, and M. Lanagan, "Low temperature dielectric relaxation in the pyrochlore (Bi3/4Zn1/4)(2)(Zn1/4Ta3/4)(2)O7 compound," Applied Ph ysics Letters, 80  480709 (2002). 86. Y. Hou, M. Wang, X. H. Xu, D. Wang, H. Wang, and S. X. Shang, "Dielectric and ferroelectric properties of nanocrystalline Bi2Ti2O7 prepared by a metallorganic decomposition method," J. Am Ceram Soc 85 [1 2] 308789 (2002). 87. B. B. Hinojosa, A. Asthagiri, and J. C. Nino, "First principles study of cubic Bi pyrochlores," Physical Review B, 77  (2008). 88. B. B. Hinojosa, A. Asthagiri, and J. C. Nino, "Capturing dynamic cation hopping in cubic pyrochlores," Applied Physics Letters, 99 082903 (2011). 89. B. B. Hinojosa, P. M. Lang, and A. Asthagiri, "The influence of sulfur substitution on the atomic displacement in Bi2Ti2O7," Journal of Solid State Chemistry, 183  26269 (2010). 9 0. E. I. Speranskaya, I. S. Rez, L. V. Kozlova, V. M. Skorikov, and V. I. Slavov, "The system bismuth oxide titanium dioxide (translated from russian)," Neorg. Mater 1 [1 6] 2325 (1965). 91. T. M. Bruton, "Study of the liquidus in the system Bi2O3TiO2," Journal of Solid State Chemistry, 9  17375 (1974). 92. Y. Masuda, H. Masumoto, A. Baba, T. Goto, and T. Hirai, "Crystal Growth, Dielectric and Polarization Reversal Properties of Bi4Ti3O12 Single Crystal," Jpn. J. Appl Phys 1, 31 [9B] 310812 (1992). 93. M. I. Morozov, L. P. Mezentseva, and V. V. Gusarov, "Mechanism of formation of Bi4Ti3O12," Russ J. Gen Chem 72  103840 (2002). 94. P. Pookmanee, P. Boonphayak, and S. Phanichphant, "Chemical synthesis of bismuth titanate microparticles," Ceramics International, 30  191719 (2004). 95. M. Alguero, P. Ferrer, E. Vila, J. E. Iglesias, and A. Castro, "Bi4Ti3O12 ceramics from powders prepared by alternative routes: Wet nocoprecipitation chemistry and mechanochemica l activation," J. Am Ceram Soc 89  334047 (2006).
123 96. V. Kahlenberg and H. Bohm, "Investigations of the AlphaBeta Transition in Bi2Ti4O11," J. Phys Condens Mat 6  621128 (1994). 97. V. Kahlenberg and H. Bohm, "The Structures of Al phaBi2Ti4O11 and BetaBi2Ti4O11," Acta Crystallogr B, 51 1118 (1995). 98. J. K. Zhou, Z. G. Zou, A. K. Ray, and X. S. Zhao, "Preparation and characterization of polycrystalline bismuth titanate Bi12TiO20 and its photocatalytic properties under vis ible light irradiation," Ind Eng Chem Res 46  745 49 (2007). 99. N. Thanabodeekij, E. Gulari, and S. Wongkasemjit, "Bi12TiO20 synthesized directly from bismuth (III) nitrate pentahydrate and titanium glycolate and its activity," Powder Technol 160  20308 (2005). 100. J. F. Carvalho and A. C. Hernandes, "Large Bi12TiO20 single crystals: a study of intrinsic defects and growth parameters," J. Cryst Growth, 205 [1 2] 18590 (1999). 101. Y. Okano, H. Wada, T. Fukuda, and S. Miyazawa "Bulk Single Crystal Growth of Bi12TiO20 by the Czochralski Method," Jpn. J. Appl Phys 2, 30 [7B] L1307L09 (1991). 102. J. Lopez Martinez, A. Romero Serrano, A. Hernandez Ramirez, B. Zeifert, C. Gomez Yanez, and R. Martinez Sanchez, "Thermal analys is and prediction of phase equilibria in the TiO2Bi2O3 system," Thermochim Acta, 516 [1 2] 3539 (2011). 103. O. Knop and F. Brisse, "Pyrochlores .V. Thermoanalytic X Ray Neutron Infrared and Dielectric Studies of A2Ti2O7 Titanates," Can J. Chemistr y, 47  97190 (1969). 104. Y. Hou, Z. M. Huang, J. Q. Xue, Y. N. Wu, X. M. Shen, and J. H. Chu, "Study of the ferroelectricity in Bi2Ti2O7 by infrared spectroscopic ellipsometry," Applied Physics Letters, 86  (2005). 105. A. Q. Jiang, Z. X Hu, and L. D. Zhang, "Investigations of morphotropic phase transformations in the solid solution of Bi4Ti3O12 and Bi2Ti4O11 accompanied by defect dipole orientation and oxygen vacancy migration," Journal of Applied Physics, 85  173945 (1999). 106. S. S. Kim, M. H. Park, J. K. Chung, and W. J. Kim, "Structural study of a sol gel derived pyrochlore Bi2Ti2O7 using a Rietveld analysis method based on neutron scattering studies," Journal of Applied Physics, 105  061641 (2009).
