By SOUMITRA SULEKAR - University of...
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DEFECT DYNAMICS IN DOPED CERIA ELECTROLYTES By SOUMITRA SULEKAR A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2017
Transcript of By SOUMITRA SULEKAR - University of...
DEFECT DYNAMICS IN DOPED CERIA ELECTROLYTES
By
SOUMITRA SULEKAR
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2017
© 2017 Soumitra Sulekar
To my family and friends
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ACKNOWLEDGMENTS
First and foremost, I would like to express my gratitude towards my advisor, Dr.
Juan C. Nino. Without his guidance and constant support, this work and my Ph.D. would
not have been possible. Throughout my time here at the University of Florida, he has
been a constant source of inspiration. At times, when I felt lost, it was he who pointed me
in the right direction and gave me motivation. His constant high standards and demand
for improvement has given me a vision for perfection, and a work ethic which I will carry
for the rest of my life. I thank Professor Perry, Professor Andrew, Professor Sigmund,
and Professor Weaver, for being on my advisory committee and giving me their time and
advice.
At the Nino Research group, I have had the privilege and pleasure of working with
some of the smartest, brightest and diverse group people I have known. I would like to
thank all the past and present members of the group for their company, the stimulating
discussions, and all the constructive criticism. I specially thank Mehrad Mehr and Ji Kim
for their contribution to the reducing atmosphere sintering work, Paul Johns for always
pushing me to grow better BiI3 single crystals, and Hiraku Maruyama and Mariia
Stozhkova for their help with the MARMOT simulation validation work. I would also like
to thank visiting researchers Andres Romero and Marcia Meireles for their help with the
impedance testing of thin films under bias. Finally, I would like to thank undergraduate
students Ji Kim, Tatiana Konstantis, Elisa Cristino, and Ryan Russell for the many hours
they have spent helping with experiments.
I would also like to thank Andres Trucco at the Nanoscale Research Facility at the
University of Florida for his help with the electron probe micro-analysis work presented in
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this dissertation. Without the help and support of all these collaborators and group
members, this work would not be possible.
I thank my family whose support and guidance has made me who I am today. I
also thank my friends at the group, especially Mehrad and Ji, for putting up with me. I
thank my roommates and friends amongst the Indian student community here who helped
me make my time in Gainesville more enjoyable.
A part of this dissertation is based upon work supported by the National Science
Foundation Grant No. DMR-1207293. Any opinions, findings, conclusions or
recommendations expressed in this publication are those of the author and do not
necessarily reflect the views of the National Science Foundation.
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TABLE OF CONTENTS page
ACKNOWLEDGMENTS .................................................................................................. 4
LIST OF FIGURES .......................................................................................................... 9
LIST OF TABLES .......................................................................................................... 16
ABSTRACT ................................................................................................................... 18
CHAPTER
1 INTRODUCTION .................................................................................................... 21
1.1 Statement of Problem and Motivation ............................................................. 21 1.2 Scientific Approach ......................................................................................... 23
1.3 Organization of Dissertation ............................................................................ 24 1.4 Contributions to the Field ................................................................................ 26
2 BACKGROUND AND MOTIVATION ...................................................................... 28
2.1 Fuel Cells ........................................................................................................ 28 2.2 Solid Oxide Fuel Cells ..................................................................................... 30
2.3 Gadolinia Doped Ceria .................................................................................... 33
2.4 Ionic Conductivity ............................................................................................ 35
2.4.1 Dopant Concentration and Defect Associates ..................................... 36 2.4.2 Dopant and Impurity Segregation ........................................................ 40
2.5 Impedance Spectroscopy ............................................................................... 47
3 EXPERIMENTAL PROCEDURES .......................................................................... 53
3.1 Sample Preparation ........................................................................................ 53
3.1.1 Bulk Samples ....................................................................................... 53 3.1.2 Sintering under Reducing Atmosphere ................................................ 56 3.1.3 Thin Film Fabrication ........................................................................... 56
3.2 Profilometry ..................................................................................................... 58
3.3 X-Ray Diffraction ............................................................................................. 59 3.4 Microstructural Characterization ..................................................................... 60 3.5 AC Impedance Spectroscopy ......................................................................... 62
3.6 DC I-V Measurement ...................................................................................... 66
4 PROTOCOL FOR IMPEDANCE TESTING AND DATA ANALYSIS ....................... 68
4.1 Common Mistakes .......................................................................................... 69 4.2 Best Practices ................................................................................................. 70
4.2.1 Definitions of Parameters .................................................................... 71
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4.2.2 Selection and Fitting of Appropriate Equivalent Circuit ........................ 74
4.2.3 Starting Values for Fitting .................................................................... 79 4.2.4 Quality of Fit ........................................................................................ 81
5 IMPEDANCE RESULTS FOR THIN FILM AND BULK SAMPLES ......................... 83
5.1 Thin Film Samples .......................................................................................... 83 5.2 Bulk Samples .................................................................................................. 88
6 EFFECT OF A DC BIAS ON IMPEDANCE RESULTS ........................................... 90
6.1 Background ..................................................................................................... 90
6.2 Bias Effect on GDC Thin Films ....................................................................... 99
6.3 Characteristic Steps in Nyquist Plots under Bias .......................................... 101
6.4 Fitting and Analysis ....................................................................................... 107 6.5 Mechanism ................................................................................................... 113
6.5.1 Low Bias ............................................................................................ 113 6.5.2 Medium Bias ...................................................................................... 116
6.5.3 High Bias ........................................................................................... 118
7 DOPANT SEGREGATION AND SINTERING UNDER REDUCING ATMOSPHERE ..................................................................................................... 121
7.1 Segregation and Defect Associates .............................................................. 121 7.2 Fast firing and Microwave Sintering .............................................................. 122
7.3 Sintering under Reducing Atmosphere ......................................................... 125
7.4 Electron Probe Micro-Analysis ...................................................................... 127
7.5 Conductivity Measurements .......................................................................... 136
8 SUMMARY AND FUTURE WORK ....................................................................... 141
8.1 Summary ...................................................................................................... 141 8.1.1 Protocol for Impedance Data Analysis ............................................... 141 8.1.2 Impedance and Effect of DC Bias ...................................................... 141
8.1.3 Sintering under Reducing Atmosphere .............................................. 143 8.2 Future Work .................................................................................................. 144
8.2.1 Effect of DC Bias ............................................................................... 144 8.2.2 Sintering under Reducing Atmosphere .............................................. 144
A IMPEDANCE DATA FITTING WITH ZVIEW ......................................................... 147
B DIELECTRIC POLARIZATION FUNCTIONS ....................................................... 151
C THERMALLY STIMULATED DEPOLARIZATION CURRENT .............................. 153
D COLOSSAL PERMITTIVITY IN BARIUM STRONTIUM TITANATE ..................... 159
D.1 Introduction .................................................................................................. 159
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D.2 Experimental procedure ............................................................................... 161
D.2.1 Fabrication ........................................................................................ 161 D.2.2 Characterization ................................................................................ 161
D.3 Results and Discussion ................................................................................ 162 D.3.1 Dielectric Spectroscopy..................................................................... 163 D.3.2 Impedance Spectroscopy.................................................................. 166 D.3.3 Polarization mechanisms .................................................................. 168
D.3.3.1 Debye Model ...................................................................... 169
D.3.3.2. Universal Dielectric Response Model ............................... 170 D.3.3.2 Thermal Hopping Polaron Model ....................................... 173
D.3.4 Internal Barrier Layer Capacitor ........................................................ 176 D.3.5 Variable Range and Nearest Neighbor Hopping ............................... 179
D.4 Summary ...................................................................................................... 185
E I DON’T KNOW WHAT THIS MEANS BUT… ....................................................... 186
LIST OF REFERENCES ............................................................................................. 189
BIOGRAPHICAL SKETCH .......................................................................................... 204
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LIST OF FIGURES Figure page 2-1 Schematic of a solid oxide fuel cell. .................................................................... 31
2-2 Ionic conductivity for different fluorite oxide electrolytes with respect to temperature adapted from B.C.H. Steele. .......................................................... 32
2-3 Cubic fluorite unit cell of cerium oxide. ............................................................... 34
2-4 Doping and oxygen vacancy jump in acceptor doped ceria. ............................... 34
2-5 Grain ionic conductivity of different doped ceria electrolyte materials as a function of temperature after Gerhardt-Anderson and Nowick. .......................... 37
2-6 Conductivity as a function of dopant concentration in the (CeO2)1-x(Sm2O3)x system at different temperatures after Yahiro et al. ............................................ 38
2-7 Arrhenius plots for the grain ionic conductivity of Sm/Nd co-doped ceria as shown by Omar et al. .......................................................................................... 41
2-8 Transmission electron micrographs showing segregation of siliceous phases. .. 42
2-9 Schematic of a grain boundary in an oxide ion conductor. ................................. 43
2-10 Atom probe tomography data for a grain boundary in 10 mol% Nd doped ceria adapted from Diercks et al. ........................................................................ 46
2-11 Impedance response in a 3D perspective plots for a 10 mol% gadolinia doped ceria sample. ........................................................................................... 49
2-12 Schematic of complex impedance plot obtained using EIS for a polycrystalline electroded sample adapted from Omar. ...................................... 51
3-1 Flow chart for conventional solid state processing of ceramic materials (left) and that for the co-precipitation route (right). ...................................................... 55
3-2 Examples of green and sintered pellets of cerium oxide. ................................... 56
3-3 The magnetron sputtering setup at Universidad del Valle in Cali, Colombia used for deposition of GDC thin films. ................................................................ 57
3-4 Schematic of a gadolinia doped ceria thin film on top of a Pt/TiO2/SiO2/Si substrate with Pt electrodes on top adapted from R. Kasse. .............................. 58
3-5 Image of a gadolinia doped ceria thin film (left) and optical micrograph showing the surface of the film with the circular Pt top electrodes (right). .......... 58
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3-6 Graph showing an example of the profilometry data for a GDC thin film under study. .................................................................................................................. 59
3-7 X-ray diffraction pattern for 10 mol% gadolinia doped ceria sintered sample. .... 60
3-8 A scanning electron micrograph showing the microstructure on the surface of a 10 mol% GDC bulk pellet................................................................................. 61
3-9 A scanning electron micrograph of the surface of a GDC thin film. .................... 61
3-10 Scanning electron micrographs of the edge of a gadolinia doped ceria film showing the different layers. ............................................................................... 62
3-11 The setup for impedance spectroscopy of bulk samples at different temperatures. ..................................................................................................... 62
3-12 The reactor setup used for EIS (left) and an example of an electroded bulk sample (right). ..................................................................................................... 63
3-13 Probe station setup for electrical testing of thin films. ......................................... 66
3-14 Schematic of probe contact adapted from R. Kasse (left) and a picture of the same (right) for across plane impedance measurement ..................................... 67
4-1 Flow diagram for the measurement and characterization of material electrode system adapted from Macdonald. ....................................................................... 68
4-2 Numbering systems for quadrants in the coordinate system used throughout this work. ............................................................................................................ 71
4-3 Schematic showing shift in complex impedance plots and the respective equivalent circuits. .............................................................................................. 75
4-4 Example data set showing the difference between linear and log representations. .................................................................................................. 76
4-5 Sample data showing a complex impedance plot and the frequency explicit plot of theta for the same data which enhances the data in the blue box. .......... 77
4-6 Imaginary part of the impedance as a function of frequency with α as a parameter. Figure adapted from Orazem et al.................................................... 80
4-7 Schematic of log Y’ against log ω with a low frequency plateau and a high frequency dispersion adapted from Abram et al. ................................................ 80
4-8 An example of residuals for the real and imaginary parts of impedance. ........... 82
5-1 Nyquist plot showing impedance data for a 267 nm 10GDC thin film at different temperatures. ....................................................................................... 83
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5-2 Complex impedance plot showing the data for a 10 GDC 267 nm thin film at 130ºC along with the equivalent circuit used to fit the data. ................................ 84
5-3 A plot of log Y’ versus log ω for estimating the values of CPE-P and CPE-T for the 10 GDC bulk sample. .............................................................................. 85
5-4 Arrhenius plot showing the grain ionic conductivity for a single electrode on the 10GDC thin film accounting for error propagation. ....................................... 85
5-5 Arrhenius plot showing the average grain ionic conductivity for multiple electrodes on a 10GDC thin film with 95% confidence bands. ........................... 87
5-6 Complex impedance data for a 10GDC bulk sample at different temperatures. ..................................................................................................... 88
5-7 Arrhenius plot showing the average grain ionic conductivity of the 10GDC samples at different temperatures. ..................................................................... 89
6-1 Schematic representation of the oxygen vacancy concentration and the space charge layer without any applied bias (left) and with an applied bias (right), as proposed by Guo and Waser. ............................................................. 90
6-2 Impedance complex plane plots for 8 mol% YSZ at different temperatures and DC bias values as shown by Masó and West where 10 V 43 V-cm-1. ....... 92
6-3 Oxygen concentration in the region adjacent to the Pt cathode interface in a TiOx single crystal after degradation under 15 V bias determined using EELS as shown by and adapted from Moballegh and Dickey. ..................................... 93
6-4 A schematic showing concentration of vacancies in an Fe-SrTiO3 film at high and low frequencies and the corresponding Nyquist plot showing an inductive loop, adapted from Taibl et al. ............................................................................ 94
6-5 The brick layer model for a polycrystalline ceramic with the paths for conduction as shown by and adapted from Macdonald. ..................................... 96
6-6 Schematic showing ionic and electronic conduction paths for a polycrystalline ceramic assumed to have a brick layer model as proposed by and adapted from Guo and Waser. ......................................................................................... 96
6-7 Inversion layer with high electron concentration near the grain boundary adapted from Guo et al. ...................................................................................... 97
6-8 Complex impedance plot showing the effect of a low DC bias on 10 mol% doped gadolinia doped ceria bulk specimen at 200ºC. ....................................... 98
6-9 Nyquist plot showing the example of a DC bias effect on a 267 nm thick 10 mol% GDC film at 120⁰C. ................................................................................... 99
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6-10 Nyquist plots showing the effect of a DC bias on a 267 nm thick 10 mol% GDC film at different temperatures. .................................................................. 100
6-11 A very detailed plot showing every step in the evolution of a 10 mol% gadolinia doped ceria thin film under bias at 130⁰C. ......................................... 101
6-12 Nyquist plot showing characteristic steps in the evolution of the impedance response of a 10GDC thin film under increasing bias. ...................................... 102
6-13 Frequency explicit plots showing the magnitude of impedance |Z| and the
phase angle as a function of different DC bias values for a 10 GDC, 267 nm thin film. ...................................................................................................... 103
6-14 Frequency explicit plots showing the real and imaginary parts of impedance (Z’ and -Z” respectively) as a function of applied DC bias for a 10GDC 267 nm thin film. ...................................................................................................... 105
6-15 Frequency explicit plot showing the real permittivity for different bias values for a 10GDC 267 nm film. ................................................................................. 106
6-16 Proposed equivalent circuit based on the visual analysis of the data in different formalisms and similar data presented in literature. ........................... 108
6-17 Equivalent circuits used to fit impedance data shown in Figure 6-12 along with the respective bias values. ........................................................................ 109
6-18 Plot showing the values of R1 (grain resistance) for different applied bias, obtained using equivalent circuit fitting of impedance data for a 10GDC 267 nm film at 130ºC. .............................................................................................. 111
6-19 Plot showing the values of R2 (grain boundary resistance) for different applied bias, obtained using equivalent circuit fitting of impedance data for a 10GDC 267 nm film at 130ºC. .......................................................................... 112
6-20 Plot showing the values of R3 (representing electronic conduction) for different applied bias, obtained using equivalent circuit fitting of impedance data for a 10GDC 267 nm film at 130ºC. .......................................................... 112
6-21 Plot showing the values of L (inductance) for different applied bias, obtained using equivalent circuit fitting of impedance data for a 10GDC 267 nm film at 130ºC. ............................................................................................................... 113
6-22 Schematic Brouwer diagram for acceptor doped ceria adapted from Eufinger et al. .................................................................................................................. 114
6-23 Schematic of a gadolinia doped ceria sample under low bias. ......................... 115
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6-24 Leakage current as a function of time and different applied DC voltages for a 10GDC 267 nm thin film measured at 120ºC. ................................................... 115
6-25 Schematic showing phenomena during impedance testing under medium bias in gadolinia doped ceria. ........................................................................... 117
6-26 Schematic band diagrams showing the cathode and anode interface under bias. .................................................................................................................. 117
6-27 Schematic showing phenomena during impedance testing under high bias in gadolinia doped ceria. ...................................................................................... 119
6-28 DC I-V measurement and complex impedance with matching resistances for a 10GDC 267 nm film at 130ºC under 2.1 V bias and oscillation voltage of 300 mV. ............................................................................................................ 120
7-1 A sub-surface triple grain junction in Sm/Nd doped ceria obtained using focused ion beam. EDS line scans were conducted across this junction (Performed by Bruce Peacock at Medtronic Inc.). ............................................ 123
7-2 EDS line scans across a sub-surface triple grain junction in a Sm/Nd doped ceria sample sintered conventionally. Sm segregation is observed (Performed by Bruce Peacock at Medtronic Inc.). ............................................ 124
7-3 EDS line scans across the surface of a Sm/Nd doped ceria sample sintered in a microwave. Both Sm and Nd are relatively uniformly distributed (Performed by Bruce Peacock at Medtronic Inc.). ............................................ 124
7-4 Schematic of dopant and vacancy distribution at grain boundaries for a sample sintered in air (left) and for one sintered in H2 and re-oxidized (right). . 126
7-5 Appearance of a 10GDC control pellet sintered at 1600⁰C for 10 hours (left) and one sintered under 4%H2-N2 at 1100⁰C for 20 hours (right). ..................... 127
7-6 WDS spectra from the LPET (top) and LLIF (bottom) detectors used to characterize Ce and Gd distribution using EPMA, shown here for a GDC conventional sample after sintering. ................................................................. 128
7-7 BSE image for 10GDC control sample. ............................................................ 129
7-8 EPMA area scan for Gd Lβ peak, for 10 GDC control sample. ......................... 130
7-9 EPMA area scan for Ce Lα peak, for 10 GDC control sample........................... 131
7-10 EPMA area scan for O Kα peak, for 10 GDC control sample. ........................... 131
7-11 Line scans of O, Gd and Ce concentration across a representative grain boundary in the 10GDC control sample. ........................................................... 132
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7-12 BSE image for 10 GDC sample sintered under 4%H2-N2 at 1100⁰C for 20 hours followed by re-oxidation at 900⁰C for 24 hours. ...................................... 133
7-13 EPMA area scan for Gd Lβ peak, for 10 GDC sample sintered under 4%H2-N2 at 1100⁰C for 20 hours followed by re-oxidation at 900⁰C for 24 hours. ...... 133
7-14 EPMA area scan for Ce Lα peak, for 10 GDC sample sintered under 4%H2-N2 at 1100⁰C for 20 hours followed by re-oxidation at 900⁰C for 24 hours. ........... 134
7-15 EPMA area scan for O Kα peak, for 10 GDC sample sintered under 4%H2-N2 at 1100⁰C for 20 hours followed by re-oxidation at 900⁰C for 24 hours. ........... 134
7-16 Line scans of O, Gd and Ce concentration across a representative grain boundary in the 10GDC sample sintered under 4%H2-N2 at 1100⁰C for 20 hours followed by re-oxidation at 900⁰C for 24 hours. ...................................... 135
7-17 Normalized Nyquist plot showing the comparison between the 10GDC control and H2 sintered samples measure at 300⁰C in air................................. 137
7-18 Arrhenius type plot of grain conductivity with respect to temperature for the 10GDC control and H2 sintered samples. ......................................................... 138
7-19 Arrhenius type plot of total conductivity with respect to temperature for the 10GDC control and H2 sintered samples. ......................................................... 139
B-1 Schematic representing the complex plane plot for permittivity according to Debye theory (left) and the effect of the exponents and . .......................... 152
C-1 Schematic diagram of polarization and heating profile for TSDC measurement. ................................................................................................... 153
C-2 A schematic of an expected TSDC spectrum for doped ceria. ......................... 154
C-3 TSDC results showing the current density with respect to temperature for a 10 mol% gadolinia doped ceria sample with different polarizing temperatures and heating rates. ............................................................................................. 155
C-4 Arrhenius plots of the current density with respect to temperature for the two peaks in Figure C-3. ......................................................................................... 157
C-5 Plot showing the effect of polarizing temperature on TSDC peak intensity for a 10 mol% gadolinia doped ceria sample. ........................................................ 157
C-6 Plot showing the effect of different dopants and different dopant concentrations on TSDC peak intensity. ........................................................... 158
D-1 Variation of the real part of relative permittivity and losses (tan) as a function
of frequency for the Ba1–xSrxTiO3– nanoceramics at 300K............................... 163
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D-2 Variation of the real part of the relative permittivity and losses (tan) as a function of temperature measured at 1 kHz for the Ba1–xSrxTiO3–δ nanoceramics. .................................................................................................. 165
D-3 Impedance complex plane plots and Z′′/M′′ spectroscopic plots at 170 K, and capacitance data at 150 and 170 K for Ba0.8Sr0.2TiO3−δ (a, c and e) and Ba0.2Sr0.8TiO3−δ (b, d and f) nanoceramics. ....................................................... 167
D-4 Variation of the real parts (a) and (c) and the imaginary parts (b) and (d) of permittivity as a function of temperature and at different frequencies for Ba0.8Sr0.2TiO3–δ and Ba0.2Sr0.8TiO3–δ nanoceramics. ......................................... 168
D-5 Temperature dependence of relaxation frequency for Ba0.8Sr0.2TiO3–δ and Ba0.2Sr0.8TiO3–δ nanoceramics. ......................................................................... 170
D-6 Variation of the real part (a) and (c) and the imaginary part (b) and (d) of permittivity as a function of frequency and at different temperatures for Ba0.8Sr0.2TiO3–δ and Ba0.2Sr0.8TiO3–δ nanoceramics. ......................................... 171
D-7 fr vs. f plot in log–log scales for (a) Ba0.8Sr0.2TiO3–δ and (b)
Ba0.2Sr0.8TiO3–δ dense nanoceramics at different temperatures (40–300K). ..... 172
D-8 Activation energy values extracted from the hopping polarons model for Ba0.8Sr0.2TiO3–δ and Ba0.2Sr0.8TiO3–δ nanoceramics. ......................................... 174
D-9 BST permittivity data fitted with IBLC model ..................................................... 177
D-10 Frequency dependence of the conductivity at different temperatures for (a) Ba0.8Sr0.2TiO3-δ and (b) Ba0.2Sr0.8TiO3−δ. ........................................................... 180
D-11 NNH model applied to BST nanoceramics. ...................................................... 182
D-12 Temperature dependence of DC bulk conductivity of Ba0.8Sr0.2TiO3−δ nanoceramic sample. ....................................................................................... 183
E-1 M” peak position frequency as a function of temperature and bias. .................. 188
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LIST OF TABLES Table page 3-1 Sources of experimental errors involved in the impedance measurement and
fitting for a GDC sample. .................................................................................... 64
6-1 The values for equivalent circuit parameters obtained after fitting of the impedance data shown in figure. ...................................................................... 110
D-1 Dielectric properties of the Ba1–xSrxTiO3–δ nanoceramics. ................................ 164
D-2 Calculated activation energies and s values for BST compounds using three different analytical models. ............................................................................... 176
D-3 Fitting parameters using the IBLC model. ........................................................ 178
D-4 Fitting parameters using the UDR model. ......................................................... 181
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LIST OF ABBREVIATIONS
10GDC 10 mol% Gadolinia Doped Ceria
AC Alternating Current
At% Atomic Percent
BSE Backscattered Electron
CPE Constant Phase Element
DC Direct Current
EDS Energy Dispersive Spectroscopy
EIS Electrochemical Impedance Spectroscopy
EPMA Electron Probe Micro-analysis
GDC Gadolinia Doped Ceria
IT-SOFC Intermediate Temperature Solid Oxide Fuel Cell
I-V Current-Voltage
Mol% Mole Percent
SEM Scanning Electron Microscopy
Sm/NdDC Samarium Neodymium Co-doped Ceria
SOFC Solid Oxide Fuel Cell
SPS Spark Plasma Sintering
WDS Wavelength Dispersive Spectroscopy
Wt% Weight Percent
XRD X-ray Diffraction
YSZ Yttria Stabilized Zirconia
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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
DEFECT DYNAMICS IN DOPED CERIA ELECTROLYTES
By
Soumitra Sulekar
May 2017
Chair: Juan C. Nino Major: Materials Science and Engineering
Gadolinia doped ceria is a well-established material use as electrolyte in
intermediate temperature solid oxide fuel cells. Trivalent acceptor dopants such as
gadolinium substitute the Ce4+ ions and lead to ionic conductivity in ceria by creating
oxygen vacancies, which act as charge carriers. Numerous doping schemes have been
studied to elicit the highest possible ionic conductivity from these materials in the
intermediate temperature range. During the sintering step of processing, these dopants,
the accompanying oxygen vacancies and any impurities tend to segregate to the high
energy grain boundaries. This high concentration of dopants at grain boundaries and
triple points, and dopant-vacancy interaction makes these regions highly resistive. Many
changes have been proposed to the conventional solid state processing route used to
fabricate these materials. Techniques like co-precipitation of starting powders, fast firing
achieved by various means, and grain size control have been successfully shown to
improve the ionic conductivity. In this work, the effect of additional new stimuli on the
defect equilibria, defect interactions and the behavior of grain boundaries was studied.
The phenomenon of mixed ionic and electronic conductivity in gadolinia doped
ceria thin films produced using magnetron sputtering under the effect of an applied DC
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bias was studied. Electrochemical impedance spectroscopy was used to measure the
change in impedance under applied biases of ~ 4 - 20 kV/mm and an alternating voltage
of 300 mV at temperatures between 25⁰C and 350⁰C. The application of a DC bias
produces a reversible decrease in both the grain and grain boundary resistances for GDC.
Many acceptor-doped dielectrics have been shown to exhibit similar mixed ionic and
electronic conductivity under the application of a DC bias. New features become visible
in the Nyquist plots with increasing bias, drastically changing the material behavior.
Particularly interesting is the appearance of inductive loops in the low frequency regime,
at very high bias values, rarely seen for this kind of a system. Here this novel behavior
was analyzed by fitting the data using equivalent circuits to understand the underlying
mechanisms at play. Through this work, it was established that the change in behavior
is attributed to electronic conduction through grain boundaries parallel to the direction of
the applied field. As a prelude to this process a protocol for better and more accurate
analysis of impedance data was established. Different impedance formalisms and
different ways of visualizing data were studied and were shown to provide more
information about the different phenomena at play, helped in identifying circuit elements
for equivalent circuits, and in general better analyzing the data.
Additionally, a novel method was proposed to arrest the segregation of dopants,
and improve the ionic conductivity. Fast firing techniques commonly used towards such
ends, exploit the kinetics of diffusion to solve this issue. In this approach, however, the
energetics of the system are also modified, where gadolinia doped ceria is sintered under
a reducing atmosphere. The reducing atmosphere changes the valence of Ce4+ to Ce3+,
thus reducing the tendency of the Gd3+ dopant ions to segregate. On re-oxidation, the
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material returns to the previous state, except without any dopant segregation. The ionic
conductivity improves as the resistance across the grain boundary drops, when compared
with conventionally processed samples. Using electron probe micro-analysis, the
distribution of dopants was characterized. It was shown that the dopants do not segregate
in samples sintered under a reducing atmosphere and subsequently re-oxidized. A
comparison of conductivity determined using impedance spectroscopy showed an
improvement in conductivity as compared to the conventional processing route.
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CHAPTER 1 INTRODUCTION
1. 1.1. Statement of Problem and Motivation
The world population as of March 2017 has been estimated at above 7.4 billion
people. It has grown from about 6 billion in the year 2000 at a growth rate of almost 1.1%
per year.1 Such a high population growth rate combined with increased per capita energy
consumption, has led to a continuous increase in demand for energy.2 Fossil fuels are a
major source of energy for the world. Given the non-renewable nature and shortage of
fossil fuels, pollution caused by their extraction and use, and global warming and its
effects on the environment and human habitat, there is a need to move towards more
sustainable and clean energy systems such as solar cells, wind mills, fuel cells, and
batteries. It also calls for sources which are portable and more adaptable to distributed
systems. Fuel cells in particular show significant promise just in terms of the number of
their potential applications. They can be used to power anything from utility power
stations to cars, to consumer electronic devices.3,4 Amongst the various fuel cell
technologies under development, solid oxide fuel cells (SOFCs) are particularly attractive
given their scalability, modularity, durability, portability, and fuel flexibility.5 Various
materials have been considered over the years as possible candidates for use in solid
oxide fuel cells6 with companies like Bloom Energy and Redox Power Systems currently
using yttria stabilized zirconia and ceria based Sm/Nd co-doped systems respectively.
Amongst the different components and materials, this work focusses on the ionically
conducting electrolyte part of the SOFCs. The material of choice for this study is gadolinia
doped ceria (GDC) owing to its relatively high ionic conductivity and thermal stability at
intermediate temperatures (400⁰C - 600⁰C).7
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High operating temperatures of SOFCs reduces their portability, and places
constraints on the materials that can be used for various components of the fuel cell stack,
eventually making them unviable economically. The ionic conductivity and stability of the
electrolyte material are the main limiting factors for low temperature SOFC use. In order
for them to be economically viable and be able to be used in portable applications,
materials that show good intermediate temperature ionic conductivity and stability are
called for. Rare earth doped ceria compounds have been shown to be some of the best
for SOFC electrolyte application.7,8 Various processing techniques have been proposed
for improving the ionic conductivity of doped ceria compounds in the intermediate
temperature range. Ionic defects are what makes ionic conductivity in doped ceria
possible in the first place. Any changes in the defect type, distribution, concentration, and
mobility has the ability to drastically improve or degrade the electrical properties of the
material. It is hence essential to understand and exploit these defects for better
performance, and tailor the processing and operational conditions accordingly. Over the
past decade, a lot of work has been done studying and optimizing various factors like the
nature of defects, their interactions and the effect of different processing parameters and
stimuli on these defects and the resulting change in ionic conductivity. This optimization
has led to several commercial applications as mentioned before.
With the basics of structure-property-processing relationships for fuel cell materials
in place, this work takes the luxury to look at newer interesting phenomena, which could
possibly open up other avenues and applications for the material, such as for mixed ionic
and electronic conducting applications or for splitting of water. The effect of a DC bias
and processing under reducing atmospheres and their effect on the distribution and
23
mobility of defects present in gadolinia doped ceria are the goal of this body of work. For
this purpose, both bulk and thin film forms of gadolinia doped ceria are studied with the
focus being on complex impedance, it being the electrical property of choice, which helps
determine different conduction mechanisms.9
1.2. Scientific Approach
The focus of this dissertation is to understand the various defect mechanisms in
rare earth doped ceria electrolytes in solid oxide fuel cells, with the goal of better tailoring
them for intermediate temperature use.
A detailed background about solid oxide fuel cells, the materials used, and the
mechanisms responsible for ionic conductivity is first provided. The principal method
used to measure ionic conductivity in ceramic materials is electrochemical impedance
spectroscopy. The analysis of data using equivalent circuits and assigning physical
models based on the different circuit elements however can be very challenging.
Towards this end, the first part of the study looks at existing analysis techniques and
compiles a protocol for impedance data fitting and analysis to give more reproducible and
accurate results. This protocol is used throughout this body of work for the analysis of
both bulk and thin film impedance data.
The various factors affecting the intermediate temperature ionic conductivity in
doped ceria materials are also discussed. Despite the extensive work done in this area,10–
14 there is still little understanding about the underlying mechanisms and the defects
responsible for the conductivity, the role of grains and grain boundaries, and their
behavior under various stimuli. To study this, the present work looks at the effect of a DC
bias on the complex impedance behavior in doped ceria materials. Novel mechanisms
24
are proposed to explain the interesting new effects being observed. To better understand
the effects being observed here, DC I-V measurements performed at different sweep
speeds are used to better inform the interpretation and analysis of impedance data.
The second part of this dissertation looks at improving ionic conductivity by
proposing new processing routes. Dopant and impurity segregation at grain boundaries
and triple points during fabrication leads to increased resistance. Various processing
techniques have been used to address this, and improve the ionic conductivity of doped
ceria in the intermediate temperature range. These techniques however, focus only on
exploiting the kinetics of the sintering process. This work exploits the thermodynamics of
defects along with the kinetics, by sintering doped ceria samples under a reducing
atmosphere, as compared to conventional techniques. The hypothesis is that the
reducing atmosphere prevents segregation of dopants, and leads to improvement in ionic
conductivity. The question is investigated using electron probe micro analysis and
impedance spectroscopy.
1.3. Organization of Dissertation
Chapter 2 provides the background information about solid oxide fuel cells, the
materials of interest, and their relevant structural information. It discusses the existing
knowledge about the underlying mechanisms for ionic conduction, the role played by
defects, and the effect of various factors like dopant concentration, impurities, and
processing conditions. In addition, the technique of electrochemical impedance
spectroscopy is also introduced, given that a bulk of this work is based on this technique.
25
Chapter 3 details the experimental procedures used to fabricate and process the
thin film and bulk ceria samples. It also covers the characterization techniques, both
electrical and microstructural, used to analyze the samples.
Chapter 4 introduces a protocol to be followed for impedance data analysis. This
protocol was developed to reduce the ambiguity in complex impedance data analysis and
get better, more accurate results.
Chapter 5 shows typical impedance results for bulk and thin film doped ceria
samples as a function of temperature, and applies the protocol described in chapter 4 to
this data, to obtain ionic conductivity results.
Chapter 6 focuses on the effect of a DC bias on the conductivity. It looks at the
changes in complex impedance plots with increasing bias and looks at possible
underlying defect mechanisms that can explain the observed unique behavior. Unlike
prior studies which focused mainly on bulk materials, the focus here is on thin films. Bias
values higher than those ever studied before are used here. DC current-voltage
measurements are used as a way of verifying the complex impedance results.
Chapter 7 discusses the effect of different processing routes on dopant and
impurity segregation and the resultant effect on ionic conductivity. It introduces sintering
under a reducing atmosphere as a means of reducing dopant segregation and improving
ionic conductivity.
Chapter 8 presents a summary of the main findings of this work and envisaged
future work.
In addition to the content above, extra information and other work performed by
the author is included in the appendices. Appendix A details the steps for analysis of
26
impedance data. Appendix B discusses the different types of dielectric functions.
Appendix C discusses thermally stimulated depolarization current as a way of studying
defect associates. Appendix D presents work on colossal permittivity in barium strontium
titanate ceramics where impedance spectroscopy was used to distinguish between
different relaxation mechanisms. Lastly Appendix E lists interesting phenomena and
trends observed by the author during the course of his work, which still remain
unexplained.
1.4. Contributions to the Field
As a part of this work, a protocol for impedance data analysis was established
using best practices in existing literature and those developed in-house. Despite the
technique of impedance spectroscopy being widely used, there is a lot of ambiguity and
room for making errors in analysis of impedance data. There are numerous instances of
erroneous interpretation of such impedance data in the literature, where inconsistencies
are simply glossed over. This protocol provides a template for better identification of
equivalent circuits, explains the significance of various parameters used in fitting, gives
more accurate values for individual circuit parameters, and helps assess the quality of the
fit.
The study of complex impedance demonstrates the possibility of a novel
mechanism in response to the bias. The study looks at thin film samples of gadolinia
doped ceria at different temperatures and bias values, which has not been looked at
before in literature. The values of bias applied (as high as 112 kV/cm) are higher than
those in any study before.15,16 The unique features observed in the complex impedance
plots, indicate the injection of electrons and by extension the possibility of a change in
27
defect equilibria under bias. The trends are similar to a shift in the Brouwer diagram
showing charge carrier concentration for different oxygen partial pressures.15
The work on processing, for the first time successfully demonstrates that sintering
under a reducing atmosphere and subsequent re-oxidation, reduces the segregation of
dopants compared to conventional sintering techniques. The more even distribution of
dopants across the grain boundaries leads to a decrease in resistance across grain
boundaries, and an overall improvement in ionic conductivity. The conductivity increases
by an order of magnitude in the samples sintered under reducing atmospheres as
compared to conventionally sintered samples. This opens up a new avenue for ceramic
material processing, where dopant segregation is not desired.
Although the work performed here focusses mainly on gadolinia doped ceria, it can
be easily extended to not only other dopants for ceria, but also to other oxide ceramic
compounds where a controlled introduction of dopants and resulting defects results in
favorable electrical properties.
28
CHAPTER 2 BACKGROUND AND MOTIVATION
2. 2.1. Fuel Cells
In today’s energy-intensive world, we are in the need of a non-polluting, high
efficiency power source. Fuel cells are a promising alternative to the current energy
systems as they directly convert chemical energy to electrical energy without any
intermediate steps. Unlike traditional fossil fuel based systems such as internal
combustion engines, fuel cells do not have any moving parts. This reduces energy losses
and makes them inherently more efficient. Instead of converting chemical energy to
mechanical and then on to electrical, fuel cells produce electrical energy by an
electrochemical reaction between a fuel (usually hydrogen or gaseous hydrocarbons) with
an oxidant (air or oxygen). Heat is produced as a by-product. Fuel cells efficiencies can
go up to 60% and even up to 85-90% if the heat produced as a byproduct is also used for
other applications, as has been shown by Siemens Westinghouse in hybrid gas turbine
fuel cell systems.17 Although fuel cells still use fossil fuels as a source of energy, they
are attractive because of their reduced greenhouse gas emissions, depending on the
source of the hydrogen fuel. Compared to other renewable sources of energy, like solar
power, fuel cells have lower capital cost and higher energy density.18 They can also be
combined with existing and legacy energy systems to improve their efficiencies, and
reduce energy wastage. They can also be used in combination with renewables, for
example, to store surplus solar energy in the form of hydrogen obtained using electrolysis
of later, and later using it as a fuel for fuel cells. All these factors place fuel cell
technologies at a unique position in the energy landscape, which warrants for their further
development.
29
Fuel cells are made up of a cathode, an anode and an oxygen ion conducting
electrolyte sandwiched in between the two. Fuel cells are usually classified on the basis
of the electrolyte used. The different types of fuel cells that have been developed are
polymer electrolyte membrane fuel cells (PEMFC), direct methanol fuel cells (DMFC),
alkaline fuel cells (AFC), phosphoric acid fuel cells (PAFC), molten carbonate fuel cells
(MCFC), and solid oxide fuel cells (SOFC). There are also reversible fuel cells, which
produce electricity as described above, but can also be fed electricity to split water by
electrolysis, enabling energy storage in the form of hydrogen. Depending on the type of
electrolyte, the mechanism with which the fuel cell produces electricity changes.19 Each
different mechanism has its own issues and hence each design presents unique
challenges. For example, PEMFCs and PAFCs need expensive catalysts and are
sensitive to impurities, AFCs have a liquid electrolyte which is difficult to handle, MCFCs
and SOFCs require high operating temperatures, amongst other challenges.20
Depending on the various electrochemical reactions taking place in the cell and the
constraints presented by the electrolyte, electrode and ancillary materials, the operating
conditions like temperature, fuel, atmosphere and catalysts are selected. Hence, each
type of fuel cell has an ideal set of operating conditions which decides its applications in
the real world. The applications are usually divided into the broad areas of stationary and
portable power generation. They have been used in a wide range of applications like the
space program, unmanned aerial vehicles, in submarines, for fuel cell vehicles, and even
residential power units. Since the term ‘fuel cell’ was first established by Charles Langer
and Ludwig Mond in 1889,21 fuel cells have come a long way in terms of their
applications,22 where portable fuel cells have seen a rapid rate of growth in the recent
30
past and are moving towards wider commercialization, with several companies like Bloom
energy, FuelCell Energy, Doosan Fuel Cell America, Watt Fuel Cell, Altergy, Redox
Power Systems, and many more all over the world setting up commercial operations.
Amongst the different kinds of fuel cells, solid oxide fuel cells are the focus of this study.
2.2. Solid Oxide Fuel Cells
Solid oxide fuel cells, amongst the different types fuel cells, have a distinct
advantage for auxiliary power, electric utility and distributed generation.19 They do not
require the use of expensive catalysts, the excess heat generated by SOFCs can be used
for secondary operations, they are fuel flexible, are easy to handle, and have a long life
expectancy, with all the components being solid.5 SOFCs have shown efficiencies higher
than 65% with possibilities for co-generation.23
Figure 2-15 shows the structure of a fuel cell and the associated reactions at the
cathode and anode are given by equations (2-1) and (2-2) respectively. The fuel is fed
to the anode and the oxidant is fed to a cathode. The electrode-electrolyte interface
provides sites for the electrochemical reactions, whereas the electrolyte serves a diffusion
medium for ions, with the electrons generated by the reactions usually flowing in the
external circuit.4
Two main types of solid oxide fuel cell designs have been looked at in literature,
planar and tubular.24 The schematic shown in Figure 2-1 is an example of a planar fuel
cell stack. Various planar stack designs with different flow patterns have been proposed,
but they have issues with sealing and temperature gradients. Tubular and micro-tubular
designs offer the advantage of seal less design. Planar cells however have higher power
densities compared to tubular designs and they can be manufactured with simpler lower
31
cost manufacturing techniques, making them popular. Planar cells can be anode
supported, cathode supported, electrolyte supported, or even externally supported using
the interconnect (shown here) or a porous substrate. The kind of cell design dictates the
fabrication processes used and also places constraints on the materials used.
Figure 2-1. Schematic of a solid oxide fuel cell.5
Anode: e2OHOH 2
2
2 (2-1)
Cathode: 2
2 Oe2O2
1
(2-2)
The materials for solid oxide fuel cells are selected based on the design of the cell,
the required electrical properties, chemical and structural stability, and matching thermal
expansion coefficients. An ideal cathode, for example, must have mixed ionic and
electronic conductivity, high porosity, and a thermal expansion coefficient matching that
of the electrolyte. SrxLa1-xMnO3 (LSM) is a perovskite material that is commonly used
and well- studied.25–28 Similarly, the anode material should be porous, should provide
32
catalytic sites for electrochemical reactions, have low ionic conductivity, and be
chemically and thermally compatible with other components. Ni-cermet anode materials
are amongst the most commonly used.29–33
Figure 2-2. Ionic conductivity for different fluorite oxide electrolytes with respect to temperature adapted from B.C.H. Steele.34
The third component of a solid oxide fuel cell, and the focus of this study is the
electrolyte. The electrolyte must be dense to be able to separate the fuel and the oxidizer.
It must possess high ionic conductivity at the desired operating temperature for easy
migration of oxide ions. It should be an electronic insulator, and should maintain its
properties over a wide range of oxygen partial pressures, since the pO2 could vary by as
much as an order of magnitude between the anode and the cathode.14 Various materials
like yttria stabilized zirconia (YSZ), rare earth doped ceria, strontium/magnesium doped
33
lanthanum gallate, and bismuth oxide based electrolytes have been considered and
studied for use as electrolyte materials for solid oxide fuel cells.35 Amongst these, YSZ
has been used extensively for high temperature (~1000⁰C) fuel cells.6,7,35,36 The goal
here, however, is to obtain enhanced ionic conductivity in the intermediate temperature
range (400⁰C to 800⁰C). Figure 2-2 shows the ionic conductivities of some SOFC
electrolyte materials.7 Bi2O3 based compounds have the highest ionic conductivity in the
intermediate temperature range. However, they are not thermally stable as they undergo
an order-disorder transition around 600⁰C, making them unsuitable. The next candidate
in the graph is gadolinia doped ceria (GDC). It is more stable than the Bi2O3 and has
higher ionic conductivity than YSZ. Hence, GDC is the material of interest for this study.
Gadolinia doped ceria has been studied extensively for ionically conducting electrolytes
and mixed ionic-electronic conducting applications and even for applications in bilayer
electrolytes.13,29,32,37–39
2.3. Gadolinia Doped Ceria
Pure stoichiometric ceria has a cubic fluorite structure as shown in Figure 2-3 with
an associated lattice parameter of 5.411 Å and space group m3Fm . Each unit cell
consists of Ce4+ ions at the corners and the face centers of the cubic cell (Wyckoff position
4a), whereas the O2- ions are located within the tetrahedral voids (Wyckoff position 8c).
Ce4+ ions have 8-fold co-ordination and the O2- ions have 4-fold co-ordination.
However, cerium oxide by itself is not a good ionic conductor. For ceria to conduct
ions, it has to be doped with rare earth acceptor dopants. Substitution of Ce4+ by trivalent
dopant cations D3+ (Gd3+ in this case) causes the formation oxygen vacancies to maintain
electro-neutrality as denoted by the Kröger-Vink notation in equation (2-3).
34
O
x
OCe2CeO32 VO3D2OD (2-3)
The vacancies created as a result of the doping allow for the discrete hopping of
oxygen ions from one tetrahedral site to another, giving ionic conduction as shown in
Figure 2-4.
Figure 2-3. Cubic fluorite unit cell of cerium oxide.
Figure 2-4.Doping and oxygen vacancy jump in acceptor doped ceria.
35
2.4. Ionic Conductivity
The hopping of these vacancies is a thermally activated process. The electrical
conductivity (σ ) due to hopping is governed by the Arrhenius relation as denoted in
equation (2-4) where oσ is a pre-exponential factor, T is the temperature in Kelvin and
aE is the activation energy.
kT
EexpT a
o (2-4)
In a detailed form, this equation can be written as (2-5).14
kT
Hexp
k
SexpaNV
k
qT mm
o
2
oo
2
v (2-5)
Here, oN is the number of oxygen sites per unit volume, OV is the fraction of free
mobile oxygen vacancies, vq is the charge of an oxygen vacancy, a is the jump distance,
𝜗𝑜 is the lattice vibration frequency and mHΔ and mSΔ are the enthalpy and entropy
involved in oxygen diffusion.
The conductivity also depends on the oxygen partial pressure (pO2). Since
diffusion of vacancies is driven by a concentration difference between the cathode and
anode, a higher concentration difference, and a high subsequent partial pressure
difference is essential for good ionic conductivity. With air at the cathode side, the lower
the partial pressure of oxygen at the anode, the better. However, under such reducing
conditions at the anode, Ce4+ gets reduced and the following defect reaction takes place,
promoting n-type conductivity and electron hopping paths in the electrolyte material. A
similar electrochemical reaction can be induced by means of an electric field. The effect
of a DC electric field has been discussed at length in Chapter 6.
36
Ce2O
x
O
x
Ce eC2O2
1VOCe
(2-6)
eonion
ioniont
(2-7)
It is important to know exactly what fraction of the conductivity of a material is ionic.
The ionic contribution to conductivity is measured using the ionic transference number,
which is the ratio of ionic conductivity to total conductivity of a sample as shown in
equation (2-7) where ion is the ionic contribution to conductivity and eon is the electronic
contribution. A material must have a high ionic transference number and a low electronic
transference number for SOFC electrolyte application. A detailed study on the
thermochemical behavior of the undoped cerium-oxygen system has been performed by
Chueh and Haile.40 With increasing temperature, this reduction of ceria is further
exacerbated, producing more electrons. This is one more reason that makes it imperative
that the electrolytes for SOFCs be developed to operate at lower temperatures. On a
side note, this redox behavior of ceria also makes it a possible for candidate for reversible
fuel cells using solar thermochemical hydrogen production.40,41
2.4.1. Dopant Concentration and Defect Associates
Various authors have found that rare earth elements like gadolinium (Gd),
neodymium (Nd) and samarium (Sm) are the best dopants for doped ceria. 42,43 Co-
doping strategies have also been studied as a means to improve the ionic
conductivity.11,17,18 Exhaustive work has been performed on the effect of various dopants
on the ionic conductivity of doped ceria.13,46 When using different dopants, the ionic
conductivity of ceria and zirconia based ceramics has been shown to be affected by the
radius mismatch between the host and dopant cations.13,47 The higher the mismatch, the
37
lower the ionic conductivity. A larger ionic mismatch leads to a higher strain in the lattice,
and the diffusion of vacancies is affected by the elastic strain energy of the lattice.48 With
higher dopant concentration, it would be expected that the grain ionic conductivity of the
material also increases. However, this is not always the case, and usually a maximum in
the ionic conductivity is observed at a certain concentration, above which the conductivity
starts to fall again, as has been shown for both ceria and zirconia based systems.42,47,49
Figure 2-6 shows a typical dopant concentration versus ionic conductivity behavior as
reported by Yahiro et al.49
Figure 2-5. Grain ionic conductivity of different doped ceria electrolyte materials as a function of temperature after Gerhardt-Anderson and Nowick.38
38
Figure 2-6. Conductivity as a function of dopant concentration in the (CeO2)1-
x(Sm2O3)x system at different temperatures after Yahiro et al.45
In the distorted cubic structure of doped ceria, the vacancies tend to interact with
the dopant cations creating defect associates. Such associates were first reported in
ceria by Nowick and coworkers.46,50,51 The interactions could be electrostatic due to
charge differences on the defects or elastic interactions due to local stresses. These
defect associates bind the oxygen vacancies, effectively reducing the number of movable
vacancies. At lower concentrations, only dimers OA VD can be assumed to be
formed, as they have been shown to be more likely to occur.52 As the concentration
increases, higher order associates such as trimers xAOA DVD and so on are
formed.53,54 The existence of defect associates can be proven using positron annihilation
39
spectroscopy as has been shown by Guo and Wang.55 Defect associates can also be
studied using the technique of thermally stimulated depolarization current as has been
shown for multiple materials and has been detailed in Appendix A.50,56 The presence of
defect associates leads to a higher required temperature for ionic conduction as the
activation energy for oxygen diffusion now consists of the energy required to break apart
the defect associates i.e. the association enthalpy ( aHΔ ) in addition to the migration
enthalpy ( mHΔ ).57,58 It has been found that the migration enthalpy ( mHΔ ) for oxygen
vacancies is independent of the dopant concentration.59
ama HHE (2-8)
Figure 2-7 shows the Arrhenius plot of the grain ionic conductivity for Sm/Nd co-
doped ceria for different dopant concentrations.42 In the dilute regime, the conductivity
increases with an increase in the dopant concentration. This has been explained on the
basis of limited defect interactions, and thus the ionic conductivity depends mainly on the
vacancy concentration. However, with an increase in dopant concentrations, more and
more oxygen vacancies are bound in complexes, effectively leading to a drop in the ionic
conductivity in the lower intermediate temperature range (< 450ᵒC). The grain ionic
conductivity plots for higher dopant concentrations all converge at a point around 475ᵒC
above which the behavior is flipped and the conductivity again starts to increase with
increasing dopant concentration. Such behavior is commonly said to be following the
Meyer – Neldel rule and this trend has been reported for doped ceria materials by various
researchers.14,58,60,61 The transition temperature T corresponds to an order – disorder
transition in the ionically conducive material, at which point the conductivity is
independent of dopant concentration and is a function only of the activation energy. It is
40
the transition between the stage where most carriers are bound to the stage where most
carriers are free.58 In many cases, a change in the slope of the conductivity plot is also
observed at this transition temperature, sometimes sharp, sometimes gradual. Above
this temperature, the activation energy drops, indicating that the defect associates have
been dissociated and the vacancies are free.48,52,62,63 The activation energy in this high
temperature regime can be considered to be the migration enthalpy of the particular
compound (assuming completely free vacancies), and the difference between the low and
high temperature migration energies can be considered the association enthalpy. The
values obtained from such measurements have been shown to agree well with calculated
values.47
Similar trends have been reported in other oxide ceramic systems, where the
conductivity decreases with increasing dopant concentration at high dopant
concentrations.64,65 Defect associates clearly play a major role, and in order to better
utilize doped ceria materials, it is essential that these defect complexes be better
understood and the effect of processing on reducing the formation of defect associates
be studied.
2.4.2. Dopant and Impurity Segregation
Many studies over the years have come to the conclusion that a major culprit for
lowering the ionic conductivity in oxide ceramics are the grain boundaries14,55,66,67. The
high resistance or the blocking nature of grain boundaries compared to the bulk has been
ascribed to various reasons like, amorphous phases, impurities, misorientation at the
grain boundaries and segregation of dopants. Due to their high energy, any anomalies
present in the crystal structure, tend to accumulate at the grain boundaries during
sintering. It is these anomalies that lead to blocking grain boundaries.
41
Figure 2-7. Arrhenius plots for the grain ionic conductivity of Sm/Nd co-doped ceria as shown by Omar et al.42
Following are a few examples amongst various studies that look at dopant and
impurity segregation:
The conventional sintering process used for most ceramics, makes use of milling
and mixing operations to get the desired particle size, and to add dopants and other
additives. However, these steps tend to introduce siliceous impurities from the milling
media into the ceramic powder. During sintering, it has been shown that these impurities
segregate at the grain boundaries and at triple point junctions showing up as a glassy
phase shown in Figure 2-8.14,68 Gerhardt and Nowick have shown that the high grain
42
boundary resistance is due to the siliceous impurities and it virtually disappears when
nearly silicon-free materials are used. Even a few hundred ppm impurities has been
shown increase the resistivity in gadolinia doped ceria by up to 100 times.66 One possible
solution to reduce the amount of impurities in the samples can be the use of alternative
processing routes like co-precipitation which avoid milling.
Figure 2-8. Transmission electron micrographs showing segregation of siliceous phases. (A) Continuous layer of a siliceous phase in the grain boundary of 10 mol% GDC and (B) glassy phase formed at triple grain junction in 5 mol% Sm/NdDC as observed by using transmission electron microscopy.14
Contrastingly, in high purity undoped ceria samples, Guo et al.55,69 have shown
that an amorphous siliceous phase is formed only at a few triple grain junctions and the
grain boundaries are relatively clean. Despite the blocking effect from the siliceous phase
being expected to be negligible, it was found that there is still a difference of about two
orders of magnitude between the grain boundary and bulk conductivity. There has been
a lot more focus on a mechanism involving space charge layers and the Mott-Schottky
model at grain boundaries, to try and explain their blocking nature. Such blocking grain
boundaries are observed not only in doped materials or materials with impurities, but even
43
in so called pure materials. The segregation of defects at grain boundaries, creates a
space charge layer, forming a sort of Schottky-type potential barrier for conduction at the
interface.67,70
Figure 2-9. Schematic of a grain boundary in an oxide ion conductor. Schottky barrier grain boundary as is commonly hypothesized (top) and a model based on recent elemental distribution studies (bottom). Segregation of dopant is not necessary for explaining the top model.
This model has a positively charged grain boundary core, with a high concentration
of oxygen vacancies, which is compensated by oppositely charged defects, usually
44
acceptor ions, and a depletion of oxygen vacancies in the adjacent region. This model
proposes a high concentration of vacancies at the grain boundaries and a depletion
region around the grain boundaries, with a lower concentration of vacancies and a higher
concentration of dopant ions. Figure 2-9 (top) shows a schematic of the space-charge
grain boundary model for doped zirconia and ceria as proposed by Guo and Waser.69
This model although widely accepted, has not been proven experimentally with actual
concentration data for different species at grain boundaries. In fact, as is discussed later
in this chapter, high resolution elemental distribution studies paint a slightly different
picture which is depicted in the bottom part of Figure 2-9.
Considerable amount of work has been done to explain the origin of blocking grain
boundaries in oxide ceramics. For SrTiO3, it has been theoretically shown that grain
boundaries in oxide ceramics are intrinsically non-stoichiometric and non-stoichiometry
in the grain boundary cores is energetically favorable in undoped SrTiO3.71 Electron
energy loss spectra (EELS) at atomic resolution have established the coordination of the
species at an atomic resolution, and provided evidence of the non-stoichiometry.71,72 It
has also been shown using atomic resolution analysis that 5 36⁰ [001] tilt grain
boundaries in SrTiO3 have incomplete oxygen octahedra, which act as effective oxygen
vacancies at the grain boundaries.73 This also suggests that the extent of accumulation
changes with the type of grain boundary. It has been established that the existence of
vacancies at grain boundaries is an intrinsic behavior that is seen even in undoped
materials. The grain boundary core has been proposed to have a positive charge due to
this accumulation of vacancies. In the case of doped materials, for example in Mn doped
SrTiO3, the dopant also tends to accumulate at the grain boundaries. During sintering,
45
the mobility of the acceptor dopant ions is high enough for them to segregate at the grain
boundaries due to the high positive charge of the grain boundary core and to relieve
elastic strain.69 The dopant segregation itself however, was said to be insufficient to
charge balance the vacancies at grain boundaries.74 The positive core charge was thus
hypothesized to cause a depletion of oxygen vacancies in the regions surrounding the
grain boundary along with the accumulation of the dopants. Similar results have been
shown for yttria stabilized zirconia (YSZ) where the vacancy accumulation at grain
boundaries has been attributed to a structure relaxation.75 Z-contrast STEM imaging and
atomic resolution EELS of well-defined grain boundaries have been performed for both
yttria stabilized zirconia and gadolinia doped ceria.74 In YSZ, it was found that the yttrium
segregates at the grain boundaries. EELS profiles across grain boundaries in GDC have
shown similar results, where the Gd/Ce ratio increases at the grain boundary whereas
the O/Ce ratio decreases. It was also found that about 70% of the Ce4+ changes to Ce3+
at the grain boundaries, leading to an excess of electrons near the grain boundaries.
This proposed Schottky barrier model for the grain boundaries has been found to
satisfactorily explain the observed electrical properties for grain boundaries. However,
as said before, there has been no proof so far for the depletion or space-charge layer
around grain boundaries. The segregation of acceptor dopants, at grain boundaries and
triple point junctions has been looked at in much more detail recently, with the
advancement in elemental characterization techniques. For example, Li et al.76 have
shown using laser assisted atom probe tomography in gadolinia doped ceria, that there
is a segregation of dopants at the grain boundaries. However, contrary to the space
46
charge model, the Ce concentration was actually found to decrease, whereas there was
no significant change in the oxygen concentration at the grain boundary.
Figure 2-10. Atom probe tomography data for a grain boundary in 10 mol% Nd doped ceria adapted from Diercks et al.77
More recent work by Diercks et al.77 using atom probe tomography for Nd doped
ceria has shown segregation of dopants and oxygen vacancies at the grain boundaries,
accompanied by a rise in Ce at the grain boundaries, as depicted in Figure 2-10. The
change in concentrations was found to be till about 4-6 nm from the grain boundary
center, similar to that shown by Li et alError! Reference source not found..76 The co-e
nrichment of vacancies and dopants at grain boundaries was suggested to be consistent
with the theory of defect-defect interactions. The electrostatic potential at boundaries was
47
calculated using the Poisson equation by Diercks et al.77 and the results match with typical
results grain boundary potentials measured using impedance spectroscopy for GDC.
Recently, a different model has been proposed by Frechero et al. for YSZ using a
combination of experimental and simulation techniques.78 Like others, no depletion layer
of oxygen vacancies was found. The Y ions segregated at grain boundaries are not
sufficient to balance the charge of the positive vacancies. Using density functional theory,
it was shown that the two electrons accompanying the formation of each oxygen vacancy,
instead of localizing around the vacancy, go into empty electronic states in the grain
boundaries. These grain-boundary induced electronic states act as acceptors, creating
a negatively charged core and it is this negative charge which acts as a trap for vacancies
and creates a barrier for ion transport at grain boundaries. This model contrasts with
established models and needs to be further studied.
It is important to be familiar with and understand the various proposed mechanisms
responsible for blocking grain boundaries since the boundaries and surfaces play
increasingly dominant roles as device sizes reduce. This knowledge can be used to
modify processing conditions and obtain better performing materials and will be revisited
in Chapter 7.
2.5. Impedance Spectroscopy
Impedance spectroscopy (IS) is a technique that can be used to study the
dynamics of charges in solids and liquids. More particularly, electrochemical impedance
spectroscopy (EIS) is the subset of impedance spectroscopy where ionic conduction is
the dominant mechanism, is of interest here. It involves the linear electrical response of
a material to a small signal stimulus in the frequency or time domain.79 The very first
48
examples of such experiments are by Randles (1947) and Jaffe (1952). Randles studied
the kinetics of rapid electrode reactions using a capillary electrode immersed in a suitable
solution, a method called polarography.80 Jaffe studied polarization in electrolytic
solutions using a sophisticated conductance cell.81 It was Bauerle in 1969 who first dealt
with impedance spectroscopy of ionic solids and measured their conductivity accurately.82
Today it is widely used as a tool for investigating electrochemical systems. It is of
particular importance because there usually exists a direct analogy between the
impedance behavior of a material and the physical processes occurring in a material.
The most common way of measuring impedance is by applying a single frequency
current or voltage to a sample and measuring the resultant phase shift or amplitude of the
resulting current at that frequency using fast Fourier transform analysis of the response.79
When an electrical response is applied to a material, many processes take place inside
it. Some examples are transport of charge carriers, transfer of charges at interfaces,
oxidation and reduction reactions etc. All these processes are characterized by a specific
frequency, at which they respond to the stimulus, thus helping in their identification. For
the study of solid electrolyte materials for fuel cells, a few hundred mV is used as a
stimulus in a frequency range of typically 0.01 Hz to 10 MHz, depending on the equipment
used. The response is usually analyzed in terms of one of the following four formalisms:
impedance (Z*), modulus (M*), admittance (Y*) and permittivity (ε*), all complex numbers.
For most solid ionic conductors, the data is usually represented as a frequency dependent
plot of Z where the real and imaginary parts of Z are as follows.
ZiZZ (2-9)
cosZZZRe (2-10)
49
sinZZZIm (2-11)
The complex impedance is data is typically represented in the form of a Nyquist
plot (also called complex impedance plot) where the frequency is implicit. The y axis is
usually -Z” (convention for capacitive systems) and the x axis is Z’. Alternatively, it can
also be represented in the form of frequency explicit plots (also referred to as Bode plots).