124 107. S. P. Yordanov I. Ivanov, and C. P. Carapanov, "Dielectric properties of the ferroelectric Bi2Ti2O7 ceramics," J. Phys D Appl Phys 31  80006 (1998). 108. W. F. Su and Y. T. Lu, "Synthesis, phase transformation and dielectric properties of sol gel derived Bi2Ti2O7 ceramics," Mater. Chem Phys 80  63237 (2003). 109. C. Fennie, R. Seshadri, and K. Rabe, "Lattice instabilities in cubic pyrochlore Bi2Ti2O7," arXiv:0712.1846 unpublished (2008). 110. B. B. Hinojosa, J. C. Nino, and A. Asthagiri, "Fi rst principles study of cubic Bi pyrochlores," Physical Review B, 77  104123 (2008). 111. C. H. Patterson, "Firstprinciples calculation of the structure and dielectric properties of Bi2Ti2O7," Physical Review B, 82  155103 (2010). 112. R. S eshadri, "Lone pairs in insulating pyrochlores: Ice rules and highk behavior," Solid State Sciences, 8 [3 4] 25966 (2006). 113. D. P. Shoemaker, R. Seshadri, A. L. Hector, A. Llobet, T. Proffen, and C. J. Fennie, "Atomic displacements in the charge i ce pyrochlore Bi2Ti2O6O' studied by neutron total scattering," Physical Review B, 81  144113 (2010). 114. A. L. Hector and S. B. Wiggin, "Synthesis and structural study of stoichiometric Bi2Ti2O7 pyrochlore," Journal of Solid State Chemistry, 177 [ 1] 13945 (2004). 115. I. Radosavljevic, J. S. O. Evans, and A. W. Sleight, "Synthesis and structure of pyrochloretype bismuth titanate," Journal of Solid State Chemistry, 136  6366 (1998). 116. A. Pramanick, J. L. Jones, S. Omar, and J. C. Nin o, "Lattice parameter determination using a curved positionsensitive detector in reflection geometry and application to Smx/2Ndx/2Ce1xO2 delta ceramics," J Appl Crystallogr 42 49095 (2009). 117. S. Shimada, K. Kodaira, and T. Matsushita, "Crys tal Growth of Bismuth Titanates and Titanium Oxide from Melts in System Bi2O3V2O5TiO2," J. Cryst Growth, 41  31720 (1977). 118. V. Kahlenberg and H. Bohm, "X Ray Diffraction Investigation of the Defect Pyrochlore Bi1.61Zn0.18Ti1.94V0.06O6.62," J. Alloy Compd 223  14246 (1995). 119. V. Kahlenberg and H. Bohm, "On the Existence of a PyrochloreType Phase in the System Bi2O3TiO2," Cryst Res Technol 30  23741 (1995).