The two kinds of plots and their interrelation is shown in Figure 2-11 in the form of 3D
perspective plots.
Figure 2-11. Impedance response in a 3D perspective plots for a 10 mol% gadolinia doped ceria sample. The different planes show the complex plane and frequency explicit projections of the data.
50
Since all the processes occurring at the atomic and microstructural level in an ionic
conductor have their own respective characteristic relaxation frequencies, they show up
as different arcs on the Nyquist plot. A typical example is that of an RC circuit, with a
fixed time constant. The response for such an element shows up as a semicircle in the
first quadrant, where the diameter of the semicircle is the resistance (R) the top of the
semicircle corresponds to the relaxation time (𝜏 = RC) where C is the capacitance. If a
process has a distribution of relaxation times, it leads to distortion of the semicircle, which
is very common among real materials. Similarly, any arc in the fourth quadrant usually
indicates that an inductance (L) is involved. The data obtained is thus usually fit to an
equivalent circuit consisting of various circuit elements. Based on the values of the
various circuit elements, inferences can be drawn as to the relaxation processes taking
place in the material.
Typical data for an electroded polycrystalline sample usually looks like Figure 2-12.
It usually has three sections, the first smaller arc denoting relaxation within the grain, the
second larger arc denoting the relaxation across the grain boundary, and the third large
arc representing processes at the electrode interface. Under ideal conditions, all the arcs
are semicircular and the data is usually modelled using an equivalent circuit that consists
of three pairs of parallel RC elements in series with each other. However, in many cases,
the semicircles are depressed and the capacitance C has to be replaced by a constant
phase element (CPE) in the circuit to simulate distributed time constants. The nature of
CPE will be discussed further in Chapter 4. R1 and CPE1 thus denote grain contribution,
R2 and CPE2 denote grain boundary contribution, and R3 and CPE3 denote electrode
contribution. The arcs also frequently overlap to a varying extent, depending on the
51
characteristic relaxation times of the respective mechanisms and the difference between
them. Similar relaxation times give more overlap between the arcs.
The resistance values obtained from the fitting of the impedance data can be used
to calculate the grain (from R1) and total ionic conductivity (from R1 + R2). The grain
boundary conductivity is not calculated, because it is extremely difficult to calculate the
area and thickness of all the grain boundaries in the sample. It can be calculated only in
very specific conditions by making certain assumptions and using some special models
depending on the material.79 Hence only the grain conductivity and total conductivity are
calculated in this work. The grain conductivity can be calculated by assuming the grain
boundary volume to be negligible and taking the sample volume as the grain volume.
Figure 2-12. Schematic of complex impedance plot obtained using EIS for a polycrystalline electroded sample adapted from Omar.14
52
Conductivity can be calculated from resistance using the following relation,
RA
L
(2-12)
where R is the resistance, L is the length and A is the cross-section area of the sample.
Further details about data fitting, circuit elements and the involved intricacies are
discussed in Chapter 4.
53
CHAPTER 3 EXPERIMENTAL PROCEDURES
3. 3.1. Sample Preparation
3.1.1. Bulk Samples
To prepare bulk samples, the conventional solid state processing route (shown in
Figure 3-1) was modified, where instead of the mixing and milling operations, the co-
precipitation technique was used to synthesize phase pure 10 mol% doped gadolinia
doped ceria powder. The co-precipitation technique has been shown to produce phase
pure powders with less siliceous impurities as compared to the conventional powder
processing route involving powder mixing and ball milling. It also gives a smaller particle
size which leads to better sintering kinetics. Thus high density pellets can be obtained
using lower sintering temperatures and times.14 For co-precipitation, stoichiometric
amounts of cerium nitrate hexahydrate (Ce(NO3)3.6H2O, 99.5%, Acros Organics) and
gadolinium nitrate hexahydrate (Gd(NO3)3.6H2O, 99.9%, Strem Chemicals) were mixed
in de-ionized water forming an aqueous solution. Under magnetic stirring, an ammonium
hydroxide solution (82-30 wt% NH3 solution in water, Acros Organics) was slowly added
to this solution till the pH was raised to 12. With the addition of ammonium hydroxide, a
brownish precipitate separates out. This precipitate was then washed with DI water and
dried in a drying oven at 120°C for 12 hours. The reactions are detailed in equations (3-3)
and (3-4). The conversion from Ce3+ to Ce4+ takes place in the solution at a high pH and
the corresponding reactions for Gd3+ and Ce3+ forming the respective hydroxide
precipitates are as shown in equations (3-3) and (3-4).83 In case of low pH, the conversion
from Ce3+ to Ce4+ does not take place in the solution, but instead occurs during drying
and calcination steps in the presence of air.
54
34x4xx1
pHHigh
2243333
NONH3OHGdCe
OH2
x1aqO
4
x1OHNH3NOGdxNOCex1
(3-1)
OH2
x4OGdCeOH
2
x4OGdCeOHGdCe 2
2
x4xx12
2
x4xx1x4xx1
(3-2)
422
3 OHCe4OH2aqOH12aqOaqCe4 (3-3)
3
3 OHGdaqOH3aqGd (3-4)
The dried powder was ground using a mortar and pestle. The ground powder was
calcined at 900°C for 10 hours. The calcination temperature and time used were
optimized previously.14 The calcined powder was ground again using a mortar pestle and
checked for phase purity using X-ray diffraction. For pressing into pellets, the powder
was sieved using a 212 µm sieve. It was uniaxially pressed into disc shaped pellets under
150 MPa using a Carver Inc. 3912 uniaxial press. This was followed by cold isostatic
pressing under 250 MPa using an MTI corporation CIP-50M isostatic press. For this
purpose, the pellet was sealed in a common rubber balloon, which was then evacuated
and tied up. The sample at this stage is the green pellet. This green pellet was
subsequently sintered at 1650°C for 10 hours in air with a heating and cooling rate of
200°C/hour in a box furnace (CM Furnaces 1600 Series Rapid Temp Furnace). The
density (following ASTM B962-15) and dimensions of both the green and sintered pellets
were measured. A flowchart in Figure 3-1 summarizes the co-precipitation process as
against the conventional solid state processing route.
55
Figure 3-1. Flow chart for conventional solid state processing of ceramic materials (left) and that for the co-precipitation route (right).
56
Figure 3-2. Examples of green and sintered pellets of cerium oxide.
3.1.2. Sintering under Reducing Atmosphere
To study the effect of sintering atmosphere, the pellets pressed using calcined
powder as described above were sintered in a 4% H2-N2 atmosphere. The green pellets
were sintered in a tube furnace (Barnstead Thermolyne 21100 Tube Furnace) at 1100°C
for 20 hours under ~2 SCFH flow of 4% H2-N2 mixture (Airgas Inc.). The heating and
cooling rate was maintained at 200°C/hr. The reduced GDC samples thus obtained were
subsequently re-oxidized under an O2 (Airgas Inc.) atmosphere in the tube furnace at a
much lower temperature of 900°C for 24 hours, with slow heating and cooling. The density
and dimensions of both the reduced and re-oxidized samples were measured.
3.1.3. Thin Film Fabrication
Gadolinia doped ceria (10 mol.% dopant concentration) thin films were prepared
by John Edward Ordonez and Professor Maria Elena Gomez at Universidad del Valle in
Cali, Colombia using a custom-made magnetron sputtering setup using a target made by
the powder processing route as described above. A picture of the setup is shown in
Figure 3-3. The films were deposited on a Pt/TiO2/SiO2/Si substrate maintained at a
temperature of 550°C under an atmosphere of highly pure oxygen (99.9992%) with a
57
base pressure of 1.2x10-4 mbar and a work pressure of 10-1 mbar. The Pt layer was
approximately 200 nm thick and the TiO2/SiO2 layer around 504 nm thick as received
(MTI Corporation). The deposition times were varied between 60 to 150 minutes to obtain
films with varying thicknesses from 100-500 nm. Based on the deposition times and film
thicknesses, a sputtering deposition rate of 1 nm/min was estimated. The samples were
annealed at 500°C for 2 hours to complete crystallization. Pt top electrodes 50 nm thick
were deposited using DC sputtering (Kurt J. Lesker Multi-Source RF and DC Sputter
System) with a shadow mask at room temperature to give a pattern of circular electrodes
each with a diameter of ~100 µm. Figure 3-4 shows a schematic of the films whereas
Figure 3-5 shows an example of a film.
Figure 3-3. The magnetron sputtering setup at Universidad del Valle in Cali, Colombia used for deposition of GDC thin films. Photo courtesy of John Edward Ordonez.
58
Figure 3-4. Schematic of a gadolinia doped ceria thin film on top of a Pt/TiO2/SiO2/Si substrate with Pt electrodes on top adapted from R. Kasse.45
Figure 3-5. Image of a gadolinia doped ceria thin film (left) and optical micrograph showing the surface of the film with the circular Pt top electrodes (right). Photo courtesy of author.
3.2. Profilometry
The thickness of the thin films was measured using a Tencor AS500 profilometer
equipped with a diamond tipped stylus. The film thickness was measured by calculating
the drop in height when crossing over from the film onto the bottom electrode. An
example profile for one off the GDC films is shown in Figure 3-6. Five different
measurements were taken for each film and an average value was used. This value also
59
matched satisfactorily with the values obtained using scanning electron microcopy as
described in the next section.
Figure 3-6. Graph showing an example of the profilometry data for a GDC thin film under study. The lower part is the bottom electrode whereas the top part is the GDC film, and the difference in the heights is the thickness of the film.
3.3. X-Ray Diffraction
Phase purity analysis was performed using a PANalytical X’Pert Powder diffraction
system to verify the complete dissolution of the gadolinia dopant in ceria. XRD patterns
were obtained using Cu Kα radiation with a wavelength of 0.154 nm. Figure 3-7 shows
the diffraction pattern for a sintered 10 mol% gadolinia doped ceria sample. Comparing
it with the calculated patterns for CeO2 and Gd2O3, it can be seen that the peaks are
similar to those for CeO2 and no extra peaks of Gd2O3 are present in the diffraction pattern
of the sample. This shows that the sample is phase pure as far as can be determined
based on the resolution and sensitivity of the instrument.
60
Figure 3-7. X-ray diffraction pattern for 10 mol% gadolinia doped ceria sintered sample. The calculated spectra for CeO2 and Gd2O3 are shown for comparison. Intensities are normalized with respect to the highest peak for each pattern.
3.4. Microstructural Characterization
Microstructural characterization was performed using optical microscopy and
scanning electron microscopy (SEM, Cameca SXFive). For the analysis of bulk samples,
the sintered ceramic samples were mechanically polished to a mirror finish using diamond
lapping films down to 0.1 μm on an Allied Multiprep polisher. They were cleaned using
sonication for 30 minutes. To make the grain boundaries visible, the samples were
thermally etched at 1400°C for 1 hour with rapid heating ramp rates of 600°C/h. For the
samples where dopant segregation during thermal etching is a concern, they were etched
using a 25 vol% HF solution in DI water with an exposure time of 4 minutes. The samples
were then either observed directly under an optical microscope or coated with an
approximately 10 nm thick layer of carbon for SEM and related analysis. Figure 3-8
61
shows an example microstructure observed in a bulk sample. Electron probe micro-
analysis (EPMA, Cameca SXFiveFE) was used to determine elemental distribution and
concentrations in the bulk samples (details of both instruments here). Scanning electron
microscopy was used to analyze as fabricated thin films, both on the surface and the
cross section. Figure 3-9 and Figure 3-10 show the surface and the cross section
respectively of a GDC thin film as observed using SEM.
Figure 3-8. A scanning electron micrograph showing the microstructure on the surface of a 10 mol% GDC bulk pellet.
Figure 3-9. A scanning electron micrograph of the surface of a GDC thin film.
62
Figure 3-10. Scanning electron micrographs of the edge of a gadolinia doped ceria film showing the different layers.
3.5. AC Impedance Spectroscopy
Ionic conductivity measurements were performed using electrochemical
impedance spectroscopy (EIS). A two-probe setup was used for both bulk and thin film
samples.
Figure 3-11. The setup for impedance spectroscopy of bulk samples at different temperatures. Photo courtesy of author.
63
Figure 3-12. The reactor setup used for EIS (left) and an example of an electroded bulk sample (right). Photo courtesy of author.
The bulk samples were tested using a Solartron 1260 impedance analyzer and a
custom-made quartz reactor. The flat faces of the samples were polished using SiC
polishing paper, cleaned using a sonicator and electroded using Pt paint (CL11-5349,
Heraeus). Each side was dried in a drying oven (details) for 1 hour at 120°C, following
which the samples were fired at 900°C for 1 hour. The sample faces electroded with
platinum were connected to platinum wires using silver paste. The Pt wires were in turn
tied to the gold wire electrodes, shielded with Pt coated alumina tubes, which were
connected to the Solartron 1260 using BNC connections. A Lindberg Blue M tube furnace
was used to provide high temperatures. Complex impedance measurements were
performed from 200°C to 650°C with an oscillating voltage of 500 mV in a frequency range
from 0.1 Hz to 10 MHz, and DC bias from 0 V to 10 V under an air atmosphere. Nulling
files for open and short circuit compensation were recorded for each data point before the
actual sample measurement. Data was recorded using ZPlot® software (Scribner
Associates Inc.). The setup is shown in Figure 3-11 and Figure 3-12.
The thin film samples were tested using an Agilent 4924 precision impedance
analyzer and a Micromanipulator Inc. probe station. Heating was achieved using a
64
hotplate and an infrared thermometer was used to measure the temperature. The test
setup is shown in Figure 3-13 and Figure 3-14. Across plane complex impedance
measurements were performed from 25°C to 150°C with an oscillating voltage of 300 mV
and an applied DC bias ranging from 0 V to 5 V. Open and short circuit compensation
were performed to account for the contribution of the test setup to the measurement.
The data obtained was fit to relevant equivalent circuits using Zview software
(Scribner Associates Inc.). Fitting protocols as described later in Chapter 4 were used to
obtain consistently good fits for the data. The quality of fit was quantified using the sum
of squares values and residuals between the measured and simulated data. Using the
grain and grain boundary resistance values obtained from fitting, the grain and total
conductivity of the samples were calculated using equation (2-12). The conductivity
plotted as a function of temperature follows an Arrhenius type equation shown in equation
(2-4). The slope of these plots was calculated (as is shown in Chapter 5 and 7) to give
the activation energy for conduction.
Table 3-1. Sources of experimental errors involved in the impedance measurement and fitting for a GDC sample.
Systematic errors Random errors
Thermocouple calibration
Chemical composition of samples
Impedance analyzer calibration
Processing furnace calibration
Precision of temperature measurement
Error in resistance values obtained from fitting
Standard deviation in dimension measurement
Sample shape effects
It is important to note here the possible error sources involved in the experiment
and the propagation of these errors to the final result. The experimental errors associated
65
with the testing of a sample can be divided into systematic errors and random errors.
They are listed below in Table 3-1. The systematic errors involved can be neglected as
they are not expected to change. All the experiments were performed with the same
thermocouple and impedance analyzer calibrations. Any error in the chemical
composition of the samples was avoided by using the same batch pf doped starting
powders for making samples.
Considering the sources of random errors, the temperature for the impedance
measurement system has a precision of 0.1ºC for thin films and 1ºC for bulk samples.
Equivalent circuit fitting using ZView® gives a percentage error for each of the resistances
used in the equivalent circuit. The error in dimension measurement can be calculated as
a standard deviation for multiple values of the thickness and diameter of the disc shaped
samples. Using the relationships for propagation of errors, the errors in different
quantities can be calculated as follows:
The error in cross sectional area is given by equation (3-5) where A is the area of
a circle, and D is the diameter.
AD
D
2A
(3-5)
Based on the error in resistance (R), thickness (l), and area (A), the error in
conductivity can be calculated by equation (3-6).
222
A
A
R
R
l
l
(3-6)
For plotting the Arrhenius plot of conductivity versus temperature, the error in (𝜎T)
is given by equation (3-7) and the error in 1000/T is given by equation (3-8).
66
22
avg
avg
avgavgT
TTT
(3-7)
TT
1
T
12
(3-8)
This should eventually lead to an Arrhenius plot with x and y error bars based on
all the random errors mentioned above for a sample as is shown later in Chapter
5. It is after this point that the sample to sample variation can be taken into
consideration by averaging for different samples processed and tested under the
same conditions.
Figure 3-13. Probe station setup for electrical testing of thin films. Photo courtesy of author.
3.6. DC I-V Measurement
The leakage current and current-voltage DC measurements were performed using
an Agilent 4156C precision semiconductor parameter analyzer. The probe and heating
setup was the same as described above for bulk and thin film samples. Leakage currents
for the thin films samples were measured for the same bias values and temperatures as
67
used during impedance spectroscopy. The sweep speeds for I-V measurements were
varied to match different frequencies in impedance data. The range for the I-V sweep
was set at twice the oscillation voltage amplitude (mostly set at 300 mV) for impedance
spectroscopy, with the bias value used lying in the middle of the sweep range. For
example, to do a measurement equivalent to a 300 mV oscillating voltage and 2 V bias,
the DC I-V sweep would be done from -1.7 V to 2.3 V, with the midpoint lying at 2 V. A
pulse sweep measurement mode on the system was used. To match the sweep speeds
with the frequency of different points on the complex impedance plot, the number of steps
in the sweep range, the step size, and the integration time at each point was varied. A
change in the integration time essentially modifies the pulse width at each of the voltage
points. Using the Agilent 4156C system, which has three default integration times, short,
medium and long, the short integration time mode was used which allows for the smallest
possible integration time of 80 μs. The pulse width on the other hand, which is the sum
of the pulse width and the hold time after each pulse was set to a minimum value of 5 ms.
Such settings allow sweep speeds equivalent to frequencies in the range of a ~100 Hz.
Figure 3-14. Schematic of probe contact adapted from R. Kasse45 (left) and a picture of the same (right) for across plane impedance measurement
68
CHAPTER 4 PROTOCOL FOR IMPEDANCE TESTING AND DATA ANALYSIS
4.
Figure 4-1. Flow diagram for the measurement and characterization of material electrode system adapted from Macdonald.84
Impedance spectroscopy is the primary technique used to analyze relaxation
mechanisms in ionically conducting materials as was described in Chapter 2. To be able
to extract meaningful parameters with some physical significance, in this case to
accurately determine grain and grain boundary contributions to the ionic conductivity, it is
essential that the correct equivalent circuit model be selected and properly fit. This fitting
69
is usually done based on the well-known flowchart shown in Figure 4-184. Based on the
user’s knowledge of the material-electrode system, a plausible physical model is
proposed in the form of an equivalent circuit. This model is then fit to the complex
impedance data usually using the complex non-linear least squares (CNLS) fitting
technique. The fitting nowadays is usually done automatically using commercial software
like ZView (Scribner Associates Inc.). Although this process seems simple enough in
principle, it can become extremely complicated very quickly.
4.1. Common Mistakes
If one is not careful, multiple things can go wrong while fitting of impedance data.
The most obvious error is the use of an incorrect model. It is very easy to miss certain
nuances during impedance data analysis, for example when using simple circuits with
parallel RC elements in series, to model impedance data. Though this might work well in
certain cases, it is a very ideal combination of circuit elements that does not apply to many
practical material systems.79 Most practical systems deviate from ideal Debye like
behavior as they have a distribution of relaxation times, due to various reasons. Another
mistake very easily committed is to go to the other extreme and keep adding elements to
the equivalent circuit to get a good fit. With enough number of circuit elements, almost
any data set can be fit. However, this circuit has little physical significance. Any number
of circuits can fit a certain data set, if they have a lot of parameters. Each parameter used
for fitting has to be used only because it has a certain physical significance in the expected
material behavior. The correct equivalent circuit should have a proper experimental
justification. Additionally, most literature does not provide information about the quality
of fit for a particular model and data set. The reader thus has to take the extracted results
70
at face value without any proof. Quality of fit is a very important part of impedance data
analysis. In fact, detailed quality of fit studies can help identify the correct model among
different competing models.
In the absence of a proper protocol for data fitting, there is very little reproducibility
in the results. A single set of data can be fit using multiple equivalent circuits. The same
set of data when analyzed by two different people can yield very different results. This
calls for standardization of the procedure for fitting of impedance data. In brief, the
different factors involved in the proper analysis of impedance data are:
Physical significance of the different circuit parameters in fitting programs
Selection of the correct equivalent circuit based on a physical model.
Approximate starting values for parameters to be fit.
Estimation of fitting quality.
4.2. Best Practices
There has been some work towards developing strategies for accurate and
reproducible analysis of impedance data. Abram et al.85 have shown how to discriminate
between competing model circuits using the four complex immitance formalisms, namely,
impedance, modulus, admittance, and permittivity. They have also provided a guide to
determine approximately accurate starting values of parameters for fitting. Macdonald
has worked on a wide variety of models for impedance analysis in addition to all the
strategies and detailed work on CNLS fitting.9,86,87 The ‘Help’ section of the Zview
software also has a lot of useful information. The following is a compilation of best
practices based on the factors listed above that should make more uniform and
reproducible analysis of impedance data possible.
71
4.2.1. Definitions of Parameters
To be able to perform fitting of data with ease, it is necessary to be familiar with
the various circuit elements commonly used for fitting, their physical significance and the
related math. Following is a list of parameters commonly used:
Resistance (R): It is the obstacle to the flow of charge carriers. It forms the real
part of impedance ( Z ), with no imaginary component (Z ) associated with it.
RZ 0Z (4-1)
Capacitance (C): It is the geometrical capacitance associated with the grain, grain
boundary or electrode. It contributes to the imaginary part of impedance, with no
associated real component. It forms a semicircular arc in the first quadrant of the
Nyquist plot when in parallel with R. Here ω is the angular frequency and the
numbering for quadrants used throughout the document is as shown in Figure 4-2.
C
1Z
0Z (4-2)
Figure 4-2. Numbering systems for quadrants in the coordinate system used throughout this work.
72
Inductance (L): At low frequencies, it indicates the reversible storage of electric
kinetic energy. It contributes to the imaginary part of the impedance, with no
associated real component. Usually pushes data towards the fourth quadrant
when it is a part of the circuit.
LZ 0Z (4-3)
Constant phase element (CPE): It models the behavior of an imperfect capacitor
(in non-homogenous systems). When in parallel to a resistor, it produces a
depressed semicircle in the Nyquist plot. In Zview software, the CPE is defined by
two values, CPE-T and CPE-P.
P
CPE iTZ 1i (4-4)
The P value here (CPE-P) determines the split of the impedance into real and
imaginary parts. CPE-T is the equivalent of a capacitance, and it represents a
perfect capacitor when CPE-P equals 1. When CPE-P equals 0, CPE-T is a
resistor, and when it equals -1, it is an inductor. At CPE-P equal to 0.5, a 45⁰ line
is produced in the plot, which indicates a Warburg element, sometimes used to
model electrodes.
In literature84, the impedance of CPE is also given as,
γ
CPE ωiAZ 1i (4-5)
where γ is a constant. A on the other hand, equals 2πncosa , where a is
constant. CPE-P thus equals γ , and CPE-T equals A from equations (4-4) and
(4-5). The value of CPE-P or γ is indicative of the amount of distribution in
relaxation time. This representation of distributed time constants originated from
73
the Cole-Cole modification to the Debye relaxation relationship, which gives a
depressed, but symmetric semicircle.88 The associated mathematical expression
for complex permittivity is denoted by equation (4-6).
α1
oωτi1
εΔεωε
(4-6)
Here is the angular frequency, is the dielectric constant at infinite frequency,
is the difference between the static and infinite frequency dielectric constants, and o
is a generalized relaxation time. Other mathematical models for dielectric relaxation have
also been proposed,89,90 the details of which are included in Appendix D. The constant α
in the Cole-Cole and other models for permittivity is should not be confused with the
constant γ used for defining CPE. These constants although related are different.
In addition to the common circuit elements, it also helps to know the different
impedance formalisms which are defined as follows:85
Admittance
Z1Y (4-7)
Relative permittivity
M1 (4-8)
oCi
Y
(4-9)
Relative electric modulus ZCiM o (4-10)
Here oC is the vacuum capacitance of the sample holder and electrode arrangement.
Impedance is the combined the effect of reactance and ohmic resistance in a circuit which
impedes the flow of current. Admittance, opposite to impedance is the ease with which
current can flow. Permittivity is the measure of the electric field or flux formed in a material
74
as a function of charge, and as expected is dependent on the admittance and capacitance
of the medium. It represents the opposition to field formation whereas modulus measures
the opposite of that. It has been shown by Gerhardt that these different formalisms can
be used to separate and magnify different effects in the materials under test. For example,
the presence of a peak in the modulus with respect to frequency indicates localized
relaxation, as opposed to long range conductivity in its absence. Similarly, a peak in the
imaginary impedance can be related to space charge effects. Long range conductivity
though clearly visible in the impedance formalism, but does not show up in the permittivity
formalism.91
4.2.2. Selection and Fitting of Appropriate Equivalent Circuit
When testing a new material, a number of competing circuits must be considered,
based on possible physical mechanisms the user can envisage in the material. One
needs to have a fair knowledge about the material under study for this purpose. Since
the objective of this work is to study gadolinia doped ceria, an ionic conductor, the typical
response for a polycrystalline ionically conducting ceramic is considered. As shown in
Figure 2-12 in Chapter 2, it typically consists of three arcs, grain in the MHz frequency
range, grain boundary in the kHz range and electrode in the Hz range. These frequency
ranges can be used as guide to identify the contributing mechanisms, as they are fairly
typical of ionic conductors, in a given temperature range. Under ideal Debye like
conditions, such semicircular arcs are fit using parallel RC elements. In ionic conductors,
the grain boundary resistance is usually much larger than the grain resistance, thus
separating the two is easier. Similarly, a C value of 10-7 or higher is characteristic of
space charge layer effects at electrode interfaces, nF range for grain boundary and pF
range for grains.85 As stated before, most materials have distributed time constants, as
75
opposed to a single constant. CPE is used to model such behavior, which shows up as
depressed and distorted arcs. The value of α associated with the CPE signifies the
distribution of time constants and the extent of depression of the semicircle in the complex
plane plot. Often two or more relaxation processes have similar time constants and hence
their arcs overlap and need to be de-convoluted and fit accordingly. In case the first arc
does not begin at the origin, an appropriate extra circuit element/s (L, C, or R) is/are used
in series to model this deviation. In case the graph is shifted along the x-axis, a series
resistance is used, a capacitance is used for the first quadrant and an inductance for the
fourth quadrant as is shown in . Same applies even between and at the end of the other
arcs. For example, there could be a series resistance between two arcs, or there could
be a resistance or even an inductance parallel to all the other circuit elements (as will be
shown later in Chapter 6). As described in section 4.2.3, approximate initial values need
to be estimated.
Figure 4-3. Schematic showing shift in complex impedance plots and the respective equivalent circuits.
76
During fitting, as has been highlighted by Abram et al.85, it is important to give full
weight to the entire frequency range measured. The data must be viewed both in the
linear scale and the log-log scale. Linear scale representation gives an initial visual
overview, whereas the logarithmic scales allow more accurate assessment as it ensures
equal weighting of the data. More features become visible in the log representation as
can be seen from Figure 4-4.
Figure 4-4. Example data set showing the difference between linear and log representations.
Similarly frequency explicit plots can be used to separate out overlapping arcs in
the complex impedance plots which are hard to distinguish. All four immitance
formalisms, Z*, Y*, M*, and ε* need to be analyzed during fitting, as each of these
highlights different circuit elements. For example, the Z formalism is dominated by
77
resistances, and Rgb being the dominant resistance, this formalism highlights the grain
boundary contribution. The M formalism on the other hand, highlights the bulk
contribution, since it is dominated by the inverse of capacitance, with 1/Cg being
dominant. The correct equivalent circuit must give a good fit to all the formalisms.
Figure 4-5. Sample data showing a complex impedance plot and the frequency explicit plot of theta for the same data which enhances the data in the blue box.
As discussed in chapter 2, the data for any of the four formalisms in addition to the
complex Nyquist representation, can also be represented by frequency explicit or
spectroscopic plots (Figure 2-11). Low impedance values which might be harder to
observe in the complex plane plots can be seen more clearly in frequency explicit plots
as is shown in Figure 4-5. These plots make it easier to identify the number of relaxation
mechanisms. For impedance and permittivity for example, each relaxation mechanism
in the material, within the frequency range measured shows up as a peak in the Z” and ε”
78
versus frequency plots and valley in θ frequency explicit plots. Broader peaks imply more
distributed time constants for the relaxation mechanisms. Slopes of these plots can thus
be used to determine the value of α as has been shown by Orazem and Tribollet.92 An
example of the same is shown in Figure 4-6. Gerhardt has shown that frequency explicit
plots in combination with various dielectric functions, can be used to distinguish between
localized relaxation and long range conductivity.91 For example, it was shown that
overlapping Z” and M” peaks imply long range conductivity. Using frequency explicit
plots, the change in the relaxation time for mechanisms with temperature can also be
followed and studied easily. As such these data representation techniques can be used
for other electroceramics to gain a better insight into the various phenomena at play.
Data should generally be fit from low temperature (or DC bias) to high, with new
circuit elements being added if and when they appear. At low temperatures, the analysis
of the bulk response is easier. Higher temperature bulk response can then be fit using
the n value obtained from the first fit as an estimate. Progressively, the grain boundary
and electrode contributions can be fitted.85 In case a circuit contains a large number of
parameters, certain features may be fixed for the initial fitting runs, and the rest of the
factors may be allowed to vary. The values of R, C (or CPE) or L as obtained from fitting
should follow the expected temperature and frequency trends for the given material. For
example, for GDC, ionic conductivity should follow the Arrhenius equation. There should
be a drop in the CPE values for GDC with increasing temperature. Similarly, Re for a
parallel electronic resistance introduced in doped ceria (looked at in Chapter 6) should
drop with increasing bias. Any deviation from such expected behavior could be due to an
incorrect circuit or fit.
79
The best circuit amongst different circuits with similar response can be determined
from the residual analysis of the fit. An incorrect model will usually have high residual
values and might even show high or low frequency tails, indicating a poor fit. After fitting,
if it is still found that multiple circuits yield the same frequency response and low residuals,
then additional experimental observations are required to validate a particular model.92
4.2.3. Starting Values for Fitting
Most fitting programs and algorithms require reasonably approximate starting
values of all the circuit elements for fitting. Poor initial values can lead to poor fits (a false
minimum) or even no fits at all. Based on the model to be fit, approximate initial values
of the parameters need to be estimated. R and C values for parallel RC elements can be
estimated either by hand fitting of individual arcs, or by the ‘Fit Circle’ option in commercial
software, if available. R is estimated as the x-axis intercepts of the arc and C is estimated
from the relation RC=𝜏, where 𝜏 is the relaxation time for the mechanism (corresponds to
the angular frequency ωmax at the highest point in the arc). As shown by Abram et al.85,
CPE values can be estimated by plotting the admittance (log Y’ vs log ω) as shown in
Figure 4-7.85 For low temperature data, this plot should contain a low frequency plateau,
with a higher frequency dispersion region with a power law gradient equal to n (calculated
from slope of the tangent). The intercept with the y-axis, is equal to log[A cos(nπ/2)].
Hence the values of A and n for CPE can be estimated. At higher temperatures, the high
frequency gradient starts to disappear and a low frequency gradient appears,
corresponding to the grain boundary dispersion. A and n values can be estimated just as
for the grain. In case a clear slope is not visible in the measured temperature range, a
typical value of n=0.6 can be assumed. The value of n (or α) can also be determined
80
from the slope of the |Z| versus log (frequency) plot as shown in Figure 4-6.93 Similarly,
if an inductance is present in the circuit, its value can be estimated from 𝜏=L/R.
Figure 4-6. Imaginary part of the impedance as a function of frequency with α as a parameter. Figure adapted from Orazem et al.93
Figure 4-7. Schematic of log Y’ against log ω with a low frequency plateau and a high frequency dispersion adapted from Abram et al. 85
81
After estimating the initial values, it is advisable to run a simulation of the circuit,
to check whether it is close to the experimental data. A fitting routine should be run only
after a satisfactory simulation.
4.2.4. Quality of Fit
Once an appropriate physical model has been selected and its parameters have
been fit to the impedance data, it is essential that the quality of fit be determined. This is
the single most important factor that helps determine whether a particular model is correct
or the CNLS routine gave a proper fit. The primary and easiest way of doing this is by
visually checking that the fitted data matches well with the measured data. Another
indicator is the actual and percentage error values for the different circuit elements,
provided by the fitting software. Low error values are desirable. A percentage error below
5% can usually be tolerated, however, this threshold is usually subjective. Very large
errors indicate an incorrect model, usually with more elements than required. The
redundant elements however do not have any effect on the goodness of fit.
The goodness of the fit can be determined by two parameters. The first is Chi-
Squared, which is the square of the standard deviation between the measured and fitted
data. However, given that the impedance values can vary by orders of magnitude, it is a
relatively poor estimate of quality of fit. A data set with a poor fit at low impedance values,
but a good fit at higher impedance values will give a low chi-squared value, thus giving
an inaccurate analysis. A much better estimate of quality is the Sum of Squares. It is
proportional to the average percentage error between the measured and fitted data. By
looking at percentage values instead of absolute values, it gives equal weightage to all
parts of the impedance curve, no matter what the magnitude. As per Macdonald and
82
Porter, proportional weighting is more accurate compared to modulus weighting for CNLS
fitting.87
Another really good measure of the quality of a fit is the analysis of residuals, as
is frequently used in statistical analysis of data.94 An example of such analysis has been
shown by Masó and West15. The values of residuals can help distinguish between a good
and a bad model for the same set of data. More, importantly, any trends in residuals with
frequency are indicative of an incorrect model. Residual analysis should in fact be
reported with impedance analysis whenever possible, so that it gives the reader more
confidence in the data. An example of residual data is shown in Figure 4-8.
Figure 4-8. An example of residuals for the real and imaginary parts of impedance.
Based on the practices described in this chapter, a detailed protocol with step-by-
step instructions for performing impedance data analysis using ZView® software was
developed. The steps are detailed in Appendix A.
83
CHAPTER 5 IMPEDANCE RESULTS FOR THIN FILM AND BULK SAMPLES
5. 5.1. Thin Film Samples
Gadolinia doped ceria thin films were tested for impedance behavior. These films
were later used to study the effect of bias, as is presented later in Chapter 6. This section
discusses the impedance data for one such thin film and follows the fitting process. As
an example, Nyquist plots showing the results of impedance spectroscopy for a 10 mol%
GDC thin film as a function of temperature are shown in Figure 5-1. As expected, the
arcs in the impedance plots shrink with increasing temperature, indicating in general, a
trend of increasing conductivity.
Figure 5-1. Nyquist plot showing impedance data for a 267 nm 10GDC thin film at different temperatures.
The data shown here was fit following the protocol described in Chapter 4. An
individual data set is shown in Figure 5-2. First step is the identification of an appropriate
84
equivalent circuit. A typical equivalent circuit for gadolinia doped ceria that has been used
extensively in literature uses a parallel R-CPE combination to represent each arc in the
data. The circuit used is shown in Figure 5-2. R1 and R2 represent the grain and grain
boundary resistance respectively.
Figure 5-2. Complex impedance plot showing the data for a 10 GDC 267 nm thin film at 130ºC along with the equivalent circuit used to fit the data.
The ‘Fit circle’ option in ZView software was used to estimate starting values for
the resistances. The estimated values are R1 = 79335 Ω and R2 = 5.84x106 Ω. The
CPE-P1 value was estimated as 0.8 by plotting log Y’ vs. log ω (Figure 5-3). The CPE-
P2 values was assumed to be 0.6. The values of CPE-T1 = 1.02 x 10-11 F, and CPE-T2
= 5.13 x 10-9 F were estimated based on the circle fit in ZView. Individual arcs were fitted
first and the values obtained were used to obtain the final fit. The grain ionic conductivity
was calculated based on R1 using the formula defined in Chapter 2. Similarly, the total
ionic conductivity was calculated from R1+R2.
85
Figure 5-3. A plot of log Y’ versus log ω for estimating the values of CPE-P and CPE-T for the 10 GDC bulk sample.
Figure 5-4. Arrhenius plot showing the grain ionic conductivity for a single electrode on the 10GDC thin film accounting for error propagation.
86
As the temperature increases, the conductivity of the films increases. The single
arc at 25ºC becomes smaller and smaller until at about 50ºC a second arc appears. With
further rise in temperature, both these arcs progressively become smaller. The low
temperature data is fit using a parallel combination resistance and a constant phase
element (R-CPE), whereas at higher temperatures, the two arcs can be reasonably fit
using two parallel R-CPE combinations in series with each other. The fitting was done
similar to the bulk sample mentioned in the previous section. The grain ionic conductivity
can be calculated using the value of R1 obtained from equivalent circuit fitting and
adjusting for area and width as per equation (2-4).
Based on the error propagation discussion in Chapter 3, the total error for
conductivity measurement of a film for a single electrode was calculated by considering
the errors in the R values as obtained from ZView®, errors in dimension measurement,
and the error in temperature measurement. Figure 5-4 shows a plot of conductivity with
respect to temperature including the respective x and y errors. The total error associated
with the fitting, dimension measurement, and temperature measurement propagating to
the conductivity of a sample is very small and will have minimal effect on the activation
energy calculated. This is expected to be the same for all samples tested if all the
instructions in the fitting protocol are followed. The conductivity values thus obtained for
each sample can hence be trusted. Given that the same procedure and protocol is
followed for measuring samples throughout this study, the error for these individual
samples will be small. The only other major factor that can affect the conductivity is the
sample to sample variation, which can be accounted for by testing multiple samples and
presenting their combined results. The error introduced from different samples is much
87
higher than the error in conductivity measurement in a single sample and hence cannot
be neglected. In the case of thin films, this can be accounted for by measuring the
conductivity for different spot electrodes. For the 10GDC 267 nm thin film, the
corresponding Arrhenius plot is shown in Figure 5-5. The plot could not be fit with a single
slope as the data points lay outside the confidence bands (95%). Fitting the data with
two slopes give a better with all the data within the confidence bands. This technique can
be used to decide whether a single slope or multiple slopes for data fitting, and has been
used throughout this work. Origin® software takes care of the errors in conductivity and
accounts for them during the calculation of the slope.
Figure 5-5. Arrhenius plot showing the average grain ionic conductivity for multiple electrodes on a 10GDC thin film with 95% confidence bands.
88
The conductivity follows Arrhenius behavior and for a 267 nm thick 10 mol%
gadolinia doped ceria film has activation energies of 1.34 eV and 0.871 eV calculated
from the slope of the graph in Figure 5-4 based on equation (2-4).
5.2. Bulk Samples
Figure 5-6. Complex impedance data for a 10GDC bulk sample at different temperatures.
Bulk samples of 10 mol% GDC were tested using impedance spectroscopy as part
of the study involving dopant segregation in Chapter 7. Impedance data for a 10GDC
control sample sintered in air at 1600⁰C for 10 hours is shown in Figure 5-6. The grain
ionic conductivity follows the Arrhenius relation and was plotted against temperature as
shown in Figure 5-7. The slope of the line was used to calculate the activation energy,
based on equation (2-4), where two slopes were found. The values of activation energy
89
calculated were 0.88 eV and 0.56 eV. The conductivity and activation energy values
obtained are comparable to those found in literature. The trends in conductivity show
that, as expected, the conductivity in thin films is higher than that for the bulk samples
given that both have similar dopant concentrations.
Figure 5-7. Arrhenius plot showing the average grain ionic conductivity of the 10GDC samples at different temperatures.
90
CHAPTER 6 EFFECT OF A DC BIAS ON IMPEDANCE RESULTS
6. 6.1. Background
There have been several studies on the conductivity of oxide electroceramics
under the influence of a DC bias. A DC bias was initially used to study the nature of grain
boundaries in acceptor doped ceria by Guo et al.95, where individual grain boundaries
showed non-linear current-voltage behavior, and the effective grain boundary thickness
(electrical thickness) was found to increase with increasing bias. Work by Guo and
Waser69 involving yttria doped ceria, has attributed the change in behavior under bias to
phenomena occurring at the grain boundaries. They use the space-charge model of grain
boundaries to explain the observed behavior, as has been detailed earlier in Chapter 2.
According to their work, at zero bias, the two space charge layers on either side of a grain
boundary are symmetrical. However, on application of a DC bias, one space charge layer
is depressed, while the other one increases in width as shown in Figure 6-1.
Figure 6-1. Schematic representation of the oxygen vacancy concentration and the space charge layer without any applied bias (left) and with an applied bias (right), as proposed by Guo and Waser.69
91
Overall, using bias measurements approximated over a single grain boundary, it
was shown that the total thickness of the grain boundary and the space-charge layers
combined increases. It was also shown that the bulk properties were almost independent
of bias, whereas, the effect on grain boundary resistance was significant. However, since
the focus of the work was on non-linear properties of the grain boundaries, the mechanism
behind the improved conduction was not further investigated. This was used to support
the space charge theory for blocking grain boundaries.
The effect of bias was studied in detail only much later by Masó and West15. Their
study concentrated on the effect of a small DC bias on the electronic conductivity in bulk
yttria stabilized zirconia (YSZ) samples. A drop in resistance was observed under a DC
bias, which was attributed to the onset of electronic conduction, and the possibility of
variable oxidation states of oxide ions and their response to a DC bias. The
corresponding complex impedance data is shown in Figure 6-2. It was found that it took
about 10 minutes for the impedance response to stabilize on the application or removal
of bias. The electronic contribution increases with increasing bias, and after a certain
bias value, it becomes more dominant than the ionic contribution to conductivity. This
happens at lower and lower bias values as the temperature is increased. The behavior
was modelled using equivalent circuits where a resistance starts to appear parallel to the
original equivalent circuit at low bias values (only low bias values were studied). This
new resistance was attributed to electronic conduction introduced along a parallel
pathway.15
Similar resistance degradation has also been reported by Wang et al.96 for Fe-
doped SrTiO3 single crystals. In this combined experimental and computational work, it
92
was found that an applied electric field induces migration of oxygen vacancies and
establishes new local defect equilibria. It is this change in the local defect structure that
causes a drop in the resistance. It was also found that oxygen partial pressure and
temperature play a major role in this degradation mechanism. There has also been work
on various other acceptor doped oxides like BaTiO3, CaTiO3 and BiFeO3 which have
attributed field enhanced conductivity in these materials variously to ionization processes,
reactions between oxygen and surface species, underbonded oxide ions, and unique
electronic structure in defect complexes in these materials.97–101
Figure 6-2. Impedance complex plane plots for 8 mol% YSZ at different temperatures and DC bias values as shown by Masó and West15 where 10 V43 V-cm-1.
It is particularly interesting to look at work by Moballegh and Dickey which studied
the effect of bias on single crystal TiO2-x electroded with Pt.102 The use of a single crystal
instead of a polycrystalline material paints a clearer picture. The Pt electrode interfaces
exhibit Schottky contact behavior. As expected it was found that the applied electric field
93
induces a redistribution of point defects throughout the crystal, causing accumulation of
Ti interstitials and oxygen vacancies at the cathode. The same is also corroborated by
the Brouwer defect diagram for titania,102 where under low oxygen partial pressures
(reducing condition) causes an increases in oxygen vacancy and titanium interstitials.
Such reducing conditions exist at the cathode under a DC bias.
Figure 6-3. Oxygen concentration in the region adjacent to the Pt cathode interface in a TiOx single crystal after degradation under 15 V bias determined using EELS as shown by and adapted from Moballegh and Dickey.98
Figure 6-3 shows the change in stoichiometry at the cathode interface as observed
by Moballegh and Dickey using electron energy loss spectra (EELS). This modifies the
Schottky barrier at the electrode and essentially degrades it. It was shown that
degradation takes place in two regimes. In the low field regime, the electrical transport is
dominated by local changes near electrodes, and results in macroscopic rectification
behavior, with one of the electrodes being forward biased and the other being reverse
biased, and leads to a drop in resistance when forward biased. However, at higher
94
voltages, the stoichiometry is altered so much that it leads to the formation of
microstructural defects, in this case even a new phase. A significant change in the bulk
stoichiometry can lead to the conduction mechanism itself changing in such modified
regions, and in this case, it leads to an increase in resistance with time under an applied
bias.
Figure 6-4. A schematic showing concentration of vacancies in an Fe-SrTiO3 film at high and low frequencies and the corresponding Nyquist plot showing an inductive loop, adapted from Taibl et al.16
This work was further strengthened by Taibl et al.16 who have shown similar
behavior in Fe-doped SrTiO3 thin films, and have supported the vacancy migration theory
and stoichiometry variations under bias using characteristic inductive loops in the
impedance spectra. The segregation of vacancies was achieved by using two different
electrodes, only one of which was blocking to oxygen vacancies. The results were
supported by DC I-V curves at different speeds, which exhibit different trends depending
on the sweep speeds. The existence of inductive loops was explained on the basis of
the time required for oxygen vacancies to redistribute after a voltage change, and hence
95
they were attributed to ion motion across the width of the film. Figure 6-4 shows a
schematic, and a Nyquist plot with a low frequency inductive loop for Fe-SrTiO3.
Since there is a possibility of electronic conduction under bias in GDC, it becomes
pertinent to look at the considerable amount work on mixed ionic and electronic
conductivity in ceria materials. Reducing atmospheres have been shown to introduce
electronic conductivity in pure ceria materials, and turning them from poor ionic
conductors to good electronic conductors. The associated reaction is shown in equation
(6-1).
e2O2
1VO 2O
x
O
(6-1)
Guo et al. have shown that under a reducing atmosphere, the bulk conductivity of
1% yttria doped ceria increases only slightly, whereas there is a drastic increase in the
grain boundary conductivity.55 Assuming a brick layer model, charge carriers can travel
either parallel to the current or perpendicular to the current direction. Thus grain
boundaries can be either parallel or perpendicular to the direction of current flow. Since
any conductivity across grain boundaries has to be in series to the bulk flow, as shown in
the schematic in Figure 6-6, a more pronounced partial electronic conductivity at the grain
boundaries was concluded to be due to conduction along grain boundaries parallel to the
current flow. It has been shown that in such a scenario, and the relations eon,
gb
ion,
gb RR
and eon||,
gb
ion||,
gb RR hold true. The electrons generated per equation (6-1) tend to
accumulate at the grain boundaries which eventually lead to such behavior.
96
Figure 6-5. The brick layer model for a polycrystalline ceramic with the paths for conduction as shown by and adapted from Macdonald.79
Figure 6-6. Schematic showing ionic and electronic conduction paths for a polycrystalline ceramic assumed to have a brick layer model as proposed by and adapted from Guo and Waser.69 Here R is the resistance, ion stands for ionic, eon stands for electronic, gb stands for grain boundary, and || and denote grain boundary directions parallel and perpendicular to the current respectively.
97
Similarly, with nanocrystalline ceria, it has been shown that under reducing
atmospheres a much higher conductivity is observed due to accumulation of electrons
and depletion of oxygen vacancies in the space-charge layer. Such regions near the
grain boundaries, within which electron concentration is higher than oxygen vacancy
concentration were designated as ‘inversion layers’. The inversion layer thickness
depends on temperature and oxygen partial pressure, and increases at higher
temperatures and lower partial pressures, as more and more electrons accumulate at the
grain boundaries, in essence decreasing the effective electrical grain boundary thickness.
It is the presence of such inversion layers with high electron concentration which makes
the grain boundaries more conductive than bulk. Hence the ions flow in the bulk and
across the grain boundaries perpendicular to the current flow, whereas electrons flow
along the grain boundaries parallel to the current flow with eon||,
gb
eon,
gb RR . This effect
was shown for both acceptor-doped and undoped ceria bulk samples.55,103
Figure 6-7. Inversion layer with high electron concentration near the grain boundary adapted from Guo et al.55
98
Such studies as the ones mentioned above are important because they
demonstrate novel mechanisms of improving conductivity, introducing mixed ionic
conductivity, or in other cases shed light on the possible degradation of properties in
electroceramic devices.
Figure 6-8. Complex impedance plot showing the effect of a low DC bias on 10 mol% doped gadolinia doped ceria bulk specimen at 200ºC.
A similar study is performed here for gadolinia doped ceria, for which such an effect
has not been studied. Preliminary tests on bulk samples of GDC show behavior very
similar to that observed by Masó and West15 as has been shown in Figure 6-8.
99
Interestingly at relatively higher bias values, a small inductive loop is observed at low
frequencies as shown in inset in Figure 6-8. To study this effect further, and understand
it in more detail, this study looks at gadolinia doped ceria thin films. Due to the small
thickness of the films, any applied voltage translates into very high electric fields, which
have not been studied before for such effects.
6.2. Bias Effect on GDC Thin Films
Figure 6-9. Nyquist plot showing the example of a DC bias effect on a 267 nm thick 10 mol% GDC film at 120⁰C. Inset is zoomed in at the origin.
To study the effect of DC bias on the observed ionic conductivity and the complex
impedance behavior of 10 mol% gadolinia doped ceria films, impedance spectroscopy
was performed as described in the previous chapters under positive DC bias values
100
ranging from 0 V to 3 V at 10⁰C intervals up to 150⁰C. At every temperature, initially the
bias values were measured at 0.5 V intervals. It was found that with increasing bias, the
impedance response for the sample begins to change. The change is not much at low
temperatures however, it becomes more and more pronounced with a rise in temperature.
Figure 6-10. Nyquist plots showing the effect of a DC bias on a 267 nm thick 10 mol% GDC film at different temperatures.
A 267 nm film is considered here, for which the DC bias values used translate to
fields of up to 112 kV/cm. Figure 6-9 shows the effects of increasing bias on the Nyquist
for the aforementioned sample. With an increase in bias, the impedance arcs in the
Nyquist plot progressively shrink and new features appear progressively. Figure 6-10
101
shows a comparison of similar data at different temperatures. It can be seen that these
changes occur only above certain temperatures depending on the processing conditions
for the films. With increased temperature, the effects of bias can be seen at progressively
lower bias values.
6.3. Characteristic Steps in Nyquist Plots under Bias
Figure 6-11. A very detailed plot showing every step in the evolution of a 10 mol% gadolinia doped ceria thin film under bias at 130⁰C.
To better understand the different stages in which bias affects the sample, even
shorter bias intervals were used. Figure 6-11 shows a plot with detailed effects of bias,
102
and all the involved steps. It is interesting to note that at lower bias values the response
moves towards higher impedance, and only after a certain point it starts moving towards
lower impedance values as the applied bias is increased. These can be treated as two
regimes in the impedance response change with bias.
Figure 6-12. Nyquist plot showing characteristic steps in the evolution of the impedance response of a 10GDC thin film under increasing bias. Individual plots are labelled A through H and later correlated with equivalent circuits.
Using this figure, and based on the data for different films at different temperatures,
five major steps can be identified in the change of behavior with bias. These steps are
characteristic of the response of GDC thin films to DC bias. These are summarized in
103
Figure 6-12 for a 10 GDC thin film sample 267 nm thick at 250ºC. A few interesting
features can be observed here. The arc ascribed to grain or bulk contribution does not
change much with increasing bias. At some intermediate bias values, a third new arc
appears. This is similar to the effect of temperature, where new additional arcs appear
at higher and higher temperatures as newer relaxation mechanisms come under the
experimental range. A pig tail like feature is also observed. Most interestingly, at higher
bias values, the plot enters the third, and even fourth quadrant in some cases.
Figure 6-13. Frequency explicit plots showing the magnitude of impedance |Z| and the
phase angle as a function of different DC bias values for a 10 GDC, 267 nm thin film.
104
Figure 6-13 shows the frequency explicit plots of the magnitude of impedance and
phase angles for the same sample at 130ºC for different bias values. It can be seen that
there is a very high change in the impedance at low frequencies (<104 Hz). In the low
frequency range, the impedance progressively decreases and then around 2.2 V bias, it
starts increasing again, and eventually stabilizes around 3 V. There is not much change
in the impedance at higher voltages. There is also a change in the impedance response
at higher frequencies, but it is relatively small. However, it is interesting to note that in
the high frequency range, there is no switch in the trend of impedance magnitude with
bias as can be seen in the inset. Impedance steadily decreases with increasing bias.
Similarly, there is a very large phase shift at higher frequencies as bias is increased,
where the phase shift decreases progressively with increasing bias and subsequently
becomes negative. Such change in impedance and phase shift can only be explained by
introduction and subsequent increase of an inductive response in the low frequency
range.
Looking at the frequency explicit plots for the real and imaginary parts of
impedance, there is a change in both the real and imaginary parts of impedance, as can
be seen in Figure 6-14. In the low frequency range the change in the imaginary part is
larger than that in the real part, indicating that although both resistive and reactive
components are changing substantially, the change in the reactive contribution is higher.
On the contrary, in the high frequency range, the behavior is reversed, with the resistive
change being more dominant than the reactive change, although the change itself is
relatively small (not shown here). In other words, in the low frequency range, most of the
change in impedance is due to changes in capacitance and/or inductance (since they
105
make up the reactance), whereas in the high frequency range, most of the small change
in impedance is due to resistance variation. The data in Figure 6-14 is plotted on a linear
scale instead of a log scale because negative values are expected in both the real and
imaginary impedance cases, and the data below the axis would have been lost in the log
scale.
Figure 6-14. Frequency explicit plots showing the real and imaginary parts of impedance (Z’ and -Z” respectively) as a function of applied DC bias for a 10GDC 267 nm thin film.
It is also helpful to look at the permittivity formalism, as it sheds some more light
on the phenomena at play. Figure 6-15 shows the frequency explicit plots for the real
part of permittivity. The real part of permittivity, increases with the value of applied
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bias.in the high frequency range, however there is a flip in the trend around 50 kHz and
starts decreasing. This flip can be seen in the inset of Figure 6-15. There is no such
corresponding change in the imaginary part of permittivity. This flip in trend means that
at high frequencies the capacitive response of the sample is more dominant, whereas in
the low frequency range the inductive response is dominant. A similar behavior is seen
in the imaginary part of admittance as expected (not shown here).
Figure 6-15. Frequency explicit plot showing the real permittivity for different bias values for a 10GDC 267 nm film. Inset shows the same plot zoomed in to the frequency range of 104-106 Hz.
Here one must note that this inductive behavior becomes more and more dominant
as the bias applied is increased, which leads to the plots crossing into the negative at
lower and lower frequencies. This corroborates the observation about inductive behavior
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from impedance and loss vs. frequency plots shown in Figure 6-13. This information
gained from the spectroscopic plots was used to determine the equivalent circuits for
fitting.
6.4. Fitting and Analysis
By fitting each of the data sets shown in Figure 6-12 using different equivalent
circuits, an idea as to the various processes and changes taking place in the material
behavior can be obtained. The trends in the values of circuit elements and the new
elements appearing, provide crucial information. Each of these data sets was then fit to
equivalent circuits as per the protocol in Chapter 4. The protocol becomes particularly
important here, as at almost every step, the equivalent circuit changes and new elements
are added.
The behavior observed in Figure 6-11 has rarely been seen for oxide ceramics, let
alone studied. Traditional interpretation of similar data has included inductive elements
related to reversible storage of electric kinetic energy. One example is the poisoning of
Pt anode in polymer electrolyte fuel cells (PEFCs), where a pseudo-inductive behavior is
observed below 3 Hz.79 Another example is that of Faradaic coupled reactions dependent
on potential and surface coverage, where an inductive loop is observed under high
potential.92 Only the very recent work by Masó and West15 and the work by Taibl et al.16
bears a resemblance to the phenomena observed here. Hence, their template for fitting
was used as a starting point. Multiple possible equivalent circuits were proposed based
on prior knowledge from literature. The circuits were tested for fitting and the most
probable circuit was identified from amongst them. The equivalent circuit proposed in this
case contains parallel pairs of R and CPE in series with each other, for each of the arcs
in the complex impedance plots. These arcs represent the grain and grain boundary
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contribution. Additionally, as shown using the spectroscopic plots in the previous section,
there needs to be an inductance parallel to these circuit elements. Any parallel inductive
path needs to have a resistance associated with it, so a resistance was also included
parallel to the inductance. This resistance has also been proposed by Masó and West
for YSZ under bias.15 The equivalent circuit proposed is depicted in Figure 6-16.
Depending on the shape of the individual plots, elements were added or removed from
this circuit.
Figure 6-16. Proposed equivalent circuit based on the visual analysis of the data in different formalisms and similar data presented in literature.
As shown in Figure 6-12, at 0 V bias the complex impedance plot shows two arcs,
common for such thin films. This data can be fit with an equivalent circuit consisting of
two parallel R-CPE pairs in series as shown in Figure 6-17, and as is commonly done for
doped ceria. With increase in bias, the value of R2 first increases and then starts
decreasing (as can be seen in figure for 0.5 V, 1 V and 1.5 V bias). In addition, a
resistance R3 appears parallel to the previous elements. The equivalent circuit is shown
in Figure 6-17. At around 1.7 V bias, a third arcs appears, barely visible as a curve in the
second arc. This arc is further enhanced at 1.9 V. Both of these data sets can be fit using
the equivalent circuit shown in Figure 6-17. An additional element CPE3 is needed in
series here to properly fit the data. This element is possibly due to an electrode effect.
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With further increase in bias, the third arc gets depressed and twists on itself creating a
pigtail like shape. At this point, an inductor must be introduced into the circuit to be able
to fit the data as shown in Figure 6-17. With further increase in bias, the pig tail opens up
and the arc crosses into the third quadrant of the Nyquist plot and then also eventually
into the fourth quadrant. The equivalent circuit remains the same although the values of
the circuit elements do change.
Figure 6-17. Equivalent circuits used to fit impedance data shown in Figure 6-12 along with the respective bias values.
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Table 6-1. The values for equivalent circuit parameters obtained after fitting of the impedance data shown in figure.
Element/Bias 0 V 1 V 1.5 V 1.7 V 1.9 V 2 V 2.1 V 2.8 V
R1 (Ω) 35301 36294 32666 33435 36247 31659 30226 12230
CPE1-T 1.7x10-10 2.1x10-10 1.3x10-10 1x10-10 1.1x10-10 9.4x10-11 8.2x10-11 1.6x10-10
CPE1-P 0.82 0.80 0.83 0.85 0.85 0.86 0.87 0.87
R2 (Ω) 1.2x1014 1.3x1015 6x1014 403840 356740 275010 166380 28632
CPE2-T 6.8x10-9 2.6x10-9 1x10-8 3.1x10-8 1.8x10-8 3.3x10-8 4x10-8 1.1x10-9
CPE2-P 0.76 0.84 0.72 0.63 0.66 0.6 0.58 0.77
CPE3-T -- -- -- 7.9x10-9 2.1x10-9 7.2x10-10 1.8x10-10 1.4x10-7
CPE3-P -- -- -- 0.86 1.27 1.54 1.85 3.65
R3 (Ω) -- 2.5x1014 5.8x1013 2.1x1011 511730 833310 156810 23567
L (H) -- -- -- -- -- 523.4 245.2 8.42
With increasing bias, the values of R1, R2, R3, and L show an overall decrease.
The value of R1 does not show much changes until at very high biases, and even then
the change is very small compared to the changes in R2 and R3. R2 increases slightly
at low biases followed by an abrupt drop. Around the same bias value as R2, R3 also
shows a drastic drop in value. CPE1 (T and P) does not change much. CPE2-T similar
to R2 increases at low bias and then decreases at higher values. CPE3-T decreases with
increasing bias, and then as the plots enter the fourth quadrant, it increases. Traditionally
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the three arcs as seen for 1.7 V bias, are usually ascribed to grain, grain boundary and
electrode effects in doped ceria systems.66,104 With increase in bias, there is a general
decrease in the values of circuit elements as would be expected. With increasing bias,
the electrode arc collapses first, followed by the grain boundary arc, whereas the arc
representing bulk conductivity remains the same although at higher bias values, its
corresponding resistance value is considerably lower.
The time required for the behavior to stabilize is about 30-45 seconds depending
on the temperature. A higher time of about 1-1.5 minutes is required for the behavior to
get back to normal after removal of the bias. The values of the different circuit elements
obtained using fitting for the various characteristic plots shown in Figure 6-12 are shown
in Table 6-1.
Figure 6-18. Plot showing the values of R1 (grain resistance) for different applied bias, obtained using equivalent circuit fitting of impedance data for a 10GDC 267 nm film at 130ºC.
112
Figure 6-19. Plot showing the values of R2 (grain boundary resistance) for different applied bias, obtained using equivalent circuit fitting of impedance data for a 10GDC 267 nm film at 130ºC.
Figure 6-20. Plot showing the values of R3 (representing electronic conduction) for different applied bias, obtained using equivalent circuit fitting of impedance data for a 10GDC 267 nm film at 130ºC.
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Figure 6-21. Plot showing the values of L (inductance) for different applied bias, obtained using equivalent circuit fitting of impedance data for a 10GDC 267 nm film at 130ºC.
6.5. Mechanism
Based on the prior work in literature, visual analysis of data, the values of circuit
elements obtained from fitting with equivalent circuits, and trends therein, a mechanism
is proposed. The various phenomena observed are divided into three regimes, based on
the three equivalent circuits and the bias values used.
6.5.1. Low Bias
At zero bias, the impedance behavior of the films is as expected. The two arcs,
small and large, can be attributed to the grain and the grain boundary relaxation
respectively. The electrode contribution is not visible in this case as it is beyond the
measurable frequency range, as is common with thin films.