125 120. C. H. Hervoches and P. Lightfoot, "A variabletemperature powder neutron diffraction study of ferroelectric Bi4Ti3O12," Chemistry of Materials, 11  335964 (1999). 121. C. Bohren and D. Huffman, "Absorption and Scattering of Light by Small Particles. Wiley : New York, (1998). 122. Y. Sun and Y. Xia, "G old and silver nanoparticles: A class of chromophores with colors tunable in the range from 400 to 750 nm," Analyst, 128  68691 (2003). 123. M. Toyoda, Y. Hamaji, K. Tomono, and D. A. Payne, "Synthesis and characterization of Bi4Ti3O12 thin films by sol gel processing," Japanese Journal of Applied Physics, 32 [9S] 415862 (1993). 124. T. Nakamura, R. Muhammet, M. Shimizu, and T. Shiosaki, "Preparation of C Axis Oriented Bi4Ti3O12 Thin Films by Metalorganic Chemical Vapor Deposition," Japanese Journal of Applied Physics, 32 408688 (1993). 125. Q. D. Zhou, B. J. Kennedy, and C. J. Howard, "Structural studies of the ferroelectric phase transition in Bi4Ti3O12," Chemistry of Materials, 15  502528 (2003). 126. M. K. Jeon, S. I. Woo, Y. I. Kim, and S. H. Nahm, "Structure Analysis of Ferroelectric Bi4Ti3O12 by Using X ray Powder Diffraction," J. Korean Phys Soc 45  124043 (2004). 127. O. Sakata, T. Watanabe, and H. Funakubo, "Application of synchrotronbased reciprocal space mapping at a fixed angular position to identification of crystal symmetry of Bi4Ti3O12 epitaxial thin films," J. Appl Crystallogr 44 385 91 (2011). 128. A. Shrinagar, A. Garg, R. Prasad, and S. Auluck, "Phase stability in ferroelectric bismuth titanate: a first principles study," Acta Crystallogr A, 64 368 75 (2008). 129. S. J. Henderson, O. Shebanova, A. L. Hector, P. F. McMillan, and M. T. Weller, "Structural Variations in PyrochloreStructured Bi2Hf2O7, Bi2Ti2O7 and Bi2Hf2xTixO7 Solid Solutions as a Function of Composition and Temperature by Neutron and X ray Diffraction and Raman Spectroscopy," Chemistry of Materials, 19  171222 (2007). 130. J. Cagnon, S. Stemmer, D. S. Boesch, N. H. Finstrom, S. Z. Nergiz, and S. P. Keane, "Microstructur e and dielectric properties of pyrochlore Bi2Ti2O7 thin films," Journal of Applied Physics, 102  044102 (2007).
126 131. L. W. Fu, H. Wang, S. X. Shang, X. L. Wang, and P. M. Xu, "Preparation and Characterization of Bi2Ti2O7 ThinFilms Grown by Metalorganic Chemical Vapor Deposition," J. Cryst Growth, 139 [3 4] 31922 (1994). 132. T. Kidchob, L. Malfatti, D. Marongiu, S. Enzo, and P. Innocenzi, "Sol Gel Processing of Bi2Ti2O7 and Bi2Ti4O11 Films with Photocatalytic Activity," J. Am Ceram Soc 93 [ 9] 2897902 (2010). 133. M. Suzuki, T. Watanabe, T. Takenaka, and H. Funakubo, "MOCVD growth of epitaxial pyrochlore Bi2Ti2O7 thin film," Journal of the European Ceramic Society, 26  215559 (2006). 134. J. C. Wang, C. H. Yang, G. D. Hu, W. B. Wu, L. Cheng, and X. M. Chen, "The influence of crystallization route on the Cedoped Bi2Ti2O7 thin film by metal organic decomposition," J. Alloy Compd 494 [1 2] 28588 (2010). 135. S. W. Wang, W. Lu, N. Li, Z. F. Li, H. Wang, M. Wang, and X. C. Shen, "Insulating properties of rapid thermally processed Bi2Ti2O7 thin films by a chemical solution decomposition technique," Mater Res Bull. 37  169197 (2002). 136. S. W. Wang, H. Wang, S. X. Shang, J. Huang, Z. Wang, and M. Wang, "PZT thin films prepared by chemical solution decomposition using a Bi2Ti2O7 buffer layer," J. Cryst Growth, 217  38892 (2000). 137. S. W. Wang, H. Wang, X. M. Wu, S. X. Shang, M. Wang, Z. F. Li, and W. Lu, "Rapid thermal processing of Bi2Ti2O7 thin films g rown by chemical solution decomposition," J. Cryst Growth, 224 [3 4] 32326 (2001). 138. X. M. Wu, S. W. Wang, H. Wang, Z. Wang, S. X. Shang, and M. Wang, "Preparation and characterization of Bi2Ti2O7 thin films by chemical solution deposition technique," Thin Solid Films, 370 [1 2] 3032 (2000). 139. S. Das, A. K. Mukhopadhyay, S. Datta, and D. Basu, "Prospects of microwave processing: An overview," Bull. Mater. Sci, 32  1 13 (2009). 140. S. Ramesh, C. Y. Tan, S. B. Bhaduri, and W. D. Teng, "Rapid densification of nanocrystalline hydroxyapatite for biomedical applications," Ceramics International, 33  136367 (2007). 141. Y. Hou, T. Lin, Z. M. Huang, G. S. Wang, Z. G. Hu, J. H. Chu, X. H. Xu, and M. Wang, "Electrical and optical proper ties of Bi2Ti2O7 thin films prepared by metalorganic decomposition method," Applied Physics Letters, 85  1214 16 (2004).