As a small bias is applied, the grain boundary resistance increases, with the grain
resistance being almost constant as shown in Figure 6-18. The small bias leads to the
accumulation of positively charged oxygen vacancies at the grain boundaries and the
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electrode. This exacerbates the already blocking nature of the grain boundaries further
and leads to a rise in resistance of the grain boundaries as recorded in Table 6-1. The
accumulation of vacancies at the cathode due to the bias leads to reducing conditions,
which as per the schematic Brouwer defect diagram in Figure 6-22 should lead to a higher
concentration of electrons.
Figure 6-22. Schematic Brouwer diagram for acceptor doped ceria adapted from Eufinger et al.105
The small bias causes electrons to move into the sample from the cathode
interface. Grain boundaries being good conductors of electrons, these electrons travel
through grain boundaries parallel to the direction of applied field, to the opposite
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electrode, thus establishing a parallel pathway for electronic conduction. A schematic of
the sample under small bias is presented in Figure 6-23.
Figure 6-23. Schematic of a gadolinia doped ceria sample under low bias.
Figure 6-24. Leakage current as a function of time and different applied DC voltages for a 10GDC 267 nm thin film measured at 120ºC.
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The introduction of a parallel pathway with resistance R3 (although its value is very
large) leads to a drop in the overall resistance and a rise in the leakage current as is
shown in Figure 6-24. A finite time is required to reach a steady state distribution of
vacancies after applying bias. The same can be seen in the leakage current plot, where
the current stabilizes around 30-50 seconds, which corresponds well with the time
required for the impedance response to stabilize (30-45 seconds).
6.5.2. Medium Bias
Platinum forms a Schottky barrier with rare earth doped ceria. As the applied bias
is increased further, and platinum being a blocking electrode for oxygen vacancies, more
and more vacancies segregate at the cathode. At the same time, more and more
electrons accumulate at the interface from the side of the electrode. With increasing field,
an increasing number of electrons can now jump across the barrier. With increasing bias,
the current along grain boundaries increases and correspondingly, the value of the
resistance R3 decreases. With the electrons moving across the electrodes in the voltage
range, the electrode interface becomes visible in the impedance response within the
measured frequency range. This is represented by the new CPE addition in the
equivalent circuit, which decreases with increasing bias in the medium range. Thus, there
are three arcs instead of two from the previous regime. As the bias is further increased,
the arcs tend to become smaller. This indicates that the grain boundaries and electrode
interface become more and more conductive. They also tend to become more circular
and bend towards the real axis, indicating a change from capacitive towards resistive
behavior, caused due to conduction of electrons. A schematic is shown in Figure 6-25.
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Figure 6-25. Schematic showing phenomena during impedance testing under medium bias in gadolinia doped ceria. Arrows indicate the motion of electrons.
Figure 6-26. Schematic band diagrams showing the cathode and anode interface under bias.
The process happening at the electrodes can be better understood from the
schematic band diagrams of the electrode interfaces under bias shown in Figure 6-26.
With increasing bias, the barrier height at the cathode is reduced and it is easier for
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electrons to flow from the Pt into the GDC, whereas at the anode, these electrons easily
flow back into the Pt electrode and the external circuit.
6.5.3. High Bias
At further higher bias values, above 2 V, more and more electrons flow across the
electrodes and through the parallel grain boundaries, leading to the collapse of first the
electrode arc followed by the grain boundary arc. The material starts exhibiting inductive
behavior. This results in the arc twisting up on itself although it stays in the first quadrant.
With increasing bias, the electrode and subsequently grain boundary arc move into the
fourth quadrant. The inductive loops can be explained by following the line of reasoning
used by Taibl et al.16 summarized at the start of this chapter. The model proposed
requires the assumption that the electronic current is much higher than the ionic current,
which mostly holds true in this case. With increasing bias, despite the low contribution of
ions to conduction, due to ion flux the vacancy segregation becomes even more
concentrated at the cathode after a steady state is achieved. The AC voltage stimulus
causes these vacancies to redistribute. However, their response depends on their
mobility. At high frequencies, there is almost no change in the distribution, as the
vacancies cannot oscillate with the AC voltage. At lower frequencies however, there is
enough time for the redistribution of oxygen vacancies within a half cycle of the sinusoidal
voltage signal. Thus every half cycle, as long as the ions can respond, a new vacancy
distribution is formed. This migration of ions is in series to the electronic current and
causes a negative phase shift, thus showing up as an inductive loop.16 With increasing
bias, there is even more vacancy accumulation, which accentuates the inductive loops.
A schematic is shown in Figure 6-27.
119
Throughout the different bias regimes, the arc representing grain contribution does
not change much, except at very high bias values where it starts shrinking. It is only
under very high biases, that the grain interior is also reduced, such that electronic
conduction takes place.
Figure 6-27. Schematic showing phenomena during impedance testing under high bias in gadolinia doped ceria.
Additionally, to verify the reasoning for the inductive loops, DC I-V measurements
were performed at various sweep speeds. This measurement was based on the work by
Taibl et al. to explain the change in vacancy distribution on the length scale of the
sample.16 The sweep speeds were varied as described in Chapter 3 to match the
frequencies of the points where the complex impedance plot crosses the real axis. It was
found that when the sweep speed matches the frequency of the point at which the
complex impedance intersects the real axis, the resistance obtained from the slope of the
I-V plot matches the value obtained for electronic resistance (R3) obtained from
equivalent circuit fitting of the data. The corresponding data are shown in Figure 6-28.
120
Figure 6-28. DC I-V measurement and complex impedance with matching resistances for a 10GDC 267 nm film at 130ºC under 2.1 V bias and oscillation voltage of 300 mV.
121
CHAPTER 7 DOPANT SEGREGATION AND SINTERING UNDER REDUCING ATMOSPHERE 7.
7.1. Segregation and Defect Associates
It has been shown that the composition and microstructure of a ceramic material
have a strong effect on its ionic conductivity.11,12,32,70,106–108 For example, the resistance
to ionic conduction is much higher for grain boundaries than for the grains or the bulk of
the material.55,66,109 Various mechanisms have been proposed to explain this high
resistance to ionic conduction across the grain boundaries. It has been shown that the
high resistance of grain boundaries is due to the segregation of dopants and impurities at
grain boundaries and triple point junctions.14 Siliceous impurities present in the starting
powder and introduced during processing lead to the formation of a glassy phase at grain
boundaries and triple points.14,55 Similarly, any other rare earth impurities and
intentionally added dopants tend to segregate at grain boundaries during sintering as has
been shown by multiple sources.14,76,77 Atom probe tomography has shown that in Nd
doped ceria, the Nd ions and oxygen vacancies segregate at the grain boundaries with
the compositional difference extending up to 4-6 nm from the structural center of the
boundaries as was summarized earlier and shown in Figure 2-10.77 Conventional
sintering procedures in general lead to a very high concentration of dopants at grain
boundaries. As per equation (2-4), increasing the dopant concentration should lead to a
higher concentration of vacancies, and higher ionic conductivity. However, at higher
dopant concentrations, the positively charged vacancies form defect associates with the
negatively charged dopant ions. The details of this phenomenon are summarized in
Chapter 2. The defect complexes effectively lock in the oxygen vacancies, reducing the
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ionic conductivity as dopant concentration increases. These defect associates lower the
overall ionic conductivity, with the grain boundary resistance being the biggest detriment.
7.2. Fast firing and Microwave Sintering
The key to getting good intermediate-temperature performance is to reduce the
resistance of grain boundaries. Various solutions have been proposed with varying
degrees of success to address this issue. The earliest and the simplest was to modify
the processing so as to reduce the amount of grain boundaries.107,108,110,111 Smaller
starting powder size, and fast firing techniques can be used to obtain smaller grain
sizes.112–114 An interesting side effect of fast firing is that it also offers the opportunity to
mitigate dopant segregation. This route takes advantage of the kinetics of diffusion and
completes the sintering process before segregation of dopants takes place. However,
except in very small samples, chances of thermal shock and cracking due to uneven
heating are very high.
It has been shown that microwave assisted sintering can be used to improve
conductivity by sintering for a short amount of time (as low as one hour) compared to
conventional sintering.14,115,116 The short sintering time prevents segregation of dopants
and impurities at grain boundaries and gives a more uniform distribution over the entire
sample. The even heating throughout the sample gets rid of thermal shock and cracking
issues. Work performed by the author in collaboration with Bruce Peacock from
Medtronic Corporation showed that microwave sintering gives a more uniform dopant
distribution compared to the conventional route. Focused ion beam (FIB) was used to
extract samples of subsurface triple grain junctions (Figure 7-1) out of a bulk pellet
specimen which were then analyzed. Figure 7-2 shows the energy dispersive
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spectroscopy (EDS) line scans across a triple grain junction in Sm0.05Nd0.05Ce0.9O2-δ after
conventional sintering. There is a definite rise in the concentration of Sm at the junction,
Nd concentration distribution curiously does not change much. Contrasting that with
microwave sintered samples (Figure 7-3), it was difficult to isolate triple grain junctions
because of the small grain sizes, however, there was no discernible segregation of either
Sm or Nd at any point in the analyzed area. The more uniform dopant distribution explains
the higher observed conductivity.
Figure 7-1. A sub-surface triple grain junction in Sm/Nd doped ceria obtained using focused ion beam. EDS line scans were conducted across this junction (Performed by Bruce Peacock at Medtronic Inc.).
Despite the higher conductivity, both microwave and fast sintering require very
specific conditions, and often due to poor processing practices lead to a drop in the
density of the sintered ceramic as there is not enough diffusion for grain growth and
densification to occur. Another technique that has been experimented with is spark
plasma sintering (SPS) which is fast, gives low grain growth, and more uniform dopant
distribution.
124
Figure 7-2. EDS line scans across a sub-surface triple grain junction in a Sm/Nd doped ceria sample sintered conventionally. Sm segregation is observed (Performed by Bruce Peacock at Medtronic Inc.).
Figure 7-3. EDS line scans across the surface of a Sm/Nd doped ceria sample sintered in a microwave. Both Sm and Nd are relatively uniformly distributed (Performed by Bruce Peacock at Medtronic Inc.).
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7.3. Sintering under Reducing Atmosphere
The above-mentioned approaches have some drawbacks, and all of them try to
solve the problem by taking advantage of the kinetics of dopant diffusion. Another
possible way of approaching the problem is by modifying the energetics of the system
along with the kinetics. The reason dopants segregate at the grain boundaries is to
reduce the overall free energy of the system. The extent to which a dopant will form a
uniform solid solution with ceria is dependent on several factors summarized as the
Hume-Rothery rules. The primary factors that affect the solid solution are, atomic or ionic
size, electronegativity difference, similarity of crystal structure and valency 117. All other
factors being similar, it is the crystal structure mismatch, cation mismatch, and the defect
charge difference between Gd+3 and Ce+4 that leads to the preferential segregation of Gd
(or other similar dopants) at the grain boundaries, with the driving force being the
reduction of grain boundary surface energy.118
To overcome this hurdle, the effect of sintering under reducing atmosphere on the
dopant segregation and ionic conductivity of doped ceria electrolytes was studied. The
hypothesis is that by sintering GDC pellets in a reducing atmosphere of 4% H2-N2, the
Ce+4 ions are expected to get reduced to Ce+3. CedG charged substitution defects are
thus not expected to form. All these factors combined are expected to lead to a more
uniform microstructure without much dopant and vacancy segregation at the grain
boundaries, thus improving the conductivity. A schematic is shown in Figure 7-4.
Esposito et al. in their work on gadolinia doped ceria have shown that sintering in reducing
atmospheres, produces highly defective GDC, and reduces the Gd/Ce cation mismatch
leading to a faster rate of mass diffusion.63 The grain growth and densification in
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conventional gadolinia doped ceria is otherwise inhibited due to a space charge effect
and is explained by the solute drag model.119 Esposito et al. use this phenomenon to
enable densification at lower sintering temperatures and also get a an increase in total
electrical conductivity.9
Figure 7-4. Schematic of dopant and vacancy distribution at grain boundaries for a sample sintered in air (left) and for one sintered in H2 and re-oxidized (right).
To prove the hypothesis of uniform dopant distribution and higher conductivity in
gadolinia doped ceria after sintering in a reducing atmosphere, control samples of 10GDC
were fabricated using the co-precipitation route as described in Chapter 3. The densities
obtained were in the range of ~97%. The other samples were sintered under a reducing
atmosphere of 4% H2-N2 as described in Chapter 2. Figure 7-5 shows the appearance of
the two kinds of samples. Control samples had a cream color, whereas, the reduced
samples showed shades of gray-black depending on the sintering conditions. The
reduced pellets were then oxidized at a lower temperature (900ºC) for 24 hours. Upon
re-oxidation, the color of the samples becomes similar to that of the control samples.
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Figure 7-5. Appearance of a 10GDC control pellet sintered at 1600⁰C for 10 hours (left) and one sintered under 4%H2-N2 at 1100⁰C for 20 hours (right).
7.4. Electron Probe Micro-Analysis
To determine the effect of processing on the segregation of dopants, electron
probe micro-analysis (EPMA) was used. EPMA uses a combination of wavelength and
energy dispersive spectroscopy (WDS and EDS), and makes possible minor and trace
analysis with high spatial resolution (sub-micron scale). For quantification of the
elemental distribution, the spectra standard materials were analyzed first. The standards
used were Gd metal (SPI supplies) for Gd, CeF3 (SPI supplies) for Ce and andradite
(Ca3Fe2Si3O12, P&H Developments Ltd. Geo Block MkII) for O, with the elemental
concentration in each of the standards already known. To identify and quantify the
elements, different peaks in the WDS spectra were used. The Lα peak was used for Ce,
since it was the highest intensity peak in the energy range analyzed. It was measured
using an LPET detector. For Gd, the Lβ peak was measured using an LLIF detector. This
is because, as shown in Figure 7-6, the Lα peak for Gd coincides with the Lγ peak for Ce,
thus making Gd detection very difficult. Similarly, a Kα peak is used to identify O using
an LLIF detector. The Gd Lβ peak has a lower intensity compared to other peaks. Hence,
for more accurate determination, longer collection times were used (10 ms).
128
Figure 7-6. WDS spectra from the LPET (top) and LLIF (bottom) detectors used to characterize Ce and Gd distribution using EPMA, shown here for a GDC conventional sample after sintering.
129
Figure 7-7. BSE image for 10GDC control sample.
Figure 7-7 - Figure 7-10 show area scans for the GDC control sample and Figure
7-12 - Figure 7-15 show the same for a sample sintered under a reducing atmosphere
and subsequently re-oxidized. Figure 7-11 and Figure 7-16 show representative line
scans across a grain boundary for the same respective samples. To obtain as
representative results as possible, multiple different area scans (total over 5000 μm2 per
sample) were performed on each sample. The initial data for each element is obtained
only in terms of intensity. This data was then converted to at% from intensity by applying
the information from the standards mentioned above. The line scans were obtained later
from the area scan data during post-processing using SX Results software accompanying
the equipment.
130
Figure 7-8. EPMA area scan for Gd Lβ peak, for 10 GDC control sample. Gd segregation is observed at grain boundaries and triple grain junctions.
Figure 7-7 shows a backscattered image for a control 10 GDC sample. The
corresponding EPMA area scan for the same area shows segregation of Gd at the grain
boundaries and triple point junctions. As can be seen from the representative line scan
data in Figure 7-11, the concentration rises from ~4 at% in the grain to ~10 at% at the
grain boundary. Similar to the atom probe study by Diercks et al.77, there is also a rise in
the concentration of Ce , from ~32 at% in the bulk to ~49 at% at the grain boundary as
can be seen from Figure 7-9 and Figure 7-11. Oxygen concentration on the other hand,
shows a drop in the vicinity of the grain boundary, from ~62 at% in the bulk to ~48 at% at
the boundary. This indicates a segregation of oxygen vacancies at the grain boundaries
and triple point junctions. These results are more or less consistent with what has been
reported in literature so far.76,77
131
Figure 7-9. EPMA area scan for Ce Lα peak, for 10 GDC control sample. Ce segregation is observed at grain boundaries and triple grain junctions.
Figure 7-10. EPMA area scan for O Kα peak, for 10 GDC control sample. Oxygen depletion is observed at grain boundaries and triple grain junctions.
132
Figure 7-11. Line scans of O, Gd and Ce concentration across a representative grain boundary in the 10GDC control sample.
In comparison, for a sample sintered under hydrogen, and re-oxidized, the area
scans do not show any evidence of segregation at grain boundaries and triple points.
Figure 7-12 shows the backscattered image for a sample sintered at 1100⁰C and oxidized
at 900⁰C. The corresponding area scans for Gd, Ce, and O are shown in Figure 7-13 -
Figure 7-15 respectively. The line scans in Figure 7-16 also show no segregation at the
grain boundary, as expected. Hence, the segregation of dopants at grain boundaries and
triple point junctions is avoided by sintering under a reducing atmosphere at a
comparatively low temperature and subsequent re-oxidation.
133
Figure 7-12. BSE image for 10 GDC sample sintered under 4%H2-N2 at 1100⁰C for 20 hours followed by re-oxidation at 900⁰C for 24 hours.
Figure 7-13. EPMA area scan for Gd Lβ peak, for 10 GDC sample sintered under 4%H2-N2 at 1100⁰C for 20 hours followed by re-oxidation at 900⁰C for 24 hours. A relatively uniform distribution of Gd is observed.
134
Figure 7-14. EPMA area scan for Ce Lα peak, for 10 GDC sample sintered under 4%H2-N2 at 1100⁰C for 20 hours followed by re-oxidation at 900⁰C for 24 hours. A relatively uniform distribution of Ce is observed.
Figure 7-15. EPMA area scan for O Kα peak, for 10 GDC sample sintered under 4%H2-N2 at 1100⁰C for 20 hours followed by re-oxidation at 900⁰C for 24 hours. A relatively uniform distribution of oxygen is observed.
135
Figure 7-16. Line scans of O, Gd and Ce concentration across a representative grain boundary in the 10GDC sample sintered under 4%H2-N2 at 1100⁰C for 20 hours followed by re-oxidation at 900⁰C for 24 hours. A relatively uniform distribution is observed.
It is interesting to note that, for the control sample, the rise in Gd and Ce at the
grain boundary and the corresponding drop in O most often do not happen at the same
distance. Most line scans showed that the peaks and valleys in concentration at the grain
boundaries were in fact a little off from each other as can be seen in Figure 7-11.
136
7.5. Conductivity Measurements
To study whether the changed processing technique has any effect on the ionic
conductivity of GDC, impedance spectroscopy measurements were performed as
described in Chapter 3. The measurements were performed at 50⁰C intervals from 200⁰C
to 650⁰C, both while heating and cooling. There was very little difference observed in the
Nyquist plots for heating and cooling, indicating that there was no oxidation of the samples
during the measurement. Figure 7-17 shows the Nyquist plot at 300⁰C for the two types
of samples normalized for their dimensions. As can be seen from the figure, the grain
boundary resistance for the conventionally sintered sample is much higher than the grain
boundary resistance for the sample sintered under reducing conditions. This is exactly
as expected, since the EPMA results show that only the first sample has segregation at
grain boundaries, and hence the higher resistance. Also, as can be seen from the inset
in Figure 7-17, the grain resistance also follows a similar trend, although the difference
between the two samples is not as much as the difference for the grain boundary
resistance. The lower grain boundary resistance for the sample sintered under hydrogen
can be explained by the fact that it now has a slightly higher dopant concentration and
more even distribution compared to the control sample. Admittedly, such a change in
grain and grain boundary resistance can also be brought about by a difference in grain
sizes. However, as can be seen from Figure 7-7 and Figure 7-12, there is not much
difference between the grain sizes of the two samples with their values being 2.64±0.15
μm and 2.46±0.36 μm respectively for the conventionally processed and reduced and re-
oxidized samples. The grain and total ionic conductivity for both the samples were
calculated from the resistances and dimensions as explained in Chapter 2. The thickness
of grain boundaries was neglected while calculating the grain conductivity.
137
Figure 7-17. Normalized Nyquist plot showing the comparison between the 10GDC control and H2 sintered samples measure at 300⁰C in air.
Figure 7-18 shows a plot of the grain conductivity for both groups of samples.
There is not much difference between the grain conductivity for the two groups. On the
other hand, there is a marked difference in the total conductivity of the two groups, with
the reduced and re-oxidized samples being more conducting by almost an order of
magnitude as shown in Figure 7-19. For example, at 350ºC, the total conductivity for the
conventionally sintered sample is 3.95x10-5 S/cm, whereas that for the reducing
atmosphere sintered sample is 1.09x10-4 S/cm with a difference of 6.99x10-5 S/cm. On
the other hand, the respective grain conductivities are 1.07x10-4 S/cm and 3.32x10-4 S/cm
with a difference of 2.25x10-4 S/cm. The large difference in total conductivity but a much
smaller difference in grain conductivity indicates that most of the change in conductivity
is due to the modification of the grain boundaries. The reducing atmosphere sintering
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and re-oxidation routine lowers the barrier at the grain boundary for oxygen ion transport.
The slight if any increase in grain conductivity on the other hand can be explained by the
fact that, since there is less segregation at the boundaries, more dopant ions and by
extension more vacancies are uniformly distributed throughout the bulk.
Figure 7-18. Arrhenius type plot of grain conductivity with respect to temperature for the 10GDC control and H2 sintered samples.
Both the grain and total ionic conductivity for the conventionally sintered samples
shows a change in slope, and subsequently activation energy, around 400⁰C. This
temperature is around the same temperature where the Meyer-Neldel rule is applicable,
and the defect associates break apart.14 Similar behavior has been observed by Esposito
139
et al.63 Interestingly, the 4% H2-N2 samples do not show this change in slope. A possible
reason for such an activation energy change could be the presence of a larger number of
defects associates which become free above a certain temperature. The defect
associates cannot be said to be just at the grain boundaries, but must be assumed to be
distributed throughout the conventional samples, because both the grain and total
conductivity show about the same change in activation energy (~ 0.3 eV). The reduced
and re-oxidized samples probably do not have such associates and hence do not exhibit
a slope change.
Figure 7-19. Arrhenius type plot of total conductivity with respect to temperature for the 10GDC control and H2 sintered samples.
140
As the temperature is increased, the difference between the grain and total
conductivity for the reduced and re-oxidized samples becomes smaller and smaller, as is
expected due the grain boundaries becoming more and more conductive. This trend is
however not as strong in the conventionally sintered samples. This difference in behavior
needs to be further explored to better understand the phenomena at play. For the
purposes of this work however, there is a clear correlation between the segregation at
grain boundaries and the conductivity.
Since the process utilizes a reducing atmosphere, the contribution of electronic
conduction cannot be completely ruled out. However, any electronic contribution has to
be mostly through the grain boundaries parallel to the field as was discussed in the
previous chapter. This should lead to the appearance of a new resistance parallel to the
original equivalent circuit. This however does not happen, and for both the conditions,
the impedance data can be satisfactorily fit using the same equivalent circuit as shown in
Figure 7-17 indicating that the samples have been oxidized to a large extent after re-
oxidation. The same can be ascertained by the change of color from black/grey to cream
color. Hence any electronic contribution to conductivity is expected to be minimal. For a
more accurate conclusion, future work envisages transport number measurements to
determine the electronic contribution to conductivity.
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CHAPTER 9 SUMMARY AND FUTURE WORK
8. 8.1. Summary
8.1.1. Protocol for Impedance Data Analysis
There is a need for a protocol for more standardized testing and analysis of
impedance data, to get accurate and reproducible results. Such a protocol was compiled
together based on best practices in literature. The identification of a correct equivalent
circuit based on a plausible physical model is of utmost importance and various methods
of ensuring the same were suggested. An understanding of the various relaxation
mechanisms possible in a material is essential for identifying the correct model. This
requires a better understanding of the response of various parameters, especially
constant phase elements (CPEs). The mathematical nature of CPEs was presented in
detail, and their relationship to other parameters like resistance, capacitance, inductance
and Warburg elements were investigated. Various ways of identifying initial estimates of
parameters for fitting were presented based on literature. Incorrect starting values for
fitting can give wrong results. Different statistical ways for assessing the quality of fit were
identified. Residual analysis can be used as a good measure of how good a fit is, and
any trends in the residuals can show whether the equivalent circuit is appropriate.
Following these practices should give better results from data fitting.
8.1.2. Impedance and Effect of DC Bias
Impedance data for both bulk and thin film GDC samples were analyzed using the
protocol described in Chapter 4. The films prepared using magnetron sputtering were
tested for impedance under a DC bias. This is the first study of this kind on gadolinia
doped ceria. The bias values used in this study are higher than any similar study
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performed before for other materials. Under the application of a DC bias, new unique
features appear in the impedance Nyquist plots for the films. Bias values ranging from 0
V to 5 V were tried. The complex impedance plots were fit to equivalent circuits. The
change in behavior under bias was ascribed to the introduction of electronic conduction
in the system in addition to the already present ionic conduction. The application of a
bias causes the opening up of a parallel path for conduction of electrons, which becomes
more pronounced at higher fields. Both bias and temperature affect this electronic
conduction, with the effect of bias becoming more pronounced at higher temperatures.
Overall, three regimes were observed in the effect of bias on GDC thin films. A low bias
regime, where the grain boundary resistance increases due to segregation of vacancies
at the boundaries. In this regime, although there is an electronic pathway, its resistance
is very high. At higher bias values, in the second regime, due to the high bias, electrons
are injected from the cathode and are conducted through the grain boundaries parallel to
the field direction. With increasing bias, the conduction across grain boundaries also
increases. In both the first and the second regime, the grain contribution to the response
remains almost unchanged. At further higher bias in the third regime, inductive loops
start to appear in the impedance data at low frequencies, which introduces an inductance
in the equivalent circuit. This inductance is attributed to the possible redistribution of
segregated vacancies near the cathode at low frequencies.
The effect of bias was found to be reversible and independent of the polarity of the
applied bias. However, there was a time lag (on the order of tens of seconds, depending
on the temperature) for the material to return back to normal behavior on removal of bias.
DC I-V measurements were also used to better understand the observed behavior. The
143
sweep rate of the of the I-V measurement was matched to the frequency of the impedance
plot intercept with the real axis. The resistance obtained from the I-V measurement was
found to match with the parallel resistance from the equivalent circuit analysis.
8.1.3. Sintering under Reducing Atmosphere
It was shown that sintering under reducing atmospheres can be used to prevent
dopant segregation. This was shown using gadolinia doped ceria as an example. The
elemental distribution was characterized using electron probe microanalysis. In 10GDC
samples sintered in air, area scans showed an increase in concentration of the dopant
gadolinium, in addition to the increase in cerium and depletion of oxygen. The depletion
of oxygen suggests a high concentration of oxygen vacancies. Such an elemental
distribution reinforces the theory of defect associate formation as has been suggested
before. Samples sintered under a reducing atmosphere in comparison, showed a
relatively uniform elemental distribution. There was no segregation of either gadolinium
ions or oxygen vacancies. With a more uniform dopant distribution and no vacancies
bound at grain boundaries in the samples sintered in a reducing atmosphere
(subsequently re-oxidized), they show both, a smaller grain boundary and grain
resistance. Hence, the hypothesis, that by reducing the cation mismatch between the
host and dopant ions, a dopant segregation can be prevented, was proven true with the
help of the new technique of sintering under reducing atmospheres. However, a lot of
questions are still unanswered. They are summarized in the next section.
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8.2 Future Work
8.2.1. Effect of DC Bias
This work was the first time the effect of bias was observed on gadolinia doped
ceria. However, the work performed only looked at thin films. Similar testing needs to be
performed with bulk GDC. Thin films have generally been shown to behave every
differently compared to bulk materials. This will help separate thin film effects from bias
effects. The testing of bulk samples however will be challenging given that it will be very
difficult to get comparable DC field levels in the bulk samples. The oscillating voltage for
impedance and its relation to the DC bias magnitude is also expected to play an important
role in the effect observed. To the knowledge of the author, no impedance measurement
system exists yet which can reproduce such conditions.
Even among thin films, further work can be envisaged. Transference number
measurements need to be performed to calculate more accurately the electronic
contribution under bias. The role of grain boundaries in this mechanism is not yet
completely understood. Their effect can be separated by testing of epitaxial thin films in
the across plane configuration. Such films should have no grain boundaries in the
conduction path between the top and bottom electrodes. Additionally, in-situ
characterization of the oxygen vacancy distribution under bias needs to be performed
which will help bolster the vacancy segregation theory. Leakage current measurements
at different temperatures and bias values can be used to measure the barrier height of
the Pt-GDC interface as further reinforcement of the theories proposed.
8.2.2. Sintering under Reducing Atmosphere
For the work on sintering under a reducing atmosphere, further work needs to be
performed to ascertain a number of issues relating to the composition and electrical
145
properties of the samples. It is still not clear as to what percentage of the ceria, gets
reduced, and what amount of the reduced oxides remain after re-oxidation. Although, the
impedance plots showed little change between heating and cooling, and the equivalent
circuit shows no new circuit elements suggesting significant electronic contribution to
conduction in re-oxidized samples, accurate assessment of electronic contribution needs
to be performed, as it is crucial and detrimental for the use of doped ceria in fuel cells.
Transference number measurements using ionic blocking electrodes need to be
performed to measure the electronic contribution. Although a lot of work has been done
on understanding the effect of grain boundaries on ionic conduction, the mechanism
behind the blocking nature of the boundaries is still under contention. Although this was
not explicitly addressed in this work, it is clear that in order to tailor electrical properties
of electroceramics, a fundamental knowledge of grain boundary behavior is essential.
Once the fundamentals are established, the technique sintering in a reducing atmosphere
can be better tailored by investigating different temperature and atmosphere
combinations.
The reducing atmosphere sintering technique can be applied to other ceramic
materials where dopant segregation leads to degradation of their electrical and
mechanical properties. The process however will be applicable only to those systems
which show variable valency states like Ce4+ and Ce3+ in cerium oxide based systems.
Various other factors like the ionic radii and crystal structure will also play an important
role, which needs to be investigated in detail. Additionally, the time behavior of the
reduced and re-oxidized sample needs to be investigated, to find out the endurance of
the samples against re-segregation after prolonged use.
146
The technique can also be used to produce high density sintered oxide ceramics
at lower sintering temperatures by exploiting the higher mass diffusion rates under
reducing atmospheres as has been shown by Esposito et al.59 Application of this
technique to other material systems needs to be investigated.
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APPENDIX A IMPEDANCE DATA FITTING WITH ZVIEW
A. Following are the steps followed for fitting using ZView® software (Scribner
Associates Inc.) based on the best practices summarized in Chapter 6.
1. Import data for the entire temperature range into ZView®. ZPlot® software
(Scribner Associates Inc.) provides the data in a format which can be read using
ZView®. For other formats (obtained for example using the Agilent 4924 Precision
Impedance Analyzer), the data has to be arranged into the required column format
for ZView® first.
2. To ensure proper weighting of data over the entire frequency range, use log-log
plots, unless otherwise needed. A linear frequency range plot can hide important
features in the data. Zoom in to the data if needed to better see certain features.
3. Use the “auto color” option and view all the data at once in the Z* formalism for all
temperatures. This will show trends in the data with respect to temperature and
help in identifying possible equivalent circuits.
4. For most oxide ionic conducting materials, three arcs will be completely or partially
visible depending on the frequency range. They can be assigned from higher to
lower frequency to the grain, grain boundary and electrode interface contribution
respectively depending on the associated capacitance values. Bulk arcs usually
have capacitance in the 10-11-10-12 F range, grain boundary in the 10-8-10-10 F
range and, electrode interface around 10-6-10-7 F. The arcs can also be identified
on the basis of the frequency ranges they lie in, where the bulk is in the MHz range,
grain boundary in the kHz and electrode interface in the Hz range, although these
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may vary widely depending on the material, its processing and measurement
conditions.
5. Observe data in both Z and M formalisms, to clearly identify the number of arcs.
Each relaxation mechanism will give a separate peak in both these formalisms.
6. Each arc can be usually fit with a parallel combination of R and CPE, as defined in
Chapter 5. Based on the number of arcs, create a tentative equivalent circuit.
7. Calculate approximate starting values for all the components. R can be calculated
either by visual observation where the diameter of the semicircle is the resistance,
or by using the ‘fit circle’ option in Zview for each arc separately. Select sections
of the plot by moving the slider at the top of the Zview window. The fit circle option
also gives a C value. However, to get a better estimate of the values for CPE-P
and CPE-T, plot Y” against log ω. The slope is CPE-P and the intercept with the
Y-axis can be used to calculate CPE-T as shown in Chapter 6.
8. A CPE can be used even in place of a pure capacitor (C), as it can also model a
capacitor, where CPE-P is 1. In case the electrode interface part of the data is a
straight line instead of a curve, it can be modelled using just a CPE instead of an
R-CPE parallel combination.
9. With the starting values in hand, perform a ‘simulation’ for the values and the
equivalent circuit. This will give a clear idea if the circuit behavior and initial values
are far off from the data. Adjust the starting values accordingly if needed.
10. After obtaining a satisfactory simulation result, perform fitting using the ‘fitting’
option. Individual arcs can be fit one by one if needed, by fixing the remaining
parameters, and keeping only the R and CPE values for that part of the data free.
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11. On fitting, the calculated plot should better match the measured data, compared
to the simulation.
12. Check the data and the fit in all four formalisms, namely Z*, Y*, M* and ε*. Visually
inspect the data and make sure that it fits equally well in all the formalisms. Any
marked deviation in any of the formalisms indicates an incorrect equivalent circuit,
given that the fit is good for other formalisms. Change the circuit accordingly,
based on knowledge of the material, and repeat the process.
13. In case the arc does not begin at the origin, select appropriate extra circuit
element/s (L, C, or R) to model this deviation in series with all the other elements
in the beginning of the circuit. A shift along the x axis indicates a series resistance.
The starting point in the first quadrant indicates an extra capacitance, whereas a
starting point in the fourth quadrant indicates an inductance.
14. Start fitting data from the lowest temperature to the highest in the measured range.
Usually, the parameter values change consistently in a progression with changing
temperature. Thus, the fit at a certain temperature can be directly used to obtain
a fit for the next higher temperature and so on. This strategy greatly speeds up
the process and works satisfactorily unless new mechanisms and parameters are
being introduced.
15. It needs to be noted that after fitting, the values obtained for the different
parameters should make physical sense.
16. The % error values for each of the parameters should be below 5%, in addition to
the visual confirmation of the fit.
150
17. The sum of squares and chi-squared values should be as low as possible. The
smaller these values, the better the fit. A good fit should have chi-squared lower
than 0.01 and sum of squares around or lower than 1.
18. To verify if there is any systematic error in the fit due to an incorrect circuit, the
residual values for the fit can be plotted against frequency, using the ‘residual’
option in Zview. For a good fit, the residual values should be low and there should
be no visible trend with respect to frequency.
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APPENDIX B DIELECTRIC POLARIZATION FUNCTIONS
B. The original theory on dielectric polarization and the related equations were
proposed by Debye.120 The related equation for the complex permittivity is given as
follows.
i1
(B-1)
Here s , with s and being the static and infinite frequency dielectric
constants, and is the relaxation time for a given temperature. On a complex plane plot,
the Debye relaxation shows up as a perfect semicircle with the two intercepts being the
static and infinite frequency dielectric constants. The highest point in the plot indicates
the dielectric relaxation frequency corresponding to the relaxation time. A schematic is
shown in Figure B-1.
However, most materials do not have a single relaxation time constant. In fact,
they exhibit a distribution of time constants. Following are a few of the important
modifications to the Debye formalism to account for distributed time constants. The Cole
-Cole88 model shown in equation (B-2), introduces an exponent , which accounts for
depression of the semicircle in the complex plane. When 0 , the relaxation is
stretched on the frequency scale, as the time constants become more distributed. This
modification accounts for arcs that are depressed, but are still symmetric. Figure B-1
shows the effect of increasing value of on the complex plane plot.
1i1
(B-2)
152
Another modification to the formalism has been proposed by Davidson and Cole90
which introduces a factor as shown in equation (B-3). This change introduces an
asymmetric nature in the data as shown in Figure B-1. This function can be used to fit
data when the plot is not depressed, but is asymmetric.
i1
(B-3)
A combination of the above mentioned approaches was proposed by Havriliak and
Negami121,122 where both and are used as shown in equation (B-4). This expression
takes care of both, a wider distribution and asymmetry in the distribution of time constants.
1i1
(B-4)
The Havriliak-Negami expression can be easily converted to the other expressions
by assuming 0 (Davidson-Cole) and 1 (Cole-Cole) or both (Debye).
Figure B-1. Schematic representing the complex plane plot for permittivity according to Debye theory (left) and the effect of the exponents and .
In addition to these there are some other distributions like the ones by Kirkwood-
Fuoss, Frohlic, and Matsumoto-Higasi, which apply to specific cases and are not
discussed here.
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APPENDIX C THERMALLY STIMULATED DEPOLARIZATION CURRENT
C. As discussed in Chapter 2, defect complexes in doped ceria hinder the movement
of oxygen vacancies. Defect complexes have dipole moments and thus their orientation
can be influenced by an applied electric field. This fact can be exploited using thermally
stimulated depolarization current (TSDC) measurements to gain an insight into the
different kinds of complexes and their dynamics and also that of the free oxygen
vacancies in a given sample.
Figure C-1. Schematic diagram of polarization and heating profile for TSDC measurement.123
Typically, in TSDC, a sample is polarized under a constant electric field (𝐸𝑝) at an
elevated polarization temperature (𝑇𝑝). The possible defects present in the system such
as defect complex dipoles and free vacancies will respond to this field and form a
polarized metastable charge or dipole distribution. The sample is then cooled with the
field still applied, so that the alignment is frozen. The field is subsequently removed and
the sample is heated with a controlled heating rate. Figure C-1 shows a schematic of the
steps described above. With increasing temperature, the lattice vibrations will activate
the motion of charges or aligned dipoles. The charge distributions or polarized states
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then undergo relaxation at specific temperatures, giving rise to a current in the external
circuit which first increases with temperature and then decays when the supply of charges
is depleted or the dipoles are randomized. A current peak will thus be observed where
dipolar disorientation, ionic migration or release of charges from traps is activated and a
complete picture of temperature – dependent relaxations can in theory be obtained in the
form of a TSDC spectrum.56,124–126
Figure C-2. A schematic of an expected TSDC spectrum for doped ceria.
All mechanisms contributing to polarization which are temperature dependent can
be measured separately using this method, namely orientation polarization of permanent
dipoles or of dipoles induced by the electric field, space charge polarization, and electrode
effects. This can be done provided the corresponding relaxation times differ considerably.
In rare earth doped ceria, the two main mechanisms of interest are dipolar polarization of
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the defect associates at relatively low temperatures and space charge polarization at high
temperatures due to ionic movement. Figure C-2 shows a schematic of the expected
TSDC spectrum for doped ceria.
Preliminary TSDC testing was performed for acceptor doped bulk ceria samples in
the low temperature range. Factors such as polarizing temperature, heating rate and the
dopant were varied. Figure shows the TSDC spectra for two gadolinia doped ceria
samples. The temperature control was achieved using a Cryodyne refrigerator. Current
measurements were performed using an Agilent 4156 Precision Semiconductor Analyzer.
It also has a built-in voltage source which was used to apply the polarizing voltage.
Figure C-3. TSDC results showing the current density with respect to temperature for a 10 mol% gadolinia doped ceria sample with different polarizing temperatures and heating rates.
It can be seen that the data is very similar to that expected from the schematic.
The different peak heights are due to the polarization difference, which is shown
156
separately later, whereas the position and width of the peaks is altered due to the different
heating rates. The data obtained can be used to determine the activation energy of the
rotation of defect complexes (and the motion of vacancies in the high temperature range).
An expression for TSDC current density was derived by Bucci and Fieschi.127
kT
Eexp
E
kT1exp
kT
Eexp
TPTJ a
a
2
o
a
o
pe
D (C-1)
Here pe TP is the equilibrium polarization at polarization temperature, pT . is the
heating rate, aE is the activation energy and o is the relaxation time at infinite
temperature. This discharge current represents an asymmetrical curve, the amplitude of
which is a linear function of the previously applied field. The first exponential which
dominates in the low temperature range represents the initial rise of current with
temperature. The second exponential dominating at higher temperatures is responsible
for gradually slowing the current rise and then depresses it rapidly.127 To determine the
activation energy for dipolar polarization, the “initial rise method” by Garlick and
Gibson.128 The current density of the initial part of the peak was plotted in an Arrhenius
form against temperature and the slope of the plot was used to determine the activation
energy as shown in Figure C-4. Figure C-5 shows the effect of different polarizing
temperatures on TSDC results for a gadolinia doped ceria sample. As expected, a higher
polarization temperature leads to a higher TSDC peak as there is more polarization.
However, the position of the peak is constant indicating that the kind of defect complexes
are the same. Peak positions act as a sort of a fingerprint for identifying different
associates, for a given constant heating rate.
157
Figure C-4. Arrhenius plots of the current density with respect to temperature for the two peaks in Figure C-3.
Figure C-5. Plot showing the effect of polarizing temperature on TSDC peak intensity for a 10 mol% gadolinia doped ceria sample.
Figure C-6 on the other hand shows the effect of using different dopants and
different dopant concentrations, all other conditions remaining the same. It was found
158
that a higher dopant concentration leads to smaller peaks. This could possibly be
because of more complicated and bigger associates forming at higher dopant
concentrations, which require higher temperature and applied fields for polarization. The
formation of different kinds of defect associates also leads to the peaks having different
widths and being slightly shifted from each other.
Figure C-6. Plot showing the effect of different dopants and different dopant concentrations on TSDC peak intensity.
A similar approach can be used to study vacancy migration in oxide ceramic
materials is sufficiently high temperatures are used for polarization. This preliminary data
presented here shows that TSDC can be a useful supplement to traditional electrical
characterization techniques by providing more information about the energetics for
polarization of different complexes and vacancy migration, and thus needs to be further
studied.
159
APPENDIX D COLOSSAL PERMITTIVITY IN BARIUM STRONTIUM TITANATE*
D. D.1. Introduction
Barium strontium titanate (Ba1–xSrxTiO3, BST) is an intensively studied and well-
known material for various electronic applications such as capacitors,129 positive
temperature coefficient resistors,130 phase shifters,131 and gas sensors.132 BST
compounds are synthesized through a variety of methods like co-precipitation,133,134 sol–
gel synthesis,135 hydrothermal,136 and solid-state reactions.9 Conventionally sintered BST
bulk ceramics show high relative permittivity with low losses ( r = 103 and tan = 0.03)
and a variable Curie temperature.137,138
Since the turn of the century, there has been renewed interest in compounds with
colossal effective permittivity.139–142 They have been studied because of their high
technological potential, especially as dielectrics for capacitor applications. These
materials, usually metal oxides, can be fabricated as bulk materials and/or thin films.
Different techniques have been used to achieve high dielectric response in such
materials.143–149 An ideal colossal permittivity material should exhibit wide windows with
temperature- and frequency-independent response. Among bulk materials, different
oxides such as CaCu3Ti4O12 (CCTO),139–141,150,151 Li–Ti co-doped NiO,152 ferrites,153,154
and reduced perovskites155,156 show remarkably high dielectric permittivity which is
* This section is comprised of the work presented in the following journal articles:
S. Dupuis, S. Sulekar, J.H. Kim, H. Han, P. Dufour, C. Tenailleau, J.C. Nino, and S. Guillemet-Fritsch, “Colossal permittivity and low losses in Ba1–xSrxTiO3–δ reduced nanoceramics,” J. Eur. Ceram. Soc., 36 [3] 567–575 (2016).
S. Sulekar, J.H. Kim, H. Han, P. Dufour, C. Tenailleau, J.C. Nino, E. Cordoncillo, H. Beltran-Mir, et al., “Internal barrier layer capacitor, nearest neighbor hopping, and variable range hopping conduction in Ba1−xSrxTiO3−δ nanoceramics,” J. Mater. Sci., 51 [16] 7440–7450 (2016).
160
temperature and frequency independent in a broad range. Such high permittivity is
attributed to a number of intrinsic and extrinsic interfacial mechanisms. For example,
Lunkenheimer et al. have shown that polarization effects at the electrode and material
contact contribute to the apparent high dielectric constant values in CCTO.151,157 The
intrinsic contribution on the other hand is attributed to hopping polarization, depletion
layers,158 and insulating domain and grain boundaries with respect to semiconducting
grains and domains.159 Moreover, in the case of barium titanate (BT), the electrode
effect has been separated out to be about 15 % by Han et al.160 Noble metals like Au
and Ag form Schottky contacts with BT, whereas Al electrodes form ohmic contacts.
The electrode effect on colossal permittivity can thus be estimated by subtracting the
permittivity obtained for Al electrode from that measured with Au. Overall, it has been
shown that for barium titanate, depending on processing conditions, the relative
contributions to colossal permittivity are approximately 65 % hopping polarization, 20 %
interfacial polarization, and 15 % electrode effects.160
Fast firing processes, such as spark plasma sintering (SPS) or microwave
sintering, have been employed to achieve colossal permittivity in BT based
ceramics.133,161–163 In these fast-fired materials, mixed valence state of the cations due
to extrinsic defects, localized in the vicinity of grain boundaries, has been proposed as a
mechanism at the origin of colossal permittivity.160,164 In addition, it has been shown that
semi-conductive grains are separated by thin insulating grain boundaries, leading to an
internal barrier layer effect (IBLC) for colossal permittivity in BT.160,164,165 The properties
of BT can be tuned by the substitution of Ba2+ by Sr2+ cations. The aim of the work
presented here was to understand the effect of Ba–Sr substitution on the dielectric
161
properties of a series of Ba1–xSrxTiO3 (0 ≤ x ≤ 1) solid solutions and netter understand the
origin of colossal permittivity and the involved underlying mechanisms.
D.2. Experimental procedure
D.2.1. Fabrication
The co-precipitation method similar to that described in chapter 3 was used to
prepare the BST nanopowders. BaCl2·2H2O (Prolabo), SrCl2·6H2O (Sigma-Aldrich), and
lab-made TiOCl2 were weighed in appropriate proportions, dissolved in water, and added
to an ethanolic oxalic acid solution. After a 5 h aging, the solution was centrifuged and
dried for 12 h at 80°C. The powders were then ground and sieved before calcination at
850°C for 4 h. Spark plasma sintering (SPS) was carried out using a Dr. Sinter 2080
device from Sumitomo Coal Mining (Fuji Electronic Industrial, Saitama, Japan) in order to
densify the BST nanopowders. The oxide powder (0.5 gm) was loaded in the graphite
die (8 mm diameter) and the powders were sintered at 1150°C in vacuum (residual cell
pressure <10 Pa). The powders were heated at a rate of 25°C/min, with a 3-minute dwell
time at 1150°C before the electric current was switched off and the pressure was
released. A thin carbon layer, due to graphite contamination from the graphite sheets,
was observed on the as-sintered pellets surfaces, as has been reported before161, and
was removed by polishing the surface. Finally, the SPS sintered ceramics were annealed
for 15 minutes at 850°C in an oxidizing atmosphere and quenched in air.
D.2.2. Characterization
The chemical composition of the different oxide powders was determined using
inductively coupled plasma-atomic emission spectroscopy (ICP-AES) with a JY 2000
device (Horiba Jobin Yvon, Kyoto, Japan). The morphology of the powders was observed
162
with a field emission gun scanning electron microscope (FEG-SEM, JSM 6700F, JEOL,
Tokyo, Japan) and the particle size was determined by ImageJ software.166 The grain
boundaries thicknesses were observed with a high resolution transmission electron
microscope (HRTEM, JEM 2100F, JEOL, Tokyo, Japan). The crystalline structure was
investigated by X-ray diffraction analysis using a D4 Endeavor X-ray diffractometer
(CuKα1 = 0.154056 nm and CuKα2 = 0.154044 nm; Bruker AXS, Karlsruhe, Germany)
from 20° to 80° (2-theta). The density of the pellets was determined by the Archimedes
method using an ARJ 220-4M balance (KERN, Murnau-Westried, Germany).167 Prior to
electrical measurements, the flat faces of the ceramic disks were coated with thin gold
electrodes (thickness ∼30 nm) by sputtering (108 Auto, Cressington Scientific
Instruments, Watford, U.K.). The relative permittivity and the dielectric losses were
obtained from impedance measurements using a 4294A Precision Impedance Analyzer
and an E4980A Precision LCR Meter (Agilent Technologies, Palo Alto, CA) in the range
of 40–100 kHz at room temperature and an applied AC voltage of 1 V. For temperature
dependence of the dielectric properties, the electroded samples were placed in a closed
cycle cryogenic workstation (CTI 22, Cryo Industries of America, Manchester, NH) and
measurements were taken as a function of temperature (40–300 K).
D.3. Results and Discussion
Only the results pertaining to the electrical characterization of the materials under
study are discussed here, since it was performed primarily by the author. The
microstructural characterization was performed by the other collaborators mentioned
above.
163
D.3.1. Dielectric Spectroscopy
The dielectric response of the BST (0 ≤ x ≤ 1) nanoceramics measured as detailed
above is shown in Figure D-1.
Figure D-1. Variation of the real part of relative permittivity and losses (tan) as a
function of frequency for the Ba1–xSrxTiO3– nanoceramics at 300K.
As can be seen in Figure D-1, colossal permittivity up to 105 with low dielectric
losses (tan < 0.05) was achieved for most of the compositions (0 ≤ x ≤ 0.6). The values
164
for rε and tan measured at 1 kHz and 300 K are reported in Table 2. It was observed
that the relative permittivity and dielectric losses of BST compounds gradually decreased
as Sr content increased.
Table D-1. Dielectric properties of the Ba1–xSrxTiO3–δ nanoceramics.
Composition r (1 kHz, 300 K) tan (1 kHz, 300 K) TCC (10−3 K−1)
BaTiO3–δ 729000 0.05 1.9
Ba0.8Sr0.2TiO3–δ 388000 0.04 1.5
Ba0.6Sr0.4TiO3–δ 174000 0.03 3.6
Ba0.4Sr0.6TiO3–δ 115000 0.03 3.3
Ba0.2Sr0.8TiO3–δ 30800 0.03 0.5
SrTiO3–δ 6300 0.01 0.04
The BST nanoceramics samples in this work exhibit much higher permittivity
compared to the results in the open literature. For instance, Fu et al. prepared the solid
solution BaxSr1–xTiO3 ceramics via solid-state reaction followed by conventional sintering,
and reported permittivity values at room temperature and for 1 kHz, ranging between
1500–3000 for increasing barium content.137 The combination of mechanosynthesis and
spark plasma sintering has been used for the first time for the Ba–Sr–Ti–O system by
Hungría et al.168 While the ceramics exhibited nanosize grains, low permittivity values
were observed, 1400 for BaTiO3 and 200 for SrTiO3 respectively. Gao et al. used an
organosol synthesis to prepare Ba0.6Sr0.4TiO3 nanoparticles with an average grain size of
35 nm and followed it by spark plasma sintering to prepare nanoceramics showing a
maximum permittivity value of 3000.169 These examples show the importance of each
step of the ceramic process to obtain controlled colossal permittivity values in the BST
ceramics: oxalate co-precipitation to synthesize homogeneous powder of controlled
165
morphology, size and stoichiometry, SPS sintering to obtain ceramics with nano-size
grains and reduced titanium cations and a short annealing treatment to retain oxygen
sub-stoichiometric compounds.
Figure D-2. Variation of the real part of the relative permittivity and losses (tan) as a function of temperature measured at 1 kHz for the Ba1–xSrxTiO3–δ nanoceramics.
166
The permittivity and the losses of BST compounds as a function of temperature
(300–450 K) are shown in Figure D-2. Colossal permittivity can be observed over a wide
temperature range (300–450 K). The ferroelectric–paraelectric transition, corresponding
to the tetragonal–cubic phase transition was seen only for pure BT ceramics by a peak of
rε occurring at the same temperature (TC = 396 K) whatever the frequency up to 100
kHz. The temperature coefficient of capacitance, TCC (variation of capacitance between
310–450 K), is determined according to equation (D-1):
K310K450
CC
C
1TCC minmax
K310
(D-1)
The lowest value of TCC, 44 ppm.K−1, observed for the composition SrTiO3–δ (Table 2),
is lower than the values reported for temperature stable capacitors, i.e., in the BaTiO3-
Bi(Zn1/2Ti1/2)O3-BiScO3 system.133
D.3.2. Impedance Spectroscopy
To analyze the behavior of the different regions of the samples, i.e., grains and
grain boundaries, impedance measurements were carried out as a function of frequency
over the temperature range from 120 to 473 K. Analysis of the impedance complex plane
plots for a high Ba-content sample and a high Sr-content sample at 170 K (Figure D-3),
showed an asymmetric arc of resistance R1 at high frequencies.
Assignment of the main impedance arc to grain regions is supported by the
representation of the same impedance data as MZ spectroscopic plots. The peak in
the M plot corresponds to the region of the sample with the smallest capacitance (
110 cmF108.2 for Ba0.8Sr0.2TiO3−δ and 110 cmF102 for Ba0.2Sr0.8TiO3−δ), and
therefore, to the grains. This also corresponds to the almost frequency independent, but
167
temperature dependent plateau at high frequencies in the spectroscopic plots of C .
Thus, R1 corresponds to the sample bulk resistance and is in the order of 3500 Ω-cm for
Ba0.8Sr0.2TiO3−δ and 7500 Ω-cm for Ba0.2Sr0.8TiO3−δ at 170 K.
Figure D-3. Impedance complex plane plots and Z′′/M′′ spectroscopic plots at 170 K, and capacitance data at 150 and 170 K for Ba0.8Sr0.2TiO3−δ (a, c and e) and Ba0.2Sr0.8TiO3−δ (b, d and f) nanoceramics. The solid data points in (a) and (b) refer to frequencies of 200 and 4.5 kHz.
168
In the spectroscopic plots for C , a second plateau is observed at lower frequency
with capacitance 18 cmF101 and 19 cmF105.6 at 170 K for Ba0.8Sr0.2TiO3−δ and
Ba0.2Sr0.8TiO3−δ, respectively, which might be attributed to a conventional (but high
permittivity) grain boundary, C2. Therefore, for both samples, the impedance data may
be represented ideally by an equivalent circuit containing two parallel RC elements in
series.
D.3.3. Polarization mechanisms
Figure D-4. Variation of the real parts (a) and (c) and the imaginary parts (b) and (d) of permittivity as a function of temperature and at different frequencies for Ba0.8Sr0.2TiO3–δ and Ba0.2Sr0.8TiO3–δ nanoceramics.
169
To investigate the relaxation phenomena observed in BST nanoceramics, the
dielectric properties of each composition were measured as a function of temperature
(40–300 K) at different frequencies. Figure D-4 shows the dielectric data for one Ba-rich
(x = 0.2) and one Sr-rich composition (x = 0.8), respectively, which exhibit distinctly
different dielectric relaxation behavior.
In the following sections, the possible mechanisms, explaining the temperature
stable dielectric properties of BST compounds by using corresponding physical models
such as Debye relaxation, universal dielectric response (UDR), and hopping polarization
models are discussed.
D.3.3.1. Debye Model
Debye-like dielectric relaxations were observed for both compositions, and the
maximum of rε shifts to higher temperature as frequency increases, indicating that
frequency dependent relaxation processes may exist in the compounds. In the Debye
model, the relaxation frequency and the activation energy can be extracted by using the
equation below:
Tk
Eexp
B
aO
(D-2)
where O , Bk , and aE are the pre-exponential factor, the Boltzmann constant, and the
activation energy for relaxation, respectively. The relaxation temperatures at different
frequencies were extracted from the maximum of r for each of the BST compounds and
plotted in the Arrhenius form to determine the activation energy.
170
Figure D-5. Temperature dependence of relaxation frequency for Ba0.8Sr0.2TiO3–δ and Ba0.2Sr0.8TiO3–δ nanoceramics.
It can be clearly seen in Figure D-5 that Ba0.8Sr0.2TiO3–δ shows two different slopes
corresponding to two activation energies, while no distinct slope change was observed
for Ba0.2Sr0.8TiO3–δ. This result indicates that, similar to BT,160 BST compounds with high
barium content might have two different polarization mechanisms, possibly hopping
polarization combined with interfacial space charge polarization, while Sr-rich BST might
have only one polarization mechanism.
D.3.3.2. Universal Dielectric Response Model
It is also well known that Jonscher’s universal dielectric response (UDR) model
can be applied to explain dielectric polarization in colossal permittivity materials, as
described by the following equations,170
O
O
1s
r
f2
stan
(D-3)
171
sfTAf r (D-4)
where O and s represent the temperature dependent constants, O and f are the
permittivity of free space and experimental frequency ( 2f ), respectively, and TA
is equal to OO2stan . Thus one can extract the value of the exponent s by plotting
flog r vs. flog . An s value as closer to 1 implies that the polarization charges are
more highly localized.171
Figure D-6. Variation of the real part (a) and (c) and the imaginary part (b) and (d) of permittivity as a function of frequency and at different temperatures for Ba0.8Sr0.2TiO3–δ and Ba0.2Sr0.8TiO3–δ nanoceramics.
172
Figure D-6 shows the real and imaginary parts of dielectric permittivity for BST (x
= 0.2) and BST (x = 0.8) samples as a function of frequency (40–100 kHz) at different
temperatures (40–300 K). Dielectric relaxation occurs at each temperature, given that
distinct relaxation peaks of imaginary part of permittivity were observed for the
compositions. Furthermore, the relaxation peaks shift to lower frequencies as
temperature decreases, which indicates that thermally activated relaxation phenomena
are involved.
Figure D-7. fr vs. f plot in log–log scales for (a) Ba0.8Sr0.2TiO3–δ and (b)
Ba0.2Sr0.8TiO3–δ dense nanoceramics at different temperatures (40–300K).
173
Figure D-7 presents fr vs. f plots in log–log scales for the same samples.
For the Ba-rich BST (x = 0.2) compound, high temperature slope is close to 1, which is
different from the value of the low temperature slope, indicating that dielectric polarization
is more localized at higher temperatures.
As has been shown in literature, the slope change in flog r vs. flog plot as
temperature decreases is associated with the hopping polarization which becomes
inactive at lower temperatures due to insufficient energy to overcome energy barrier for
polarization.160 For the Sr-rich BST compound (x = 0.8), no slope change was observed
for the different temperature regions. Thus, one can expect that hopping polarization
might not be significant in Sr-rich BST compounds.
D.3.3.2. Thermal Hopping Polaron Model
To investigate the behavior of Sr-rich compounds, it is important to recall the
thermally activated hopping polaron (THP) model,172 where the maximum of r is
proportional to the number of polarons participating in hopping polarization.
Tk3
N
B
2
maxr
(D-5)
Tk
EexpNN
B
aO
(D-6)
Nand represent the number of hopping polarons and the hopping dipole moment
respectively. ON and aE are the pre-exponential factor and the activation energy related
with relaxation of hopping dipoles respectively. By substituting equation (D-5) into (D-6),
the equation for the thermally activated hopping polaron model can be obtained as below.
174
Tk
Eexp
k3
NT
B
a
B
2
Omax
(D-7)
Thus, activation energy for hopping polarization can be calculated from the
Tln max vs. T1 plot. Figure D-8 shows the same for BST compounds (x = 0.2 and
0.8). It should be noted that, if hopping polarization is present in colossal permittivity
material, activation energy of hopping polarization at high temperature region is
comparable to the difference of activation energies at high and low temperatures obtained
by using Debye model (Figure D-5).
Figure D-8. Activation energy values extracted from the hopping polarons model for Ba0.8Sr0.2TiO3–δ and Ba0.2Sr0.8TiO3–δ nanoceramics.
This statement seems to hold true for the case of Ba-rich BST sample (x = 0.2),
where the activation energy difference from Debye model (0.081 eV) is well comparable
with the activation energy for hopping polarization in the high temperature region (0.036
eV). However, for Sr-rich BST (x = 0.8), the value of Tln max remains constant at
175
different temperatures, indicating that no thermally activated hopping process is present
in Sr-rich BST compounds (Figure D-8). Thus, one can conclude that the colossal
permittivity in Ba-rich BST compounds is due to hopping polarization combined with
interfacial polarization, while mostly interfacial polarization is responsible for Sr-rich BST
compounds.
Table D-2 summarizes calculated activation energy and extracted s values for
BST (x = 0.2 and 0.8) compounds by using Debye, UDR, and THP models, respectively.
The two BST compounds, Sr-rich and Ba-rich, were again selected for the analysis since
those compounds exhibit most distinct dielectric properties in terms of polarization
mechanisms. As observed by De Souza et al.,173,174 BaTiO3 exhibits lower oxygen
diffusion and surface exchange coefficients 1213
C850,Oscm102.1D
and
18
C850,Oscm108.3k
respectively than SrTiO3 1211
C850,Oscm102D
and
110
C850,Oscm105.7k
. Therefore, the faster diffusion of oxygen during the post
annealing treatment in BST compounds, compared to BT, leads to an increase of the Ti3+
to Ti4+ oxidation rate, which results in the decrease of hopping dipole concentration in the
material with increasing Sr concentration. Furthermore, it is well known that
ferroelectricity of BST decreases as Sr content increases, and transformation from the
ferroelectric phase to the paraelectric phase occurs when the Sr content increases above
0.3.175,176 It is thus clear that depending on the concentration of Sr in BST nanoceramics,
colossal permittivity is a result of interfacial polarization at insulating grain boundaries,
and thermally activated hopping polarization in the semiconducting grains. The following
sections discuss these in more detail.
176
Table D-2. Calculated activation energies and s values for BST compounds using three different analytical models.