127 142. J. F. Scott, "Ferroelectrics go bananas," Journal of Physics: Condensed Matter, 20  021001 (2008). 143. I. Levin, T. G. Amos, J. C. Nino, T. A. Vanderah, C. A. Randall, and M. T. Lanagan, "Structural study of an unusual cubic pyrochlore Bi1.5Zn0.92Nb1.5O6.92," Journal of Solid State Chemistry, 168  6975 (2002). 144. R. S. Roth, T. A. Vanderah, P. Bordet, I. E. Grey, W. G. Mumme, L. Cai, and J. C. Nino, "Pyrochlore formation, phase relations, and properties in the CaO TiO2(Nb,Ta)2O5 systems," Journal of Solid State Chemistry, 181  40614 (2008). 145. T. A. Vanderah, M. W. Lufaso, A. U. Adler, I. Levin, J. C. Nino, V. Provenzano, and P. K. Schenck, "Subsolidus phase equilibria and properties in the system Bi2O3:Mn2O3+/x:Nb2O5," Journal of Solid State Chemistry, 179  346777 (2006). 146. H. Wang, S. Kamba, H. L. Du, M. L. Zhang, C. T. Chia, S. Velj ko, S. Denisov, F. Kadlec, J. Petzelt, and X. Yao, "Microwave dielectric relaxation in cubic bismuth based pyrochlores containing titanium," Journal of Applied Physics, 100  (2006). 147. X. Wu, S. W. Wang, H. Wang, Z. Wang, S. X. Shang, and M. Wang, "Preparation and characterization of Bi2Ti2O7 thin films by chemical solution deposition technique," Thin Solid Films, 370 [1 2] 3032 (2000). 148. L. Cai, S. Denev, V. Gopalan, and J. C. Nino, "Phase Transition in WeberiteType Gd3NbO7," J. Am Ce ram Soc 93  87580 (2010). 149. L. Cai, "Fundamental Structure Dielectric Property Relationships in FluoriteRelated Ceramics," pp. 267. in Department of Materials Science and Engineering, Ph.D. University of Florida, Gainesville, 2010. 150. I. P. Swainson and M. T. Dove, "Low Frequency Floppy Modes in BetaCristobalite," Physical Review Letters, 71  19396 (1993). 151. S. A. Wells, M. T. Dove, M. G. Tucker, and K. Trachenko, "Real space rigidunit mode analysis of dynamic disorder in quartz, cristobalite and amorphous silica," J. Phys Condens Mat 14  464557 (2002). 152. J. C. Nino, M. T. Lanagan, C. A. Randall, and S. Kamba, "Correlation between infrared phonon modes and dielectric relaxation in Bi2O3ZnO Nb2O5 cubic pyrochlor e," Applied Physics Letters, 81  440406 (2002). 153. P. C. Dunn, "Gateways Into Electronics, pp. 658. John Wiley & Sons: New York, (2000).
128 154. A. K. Singh, "Electronic Devices And Integrated Circuits, pp. 608. PrenticeHall of India Private Limited: New Delhi, (2008). 155. J. W. Lu and S. Stemmer, "Low loss, tunable bismuth zinc niobate films deposited by rf magnetron sputtering," Applied Physics Letters, 83  241113 (2003). 156. E. Barsoukov and J. R. Macdonald, "Impedance spectr oscopy : theory, experiment, and applications. Wiley Interscience: Hoboken, N.J., (2005). 157. P. J. W. Debye, "Polar molecules. The Chemical Catalog Company, inc.: New York, (1929). 158. K. Cole, "Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics," J. Chem. Phys., 9  341 (1941). 159. D. Davidson, "Dielectric Relaxation in Glycerol, Propylene Glycol, and nPropanol," J. Chem. Phys., 19  1484 (1951). 160. S. Havriliak and S. Negami, "A complex plane representation of dielectric and mechanical relaxation processes in some polymers," Polymer, 8 [ 4 ] 161205, appendix 0610 (1967). 161. R. Gerhardt, "Impedance and dielectric spectroscopy revisited: Distinguishing localized relaxation from longrange conductivi ty," J. Phys Chem Solids, 55  1491506 (1994). 162. W. Cao and R. Gerhardt, "Calculation of various relaxation times and conductivity for a single dielectric relaxation process," Solid State Ionics, 42 [3 4] 21321 (1990). 163. C. T. Lin, P. Lin, and F. QuitianPuello, "Interfacial chemistry of a singlestep phosphate/paint system," Ind. Eng Chem Res 32  81825 (1993). 164. C. Ang, Z. Yu, H. J. Youn, C. A. Randall, A. S. Bhalla, L. E. Cross, J. Nino, and M. Lanagan, "Low temperatur e dielectric relaxation in the pyrochlore (Bi3/4Zn1/4)2(Zn1/4Ta3/4)2O7 compound," Applied Physics Letters, 80  480709 (2002). 165. G. S. Babu, M. Valant, K. Page, A. Llobet, T. Kolodiazhnyi, and A. K. Axelsson, "New (Bi1.88Fe0.12)(Fe1.42Te0.58)O6.87 Pyrochlore with Spin Glass Transition," Chemistry of Materials, 23  261925 (2011). 166. H. Du and X. Yao, "Dielectric relaxation characteristics of bismuth zinc niobate pyrochlores containing titanium," Physica B: Condensed Matter, 324 [1 4] 12 1 26 (2002).