Ba0.8Sr0.2TiO3–δ Ba0.2Sr0.8TiO3–δ
Debye model (EA, eV) Low temp 0.029 0.165
High temp 0.110
UDR model (s value) Low temp 0.80 0.98
High temp 0.99 0.98
THP model (EA, eV) Low temp 0.015 ∼0
High temp 0.036
D.3.4. Internal Barrier Layer Capacitor
The interfacial polarization at the grain boundaries is modelled using the internal
barrier layer capacitor (IBLC) model. The IBLC model can be described by Koop’s
equivalent circuit consisting of capacitive, conductive, and a constant phase element in
parallel and/or in series. For colossal permittivity materials, electrical heterogeneities
between grains and grain boundaries drive the properties.150 According to the Koop’s
equivalent circuit, the grain and grain boundary responses are built in series and each
part is composed of a dc,gbggbg ,C parallel circuit, described by the following
equation.177
1iCbiCi
1iiCiiC
2
o
2
dc,ggP1
gdc,gbgbP1
gbo
odc,gbgbP1
gbodc,ggP1
g
(D-8)
dc,g is the DC conductivity of grain and dc,gb is the DC conductivity of grain boundary in
the frequency-independent part of Jonscher’s model. 0 , i , , and are, respectively,
the permittivity of vacuum/sample at infinite frequency, the imaginary unit, the angular
frequency, and the ratio of grain boundary thickness on average grain size. In addition,
equation (D-8) points out a gbgP contribution representing the conductive and capacitive
177
trends of grains and grain boundaries. A value of P close to 1 indicates a conductive
behavior while a value close to 0 implies a capacitive response. Finally, gbgC is a function
of gbgP , as given by the equation (D-9) where O,gbg is the static conductivity of
grains/grain boundaries.
gbgO,gbggbg P1cos5.0C (D-9)
Experimental data for Ba1−xSrxTiO3−δ nanoceramics (0 ≤ x ≤ 1) are plotted in Figure
D-9 and the fitted curves using equation (D-9) are presented. The different fitting
parameters ( gbgP , gbg , gbgC , , and ) are shown in Table D-3. For all the
compositions, they are in good agreement with the experimental data (R2 > 0.997, except
for SrTiO3 where R2 = 0.950). As discussed above, the electrical properties of SrTiO3
are not driven by the thermally activated hopping polaron model, and thus this particular
composition is excluded from the following discussion.
Figure D-9. BST permittivity data fitted with IBLC model
178
The values of gP of all the compounds are close to 1 and those of gbP are close
to 0, indicating a conductive response of the grains and a capacitive response of grain
boundaries. Moreover, dc,g are at least two orders of magnitude higher than dc,gb , which
is in accordance with the IBLC model. In addition, the values of gbgC support the fact that
grains are conductive (or semiconductive) while grain boundaries are insulating.
Table D-3. Fitting parameters using the IBLC model.
Composition
Ba1−xSrxTiO3−δ gP
gbP dc,g
(S/cm)
dc,gb
(S/cm)
gC
gbC
gbg tt
BaTiO3−δ 0.92 0.02 5.1×10−2 5.6×10−6 1.18 6.2×10−8 0.00996 479
Ba0.8Sr0.2TiO3−δ 0.92 0.01 8.1×10−4 2.5×10−6 0.23 2.9×10−8 0.00998 505
Ba0.6Sr0.4TiO3−δ 0.92 0.02 2.5×10−3 1.9×10−6 0.09 1.2×10−8 0.00996 512
Ba0.4Sr0.6TiO3−δ 0.89 0.04 2.3×10−2 2×10−12 0.04 1.4×10−8 0.00984 509
Ba0.2Sr0.8TiO3−δ 0.80 0.01 0.2 3.8×10−10 0.01 3.5×10−9 0.01307 500
SrTiO3−δ 0.028 0.0002 3.3 × 10−7 1.5 × 10−7 10−7 9.9 × 10−8 0.02113 553
Finally, a simple comparison between the six compositions could give us some
general trends about Ba–Sr substitution on electrical properties. In fact, we observe a
quasi-constant value of gP (≈ 0.92) until x = 0.4, then gP substantially decreases as x
increases above 0.4. This means that the grain conductivity behavior is similar for the
three highest Ba-content nanoceramics, while this conductive behavior drastically
decreases for the three other samples (i.e., Sr-rich BST compound). However, gbP is
almost constant for all the compositions, showing a similar trend of grain boundaries to
be capacitive. dc,gb shows a slow decrease as Sr content increases from 0 to 0.4, then
drastically decreases for higher Sr concentration. The values of gC and gbC related with
179
gP and gbP decrease when x increases. is constant (≈ 1 × 10−2), indicating a grain
boundary thickness 100 times smaller than the grain size, which is consistent with the
results determined from HREM-TEM observations (not included here).178 The grain size
of the BaTiO3−δ nanoceramics lies between 100 and 250 nm, and the grain boundary
thickness was estimated to be 1 nm. Lastly, , corresponding to the permittivity at infinite
frequency remains quasi-constant for all the compositions tested.
D.3.5. Variable Range and Nearest Neighbor Hopping
The long-range hopping polarization within grains in BST and its variation with Sr
content can be explained on the basis of the conduction mechanisms involved. In order
to investigate the conduction mechanisms, it is necessary to link dielectric properties to
the bulk conductivity ( ), as shown in equation (D-10).
roo (D-10)
The universal dielectric response (UDR) model developed by Jonscher,179,180
established the relation between the bulk conductivity and the grains conductivity in the
high frequency-independent area. In this way, by plotting the bulk conductivity as a
function of frequency, it is possible to determine the dc conductivity ( dc ) of the grains.
s
odc f (D-11)
o is a pre-factor, f is the experimental frequency, and s is a temperature-dependent
constant. The value of s is between 0 and 1, and a value close to 1 indicates a localized
polarization mechanism, while a value closer to 0 indicates that charge carriers are free
to move through the entire bulk. In order to better understand the electrical properties of
the BST system, we will focus on two compositions: Ba-rich BST compound
180
Ba0.8Sr0.2TiO3−δ and Sr-rich BST compound Ba0.2Sr0.8TiO3−δ, since these two compounds
show the most distinct dielectric behavior from each other.
Figure D-10. Frequency dependence of the conductivity at different temperatures for (a) Ba0.8Sr0.2TiO3-δ and (b) Ba0.2Sr0.8TiO3−δ.
versus f curves are plotted for different temperatures and the corresponding
fitting curves extracted from equation (D-11) are presented in Figure D-10 for these two
compositions. The results for fitting parameters are also presented in Table D-4. dc
181
and o decrease as temperature decreases regardless of the composition. However, for
Ba0.8Sr0.2TiO3−δ, s values increase as temperature decreases from 140 to 80 K, then
further decreases at lower temperatures, while the s value is quasi-constant for
Ba0.2Sr0.8TiO3−δ. These contradictory dependences of s values as a function of
temperature for two compositions were further investigated using the two different
thermally activated hopping polaron models, the nearest neighbor hopping (NNH) and the
variable range hopping (VRH) model.
Table D-4. Fitting parameters using the UDR model.
Composition T(K) σdc (S-cm−1) σ0 s R2 Δf (kHz)
Ba0.8Sr0.2TiO3−δ 140 0.01799 2.1E−4 0.39488 0.99618 10–100
120 0.00636 1.4E−6 0.76218 0.99919 3–100
100 0.00227 3.3E−7 0.86625 0.99881 1–100
80 7.49E−4 9.3E−8 0.97315 0.99949 0.04–100
60 1.92E−4 4.5E−7 0.7935 0.9997 0.02–100
Ba0.2Sr0.8TiO3−δ 160 0.00959 3.04E−5 0.50982 0.99865 20–200
140 0.00262 5.08E−6 0.60553 0.99909 3–200
120 4.98E−4 2.8E−6 0.60234 0.99983 1–200
100 7.5E−5 1.13E−6 0.61787 0.99949 0.2–200
80 2.91E−6 1.28E−7 0.74267 0.99821 0.2–200
NNH conduction model considers a constant distance of hopping between nearest
neighbors, as described in equation (D-12),181 and is based on the linear variation of ln
dc as a function of 1/T:
TkEexp B1a1dc (D-12)
182
where 1 is the pre-exponential factor dependent on the concentration and size of
defects, T is the absolute temperature, 1aE is the activation energy required for the
hopping polaron, and Bk is the Boltzmann constant.
Figure D-11. NNH model applied to BST nanoceramics.
The logarithm of dc was plotted as a function of 1/T for the two compositions of
Ba0.8Sr0.2TiO3−δ and Ba0.2Sr0.8TiO3−δ (Figure D-11), and it can be clearly seen that two
different behaviors exist for the compositions. In other words, for the case of the Sr-rich
composition, the variation of the grain’s conductivity with temperature fits well with the
NNH model. The calculated activation energy, 0.110 eV, is in agreement with a hopping
conduction process occurring between nearest neighbors.182,183 Moreover, this value is
in the same range of the value of 0.165 eV, determined using Debye model. On the other
hand, the Ba-rich composition does not follow NNH model and conductivity values deviate
from the linear relationship with 1/T as temperature decreases. In this latter case, one
can consider VRH model, in which the activation energy and the hopping distances of
183
charge carriers are temperature dependent.184 This behavior was pointed out for the first
time by Mott184 and leads to an po TTexp conductivity dependence, as described in
equations (D-13) and (D-14).
p
o2dc TTexp (D-13)
F
3
o EkN24T (D-14)
Here 2 is the pre-exponential constant dependent on the defect concentration and size,
is the length of the localized wave function, and N(EF) is the number of electrons per
unit volume within a range of the Fermi level. Generally, the reported p exponent equals
1/4 (or 1/3 in two dimensions) as observed by Mott, Zhang, Ang, Zheng, and others for
space charge-disordered semiconductors.185–188 Furthermore, a p value of 1/2 was
already reported by Efros, Overhof and Thomas, and more recently by Han et al.165,189,190
However, these reported values have not been clearly explained yet.
Figure D-12. Temperature dependence of DC bulk conductivity of Ba0.8Sr0.2TiO3−δ nanoceramic sample.
184
The p exponent can be deduced from the slope of the equation expressed in
equation (D-15) as shown in Figure D-12.
ATlogp1Tk1dlndlog Bdc (D-15)
For Ba0.8Sr0.2TiO3−δ the p value determined here is 1/4. The value of To is on the
order of 1.81×107 K, which is lower than the value published by Zheng187 for a
Ni0.5Zn0.5Fe2O4 ceramic exhibiting colossal permittivity or by Ang191 for Cu-doped BaTiO3
following variable range hopping conduction mechanism. Considering the value, which
is on the order of magnitude of the lattice parameter ( = 0.4 nm) and knowing the value
of To (from the fit of Figure D-12), it is then possible to calculate N(EF) = 7.6×1019 eV−1cm−3
from (D-14), which is in agreement with other authors,185–187 and the activation energies
(Ea2) and the hopping distances (R) at different temperatures following the VRH model.
4341
oB2a TTk25.0E (D-16)
41
BF TkEN23R (D-17)
The activation energies of the hopping process at low temperature are in the range
of 0.022 ± 0.002 ≤ Ea2 ≤ 0.057 ± 0.003 eV, which is in the same order as low-temperature
Debye’s activation energy. In addition, the most probable hopping distance increases
from 3.8 to 5.2 nm as the temperature decreases from 140 to 40 K. These distances that
are approximately 10 times higher than the nearest neighbor distance, can be explained
by the remarkably high concentration of polarons in the grains, allowing long-distance
hopping to reach an equivalent site with comparable energy.
185
D.4. Summary
The electrical properties of a series of Ba1−xSrxTiO3−δ nanoceramics (0 ≤ x ≤ 1)
were investigated. Colossal permittivity (~105) with low losses (tan δ = 0.03) was
achieved. The electrical properties were analyzed in detail using Debye, UDR and
hopping polaron models. In Ba rich compounds, the properties are attributed to
polarization mechanisms at the grain boundary interfaces and to hopping in the grains.
In general, the grain conductivity decreases as Sr concentration increases. The
permittivity value also decreases as the Sr-content increases, attributed to a decrease of
the hopping contribution. The composition of Ba0.6Sr0.4TiO3–δ can be chosen as an
optimal BST compound for the colossal permittivity material as it shows the highest value
of r (174,000) and the lowest value of tanδ (0.03) over a wide temperature range.
Moreover, the strontium rich BST reduced nanostructured ceramics exhibit temperature
stable permittivity, albeit with lower values.
The hopping conduction mechanisms were further investigated in detail for two
compounds: Ba-rich (Ba0.8Sr0.2TiO3−δ) ceramic and Sr-rich (Ba0.2Sr0.8TiO3−δ) ceramic.
The Sr-rich ceramic exhibits a linear evolution of the DC grain conductivity versus 1/T,
which is in accordance with the NNH model, with an activation energy of 0.110 ± 0.002
eV. In Ba-rich compositions, the DC conductivity deviates from the 1/T law at low
temperature, which is typical of a VRH mechanism. The use of VRH model for Ba rich
compounds, indicates an increase of polaron activation energy (from 0.022 ± 0.002 to
0.057 ± 0.003 eV) and a decrease of hopping distances (from 5.2 to 3.8 nm) as the
temperature increases from 40 to 140 K.
186
APPENDIX E I DON’T KNOW WHAT THIS MEANS BUT…
E. Over the course of this doctoral work, the author has come across many interesting
phenomena and trends in data that do not make a direct contribution to the topics covered
in this dissertation. These trends though unrelated are worthy or further exploration and
at this point, the author does not have a clear explanation for these based on his literature
review. Following is a short list of a few of such observed but unexplained phenomena.
The deviation from ideal Debye type behavior, with a distribution of time constants
is modelled by introducing a factor α, in the case of the Cole-Cole model as has
been shown in Appendix B in equation (4-6). In the impedance formalism, a
constant phase element is used to model similar behavior for fitting the data with
equivalent circuit fitting. The constant γ in this case as is introduced in equation
(4-5) acts as a distribution coefficient. Given that both α and γ are introducing a
distribution of time constants, there must be a certain equivalence between them.
It is not clear however, what the exact relation between the two constants is.
Continuing with modifications to Debye behavior, a factor β is used to model
asymmetry in the permittivity arc as has been shown in equation (B-3). Similar
asymmetry can also be often found in complex impedance data. However, as of
now it is not clear how it can be modelled using software like Zview, with a circuit
element or combination of circuit elements.
During the study of the effect of high bias values on complex impedance behavior
of gadolinia doped ceria thin films, at very high bias values it was found that the
behavior in the low frequency range starts becoming less inductive as opposed to
187
the general trend of the samples showing more inductive behavior with increasing
bias. It is not clearly understood what this flip in behavior means and what is its
physical significance.
Similarly, at high bias values, the complex impedance plot has some data in the
third quadrant as can be seen from Figure 6-9. Although the CPE-P values take
care of it mathematically, it is not understood what a negative resistance (implied
by the third quadrant) means. It is not clear whether this is just a mathematical
phenomenon or whether it has any physical significance. It will be interesting to
see if this indicative of a current in the opposite direction.
During the analysis of impedance data under bias, the data was also analyzed in
the modulus formalism. A peak is observed in the imaginary modulus (M”) data
when plotted against frequency. This peak moves from low frequency to high with
increasing temperature and bias, although the effect of bias on peak movement is
observed only at high bias values. To analyze this further, the peak positions with
respect to frequency were calculated and the values so were plotted for different
temperatures and bias values as shown in Figure E-1. The data seems to follow
an Arrhenius type relationship denoted in equation (E-1). With increasing bias,
there is a slight change in the slope of the graphs, indicating a change in the
activation energy. However, more prominent is the shift in the plots with increasing
bias, which indicates a new conduction mechanism with its unique activation
energy related to the applied bias (B). This behavior ties in well with the hypothesis
of a parallel electronic conduction pathway. Equation (E-1) can be modified to
include the effect of bias as equation (E-2) where f1(B) and f2(B) are functions of
188
the bias B. This effect needs to be further studied to better understand the effect
of bias.
kT
EexpFF a
1o (E-1)
kT
BfexpF
kT
BfEexpFF 2
2o1a
1o (E-2)
Figure E-1. M” peak position frequency as a function of temperature and bias.
189
LIST OF REFERENCES
1 Population Reference Bureau, 2016 World Population Data Sheet, (2016). Available at: http://www.prb.org. Accessed February 5, 2017.
2 International Energy Outlook 2016, DOE/EIA-0484(2016), (2016). Available at: http:// http://www.eia.gov/outlooks/ieo/. Accessed February 5, 2017.
3 L. Carrette, K.A. Friedrich, and U. Stimming, “Fuel Cells – Fundamentals and Applications,” Fuel Cells, 1 [1] 5–39 (2001).
4 Fuel Cells | Department of Energy. Available at: https://energy.gov/eere/fuelcells/fuel-cells. Accessed February 5, 2017.
5 NETL: Solid Oxide Fuel Cells, Available at: https://www.netl.doe.gov/research/coal/energy-systems/fuel-cells. Accessed March 10, 2014.
6 B.C.H. Steele and A. Heinzel, “Materials for Fuel-Cell Technologies,” Nature, 414 [6861] 345–352 (2001).
7 H. Inaba and H. Tagawa, “Ceria-based Solid Electrolytes,” Solid State Ion., 83 [1–2] 1–16 (1996).
8 K. Eguchi, T. Setoguchi, T. Inoue, and H. Arai, “Electrical Properties of Ceria-based Oxides and their Application to Solid Oxide Fuel Cells,” Solid State Ion., 52 [1] 165–172 (1992).
9 J.R. Macdonald, “Impedance Spectroscopy: Models, Data Fitting, and Analysis,” Solid State Ion., 176 [25–28] 1961–1969 (2005).
10 D.A. Andersson, S.I. Simak, N.V. Skorodumova, I.A. Abrikosov, and B. Johansson, “Optimization of Ionic Conductivity in Doped Ceria,” Proc. Natl. Acad. Sci. U. S. A., 103 [10] 3518–3521 (2006).
11 G. Baure, “Microstructural effects in textured neodymium doped ceria;” in ECS Conference, Orlando, FL, USA, (2014).
12 S. Omar, E. Wachsman, and J. Nino, “A Co-doping Approach Towards Enhanced Ionic Conductivity in Fluorite-based Electrolytes,” Solid State Ion., 177 [35–36] 3199–3203 (2006).
13 S. Omar, E.D. Wachsman, J.L. Jones, and J.C. Nino, “Crystal Structure-Ionic Conductivity Relationships in Doped Ceria Systems,” J. Am. Ceram. Soc., 92 [11] 2674–2681 (2009).
14 S. Omar, Enhanced ionic conductivity of ceria-based compounds for the electrolyte application in SOFCs. PhD Dissertation, University of Florida, Gainesville, Fl., 2008.
190
15 N. Masó and A.R. West, “Electronic Conductivity in Yttria-Stabilized Zirconia under a Small dc Bias,” Chem. Mater., 27 [5] 1552–1558 (2015).
16 S. Taibl, G. Fafilek, and J. Fleig, “Impedance Spectra of Fe-doped SrTiO3 Thin Films upon Bias Voltage: Inductive Loops as a Trace of Ion Motion,” Nanoscale, 8 [29] 13954–13966 (2016).
17 W.F. Domeracki, W.L. Lundberg, T.E. Dowdy, and J.M. Linder, Integrated Gas Turbine Solid Oxide Fuel Cell System; US5413879 A, 1995.
18 A. Kirubakaran, S. Jain, and R.K. Nema, “A Review on Fuel Cell Technologies and Power Electronic Interface,” Renew. Sustain. Energy Rev., 13 [9] 2430–2440 (2009).
19 Types of Fuel Cells | Department of Energy. Available at: https://energy.gov/eere/fuelcells/types-fuel-cells. Accessed February 5, 2017.
20 Comparison of Fuel Cell Technologies | Department of Energy. Available at: https://energy.gov/eere/fuelcells/comparison-fuel-cell-technologies. Accessed February 5, 2017
21 L. Mond, Process of Obtaining Electricity from Gas Batteries; US409366 A, 1889.
22 Fuel Cell History - Fuel Cell Today. Available at: http://www.fuelcelltoday.com/history. Accessed February 3, 2017.
23 EG&G Technical Services, Inc. (ed.), Fuel Cell Handbook, 7th ed. U.S. Department of Energy, Office of Fossil Energy, 2004.
24 K. Kendall, N.Q. Minh, and S.C. Singhal, “Chapter 8 - Cell and Stack Designs;” pp. 197–228 in High Temp. Solid Oxide Fuel Cells. Elsevier Science, Amsterdam, 2003.
25 V. Dusastre and J.A. Kilner, “Optimisation of Composite Cathodes for Intermediate Temperature SOFC Applications,” Solid State Ion., 126 [1–2] 163–174 (1999).
26 B. Morel, R. Roberge, S. Savoie, T.W. Napporn, and M. Meunier, “Catalytic Activity and Performance of LSM Cathode Materials in Single Chamber SOFC,” Appl. Catal. Gen., 323 181–187 (2007).
27 J. Malzbender, P. Batfalsky, R. Vaßen, V. Shemet, and F. Tietz, “Component Interactions after Long-term Operation of an SOFC Stack with LSM Cathode,” J. Power Sources, 201 196–203 (2012).
28 S.J. Skinner, “Recent Advances in Perovskite-type Materials for Solid Oxide Fuel Cell Cathodes,” Int. J. Inorg. Mater., 3 [2] 113–121 (2001).
191
29 T. Ishihara, T. Shibayama, H. Nishiguchi, and Y. Takita, “Nickel–Gd-doped CeO2 Cermet Anode for Intermediate Temperature Operating Solid Oxide Fuel Cells using LaGaO3-based Perovskite Electrolyte,” Solid State Ion., 132 [3–4] 209–216 (2000).
30 H. Koide, Y. Someya, T. Yoshida, and T. Maruyama, “Properties of Ni/YSZ Cermet as Anode for SOFC,” Solid State Ion., 132 [3–4] 253–260 (2000).
31 S. Zha, W. Rauch, and M. Liu, “Ni-Ce0.9Gd0.1O1.95 Anode for GDC Electrolyte-based Low-Temperature SOFCs,” Solid State Ion., 166 [3–4] 241–250 (2004).
32 C. Xia and M. Liu, “Microstructures, Conductivities, and Electrochemical Properties of Ce0.9Gd0.1O2 and GDC–Ni Anodes for Low-Temperature SOFCs,” Solid State Ion., 152–153 423–430 (2002).
33 S.T. Aruna, M. Muthuraman, and K.C. Patil, “Synthesis and Properties of Ni-YSZ Cermet: Anode Material for Solid Oxide Fuel Cells,” Solid State Ion., 111 [1–2] 45–51 (1998).
34 B.C.H. Steele, “Oxygen Ion Conductors;” in High Conduct. Solid Ion. Conduct. Recent Trends Appl. Edited by T. Takahashi. World Scientific, 1989.
35 J.W. Fergus, “Electrolytes for Solid Oxide Fuel Cells,” J. Power Sources, 162 [1] 30–40 (2006).
36 H. Yokokawa, N. Sakai, T. Horita, K. Yamaji, and M.E. Brito, “Electrolytes for Solid-Oxide Fuel Cells,” MRS Bull., 30 [8] 591–595 (2005).
37 J.-Y. Park and E.D. Wachsman, “Stable and High Conductivity Ceria/Bismuth Oxide Bilayer Electrolytes for Lower Temperature Solid Oxide Fuel Cells,” Ionics, 12 [1] 15–20 (2006).
38 E.D. Wachsman and K.T. Lee, “Lowering the Temperature of Solid Oxide Fuel Cells,” Science, 334 [6058] 935–939 (2011).
39 A. Kossoy, Y. Feldman, R. Korobko, E. Wachtel, I. Lubomirsky, and J. Maier, “Influence of Point-Defect Reaction Kinetics on the Lattice Parameter of Ce0.8Gd0.2O1.9,” Adv. Funct. Mater., 19 [4] 634–641 (2009).
40 W.C. Chueh and S.M. Haile, “A Thermochemical Study of Ceria: Exploiting an Old Material for New Modes of Energy Conversion and CO2 Mitigation,” Philos. Trans. R. Soc. Lond. Math. Phys. Eng. Sci., 368 [1923] 3269–3294 (2010).
41 A. Le Gal and S. Abanades, “Dopant Incorporation in Ceria for Enhanced Water-Splitting Activity during Solar Thermochemical Hydrogen Generation,” J. Phys. Chem. C, 116 [25] 13516–13523 (2012).
192
42 S. Omar, E. Wachsman, and J. Nino, “Higher Conductivity Sm3+ and Nd3+ Co-doped Ceria-based Electrolyte Materials,” Solid State Ion., 178 [37–38] 1890–1897 (2008).
43 E. Gourba, P. Briois, A. Ringuedé, M. Cassir, and A. Billard, “Electrical Properties of Gadolinia-Doped Ceria Thin Films Deposited by Sputtering in view of SOFC Application,” J. Solid State Electrochem., 8 [9] 633–637 (2004).
44 R.M. Kasse and J.C. Nino, “Ionic Conductivity of SmxNdyCe0.9O2−δ Codoped Ceria Electrolytes,” J. Alloys Compd., 575 399–402 (2013).
45 R.M. Kasse, Size and composition effects on ionic conductivity Doped Ceria Bulk Ceramics and Thin Film. University of Florida, Gainesville, Fla., 2013.
46 R. Gerhardt-Anderson and A.S. Nowick, “Ionic Conductivity of CeO2 with Trivalent Dopants of Different Ionic Radii,” Solid State Ion., 5 547–550 (1981).
47 Y. Arachi, H. Sakai, O. Yamamoto, Y. Takeda, and N. Imanishai, “Electrical Conductivity of the ZrO2–Ln2O3 (Ln=Lanthanides) System,” Solid State Ion., 121 [1–4] 133–139 (1999).
48 J.A. Kilner and R.J. Brook, “A Study of Oxygen Ion Conductivity in Doped Non-Stoichiometric Oxides,” Solid State Ion., 6 [3] 237–252 (1982).
49 H. Yahiro, Y. Eguchi, K. Eguchi, and H. Arai, “Oxygen Ion Conductivity of the Ceria-Samarium Oxide System with Fluorite Structure,” J. Appl. Electrochem., 18 [4] 527–531 (1988).
50 M.P. Anderson and A.S. Nowick, “Relaxation Peaks Produced by Defect Complexes in Cerium Dioxide Doped with Trivalent Cations,” J. Phys. Colloq., 42 [C5] C5–823 (1981).
51 H.L. Tuller and A.S. Nowick, “Defect Structure and Electrical Properties of Nonstoichiometric CeO2 Single Crystals,” J. Electrochem. Soc., 126 [2] 209–217 (1979).
52 P.S. Manning, J.D. Sirman, R.A. De Souza, and J.A. Kilner, “The Kinetics of Oxygen Transport in 9.5 mol % Single Crystal Yttria Stabilised Zirconia,” Solid State Ion., 100 [1] 1–10 (1997).
53 V. Butler, C.R.A. Catlow, and B.E.F. Fender, “The Defect Structure of Anion Deficient ZrO2,” Solid State Ion., 5 539–542 (1981).
54 W.C. Mackrodt and P.M. Woodrow, “Theoretical Estimates of Point Defect Energies in Cubic Zirconia,” J. Am. Ceram. Soc., 69 [3] 277–280 (1986).
55 X. Guo, W. Sigle, and J. Maier, “Blocking Grain Boundaries in Yttria-Doped and Undoped Ceria Ceramics of High Purity,” J. Am. Ceram. Soc., 86 [1] 77–87 (2003).
193
56 W. Liu and C.A. Randall, “Thermally Stimulated Relaxation in Fe-Doped SrTiO3 Systems: II. Degradation of SrTiO3 Dielectrics,” J. Am. Ceram. Soc., 91 [10] 3251–3257 (2008).
57 D.M. Smyth, The defect chemistry of metal oxides, Oxf. Univ. Press, 2000.
58 A.S. Nowick, W.K. Lee, and H. Jain, “Survey and Interpretation of Pre-Exponentials of Conductivity,” Solid State Ion., 28 89–94 (1988).
59 K. Fuda, K. Kishio, S. Yamauchi, and K. Fueki, “Study on Vacancy Motion in Y2O3-Doped CeO2 by 17O NMR Technique,” J. Phys. Chem. Solids, 46 [10] 1141–1146 (1985).
60 D. Hohnke, “Ionic Conduction in Doped Oxides with the Fluorite Structure,” Solid State Ion., 5 531–534 (1981).
61 I.E. Stephens and J.A. Kilner, “Ionic Conductivity of Ce1- xNdxO2- x/2,” Solid State Ion., 177 [7] 669–676 (2006).
62 M. Filal, C. Petot, M. Mokchah, C. Chateau, and J.L. Carpentier, “Ionic Conductivity of Yttrium-Doped Zirconia and the ‘Composite Effect,’” Solid State Ion., 80 [1] 27–35 (1995).
63 V. Esposito, D.W. Ni, Z. He, W. Zhang, A.S. Prasad, J.A. Glasscock, C. Chatzichristodoulou, S. Ramousse, et al., “Enhanced Mass Diffusion Phenomena in Highly Defective Doped Ceria,” Acta Mater., 61 [16] 6290–6300 (2013).
64 D.Y. Wang, D.S. Park, J. Griffith, and A.S. Nowick, “Oxygen-Ion Conductivity and Defect Interactions in Yttria-Doped Ceria,” Solid State Ion., 2 [2] 95–105 (1981).
65 R. Ramamoorthy, D. Sundararaman, and S. Ramasamy, “Ionic Conductivity Studies of Ultrafine-Grained Yttria Stabilized Zirconia Polymorphs,” Solid State Ion., 123 [1–4] 271–278 (1999).
66 R. Gerhardt and A.S. Nowick, “Grain-Boundary Effect in Ceria Doped with Trivalent Cations: I, Electrical Measurements,” J. Am. Ceram. Soc., 69 [9] 641–646 (1986).
67 X. Guo, W. Sigle, J. Fleig, and J. Maier, “Role of Space Charge in the Grain Boundary Blocking Effect in Doped Zirconia,” Solid State Ion., 154–155 555–561 (2002).
68 R. Gerhardt, A.S. Nowick, M.E. Mochel, and I. Dumler, “Grain-Boundary Effect in Ceria Doped with Trivalent Cations: II, Microstructure and Microanalysis,” J. Am. Ceram. Soc., 69 [9] 647–651 (1986).
69 X. Guo and R. Waser, “Electrical Properties of the Grain Boundaries of Oxygen Ion Conductors: Acceptor-Doped Zirconia and Ceria,” Prog. Mater. Sci., 51 [2] 151–210 (2006).
194
70 H.J. Avila-Paredes, K. Choi, C.-T. Chen, and S. Kim, “Dopant-Concentration Dependence of Grain-Boundary Conductivity in Ceria: A Space-Charge Analysis,” J. Mater. Chem., 19 [27] 4837–4842 (2009).
71 M. Kim, G. Duscher, N.D. Browning, K. Sohlberg, S.T. Pantelides, and S.J. Pennycook, “Nonstoichiometry and the Electrical Activity of Grain Boundaries in SrTiO3,” Phys. Rev. Lett., 86 [18] 4056–4059 (2001).
72 M.M. McGibbon, N.D. Browning, A.J. McGibbon, M.F. Chisholm, and S.J. Pennycook, “Direct Determination of Grain Boundary Atomic Structure in SrTiO3,” MRS Online Proc. Libr. Arch., 357 (1994).
73 N.D. Browning, J.P. Buhan, H.O. Molatji, S.J. Pennycook, G. Duscherk, K.D. Johnson, R. Rodrigues, and V.P. Dravid, “The Influence of Atomic Structure on the Formation of Electrical Barriers at Grain Boundaries in SrTiO3,” Appl. Phys. Lett., 74 [18] 2638–2640 (1999).
74 Y. Lei, Y. Ito, N.D. Browning, and T.J. Mazanec, “Segregation Effects at Grain Boundaries in Fluorite-Structured Ceramics,” J. Am. Ceram. Soc., 85 [9] 2359–2363 (2002).
75 C.A.J. Fisher and H. Matsubara, “Molecular Dynamics Investigations of Grain Boundary Phenomena in Cubic Zirconia,” Comput. Mater. Sci., 14 [1–4] 177–184 (1999).
76 F. Li, T. Ohkubo, Y.M. Chen, M. Kodzuka, F. Ye, D.R. Ou, T. Mori, and K. Hono, “Laser-Assisted Three-Dimensional Atom Probe Analysis of Dopant Distribution in Gd-doped CeO2,” Scr. Mater., 63 [3] 332–335 (2010).
77 D. R. Diercks, J. Tong, H. Zhu, R. Kee, G. Baure, J. C. Nino, R. O’Hayre, and B. P. Gorman, “Three-Dimensional Quantification of Composition and Electrostatic Potential at Individual Grain Boundaries in Doped Ceria,” J. Mater. Chem. A, 4 [14] 5167–5175 (2016).
78 M.A. Frechero, M. Rocci, G. Sánchez-Santolino, A. Kumar, J. Salafranca, R. Schmidt, M.R. Díaz-Guillén, O.J. Durá, et al., “Paving the Way to Nanoionics: Atomic Origin of Barriers for Ionic Transport through Interfaces,” Sci. Rep., 5 (2015).
79 E. Barsoukov and J.R. Macdonald, Impedance Spectroscopy: Theory, Experiment, and Applications. John Wiley & Sons, 2005.
80 J. Randles, “Kinetics of Rapid Electrode Reactions,” Discuss. Faraday Soc., 1 11–19 (1947).
81 G. Jaffé, and J.A. Rider, “Polarization in Electrolytic Solutions. Part II. Measurements,” J. Chem. Phys., 20 [7] 1077–1087 (1952).
195
82 J.E. Bauerle, “Study of Solid Electrolyte Polarization by a Complex Admittance Method,” J. Phys. Chem. Solids, 30 [12] 2657–2670 (1969).
83 S.A. Hayes, P. Yu, T.J. O’Keefe, M.J. O’Keefe, and J.O. Stoffer, “The Phase Stability of Cerium Species in Aqueous Systems I. E-pH Diagram for the Ce HClO4 H2O System,” J. Electrochem. Soc., 149 [12] C623–C630 (2002).
84 J.R. Macdonald, “Impedance Spectroscopy,” Ann. Biomed. Eng., 20 [3] 289–305 (1992).
85 E.J. Abram, D.C. Sinclair, and A.R. West, “A Strategy for Analysis and Modelling of Impedance Spectroscopy Data of Electroceramics: Doped Lanthanum Gallate,” J. Electroceramics, 10 [3] 165–177 (2003).
86 J.R. Macdonald, “Comments on the Electric Modulus Formalism Model and Superior Alternatives to it for the Analysis of the Frequency Response of Ionic Conductors,” J. Phys. Chem. Solids, 70 [3–4] 546–554 (2009).
87 J.R. Macdonald and L.D. Potter, “A Flexible Procedure for Analyzing Impedance Spectroscopy Results: Description and Illustrations,” Solid State Ion., 24 [1] 61–79 (1987).
88 K.S. Cole and R.H. Cole, “Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics,” J. Chem. Phys., 9 [4] 341 (1941).
89 M.F. Causley and P.G. Petropoulos, “On the Time-Domain Response of Havriliak-Negami Dielectrics,” Antennas Propag. IEEE Trans. On, 61 [6] 3182–3189 (2013).
90 D.W. Davidson, and R.H. Cole, “Dielectric Relaxation in Glycerol, Propylene Glycol, and n‐Propanol,” J. Chem. Phys., 19 [12] 1484–1490 (1951).
91 R. Gerhardt, “Impedance and dielectric spectroscopy revisited: Distinguishing localized relaxation from long-range conductivity,” J. Phys. Chem. Solids, 55 [12] 1491–1506 (1994).
92 M.E. Orazem and B. Tribollet, Electrochemical Impedance Spectroscopy. John Wiley & Sons, 2011.
93 M.E. Orazem, N. Pebere, and B. Tribollet, “Enhanced Graphical Representation of Electrochemical Impedance Data,” J. Electrochem. Soc., 153 [4] B129 (2006).
94 D.C. Montgomery, Design and Analysis of Experiments. Wiley, 2012.
95 X. Guo, S. Mi, and R. Waser, “Nonlinear Electrical Properties of Grain Boundaries in Oxygen Ion Conductors: Acceptor-Doped Ceria,” Electrochem. Solid-State Lett., 8 [1] J1–J3 (2005).
196
96 J.-J. Wang, H.-B. Huang, T.J.M. Bayer, A. Moballegh, Y. Cao, A. Klein, E.C. Dickey, D.L. Irving, et al., “Defect Chemistry and Resistance Degradation in Fe-Doped SrTiO3 Single Crystal,” Acta Mater., 108 229–240 (2016).
97 M. Prades, N. Masó, H. Beltrán, E. Cordoncillo, and A. R. West, “Field Enhanced Bulk Conductivity of BaTiO3:Mg Ceramics,” J. Mater. Chem., 20 [25] 5335–5344 (2010).
98 H. Beltrán, M. Prades, N. Masó, E. Cordoncillo, and A.R. West, “Voltage-Dependent Low-Field Bulk Resistivity in BaTiO3:Zn Ceramics,” J. Am. Ceram. Soc., 93 [2] 500–505 (2010).
99 N. Masó, H. Beltrán, M. Prades, E. Cordoncillo, and A. R. West, “Field-Enhanced Bulk Conductivity and Resistive-Switching in Ca-doped BiFeO3 Ceramics,” Phys. Chem. Chem. Phys., 16 [36] 19408–19416 (2014).
100 Q.-L. Zhang, N. Masó, Y. Liu, H. Yang, and A. R. West, “Voltage-Dependent Low-Field Resistivity of CaTiO3:Zn ceramics,” J. Mater. Chem., 21 [34] 12894–12900 (2011).
101 L. Gil Escrig, M. Prades, H. Beltrán, E. Cordoncillo, N. Masó, and A.R. West, “Voltage-Dependent Bulk Resistivity of SrTiO3:Mg Ceramics,” J. Am. Ceram. Soc., 97 [9] 2815–2824 (2014).
102 A. Moballegh and E.C. Dickey, “Electric-Field-Induced Point Defect Redistribution in Single-Crystal TiO2–x and Effects on Electrical Transport,” Acta Mater., 86 352–360 (2015).
103 S. Kim and J. Maier, “On the Conductivity Mechanism of Nanocrystalline Ceria,” J. Electrochem. Soc., 149 [10] J73–J83 (2002).
104 S. Omar, E.D. Wachsman, and J.C. Nino, “Higher Ionic Conductive Ceria-Based Electrolytes for Solid Oxide Fuel Cells,” Appl. Phys. Lett., 91 [14] 144106–144106 (2007).
105 J.-P. Eufinger, M. Daniels, K. Schmale, S. Berendts, G. Ulbrich, M. Lerch, H.-D. Wiemhöfer, and J. Janek, “The Model Case of an Oxygen Storage Catalyst – Non-Stoichiometry, Point Defects and Electrical Conductivity Of Single Crystalline CeO2–ZrO2–Y2O3 solid solutions,” Phys. Chem. Chem. Phys., 16 [46] 25583–25600 (2014).
106 H. Huang, T.M. Gür, Y. Saito, and F. Prinz, “High Ionic Conductivity in Ultrathin Nanocrystalline Gadolinia-Doped Ceria Films,” Appl. Phys. Lett., 89 [14] 143107 (2006).
107 H.L. Tuller, “Ionic Conduction in Nanocrystalline Materials,” Solid State Ion., 131 [1–2] 143–157 (2000).
197
108 G.M. Christie and F.P.F. van Berkel, “Microstructure — Ionic Conductivity Relationships in Ceria-Gadolinia Electrolytes,” Solid State Ion., 83 [1–2] 17–27 (1996).
109 S.K. Kim, S. Khodorov, C.-T. Chen, S. Kim, and I. Lubomirsky, “How to Interpret Current–Voltage Relationships of Blocking Grain Boundaries in Oxygen Ionic Conductors,” Phys. Chem. Chem. Phys., 15 [22] 8716 (2013).
110 M.G. Bellino, D.G. Lamas, and N.E. Walsöe de Reca, “Enhanced Ionic Conductivity in Nanostructured, Heavily Doped Ceria Ceramics,” Adv. Funct. Mater., 16 [1] 107–113 (2006).
111 O.J. Durá, M.A. López de la Torre, L. Vázquez, J. Chaboy, R. Boada, A. Rivera-Calzada, J. Santamaria, and C. Leon, “Ionic Conductivity of Nanocrystalline Yttria-Stabilized Zirconia: Grain Boundary and Size Effects,” Phys. Rev. B, 81 [18] 184301 (2010).
112 G.J. Pereira, R.H.R. Castro, D.Z. de Florio, E.N.S. Muccillo, and D. Gouvêa, “Densification and Electrical Conductivity of Fast Fired Manganese-Doped Ceria Ceramics,” Mater. Lett., 59 [10] 1195–1199 (2005).
113 V. Esposito, B. Luong, M. Fronzi, and E. Traversa, “Synthesis, Characterization, and Densification of Samaria Doped Ceria Ultra-Fine Powders,” ECS Trans., 1 [7] 35–50 (2006).
114 V. Esposito, M. Fronzi, and E. Traversa, “Synthesis and Densification of Nanometric Ce0.8Sm0.2O1.9-δ,” MRS Online Proc. Libr. Arch., 972 (2006).
115 F.T. Ciacchi, S.A. Nightingale, and S.P.S. Badwal, “Microwave Sintering of Zirconia-Yttria Electrolytes and Measurement of their Ionic Conductivity,” Solid State Ion., 86 1167–1172 (1996).
116 S. Mahboob, G. Prasad, and G.S. Kumar, “Impedance and a.c. Conductivity Studies on Ba(Nd0.2Ti0.6Nb0.2)O3 Ceramic Prepared through Conventional and Microwave Sintering Route,” Bull. Mater. Sci., 29 [4] 347–355 (2006).
117 W. Hume-Rothery, Atomic theory for students of metallurgy. Institute of Metals, 1952.
118 Wiley: Introduction to Ceramics, 2nd Edition - W. David Kingery, H. K. Bowen, Donald R. Uhlmann, (n.d.).
119 H. Inaba, T. Nakajima, and H. Tagawa, “Sintering Behaviors of Ceria and Gadolinia-Doped Ceria,” Solid State Ion., 106 [3–4] 263–268 (1998).
120 P. Debye, “Part I. Dielectric Constant. Energy Absorption in Dielectrics with Polar Molecules,” Trans Faraday Soc, 30 [0] 679–684 (1934).
198
121 S. Havriliak and S. Negami, “A Complex Plane Representation of Dielectric and Mechanical Relaxation Processes in Some Polymers,” Polymer, 8 161–210 (1967).
122 S. Havriliak and S. Negami, “A Complex Plane Analysis of α-Dispersions in Some Polymer Systems,” J. Polym. Sci. Part C Polym. Symp., 14 [1] 99–117 (1966).
123 S.-H. Yoon, C.A. Randall, and K.-H. Hur, “Effect of Acceptor (Mg) Concentration on the Resistance Degradation Behavior in Acceptor (Mg)-Doped BaTiO3 Bulk Ceramics: II. Thermally Stimulated Depolarization Current Analysis,” J. Am. Ceram. Soc., 92 [8] 1766–1772 (2009).
124 T. Nedetzka, M. Reichle, A. Mayer, and H. Vogel, “Thermally Stimulated Depolarization. Method for Measuring the Dielectric Properties of Solid Substances,” J. Phys. Chem., 74 [13] 2652–2659 (1970).
125 J. Vanderschueren and J. Gasiot, “Field-Induced Thermally Stimulated Currents;” pp. 135–223 in Therm. Stimul. Relax. Solids. Edited by P.D.P. Bräunlich. Springer Berlin Heidelberg, 1979.
126 W.-E. Liu, “Impedance/Thermally Stimulated Depolarization Current and Microstructural Relations at Interfaces in Degraded Perovskite Dielectrics;” The Pennsylvania State University, 2009.
127 C. Bucci, R. Fieschi, and G. Guidi, “Ionic Thermocurrents in Dielectrics,” Phys. Rev., 148 [2] 816 (1966).
128 G.F.J. Garlick and A.F. Gibson, “The Electron Trap Mechanism of Luminescence in Sulphide and Silicate Phosphors,” Proc. Phys. Soc., 60 [6] 574 (1948).
129 L.Y.V. Chen, R. Forse, D. Chase, and R.A. York, “Analog Tunable Matching Network using Integrated Thin-Film BST Capacitors;” p. 261–264 Vol.1 in 2004 IEEE MTT- Int. Microw. Symp. Dig. IEEE Cat. No. 04CH37535. 2004.
130 M. Viviani, M. Leoni, M.T. Buscaglia, V. Buscaglia, and P. Nanni, “Positive Temperature Coefficient of Electrical Resistivity below 150K in Barium Strontium Titanate,” J. Am. Ceram. Soc., 87 [4] 756–758 (2004).
131 F. Zimmermann, M. Voigts, C. Weil, R. Jakoby, P. Wang, W. Menesklou, and E. Ivers-Tiffée, “Investigation of Barium Strontium Titanate Thick Films for Tunable Phase Shifters,” J. Eur. Ceram. Soc., 21 [10–11] 2019–2023 (2001).
132 G.H. Jain, L.A. Patil, P.P. Patil, U.P. Mulik, and K.R. Patil, “Studies on Gas Sensing Performance of Pure and Modified Barium Strontium Titanate Thick Film Resistors,” Bull. Mater. Sci., 30 [1] 9–17 (2007).
133 N. Raengthon, T. Sebastian, D. Cumming, I.M. Reaney, and D.P. Cann, “BaTiO3–Bi(Zn1/2Ti1/2)O3–BiScO3 Ceramics for High-Temperature Capacitor Applications,” J. Am. Ceram. Soc., 95 [11] 3554–3561 (2012).
199
134 Y.B. Khollam, S.B. Deshpande, H.S. Potdar, S.V. Bhoraskar, S.R. Sainkar, and S.K. Date, “Simple Oxalate Precursor Route for the Preparation of Barium–Strontium Titanate: Ba1−xSrxTiO3 Powders,” Mater. Charact., 54 [1] 63–74 (2005).
135 H. Shiibashi, H. Matsuda, and M. Kuwabara, “Low-Temperature Preparation of (Ba,Sr)TiO3 Perovskite Phase by Sol-Gel Method,” J. Sol-Gel Sci. Technol., 16 [1–2] 129–134 (1999).
136 L. Yang, Y. Wang, Y. Wang, X. Wang, and X. Wang, “Facile Morphology-Controlled Synthesis of Ba1−xSrxTiO3 (0 ≤ x < 1) Crystals via a Hydrothermal Method,” J. Ceram. Soc. Jpn., 120 [1397] 43–46 (2012).
137 C. Fu, C. Yang, H. Chen, Y. Wang, and L. Hu, “Microstructure and Dielectric Properties of BaxSr1−xTiO3 Ceramics,” Mater. Sci. Eng. B, 119 [2] 185–188 (2005).
138 W. Li, Z. Xu, R. Chu, P. Fu, and J. Hao, “Sol–Gel Synthesis and Characterization of Ba(1−x)SrxTiO3 Ceramics,” J. Alloys Compd., 499 [2] 255–258 (2010).
139 M.A. Subramanian, D. Li, N. Duan, B.A. Reisner, and A.W. Sleight, “High Dielectric Constant in ACu3Ti4O12 and ACu3Ti3FeO12 Phases,” J. Solid State Chem., 151 [2] 323–325 (2000).
140 A.P. Ramirez, M.A. Subramanian, M. Gardel, G. Blumberg, D. Li, T. Vogt, and S.M. Shapiro, “Giant Dielectric Constant Response in a Copper-Titanate,” Solid State Commun., 115 [5] 217–220 (2000).
141 C.C. Homes, T. Vogt, S.M. Shapiro, S. Wakimoto, and A.P. Ramirez, “Optical Response of High-Dielectric-Constant Perovskite-Related Oxide,” Science, 293 [5530] 673–676 (2001).
142 D. Capsoni, M. Bini, V. Massarotti, G. Chiodelli, M.C. Mozzatic, and C.B. Azzoni, “Role of Doping and CuO Segregation in Improving the Giant Permittivity of CaCu3Ti4O12,” J. Solid State Chem., 177 [12] 4494–4500 (2004).
143 D. O’Neill, R.M. Bowman, and J.M. Gregg, “Investigation into the Dielectric Behavior of Ferroelectric Superlattices Formed by Pulsed Laser Deposition,” J. Mater. Sci. Mater. Electron., 11 [7] 537–541 (2000).
144 P. Zubko, N. Stucki, C. Lichtensteiger, and J.-M. Triscone, “X-Ray Diffraction Studies of 180º Ferroelectric Domains in PbTiO3/SrTiO3 Superlattices under an Applied Electric Field,” Phys. Rev. Lett., 104 [18] 187601 (2010).
145 M.B. Okatan, I.B. Misirlioglu, and S.P. Alpay, “Contribution of Space Charges to the Polarization of Ferroelectric Superlattices and its Effect on Dielectric Properties,” Phys. Rev. B, 82 [9] 094115 (2010).
200
146 M.B. Okatan, J.V. Mantese, and S.P. Alpay, “Effect of Space Charge on the Polarization Hysteresis Characteristics of Monolithic and Compositionally Graded Ferroelectrics,” Acta Mater., 58 [1] 39–48 (2010).
147 A.K. Tagantsev, V.O. Sherman, K.F. Astafiev, J. Venkatesh, and N. Setter, “Erratum: ‘Ferroelectric Materials for Microwave Tunable Applications’ [J. Electroceram. 11, 5 (2003)],” J. Electroceramics, 14 [3] 199–203 (2005).
148 M.W. Cole, E. Ngo, C. Hubbard, S.G. Hirsch, M. Ivill, W.L. Sarney, J. Zhang, and S.P. Alpay, “Enhanced Dielectric Properties from Barium Strontium Titanate Films with Strontium Titanate Buffer Layers,” J. Appl. Phys., 114 [16] 164107 (2013).
149 T. Harigai, S.-M. Nam, H. Kakemoto, S. Wada, K. Saito, and T. Tsurumi, “Structural and Dielectric Properties of Perovskite-Type Artificial Superlattices,” Thin Solid Films, 509 [1–2] 13–17 (2006).
150 D.C. Sinclair, T.B. Adams, F.D. Morrison, and A.R. West, “CaCu3Ti4O12: One-step internal barrier layer capacitor,” Appl. Phys. Lett., 80 [12] 2153–2155 (2002).
151 P. Lunkenheimer, R. Fichtl, S.G. Ebbinghaus, and A. Loidl, “Nonintrinsic origin of the colossal dielectric constants in CaCu3Ti4O12,” Phys. Rev. B, 70 [17] 172102 (2004).
152 J. Wu, C.-W. Nan, Y. Lin, and Y. Deng, “Giant Dielectric Permittivity Observed in Li and Ti Doped NiO,” Phys. Rev. Lett., 89 [21] 217601 (2002).
153 N. Ikeda, H. Ohsumi, K. Ohwada, K. Ishii, T. Inami, K. Kakurai, Y. Murakami, K. Yoshii, et al., “Ferroelectricity from Iron Valence Ordering in the Charge-Frustrated System LuFe2O4,” Nature, 436 [7054] 1136–1138 (2005).
154 A.A. Pronin, V.I. Torgashev, A.A. Bush, B.P. Gorshunov, A.A. Volkov, and A.S. Prokhorov, “Low-Frequency Dynamic Response of the Bismuth Strontium Ferrite (Bi,Sr)FeO3−x,” Phys. Solid State, 51 [3] 498–502 (2009).
155 C. Pecharromán, F. Esteban-Betegón, J.F. Bartolomé, S. López-Esteban, and J.S. Moya, “New Percolative BaTiO3–Ni Composites with a High and Frequency-Independent Dielectric Constant (ϵr ≈ 80000),” Adv. Mater., 13 [20] 1541–1544 (2001).
156 S. Guillemet-Fritsch, M. Boulos, B. Durand, V. Bley, and T. Lebey, “Electrical Characteristics of BaTiO3 Ceramics from Hydrothermal Prepared Powders,” J. Eur. Ceram. Soc., 25 [12] 2749–2753 (2005).
157 P. Lunkenheimer, V. Bobnar, A.V. Pronin, A.I. Ritus, A.A. Volkov, and A. Loidl, “Origin of Apparent Colossal Dielectric Constants,” Phys. Rev. B, 66 [5] 052105 (2002).
201
158 W. Li and R.W. Schwartz, “Maxwell-Wagner Relaxations and their Contributions to the High Permittivity of Calcium Copper Titanate Ceramics,” Phys. Rev. B, 75 [1] 012104 (2007).
159 T.-T. Fang and C.P. Liu, “Evidence of the Internal Domains for Inducing the Anomalously High Dielectric Constant of CaCu3Ti4O12,” Chem. Mater., 17 [20] 5167–5171 (2005).
160 H. Han, C. Voisin, S. Guillemet-Fritsch, P/ Dufour, C. Tennailleau, C. Turner, and J.C. Nino, “Origin of Colossal Permittivity in BaTiO3 via Broadband Dielectric Spectroscopy,” J. Appl. Phys., 113 [2] 024102 (2013).
161 S. Guillemet-Fritsch, Z. Valdez-Nava, C. Tenailleau, T. Lebey, B. Durand, and J.-Y. Chane-Ching, “Colossal Permittivity in Ultrafine Grain Size BaTiO3–x and Ba0.95La0.05TiO3–x Materials,” Adv. Mater., 20 [3] 551–555 (2008).
162 U-C. Chung, C. Elissalde, S. Mornet, M. Maglione, and C. Estournès, “Controlling Internal Barrier in Low loss BaTiO3 Supercapacitors,” Appl. Phys. Lett., 94 [7] 072903 (2009).
163 H. Han, D. Ghosh, J.L. Jones, and J.C. Nino, “Colossal Permittivity in Microwave-Sintered Barium Titanate and Effect of Annealing on Dielectric Properties,” J. Am. Ceram. Soc., 96 [2] 485–490 (2013).
164 A. Artemenko, C. Elissalde, U-C. Chung, C. Estournès, S. Mornet, I. Bykov, and M. Maglione, “Linking Hopping Conductivity to Giant Dielectric Permittivity in Oxides,” Appl. Phys. Lett., 97 [13] 132901 (2010).
165 H. Han, C. Davis, and J.C. Nino, “Variable Range Hopping Conduction in BaTiO3 Ceramics Exhibiting Colossal Permittivity,” J. Phys. Chem. C, 118 [17] 9137–9142 (2014).
166 C.A. Schneider, W.S. Rasband, and K.W. Eliceiri, “NIH Image to ImageJ: 25 Years of Image Analysis,” Nat. Methods N. Y., 9 [7] 671–5 (2012).
167 Standard Test Methods for Density of Compacted or Sintered Powder Metallurgy (PM) Products Using Archimedes’ Principle. ASTM International, 2015.
168 T. Hungría, M. Algueró, A.B. Hungría, and A. Castro, “Dense, Fine-Grained Ba1-
xSrxTiO3 Ceramics Prepared by the Combination of Mechanosynthesized Nanopowders and Spark Plasma Sintering,” Chem. Mater., 17 [24] 6205–6212 (2005).
169 Y. Gao, V.V. Shvartsman, D. Gautam, M. Winterer, and D.C. Lupascu, “Nanocrystalline Barium Strontium Titanate Ceramics Synthesized via the ‘Organosol’ Route and Spark Plasma Sintering,” J. Am. Ceram. Soc., 97 [7] 2139–2146 (2014).
202
170 A.K. Jonscher, “Dielectric Relaxation in Solids,” J. Phys. Appl. Phys., 32 [14] R57 (1999).
171 A.S. Nowick and B.S. Lim, “Electrical Relaxations: Simple versus Complex Ionic Systems,” Phys. Rev. B, 63 [18] 184115 (2001).
172 S. Komine and E. Iguchi, “Relation of Conduction Changes and Magnetic Properties in Nd1− xPbxMnO3 (0.10 ≤ x ≤ 0.25),” J. Phys. Condens. Matter, 16 [7] 1061 (2004).
173 R.A. De Souza, V. Metlenko, D. Park, and T.E. Weirich, “Behavior of Oxygen Vacancies in Single-Crystal SrTiO3: Equilibrium Distribution and Diffusion Kinetics,” Phys. Rev. B, 85 [17] 174109 (2012).
174 R.A.D. Souza, C. Voisin, H. Schraknepper, M. Teusner, M. Kessel, P. Dufour, C. Tenailleau, and S. Guillemet-Fritsch, “Complex Diffusion Behavior of Oxygen in Nanocrystalline BaTiO3 Ceramics,” Phys. Chem. Chem. Phys., 16 [6] 2568–2575 (2014).
175 S.U. Adikary and H.L.W. Chan, “Ferroelectric and Dielectric Properties of Sol–Gel Derived BaxSr1−xTiO3 Thin Films,” Thin Solid Films, 424 [1] 70–74 (2003).
176 M.S. Mohammed, R. Naik, J.V. Mantese, N.W. Schubring, A.L. Micheli, and A.B. Catalan, “Microstructure and Ferroelectric Properties of Fine-Grained BaxSr1−xTiO3 Thin Films Prepared by Metalorganic Decomposition,” J. Mater. Res., 11 [10] 2588–2593 (1996).
177 H. Zheng, L. Li, Z. Xu, W. Weng, G. han, N. Ma, and P. Du, “Ferroelectric/Ferromagnetic Ceramic Composite and its Hybrid Permittivity Stemming from Hopping Charge and Conductivity Inhomogeneity,” J. Appl. Phys., 113 [4] 044101 (2013).
178 S. Sulekar, J.H. Kim, H. Han, P. Dufour, C. Tenailleau, J.C. Nino, E. Cordoncillo, H. Beltran-Mir, et al., “Internal Barrier Layer Capacitor, Nearest Neighbor Hopping, and Variable Range Hopping Conduction in Ba1−xSrxTiO3−δ Nanoceramics,” J. Mater. Sci., 51 [16] 7440–7450 (2016).
179 A.K. Jonscher, “Physical Basis of Dielectric Loss,” Nature, 253 [5494] 717–719 (1975).
180 A.K. Jonscher, “The Universal Dielectric Response and its Physical Significance,” IEEE Trans. Electr. Insul., 27 [3] 407–423 (1992).
181 N. Goryunova and B. Kolomeits, “New Vitreous Semiconductors,” Izv Akad Nauk SSSR, ser fiz 20 [12] 1496–1500 (1956).
182 A. Miller and E. Abrahams, “Impurity Conduction at Low Concentrations,” Phys. Rev., 120 [3] 745–755 (1960).
203
183 G.H. Jonker, “Analysis of the Semiconducting Properties of Cobalt Ferrite,” J. Phys. Chem. Solids, 9 [2] 165–175 (1959).
184 S.N.F. Mott and E.A. Davis, Electronic Processes in Non-Crystalline Materials. Clarendon Press, 1971.
185 L. Zhang and Z.-J. Tang, “Polaron Relaxation and Variable-Range-Hopping Conductivity in the Giant-Dielectric-Constant Material CaCu3Ti4O12,” Phys. Rev. B, 70 [17] 174306 (2004).
186 C. Ang, Z. Yu, Z. Jing, P. Lunkenheimer, and A. Loidl, “Dielectric Spectra and Electrical Conduction in Fe-doped SrTiO3,” Phys. Rev. B, 61 [6] 3922–3926 (2000).
187 H. Zheng, W. Weng, G. Han, and P. Du, “Colossal Permittivity and Variable-Range-Hopping Conduction of Polarons in Ni0.5Zn0.5Fe2O4 Ceramic,” J. Phys. Chem. C, 117 [25] 12966–12972 (2013).
188 M.A. Kastner, R.J. Birgeneau, C.Y. Chen, Y.M. Chiang, D.R. Gabbe, H.P. Jenssen,
T. Junk, C.J. Peters, et al., “Resistivity of Nonmetallic La2-ySryCu1-xLixO4- Single Crystals and Ceramics,” Phys. Rev. B, 37 [1] 111–117 (1988).
189 A.L. Efros and B.I. Shklovskii, “Coulomb Gap and Low Temperature Conductivity of Disordered Systems,” J. Phys. C Solid State Phys., 8 [4] L49 (1975).
190 H. Overhof and P. Thomas, “Electronic Transport in Hydrogenated Amorphous Semiconductors,” Springer Tracts Mod. Phys., 114 (1989).
191 C. Ang, Z. Jing, and Z. Yu, “Variable-Range-Hopping Conduction and Metal-Insulator Transition in Cu-doped BaTiO3,” J. Phys. Condens. Matter, 11 [48] 9703 (1999).
204
BIOGRAPHICAL SKETCH
Soumitra Sulekar was born in 1989 in Akola, India. He grew up in multiple cities
in the state of Maharashtra where he completed his schooling. After taking the national
entrance exams for engineering, he got accepted at the Visvesvaraya National Institute
of Technology in Nagpur, India, one off the premier engineering institutes in the country.
Here he studied Metallurgical Engineering and Materials Science, earning a Bachelor of
Technology degree in 2012. During this period, he was involved in different research
projects relating to solid oxide fuel cells. Inspired by the research experience during his
internships and senior year thesis, he decided to pursue a graduate degree in the United
States. He joined the Department of Materials Science and Engineering at the University
of Florida as a master’s student and started working with Professor Nino’s research group
from Spring 2013. Given the multidisciplinary and diverse nature of the group, he got
involved in multiple research projects involving energy applications, electronic device
components, geopolymers, radiation detectors and even plant derived biomaterials. A
bulk of his work however concentrated on studying defect dynamics in electroceramic
materials, which also forms the basis of his Ph.D. from the University of Florida.
![Soumitra Pal [05305015]](https://static.fdocuments.in/doc/165x107/56814740550346895db47e1a/soumitra-pal-05305015.jpg)