129 167. L. Wucherer, "Synthesis and Characterization of Electroceramic Foams for 33 Piezoelectric Composites," pp. 84. in Department of Materials Science and Engineering, M.S. University of Florida, Gainesville, 2008. 168. L. Wucherer, J. C. Nino, F. Basoli, and E. Traversa, "Synthesis and Characterization of BaTiO3Based Foams with a Controlled Microstructure," International Journal of Applied Ceramic Technology, 6  65160 (2009). 169. T. Hirata and T. Yokokawa, "VariableTemperature X ray Diffraction of the Ferroelectric Transition in Bi4Ti3O12," Solid State Commun 104  67377 (1997). 170. Y. I. Kim, M. K. Jeon, and S. I. Woo, "Structural study of Bi4Ti3O12 using neutron powder diffraction data," J. Mater Sci. Lett 22 [2 3] 165557 (2003). 171. Y. M. Kan, P. L. Wang, Y. X. Li, Y. B. Cheng, and D. S. Yan, "Low temperature sintering of Bi4Ti3O12 derived from a coprecipitation method," Mater Lett 56  91014 (2002). 172. T. Thongtem and S. Thongtem, "Characteriz ation of Bi4Ti3O12 powder prepared by the citrate and oxalate coprecipitation processes," Ceramics International, 30  146370 (2004). 173. Y. L. Du, M. S. Zhang, Q. Chen, and Z. Yin, "Investigation of sizedriven phase transition in bismuth titanate nanocrystals by Raman spectroscopy," Applied Physics A: Materials Science & Processing, 76  1099103 (2003). 174. M.S. Zhang, Z. Yin, Q. Chen, W. Zhang, and W. Chen, "Study of structural and photoluminescent properties in barium titanate nanocrystals synthesized by hydrothermal process," Solid State Commun 119  65963 (2001). 175. C.J. Xiao, Z.H. Chi, F.Y. Li, S.M. Feng, C.Q. Jin, X.H. Wang, X.Y. Deng, and L.T. Li, "Ferroelectric behaviour of 30 nm BaTiO3 ceramics prepared by high pressur e assisted sintering," Chinese Physics, 16  312528 (2007). 176. Z. Zhao, V. Buscaglia, M. Viviani, M. T. Buscaglia, L. Mitoseriu, A. Testino, M. Nygren, M. Johnsson, and P. Nanni, "Grainsize effects on the ferroelectric behavior of dense nanocrys talline BaTiO3 ceramics," Physical Review B, 70  (2004). 177. B. D. Cullity and S. R. Stock, "Elements of Xray Diffraction," pp. 664 3rd ed. Prentice Hall, Inc.: Upper Saddle River, (2001). 178. Z. Lazarevic, B. D. Stojanovic, and J. A. Varela, "An approach to analyzing synthesis, structure and properties of bismuth titanate ceramics," Sci. Sinter 37  199216 (2005).
130 BIOGRAPHICAL SKETCH Roberto Esquivel was born in Mexico City in 1985. He graduated from the Universidad de las Amricas, P uebla, Mexico in 2008 with his B.S. in chemical engineering. He started his professional career in Puebla with the consulting company Ingesa Consultores S.A. de C.V. helping on the design of water treatment plants and supervising water well drilling. A y ear later he accepted an employment offer from Kimberly Clark and worked as a process engineer in Apizaco, Tlaxcala. One year later he decided to look for a higher academic degree in the United States in order to have a better education. The Materials Sc ience and Engineering Department of the University of Florida kept his attention and in spring 2010, he met Dr Juan Claudio Nino who gave Esquivel the opportunity to join his research group in Gainesville, Florida. On December of 2011 Roberto received hi s masters degree after doing research on ceramics for energy applications.